{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Augmented Markov models, a walk-through tutorial\n", "Author: Simon Olsson (simon.olsson@fu-berlin.de) [@smnlssn](http://twitter.com/smnlssn)\n", "\n", "Dec 2017-Jan 2018\n", "\n", "Augmented Markov models (AMM) are a flavor of Markov state models (MSM) which take into account experimental data during model estimation. Using AMMs we can partially compensate for systematic errors in empirical MD forcefields or equivalently in coarse-grained models, and thereby hopefully get more accurate physical descriptions of thermodynamics and molecular kinetics of molecular systems.\n", "\n", "In our [recent paper](http://www.pnas.org/content/114/31/8265.abstract) we present the first statistical estimator of its kind, which allows for the integration of stationary expectation values as restraints. By stationary expectation value we mean\n", "$$ \\mathbf{o} = \\int \\mathrm{d}x\\; o(x)p(x)\\, , \\; \\, \\, \\, \\, \\,p(x)=\\mathcal{Z}^{-1}\\exp(-\\beta E(x)) $$\n", "where $\\mathbf{o}$ is an experimentally measured value, $o(x)$ is a '_forward model_' which back-computes a micro-scopic, instantaneous value of the experimental observable. Below we will given an example of such a forward model, the Karplus equation. $p(x)$ is the Boltzmann distribution corresponding to the potential energy function $E(x)$ and $x$ is a molecular configuration. Consequently, these observables are time and ensemble averages over a large number of molecules, such as those obtained in bulk experiments including NMR spectroscopy. \n", "\n", "Although we currently only allow for integration of stationary observables, we anticipate to extend support to dynamic observables in the near future. In the mean-time dynamic observables from experiments such as [FRET](http://www.pnas.org/content/108/12/4822.abstract) and [NMR Relaxation dispersion](http://pubs.acs.org/doi/abs/10.1021/jacs.6b09460) may be used for validation. We show an example of this in the end of this notebook\n", "\n", "Special thanks to Tim Hempel, Andreas Mardt and Fabian Paul for comments on early versions of this notebook.\n", "\n", "### Prerequisites \n", "In this tutorial I assume some familiarity with MSM theory and possibly also some practical experience, such as going through [this](http://www.emma-project.org/latest/generated/MSM_BPTI.html) PyEMMA tutorial. I recommend working your way through this tutorial if you are not already familiar with MSMs or if you are not familiar with PyEMMA.\n", "\n", "### Technical requirements\n", "* Python 3\n", "* PyEMMA 2.5 \n", "* Numpy\n", "* matplotlib\n", "\n", "### Content of this notebook\n", "* A quick primer to AMMs using a simple 1D double-well potential\n", "* Using experimental J-couplings and MD simulations to build an AMM of the protein GB3\n", "* Sanity checks and hyper-parameter optimization" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import pyemma as pe\n", "from pyemma.datasets import double_well_discrete\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import matplotlib as mpl" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PyEMMA version 2.4+529.g43a3c781.dirty\n", "numpy version 1.13.1\n", "matplotlib version 2.0.2\n" ] } ], "source": [ "print(\"PyEMMA version\", pe.version)\n", "print(\"numpy version\", np.version.full_version)\n", "print(\"matplotlib version\", mpl.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preparation of double-well data\n", "We extract pre-generated data from a double-well potential and discretize it into 20 evenly sized bins. In a practical setting of a molecular system one would perform dimensionalty reduction of some molecular features, cluster the simulation data in this space, and then use use the discretized trajectories down-stream." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "double_well_data = double_well_discrete.DoubleWell_Discrete_Data()\n", "reaction_coordinate = np.linspace(10,90,25, dtype='int')[:-1]\n", "discrete_trajectory_20bins = double_well_data.dtraj_T100K_dt10_n(np.linspace(10,90,25, dtype='int').tolist())" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IatM+6gdS1c/bk2hND8a0yJCenbng1F48/8F2vnXOkJheZyOQQwKtiql16qeD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\nCcsShDHGmLD+P4Yl9Lzw9S/+AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(reaction_coordinate, np.bincount(discrete_trajectory_20bins),'o-')\n", "plt.xlabel('reaction coordinate')\n", "plt.ylabel('frequency')\n", "plt.title('Double-well potential in %i bins'%(len(np.bincount(discrete_trajectory_20bins))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Selecting a suitable Markov state model\n", "Plotting implied time-scales and selecting the model with lag-time of 35 time-steps" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 9/9 [00:01<00:00, 5.27it/s] \n" ] }, { "data": { "text/plain": [ "(0, 350)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jMAkYLiIrgSuBSSIyjqj5aAVwEYCqviQidwP/BnzgS/YEkzHGlFaSK4gPqepY\nEXleVb8nIj8hwf0HVT2rQPHNnSz/feD7CeIxxhjTA5IkiFwnLU0isgvwLrBX8UIyxvSkT33qU6UO\nwZSpJAlirogMBn4ELCFqHrqpqFEZY3rMF7/4xVKHYMpUkhflrokn54jIXKBKVbvsasMY0zs0NTUB\nUFNTU+JITLlJ0t33l+IrCOI3nR0RsVMOY/qIE088kRNPPLHrBU2/k6Szvs+r6sbcTPzm8+eLF5Ix\nxphykCRBOCLS+qaziLhARfFCMsYYUw6S3KR+BLg7fh9CgS8ADxc1KmOMMSWXJEF8i6jvo4uJ+kya\nhz3FZIwxfV6Sp5hC4DfAb0RkKLCbveVsTN9x3nnnlToEU6aSdLXxJHByvOxS4B0R+auqfr3IsRlj\neoAlCNORJDepB6nqZuBU4HeqOgGYXNywjDE9Zd26daxbt67UYZgylOQehCciI4FPAd8pcjzGmB52\n+unRF4TtexCmvSRXEFcTPcm0XFWfFZG9gdeKG5YxxphSS3KT+h7gnrz5N4DTihmUMcaY0kvS1cZo\nEZkvIi/G82NF5Irih2aMMaaUkjQx/RaYDmQBVPV54MxiBmWMMab0ktykrlHVZ/J624Doq2/GmD7g\n4osvLnUIpkwlSRDrRGQfom42EJHTgfrOVzHG9BZnnHFGqUMwZSpJgvgSMAvYT0TeBv4DnF3UqIwx\nPeatt94CYNSoUSWOxJSbJE8xvQFMFpFawFHVLcUPyxjTUz7zmc8A9h6E2VaSrjYGA+cAexK9NAeA\nqn61qJEZY4wpqSRNTA8BTwMvAGFxwzHGGFMukiSIKuuYzxhj+p8k70HcISKfF5GRIjI0N3S1kojc\nIiJrcy/YxWVDReRREXktHg+Jy0VEfi4ir4vI8yIy/j0ckzHGmG6Q5AoiA/yIqKM+jcsU2LuL9W4F\nfgncnld2OTBfVa8Xkcvj+W8BJwD7xsMHgRvjsTGmyL7xjW+UOgRTppIkiK8D71PV7eoPWFX/JiJ7\ntis+BZgUT98GPEmUIE4BbldVBZ4WkcEiMlJV7X0LY4rspJNOKnUIpkwlaWJ6CWjqpv3tnKv04/FO\ncfmuwFt5y62My7YhIheKyCIRWfTOO+90U1jG9F/Lli1j2bJlpQ7DlKEkVxABsFREngDSucJufsxV\nCpRpgTJUdRbRi3tMnDix4DLGmOQuuugiwN6DMNtKkiDuj4fusCbXdBR/hGhtXL4SyH+NczdgVTft\n0xhjzA6sn2aqAAAbiUlEQVRI8ib1bd24vweAc4Hr4/Gf88q/LCJ3Ed2c3mT3H4wxprQ6TBAicreq\nfkpEXqBAc4+qju1swyLyR6Ib0sNFZCVwJVFiuFtELgDeBD4ZL/4QcCLwOtH9jvO3/1CMMcZ0p86u\nIC6Jxx/fkQ2r6lkd/HRMgWWVqFNAY4wxZaLDBJHXxPNFVf1W/m8i8kOix1ONMb3cFVfYByJNYUke\nc/1YgbITujsQY0xpTJ48mcmTJ5c6DFOGOrsHcTHwRWBvEXk+76c64B/FDswY0zOWLl0KwLhx40oc\niSk3nd2DuBP4C/ADoi4xcrao6vqiRmWM6THTpk0D7D0Is63O7kFsAjYBHd1sNsYY04cluQdhjDGm\nH7IEYYwxpiBLEMYYYwpK0heTMaYPu+6660odgilTliCM6ec+9KEPlToEU6asicmYfm7BggUsWLCg\n1GGYMmRXEMb0c9/+9rcBew/CbMuuIIwxxhRkCcIYY0xBliCMMcYUZAnCGGNMQXaT2ph+bsaMGaUO\nwZQpSxDG9HPWzbfpiDUxGdPPPfbYYzz22GOlDsOUIbuCMKafu/baawHsq3JmG5YgjDGmj2tpaaG+\nvp76+npWrVqVeD1LEMYY00ul0+nWSj83LjS9fn3bj4B6nleZZPslSRAisgLYAgSAr6oTRWQo8Cdg\nT2AF8ClV3VCK+IwxppTS6TSrV6/usMLPTbev+Dviui6DBw9m6NChDBkyhNdee+2/kqxXyiuIj6rq\nurz5y4H5qnq9iFwez3+rNKEZY0z3y1X8nZ3tr1q1infffTfR9hzHYciQIa0Vf248bNgwhg8fzvDh\nwxkxYgRDhw7F87ZW96eeeqok2X45NTGdAkyKp28DnsQShDFFN3PmzFKH0OtlMplEZ/w7UvHnKv1c\nxT9s2DBGjBhRsOLvbqVKEArMExEFZqrqLGBnVa0HUNV6Edmp0IoiciFwIcDuu+/eU/Ea02eNGTOm\n1CGUrVzF39UZ/7p167reGB2f8Q8dOrT1bL8nKv6kShXBh1V1VZwEHhWRV5KuGCeTWQATJ07UYgVo\nTH/x4IMPAnDSSSeVOJKek81mW8/4O6v833nnnUTby1X8+Wf9gwcPbtPUs9NOOzFkyBBSqVSRj677\nlCRBqOqqeLxWRO4DDgXWiMjI+OphJLC2FLEZ09/85Cc/AfpGgshV/F2d8W9PxZ9/czd/PGLEiDZt\n/L2p4k+qxxOEiNQCjqpuiaePBa4GHgDOBa6Px3/u6diMMeUpm82yZs2aRGf8ql03LOQq/vbt/P2l\n4k+qFFcQOwP3iUhu/3eq6sMi8ixwt4hcALwJfLIEsRljelCu4u/qWf7trfjzK/zcdK6ZZ/jw4Qwb\nNqxfV/xJ9XiCUNU3gIMLlL8LHNPT8Rhjup/v+4nO+NeuXbtDZ/z5lX/+zV2r+LtX6W+TG2N6Dd/3\nWbt2bZePcyat+EWkzc1dq/jLiyUIY/q5O+64A9/3uzzbz1X8YRh2uU0RaW3qKfQc//Dhw9l5552t\n4i9zliCM6cOCIOjyjL++vp41a9ZsV8Xf1eOcw4cPx/M84nuNppeyBGFML5Rf8Xd2gzdpxQ8waNCg\nLt/cHT58OKlUyir+fsIShDFlJAgC3nnnnS7b+Le34i/0OGfujH/mzJlUVFQwY8YMq/hNG5YgjOkB\n+RV/R808uYo/CIJE2xw4cOA2lf7QoUNbz/hzzT1dnfFXVkY9P1tyMO1ZgjDmPchV/F09x/9eKv72\nZ/y55p6Kigqr1E1RWYIwpoAwDDs9489Nr1692ip+02dZgjD9Sq7i76yZJ3fG7/t+om3mKv5CvXPm\nKv7hw4dTWVlpFb/pVSxBmD4hDEPWrVuX6Ix/eyr+/Eq/o6d6envF/73vfa/UIZgyZQnClLVcxd/V\nC1zbU/HX1dUlOuOvqqrq1RV/UoMGDSp1CKZMWYIwJRGGIe+++26nzTz19fXU19cnrvgHDBjQ5pOL\nubP+/Pb9/lTxJ/Xwww8DcPzxx5c4ElNuLEGYbpWr+Ls649/Rir+jM/4RI0ZYxb+DLEGYjliCMImo\nasEz/vbTq1evJpvNJtrmgAEDtumyIf85/lyXDdXV1VbxG1MCliD6uVzFn+SMP2nFX1tbW/Bxzvyb\nuyNGjLCK35j3QhUnncZtacFtacFpbm6ddltakOYmgpZGWtJbyGQaaM40ks420uw3Jd6FJYg+SlVZ\nv359l0/11NfXk8lkEm2ztrZ2my4b2rfxW8Vv+i1VxPdxslkkm8VpNy2ZTDTOZnGy2dbKXVqaybY0\n0JJpIJ1poCXbSIvfRLPfTEvQTHPYQpOm2Zxy2FLhsrkqRUNlBQ0V1TRX1tKcqsX3qpFUJa5TQaVb\nRZ1UM6CmirrqGgYGQ6jKVpNKV+OlK3EyVcBXEx2SJYheRlXZsGFDl00921Px19TUbNNlQ67iz3XX\nYBW/Kbkg6LrSzZtuX0mLnyXItBAEGbJBhiDbgh9kyAbpaBxm8YMMmTBDiwvNjtAiSovn0CxCxnXI\nOi6B5xA6DoHrgOuijoPjCLgujiOI6+A6gut4VDgeKTwqHZdKcUkRjStwqcSlsjJFZWWKirqhqL8L\nYaYGMlV4LRXUNAlVzUJdixCkFX9zQHM2Q4OXZUvKp6EyoLEyoKkqpKVaaa4OSVdDS42wocZldY1L\ntsrDr/AQ16HaSVMpaWrZDH9M9k9uCaJM5Cr+rrpsqK+vJ51OJ9pmruIv9OnFYcOGtVb8NTU1VvH3\nY9dff3109ttBxbpNRdzJb5pNE/gZskELWT9DCwHNEtAiSjMhaVdokZAWV2h2hDRCVhx8BwIR1HVQ\nB1QcEEFcQQREIJWrcMWlQjxS4lCBS4U4pHCoFBcJHdwghROmkMCDMIUE1aAehBUoLqhAKIiCBgJ+\nNFZfo2lfSfkKgY8jAa4onheSdpSME5J2Q7KeErpK1lOybkg2BZkU+F5I4EHWA78CAhd8F0IVAnFQ\n1yF0hBAh9DxCx0PEoUKUagmoRKnWZqrDBgaqMkihzoearIfbUoGTqaAmXU1VuoKh6UqymUoy2SrS\nDZWEaQe/RQnSkE2HhOkQPx2iGZ8wk4VsJh5aWFib7G/DEkRHfB+am6NxTv4Xstp/LauD31SVjRs3\nsmr1aurXrGHV6tWsWrNm2+k1a5JX/FVVDBs8mGEDBzJs0KBoPHAgwwcNYqchQ9hpyBB2HjyYmspK\nRBXJxRSG0XQYRhXC5s2waVM0rdpm3LpsofXaL1tovfewLNBm+db5XDztl8n7N2+/XtKybeZzMeXH\nFoZtx7njKbRs3nySZbpaVjXEJyQjIVkC0i40pRyaKlM0VKZoqkzRVJWiqSJFY2UFzV4lzV4FQSpF\nNpVCUw6B64LrgusgnovnuKTEIyUebliJE3o4mkKCFG7oIaGHE3pxReshQQoJKtDABd/B9YEsOL4i\nAWhWkCAk9EMCzZIlJOMEpJ2QjBuS8RTfDcm60TjjhfgpiSpYVwlF8R0h9JRQhNAJEE9wnBBxQhxH\ncVzFccCREE9CXAFHwEVJIaQcqHAcPAJSBKTIkgJSKqQAJ3Dw1EUCwQ0dnMBBQgdRFycUnMCB0EFD\nF0cd3MCjOnSoUSEMHAii4yU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IyLHAvkT95QjwgIgcGXfLnm8yUT/++ftfISK/Ie8KQkSO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\nfNsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lags = [1,5,10,15,20,25,35,50,55]\n", "implied_ts = pe.msm.its(dtrajs=discrete_trajectory_20bins,lags=lags)\n", "pe.plots.plot_implied_timescales(implied_ts,units='time-steps', ylog=False)\n", "plt.vlines(35,ymin=0,ymax=350,linestyles='dashed')\n", "plt.annotate(\"selected model\", xy=(lags[-3], implied_ts.timescales[-3][0]), xytext=(15,250),\n", " arrowprops=dict(facecolor='black', shrink=0.001, width=0.1,headwidth=8))\n", "plt.ylim([0,350])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "M = pe.msm.estimate_markov_model(dtrajs=discrete_trajectory_20bins, lag = lags[-3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Performing a Chapman-Kolmogorov test\n", "The Chapman-Kolmogorov test checks whether the MSM we have build makes predictions which are consisent with direct estimates from our simulation data. The test is based upon the Chapman-Kolmogorov equation which in the context of Markov models can be written as\n", "$$ \\underbrace{T(K\\tau)}_{\\text{black line}} = \\underbrace{T(\\tau)^K}_{\\text{blue dashed line}} $$\n", "which states that transition matrix estimated at lag-time $\\tau$ to the $K$'th power should be equal to a transition matrix estimated at lag-time $K\\tau$. Therefore, if we have built a good MSM the two lines will be close in the plot below:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 9/9 [00:01<00:00, 5.12it/s] \n" ] } ], "source": [ "cktest = M.cktest(nsets=2)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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fKSkpJCcn07hx42CXXi4oFEQk4A4d8kLg008P8uWXuezYUQ2Ae+/tCayjTp02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\nzNICUZBIIBw9CmvXwrJl3o//1VdDVBR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cktplt = pe.plots.plot_cktest(cktest)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks good!\n", "\n", "\n", "### Experimental observables\n", "\n", "Now, let's check agreement with some synthetic experimental value which depends on our reaction coordinate from above.\n", "\n", "First we compute the observable for each discrete states in our simulation data. Here, we map each bin on our axis to a point in the range $\\theta \\in [0,\\pi]$ and compute a faux experimental J-coupling observable using the Karplus equation,\n", "$$ ^3J(\\theta) = 3.2\\cos^2(\\theta) - 1.3\\cos(\\theta) + 4.2. $$\n", "The Karplus equation is an example of a forward model, which maps a molecular feature -- in this case a dihedral angle -- to an experimental observable, here the $^3$J-coupling or scalar coupling." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "_theta = np.linspace(0, np.pi, len(reaction_coordinate))\n", "f_obs = 3.2*np.cos(_theta)**2 - 1.3*np.cos(_theta) + 4.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the case of a molecular system, one would compute some observable of interest for all the frames in our molecular simulation, and then average the predicted observable in each cluster/Markov state. But more about that below ...\n", "\n", "We can use the ``expectation`` method of our PyEMMA MSM instance to compute weighted ensemble averages:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Our simulated J-coupling is: 5.5Hz\n" ] } ], "source": [ "print(\"Our simulated J-coupling is: %1.1fHz\"%M.expectation(f_obs[M.active_set]).round(2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note how we have selected a subset (M.active_set) of the original clusters/discrete states. We do this, as there is no gaurantee that the MSM describes all of the states well. In general, PyEMMA finds the 'largest connected set', which is the larget set of clusters which we have both entered and exited.\n", "\n", "Say we have measured an experimental value, which is 4.1Hz with an uncertainty of 0.8Hz. In such a case, we have a clear discrepancy between the predicted and experimental values. In these cases we can use AMMs to hopefully improve the model. With PyEMMA it is easy to try this out once you have established a regular Markov state model.\n", "\n", "First we compute the experimental observable for all our simulation frames and store them in `ftrajs`" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "ftrajs = f_obs[discrete_trajectory_20bins].reshape(-1,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we have a convienence function ``estimate_augmented_markov_model`` to estimate AMMs by simply providing the ftraj, experimental averages and uncertainties:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "04-01-18 00:33:43 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[2] INFO Total experimental constraints outside support 0 of 1\n", "04-01-18 00:33:43 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[2] INFO Converged Lagrange multipliers after 234 steps...\n", "04-01-18 00:33:43 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[2] INFO Converged pihat after 234 steps...\n" ] } ], "source": [ "AMM = pe.msm.estimate_augmented_markov_model(\n", " dtrajs = [discrete_trajectory_20bins], #Discrete trajectories as for the MSM\n", " ftrajs = [ftrajs], #Trajectories projected onto experimental observable\n", " lag = lags[-3], # same lag-time as the one validated for the MSM\n", " m = np.array([4.1]), # experimental average\n", " sigmas = np.array([0.8]), # experimental uncertainty\n", " maxiter=50000) # Maximum number of iterations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## That is it! \n", "We get some useful information as output here: All our experimental data are within the support, ie. the range of our observable sampled during the MD simulations. Lagrange multipliers and biased ensemble estimate both converged after 2 iterations.\n", "\n", "Let's compare the stationary properties of our AMM with the corresponding MSM." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ux6+G0M4VOpWjC5xRwAAp5WP57x8AukgpJ5ZxfC9gJOABHJBSXlMiWmVElZ2q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\nKioiNTV4TfMmPNn37nWh5VBDyxrrZGxMFDlYy92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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bias_potential=np.exp(AMM.lagrange[0]*f_obs[M.active_set])\n", "bias_potential=bias_potential/bias_potential.sum()\n", "\n", "fig,ax=plt.subplots(ncols=2,figsize=(8,3))\n", "ax[0].semilogy(_theta[AMM.active_set], AMM.stationary_distribution,'-o',label='AMM')\n", "ax[0].semilogy(_theta[M.active_set], M.stationary_distribution, label='MSM')\n", "ax[0].set_xlabel(r'$\\theta\\, /\\, \\mathrm{rad}$')\n", "ax[0].set_ylabel(r'$p(\\theta)$')\n", "ax[1].semilogy(f_obs[AMM.active_set], AMM.stationary_distribution,'-o',label='AMM')\n", "ax[1].semilogy(f_obs[M.active_set], M.stationary_distribution, label='MSM')\n", "ax[1].semilogy(f_obs[M.active_set], bias_potential,'--', label='Experimental bias')\n", "ax[1].set_xlabel(r'$^3J\\, /\\, \\mathrm{Hz}$')\n", "ax[1].set_ylabel(r'$p(^3J)$')\n", "ax[1].legend()\n", "plt.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plots above show the AMM stationary distribution versus the $\\theta$ and $^3J$ variables defined above. The dashed green line in the plot on the right shows the bias introduced by the experimental data. The slope of this curve is given by the Lagrange multiplier estimated. Note how the distribution in our observable space $p(^3J)$ maps different $\\theta$-values to similar values, this causes of the knotted appearence of the curve.\n", "\n", "We can also check whether we are closer to the experimental - _drumroll_ ..." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Our AMM J-coupling is: 4.2Hz\n" ] } ], "source": [ "print(\"Our AMM J-coupling is: %1.1fHz\"%AMM.expectation(f_obs[AMM.active_set]).round(2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which closer to our 'experimental' average of 4.1Hz. \n", "\n", "Try to play around with the experimental average and uncertainty to get some intuition how the AMM estimator changes the stationary properties as a function these parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bonus information for advanced users\n", "\n", "Instead of using the convienence function above we can also build AMM instances directly. In this manner we have more flexibility in terms of input and manipulation of the object before actually estimating the AMM. We may for instance use an E-matrix as a way to input our predicted observables for each Markov state. This matrix must have the dimensions ``number_of_discrete_states`` times ``number_of_experimental_observables``. An example of how to compute such a matrix can be found [below.](#Compute-E-matrix) Note how we here specify a weight $w$ instead of the uncertainties $\\sigma$ -- they are related as $\\sigma = \\sqrt{\\frac{1}{2w}}$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "04-01-18 00:33:44 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[3] INFO Total experimental constraints outside support 0 of 1\n", "04-01-18 00:33:44 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[3] INFO Converged Lagrange multipliers after 234 steps...\n", "04-01-18 00:33:44 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[3] INFO Converged pihat after 234 steps...\n" ] } ], "source": [ "AMM_Advanced_inst = pe.msm.AugmentedMarkovModel(lag=lags[-3], \n", " E = AMM.E, #Average experimental observable in each discrete state\n", " m = np.array([4.1]),\n", " w = np.array([1./2./0.8**2]),\n", " maxiter = 50000\n", " )\n", "AMM_Advanced_est = AMM_Advanced_inst.estimate(discrete_trajectory_20bins)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We check whether the results are consistent: True\n" ] } ], "source": [ "print(\"We check whether the results are consistent:\",np.allclose(AMM_Advanced_est.stationary_distribution, AMM.stationary_distribution))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# AMM of GB3 \n", "To illustrate the use of AMMs for a small molecular system, we turn to GB3. We use back-bone torsions from a number of residues previously shown to be flexible. Below we execute the following protocol:\n", "\n", "* We featurize 35 short MD trajectories, \n", "* Perform TICA dimensionality reduction to 2 dimensions\n", "* Cluster to 112 cluster centers\n", "* Select a MSM with lag-time 40 nanoseconds (based upon an implied time-scale plot and a CK test above.)\n", "\n", "Please note that this data-set is relatively small (~14 microseconds) and uncertainties of the quantities therefore will be large. For illustrative purposes we will not dwell on this point further in this tutorial.\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "feat = pe.coordinates.featurizer(\"gb3_data/gb3_backbone_top.pdb\")" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "for ri in [8,9,10,11,12,13,14,36,37,38,39,40,41]:\n", " feat.add_backbone_torsions(selstr='residue %i'%ri, cossin=True)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 35/35 [00:00<00:00, 315.85it/s] \n" ] } ], "source": [ "source = pe.coordinates.source(['gb3_data/gb3_backbone_{:03d}.xtc'.format(i) for i in range(35)], features=feat)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 35/35 [00:02<00:00, 19.09it/s] \n", "100%|██████████| 35/35 [00:01<00:00, 22.83it/s] \n" ] } ], "source": [ "lag=55\n", "tica_obj = pe.coordinates.tica(source, lag=lag, dim=2)\n", "\n", "Y = tica_obj.get_output() # get tica coordinates" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "04-01-18 00:34:11 pyemma.coordinates.clustering.kmeans.KmeansClustering[6] INFO Cluster centers converged after 11 steps.\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tX/Pd77+fXuR7LhH5I3AWcChQB3xXKbVEROYBdwE5wANKqdt6M9ZMerOUAl1K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\nBM4XKwioqZFIQCjo7OL6x1YiwQhPfCiqNx9hSS1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JoMpcURSlBFBlriiKUgKo\nMlcihYgMdVUP3CUi/+d63+4aN0ZEVtqV+zaLyLMiUu9xvtUisk9EVhT2myhKYdHQRCWyiMidWJUa\nf2q/32+MGSQiFVjxzXOMMcvtY5OBVmNM81HnmAJUAj8wxlxa0C+gKAVELXOlGPlr4E1HkQMYY5qO\nVuT2/jVAWyGFU5QwUGWuFCPjgfVhC6EoUUKVuaIoSgmgylwpRjYBE8IWQlGihCpzpRh5EjhbRKY7\nO+w+myeFKJOihIoqc6XoMMZ0AJcCf283of49Vh/NlDrsIvI6VhXFKSKyXUQuKqiwilIgNDRRURSl\nBFDLXFEUpQRQZa4oilICqDJXFEUpAVSZK4qilACqzBVFUUoAVeaKoiglgCpzRVGUEuD/AVWyymRp\nPlTEAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pe.config.show_progress_bars = False\n", "Y_all = np.vstack(Y)\n", "n_clusters = 112 # number of k-means clusters\n", "\n", "clustering = pe.coordinates.cluster_kmeans(Y, k = n_clusters, max_iter = 100, stride = 10)\n", "\n", "dtrajs = clustering.assign(Y)\n", "\n", "cx = clustering.clustercenters[:,0]\n", "cy = clustering.clustercenters[:,1]\n", "\n", "plt.hist2d(Y_all[:, 0], Y_all[:, 1], bins=100, norm = mpl.colors.LogNorm())\n", "plt.colorbar()\n", "plt.scatter(cx, cy, marker='o', color='red')\n", "plt.xlabel('TIC 1')\n", "plt.ylabel('TIC 2')\n", "plt.title('TICA 2D Histogram, log-scaled')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model selection and self-consitency checks" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "time_step_ps = 200\n", "lags = range(5,400,40)\n", "its = pe.msm.its(dtrajs, lags=lags, nits=1, reversible=True)\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 1500)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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45opIA+BxXIe24pqsDLBoEaxd6646jAmnX375xe8QjAGCuwHwIe/lTBGZC9RS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\ncrBrhgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pe.plots.plot_implied_timescales(its, ylog = False, dt=time_step_ps*1e-3, units='ns')\n", "plt.vlines(40,ymin=0,ymax=1500,linestyles='dashed')\n", "plt.annotate(\"selected model\", xy=(40, 1350), xytext=(15,900),\n", " arrowprops=dict(facecolor='black', shrink=0.001, width=0.1,headwidth=8))\n", "plt.ylim([0,1500])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "M_gb3 = pe.msm.estimate_markov_model(dtrajs, lag=200)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "ckt_gb3 = M_gb3.cktest(2, mlags=5)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(,\n", " array([[,\n", " ],\n", " [,\n", " ]], dtype=object))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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E3XfqZpSw225jYzN33vket91WygcfZNPYWEhOTg6HHvpbTjttHJdddgjp6bvl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\nATeGFZiIiHS/eB+dvQZIj5l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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pe.plots.plot_cktest(ckt_gb3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computation of scalar couplings from simulation data\n", "We use a dataset of HN-HA scalar couplings and Karplus parameters [from this paper](https://doi.org/10.1016/j.dib.2015.08.020) to test the quality of our MSM. This observable is sensitive to the ensemble of sampled $\\phi$ angles. \n" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "#Karplus parameters\n", "A_ = 8.754 \n", "B_ = -1.222 \n", "C_ = 0.111" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "# Load data\n", "expljc = np.loadtxt('gb3_data/HN_HA_JC.dat')\n", "\n", "# Get all phi-angles\n", "feat_jcoupl = pe.coordinates.featurizer(topfile='gb3_data/gb3_backbone_top.pdb')\n", "feat_jcoupl.add_backbone_torsions()\n", "phi_indices = [i for i,st in enumerate(feat_jcoupl.describe()) if \"PHI\" in st] \n", "md_phi_rindex=[int(a.split(\" \")[-1]) for a in np.array(feat_jcoupl.describe())[phi_indices].tolist()]\n", "sourcejc = pe.coordinates.source(['gb3_data/gb3_backbone_{:03d}.xtc'.format(i) for i in range(35)], features=feat_jcoupl)\n", "phis_ = [dih[:, phi_indices] for dih in sourcejc.get_output() ]\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "#Compute scalar-couplings\n", "Phi_all = np.vstack(phis_)-np.pi/3 # correct the phase \n", "cosPhi_all = np.cos(Phi_all)\n", "cossqPhi_all = cosPhi_all*cosPhi_all\n", "JC_all = A_*cossqPhi_all+B_*cosPhi_all+C_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute E-matrix" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# Compute E-matrix\n", "dta = np.concatenate(dtrajs) # concatenate our discretized trajectories \n", "all_markov_states = set(dta) # get set set of all possible states\n", "_E = np.zeros((len(all_markov_states), JC_all.shape[1])) # initialize E-matrix\n", "for i, s in enumerate(all_markov_states): # loop over all Markov states\n", " _E[i, :] = JC_all[np.where(dta == s)].mean(axis = 0) # compute average observable over Markov state i" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "#Find intersection in set of computable and measured scalar couplings.\n", "a=[int(i) for i in set(md_phi_rindex).intersection(expljc[:,0])]\n", "idx_expl = [np.where(expljc[:,0]==i)[0][0] for i in a]\n", "idx_md = [np.where(np.array(md_phi_rindex)==i)[0][0] for i in a]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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C24HJZnZRkeOpaj0a6VREssr7BlXSSd4Jwt2vcPerwr8flyKoapX3SKci0qW8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\nIiISSQlCREQiKUGIiEgkJQgREYn0/wEdzIh71bt6/AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(np.array(md_phi_rindex)[idx_md], M_gb3.stationary_distribution.dot(_E[:, idx_md]),'o',label='MSM')\n", "plt.plot(expljc[idx_expl,0], expljc[idx_expl,1],'x', label='Experiment')\n", "plt.xlabel('residue index')\n", "plt.ylabel(r'$^3J_{\\mathrm{H}^{\\mathrm{N}}-\\mathrm{H}^{\\alpha}}\\, / \\, \\mathrm{Hz}$')\n", "plt.title(r'Comparison of MSM predictions with $^3J_{\\mathrm{H}^{\\mathrm{N}}-\\mathrm{H}^{\\alpha}}$ data')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, we observe a fair qualitative agreement with the data. However, considering the upper error of 0.3Hz has been reported for these data a quantitative agreement is clearly missing. " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "#Setup input for AMM estimation\n", "ftrajs = np.split(JC_all[:, idx_md], np.cumsum([len(p) for p in phis_])[:-1], axis=0)\n", "expl_data = expljc[idx_expl, 1].reshape(-1)\n", "expl_sigmas = 0.3*np.ones(expl_data.shape)\n", "\n", "# We increase the uncertainty for a subset of the data to illustrate non-uniform errors\n", "expl_sigmas[18:21] = expl_sigmas[18:21] + 0.5" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.773668 is outside the support (8.864312,9.617295)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.678525 is outside the support (8.688147,9.656137)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.735873 is outside the support (7.894706,9.565636)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.571859 is outside the support (8.513741,9.428110)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.898549 is outside the support (8.409517,9.767085)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 5.083449 is outside the support (5.162310,6.510399)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 10.289247 is outside the support (8.668080,9.411788)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.841005 is outside the support (8.114074,9.749027)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 8.359442 is outside the support (6.155785,8.071151)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 6.783495 is outside the support (7.617393,8.474687)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.351349 is outside the support (7.728871,8.916314)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 7.265520 is outside the support (5.625987,6.574851)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 4.320463 is outside the support (7.365972,8.813777)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 6.322209 is outside the support (6.639600,8.443197)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 2.378610 is outside the support (4.092054,5.080344)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.206853 is outside the support (4.378050,9.200555)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 8.725843 is outside the support (6.703235,8.699459)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.778475 is outside the support (8.256344,9.650097)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 4.034841 is outside the support (5.142444,6.329253)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 10.008991 is outside the support (8.352021,9.150212)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 10.167532 is outside the support (9.163187,9.708717)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.393146 is outside the support (7.423058,8.607732)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.957418 is outside the support (8.692350,9.683921)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Experimental value 9.882909 is outside the support (9.046996,9.819023)\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Total experimental constraints outside support 24 of 35\n", "04-01-18 00:34:27 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Converged Lagrange multipliers after 3 steps...\n", "04-01-18 00:34:28 pyemma.msm.estimators.maximum_likelihood_msm.AugmentedMarkovModel[10] INFO Converged pihat after 334 steps...\n" ] } ], "source": [ "amm_gb3 = pe.msm.estimate_augmented_markov_model(dtrajs = dtrajs,\n", " ftrajs = ftrajs,\n", " lag = 200,\n", " m = expl_data,\n", " sigmas = expl_sigmas\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### And we have our first AMM on a molecular system!\n", "Note how we get more output this time. We get notified that some of our data-points are outside the support sampled during our MD simulation. We cannot hope to fit these data exactly, yet these data are still taken into account during estimation.\n", "\n", "We can now see if we actually fit the experimental data better with the estimated AMM:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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UJgYteXcl1cM8tEbt23aMKd3vrASR5dLxdmYsIo38aiPCxi+Wp9HAg0TgWgk8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\nfN555x0++OADZs6c2fi7nj1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(np.array(md_phi_rindex)[idx_md], M_gb3.stationary_distribution.dot(_E[:,idx_md]),'o',label='MSM')\n", "plt.plot(expljc[idx_expl,0], expljc[idx_expl,1],'x', label='Experiment')\n", "plt.plot(expljc[idx_expl,0], amm_gb3.mhat,'o', label='AMM')\n", "\n", "plt.xlabel('residue index')\n", "plt.ylabel(r'$^3J_{\\mathrm{H}^{\\mathrm{N}}-\\mathrm{H}^{\\alpha}}\\, / \\, \\mathrm{Hz}$')\n", "plt.title(r'Comparison of MSM/AMM predictions with $^3J_{\\mathrm{H}^{\\mathrm{N}}-\\mathrm{H}^{\\alpha}}$ data')\n", "\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMS error MSM: 1.103\n", "RMS error AMM: 1.048\n" ] } ], "source": [ "print(\"RMS error MSM: {:.3f}\".format(np.std(M_gb3.stationary_distribution.dot(_E[:,idx_md])-expljc[idx_expl,1])))\n", "print(\"RMS error AMM: {:.3f}\".format(np.std(amm_gb3.mhat-expljc[idx_expl,1])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This improved the overall fit a bit, but some individual data-points improve a lot - Let us now coarse-grain the model into 2 meta-stable states using PCCA, to better understand what changes including the experimental data result in:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M_gb3.pcca(2)\n", "amm_gb3.pcca(2)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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UbPaTeIGxatipaVXnVhFpAdLABaraLSIfAVDVq702pwJ3qeqeUscG9hVYQCwT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PAAAg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\nb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colors = ['orange', 'magenta']\n", "\n", "fig,ax=plt.subplots(ncols=2,figsize=(8,4))\n", "\n", "pe.plots.scatter_contour(cx, cy, -np.log(M_gb3.stationary_distribution), cmap='viridis',ax=ax[0])\n", "pe.plots.scatter_contour(cx, cy, -np.log(amm_gb3.stationary_distribution), cmap='viridis',ax=ax[1])\n", "\n", "for i, st in enumerate(M_gb3.metastable_sets):\n", " ax[0].scatter(cx[st], cy[st], c = colors[i], s = 5)\n", "for i, st in enumerate(amm_gb3.metastable_sets):\n", " ax[1].scatter(cx[st], cy[st], c = colors[i], s = 5)\n", "\n", "ax[0].set_title('GB3 MSM')\n", "ax[1].set_title('GB3 AMM (scalar couplings)')\n", "fig.tight_layout(pad=2.5)\n", "\n", "fig.suptitle(r'$-\\log{\\pi_i}$ plots', fontsize=16)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We show minus log probabilities of the GB3 MSM and the GB3 AMM, and show the different meta-stable assignments using orange and magenta colors. Note how the meta-stable state assignments are slightly different in the two model in low-probability regions.\n", "\n", "Some regions of conformational space are substantially downweighed in the AMM, in particular in the orange meta-stable configuration. Let's compare the coarse-grained stationary distributions to better quantify these differences:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax=plt.subplots(figsize=(4,4))\n", "xticks = []\n", "for i, st in enumerate(M_gb3.metastable_sets):\n", " ax.bar(i/2.-0.11, M_gb3.stationary_distribution[st].sum(), color = colors[i], width = .2)\n", " ax.text(i/2.-0.11-0.055, M_gb3.stationary_distribution[st].sum()+0.01, \"{:.3f}\".format(M_gb3.stationary_distribution[st].sum()))\n", " xticks.append(i/2.-0.11)\n", " \n", "for i, st in enumerate(amm_gb3.metastable_sets):\n", " ax.bar(i/2.+0.11, amm_gb3.stationary_distribution[st].sum(), color = colors[i], width = .2)\n", " ax.text(i/2.+0.11/2., amm_gb3.stationary_distribution[st].sum()+0.01, \"{:.3f}\".format(amm_gb3.stationary_distribution[st].sum()))\n", " xticks.append(i/2.+0.11)\n", "ax.set_xticks(xticks)\n", "ax.set_ylim((0.,1.05))\n", "ax.set_xticklabels([ 'MSM','MSM', 'AMM', 'AMM'], rotation = 45)\n", "ax.set_ylabel('probability of meta-stable state')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see a strong repopulation towards the magenta state in the AMM compared to the MSM. \n", "\n", "Finally, let us inspect the slowest time-scale of the AMM vs the MSM:\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slowest MSM time-scale is 1.367 microseconds.\n", "Slowest AMM time-scale is 2.582 microseconds.\n" ] } ], "source": [ "print(\"Slowest MSM time-scale is {:.3f} microseconds.\".format(M_gb3.timescales(k = 1)[0]*time_step_ps/1e6))\n", "print(\"Slowest AMM time-scale is {:.3f} microseconds.\".format(amm_gb3.timescales(k = 1)[0]*time_step_ps/1e6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case we see a slow-down of the slowest time-scale. But note this value is very sensitive to numerical fluctuations in the estimation algorithm such as number of cluster-centers as we have very little simulation data in this example. Consequently, caution must be taken before making inferences about changes in time-scales with small data-sets like this. Generally we recommend repeating the estimation with multiple independent discretizations to test the robustness of these values. The meta-stable state distribution will also fluctuate as we change the number of clusters but this result is generally more robust. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Validations and sanity checks\n", "To finish off, we will inspect our estimated AMM to ensure everything makes sense.\n", "\n", "An interesting thing to inspect first is the Lagrange multipliers $\\lambda_i$, which compensate for the systematic errors between the simulation and experimental ensembles." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax=plt.subplots(ncols=3,figsize=(12,4))\n", "\n", "ax[0].plot(expljc[idx_expl,0], amm_gb3.lagrange, 'o')\n", "ax[0].set_xlabel('residue index')\n", "ax[0].set_ylabel(r'$\\lambda_i$')\n", "\n", "ax[1].hist(amm_gb3.lagrange)\n", "ax[1].set_xlabel(r'$\\lambda_i$')\n", "ax[1].set_ylabel(r'count $\\lambda_i$')\n", "\n", "ax[2].scatter(amm_gb3.lagrange, amm_gb3.m-M_gb3.stationary_distribution.dot(_E[:,idx_md]) )\n", "ax[2].set_xlabel(r'$\\lambda_i$')\n", "ax[2].set_ylabel(r'MSM prediction error')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see many of the Lagrange multipliers cluster around zero, which is good news for the forcefield as it illustratess that a substantial fraction of the observables are fairly well described by the unbiased simulation. However, a few larger values are also seen -- this can mean three different things: \n", "* the forcefield does not describe this observable well, \n", "* we have under-estimated the uncertainty of these observations \n", "* the experimental values are not assigned to the right molecular feature.\n", "\n", "The latter of these points can be due either to mislabeling in either the computational analysis or on the experimental side. \n", "\n", "Note, the weak correlation between the MSM prediction error of our AMM lagrange multipliers is visible, which is naively expected.\n", "\n", "Next, we look at population weighed variances of our experimental observable in the MSMs and AMMs,\n", "\n", "$$ \\sigma_i^2(\\pi) = \\sum_j \\pi_j(E_{ji}-e_i)^2 $$\n", "where $ e_i = \\sum_j \\pi_j E_{ji}$ (the expectation of observable $i$), $\\pi$ is the stationary vector of the AMM or MSM and the $E$-matrix is as defined [above.](#Compute-E-matrix)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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ULcGTiQCl66BEJGmyNFMqJRN7UKpmLiKSPJkIUCIikjwKUCIi4iQFKBERcZIC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\npAAlIiJOUoASEREn/X9zFFfiMTAjiwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax=plt.subplots(ncols=1,figsize=(6,4))\n", "\n", "msm_obs_var = M_gb3.stationary_distribution.dot((amm_gb3.E_active- M_gb3.stationary_distribution.dot(amm_gb3.E_active))**2. )\n", "amm_obs_var = amm_gb3.stationary_distribution.dot((amm_gb3.E_active-amm_gb3.mhat)**2.)\n", "\n", "ax.semilogy(expljc[idx_expl,0], amm_obs_var, 'o', label=\"AMM\")\n", "ax.semilogy(expljc[idx_expl,0], msm_obs_var, 'x', label=\"MSM\")\n", "ax.set_xlabel('residue index')\n", "ax.set_ylabel(r'$\\mathrm{var} (J)\\; \\; / \\; \\; \\mathrm{Hz}^2$')\n", "ax.legend()\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We generally expect these variances to decrease as we are enforcing additional information about these quantities. Indeed, we see most of these decreasing dramatically, and a few remaining more or less unchanged. Note the `log`-scale on the `y`-axis.\n", "\n", "### Cross-validation with other experimental data\n", "\n", "Finally, we cross-validate the AMM using another set of scalar-couplings which are also sensitive to the backbone $\\phi$ angle but is measured through the dihedral between the planes defined by the vectors ($H^N-N$, $N-C^{\\alpha}$) the ($C^{\\alpha}-C^{\\beta}$,$C^{\\alpha}-N$).\n", "\n", "For this we can reuse alot of our featurization from above - but need a new set of Karplus parameters:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "A2_ = 3.693 \n", "B2_ = -0.514 \n", "C2_ = 0.043 " ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "# Load data\n", "expljc2 = np.loadtxt('gb3_data/HN_CB_JC.dat')\n", "\n", "#Compute scalar-couplings\n", "Phi_all = np.vstack(phis_)+np.pi/3 # correct the phase \n", "cosPhi_all = np.cos(Phi_all)\n", "cossqPhi_all = cosPhi_all*cosPhi_all\n", "JC_all = A2_*cossqPhi_all+B2_*cosPhi_all+C2_" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "#Find intersection in set of computable and measured scalar couplings.\n", "a=[int(i) for i in set(md_phi_rindex).intersection(expljc2[:,0])]\n", "idx_expl = [np.where(expljc2[:,0]==i)[0][0] for i in a]\n", "idx_md = [np.where(np.array(md_phi_rindex)==i)[0][0] for i in a]" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "# Compute E-matrix\n", "dta = np.concatenate(dtrajs)\n", "all_markov_states = set(dta)\n", "_E = np.zeros((len(all_markov_states), JC_all.shape[1]))\n", "for i, s in enumerate(all_markov_states):\n", " _E[i, :] = JC_all[np.where(dta == s)].mean(axis = 0)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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enrT4m2gN5rs5NOM4TES+DHwEqKp28nHMeuAWVa0SkY7AGhF5UVU/COpzAXC8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\nnfEZk+zKqvsscKXrdTUM2NW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(np.array(md_phi_rindex)[idx_md], M_gb3.stationary_distribution.dot(_E[:,idx_md]),'o',label='MSM')\n", "plt.plot(expljc2[idx_expl,0], expljc2[idx_expl,1],'x', label='Experiment')\n", "plt.plot(np.array(md_phi_rindex)[idx_md], amm_gb3.stationary_distribution.dot(_E[:,idx_md]),'o',label='AMM')\n", "\n", "plt.xlabel('residue index')\n", "plt.ylabel(r'$^3J_{\\mathrm{H}^{\\mathrm{N}}-\\mathrm{C}^{\\beta}}\\, / \\, \\mathrm{Hz}$')\n", "plt.title(r'Crossvalidation of MSM/AMM predictions with $^3J_{\\mathrm{H}^{\\mathrm{N}}-\\mathrm{C}^{\\beta}}$ data')\n", "\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMS MSM: 0.502\n", "RMS AMM: 0.443\n" ] } ], "source": [ "print(\"RMS MSM: {:.3f}\".format(np.std(M_gb3.stationary_distribution.dot(_E[:,idx_md])-expljc2[idx_expl,1])))\n", "print(\"RMS AMM: {:.3f}\".format(np.std(amm_gb3.stationary_distribution.dot(_E[:,idx_md])-expljc2[idx_expl,1])))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe an ever so slight improvement in the agreement with these complementary experimental data which suggests that our AMM is an overall more accurate model compared to the MSM. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cross-validating with relaxation-dispersion data and other dynamic observables\n", "Is covered in [this notebook](https://github.com/psolsson/NMR_ChemEx_Pred) and [here](http://www.emma-project.org/latest/generated/MSM_BPTI.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Double-checking AMM estimation convergence\n", "Sometimes it is instructutive to inspect model log-likelihood as a function of iteration, along with its absolute $\\Delta$. Current default values for convergence is when $\\Delta$ is less than $10^{-8}$." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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mloiIuCsizgL2AB4EPgMsknQT0D/R4MzlGqzoOcExs0RFxLqIuCUiTgL2AWYA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\nO/WyJldGtQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax=plt.subplots(ncols=2,figsize=(8,4))\n", "\n", "ax[0].semilogx(amm_gb3._lls, '-')\n", "ax[0].set_xlabel('iteration')\n", "ax[0].set_ylabel(r'Log-Likelihood')\n", "\n", "ax[1].loglog(np.abs(np.diff(amm_gb3._lls[:])))\n", "ax[1].set_xlabel(r'iteration')\n", "ax[1].set_ylabel(r'$\\mid\\Delta\\mid$Log-Likelihood')\n", "\n", "fig.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }