{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Markov state model for BPTI\n", "=====\n", "\n", "
 \n",
    "Antonia Mey                antonia.mey@fu-berlin.de  \n",
    "Guillermo Perez-Hernandez  guille.perez@fu-berlin.de \n",
    "Frank Noe                  frank.noe@fu-berlin.de    \n",
    "
\n", "\n", "First import the pyemma package and check if we have the right version number:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'2.4+421.gbdd99b6c.dirty'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pyemma\n", "pyemma.__version__" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook has been tested for PyEMMA 1.2.2. If you have a later version, changes may be required.\n", "\n", "Now we import a few general packages that we need to start with. The following imports basic numerics and algebra routines (numpy) and plotting routines (matplotlib), and makes sure that all plots are shown inside the notebook rather than in a separate window (nicer that way)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "import numpy as np\n", "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we import the pyEMMA package that we will be using in the beginning: the coordinates package. This package contains functions and classes for reading and writing trajectory files, extracting order parameters from them (such as distances or angles), as well as various methods for dimensionality reduction and clustering. \n", "\n", "The shortcuts module is a bunch of functions specific to this workshop - they help us to visualize some of our results. Some of them might become part of the pyemma package once they are more mature." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import pyemma.coordinates as coor\n", "\n", "# some helper funcs\n", "def average_by_state(dtraj, x, nstates):\n", " assert(len(dtraj) == len(x))\n", " N = len(dtraj)\n", " res = np.zeros((nstates))\n", " for i in range(nstates):\n", " I = np.argwhere(dtraj == i)[:,0]\n", " res[i] = np.mean(x[I])\n", " return res\n", "\n", "def avg_by_set(x, sets):\n", " # compute mean positions of sets. This is important because of some technical points the set order \n", " # in the coarse-grained TPT object can be different from the input order.\n", " avg = np.zeros(len(sets))\n", " for i in range(len(sets)):\n", " I = list(sets[i])\n", " avg[i] = np.mean(x[I])\n", " return avg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "BPTI 1 ms trajectory - load data\n", "------\n", "\n", "In this workshop we will be using the 1 millisecond trajectory of Bovine Pancreatic Trypsin Inhibitor (BPTI) generated by DE Shaw Research on the Anton Supercomputer [1]. In order to make the data size manageable we have saved only the Ca-coordinates and only every 10 ns, resulting in about 100000 frames.\n", "\n", "First we define coordinate and topology input file by pointing to a local data directory. Note that instead of using a single trajectory file you could specify a list of many trajectory files here - the rest of the analysis stays the same." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "trajfile = '../../unpublished/bpti_data/bpti_ca_1ms_dt10ns.xtc'\n", "topfile = '../../unpublished/bpti_data/bpti_ca.pdb'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we decide which coordinates we would like to use in the further analysis. Since this trajectory is already RMSD-aligned we can simply use the Cartesian coordinates, here Ca-coordinates:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "feat = coor.featurizer(topfile)\n", "# just use all xyz-coordinates\n", "feat.add_all()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can ask the featurizer to tell describe the coordinates used - so we can later remember what we did. The return is a list of strings and we will just print the first few labels here:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['ATOM:ARG 1 CA 0 x',\n", " 'ATOM:ARG 1 CA 0 y',\n", " 'ATOM:ARG 1 CA 0 z',\n", " 'ATOM:PRO 2 CA 1 x',\n", " 'ATOM:PRO 2 CA 1 y',\n", " 'ATOM:PRO 2 CA 1 z',\n", " 'ATOM:ASP 3 CA 2 x',\n", " 'ATOM:ASP 3 CA 2 y',\n", " 'ATOM:ASP 3 CA 2 z',\n", " 'ATOM:PHE 4 CA 3 x']" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "feat.describe()[:10]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we want to load the coordinates from disc. Often, coordinates will not fit into memory, so we'll just create a loader by specifying the source files as follows:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "trajectory length = 103125\n", "number of dimension = 174\n" ] } ], "source": [ "inp = coor.source(trajfile, feat)\n", "print('trajectory length = ',inp.trajectory_length(0))\n", "print('number of dimension = ',inp.dimension())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's 174 coordinates for 58 Ca-atoms. In practice you will often be using more coordinates in the beginning, but we want to keep our example simple and fast.\n", "\n", "time-lagged independent component analysis (TICA)\n", "----------\n", "In principle we could now directly go on to do data clustering. However, doing anything in 174 dimensions is quite inefficient. Not so much because of the CPU time needed, but rather because in such a high-dimensional space it is difficult to efficiently discretize data where it matters. So we would like to first reduce our dimension by throwing out the 'uninteresting' ones and only keeping the 'relevant' ones. But how do we do that?\n", "\n", "It turns out that a really good way to do that if you are interesting in the slow kinetics of the molecule - e.g. for constructing a Markov model, is to use the time-lagged independent component analysis (TICA) [2]. Amongst linear methods, TICA is optimal in its ability to approximate the relevant slow coordinates / reaction coordinates from MD simulation [3], and therefore it's ideal to construct Markov models. Probably you are more familiar with the principal component analysis (PCA), but we will come back to that later..." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "756bce5c1b9d412db5ff8e8cf7f2d475", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='calculate covariances'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=1031), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d436c949ddf44b4ea9a5198a239fe17a", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='getting output of TICA'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=1032), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "Projected data shape = (103125, 2)\n" ] } ], "source": [ "lag=100\n", "tica_obj = coor.tica(inp, lag=lag, dim=2, kinetic_map=False)\n", "# here we get the data that has been projected onto the first 2 IC's. It's a list, because we could generally\n", "# have a list of trajectories, so we just get the first element.\n", "Y = tica_obj.get_output()[0]\n", "print('Projected data shape = ', Y.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The TICA object has a number of properties that we can extract and work with. We have already obtained the projected trajectory and wrote it in a variable Y that is a matrix of size (103125 x 2). The rows are the MD steps, the 2 columns are the independent component coordinates projected onto. So each columns is a trajectory. Let us plot them:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'time (10 ns)')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DJCcJxdon11asBDmcKiKtgLZG0mql1MlwTqqUuspH+g5ghNv2t8C34ZxLo9FU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\n+MZtkmS+4RRRosr2zp6cFvr4EETv//O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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot2grid((2,1),(0,0))\n", "plot(Y[:,0])\n", "ylabel('ind. comp. 1')\n", "subplot2grid((2,1),(1,0))\n", "plot(Y[:,1])\n", "ylabel('ind. comp. 2')\n", "xlabel('time (10 ns)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even in a 1 ms simulation we have a rare event in the first coordinate. Damn sampling problem. It looks like no trajectory can ever be long enough\n", "\n", "A particular thing about the IC's is that they have zero mean and variance one. We can easily check that:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean values: [ 0.00013578 0.00067149]\n", "Variances: [ 0.99914652 1.00026047]\n" ] } ], "source": [ "print('Mean values: ', np.mean(Y, axis=0))\n", "print('Variances: ', np.var(Y, axis=0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The small deviations from 0 and 1 come from statistical and numerical issues. That's not a problem. Note that if we had set kinetic_map=True when doing TICA, then the variances would not be 1 but rather the square of the corresponding TICA eigenvalue.\n", "\n", "TICA is a special transformation because it will project the data such that the autocorrelation along the independent components is as slow as possible. The eigenvalues of the TICA transform are the values of these autocorrelations at the chosen lag time (here 100). We can even interpret them in terms of relaxation timescales:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2121.98368872 946.55524452 669.04609256 373.33673652 305.70383507]\n" ] } ], "source": [ "print(-lag/np.log(tica_obj.eigenvalues[:5]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will see more timescales later when we estimate a Markov model, and there will be some differences. For now you should treat these numbers as a rough guess of your molecule's timescales, and we will see later that this guess is actually a bit too fast. The timescales are relative to the 10 ns saving interval, so we have 21 microseconds, 9 microseconds, .." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we histogram this data and compute the apparent free energy landscape" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/mi/marscher/miniconda/lib/python3.6/site-packages/ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in log\n", " after removing the cwd from sys.path.\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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nVtqPofddSffPNXRdQTI7iAttdWEo8bkcPOuHhP+tqMjYSrNlCgDorhvASU2J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\nWxrWaM6nKwNr/HWpIiiaDdQIf2LWPu6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# histogram data\n", "z,x,y = np.histogram2d(Y[:,0],Y[:,1], bins=50)\n", "# compute free energies\n", "F = -np.log(z)\n", "# contour plot\n", "extent = [x[0], x[-1], y[0], y[-1]]\n", "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we nicely see that there are a couple of different energy minima are present and clearly separated in the TICA projection." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clustering the data\n", "------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "we use k-means clustering and get the discrete trajectories" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "15993b938aa7402bb4d3dbe1d94c4339", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

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\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='initialize kmeans++ centers'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "37b9275f3eb24269ba2533331a0caf1c", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

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\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='kmeans iterations'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=10), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "23-11-17 15:35:33 pyemma.coordinates.clustering.kmeans.KmeansClustering[2] INFO Algorithm did not reach convergence criterion of 1e-05 in 10 iterations. Consider increasing max_iter.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "74e06fa0a99445a386954a42f7c0fcd6", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

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\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='getting output of KmeansClustering'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=21), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] } ], "source": [ "cl = coor.cluster_kmeans(data=Y, k=100, stride=1)\n", "# for later use we save the discrete trajectories and cluster center coordinates:\n", "dtrajs = cl.dtrajs\n", "cc_x = cl.clustercenters[:,0]\n", "cc_y = cl.clustercenters[:,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where are the clusters?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Efz+WfVT832QxRb1XF5X+Rx8j6wvIcPEQJzRN17RJmCtILiCFKC4gG0zVOzbhvx6C3yb0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\nj1cp366NdlztUPpcT1ifwhP+v3twnrO+UG9OTPPHB+d5ds8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)\n", "plot(cc_x,cc_y, linewidth=0, marker='o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For our purpose, the main result from the clustering algorithm are discrete trajectories:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[array([50, 79, 55, ..., 65, 65, 95], dtype=int32)]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cl.dtrajs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a list of integer-arrays, one for each trajectory used (here only one). The integer-array contains one number between 0 and 99 (because we have used 100 cluster centers) for each MD trajectory frame." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's play\n", "-----\n", "\n", "Now let's play around a little bit. Please refer to the pyEMMA coordinates documentation at:\n", " http://www.emma-project.org/latest/api/index_coor.html\n", "\n", "and try to vary the code above in the following ways:\n", "\n", "1. Try different clustering methods, such as regspace and uniform time clustering instead of using k-means. Also try to change the parameters. What are the differences you observe? What do you think is the best strategy for clustering your data?\n", "2. Instead of using TICA to project your high-dimensional data, try to use PCA. Discuss the differences in the projected trajectories and in the free energy plot. Which one do you think will be better to detect the slow conformational changes\n", "3. In the approach above you have streamed everything from the file because we wanted to keep the memory requirements small. For example, when you did the k-means clustering, the data was read from the file, transformed through your TICA transformation, and then clustered. Our data is small enough that we could have loaded everything into memory. Try to do that using the load function, and pass the result directly into TICA instead of passing the source object (inp). Likewise, take the resulting data from TICA (Y), and pass it directly to k-means. What is different now?\n", "4. For large data sets you can further speed things up by using strides. Play around with the stride parameter using in k-means and see what changes. You can use a stride at every step of your data processing pipeline\n", "5. Play around with different coordinates. Instead of just looking at Ca-positions, try angles, distances etc. Look at the result when you load data. Try to push it - can you compute all pairwise distances and still load the data into memory?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1) Different clustering methods\n", "-------" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Co9k/r/N26aL+fQ6dLjvRzHKRrABKhoS5lIDhF1OIP0DLnuTvc/hNFdtGRjrBddPTNbeM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\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clu = coor.cluster_uniform_time(data=Y, k=100)\n", "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)\n", "plot(clu.clustercenters[:,0], clu.clustercenters[:,1], linewidth=0, marker='o')" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TrNO+B66YNOGfxmF0qw/IUb+pRIR8D/QPPGMBz5VAn/CXVeQScilbFdc9qgBy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\nrfibCfo+6Tc0Hce10qjhXsiS8JWxd4DUId+86xSeeOA0LsV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Failed to display Jupyter Widget of type HBox.

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\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='getting output of PCA'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=1032), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] }, { "data": { "text/plain": [ "Text(0.5,0,'time (10 ns)')" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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p1/UfzjmLWoeYEtHhoXb5WbTE1X4z1wfKit5RGLTUN8uGh7iVE0lrPHOLtTmL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\nsGDsmdANXz1u3eBtHdMZ7WrF4KXONRETEYraEi9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pca_obj = coor.pca(inp, dim=2)\n", "Ypca = pca_obj.get_output()[0]\n", "subplot2grid((2,1),(0,0))\n", "plot(Ypca[:,0])\n", "ylabel('principal comp. 1')\n", "subplot2grid((2,1),(1,0))\n", "plot(Ypca[:,1])\n", "ylabel('principal comp. 2')\n", "xlabel('time (10 ns)')" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/mi/marscher/miniconda/lib/python3.6/site-packages/ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in log\n", " after removing the cwd from sys.path.\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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J/Bze21HT0KXHzIPXNhdImsqkRYW0mqI0eOdNIVVLiEmynou8pSoaxdQRk/W8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\n+wXS+DQhUDuPITKDZUpI21zhcBxzaed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Failed to display Jupyter Widget of type HBox.

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Failed to display Jupyter Widget of type HBox.

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\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='getting output of TICA'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=21), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f045da8c0ca648bf8c392cf2c96c1cd3", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

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\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='initialize kmeans++ centers'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2cf21f4d3e9d461d8b5acaf363ba9023", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

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\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='kmeans iterations'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=10), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "23-11-17 15:35:46 pyemma.coordinates.clustering.kmeans.KmeansClustering[9] INFO Cluster centers converged after 5 steps.\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HgUcKJSrv+zj5My3Kz9Yofr8RFP7S/ZObwmMkDrVkj8RlWgmsY4/22TIVMvjm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\nI8ciGUCNeI60wV+FQV1Avw582XXdTzqO8+v+918zrNdxXfd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = coor.load(trajfile, feat)\n", "Y1 = coor.tica(X, lag=lag, dim=2).get_output()\n", "km = coor.cluster_kmeans(Y1, k=100)\n", "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)\n", "# sign of -km.clustercenters[:,0] is changed here to be correct in the plot.\n", "# the direction may change due to a random initialization of the eigenvectors.\n", "plot(km.clustercenters[:,0], km.clustercenters[:,1], linewidth=0, marker='o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4) Do everything as a pipeline\n", "-------" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "889f4bf593784f95ad3cefe24e30e536", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

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\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='calculate covariances'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=104), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "27eb42a367354ca8aae86ab71abf48db", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

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\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='creating data array'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=104), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "aad0fa4f885a4b388e5b51921f6f134c", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='initialize kmeans++ centers'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "836dcee2fdd249ac8f934bf852106979", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='kmeans iterations'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=10), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "23-11-17 15:35:55 pyemma.coordinates.clustering.kmeans.KmeansClustering[10] INFO Algorithm did not reach convergence criterion of 1e-05 in 10 iterations. Consider increasing max_iter.\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+oAh87sXSl08/zpibFGouC6GjHCC5xXLVgYRM+G8OxP3OC+w5Wf5qMxU3kABz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\nw6dgNojHtOomCZImZ3nSmitAXfXKF+ArgeD5Vuc+EBD+gNc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stage1 = coor.source(trajfile, feat)\n", "stage2 = coor.tica(lag=lag, dim=2)\n", "stage3 = coor.cluster_kmeans(k=100)\n", "coor.pipeline([stage1,stage2,stage3])\n", "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)\n", "plot(stage3.clustercenters[:,0],stage3.clustercenters[:,1], linewidth=0, marker='o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5) Striding\n", "-------" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "9306e466c1674477b1f4d407e9042480", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='initialize kmeans++ centers'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f3e31f7dd93b421c9ca93bc2bf392051", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

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\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

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\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='kmeans iterations'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=10), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "23-11-17 15:36:04 pyemma.coordinates.clustering.kmeans.KmeansClustering[14] INFO Cluster centers converged after 8 steps.\n", "CPU times: user 3.22 s, sys: 4 ms, total: 3.22 s\n", "Wall time: 944 ms\n" ] }, { "data": { "text/plain": [ "KmeansClustering(clustercenters=array([[ 5.63838e-01, 1.83048e+00],\n", " [ 2.04292e-01, -6.47599e-01],\n", " ...,\n", " [ 1.39136e-03, 1.22476e-01],\n", " [ -2.15672e+00, 3.74665e-01]], dtype=float32),\n", " fixed_seed=3200810567, init_strategy='kmeans++', keep_data=False,\n", " max_iter=10, metric='euclidean', n_clusters=100, n_jobs=4,\n", " oom_strategy='memmap', skip=0, stride=10, tolerance=1e-05)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time coor.cluster_kmeans(data=Y, k=100, stride=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6) Different coordinates\n", "-------" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of dimension = 1540\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "08f13568371b4b93a52165cf12a2366d", "version_major": 2, "version_minor": 0 }, "text/html": [ "

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NRuOBaM5xjMFtmEpEGgJvKaVGAvWAL2zz5yQBk5RSP5gJOD8/f7+IbAkyXbWB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\nsQo2VEpKFUopkhIT2HG4vG0ndyJVZDo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "feat2 = coor.featurizer(topfile)\n", "feat2.add_distances_ca(periodic=False)\n", "inp_ = coor.source(trajfile, feat2)\n", "print('number of dimension = ', inp_.dimension())\n", "tica_obj_ = coor.tica(inp_, lag=lag, dim=2)\n", "# plot\n", "Y_ = tica_obj_.get_output()[0]\n", "subplot2grid((2,1),(0,0))\n", "plot(Y_[:,0])\n", "ylabel('ind. comp. 1')\n", "subplot2grid((2,1),(1,0))\n", "plot(Y_[:,1])\n", "ylabel('ind. comp. 2')\n", "xlabel('time (10 ns)')" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2f6957f593664a3da53c089febf15a93", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='initialize kmeans++ centers'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e277a71fe6814328ab87d28704419639", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='kmeans iterations'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=10), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "23-11-17 15:37:48 pyemma.coordinates.clustering.kmeans.KmeansClustering[18] INFO Algorithm did not reach convergence criterion of 1e-05 in 10 iterations. Consider increasing max_iter.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/mi/marscher/miniconda/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in log\n", " \n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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hfS5vCuACpbnd1BpD5LJrFGbO4E19m87Zid0MVJh5IlLWEcJF2HsUM5kUhIqQ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\nksJt8jgAh8Nx7aCagOICv7oZYCUpAtVzSDX/ynU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# cluster\n", "km = coor.cluster_kmeans(Y_, k=100)\n", "# histogram data\n", "z_,x_,y_ = np.histogram2d(Y_[:,0],Y_[:,1], bins=50)\n", "# compute free energies\n", "F_ = -np.log(z_)\n", "# contour plot\n", "extent_ = [x_[0], x_[-1], y_[0], y_[-1]]\n", "# plot\n", "contourf(F_.T, 50, cmap=plt.cm.hot, extent=extent_)\n", "plot(km.clustercenters[:,0],km.clustercenters[:,1], linewidth=0, marker='o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "MSM estimation\n", "---------\n", "In this chapter we want to estimate a Markov model, and then analyze it. First we import the msm package from pyemma, and then we also import a plotting package which offers a few standard ways for visualizing data." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "import pyemma.msm as msm\n", "import pyemma.plots as mplt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The quality and the practical usefulness of a Markov model depend on two main parameters:\n", "\n", "1. The state-space discretization, i.e. which steps we have conducted before (choice of coordinates, projection method, clustering method)\n", "2. The lag time, i.e. at which time do we count transitions.\n", "\n", "The first choice is quite complex and there are some ways to deal with this complexity and the reduce the number of choices, although we won't discuss them in detail here. The second parameter is extremely important, and we should scan it in order to make a good selection. So Let us compute the so-called implied timescales, or relaxation timescales of the Markov model at different lag times:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0f79e07a6d154d6d8ac4d9a356d6c026", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='estimating MaximumLikelihoodMSM'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=8), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] } ], "source": [ "lags = [1,2,5,10,20,50,100,200]\n", "its = msm.its(dtrajs, lags=lags)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What this function does is to estimate a Markov model at each of the given lag times $\\tau$ (that are multiples of our saving step, i.e. multiples of 10 ns), compute the eigenvalues of each transition matrix, $\\lambda_i(\\tau)$, and then compute the relaxation timescales by:\n", " $$ t_i = \\frac{-\\tau}{\\ln | \\lambda_i(\\tau) |}$$\n", "The its object will mainly give us these estimated timescales. We can simply push the result to a standard plotting function:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VwBuJxnxsJk7b4dh/HRsKyLH/OjYc6FfcW2TfC/ex67pdzFw3Q2V/5dIb7S0l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bMZFH9mb7kz+r+pD7zKSxAEFaCWJOl/9OiVJkOTdF/3fdyy+RaKrz5MYtMNaFfkUJ1V2cBq0/MJ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\nldirquh32zDuW9kTW3Eht//zH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_implied_timescales(its)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It has been shown [4] that these timescales should be independent of the lag time. You can see that for short lag times they are not, but after about 100 steps (1 microsecond), they are pretty constant. The faster timescales still increase. Part of this is normal and due to numerical issues. Part of this is because our state space discretization is rather naive - we cannot hope to capture a lot of relaxation processes when using only two dimensions.\n", "\n", "In a nutshell: longer timescale is better, at least as long you stay away from the grey area. The grey area is defined by lag > timescale, and in this area we cannot make a reliable estimate because the process under investigation has already decayed. Everything within or close to the grey area is distorted.\n", "\n", "Of course looking at a plot and judging the flatness by eye is not really sophisticated. Especially because the error bars on these timescales can be pretty big. Let's compute some errors using Bayesian MSMs and plot again..." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "9bb633c2c6c0422a871d61d59213ecd5", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type HBox.

\n", "

\n", " If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

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\n", " If you're reading this message in another frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "HBox(children=(HBox(children=(Label(value='estimating BayesianMSM'),), layout=Layout(max_width='35%', min_width='35%')), HBox(children=(IntProgress(value=0, max=8), HTML(value='')), layout=Layout(padding='0 0 0 20px'))), layout=Layout(display='flex', width='100%'))" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\r" ] } ], "source": [ "its = msm.its(dtrajs, lags=lags, errors='bayes')" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 200)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CmIwVKyYW+qmUWBdaS7xlyRIZNzIXR14bDIbDg1Jqi9a6/ZDPN4pjfPbtE/dUbW1xTamx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GHzuF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\nbMdHtPJ0x/vrz3gnKYic2f1J7d2Pywdb7DvyAsOndOL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_implied_timescales(its)\n", "ylim(10,10000)\n", "xlim(0,200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to be approximately constant with the lag time, approximately 100 steps are reasonable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "MSM\n", "---\n", "So finally we can estimate a Markov model. In fact we have already estimated a several Markov models (for different lag times above), but now we construct an msm object which will give us access to a wide variety of interesting quantities. All we need to put in are the discrete trajectories obtained from the clustering and the lag time:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "M = msm.estimate_markov_model(dtrajs, 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Markov model will be constructed on the largest connected set of states. That could mean that we exclude some states from the analysis. Let us verify that this is not the case here:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fraction of states used = 1.0\n", "fraction of counts used = 1.0\n" ] } ], "source": [ "print('fraction of states used = ', M.active_state_fraction)\n", "print('fraction of counts used = ', M.active_count_fraction)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spectral analysis\n", "-----------\n", "\n", "Let us have a closer look at the timescales that were already seen in the its plot:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 10.5)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(M.timescales(),linewidth=0,marker='o')\n", "xlabel('index'); ylabel('timescale (10 ns)'); xlim(-0.5,10.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look at that data by taking the ratios of subsequent timescales. This shows us how big the gap of timescales (or rates) are." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 10.5)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(M.timescales()[:-1]/M.timescales()[1:], linewidth=0,marker='o')\n", "xlabel('index'); ylabel('timescale separation'); xlim(-0.5,10.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be seen that there is a large timescale separation between the second and third relaxation timescale. That means that if we are interested in coarse-graining our dynamics, retaining two relaxation timescales, or three metastable states, is a good choice.\n", "\n", "Now let us look at the second (slowest) right eigenvector" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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+PY9bbvAKj0ma53ds2g7cbGY/igw5AThB0gZJP5QUrql8sKRN/vr/EFr/AuCN\n/rZvRlr/zcG5aHyGhmA8Jk5y3IxtTXToFk18ypPdWgFJSU+1owrrvVLiGmtnEW28fROe5V5Pcd/P\nvCKuvhFJm0LL68xsXXiAme0HTpe0CLhW0qlmdm9oyDBendDVeL+s7/tjdgPLzWyrpOOAWyTdY2Y/\nw8umeMbMVkh6HXAlcHbSRZZiwUs6R9JDkjZLen/M9oskTYUmDf6sjPP2ikoTjtqlDxqCxFG7ujJZ\n/vmqYulLp4hV3249+DjqKe5tsMPMVoRe65IG+oK9nrldTyaB681sn5n9HHgIT/Axs63++xZ/35eE\n9vmG//la4LS0i+xY4CXNw2sU+2rgZOACSSfHDP2amZ3uvz7b6XkdbdJHDUEq9733OjSylnRSD35w\nkTTqW+5Ieg7wSuDByLDrgDX+mBE8l80WSYslHRRavwq4P7TPWv/zvwUeTruOMiz4s4DNZrbFzPYC\nVwHnlXDc2tAIX3xV5ykQMlmktG+RePg09u5Y2Pa+c+i29d7Ok+Icp2un/vdO68EPLEcCE5LuBm7D\n88H/H0mXSTrXH/MtYKek+4EJ4D+b2U7gJGCTpLv89ZebWSDwlwO/L+ke4H8Cqd6QMnzwRwGPhJYn\ngX8TM+73Jb0c747zF2b2SMyY2tL3vviyipB1yefecahjXWiU9R5wB+354PuLaYYPhOl2ipndzYxb\nJbz+Q6HPBrzbf4XHbAR+K+G4u4HfzXsdZVjwcaoXNXn/P+AYMzsN+A7wxdgDSRf7s8Obpqbq903p\n68iablDAkC5SuqB2fvg4eul7z1OPJpV2YlqbLe5NpQyBn8QLvA9YBmwNDzCznWb2rL/4GeClcQcy\ns3XBpMXoaM1qtITZ0UciX1URsgLuoCK+9aSyBV2nBTxJse5L9bNJHANOGQJ/G3C8pGMlLQDOB24I\nD5AUTsc4F3ighPP2ln4S+TIo4vbu9zyxFvA54MPAPzFX5Ps2ciaNboVauZo0vaRjgTezaeBteBMG\nDwBXm9l9kcmEd/i1Fu4C3oGXbtv/+CLfTn33SilqxRc5XofUMuHpl/6rhddQ4+neXk5nVFEE21FX\nSkl0MrMbgRsj68KTCR/Aq7nQOFrbjTUHrWfj9CpWDm9gYuFahlRXpc9Jkc5OGWPD7fyK0G5dmlI4\nFFiOJ/JHAofk2Kdv3DPdfrzq38nYYh2d+gOXydohU1OwkdVMw4H67l0rJNYmLRNTO0YZW+r3jg1H\nyGRRZGwG4eJjtUbAW/As998wO4ygiHsm/ITUzeS4IynYuq9bnMFM4bGs2jSOKnC1aDpkVqGyl88v\nt757CczqIDUZ00GqiG89a2yWLIS6AAAgAElEQVSbE62dxLV3jSHgueRrsZfHem/3R6wka7qM/1mX\nEFVHnMB3yJxCZTvr5Z6Z1UHqmVVM7U+JTiozMapNT0CWH76SSJqRhM9FiBP0WtzHuuWTT0uIchOt\nvcK5aEpgTqGyHQYj9UiKCjpIBXMEY/NyWmtZfvgCCU9l+OFrS1Hfe5H5jb6jvxOimuiDdxZ8t9hh\ntQilTOwgVaYnqc2Ep76t855F1u+jFpZ8u2TdqPtT3JuKE/huUwORH5IxPrQ9uY1dluBUMK2Q5Ydv\n7M2gG3TtubzMqpKOKnACXwUZIl/7OPowRSZau+SH7ylHlHSc2ljxwd07yzIvYxK12V2c6ogT+KpI\nEPlZUS57YqJcqqZLFSiT6sNn0Rd1acKUGZWURsf1aALGyGeZd1pV8hzgDcwtie7oJk7gqyTGLz8r\nysWPo+8qRRqBRASo1RLbngg9aZRwMyjqeunJJFhpYhpDzy35YfJb5nn7r0ZZQD/0Y51mmJ0szfXK\nQtLRkiYkPeBn8b8zZsxiSddKulvSjyWdmmdfSW/3GyzdJ+lv067DCXwvCIl8EOUyzD4vyqVXcfQZ\nQtNqiTXrbmHZ30yy+iMTtFop8fRtCn8tyxZkEXc/NmAf+QuVZYl8V6NutlLMMm9nEnUvg9aPFZgG\n/tLMTgJeBlwa0wjpg8CdfpXdNwGfyNpX0hq8fhunmdkpwBVpF+HCJHvFDoMThB7zolymbJQxpUyE\n9pipX4yy8RermG7NZ+PmVUw9Mcr44TluRtuoZzmUrIzUEdrr8GTAT4Gn8EoeHE++ZKmuhk+Okz4h\nUkV4Y737sZaNmT2Kn19sZk9IegCvd8b9oWEn4zXtwMwelHSMpPGMfd+K1wDkWX976pfQWfC95GGD\nJTC0NCPKpWyy3DQxFvjYIdtZ+fwNDA/tY+XzNzC2sPiTRrt++MrI64pJm2idxhN3/PfpAufvqbum\nivDGwRD3KJKOwWv+8aPIpruA1/ljzgKeTyQrLGbfE4CzJf1I0nclnZl2bmfB95qHPUv+QNJQVW32\n8uJblhJMXLyWqadGGXtu6GaU1BGqAJUXE+smw3iWe2DBF/2GtWvJ16YeTf9SMNFpRNKm0PK6uMbb\nkp6L1yT7XWa2J7L5cuATku4E7gF+QsgkSNh3GFiM57o5E7ha0nF+d6g5OIGvAw/7f5uqhD4pAzVD\nXIZ2GONjOS33Nlv7LWVnrkmsysnrsgmeAqbxvl3tPJX1ZbZr/2awtskOM1uRNkDSfDyB/rKZXRPd\n7ov2m/2xAn7uv9L2nQSu8QX9x5JaeP91sTnVzkVTJx4O3YS70Pe0EF2qS5PViLsRCJhPe+IesDPh\ncy1xCVBRfMH+HPCAmX0sYcwiv0kSeM2zv2dmezL2vQ5Y6+9/At6dNdH0cAJfN6IiX7bQxx2vncCd\nEqJmaumHD5PXJ9+tyNbaCzu4KpKJrAL+BFgr6U7/9RpJl0i6xB9zEnCfpAeBVwPvTNvX33YlcJyk\ne4GrgAuT3DPgXDT1JPDLB3Tqtun0JlFiA5AkGuWHX0p54lzKcbrZ5CNIgArqwA/AE1oOzOxWMp7h\nzOwHeHFWufc1s73AH+e9DifwdSXslw9YQn6Rb1fUswS6SAOQsB++ruGSUfL62o8gPdSyTJGvDUl+\n9v6uIhkwzTC7mmJk+DgXTd15OPL0lea2WZKxvShZN5M2BWwg/PDgiXztJkvbteaz/OwD8jftM5zA\n9ytLYl6dULBswRz62Q+f19febsmC2ol8UZyfvV9xAt8PlNQTNTeduhZKmIDtOmVVhczL0phXUYqW\nQCiNTguNOXqF88H3A7ca/I4qqcuei3YbcfeLHz5MXp/8KMW7O0VFPu3GGlcCoVKa4WdPw0t0qnkH\nsYKUYsFLOsevbrZZ0vtjth8k6Wv+9h/56beOItxqnqhWbc07P3x1pFn5nZRAKA33N+s3OhZ4SfOA\nT+HFcZ4MXBBTNe0twC4zeyHwd8CHOz3vQHKrzQh9N+iRH752tFuTphvx8IHQj+NZ7hBfAqGtMgV1\neSR0dIsyLPizgM1mtsWP0bwKr5xlmPOAL/qfvw68ws/WcrRDFdZ8p238+sEP308Ir/rIqWRXqKzU\nus8z4TrZ9atwxFOGwB8FPBJanvTXxY4xs2ngcRoQW9BTbvVn2qpw25Tppulmzo1PUMumUOJUWZE0\n3ezX0lYJhHZ+4XmjZFyJgrpTxiRr3L9bdJ4/zxgkXQxcDLB8+fLOr6zpBJOvMCPynT51tzuBGlCg\nyNjCx/ayZ0kDQ+4CkS866ZqHridQncFMVmpa56a40MkkH31/1IEPOjo1iTIs+Eng6NDyMrw2MbFj\nJA0DhxNjF5rZOjNbYWYrRke73LquKQR++YBuW/NV9Rytgryhku3Gv9fuXzjLmi8S7543dPIMXC/W\n3lGGwN8GHC/pWL8y2vnADZExNwAX+p9fD9ySViDH0QZRkS9D6Dv1w4dpqh8+6yYxSg2FHuL/eEXj\n3bN6tIZvGPXtxdpkOhZ436f+NuBbwAPA1WZ2n6TLJJ3rD/scsFTSZuDdwJxQSkcJ3Bq5Z5ZpzfeZ\nHz6JBSPRngsJlN1ou6jIj9Kjm0PRxtppN4HwDWNgerHWilISnczsRuDGyLoPhT4/A/xBGedyZBD2\ny0N7vvksP3xWQbI2m330De32aw2SoQxP+xYwMzuVJuTtJFF1RJnx7nfg/bLixd3sohLP1RkFOzql\nIulo4Et4z3gtvI5Pn4iMeRHweTw/1l+Z2RWhbe8E/iPef8hnzOzjoW1vxzOqp4F/NrP3Jl2HK1XQ\nRKKWPLRvzZcZLll32rXai5Q9GAHuxjOS7/aX81jptXTz5GGSfhD3LjAN/KWZnYQX4HppTH7QY8A7\ngCvCKyWdiifuZwEvBl4r6Xh/2xq8sPPTzOyU6L5RnMA3lejkK3Tum+/ATdNqiW2bx+jbmZcs8c8r\n8s/gGbRGmmHbeBou7pjZo2Z2h//5CTz39VGRMdvN7Da8CkNhTgJ+aGZP+y7w7wK/5297K3C5mT0b\nHCPtOpzAN50yrfkihG4GrZZY865bWPb6SVa/eYJWq0Y5bmUWHctzrIPxbhby3/tq3rG8kNZWC7Zt\no39v+AXwS7O8BPhRzl3uBV4uaamkQ4DXMBOpeAJwtl/y5buSzkw7kCs2NghE/fLgiXwnMfMFOjdN\n/XyUjfeuYnr/fDbeuYqpx0YZP3Lm5Iv272b3vBo2WmjH157VCETAK/As94PprG9rpeSNj8/HmjWw\ncSOsXAkTEzBUA1Nz//Q8dj+W+/9wRNKm0PI6M1sXHSTpuXjNs9/lN9nOxMwekPRh4GbgSeAuZvKT\nh4HFeG6fM4GrJR2XFJVYg1+roxKSLPkkaz4s/h364ccO387KUzcwPG8fK0/fwNjS3tZAyR1J0y5H\nkG7NC3gO8eJ+RMyrKxR5jGu3HnxSiYKD2bgRpqc9kZ+qdAK5NHYEOTv+K07c5+OJ+5fN7JoiBzez\nz5nZGWb2crzn4Z/6myaBa8zjx3gTuIkORCfwg0ScXx7mfNdbJrZNJ/jL2/DDSzDx8bVMfn0Z6z+6\nhqQqRIvIbv6RZwyAtaC1bai4C6DM5h95RLoSMY9S9MG97Hrwz7ByJQwPexb8WNUVUivAr7X1OeAB\nM/tYG/uP+e/LgdcBX/U3XQes9bedgHe3TXzOdC6aQSTJZQO0tok1k7ew8ZlVrNy5gYlT1zKkBJUs\nEC45NGSMLwlZ7im14Zeys6OU8SWtndy15kx+s/FQ5q98lkUT21m0ZHeRx+/y6YZ4txWueRxeOcqn\nKOajy6oHX6xW/MSEZ7mPjZF4w+9zVgF/Atwj6U5/3QeB5QBm9mlJRwCbgIVAS9K7gJN9V843JC3F\nm4C91Mx2+ce4ErhS0r14v/AL05JGncAPKrcanKc5FvfU4lE2/mwV08xn4xOrmNo3yviCHELQZux8\nWj2axexObIIc3AQWsXtO7PK+qfn8ZuOhMC32bTwImxpC463ka8vymwe0G/9eNm3XoxnGE3f570Ub\neKSVI4j659MrSA4NwXi/NX8pgJndSsYMi5n9Gq+0S9y2sxPW7wX+OO91OBfNIHO9zWksMTZ/OysP\n28Cw9rHysA2MzffFvcvx7Gm9WRexK3FbwOKQ62b+2D6es/IpGDaes/IpNOaJ+6IlM2NK8cOXne2a\nRcex8EHXEPPfy0hoak6/Vpuex94dC3O9+gVnwQ861/tPd741L8HEqWuZ2jfK2Pzt8Y/PWZmqYWs9\nbmzK/nEWeZ5tM2N2sVuLefHEbWyfGmfe2DRSwdLBYbKs9rpY9bnZgve1L6tofOCfDyz4tJtGf1SV\nbBLOgnd4hKz5IRnjCxLEPUon1SVTatIsTTlwMNGaNGYRu9AQjI9vO/AzBPuUbsWDJ/LBq4xjRI9V\nuv++7I4geerXnIOrKlk9TuAdMwTWfLvzm21GP6b1Z11cILImbmzcTSBW5MMiWrZQ53lVTtmhquG/\nYdT/fjDeBI2rKlk1TuAds0kS+aKin9SyL8Xiz+OHzwqTDEQ+7LcPRD68b1jkD5DHUu6JGHeDKmMT\nn8G7odS8quQ03mR7nlef4ATeMZfrbfYEbJy4d1rfPWX/duLh4/bJK/KzXDWByIeFPPy5hZdbWEWK\nfc9vJp1OmIYt9ZuAq/13R1U4gXckc31OFcvjh08S9Bx++DQ3TdgFE+eqiYvAibsZ5BL5FvAx4MPA\nZ/3lxtJpv9U4n3tNLfcG4wTekU5ekQ8oUuIgRJofPiAq1nGTrWkiHzcuc9I1LPILgJ/hCfsvabAr\nudPQR+dzrwtO4B3ZFBX5LHL44dPcNHHb4iZTS590PRx4ETAPeAFwGJ1NqvZ8wjXJD99paYI+8bkP\nAC4O3pGP6/3M16KkxcTn6PyUVbYgHBsfl90aZMMuYhe7WZw4LlzKYMHIHi+ZJRD5XzMjvP8d2IMn\n9p0kf/Xcv55Fp6UJbiIt7r3VqmGpgmn6LKchG2fBO/ITTL4GJEXHFI3Ay9GjNRodM2uyNHaCtf1J\nV4jxyQdiPwa8kJl67t0Q6naOeWTpV0F6aYIk/3w4RDLZcl+zBpYtg9WrPbF3dAcn8I7iFHXZJIVM\nRgj88GnhkpAu8kUmXcMiH/bJh6NrYidfId7V0gsKnbeM4i9llCZoRLngvsAJvKM9rrd090oJvVqj\nVnicTz3LH59X5KPHShT6aFnfaKRNVULffrHNDimjdHDzywXXhY4EXtISSTdL+qn/vjhh3H5Jd/qv\nGzo5p6NGfN6z5Fsmtv1mDGvHfxlY9DnLFsQlMh2wvkMCnTXpuohds6Jr4qx5mOu2iRX6qLC3M2Ha\ny6eAwuQpTZDOxARMTsL69TXywe/D88HneWUg6UpJ2/2yvmnjzvT18fWhdcslfVvSA5Lu91v+IY//\nIelhf9s7sq6jUwv+/cC/mNnxwL/4y3H8xsxO91/ndnhOR41omVhz0y0su3qS1TdN0LKEb2vOCcmk\ncMnY6JecIh8W7cXsTrXms9w2kOKfjxPpsksVdFxRsiyyLPf00MigXHBtxL18vkBG4R1J8/CyKr4V\n2fQl4CNmdhJwFjPPwxfh9WZ9kb/tqqyL6FTgzwO+6H/+IvAfOjyeo8+Yes4oG7evYtrms3H7Kqae\nDilQkpsmsNoLhkvGJT5lJTJFXTBxQh+25tP2acs/XxaVdXvqhGCCNamw2ODEw5vZ98jO9347Xku/\nA98USScDw2Z2s3+cJ83saX/zW4HLzKzlb8sMZ+hU4MfN7FH/ZI+SHFh7sKRNkn4oyd0EGsTY/97G\nyrPnMzy0j5VHbWDskJT/uSRBz/ga5BX5WWIc+hy2zKPHSxL6tH0K+ec7Ffqi+7eVslBmDfekJCdX\nTTKMpKOA3wM+Hdl0ArBb0jWSfiLpI76lD172xRt9Lf2mpOOzzpMp8JK+I+nemNd5BX6e5Wa2AvhD\n4OOSXpBwrov9i9805abW+wLJ96dunc/6N8T0Wy0SMun74eOiaeImU5Ms+Wh0TZzQR33tXfPPQ3X+\ndQP2F93pZXRWkiAgsN7jkpwamdk6EmiV/7q44P4fB95nZtG/2DBwNvAe4Ey8HosX+dsOAp7xtfQz\neO37UslMdDKzVyZtk7RN0pFm9qikI0n4OpvZVv99i6T1wEvwkr6j49YB6wBWrFhRRTknRwkcaL/2\nUYP3ZDhVg8SnHElO4In87nl+MpKfmBROfgqEOUhmAtjN4gNCfCCRKZIQ5V3K0lnjwsfy9pmdHBW3\nTyDyc5KkYHaiFMyIfJ7J6NIaiYwzewY7vBxu4ReEPJbR5Sma5BSI/hi1zmwtlui0wxfadlkBXOX1\n5mYEeI2kabw75U/MbAuApOvw7sKf87d9w9//WuDzWSfp1EVzA3Ch//lC4ProAEmLJR3kfx7Ba0Z7\nf4fnddSVK2Luy2lWfEITkPBka5wlH3WhJFngSW6b4Bjh43bVPx9n0SdNyrZL4WSnoIVfJyGP4OlO\n1CqPirirJhnGzI41s2PM7Bjg68Cfm9l1wG3AYknBZNZaZvTyOn8Z4N8CD2edp1OBvxx4laSfAq/y\nl5G0QtJn/TEnAZsk3QVMAJebmRP4JnOFxQt9GmE/fA6RjxP6tAiZbvvnC0/EhinLTy+8OjnzUsbO\nYQudhjzm96/X1HLvApK+CvwAOFHSpKS3SLpE0iVp+/kum/cA/yLpHry/6mf8zZcDv++v/5/An2Ve\nh1k9PSErVqywTZs29foyHJ0SdtkEU/BBks6SyHJ4HcxKvNyzZGYiMHDZwNxeq+G6NbsIj1ucuE94\nObx/eP2uOfssztwHZlw3wOxmzYHbJjCe9+N9lWHGTRB9D/YJT0/tjIx51H+f1ZUvmmQQXe6ku9MC\nPB/+EN4PczWzhTy+Ho3ZRR2ccy6Sbu/QZYKOWmFcmlNz/qrz81WBy2R1dJc4Sz4QpbhwyRhLHjxr\nPjz5Gg6jTHK7JFngcyZLI/u3Ez8fPlbu+jYt4F3A64G/Jru+fPAEkCcWvvQygkmRNntJrhw517I3\nu6h0cS+NwAdfQqJTXXAC7+g+V9gB673VEtueGOPAg2NY5MPCH85wjQh9QJLQd8M/n3SsuPHRfRJF\nfgFwL571fi9elco4irhwulJ0LKv5R5x/vZGRM32HE3hHNbzXaL3HWLPuFpb9zSSrPzJBqxUTcZPT\nmk8izZrvhHZEPpOlwKl4PvNT8UoQw+wiZnnpWhhmVnGxcHhkQOCWcTXhe42rB++ojKkp2PjIaqZb\nsHHLaqaeGGX88O25QybDLHxs7wG/fDiUsq8QXjT0bmAxxerLj+L54pfm2S8aKlmEoLjYIvJF2pzD\nTDhkek14R/dxAu+ojLExr3rgxo1+FcG/2AZXZsTNh8V/G+VUvK0TQxS7uR3BzGRrFsNEJlvbJav5\nR0CcW6aPxH2a/L/bPsEJvKMygqzXWZ183pISxfW93laiyuomVQlBwlORxKcjmYmmKY08MfJJCU0z\nQl/LTk4NxvngHZVSqIrgyzNqzjs8gntQT8oNRydPoxOusyNpXCenanEC76g3p9rMq2numaIEAl4k\nXPIA3fjlnUp8glPYcg+7bA53nZwqxgm8o38YNe81CEQbiBQlCJfsmhN2AfFhkFGLPhxJ87jr5FQx\nzgfv6D98kQ/lhbIQ+OUgmfhJk62lFSnLIkhwCvvbwxE0hD7PZLfOmYOpE/uYnSXcAJwF72gMy9k2\np1RA4dj0uhO15gM3TaG54LJuhGF/e9QdE/48wwB0cqoVzoJ3NIrTeGjW8t2ceODzYnbPqSkTJVxW\nuDEcCJfsJB4+iaSSwFD78sADgBN4R6M5jYeYYGXqmL4V9cBNE016Ctw0XQmXDLOMmUxWmJvYlPTZ\nURVO4B2NZw0bY9dfyR9VfCV1ohvWPMQL+oxvvtXy3DS1ZJpi2cR9QF1/1Q5H1/lTvhy7Pq49YCV0\nEsce9cUHx5oTTdPNiei4/quzffODFBop6RxJD0naLOn9Mdv/TtKd/uthSbv99c+XdLu//r5wDXlJ\n6/1jBvulxiI5C94x0ERF/mNcCsS3B3SklSsIrPQg7TY8wTrjmx8bS+p60iz8RtmfwmuENAncJumG\ncLMjM/uL0Pi347UyBc+xttLMnpX0XOBef9+t/vY/MrNcheudBe9whHg3n+r1JXROphUfJU9AelrJ\n4LCVHkwAhKtIzkTbDFD0zFnAZjPbYmZ7gauA81LGXwB8FcDM9prZs/76g+hAp50F73BESBL5Pwo1\nsc8TkVNfAv971A+fZKHHlQwOj4tG0ASTrcwaU9tGH+0xIilsRa8zs3Wh5aOAR0LLk8C/iTuQpOcD\nxwK3hNYdDfwz8ELgP4esd4DPS9qP14D7/7aUtnxO4B2OnHyZPwVmC32U2rl0ohE1iRUmz2CmJHC0\nP2ueksHRCJrVhAV///6L2LatpglOAUFHp3zsyGjZF/dTJgnx+cDX/X6s3kCzR4DTJD0PuE7S181s\nG5575leSDsMT+D8BvpR0EU7gHY6CBEIfZSUTQEGRL1L+t1TCVvxOvIL0It5Ch3wlg+Nr0GzdehFr\n1syUiZ6YqHEkTXlMAkeHlpcBWxPGng/+5E8EM9sq6T7gbLybwK/89U9I+gqeKyhR4Jv/a3Y4KmIj\na2Ytz2oJmNS2rxZMA08x0wE8ScTzlAyGaDcniUEsMnYbcLykYyUtwBPxG6KDJJ2Id3f9QWjdMknP\n8T8vBlYBD0kaljTir58PvBav2WMizoJ3OEokKvIncvdM2OUS2P1YD/32c9w0YSt+i78hycjMIprI\nNOOyGR+/aHajlwEoMmZm05LeBnwLrynjlWZ2n6TLgE1mFoj9BcBVET/6ScBHJRneY9UVZnaPpEOB\nb/niPg/4DvCZtOvoSOAl/QHw3/wLOispdEfSOcAn/Iv6rJld3sl5HY5+4SFO40TuTh/UMzdNlHbb\nP0Xb9AV4gh/b6KWO7KPUzF8zuxG4MbLuQ5Hl/xaz383AaTHrnwJeWuQaOnXR3Au8Dvhe0oBQPOir\ngZOBCySd3OF5HY6+4SFO4yFOYxvLeXbJQp5dshA7wdt2wF0ThIdX1bRjTuJT8F7UvI5r0wfRKBpX\nZKw3dCTwZvaAmT2UMaxoPKjDMRAEIj+Hkch7rZntb58pGxzXCMRRNVX44IvEg14MXAywfPny7l+Z\nw9Fjnl2ycKYt4Qmg7zFjzQcU7clamGhcfLgiZBpBobFwiGSSRe/oBZkWvKTvSLo35pXXCs8dD2pm\n68xshZmtGB0t1I/M4WgE9vKUjSORF8y9GRShVPMuWjY4bNE7ekXmn9jMXtnhOYrEgzocA4+dAMS4\nbxTkSQbWfFes+qJWfBzRpKc+ot155ppSRRx8rnhQh8ORjl0cs3IEr/f1EXgVJbM6PB2ZsL70KpMz\n4t5qwbZtkJxQ7+gWHQm8pN+TNAn8NvDPkr7lr3+epBvBiwcFgnjQB4Crzey+zi7b4RhM7GL/9UHv\ndYARPJEPhB7mFh0rTDkB62vWwLJlsHq1J/aO6ujIC2dm1wLXxqzfCrwmtDwnHtThcHSOfRD0NzEb\nwl2ewuRy6ZTZDOTgOVms4wPUG73XuExWh6PPmWXJh9CrmLHmYaadX0CupJ40X3y0ZR/M9b0/00dZ\nrPvoTper3uEE3uFoKHaz964/9FcEPVsDwj1bS2nKHZ/R2hdZrA3FCbzD0XDsK/HrtZyZSdcDQp9U\nKx7Sq0nGxb/P1IB3bpne4ATe4RhQ7Je+yIcZxhf5KMcBhxBfLx7mNv1oXIOPvsQJvMMxwNgvZy9r\nPjOqcEDoh4BDSa8XD30d/95QXD14h8NxANsXepn3arVG8erFG/A0zGpVuCxyhH4W92k8t1SeVzaS\nzpH0kKTNkt4fs/0gSV/zt/9I0jGhbR/w1z8k6d+H1v+rpHsk3RlpGRiLs+AdDkcqEuzf/1zmzZvC\nK0EQWPZBdE1cNM1gE6qi+yq8X85tkm4ws/tDw94C7DKzF0o6H/gw8Ea/2u75wCnA84DvSDoh1NJv\njZnlCnh1FrzD4chkaAjMRjEb919BufIg7jFqyQ88earongd80f/8deAVkuSvv8rMnjWznwOb/eMV\nxgm8w+Foi5kyVWP+a6BEfkTSptArWkgiroruUUlj/Iz/x/GCWdP2NeDbkm6POeccnIvG4XC0zYwl\nP5ug/kx/xb7vo0CBtR1mtiJle54quklj0vZd5TfiHgNulvSgmSU2XHIWvMPhKJVWy9WfIV8V3QNj\nJA0DhwOPpe3rl4HBzLbjlYlJdd04gXc4HKUyNcWc+jMDSJ4qujcAF/qfXw/c4jffvgE434+yORY4\nHvixpEMlHQbgN+D+d3htUxNxLhqHw1EqY2P0Uf2Z7mBm05KCKrrzgCvN7D5JlwGbzOwG4HPA/ytp\nM57lfr6/732Srgbux4vdvNTM9ksaB6715mEZBr5iZjfNOXkIWU2LNK9YscI2bcoM83Q4HDWk1aq2\n/oyk2zN84jmOcazBf805+s0dn68KnAXvcDhKZ2jI1Z+pA84H73A4HA3FCbzD4XA0FCfwDofD0VCc\nD97hcDiAgolOfYGz4B0Oh6OhOIF3OByOhuIE3uFwOBpKbROdJE0Bv+j1dRRkBMhVp7mhDPLPP8g/\nO/T+53++mY12cgBJN+H9HHnYYWbndHK+KqitwPcjkjb1Q3Zbtxjkn3+Qf3ZwP39dcS4ah8PhaChO\n4B0Oh6OhOIEvl3W9voAeM8g//yD/7OB+/lrifPAOh8PRUJwF73A4HA3FCXzJSHq7pIck3Sfpb3t9\nPb1A0nskmaS8IWeNQNJHJD0o6W5J10pa1OtrqgJJ5/j/85slvb/X1+OYwQl8iUhaA5wHnGZmpwBX\n9PiSKkfS0cCrgF/2+lp6wM3AqeZ1on4Y+ECPr6frSJoHfAp4NXAycIGkk3t7VY4AJ/Dl8lbgcjN7\nFg40xh00/g54L3M7yDceM/u2mU37iz/Ea5bcdM4CNpvZFjPbC1yFZ+Q4aoAT+HI5AThb0o8kfVfS\nmb2+oCqRdC7wKzO7q9QWTZEAAAFmSURBVNfXUgP+FPhmry+iAo4CHgktT/rrHDXAlQsuiKTvAEfE\nbPorvN/nYuBlwJnA1ZKOswaFKmX8/B/E6/TeWNJ+fjO73h/zV3jNkr9c5bX1iLiOq435f+93nMAX\nxMxembRN0luBa3xB/7GkFl5ti6mqrq/bJP38kn4LOBa4y+/6vgy4Q9JZZvbrCi+xq6T9/QEkXQi8\nFnhFk27sKUwCR4eWlwFbe3QtjgjORVMu1wFrASSdACxgQApQmdk9ZjZmZseY2TF4X/wzmiTuWUg6\nB3gfcK6ZPd3r66mI24DjJR0raQFwPnBDj6/J4eMs+HK5ErhS0r3AXuDCAbHiHB6fBA4CbvafYn5o\nZpf09pK6i5lNS3ob8C1gHnClmd3X48ty+LhMVofD4WgozkXjcDgcDcUJvMPhcDQUJ/AOh8PRUJzA\nOxwOR0NxAu9wOBwNxQm8w+FwNBQn8A6Hw9FQnMA7HA5HQ/n/AWZq46AbhY+lAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r2 = M.eigenvectors_right()[:,1]\n", "ax = mplt.scatter_contour(cc_x, cc_y, r2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, the slowest process (about 40 microseconds) involves a change along the first TICA component. This is great news for TICA, because it means that even before computing a Markov model we have done a very good job in finding a slow order parameter. However, remember that this process has occurred only once in the trajectory, so unfortunatly our data is quite poor with respect to quantifying it.\n", "\n", "Let us then look at the third (next-slowest) right eigenvector" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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2Fo5qwchah3MQJySBFlDWpNIBNKSNzEFfnzEyPMtRe7xomjUsOYgDgdCD2sCV\nwLfM7BTgW/7nKE8DbzazF+L1avlbSYMAZvYKM1tnZuuAO4Av+9fsBt4BfLiWwfS0EGgkeeyo/Dwv\nGLuf/oEFXjB2P0flWx+2WU0bcNRJyovUqiaVjFOzNhJOGoOSnIGAHu9xcQFwnf/+OuC10RPM7KGg\nUbyZ7cTTW0v+cCQdCWzEK8aNmc2a2Z3AwVoG09NCAJYLgqTOYAn+cvJKNk2/mfdveXfb1PVKtN1B\nnIU6LBmwOmTBwZsKczFbwG6WnMPRa2BZdVEgs2ahFjASFND0X/OVTpZ0Fl7x7R9HDl2Ip1E0pEa5\nZDHqryvU12cMjvT0iqYxqtUTCjpW1XB9sSgK+3LkV1VZuaYxDyd0CAcmlcIzOfKHtc++3xDl/h0q\ndSCrUBgvrAkMMs/M0PENDC4dDtFfg69sdljSttCOTWa2Kfgg6TbiA1+vqmVMfiP6fwEuNbNi5PAl\neG15GsIJgRCtCgktFsXewlEclZ9veEJod3XRLFEsiokPb2ZqxzhjJ29l8l0b6ctIy6rApNJ2WrHw\nDr5mIBxCzwzaT/6EE73P7GGKiRYMKnV2mdn6cgfN7JxyxyTNBO11/Uk+9g9D0irga8B7zew7kWNr\ngLPwtIGG6HlzUKtpd1RR2rTdQRy6vrAvx9SOUH37fXXY3pNOku0u9BYmzkxTbmvW88u9j/gGgnLk\ng+zpVVMQeP1VLvXfXwp8NXqCpJXAjXi92b8Qc4/XA/9uZvsbHYwTAj6t0gKaEVXk2k965FfNMnby\nVgb6DjJ28lbyBzOw8m42bZ5HiyZmDvihr+EJP/zTB/4Cn7Dm2aN1sK4GzpX0MHCu/xlJ6yUF5p03\nAK8ELguFg64L3eNi4PrwTSUd7fdzeSfwXknTvjZREScEfF5bvLkliV9ZiCqK0nYHcUrhohJMvmsj\n0x8aZcsVFcIZG5UNtWoBXbrgLZqYuHczo9um2fAfodDXSppBqOdEr0YImdmcmb3KzE7xX3f7+7eZ\n2Vv99/9qZiuCUFB/2x66xwYz+0bkvk+Y2aiZrTKzQf99Vaex8wkAxSJMTMDU1P/l+WP38JeTV9LX\n1xxpEEQVpeUTCHDVRT36+oyRozKkAcyFXjstE7oKhYM5pvb5oa/7vNDXkd2zS0J9lqW4l91QHBSF\nXTnMYLXmeZRsCYIFBnpGaw7jNAGgUICpKVhYgIemXtT0xK8gqqiVUSIuXDQBSSbVRnwBXaYR5FfM\nMnakH/p6ZOXQ12JRTLxvM6PnTPOmX/0CxaIyJQB6GScEgHwexsZgYMB7fUv+/7Z7SL1HVtsqNkK5\nhitdggST+Y1Mrx1ly+kTKFooPWx4AAAgAElEQVRQLvS+sC/H1IPjLBxawXfvOJu+gqdp97BzODM4\nIYD/xzwJ09OwZYv3+SJu5iJubvfQaqLd1UUzRbm5pRFLUS1aQKW5LY15Lwtz56wf+joQyX2IcRDn\nV80y9rytDPQfZOzMrQzll/cXcLQH5xPw6euDkRiTxUXczJd5TesH1IHsHVq5GAIYS7Vm9N1Ckgm6\nGT6CJlE0UTiYI78iNNlHhWnY/h+DdntO+0IuR35slp/JOzlLJqFD9PdkKZZUNAFJ50l6UNIOScuK\nIUm6TFIhFOr01jSe61iOCxetk2oTd5byAlpISQTQvX4EUCVtqlxkEL7T3jo0Y7qLaVgISOoHPg68\nGjgNuETSaTGnfj4U6tRwqrOjOXRNw5l2UYuZpp0mndkEGzERQPV0NwuERqiOEPRsjkDmSEMTOAvY\nYWaPmNkB4HN4VfK6hk7zDThSJqkWUM+k3uxrKkzwSa7N7/EjgDjI2GFbyfcnvLjKbxaUIsmSOahX\nSUMIPBf4WejztL8vyuv85ghflHRcCs9tKZ0kCJyDuMNolkaQQrrEYgTQiaNsGa3STyDueXORY6G2\nlFmLDFpgwK9xWn3rJtIQAnF/FtFMq38D1prZGcBtLNXSLr2RdLmkbZK2FQqFFIaWLp0YMdST1BoZ\nVGkuaqYWkOb1UVLMl4uNAKpEgt8/XEPI0V7SEALTQHhlPwrsDJ/gp0k/43/8Z+CX425kZpvMbL2Z\nrc/lstt4oxsEQde0n2ySw7ZoYuYXCdtBpjWBZ2thXB/RmkFQ9ns5U1A2SEMI3AmcIulEv/LdxXhV\n8hbxy6UGnA/cn8Jz20rWBUHXhbq1MKipaGLiG5sZvSGD7SA7RVAE44wKgqCaqXMOZ4aGhYCZLQBv\nB27Bm9xvMLP7JL1f0vn+ae/wGyb/EK8H5mWNPjcLBIKgWFRLis/VigsXrY/C/hxTswnbQaY9Kadx\nvwyVTioh8t06pU9Ft5NKspiZ3QylS2Mze1/o/XuA96TxrKzx2uLNvGjiHh6cOpUXjN3f1OJzjtaQ\nP3yWsfxWpmbHK7eDbGZ9/g6Uz0UThUM58jOzaISl7xHtMBYy4WXJOVxbZ7H6kTQEfB5YCzwKvMHM\nljlHJB0C7vE/PmZm5/v7Pwmsx/PHPgRcZmY/l3QZ8CHgv/xrPpYkHN+VjWiQQsErOpdmf4C0KRbF\n7pnVmdNUWkoNq2MJJs/byPS5o2wZqxIR0yw6rO5Q0cTE9GZGfzLNhumYstLBxB+KEqqYXd7dXInX\nG/gU4Fv+5zh+EcqtOj+0/0/N7MV+oM1jeJaYgJrzsZwQaJBw8bnxsYFM9AcIUyyKd058lDeOfpU/\n3fCxju9kVpVaJ8oy5wftIMsKgFZMyBme9IGlcM/dUJjLMbV/nAVWMLU/eVJZjzqHL2ApQvI64LW1\nXBz0CJAk4Fksj8asCScEGiRafO51ypbDeL4wyH1TZ3BoYYD7ps5gvtBcdbcnVnetnJxrfVat/oDd\nka2Wa0LkNcvYgJ9UdrifVBbNFA47ibMu4JrLiJk9DuC/lqu6dLgfMv8dSSWCQtKngCeAXwI+GjpU\ncz6WKyCXAtHic5kqOpc3Xjh2N/dNncELx+5mdT7DcdlDdE+NnmACrFBULTHNmDDL/c51/v4STK7a\nSMFy5NfEaFCBf2COpd9kxms8T399z0ybGn0Cw5K2hT5vMrNNwQdJtwFHx1x3VQ1DOt7Mdko6Cdgs\n6R4z+zGAmb3FL9nzUeCNwKfw8rGuN7NnJP0BnpaxsdpDnBBoEkHkULuFwZDm+cjkHzFfGGR1fk93\nFe/KqsCYjbxPQxCkSZ2/W9HkTfKKN5P1yRjRbGn6aLnvn9V/u+TsMrP15Q6a2TnljkmakXSMmT3u\nh8/H6m9mttN/fUTSFuAlwI9Dxw9J+jxwBfApMwsvF/4Z+GCSL+LMQU2mnfkEQQx2X58xNJKeAHCh\nfTWS1ZDNGiiamNi7mdE902zYWyV3IjrBR81Czjl8E3Cp//5S4KvREyStlnSY/34YGAd+JI+T/f0C\n/hvwgP+5rnwsJwRaQDVBkNU8g0zRiEmknnIRaT+rFYKgzmcUTcwUK2dHFyzH1ILv+F0Yp2C1ZfQX\nTcwcyGPhpLHe5WrgXEkPA+f6n5G0XlIQ0XMqsM3PrZoErjazH+HpWddJugcvfPQY4P3+NXXlYzkh\n0CLKCYJiUfzFxNVcPvoZ3rfhg6lF77QrE7OnS0l34Io/6Qq/xPE7sJW8kn/Zkp4EU5MUd0XCR3sM\nv4zOq8zsFP91t79/m5m91X8/ZWYv8kNBX2Rmn/T3F81s3N93upm9KYgWMrP3mNkL/WsmzOyBJONx\nPoEWEucn2Fs4igenTi3JMxgcaWwCr0UAzLEmccJOsSjmCsMctWa+u3wLrSIL/oGIqSZuhT8SM8GX\nOH7L+ATKUTiUY2qv/4zd4xT25xgJJOYMkJEyYQsM9GQWvdME2kAgDFYzz1H5eV4wdj/9Awu8YOz+\nhvMMmqUBFIvi4okv8/LRH/AbG2+tX2OJaeGZGhlZWRZNzCyUMa9kTFuoZYXfJ2Okr/bOYPn+WcYO\n959x5Fbyh/vho53vHO4KnCbQJi7iZiYZY0jz/P3kH/DTwgkclW9shd1ME9BcYZi7ps5kYWEF373j\nbHYVcuRHMjajZYAgc3Zq/zhjh29lcnQjfYpIg2ZoBHX+UzSywq9IqFSEBJOjG72SEsfMoj3AcOg8\nR1txmkAbmWAK8KJ3Thx5lCHVP4k32wcwnC/wy2N3MjBwkJedfQe5fJsFQEYnj8KhSObsoYzYOqDs\nb1bvCr8WlvUkcAljmcFpAm1mgikmGVv8HEzmtZSCblQAlPMLzDO4mNYvwecmL2KuMMzJax5u3oSR\ndsJYvZFBdY4hMH0EmkDZdoxZ8A80m2jhuDgyJAhaVUAuazghkAECjaAeYdDKKKC+PiM3UuBJBl2u\nQBlKTB/9VVbXrRQETdScKiaRRQWBsyBmDmcOyhCBMAgTdDWNo2cacmRotZiEmtoxpjEptnFiTRRi\nWk4AOYGQCZwQyBhxggCWC4MsC4CGcgUyauvvaCr8pjNz8VtSfrQ7YRJZuQJ17t+77TghkEHKCQKo\nrBk0Qrn46F60kXYVVQRApWPljoeFxTCznIkX/nkmCZPInAaQKZxPIKPE+QmyxHx/xvwCHWYyAjrC\nMRwIgiJijhzDzJbUhxPwJTYuHpvdDSNJ8q3mgFPSH28jLDDQfb25E+A0gYxTSSvoWJqZMBamlTWD\nqpGP2dKg0qq6Ti0gShHxOjbzEqa5iEmKlNr9+zByIeFQ8d7hMXWi4O5CnBBwdB5ZtSNHJ/a0J/xa\nSEkAAMyR4048u/+djDOXoM5Drc9wtA8nBByLOL9ASjRp4l+sxBkkILfIth61+w8nfHBFQeD8ApnB\nCYEOIKsmofl+JxyW0aRVf0klzntrrOcfop4VemD3/wGjfJkJGs4TzKhJyEsWW51oawRJQ5JulfSw\n/7rshpImJG0PbfuDFpOSNkr6vqR7JV0nacDfv1rSjX57ye9JOj3JeFIRApLOk/SgpB2Srow5fpik\nz/vHvytpbRrP7SWyKgiaToYmiXZSOJhjat84C7aCqX3JG7mHacREE7X7t+KZXcyVwLfM7BTgW/7n\nEsxs0szWmdk6vBaRTwPflNSH1zbyYjM7HfgpSw1q/hzYbmZnAG8G/i7JYBoWAn6fy48DrwZOAy6R\ndFrktN8D9pjZycDfkLDtmaOUCaaaLgx6sZRuJ5BfMcvYkVsZkF+Js1w5igz6S8rmH2RwrC3iAryJ\nHP/1tRXOBfgt4Otm9jRep+ZnzOwh/9itwOv896fhCRX8XgJrJVUNw0hDEzgL2GFmj5jZAeBzeF8y\nTPhLfxF4ld8azVEH7dAKavUL1JUw1oqaQR2KBJOnb2R6/Shb8hPx2cgpm4GqUUQUyFNLQ7zFcfSu\nAAAYMbPHAfzXakbEi4Hr/fe7gBWSgv7GvwUc57//IXARgKSzgBOA0WqDSUMIPBf4WejztL8v9hwz\nWwCeBLfkbISsmIcy4RfoEZNDn4yRlc2t9pl0Yq8WNlqJLjERDUvaFtouDx+UdJtvs49u0QVyRfy+\nwS8CbgEwM8MTCn8j6XvAPmDBP/1qYLWk7cAfAT8IHStLGslicf/60b+hJOfg/5CXAxx//PGNj6zL\niVYgdfQwKWgBwcR+J+OcyVa+xEb6yoiDuLDRXIz6VS7JLIvU2Flsl5mtL3fQzM4pd0zSjKRjzOxx\nf5KvpLe+AbjRzA6G7n0H8Ar/Xr8GPN/fvxd4i79fwE/8rSJpaALTLKkj4KkfO8ud43uyjyLmz9bM\nNpnZejNbn8tlqA57hmmGnyDTfoHeNiPUTC2r7lryAZKEjTaiLXQ5N7HkzL0U+GqFcy9hyRQEgKS8\n/3oY8G7gE/7nQUmBHfatwO1B/+FKpCEE7gROkXSiP4CL8b5kmPCX/i1gs6/WOFKiFeYhly/Q3dSS\nD5AkbLSqUJmj63w3CbkaOFfSw8C5/mckrZd0TXCSH0V5HPAfkeuvkHQ/cDfwb2a22d9/KnCfpAfw\nAnX+OMlgGjYHmdmCpLfj2az6gWvN7D5J7we2mdlNwCeBf5G0A28td3Gjz3Usp13moczVEXIAtdve\no3WAqq3bg7DRcgRCJTAvhYXKzFzrqodkDTObA14Vs38b3go++Pwoy/2rmNkVwBUx+++gjopMqRSQ\nM7Obwe+evrTvfaH3+4HXp/EsR2Wy5CfYO7SSVbsP1H+DZjgQM+CULJooHMyRX5GSk7cOE9lMmf0j\nVSb2WkgkVD6cHYNAr3YWcxnDXUgapqFM+wWq0egc1uQuXIkzfxugYpnopPcIbfVSMcns29kRAL2M\nKyXdpQSC4G5eAKQ3qYf7DtdCsSgKu3Lkc2VWv/VOvBlY2dfCsszfgzlGVrbOMF7vhF7tuqSmneA+\nZziXYGZwmkCXcwYPArCGudhm8q2gWBQTF25mdN00G147SbHYu1EiyzJ/V3SGZ9QL9SyfP1BNa4ge\nKxZhZgacLGg/ThPoAc7gwUWNIBAEaZt7KjmHC7tyTN05zsLCCqbuHKewK8dIj4aFBJm/qfoEEpJE\nC5hh+aq+iHgrm9nOOOvYyjUV8geizxmJeW4RMTEBU1MwNgaTk9CXgeXooYV+5nc7n4CjSwk0goAk\nmkEagmLv0EryuVnGztzKwMBBxs7cSj5XpwDokhyBVmT+RmnErr+HHNsZ5xAr2M44exL0E6j03D3k\nmJqChQVPEBQKDQzO0TBOCPQQZ/BgrDCIUiyK3TOry6rqtUZQSDB540amt4+y5Stl6t6kTNHEzFP5\nbJob1tSwpUw1s04cQ8yyjq30c5B1bGWoQS1uiFnGxmBgwNME8h3QZrObcUKgB6mkFRSL4p0TH+WN\no1/lTzd8LDX7fV+fMZKvsPodSnCTJOfgR+DcsJnRTdNsuKF5ETg1k8bE3sD8G5h1zmWa36uSwRte\nwQu4ho3cyiifjEkMq1WwCM8END0NW7bQUo3IsRwnBHqUqCAATxjMFwa5b+oMDi0McN/UGewpJJx5\nyUgxOaDwdI6pneMsFFcwtXOcwtMplyCpZSJv4qq+VpKadeJMOH0Ya2JCPWsRLCX364OREScAsoAT\nAj1MnCA4Ob+DdWPfp39ggReO3Y2loKrHlpVOElOYZOKMOSf/7FnGjt3KQN9Bxo7dSv7ZbXBCt3Hi\nL5cjkLZZBxrzF2QNW+jnwK5VibZuwkUH9TiBIAiihyS4ZvLN7CkMYfnOXKlpBCbfsJHC0znyz26t\nAzYLK/5yBGadPeQYSqmqZyBYgsihcoKliFJ9riM9nCbgAEq1gr4+Y83IHMMqH0HUlPT6FP0CfSPG\nyHNiBEBak/SayPuMmHyqUc6sUy/V/AVQv8nI0RqcEHAsEmceqpVyfoG6Oo01izQFQTMn/g7Jhq4m\nWLrJZNSNOCHgKCENQZCYJvoFgMpN+zpg1d4tNMMX0RQWgCcSbl2EEwKOZcTlE2SeegRBOSqYnIom\nZvZnNP8gRerJJyh3fRKTUS8h6fWS7pNUDPUKjjvvPEkPStoh6crQfkn6gKSHJN0v6R3+/gsk3S1p\nu9/y8leSjMcJAUdZ0hYEiUxCKfoFFiknCCppAzHPKJqYmNrM6K3TbJjKUP5ByjRqw4+7Pm1fRIdz\nL15D+NvLnSCpH/g4XnOY04BLJJ3mH74Mr9nML5nZqcDn/P3fAl5sZuuA3wWuIQFOCDgqUkkQlHMO\n15QvkGZnkUqTej2CIELhmRxTu/0KoLvHKTzTObbtWn7mRm34zgdQGTO738yqrbDOAnaY2SNmdgBv\nog+a1L8NeL+ZFf37zfqvPw91bHwOMX3c43BCwFGVtpuG4ibqctpAPbb+ctdEnpE/bJaxIb8C6NBW\n8odlwLbdhHpKjdrwO8YH0BjDvskl2C5P+f7PBX4W+jzNUpex5wFv9J/7dUmL3cQkXei3l/wanjZQ\nFZcn4EhEuBJpIyTqNjZEY5PbGuIja/KUL7tQ7ppAEOz2ayCNbaTwTI78YS3OP2gh1fIJqsX8J8lH\nKBa9wnH5LOWiLAC7Ep+9y8wq2fNvA46OOXSVmVVqLL94i5h9wcr+MGC/ma2XdBFwLfAKADO7EbhR\n0iuBvwLOqfYgpwk4ElOLw7glJSQq+QbSdBSHntUnY+TwzhQAtZiEGi0TsauCDyAoJT06Chs2eAKh\n2zCzc8zs9JgtiQAAb+V/XOjzKLAzdOxL/vsbgTNinn878DxJw9Ue5ISAo2bCgiCVpLFGQkVrdRJD\nZf9ANWdxPc/rIpLY+2cjr3H3cKWkq3IncIqkEyWtBC4GbvKPfQXY6L//VeAhAEknS97yRNJLgZUk\nyDZxQsBRF4EgqKfVZOrU4x+olkPQpcKgUT98JXv/LMmKnPZ6KWnfbj8NnA18TdIt/v5jJd0MYGYL\nwNuBW4D7gRvM7D7/FlcDr5N0D/B/gLf6+18H3CtpO15k0RtDjuLy40lwTqUvMwR8HlgLPAq8wcz2\nxJx3CLjH//iYmZ1f7d7r16+3bdu21T02R2t4jBGKRTFXGGY4X1hmJinXbWyZXyCudGWcX6DSuqac\nH6HSNdVmrSRZu81qdhN9dtxYY55dqck8NNZgBpb7BCr9hOXm99MPWao+AUl3VbLRJ7rHCeuNqxLO\nOb/f+POyQqOawJXAt8zsFLwY1SvLnPcLM1vnb1UFgKNzKBbFxRNf5uWjP+CNG25sfv/gNKN/wJul\nGtEKoOO0gka1gbC/IE4AeELCSxQrJyBcKens0KgQuAC4zn9/HfDaBu/n6DDmCsPcNXUmCwsruGvq\nTOYKpX6oxA7iuJmpVjNPNUdxM4VBB5uI6qWcAHgXm7mEaf5HyHHcaAayo3k0KgRGzOxxAP+13P9G\nh/sxrd+R5ARFF/HS/L2Mja1gYOAgvzx2J8P5Fnn56nUUV1vVV7NPZ1wYFE0UEky2gcytd3Iut8J/\nkhw/8h3HP2KcJ8nxhKsimmmqCgFJt0m6N2a7oNq1IY737We/DfytpOeVedblQfJFwYUMdARS0Cpw\nBZ/fcmFi9T5xVdF6JtRqE3GjWkFwj0bG0ASKJib2buYlTHNRgsm2GSWeB5nlNN9xfBpbGWSWJyMR\nRQ+7DOJMUTVZzMzKJhtImpF0jJk9LukYyiwQzGyn//qIpC3AS4Afx5y3CdgEnmM40TdwtJ3Avgsz\nPBZj15nvHyzrIC5hhHivZbnksWAiLucIDSV6xVLt+kAQVEowq3R9kjGUo44y0gXLMbUwzgIruJNx\n5siRq+C2jQv3XNNgdq+AD7ORJ8kx6PsNAsHwI8YXBUMmqS1ZrGto1Bx0E3Cp//5SYFkihKTVkg7z\n3w8D48CPGnyuI6Mc33DsSRnqSQxLcm1wfSucx+W2lMhrlrGBrQxwkDPZynCVybbe8g7Rs8KOYPAc\nx6tDiWKBYLieUf5/V0U0czRaNuJq4AZJvwc8BrwewC+P+gdm9lbgVOCfJBXxhM7VZuaEQBcTCII4\nraAq5bQBqFxOolGtILhHpRV4GppBE5FgctVGfrQ7x3CVip0zpNNuMnAEB6v8D7ORvhgPQyAYHNmj\nISFgZnPAq2L2b8NPYDCzKeBFjTzH0ZkcHzIPxZmEytYRqiYIoHnCIMlEXqkGUXCPhIKgaKKwP71a\nRH2yiiagZef74Z5JiZ4Z5wgOJvsiKjELObKJyxh2NJW6zUPVlIhGo4Ca7TxOYCIqmpj4Rvb7E1SK\nIArs/X0c5Hls5efMMg08ViZU9BwzzslqR57AJ5Bk6yKcEHA0nUAQzPcPUiyK2ZmlzlwVo4RGqCwM\nGp3Ig3tUIo2Q0jIU9ueYmi3TnyDuupTKK9QilqtFEAn4EzbyEUa5MmTv30eO+yIagiObOCHgaAnH\nM8NocYbffNU3OfWER/iNjbcuZhfvHVrZXmGQhlZQiTLX5g+fZSzfYH+CmHGPpNg/ORpBFDeZ92Ec\n5Zt8PBNQniOZ5eSQhpDZiCCH6yfgaB2FAnz3jleysOC97irkyI/07uQgweR5Gz2fwNOtKU9dq3Eu\niCDazjjrqkzmRcQH2cwOxjmZrVzBq3iKYVY5n0CmcULA0TLyea9q5NSU9/q8Y37GvuJhi8erNpyp\n5DBuNk2K+OmTMfKL2fgWIhkgHEG0UGUy30eOHYxTZAU7GOcphjmqkzSABeCJdg+i9ThzkKNlLGUX\nw5Yt3udV/c+UbORsaYvSTAHQrEqgXUDSJvGrQiagk9nKKmYXzUNBn8RiEWZmIKu+4VYg6fWS7pNU\n9MPp4845XNL3JP3QP/cvQ8c+K+lBv3LDtZJW+PuvkLTd3+6VdMiv9FwRJwQcLaWm6pFxgqATqVeL\nSNG2D+nL0GiSmIB3h5zE5puH3sk0VzPJAn1d31EsIfcCFwG3VzjnGWCjmb0YWAecJ+nl/rHPAr+E\nF3r/LJbC8T8UVGsG3gP8h5lVXd44IeDINpU0g1poZgJXKy0ecU7ohFnHjZaQDhMkiV3sT/BB1FDY\nSRw1D/2MU11HMcDM7jezin1azePn/scV/mb+sZv94wZ8D6/1ZJRLgOuTjMcJAUfncLp5WxzNNOe0\nKQO4EdKMEIojSBILJvh95BZNP4YnJAxKzEMncF83dRQbDopd+tvlaT9AUr/fJWwWuNXMvhs5vgL4\nHeAbkf3PBs5jqQ9xRZxj2NF5lBMEt2fUu1qJDvFFRJWdIEnsPj8S6AgKocigKQzjx4zzPLbyYY5j\nkBl24vmE0uwolioHgeTaya5KncUk3QYcHXPoqqTN5s3sELBO0iBwo6TTzeze0Cn/ANxuZv8ZufS/\nAVuTmILACQFHN/FKq08QdJoWUa1sRQsIisLdT45VzLKXfMj0M4YBxgp+zDh92KJTeanibHdTqfpy\nHfea96svn4fnT0DSXwA54PdjLrmYhKYgcOYgR7fxSivdoCPNOZ1A2P4fjQyKRgk5akNSztcAkPQs\n4BzgAf/zW4FfBy4xs2LkuqOAXyWmonM5nCbg6G5eaXBjE+0OzZzfailiV6nCaoMk+YpBZNA+XzMw\nVPJ+r//eAZIuBD6Kt5L/mqTtZvbrko4FrjGz1wDHANdJ6sdbrN9gZv/u3+ITwE+BO+TZ1L5sZu/3\nj10IfNPMnko6HicEHN3PhWV8CEmEQwdrESNrYKaB8dc6ZQeaQTEiAMJZxJcWPZNQJlmgJf/eZnYj\ncGPM/p3Aa/z3d+M134q7vuy8bWafBj5dy3iy+s/hcDSfcsKhVaS9ck8QKprUHF+rAAgigw5FcgOe\nLPEVjPdsWGiWcZqAo7eJCoJPpmg66tDchLhbV+oNEK4ZtJbv8ShnLU76wjiZrYuaQD6/oXkDd9SF\n0wQcjjC/V4N2kEUTd0QbqDVfoJwAiOsNEBBOCvsJZ3Eidy46hY9itiSLOHNhoQ6nCTgcyygnCP66\nhTNYi30RRcTDZVb6lbqHwVJkULDa/zM2spe8ny625Cu4rJcLBmUYJwQcjqT8mT+JpSEMWpgkFnUQ\nR4uxBo1jtpfpExwkhgV9hINy0tP+8bjIoE/wuUWh8G42ctmhIjMzGU0SCwg6i/UYTgg4HLXyZ2VW\ntO8KzW4dFFUUbhwTt9IPEsMq9QsOVvsAeyM1g169s8jExFIJ8cnJDEcI9SDun8LhSIsPt8jcUYcv\nIuobCEcJBY1j+jlYstIP04exOmFzmGjimIQrHJdhnCbgcKRJVBC8pQ7bR4u1iFoax8QRzgsQy81D\nIyNW0kyowwvHdR0NaQJJmiP4553nN0HYIenKRp7pcHQUn8qOM7SSNpC0cUyUYiQvIK6kdFwzoUxy\nEHg84dZFNKoJBM0R/qncCX7a88eBc/F8SXdKusnMftTgsx2OzqCcILigCbNhgw7nWmvTRXsG7CPH\nkRRKNAPoncJxnUhDmkCS5gjAWcAOM3vEzA4AnwMuaOS5DkdX8NX2awmNzstR+39QUjqqGTiySyt8\nAs+FxRaj4GkDL4s70W/McDnA8ccf3/yRORztJioIfqXKpJmxBLWo/X9vpEzEPnLtHqKjClU1AUm3\n+U2Lo1vS1XzcX3XsEsjMNpnZejNbn8u5Px5HD/Lt5mkH5YrJRbWBWv22lUpKu8qh2aeqJpBCc4Rp\n4LjQ51FgZ4P3dDi6l3KCoJqWkAGimkH2RxxhofmPkPR64H8CpwJnmdm2Muc9CuwDDgELQSczSS/G\nKyd9BPAo8CYz2ytpDfBF4Ezg02b29iTjaUWewJ3AKZJOlLQSr+vNTS14rsPRXVTTElLMQm4kijOs\nGQAUizAzA65qxCJBQM3tCc6dMLN1kVaW1wBXmtmL8EpSX+Hv3w/8f8C7ahlMoyGiF0qaBs7Ga45w\ni7//WEk3A5jZAvB24BbgfrzmCPc18lyHo2d5yEq3jFNETEzA6Chs2OAJhF4nYUBNJV7AkgC5FXid\nf9+nzOzbeMIgMY1GB91oZqNmdpiZjZjZr/v7d/rdcYLzbjaz55vZ88zsA4080+FwhEgoCOppLpNG\nTtc+ci5buH4M+Kaku571BN4AAAZVSURBVPygmYB7gfP996+n1NxeMy5j2OHodMoJguHWWuSjmcPg\nOYo7J1v4IKWl9SoyLClsy99kZpuCD5JuA46Oue4qM0va/3fczHZKygO3SnrAzG4Hfhf4e0nvwzOt\nH0g66DicEHA4upVdvnBoQBgkTR4LN5YJKof2YQgvW7hQyHgF0drZFbHTl5BCQE3QbhIzm5V0I17O\n1e1m9gDwawCSng/8RiPPcQXkHI5uZ5cxYsu3gCRr3yJiD/n42G7iM4cBLjNbzBbuIgHQdCQ9R9KR\nwXu8Sf9e/3Pef+0D3osXKVQ3Tgg4HD3KSMJwnWqdxSA+P8A1kYknSUANXvrGtyX9EPge8DUz+4Z/\n7BJJDwEP4IXbfyp070eBjwCXSZqWdFrV8VhG/6HWr19v27bFhs86HI4mcXfMcv1B8lzCNIdYQT8H\nuZ5RVjO72FQmIOoTaKUQkHRXJfNMsnu82OCbCc8+uuHnZQXnE3A4HIucETNxv8jgr/q2LOssFiXc\nWKYzWaAGx3DX4ISAw+GoiATbD23gS/0jJZ3FRmGZNuDoPJwQcDgcVenrg9db6Sr5Nufp7QqcY9jh\ncNTFORn1Jzpqw2kCDoejbso5f4N6QZ2VG3CQzNXqbgFOE3A4HKlSLOLqBXUQTgg4HI5UKRRw9YI6\nCCcEHA5HquTzXp2ggYFOqBfkcD4Bh8ORKlKn1gs6SC8GvToh4HA4UieoF+TIPs4c5HA4HD2MEwIO\nh8PRwzgh4HA4HD2MEwIOh8MBLCWLJdnqR9LrJd0nqSipbCVSSX/qn3evpOslHe7v/7Skn0ja7m/r\n/P0bJD0Z2v++JONxjmGHw+FoLfcCFwH/VO4ESc8F3gGcZma/kHQDcDHwaf+UK8zsizGX/qeZ/WYt\ng3FCwOFwOFqImd0PoOqxswPAsyQdBJ6N10AmdZw5yOFwODKGmf0X8GHgMeBx4EkzC3e8+YCkuyX9\njaTDQvvPlvRDSV+X9MIkz8psZzFJBeCn7R5HjQwDu9o9iDbSy9+/l787tP/7n2BmuUZuIOkbeN8j\nCYcD+0OfN5nZptC9bgOOjrnuKjP7qn/OFuBdZrashaKk1cCXgDcC88AXgC+a2b9KOgZ4AlgJbAJ+\nbGbvl7QKKJrZzyW9Bvg7Mzul2hfJrDmo0X/QdiBpW7e0nKuHXv7+vfzdoTu+v5mdl+K9zmnwFucA\nPzGzAoCkLwNjwL+a2eP+Oc9I+hTwLv+Ze0PPv1nSP0gaNrOKwtmZgxwOhyN7PAa8XNKz5TkPXgUE\nvoRj/FcBr8VzNCPpaH8fks7Cm9/nqj3ICQGHw+FoIZIulDQNnA18TdIt/v5jJd0MYGbfBb4IfB+4\nB2+uDsxNn5V0j79/GPhf/v7fAu6V9EPg74GLLYG9P7M+gU5E0uVhu2Cv0cvfv5e/O7jv38k4IeBw\nOBw9jDMHORwORw/jhEDKSPojSQ/66d5/3e7xtANJ75JkkpKG23UFkj4k6QE/fvtGSYPtHlMrkHSe\n/ze/Q9KV7R6PozacEEgRSRPABcAZZvZCvGSPnkLSccC5eNENvcatwOlmdgbwEPCeNo+n6UjqBz4O\nvBo4DbhE0mntHZWjFpwQSJe3AVeb2TMAZtZYpanO5G+APwN6ztlkZt80swX/43eA0XaOp0WcBeww\ns0fM7ADwObyFkKNDcEIgXZ4PvELSdyX9h6Qz2z2gViLpfOC/zOyH7R5LBvhd4OvtHkQLeC7ws9Dn\naX+fo0PIbMZwVqmUDo73e64GXg6cCdwg6aQksbqdQpXv/+fAr7V2RK0lYTmAq4AF4LOtHFubiKuC\n1jV/772AEwI1UikdXNLbgC/7k/73JBXxkjkKrRpfsyn3/SW9CDgR+KGftDgKfF/SWWb2RAuH2FSq\nlQOQdCnwm8Crukn4V2AaOC70eZQmVbt0NAdnDkqXrwAbASQ9H6/AU08UFTOze8wsb2ZrzWwt3uTw\n0m4SANWQdB7wbuB8M3u63eNpEXcCp0g6UdJKvJr3N7V5TI4acJpAulwLXCvpXuAAcGmPrAYdHh8D\nDgNu9bWh75jZH7R3SM3FzBYkvR24BegHrjWz+9o8LEcNuIxhh8Ph6GGcOcjhcDh6GCcEHA6Ho4dx\nQsDhcDh6GCcEHA6Ho4dxQsDhcDh6GCcEHA6Ho4dxQsDhcDh6GCcEHA6Ho4f5f5QNKDl2dDvCAAAA\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r3 = M.eigenvectors_right()[:,2]\n", "mplt.scatter_contour(cc_x, cc_y, r3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This process is between 15 and 20 microseconds and clearly transitions between the two prominent minima on the left.\n", "\n", "Now we want to coarse-grain our system to get a simpler description. The PCCA method [5] uses the eigenvectors in order to perform a spectral clustering. This clustering is fuzzy, i.e. each of our k-means clusters is linked to one of the metastable states with a certain probability or membership. Here we plot the Bayesian inverse, i.e. the probability to be in a small state given that we are in a metastable state. We choose three metastable states, so we have three distributions:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TbApBU2MTQaSNl5D0chfPOj7VQtgxZs6sOX4caL3m4+u7Si5ZOye6pruOPXCO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\n04ouurJ26Tr3dFFhfVf959RKXB+mValUlmmOPPDn2QVLMBeNkstgaaY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08EOCI0cYm4ii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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M.pcca(3)\n", "pcca_dist = M.metastable_distributions\n", "f, (ax1,ax2,ax3) = subplots(ncols=3)\n", "f.set_size_inches(15,5)\n", "cmap=plt.cm.Blues\n", "mplt.scatter_contour(cc_x, cc_y, pcca_dist[0], fig=f, ax=ax1, colorbar=False, cmap=cmap)\n", "mplt.scatter_contour(cc_x, cc_y, pcca_dist[1], fig=f, ax=ax2, colorbar=False, cmap=cmap)\n", "mplt.scatter_contour(cc_x, cc_y, pcca_dist[2], fig=f, ax=ax3, colorbar=False, cmap=cmap)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "MSM trajectory\n", "-------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's generate a synthetic MSM trajectory (100 milliseconds). This is just for playing around\n", "There's nothing you can compute from this trajectory that you couldn't do better with a \n", "direct matrix analysis, but for some reason people seem to love it..." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "index_traj = M.generate_traj(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "let's just read out the x/y coordinates of our cluster centers using the synthetic trajectory" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "I = index_traj[:,1]\n", "dtraj_synthetic = M.discrete_trajectories_full[0][I]\n", "x_synthetic = cl.clustercenters[dtraj_synthetic,0]\n", "y_synthetic = cl.clustercenters[dtraj_synthetic,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot them. You can see the rare excursions to the low-populated state happening \n", "about 6 times in the first 10 ms.\n", "The next process is much more frequent. " ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 10000)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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f2qMZlj8wLEBlJBcERjI9OooE1M0LOyrbpSkj20mdzCt6+xdKvnmVv6wOzs2QwgnFHJcr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\nfd4iGCi22nfgj/6kt7hvmsG7VsLR8d8fD7+LnUd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot2grid((2,1),(0,0))\n", "plot(x_synthetic)\n", "xlim(0,10000)\n", "subplot2grid((2,1),(1,0))\n", "plot(y_synthetic)\n", "xlim(0,10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Representative Structures\n", "--------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we want to see some structures. Let us use the PCCA distributions in order to select structures.\n", "We will get 100 frame indexes for each of the three distributions" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "pcca_samples = M.sample_by_distributions(pcca_dist, 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and now we save them." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "23-11-17 15:38:09 pyemma.coordinates.api INFO Created file ./data/pcca1_100samples.xtc\n", "23-11-17 15:38:09 pyemma.coordinates.api INFO Created file ./data/pcca2_100samples.xtc\n", "23-11-17 15:38:09 pyemma.coordinates.api INFO Created file ./data/pcca3_100samples.xtc\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/mi/marscher/miniconda/lib/python3.6/site-packages/mdtraj/utils/unitcell.py:97: RuntimeWarning: invalid value encountered in greater\n", " a[np.logical_and(a>-tol, a-tol, a-tol, b-tol, b-tol, c-tol, c" ] }, "execution_count": 43, "metadata": { "image/png": { "width": 800 } }, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image(filename='./data/pcca_structures.png', width=800) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So you see that the red state is more flexible has a loop folded outward while the other two states are more compact and quite similar. Probably there are more differences in the side-chains, but we don't have the all-atom data here to go further at this point. You get the idea how to do this though...\n", "\n", "In order to relate the structures above to the metastable states on our TICA plot, let us (ab)use PCCA to do a crisp clustering, and show the colors correspondingly. We can see that the red state is our single event state on the right hand side:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Qx/FvA+8A/mUURVeBF4F3xnGcw6rOi3KXL3Un6me5yKFbuE1jJvoX/lmSTx3T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Bh6qj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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(8,5))\n", "pcca_sets = M.metastable_sets\n", "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)\n", "scatter(cl.clustercenters[pcca_sets[0],0], cl.clustercenters[pcca_sets[0],1], color='red', s=50)\n", "scatter(cl.clustercenters[pcca_sets[1],0], cl.clustercenters[pcca_sets[1],1], color='blue', s=50)\n", "scatter(cl.clustercenters[pcca_sets[2],0], cl.clustercenters[pcca_sets[2],1], color='green', s=50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Experimental observables\n", "-------------\n", "\n", " Now let us play some hypothetical games with experimental observables. We would like to design\n", " an experiment that allows us to resolve the slowest process in BPTI. By looking at the structures\n", " we find that the distance between residue 10 - 34 (indexes 9 - 33) exhibits a significant change.\n", " This is a difference we could measure by a fluorescent probe\n", "\n", "Here we use the feature reader to just read this one distance and get it as a vector:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 45, "metadata": { "image/png": { "width": 500 } }, "output_type": "execute_result" } ], "source": [ "feat2 = coor.featurizer(topfile)\n", "feat2.add_distances(np.array([[9,33]]))\n", "D = coor.load(trajfile, feat2)\n", "Image(filename='./data/observable.png', width=500) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us compare this experimental observable with the slowest TIC...\n", "Not too bad. Much more noisy, but at least there is some correlation." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'time (10 ns)')" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jgkLH0MvqXUf5fethV7mB8NZPm9l20NPGdPBELsdP5bsmN57MK/CwwXjbOY5k+3YuWLHj\nCPPW7yuW/uP6/Rw/lR9Qz/HdEtxTncNZvjiVX8C4TxzebouyDnHHh78Xi4dVErPX7nW5Soebl37Y\nyFs/Z7F611HGvrOIvDAMPX/623ZGPjfPI2R7ZcEuxZFsjFnolRb9cQu8aPfgt6XmiaQt5OUfNnD9\nm796rFk9b/1+wGFoLYmTXj0l56TA417G1ste/cXnTNy1u4uHW3FGNfV5vrwCdh3JCehF9+rcTR77\nq/xEKHbibeNYseNosV7OQ1+sKLbk74lT+cywXuAt7/uGG99exIjn5rmOG+DvU5aRMW4qL/2wwefc\nnmMn85jw1SrGTJ7vkd79kemc/eRsj1nQJTkwdJn4vc/0t37O4ur/eD+KcOdHS+j40HeusCIl4d5I\n8J7s2e/Jojkja3Yf5arXF7j2J3y5ynU/HTuZzxdLdnLDm7/y+e/F5xv44vo3f+XW936z3VYUDDe9\nvYjvV+1hyDPF527YzV3/W8qqXUe58KWfOZydG9HrDha7FMd+EWmJ1RMWkUuAUpsOIvKGiOx1DnH5\nOC4i8ryIbBCRZSLS3SZ5I8b8CHpKPP29Y/Z1ltsLyd333Psl7d66LO39PfqFeWTtP+E3fMOwZ+fy\n/UrPGb7XvrGQp75bQ8a4qcXCRrR94Ft6PzGLN37KKvnEFt0mfu96US/fUfLY71s/Fy/z+Kl8V4t8\n15Ec3v5lC+M/W8G05bt4+YeNZIybypWvL+CmdxbxmqWoZnmF1H92xjo+WuSwCTz57Vre8GFYdv6N\nR3LyGDP5FzLGTXUdO3Ailx/WOpTpr1kHPZSLXbPdvcsZ/MwcppXQyj+Sk0deQSGLtxwsVn/Dn53H\njxv2u/bde3juPbg7g4wMPeErzyGj6av2kDFuqt9elp04Z2JnHchmzGT7Pf+uecOh1L17NP/4dm3I\n81HCidjh6SAiLYDJQB/gELAZuMoYk1XK7/oDx3HEuuro4/hI4M/ASOBM4DljzJmlyZOZmWkWLVoU\n7GUEjPvDHiyvX5PJ4PYNAEfYjXfnb+HuoacTEyMs2XaYC178iWl39GPm6j2s2nWUl67sEVC5p/IL\nyM0vJDUpno9+3UqnJrVo37iGT7ljY8SnkT42Rtj4+EjAYXg7798/lXjOB0a3D2ry3IiODZlWQniI\nKTf3LuamWzs5nkMBvjAGt6tPdm5BsXAPgSJib4juP/RrzvRVe1yK+vkrutEgNZHLvXobvVvUKbUn\n0KRWtWLhJcrCIxd05IHPA/fSAoiLEfJtag2XNG/I/blyz3fxyz+zeMshptzcm8yM4vNWQnkeI8EF\nXRvz+ZLAZpN7/18/b9xP56a1qJ4Y5/e6A52b5Y2ILDbGZAaS164JgJuAwSKSAsQYYwIKA2uMmSsi\nGSVkOR+HUjHAfBGpJSKNjDFhHwi9+d3FdGxSg9sGtg6pnFi3sJm3f/A7i7YcolHNJK7pncEFLzpe\n1LPX7nX1Drw5kpPHBwu38sf+LTw8aE6/3zFMljVpFH//xGEUnnx1Dwa1a+BxTvDv2VVQaPjX9HU8\nN3N9QNcS7IzrkpQG+J7bEajSAJhRglE3EOz2Fn1tnmeP43Y/xu1Aho/sUBpQtoB+dikNJ8YYNu8/\nwcB/zuGFK7pxbpfGJeZ33r5l8Ui0uzFgB4EqDW/2Hz/F/722gAGn1+PN63vaLFVw2OVV9biI1DLG\nnDDGHBOR2iLyqA1FNwHc/QG3W2lhxRjDtyt3+32ZB8P3q3bzwsz1FBYa1wP54BcrPYyls9xegB0e\n/JZtB7Pp8ch0Nu47zkNfrGDStDWMmTyf52eu58rX53OFWwvW3Rg59t3FvPVzFruO5DD82cAi8waq\nNJTKSXnFTQqUI9l5NL/3G1f8J3+eYs55IRv3HedXKwT8/uO5/H3KMk7mFbDtYDatx39T6lIFFXyO\nZ6lkjJvKb1sP8cPava45NbPX7oto5AWwqccBjDDG3OfcMcYcsoaZQnXJ9VXvPtsPIjIWx7rnpKen\nl+lkv2w8QKOaSWTUTSEnt4CJX69kcLsGQc+yLgnnDPMuzWp5eM24Gx3dXSNP5Ba4jk2es4lj1vKY\nCzYfZIGP1uOlXq32z3/fwf7jp1jjwzitKOHm+VnFGyYv/bDBtTCak64Tp/PcmK7c8WGRfcQ5x+Gj\nRduonhhHXoHh9XnF7UjuJMXHBu0SXtG4yMfkwk4TfDtHhAu7bBzLgDOMMaes/WrAImNMhwB+mwF8\n7cfG8SrwgzHmA2t/LXBOaUNVZbVxOMcMPxzbq5jXi5POTWuyrIwB/hSlqnNdnwyfzgnlxd+Ht+Uf\n364J2/kqAuGwcdjlVfVfYKaI3CgiNwDTgbdtKPdL4BrLu6oXcCQc9g1/SgNQpaEoIRBOpQGQFK/B\nMcoDu4zjT4rIcmAQjuGlR4wx35X2OxH5ADgHqCsi24GHgHirzFdwLEE7EtgAZAPX2yGvoiiKUnbs\nsnFgjJkGTAvyN1eUctwAfwpFLkVRqjZJ8TGc9LGgl1J27PKqukhE1ovIERE5KiLHRKTyzGZRFCVq\nWfPIiEiLEHXY1eN4EjjXGLO61JyKoihKpcYuy9EeVRqKolQ0Kvs8joqKXT2ORSLyEfA54IqQZoz5\n1KbyFUVRgsbX+iRK6NilOGrg8Hoa6pZmAFUciqIoUYZd7rjqJqsoilJFsEVxiEgScCPQAUhyphtj\nbrCjfEVRlLKgI1Xlg13G8XeBhsAwYA7QFNDgSIqiKFGIXYqjlTHmAeCEMeZtYBTQyaayFUVRlAqE\nXYrDGeP3sIh0BGoCGTaVrSiKUiZ0pKp8sMurarKI1MYRRv1LoDrwgE1lK4qiKBUIu3ocM40xh4wx\nc40xLYwx9YHIBoxXlCrI+zeVurKyEsXcck7LsJzHLsXxiY+0KTaVrSh++dflXXymv31DZJfWjBS9\nW9Zhzt3nRFqMikMVcau6a0gbwLE+fDgISXGISFsRuRioaQU6dH6uw80tV4kuMuokB5Rv0+MjmXFX\nfy7o6rmm9BU907nxrObF8o/s1BCAxfcPDliWC7s19Zl+dpt6/DxuoGt//WMlB7p7+cruAKQmBjZ6\nu+TBIQFKGF5EhNPqpAScf0THhkGfY+H4QUH/prJweWazSItQJhLjHK/yhNjwrD8S6llOB0YDtYBz\n3T7dgT+EWHaFID0tsJdkZWPaHf0AuH1gK5ZPGFpK7qLfnJFRm2/u6Mf6x0bw9Z/P4slLOvvMu/6x\nEcTECK3qp/K3Yad7HDuvS2MeGN2+2G/+fUV3siaNok71RNcqZglxMcy462y+uu0sj7zjR7Zjys29\nAcdLfOrtZ7m66Vf1ciwd3LhWNVf+eLcHqlOTmgB0T6/lOO//dWNEp0b8+PcBLHloKP+5tmgRtLrV\nE5hyc29WTxzOF3/qy7gRbRnZqSG1khN8XnedlAQW3z+Yqbc75B3eoSH/+2NvjzwTznVc+1mt6rJ8\nwlA2Pj6SRy/oSK8WaQB8fHNvsiaNYtPjI2lR11MJjDmjGe/c0JP/3hj6kNTozo14+aoeHmk1q8VT\nPzXRZ/7mdVN447pM6qcmMfOvZ/PJLX349/9147o+GYCjQeDk2cu7AvDprX347s7+IctanrxyVQ/q\nVk/k53ED6dOqjs8853s1fkKhY5MagKP+nZzbJbTyr+2TwW0DWvGH/i1CKidQQjKOG2O+AL4Qkd7G\nmF9K/UEl4vQGqfzzsi50bFLTtaRsSUw4tz01k+P5y0dL/eZJiIshN9+xLsCVZ6bz3oKtAcvTtmFq\nieuGX9qjKR8v3g5AgxqJ7DnqCBn21yFt+Of0dR55Nz4+ktgYYeH4QdRNSSQmRljzyHBe/mEjz810\nrAn9w9/O4duVuzl0IpdX524CoF2jGnx8cx9XOR2b1KRV/ercM2UZT17SmQu7NWH/8VM0qlnN43xN\nayfz9Z/PonWD6iTGxbrS37mhJ9e8sRDwvdzlJ7f0pnGtaq7yHruwI+M/WwHg8YDUSk6gVnICB0/k\n8vIPGxlwev2S/kqu6X0ad09ZRkbdFD69ta+HnAAD29YnPS2ZIzl5LLq/qGfRpVktujSr5dof3K4+\nM1bv5bs7+/P6vE1MurgzsdZQQZ3qicy7ZwD1UhNJio/l2cu7cudHS5j9t3NoXjeFto1q0KFxDVKT\n4gG4qtdpXNXrNA85Y2KEWX87h5HPzWPVrqN8emsfuqfXLvHa/JEYF8OoTo349PcdrrTnxnQrlm9M\nz2bcO6IdnSZ8x7GT+VzT+zTe+WULAN/d2Z8Eq2Xbsl516xe1Gd25MVf1Sic9LYVpK3bxh34tuKBb\nEy7o1sRV7uL7B9Pj0Rllkj0UShu4eezCjgzv2JDhVs+rbnXfSrNu9USapVVj28GcUs+ZnpbM1oPZ\nrv3ayfEcys5z7Q9r35AVO47yzOVdmL5qD3ExwoJNBwF4/MJOzFi9h1lr9hYrd2j7Bny/ag8Ab11/\nBhl1Ujjn6R9oWS+FpPjYYg208sQur6oLRWQlkAN8C3QB7jTG/Nem8sPKnLvPIT0t2RUg7fcHhpBb\nUMiZj88EYM0jw+n35Gz2HXPFc+S6vo6hl5IUx7pHR3Ayr4D42BhiY4T3FmylfmoiY/u34Ilpazi/\na2PS05LZdjCHT37b7vrdoLb1efXqHrQa71gnK2vSKHo/MZOLuzflzsGtEREEuOLMdNeL5fx//8jS\n7Ue47Ixmrpb46z9uplW96q6XW/3UotHEpPhY/jKkDed3bUzzuimICDef3ZJnZ3gqHW+S4mM9Xvre\nSsNJR6uV707/NvWYfHUPvwq0x2lpHvtSymugX+t6LLp/sMfDv/C+QeTkFQDw0pXdmbl6L6aU8kSE\nufcMKPFcAK9fe4Zr+6lLi9tamrn1Vr1fpL1a+G7Z+uLTW/uwcPPBYkrjuTFduePDJQDUS030uB+d\n1EqO58mLOzO0g+PF+MTFnTj9/m9JsO5BgJUPD+OVORt5YdYG1+9evrIH9362jPtGtiMlMY7RnRu5\nlIYvWtVPBWDJg757r3WqJ/L0pV3o3LQmzWon0+7BbwEY3K4BmRm1mTTNsS74oLb1Wbr9MPuP5wJw\nfd8MrjwznZb1qvPmT1k0rJlESmIcObkFJCfEsmLnEZ78dq3rPFf0TOeDhUX3U2pSya84Yzz3+7r1\nAnq3qMMvmw4AcPvA1vyy8QCOV1xxsiaNcjUwuzSr5aE4nr60Cze+vci1/6cBrbimTwY1q8Vz5ZmO\nxsLQ9g2pnZLApZlN+b8z0z0aq83rprB5/wkuP6OZS3H0bJ5GckIcSx8cSmIElse1S3EMNcbcIyIX\nAtuBS4HZONYir3R4jxHXTvEclkiKj/UYS7xvZFvXdo2kOI6ezPdbdlJ8UYt75l/PJi05gdopCdzU\nr6gFPW/9Ppfi+O2BIaRZ5z+vS2O+XLoTgF/uLT7O7P5iee3aTH5Yu48GNYqUw81nl+5x0cLVknQQ\nU87GxaEdGrpeanbg3WKs73b9Izs1YmSnRhw4foomtapx89nh6daHSlJ8LP3b1CuW7h759bNb+7Ao\n61CxPAvuG+TRy/NFSmIcta2hN2fes1rXZd49DhvR34e39fvbYLikR5E9qmdGGguzDvK6NSx401nN\niY0RRIS9x06y8/BJGtRIpH5qkkvB3eDDLta/TT1emr2R46ccz1z39FoeiqN3KQq6RT3/9iBDkVap\nmRzPyE4NWbUr+PXpnMooMS6GtY86bG01q8V75KmdkuBz+BaKFIcx8NO4gdRJSXC9R2omx/v8TXlj\nl+JwSj8S+MAYc7AyhjNullaNbs1KHgpwv/mdNKlV1LJcdP8Q2txffAVdX84OLb1e0k5SLAPtFT3T\nXUoDHOPG/7zMtxeRN/VTk7jMBkPfsA4NeWb6Or+2jHDi/iCHQp3qifzkZjivrBi35nLT2smuoTZ3\nSlMaTq7slc7h7FxuCaBxYQfv3tSTk7lFy7nGuTXE6qcmefSGS+Oa3qfx0g8bAWjTINXzoJ/X0JOX\ndOZwdi59Wtb1nYHivZGBbRvw9Pcl98DtZliHBsTFOP6b2BihSS3fPfpwY5fi+EpE1uDox90qIvWA\nkzaVHTacLSx/+BqHB1wtIsBvd37SRYG/eLun1+blK7szoK3nWH1MjBAT5rmwpzdM9Xvd4cb7Qa7q\nFJbwhzxyfgcWbSneA/FHYlwsdw0N3xh5YlxswEqtNIJtowZqK0qM95SvbcNUmtSqxo7Dpds5nLSo\nl+JykQ3GwP6vy7tQs1o8A9sVsqLrAAAgAElEQVQ24OCJXJrXTfHZ64wUdoVVHyci/wCOGmMKROQE\ncL4dZVdU/nV5Vy571eEPEIjrdLCt5RGdGpVFrCpBUgTGdCsiaSm+DbkAV/fO4OreGcXSY6237OjO\n0XN/leT56MuO1bVpLR85i7iga2M+X7KTIe0bMHfdPlrVd4wMxMQIP40byIQvV/LWz1l+f3/7wFbE\nxQh9WtbhUqvXv/TBoaQkBq4o3d3M01ISwmr4DoSQFIeIDDTGzBKRi9zS3LNE7UJOPZuncUPf5rzx\n02a/rpnuxIfJvzqacarei7r7nrtR1XD67vfMSCslZxFxsTEsvn8wNapFZmy8PLgssxnTV+2hfaMa\nAeWPKaWl57QfxFnehrEl5Pf2oAJo3SCVf1nuyE4iZYsoL0LtcZwNzMIxd8ObqF8B8O8jTqd3yzr0\nbF7yg3vn4NacF6KftlL0oqwWb88QR2XnNGsi5rldgus91PHjclpZERGXh9vSbYc9jjl7+sM6NOC7\nlXs8bIb+cOapkRTv4czii2/u6EdyFbwfQ53H8ZD1XSVXAEyMi2VI+wal5rtzcJswSBP9XNitCTsP\n5zA2TJOcKjqNalZj7aPDwzZbuDLiNAO9enUmObkFAdlD7hjcmow6Ka5IBiURFyOuHsyozo2YumxX\nKOJWGkIdqrqrpOPGmGdCKb+y0qp+dTbsPR5pMaKO+NgYVcJe2GVgjhZOb+jpVZVfWGRbrJYQ2H+V\nGBfLZWcE5pHo7q7+7OVdefzCqrEMUahNlVTrkwncAjSxPjcDvp2SqwCt6/t2s1UUpXxJio9l4vkd\nXPvl0Rtzzo26pvdpHl6U8bExxeZnRCuhDlU9DCAi3wPdjTHHrP0JwMchS1dJaRal8a0UpTJwWWYz\nHvxiJS3rpVDPT9ytUPhDv+Y0rV0tqjzTgsWueRzpQK7bfi5VeAXAvw09ne7ptTkjozYFhTr5QFHC\nSVJ8LMsmDCUlwa7XmydxsTEhByWs7Nj1z74LLBSRz3B4U10IvG1T2ZWOhLgYV9A0RVHCT42kqjFk\nFCnsmgD4mIhMA/pZSdcbY363o2xFURSlYmFbX84Y8xvwm13lKYqiKBUTMVEYAEhE9gFbyvjzusB+\nG8WpyOi1Rid6rdFJeV/racaYgAJiRaXiCAURWWSMySw9Z+VHrzU60WuNTirSteqUU0VRFCUoVHEo\niqIoQaGKoziTIy1AGNFrjU70WqOTCnOtauNQFEVRgkJ7HIqiKEpQqOJQFEVRgkIVh4WIDBeRtSKy\nQUTGRVqeQBGRZiIyW0RWi8hKEbnDSk8Tkekist76rm2li4g8b13nMhHp7lbWtVb+9SJyrVt6DxFZ\nbv3meZFgV3m2FxGJFZHfReRra7+5iCyw5P5IRBKs9ERrf4N1PMOtjHut9LUiMswtvcLcByJSS0Sm\niMgaq357R2u9ishfrPt3hYh8ICJJ0VKvIvKGiOwVkRVuaeVej/7OYQvGmCr/AWKBjUALIAFYCrSP\ntFwByt4IR2RicIS4X4cjpP2TwDgrfRzwD2t7JDANEKAXsMBKTwM2Wd+1re3a1rGFQG/rN9OAERG+\n5ruA94Gvrf3/AWOs7VeAW6ztW4FXrO0xwEfWdnurjhOB5lbdx1a0+wBHvLebrO0EoFY01iuOpRg2\nA9Xc6vO6aKlXoD/QHVjhllbu9ejvHLZcU6Qeior0sf7079z27wXujbRcZbyWL4AhwFqgkZXWCFhr\nbb8KXOGWf611/ArgVbf0V620RsAat3SPfBG4vqbATGAg8LX1sOwH4rzrEvgO6G1tx1n5xLt+nfkq\n0n0A1LBepuKVHnX1ikNxbLNeinFWvQ6LpnrFES3cXXGUez36O4cdHx2qcuC8cZ1st9IqFVaXvRuw\nAGhgjNkFYH3Xt7L5u9aS0rf7SI8UzwL3AIXWfh3gsDEm39p3l891TdbxI1b+YP+DSNAC2Ae8aQ3L\nvS4iKURhvRpjdgBPA1uBXTjqaTHRWa9OwlGP/s4RMqo4HPga261UfsoiUh34BLjTGHO0pKw+0kwZ\n0sOOiIwG9hpjFrsn+8hqSjlW4a8VR0u6O/CyMaYbcALHcIM/Ku21WmPv5+MYXmoMpAAjfGSNhnot\njUpxbao4HGwH3BcZbgrsjJAsQSMi8TiUxnvGmE+t5D0i0sg63gjYa6X7u9aS0pv6SI8EfYHzRCQL\n+BDHcNWzQC0RcUZ6dpfPdU3W8ZrAQYL/DyLBdmC7MWaBtT8FhyKJxnodDGw2xuwzxuQBnwJ9iM56\ndRKOevR3jpBRxeHgV6C15cWRgMPg9mWEZQoIy4PiP8BqY8wzboe+BJyeF9fisH0406+xvDd6AUes\nbux3wFARqW21AIfiGBfeBRwTkV7Wua5xKyusGGPuNcY0NcZk4KijWcaYK4HZwCVWNu9rdf4Hl1j5\njZU+xvLOaQ60xmFgrDD3gTFmN7BNRE63kgYBq4jCesUxRNVLRJItWZzXGnX16kY46tHfOUInnAai\nivzB4c2wDof3xfhIyxOE3Gfh6JouA5ZYn5E4xnxnAuut7zQrvwAvWte5HMh0K+sGYIP1ud4tPRNY\nYf3m33gZbCN03edQ5FXVAscLYgOOte4TrfQka3+DdbyF2+/HW9ezFjdvoop0HwBdgUVW3X6Ow5sm\nKusVeBhYY8nzLg7PqKioV+ADHLabPBw9hBvDUY/+zmHHR0OOKIqiKEGhQ1WKoihKUKjiUBRFUYJC\nFYeiKIoSFHGlZ6l81K1b12RkZERaDEVRlErD4sWL95sA1xyPSsWRkZHBokWLIi2GoihKpUFEtgSa\nV4eqFEVRlKBQxaEoSoVj77GTHDyRG2kxFD+o4ggje4+dZPeRk8XSN+w9zuIthwBYseMI2w9lu44d\nOpHLgeOniv1m28Fsxn+23FXegeOn+GDhVgBOnMpn9a6jHDuZF5Bce47qQ6pUDHYczmHdnmP0fGwm\n3R+Z7nEsN7+QgkLDmt1H+dvHS3n061UAAd/nlZmdh3MoLKw4c+6icgJgZmamKYuNY/QL81ixw398\nwJSEWAoN5OQV8PO4gTSuVS3gso0xNL/3GwDGjWjLpGlrgpbPDv42tA23DWztkZYxbioAz43pSnpa\nMg1rJtGopu9rO3Yyj9Sk+IDPV1DomGkaF1v2Nsrh7FwS4mJITohKk1ypPPP9WnILDONGtI20KGVm\n5c4jjHr+R4+0W85pSaExfLJ4B/t9NI4AJl/dg7HvLvZ5zJ1PbulNj9PSbJG1LPy29RDdmtWipLWw\nNu8/Qa1q8dROSQiozCPZeXSZ+D0t6qawaf+JYsfn3H0O6WnJJZ4zGERksTEmM6C8qjiKcL5AAyVr\n0qiA8/7nx808YrWQIo233L6u29e1fb9yN2PfXcy5XRrz3OVdiYkp/YYd8PQPbN5/Iqj/6vipfKon\nFikJp3xjzmjGpIs7B1xOSZzMK+CvHy9l/Mh21EqOL6aUdhzOobaPdCcfLtxKep1k+rSsa4s8K3Yc\noXpiHJv2H+eGtxax6P7B1K2eyNx1+7jmjYWufD/+fQBNaycDsGnfcSZ+vYpXrupBUnxsqefIzs1H\nENbuOcbxk/mc1bpI9oMncsnOzXeVXVBoyM0vJCEuhhU7jtClWS1X3s9+3067RjVo27BGQNd27GQe\nnSZ8H1DeUAjmHrOLyXM38vg3RY3ABfcNokGNJACen7megydymXBeB6DoPj6vS2Oev6JbqWUH+j6y\n67qDURxVswlnIz9v3E9iXCw9TnOsyrj36ElGPDePT2/tw2l1Ulz5KorSAPh40TYuzXQE2jxUyhDV\n/uOnyHx0BvePasdnv+8A4KulO6mfmsgDo9uzcPNBpq3YxYOj2yMiXPn6fH7acIDbBrTitoGt2Gy1\nlAoLDYdz8sgrKOTMx2fy7Z39PF48a3YfpUXd6rwyZyPPTF/HzWe3LNbC/vDXbUy6uDOb95/gxKl8\nOjap6Tr23/lbuP/zFSx9aCg1kuJcrbD5mw6Qk1vAgLb1OZVfwOvzNtO2YSozVu9l6rJdTF22C4Br\ne5/Gw+d3dJXXd9Is2jeqwfhR7dh//BTnd/VcvmHcp8sBx0M7+Jk5pCTE8sVtZwGOF8bAtvW5+b+L\n+UO/Fizdfpj7R7Vnzrq9jOzUiMS4ope8s1Xpzbz1+9h5+CRPfbfWI/2sf8xm7t0DSK+TzMB/zgHg\nu5W7i8nnzbhPlvHhr9uKpc+7ZwDN0pI58/EZ5BUY2jZMZWSnRjwzfR0AdwxqzXMz1/PujT3p19rh\nqfmXj5YCsOnxkeQVOoaPPv1tB12a1qJjkxpMnruJC7o1cb1AP7fum4rIybwC2j7wLQC3D2zFXUNP\ndx07lV9AjAjxsTF8sHArq3cdpWa1eP469HRenL0BoFj9/Om935hySx8A13844bwOrmFkgC+X7uSp\nSzt73AfGGLYezOa0OilBN2B3Hs4JavTDDrTH4UawFTbvngH0e3I2AHVSEji/axPe+GkzAEPbN+Dx\nizqxetdR+rWuF3TZ5U18rJBX4L/u+7SsQ36hYeHmg37z3DP8dJ781vHg/LF/C95bsJXjp/L95rdb\nxtsHtWbuun08P6Yb/Z+a7XFscLsGzFi9x7WfNWkUt3/wO18uLVs07Zev7E7HJjWZ8OVKHjq3Q7Hz\nBcsb12Xy71kb+G3r4ZDKAcfw4zV9Mnjoi5U8MLo9S7cd5scN+/nPj5t56pLOXJrZzJb7b1iHBny3\nck/pGSNEMC3vbQezKSg0nPP0Dx7pfxnchs5Na9KyXnVXHd9yTkte/mGjK8+HY3sxZvL8EuWYtWYP\nN7y1yLXv/f/3bVWHgkLD/E0H6d+mHtUTY/lm+e6A5XenT8s6vP+HXmX6rTs6VBUmxREoLeqlsGlf\n8TFKJXyse3QEbe6fFmkxyoWezdNYseMI2bkFkRYlogSqOKav2sMf3in7PK8GNRLZc9S3TQbgyjPT\nWbv7GIssh5fbB7Xm+Znry3y+QLBjuCoYxRFRryoRGS4ia0Vkg4gUW93Miqv/kXV8gbU0aqVDlUbk\niValAbBw88EqrzSCIRSlAZSoNADeW7DVpTSAclcaEH7PsojZOEQkFkfc+SE4YtT/KiJfGmPcjQE3\nAoeMMa1EZAzwD+Dy8EurKEpFJye3gGoJJTsJLN7if+i1MuN0PujQuAZTb+9X7ueLZI+jJ7DBGLPJ\nGJOLYynQ873ynA+8bW1PAQaJXb5nPriuT0Z5FR00qUlxvHJVD9o0qF7sWJemNT323fOse9TXUs2K\nEv2s2uXfld7JxS//EgZJIsfKnaX/B3YQSa+qJoC7m8d24Ex/eYwx+SJyBMeqVvvLQ6AJ53VgQNv6\nfLFkB+NGtKV+ahL/+XEzhYWG0V0acexkPre+9xsb9h4v8znqpCSw+IEhbD+UzatzNrFs+2HGjWjH\nFa8VGdveuv4MeresQ2JcLMM7NgQcLqodH/qOs9vU4+0bejJ/0wHGTJ7PlJt7k5mR5rLPJMR5tgVe\nuao73dNr88umA9zx4ZIyy60odjD37gFsPZjN71sP0adVHdo3qkleYSE1kuJ92hgX3jeIWskJJMTF\nkFdQSLeJ010OGJufGImIuH4XH1tubcqIUSMpjmUThvHzxv3832uO5ec3PT6Sb1bs4rb3f4+YXBEz\njovIpcAwY8xN1v7VQE9jzJ/d8qy08my39jdaeQ74KG8sMBYgPT29x5YtAcfrCppQjOhnZNTm45v7\nFEt3KoJayfEseXCoz9/uPXaStOQE12S6wkLjmktx4Pgp4mJiqJkcz4Hjp3hh1gbe+jmLxfcPpk71\nRAoLDe0e/JZT+YVlll1RQqUkI677c7Vq4jBycguoUz2xWL5T+QUczs5zufs6f/fdnf05vWFqieev\naN6NpbHp8ZGuZ/xITh57j56kdQPHNfq7lrIayiuLcXw70Mxtvyng7SvpyiMicUBNwOcgpTFmsjEm\n0xiTWa9eQJGBI0L91CSf6b1a1OGuIW2YcnPvEn/rPgPbfQJeneqJ1EyOd20/MLq9S2k4867VYawq\nT4t6KaVnijAdGtcgOSHOp9IASIyLdSkNd6onRd+0NPdnvGa1eJfSiDSRVBy/Aq1FpLmIJABjgC+9\n8nwJXGttXwLMMpXcf/iJizv5PXb7oNa0qm/PjREbIz4fvB//PsDvb7xbKo+c38Fv3s5Na/L5n/q6\n9ufdM4ApN/cma9IoruqVDsCfB7ZyHV98/2CeusT3rG9fE9CzJo1i2QRHz+v2Qa2LHe/VIo2reqXz\n9g092fBYkUJc8fAwNj8xkmUThpbY8mrXqAZZk0bx2wNDyJo0yuNanrioqI6WTxjK7L+dw6e39uGl\nK7v7lNPJK1d1Z+7dA1jx8DCyJo1yfW7o2xyA+0YWTWh88f+6M/OvZ7Pi4WGsfHiYK/2zW/twXZ8M\nnvT6r85qVZek+NAf16//fFaxtCcu6kSjmp4v4ufGdGXpQ0O5f1S7Yvl/f2CIq27AUT9rHx1O1qRR\nfHqrozfduGYSqyYO4+s/n0UdK8RGSimGayfv31S2OQnfLNvlmphXVoZ1aEDzug7l+sezWwT8u39e\n2iWgfJseH8m8ewaw9tHhrrQxZzRj3aMjXPdLZSBiKtqyWdwGfAfEAm8YY1aKyERgkTHmS+A/wLsi\nsgFHT2NMpOQNhN8fGEI3r8Bs3tQIIs5TedC0drLHxMWsSaOYuXoPbbxaMmsfHc76Pf5tOZdmNqOr\nWxiKlMQ4MjMcsYJiLP+FOm4xeepUT+TSzGbcPWWZRzkvXNGNc7s05s2fNtOxSU0ufeUX/jqkDeD4\nr5wPkrdL48tX9vCI+fP6NZl8v2q3K1RJSf/zqE6NeMEK+ZBmleF+LX3dwoikJsWTmhRPcxwvk6UP\nDvU50xugoBDS6yQXS39gdDv6ta7L2W3qucJTjOrcyCPPl7f15ZU5G+nctBbd0h1RCJITYl3j2E75\nftzgMO/5mlQWCN4hVCae34Ereqazce9xXv/RMXn13hFtXTPRW9Uv7pzhHWvpLqu+ALo1q8X9o9px\nbpfGJCfE0bFJTb6+/Sx6PzEr4B6Bs+ccLI99sxqAq848rUxlvH/TmZzZog77j59i4leruGNQa16d\nsymg3wbak4uJEZqlFd0jt57TknuGV74YZBHt2xljvgG+8Up70G37JHBpuOUqK4EGL4s07jcuwKB2\nDYrlSYyLJbegyB5yUbcmfOoeOsLq+FVPjOP4qXzi3AyTTsVRWjDPpy/twmjrBXq91SoPtMXl/V8P\nbt+Awe2LX4cvmqZVKzHOVmEJndqSXkj+ficiDGhbH3C0LqevKj77unPTWrx0ZQ+PtGa1i+opJkZ4\n4qJOLoXvj4fObc+h7LyA5w44/4XWbp557nGp4ksITlm3egKZXoEFRYSb+nm21GOt+6EgTOa1kuqv\nJPq0cjQYGtRI4kUfvcuSiA0gbps3laV34QsNq674xf1R8PaCdj6aLa0WaYK77cWlOEp+gC/p0dS2\nyJ7BULOa75d/Z8vNOTkxsCEV72G/QF5Yky7uzOIHhgRUvruhNyFWXMq5oY/xfSeNalbz6AEAxexm\nL1/ZnTMyanukXZZZZG50733FlFA/i+4fwitX9/B73IkzJlOGj95YeRCBWyrggI/RQpl6HCLS1hgT\nmbjgFYDnxnStEq6t7i/1OK8WlfMd+dZ1Z7B611GP6Kz92tTljZ82u4ZcKhruLXl3Pr65N3kFhuqJ\ncdzQtzkXdis5cGBTr3IKbF4vIdHNtVpECKQh7eul6RxCdDKiUyN+2rifX7OKZjeLiCs2mHsZ7j3J\nOXefU6YZ6jWT43nzujM8FFJ5ItivOWpWi+dIjv/Z2d5u8NFOWa+2/GMkV2DO69K4WFrvFnUiIEn5\nku42pOU9Pu30UaidkuDq4jsZcHp9Vk8c7ooY7E5iBXjA/LVIE+NiXTaSB89tTyeviZal0cXmF6O7\n4nYfCimpRe3v0Od/6svcu4t6SL6U0DOXdaVNg+oevUf3+jqtTgrtGpWtZT2gbf3wDeX6+RNCUexO\no7/iwO9TLCLP+/m8AISn6VBBERGu7X2aR1ogN+WMu84uL5GC5rs7+/OBj4iabd2GR6q59SIEuKBr\nkcIs7Wr9hX6oU8aXh9PTxQ7S0+wdMnF6w7SsV9yQbBeBvrD9Df11bVbLw3B/UXdHb+qs1kWu6+d2\nacz3fznbowxvp4mKSLd0z9eRP8W675j/GFPe0Ri8yXBbIuHZy7sCjqi0JVHLsof9oV/zEvOVFV8N\n2JeDtM2UlZKaf9cDK4DFXp9FQJVfZ/Rvw0732O/SrOQbr1/rurSw8eUXKqc3TKW3jxv/45t7u1qm\n7q3c2ikJHsZu97UESmL8yHa8d1NRQICy2jTch8oyffRk/PHR2OLKsXPT0Ns9o728osqbpLgY6lZP\nJDUpjvFeLrLf/6W/azvQf7fHaWlkTRpVqkJ2VldCCCs4BkrjmkkejZVA8bZZ+fsP8kqwzru7Y/vC\nWebY/i24oFsT1j82gndvLLqvvWcJXNKjKbUsuf54dssSy/ambvXAGlfPjenq2v5Dv+bcO6ItIzqF\n574sycbxK7DCGPOz9wERmVBuElUS3JdP/fbOfsVam52a1GT5jiOuffebrCLjdD8FzxAO6WnJrLZi\nAbVpUJ1LM5sGVN4f+nt62JTVcOlUYh+N7cWZQQwLOvMmxcdwMs8et57lE4aW6QUXCt3Sa5MQF8Py\nCcOKHWvTIJUBp9dj9tp9xf7f3wI0xPvDaS8oq6dSMMz7+8Ay/e5QtqftwV/jpKRLKK1BExMjHl5Q\nvrzN5tx9Dmc/9QPg8BjcdjCbaSt2Ubd6Ij0z0lzhg0oj0L9aRGhYI4nhHRsyflT7wH5kEyUpjkuA\nk74OGGPKp+9VyVh8/2BXmA9vvvrzWazYcYTRL/zo45eVA/eHqUntalzYrQlfL9vFa9dkluimWRLO\nlmugE6acNK1djTW7j1E31fds4pJYPXE4Io4AcL+5hbsuK8GsuR4q1/XJ4K2fs0o1vo4f1Y7s3IJi\nvci0EO0Kzo7eaWHwiCqLS6svNu077rNXaUodYA0N9xU/weH2Pra/o7fxvxIiQngTjJTz7xsURG77\n8Ks4jDHRGX/YRvyFRHDivrRpZeV/f+zNoexculseUqH6nju9dEob2vPmmcu7MnfdvjLZEZz2lh6n\n1fZpsK/IPHRuex46t/TWZKv6qXz0x8BfToESFxvD69dk0jnI+ooku46cpLOPDnFliTnhHPbyNcxa\nUYi+4C6KrfRsnlZ6piCYfHUm7y/cGrQCqJEUz+jOxY2B0U5JQyhtG6bSp2Vdv8ftItCJlRHDSyP4\nUxBl0Rv/+2NvkgMIlWKMffNHnLbEiuyYoIpDCSsZdVO4b2Tx+EdK8Hx7Z//SM1UFir2xfauIkuZh\n+MPuhlMgOHsckZjIGCiRd6pXFEUJAe/3qz+323d+zip3Wexg8jWZDGnfIOJx7UqirDPHxxpjJtst\njKIoSrB49y+OWQs9eVMenmEijmEqO0vu1aIOvSr4hOKy9jgqcCdKUZSqRGFhYDYOmyPCAEUvwkq+\n2kPQlKnHYYx51W5BooX59w4iv1BX2VOUcJGT5xk/K5wvcbG6HFVLbQSgOESkDjAB6IujR/YjMNHX\n8q0KNKxZPHJpOHzgFaWqEuj0j/J4uVfVoZdAehwfAnOBi639K4GPgMHlJVQ0seaR4SWGplYUJTTi\nYjxH3P0OVZXDWJXz0a5iI1UBKY40Y8wjbvuPisgF5SVQtJEU5tAUilLV8DZ6+3uHl4txHAFMWEKy\nVCQCURyzRWQM8D9r/xIg+DUrFUVRygHvd7Z/43g5Wsct5t0zgEPZ0R8DNhCvqj8C7+OIiJuLY+jq\nLhE5JiJHy3JSEXlKRNaIyDIR+UxEfIYrFZEsEVkuIktEZFFZzqUoSnTjbZo+me97sany8KoabUWj\ndcbZapaWbEv05YpOqYrDGJNqjIkxxsRZnxgrLdUYU9b1EqcDHY0xnYF1wL0l5B1gjOlqjMks47kU\nRYlivBXCyz9s9JmvPLyt/nFJZxbdP7jMQT8rKwG544pIZyDDPb8x5tOyntQY476C4Hwcw1+KoihB\nE6jrSXn0OOJjHeukVDUCccd9A+gMrAScExQMUGbF4cUNOLy0fGGA70XEAK+WNFtdRMYCYwHS09Nt\nEk1RlIpOs7Rk1u89Xmo+fzaOQKIPK54E0uPoZYwJ+p8VkRmAr5VLxhtjvrDyjAfygff8FNPXGLNT\nROoD00VkjTFmrq+MllKZDJCZmVm1XBwUpQoza83egPL5W945JUFjvQZLIP/YLyLS3hizKpiCjTEl\nzvMQkWuB0cAg42fw0Riz0/reKyKfAT1xzClRFKUEPhrbixO5vmM2VVX8mThGdApsZT6liEAUx9s4\nlMdu4BSOIUVjGbbLhIgMB/4OnG2MyfaTJwWIMcYcs7aHAhPLek5FqUoEs7xuVSBjnOcMgv5t6jF3\n3T4gvCs6RguBKI43gKuB5RTZOELl30AijuEngPnGmJtFpDHwujFmJNAA+Mw6Hge8b4z51qbzK4pS\nhalqQQntJhDFsdUY86WdJzXGtPKTvhMYaW1vAoJbmFpRlCrHJT2aMmXx9kiLUaUIRHGsEZH3ga9w\nDFUBobnjKoqi2EVKKUu7rtldpnnKSgkEojiq4VAYQ93S7HTHVRRFKTMlrcsOcPBE8RAgGng0NEpV\nHMaY68MhiKIoSnkgPqYI/t+Z6cxZt48HR+scjrIQyATApsALeK7HcYcxRgcVFUWJOGXpPAzr0JC1\njw4nMU6jV5eFQAKsvAl8CTQGmuCwdbxZnkIpiqIEiq8ehcdxP4dVaZSdQBRHPWPMm8aYfOvzFlCv\nnOVSFEUJCDVXhJ9AFMd+EblKRGKtz1WALhurKEqFoF2j4kG6j2TncfRkns/853VpXN4iRT2BKI4b\ngMuA3cAuHJFsbyhPoRRFUQLl4u5NeOKiTh5pXSZ+T+cJjiDc3h2SbA3FEjKBeFVtBc4LgyyKoihB\nIyI+ex1ODmV79jwSdeBJVCoAAA1hSURBVDnnkCm1xyEib7uv0Ccita1Q64qiKBWCkswcp7xWBExW\nxREygQxVdTbGHHbuGGMOAd3KTyRFUZTgaF4vxe+xtbuPeezXqYILL9lNIIojRkRqO3dEJI0AVw5U\nFEUJBzWS4hk/sl2x9DW7j/L71sMeaRl1ksMlVtQSiAL4J/CziEzBMQHwMuCxcpVKURQlSHy55Z7M\nKyy28t9ZreuGSaLoJRDj+DsisggYiGMo8aJgF3VSFEUpb/zFrPKOoN6oZrUwSBPdBDTkZCkKVRaK\nolRYfKkNYwwGT80RoxMGQyYQG4eiKEqFx5dCKDSePY6E2JhSo+kqpaOKQ1GUqMC3QjAeNo6Zfz07\nfAJFMao4FEWJCnz1OIxx9DqcNEtTjyo7KJPiEJHJoZxURCaIyA4RWWJ9RvrJN1xE1orIBhEZF8o5\nFUWJcnz0OAxwOLv4Qk5KaJR1PsarNpz7X8aYp/0dFJFY4EVgCLAd+FVEvlSPLkVRfOHbOA5ZB7LD\nLku0U6YehzFmsd2C+KAnsMEYs8kYkwt8CJwfhvMqilIJ8bUcrPccDsUe/PY4ROQrwO+/bowJNfDh\nbSJyDbAI+KsVysSdJsA2t/3twJn+ChORscBYgPT09BBFUxSlsuHLNv6/X7cVT1RCpqQex9M4Zo1v\nBnKA16zPcWBFaQWLyAwRWeHjcz7wMtAS6IojVPs/fRXhI60kRTbZGJNpjMmsV0/XmVKUqoavF8b+\nE2rfKA/89jiMMXMAROQRY0x/t0Nficjc0go2xgwORAAReQ342seh7UAzt/2mwM5AylQUperha6iq\noLAwApJEPwEtHSsiLZw7ItKcEJeOFZFGbrsX4rsH8yvQWkSai0gCMAbH2ueKoijF8dHl2H4oJ/xy\nVAEC8ar6C/CDiGyy9jOAP4Z43idFpCuOoacsZ3ki0hh43Rgz0hiTLyK3Ad8BscAbxpiVIZ5XUZQo\nxVePY8uBbOJjhbwCNZLbSSBBDr8VkdZAWytpjTHmVCgnNcZc7Sd9JzDSbf8b4JtQzqUoStXAXyAR\ndayyn0DncfTA0dOIA7qICMaYd8pNKkVRlCDJySvwmZ5fqJrDbkpVHCLyLg4PqCWAs2YMoIpDUZQK\nw0k/ikOxn0B6HJlAe2O0w6coSsVF31DhIxCvqhVAw/IWRFEUJRQ0Wnr4CKTHURdYJSILAZdR3IaZ\n44qiKLbRsl71SItQZQhEcUwobyEURVFCJVaX9gsbgbjjzgmHIIqiKKHgax6HUj6UFOTwR2PMWSJy\nDM8YUQIYY0yNcpdOURQlQLTDET5KilV1lvWdGj5xFEVRyoauJR4+dOlYRVGiAtUb4UMVh6IoUUFp\neqNtQx08sQtVHIqiRAWlDVVt0SVkbUMVh6IoVQJ117UPVRyKokQFpdk4xvZvUXIGJWBUcSiKEhW0\nb1Q0Q+CCro2LHc+omxJOcaIaVRyKokQFKYlFswtiY4q/2pLjY8MpTlSjikNRlKgjr6D4WuOdm9aM\ngCTRSUQUh4h8JCJLrE+WiCzxky9LRJZb+RaFW05FUSoX1/fNAODGs5oXO6YTBO0j0BUAbcUYc7lz\nW0T+CRwpIfsAY8z+8pdKUZTKzoOj23PLOS2pn5pU7Jg6VdlHRBSHE3E0AS4DBkZSDkVRogMR8ak0\nAOLjdGTeLiKqOIB+wB5jzHo/xw3wvYgY4FVjzOTwiaYoSjSw5MEhLNl2mBpJ8ZEWJWooN8UhIjPw\nvXLgeGPMF9b2FcAHJRTT1xizU0TqA9NFZI0xZq6f840FxgKkp6eHILmiKNFAl2a1OHjiFLWSEzjn\n9PqRFieqkEgtJS4iccAOoIcxZnsA+ScAx40xT5eWNzMz0yxapLZ0RVGUQBGRxcaYzEDyRnLQbzCw\nxp/SEJEUEUl1bgNDcax/riiKokSQSCqOMXgNU4lIYxH5xtptAPwoIkuBhcBUY8y3YZZRURRF8SJi\nxnFjzHU+0nYCI63tTUCXMIulKIqilELEbBzliYjsA7aU8ed1gaoyb0SvNTrRa41OyvtaTzPG1Ask\nY1QqjlAQkUWBGogqO3qt0Ylea3RSka5VZ8QoiqIoQaGKQ1EURQkKVRzFqUqz0/VaoxO91uikwlyr\n2jgURVGUoNAeh6IoihIUqjgsRGS4iKwVkQ0iMi7S8gSKiDQTkdkislpEVorIHVZ6mohMF5H11ndt\nK11E5HnrOpeJSHe3sq618q8XkWvd0ntY66JssH4b0QDVIhIrIr+LyNfWfnMRWWDJ/ZGIJFjpidb+\nBut4hlsZ91rpa0VkmFt6hbkPRKSWiEwRkTVW/faO1noVkb9Y9+8KEflARJKipV5F5A0R2SsiK9zS\nyr0e/Z3DFowxVf4DxAIbgRZAArAUaB9puQKUvRHQ3dpOBdYB7YEngXFW+jjgH9b2SGAaIEAvYIGV\nngZssr5rW9u1rWMLgd7Wb6YBIyJ8zXcB7wNfW/v/A8ZY268At1jbtwKvWNtjgI+s7fZWHScCza26\nj61o9wHwNnCTtZ0A1IrGegWaAJuBam71eV201CvQH+gOrHBLK/d69HcOW64pUg9FRfpYf/p3bvv3\nAvdGWq4yXssXwBBgLdDISmsErLW2XwWucMu/1jp+BY7Q9bjns46tcUv3yBeB62sKzMSxhsvX1sOy\nH4jzrkvgO6C3tR1n5RPv+nXmq0j3AVDDepmKV3rU1SsOxbHNeinGWfU6LJrqFcjAU3GUez36O4cd\nHx2qcuC8cZ1st9IqFVaXvRuwAGhgjNkFYH0740r7u9aS0rf7SI8UzwL3AM5FpesAh40x+da+u3yu\na7KOH7HyB/sfRIIWwD7gTWtY7nVxBPuMuno1xuwAnga2Artw1NNiorNenYSjHv2dI2RUcTjwNbZb\nqdzNRKQ68AlwpzHmaElZfaSZMqSHHREZDew1xix2T/aR1ZRyrMJfK46WdHfgZWNMN+AEjuEGf1Ta\na7XG3s/HMbzUGEgBRvjIGg31WhqV4tpUcTjYDjRz228K7IyQLEEjIvE4lMZ7xphPreQ9ItLIOt4I\n2Gul+7vWktKb+kiPBH2B80QkC/gQx3DVs0AtcazvAp7yua7JOl4TOEjw/0Ek2A5sN8YssPan4FAk\n0Vivg4HNxph9xpg84FOgD9FZr07CUY/+zhEyqjgc/Aq0trw4EnAY3L6MsEwBYXlQ/AdYbYx5xu3Q\nl4DT8+JaHLYPZ/o1lvdGL+CI1Y39DhgqIrWtFuBQHOPCu4BjItLLOtc1bmWFFWPMvcaYpsaYDBx1\nNMsYcyUwG7jEyuZ9rc7/4BIrv7HSx1jeOc2B1jgMjBXmPjDG7Aa2icjpVtIgYBVRWK84hqh6iUiy\nJYvzWqOuXt0IRz36O0fohNNAVJE/OLwZ1uHwvhgfaXmCkPssHF3TZcAS6zMSx5jvTGC99Z1m5Rfg\nRes6lwOZbmXdAGywPte7pWfiWERrI/BvvAy2EbrucyjyqmqB4wWxAfgYSLTSk6z9DdbxFm6/H29d\nz1rcvIkq0n0AdAUWWXX7OQ5vmqisV+BhYI0lz7s4PKOiol5xrDu0C8jD0UO4MRz16O8cdnx05rii\nKIoSFDpUpSiKogSFKg5FURQlKFRxKIqi/H97dxBiVRmGcfz/hGAFuhBc5EqYEAWxUauFYeHKViqR\nG90EusqEEIVWQUWiDAy0KZKglatExFEUFAJjVNARbRpaxbhoJaMSQiKYT4vvu8xlODFzvHdscZ8f\nDPecc89873dmMe/9Dve8b7SSxBEREa0kcURERCtJHBER0UoSRwwklZLlH3ftr5J0apFi7ZL0ed1+\nV9ItSU8lfTjnvMay2T3EXSnpYq/jRMyV5zhiINWCkOdsr38Bsa4CO2zP1LjLgcPAWdun6jkrKA/7\nvUl5oHMC2Gz7YY+xfwR+sD3eyzgR3bLiiEF1DBiSdFvSiKTVnUY7kj6SdEbSmKRpSZ9IOlSr1F6v\n/+SRNCTpoqQJSb9IWjs3iKQ1wBPbMwC279r+ldnqvh3bgUu2H9RkcQl4v2G8u5K+qKuWyU5MSe/V\na7ld57ms/soZYG9f/mIRVRJHDKrPgD9sD9s+0vD+emAP8DbwNfC3S5Xaa5R6QAAngIO2N1NWEN82\njPMOcGsB82lT+nvG9ibguxqX+nrA9jCwFXhcj9+s+xF9s2T+UyIG0s+2H1EKyP0FjNXjk8CGWsZ+\nC/CTZjuuLm0Y5zVKX435tCmP3amAPAF8ULfHgVFJJ4HTtjs9Gu5RSpVH9E1WHBHNnnRtP+vaf0b5\nwPUSpdHQcNfPuoZxHlOK8s2nTenvzlz+qXPB9jFgP/AKcL3rttnLzK4+IvoiiSMG1SNKj/bn4tIs\na1rSbijl7SW90XDq78DrCxiysWz2Qucjacj2pO3jlNtTncSxhlI5NaJvkjhiINm+D4xL+k3SyHMO\nsxfYJ+kOMEXpYjfXFWBj7ZWApLck/QnsBr6XNFXn8wD4itI74gbwZT22UJ/Wa7lDWWFcqMe3Aefb\nX1rEf8vXcSMWmaRvgDHbl/+H2FeAnb1+rTeiW1YcEYvvKPDqiw4qaSUwmqQR/ZYVR0REtJIVR0RE\ntJLEERERrSRxREREK0kcERHRShJHRES08i/9ksElXiEXnAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot2grid((2,1),(0,0))\n", "plot(D)\n", "ylabel('distance res 10-34')\n", "subplot2grid((2,1),(1,0))\n", "plot(Y[:,0])\n", "ylabel('ind. comp. 1')\n", "xlabel('time (10 ns)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " You can see that the variations are roughly between 0.8 and 1.5 nanometers. This is actually the perfect distance\n", " for FRET (although I'm sure that the bulky FRET labels would mess up everything here, but again this is just a \n", " hypothetical game). On the other hand they might be close enough to use fluorescence quenching. So one option is \n", " to check if there are any trytophanes nearby that can be used as a quencher - that way we could get away with one\n", " extrinsic fluorophore.\n", "\n", "let us average the observable by state:\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "dmean = average_by_state(dtrajs[0], D, M.nstates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " plotting the observable on the TICA-map. It's decently correlated with the first TIC, and a good indicator\n", " of whether we are in the low-populated state." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Knk4ewLh6AH1U8WyqG12UKbgv83ARwnvvqweQnRtwN7PvJ4pQUX+Y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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.scatter_contour(cl.clustercenters[:,0], cl.clustercenters[:,1], dmean, colorbar=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " this is the ensemble average of our probe distance:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.90942998139140785" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.expectation(dmean)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Now let us conduct a correlation experiment. This could be done by using FRET as an observable and then running a\n", " fluorescence time correlation experiment - very easy to do." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'autocorrelation')" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "times, corr = M.correlation(dmean)\n", "plot(times, corr, linewidth=2)\n", "xlabel('time / microseconds (10 ns)')\n", "ylabel('autocorrelation')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " We do see a nice decay that contains our slowest timescale.\n", " Unfortunately, the change in the signal (y-axis) is really small, so that we cannot expect to see anything in\n", " the presence of experimental errors.\n", " The problem is that the extra state is too little populated - in an equilibrium measurement such as FCS\n", " it will have too little contribution, and this is why the amplitude is so small.\n", " \n", " We need to find a way to increase the amplitude of the signal. The observable is already pretty good, we can't get\n", " much better there. But we can do a different experiment that hopefully gives a larger signal: Let us do a \n", " perturbation-relaxation experiment. Suppose we would have some way of preparing our ensemble in the low-populated\n", " state of interest (different temperature, pH, ...?), and then let the system relax towards equilibrium while we\n", " measure the expectation of the fluorescence." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'mean distance')" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p0 = pcca_dist[0]\n", "times, rel = M.relaxation(p0, dmean)\n", "plot(times, rel, linewidth=2)\n", "xlabel('time / microseconds (10 ns)')\n", "ylabel('mean distance')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Now we can see a much stronger signal (variation between 0.9 and 1.15) - this will be measurable even with large\n", " experimental errors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " This is a very nice and clear observable. If we only could measure whatever we wanted...\n", " \n", " now let's plot the relaxation curve in a log-plot.\n", " And let's add single exponentials with the MSM timescales (showing up as lines), to see if we can match timescales " ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'distance perturbation')" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OrVL5iLgUxOgFg5KThq9nDD89M5iige/R9v2fWfz3cb1xUGU6TRxKZUFViuZh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\nXKzKrd72euNFZIf93nfstkIiMldENtm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(times, rel-M.expectation(dmean), linewidth=5)\n", "t2_tau = M.timescales()[0]\n", "plot(times, 0.24*np.exp(-times / t2_tau), color='yellow', linestyle='dashed', linewidth=2)\n", "semilogy()\n", "xlabel('time / microseconds (tau)')\n", "ylabel('distance perturbation')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " We can nicely see that the main part of the relaxation is exactly due to the slow process. So we have designed an\n", " experiment that can measure the slow process!\n", " There are more fast timescales contributing, but their amplitudes are so small that we can hardly see the deviation from a single-exponential. These other timescales could be measured by choosing other coordinates\n", " \n", "A more systematic analysis could be done using dynamical fingerprints concept described in [6]. Please check the msm functions fingerprint_correlation and fingerprint_relaxation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transition pathways and Committors\n", "---------------\n", "\n", "Finally, let us compute transition pathways between two selected endstates. This is a very nice mechanistic analysis that is often revealing when we have a two-state process between such as folding or binding. In the present case we would like to know which pathways does the system take to partially unfold into the rarely populated 'right' state. \n", "\n", "At first we have to select what the two end-states of our interest are. We have done PCCA which gives us an idea of metastable sets, but if we do a transition path analysis with three states that's a bit boring, because there are only two options: the single intermediate state is on-pathway or off-pathway. \n", "\n", "We want to get a more detailed analysis. Therefore we reconsider PCCA an this time ask for six metastable sets:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "# do pcca with 6 states now\n", "M.pcca(6)\n", "pcca_sets_6 = M.metastable_sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which are assigned to the TICA plot as follows:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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Au/nf7KVQ49Sa/qE0aO0gbbbT5ZxBwHfQ5Tlp8ZYqGUFrOdnk4g3Jw7lUwH5s1XhEvuDc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Hk0XnFtDeMSv+cE/FakfajCBLsFc7vdMVtrf3f66W0E0hJUEARByIntTb0fOES1/eih5M825DiU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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(8,5))\n", "pcca_sets = M.metastable_sets\n", "contourf(F.T, 50, cmap=plt.cm.hot, extent=extent)\n", "size = 50\n", "cols = ['orange', 'magenta', 'red', 'black', 'blue', 'green',]\n", "for i in range(6):\n", " scatter(cc_x[pcca_sets_6[i]], cc_y[pcca_sets_6[i]], color=cols[i], s=size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we select as two end-states the leftmost and the rightmost of these 6 sets. Since the ordering of metastable sets could differ in different runs, we actually compute their average positions along the first TICA coordinate:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "xavg = avg_by_set(cc_x, pcca_sets_6)\n", "A = pcca_sets_6[xavg.argmax()]\n", "B = pcca_sets_6[xavg.argmin()]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we compute the transition pathways. This is done by discrete transition path theory [7] in its MSM formulation [8]." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "fluxAB = msm.tpt(M, A, B)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1545.42169847\n", "110.634856466\n" ] } ], "source": [ "# mean first passage times in microseconds\n", "print(0.01*M.mfpt(A, B))\n", "print(0.01*M.mfpt(B, A))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "so, it takes about 1.5 milliseconds on average to go into the low-populated \"open\" state, and about\n", "100 microseconds to switch back." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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WeBu1dp8mv8J5KBZ5nCPKUcfNilm0BSNMb9s0C2C0d3ejk5P13Tw1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\ntWf5O/lk1lwgSfJkCRtGHZjQGvniOwr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(8,5))\n", "mplt.scatter_contour(cl.clustercenters[:,0], cl.clustercenters[:,1], fluxAB.committor, colorbar=True, ncontours=15)\n", "scatter(cl.clustercenters[A,0], cl.clustercenters[A,1], color='black', s=200)\n", "scatter(cl.clustercenters[B,0], cl.clustercenters[B,1], color='white', s=200)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "cg, cgflux = fluxAB.coarse_grain(pcca_sets)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "# compute mean positions of sets. This is important because of some technical points the set order \n", "# in the coarse-grained TPT object can be different from the input order.\n", "avgpos = np.zeros((6,2))\n", "avgpos[:,0] = avg_by_set(cc_x, cg)\n", "avgpos[:,1] = avg_by_set(cc_y, cg)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/mi/marscher/miniconda/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'fig'\n", " s)\n" ] }, { "data": { "image/png": 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CaytW4Hse03bvZs/8+aQbGorbb2zMl9WSCEor0FUzKBkYQc6TlaO0Lmc2NmND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\nY2OMROIImzfvZunSbpYsWUY8PsAnP7mS9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, _ = mplt.plot_flux(cgflux, avgpos, cgflux.stationary_distribution, max_width=10, max_height=7)\n", "cf=contourf(F.T, 50, cmap=plt.cm.hot, extent=extent, fig=fig, zorder=0)\n", "fig.set_size_inches(12, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This shows us the probability fluxes of pathways from the rightmost state to the leftmost (rare-event) state. You can see that the main pathway leads us to the most stable state, that then splits into two pathways that merge in an intermediate, and then split again before uniting in the target state.\n", "\n", "We can decompose the flux into individual pathways, along with their fluxes by:" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "percentage \tpath\n", "-------------------------------------\n", "0.436861309013 \t [0 4 2 5]\n", "0.232607097778 \t [0 4 3 2 1 5]\n", "0.134176054211 \t [0 3 2 5]\n", "0.0779145786193 \t [0 3 2 1 5]\n", "0.0569672479143 \t [0 4 1 5]\n", "0.0454107176694 \t [0 2 1 5]\n", "0.0160629947944 \t [0 3 1 5]\n" ] } ], "source": [ "paths, path_fluxes = cgflux.pathways(fraction=0.99)\n", "print('percentage \\tpath')\n", "print('-------------------------------------')\n", "for i in range(len(paths)):\n", " print((path_fluxes[i] / np.sum(path_fluxes)),' \\t', paths[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get a cleaner picture by just plotting the dominant flux, i.e. the flux that only contains the few most important pathways by setting *minflux* to a higher value" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/mi/marscher/miniconda/lib/python3.6/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'fig'\n", " s)\n" ] }, { "data": { "image/png": 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51UA+56ujg5nqzYJbdBZlvkxl3WOLF3Omo4P8xARr9u3j5VWrahbLFgo16Qa6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unt7Y0sX778Fks3dttlbEsQGA4sAi4EfidJ0niR5CPmN+WbF7mVtU5HdhDrNR2cjZU267KDWpAk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\nEEIIMbP8f0TfNx/WzFaXAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, _ = mplt.plot_flux(cgflux, avgpos, cgflux.stationary_distribution, minflux=1e-6)\n", "cf = contourf(F.T, 50, cmap=plt.cm.hot, extent=extent, fig=fig, zorder=0)\n", "fig.set_size_inches(12, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "References\n", "------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. 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