{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculating the Dimension Reduction Ensemble Similarity between ensembles\n", "\n", "Here we compare the conformational ensembles of proteins in four trajectories, using the dimension reduction ensemble similarity method.\n", "\n", "**Last executed:** Feb 06, 2020 with MDAnalysis 0.20.2-dev0\n", "\n", "**Last updated:** January 2020\n", "\n", "**Minimum version of MDAnalysis:** 0.20.1\n", "\n", "**Packages required:**\n", " \n", "* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "* [scikit-learn](https://scikit-learn.org/stable/)\n", " \n", "**Optional packages for visualisation:**\n", "\n", "* [matplotlib](https://matplotlib.org)\n", "\n", "\n", "
\n", " \n", "**Note**\n", "\n", "The metrics and methods in the `encore` module are from (Tiberti *et al.*, 2015). Please cite them when using the ``MDAnalysis.analysis.encore`` module in published work.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import (PSF, DCD, DCD2, GRO, XTC, \n", " PSF_NAMD_GBIS, DCD_NAMD_GBIS)\n", "from MDAnalysis.analysis import encore\n", "from MDAnalysis.analysis.encore.dimensionality_reduction import DimensionalityReductionMethod as drm\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "# This import registers a 3D projection, but is otherwise unused.\n", "from mpl_toolkits.mplot3d import Axes3D \n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading files" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The test files we will be working with here feature adenylate kinase (AdK), a phosophotransferase enzyme. (Beckstein *et al.*, 2009)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "u1 = mda.Universe(PSF, DCD)\n", "u2 = mda.Universe(PSF, DCD2)\n", "u3 = mda.Universe(PSF_NAMD_GBIS, DCD_NAMD_GBIS)\n", "\n", "labels = ['DCD', 'DCD2', 'NAMD']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The trajectories can have different lengths, as seen below." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "98 102 100\n" ] } ], "source": [ "print(len(u1.trajectory), len(u2.trajectory), len(u3.trajectory))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating dimension reduction similarity with default settings" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dimension reduction similarity method projects ensembles onto a lower-dimensional space using your chosen dimension reduction algorithm (by default: stochastic proximity embedding). A probability density function is estimated with [Gaussian-based kernel-density estimation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html), using Scott's rule to select the bandwidth.\n", "\n", "The similarity of each probability density function is compared using the Jensen-Shannon divergence. This divergence has an upper bound of $\\ln{(2)}$ and a lower bound of 0.0. Normally, $\\ln{(2)}$ represents no similarity between the ensembles, and 0.0 represents identical conformational ensembles. However, due to the stochastic nature of the dimension reduction, two identical symbols will not necessarily result in an exact divergence of 0.0. In addition, calculating the similarity with `dres()` twice will result in similar but not identical numbers.\n", "\n", "You do not need to align your trajectories, as the function will align it for you (along your `selection` atoms, which are `selection='name CA'` by default). " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "dres0, details0 = encore.dres([u1, u2, u3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`encore.dres` returns two outputs. `dres0` is the similarity matrix for the ensemble of trajectories." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.57140127, 0.64493087],\n", " [0.57140127, 0. , 0.63572664],\n", " [0.64493087, 0.63572664, 0. ]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dres0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`details0` contains information on the dimensionality reduction, as well as the associated reduced coordinates. Each frame is in the conformational ensemble is reduced to 3 dimensions." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(3, 300)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reduced = details0['reduced_coordinates'][0]\n", "reduced.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As with the other ensemble similarity methods, we can plot a flat matrix of similarity values." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig0, ax0 = plt.subplots()\n", "im0 = plt.imshow(dres0, vmax=np.log(2), vmin=0)\n", "plt.xticks(np.arange(3), labels)\n", "plt.yticks(np.arange(3), labels)\n", "plt.title('Dimension reduction ensemble similarity')\n", "cbar0 = fig0.colorbar(im0)\n", "cbar0.set_label('Jensen-Shannon divergence')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the reduced coordinates to directly visualise where each trajectory lies in the lower-dimensional space.\n", "\n", "For the plotting of the reduced dimensions, we define a helper function to make it easier to partition the data." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def zip_data_with_labels(reduced):\n", " rd_dcd = reduced[:, :98] # first 98 frames\n", " rd_dcd2 = reduced[:, 98:(98+102)] # next 102 frames\n", " rd_namd = reduced[:,(98+102):] # last 100 frames\n", " return zip([rd_dcd, rd_dcd2, rd_namd], labels)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rdfig0 = plt.figure()\n", "rdax0 = rdfig0.add_subplot(111, projection='3d')\n", "for data, label in zip_data_with_labels(reduced):\n", " rdax0.scatter(*data, label=label)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating dimension reduction similarity with one method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dimension reduction methods should be subclasses of `analysis.encore.dimensionality_reduction.DimensionalityReductionMethod`, initialised with your chosen parameters. \n", "\n", "Below, we set up stochastic proximity embedding scheme, which maps data to lower dimensions by iteratively adjusting the distance between a pair of points on the lower-dimensional map to match their full-dimensional proximity. The learning rate controls the magnitude of these adjustments, and decreases over the mapping from `max_lam` (default: 2.0) to `min_lam` (default: 0.1) to avoid numerical oscillation. The learning rate is updated every cycle for `ncycle`s, over which `nstep` adjustments are performed.\n", "\n", "The number of dimensions to map to is controlled by the keyword `dimension` (default: 2)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "dim_red_method = drm.StochasticProximityEmbeddingNative(dimension=3,\n", " min_lam=0.2,\n", " max_lam=1.0,\n", " ncycle=50,\n", " nstep=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also control the number of samples `nsamples` drawn from the ensembles used to calculate the Jensen-Shannon divergence.\n", "\n", "By default, MDAnalysis will run the job on one core. If it is taking too long and you have the resources, you can increase the number of cores used." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "dres1, details1 = encore.dres([u1, u2, u3],\n", " selection='name CA',\n", " dimensionality_reduction_method=dim_red_method,\n", " nsamples=1000,\n", " ncores=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reducing the learning rate, number of cycles, and number of steps for the stochastic proximity embedding seems to have left our trajectories closer on the lower-dimensional map." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig1, ax1 = plt.subplots()\n", "im1 = plt.imshow(dres1, vmax=np.log(2), vmin=0)\n", "plt.xticks(np.arange(3), labels)\n", "plt.yticks(np.arange(3), labels)\n", "plt.title('Dimension reduction ensemble similarity')\n", "cbar1 = fig1.colorbar(im1)\n", "cbar1.set_label('Jensen-Shannon divergence')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "reduced1 = details1['reduced_coordinates'][0]\n", "\n", "rdfig1 = plt.figure()\n", "rdax1 = rdfig1.add_subplot(111, projection='3d')\n", "for data, label in zip_data_with_labels(reduced1):\n", " rdax1.scatter(*data, label=label)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating dimension reduction similarity with multiple methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may want to try different dimension reduction methods, or use different parameters within the methods. `encore.dres` allows you to pass a list of `dimensionality_reduction_method`s to be applied.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "To use the other ENCORE methods available, you need to install [scikit-learn](https://scikit-learn.org/stable/).\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trying out different dimension reduction parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Principal component analysis uses singular value decomposition to project data onto a lower dimensional space. [(See the scikit-learn user guide for more information.)](https://scikit-learn.org/stable/modules/decomposition.html#pca)\n", "\n", "The method provided by MDAnalysis.encore accepts any of the keyword arguments of [sklearn.decomposition.PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) *except* `n_components`. Instead, use `dimension` to specify how many components to keep." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "pc1 = drm.PrincipalComponentAnalysis(dimension=1,\n", " svd_solver='auto')\n", "pc2 = drm.PrincipalComponentAnalysis(dimension=2,\n", " svd_solver='auto')\n", "pc3 = drm.PrincipalComponentAnalysis(dimension=3,\n", " svd_solver='auto')\n", "pc4 = drm.PrincipalComponentAnalysis(dimension=4,\n", " svd_solver='auto')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we pass a list of clustering methods to `encore.dres`, the results get saved in `dres2` and `details2` in order." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4 4\n" ] } ], "source": [ "dres2, details2 = encore.dres([u1, u2, u3],\n", " selection='name CA',\n", " dimensionality_reduction_method=[pc1, pc2, pc3, pc4],\n", " ncores=4)\n", "print(len(dres2), len(details2['reduced_coordinates']))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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594mj6uCqOhi4FtivqpZV1f7AvsDqfp/HAkWSJElqs4LakJ5bL0kWA6cBzwT2BI5Jsuck170DWDFFRHtU1XfvCa/qe0Dfq45aoEiSJEltV1NsvR0IrK6qNVV1N3AOcMQE170K+Fc6K8T38v0kZyR5epKnJfkQ8P1+H8UxKJIkSVKrTd1LAixJcmnX/ulVdXrzeSlwXde5tcAT7/UNyVLgucAzgAOm+K6XAn8G/EWzfyHwgakC3MgCRZIkSWqz5hWvKdxcVcsmOTdR4/H9LqcAb6iqsaT3d1XVr4F/aLZps0CRJEmSWm+gWbzWAo/o2t8JuGHcNcuAc5riZAnwrCTrq+qzg3zxRCxQJEmSpLbbMFDrS4Ddk+wKXA8cDRzbfUH34otJzgQ+PxfFCVigSJIkSe1WwAAryVfV+iQn0JmdazHw4apaleT45vzyWYmzTxYokiRJUsvVYD0oVNX5wPnjjk1YmFTVS3rdK8ljgNcDO9NVb1TVM/qJxQJFkiRJarsBelDmwL8Ay4EPAWPTbWyBIkmSJLVZQQbsQZll66uq72mFx7NAkSRJklotMPU0w/Pp35L8OfAZ4K6NB6vq1n4aW6BIkiRJbTf1avHz6cXNn6/vOlbAbv007rtASTIGfBfYDFgPnAWcUtUZkpPkQOBk4KFNAP8JvBr4I+BddOZXfiCwBjipqi5q2r0LeDZwN3AN8NKq+nm/cUmSJEkLWjFSPSjdUxLPxKJpXHtnVe1TVY8HDgGeBbwFIMlD6QyGeUNVPRZ4HPBFYOum7Serat+q2h14O3Buksc1574M7FVVewM/BN44yANJkiRJC02q9zavsSSbJXl1kk832wlJNuu3/XQKlHtU1U3AccAJ6Swn+UrgrKr6RnO+qurTVXXjBG2/CpzetKeqvlRV65vTF9NZuVKSJElSv2qKbX59ANgfeH+z7d8c68uMx6BU1Zoki4AdgL3ovPLVr28DfzrB8ZcBn5yoQZLjaIqaRy516Izaw9xVG5m3aitzVwvVfPeSTOGAqnpC1/7/S3J5v41n1IPSZaYvu92nXZI30Rnb8s8TNaiq06tqWVUt2/4hi2f4tdL8M3fVRuat2src1YK0cQxKr21+jSV51MadJLsxjfVQZvyrha4vuglYRafr5nN9Nt8X+H7XvV4MHA78blWNVv0nSZIkjbgRWwfl9cBXk6yh0zGxM/DSfhvPqEBJsj2d1SFPrapKcirwrST/XlXfbK55IfCVCdo+jU7X68HN/mHAG4CnVdUdM4lHkiRJWtBG6Ff8VXVBkt2Bx9IpUH5QVXdN0ewe0ylQtkyykt9MM3w28J4miBuTHA2cnGQHYANwIXBu0/aoJAcBDwB+BBxZVRt7UE4F7g98uTPenour6vhpxCVJkiQtWBm9leSh83bVLnTqjSckoao+2k/DvguUqur5Imczg9fvTHDqzGabrN2j+41BkiRJ0gRqdNZBSXI28ChgJb8Ze1LA7BYokiRJkkbTiPWgLAP2nOnY8kFn8ZIkSZI0bKO1Dsr3gB1n2tgCRZIkSWqzZgxKr20qSQ5LclWS1UlOnOD8EUmuSLIyyaXN+PLJLAGuTLIiyXkbt34fx1e8JEmSpJYb5BWvJIuB04BDgLXAJUnOq6oruy67ADivmcF3b+BTwB6T3PKtM4/GAkWSJEla6A4EVlfVGoAk5wBHAPcUKFX1y67rt6LHi2NV9bVBgvEVL0mSJKnN+nvFa0nzatbG7biuOywFruvaX9scu5ckz03yA+DfgZdNFk6S5yW5OsltSW5P8oskt/f7OPagSJIkSW039UD4m6tq2STnJpqj+D53rKrPAJ9J8lTgb4H/Ncn93gk8u2vdw2mxB0WSJElqsTDwIPm1wCO69ncCbpjs4qq6EHhUkiWTXHLjTIsTsAdFkiRJar/BphK+BNg9ya7A9cDRwLHdFyR5NHBNM0h+P2Bz4JZJ7ndpkk8CnwXuuifEqnP7CcYCRZIkSWqzGmwWr6pan+QEYAWwGPhwVa1KcnxzfjlwJPDHSdYBdwJH9ViIcRvgDuD37h0lFiiSJEnSQjDoSvJVdT5w/rhjy7s+vwN4R5/3eukgsVigSJIkSW03/6vFTyrJFsDLgccDW2w8XlWTzvzVzUHykiRJUpvNwkrys+xsYEfgUOBrdAbd/6LfxhYokiRJUtvVFNv8enRV/TXwq6o6C/h94Lf6bewrXpIkSVLLDaGXpJd1zZ8/T7IX8FNgl34bW6BIkiRJbTacXpJeTk+yHfDXwHnAA4E399vYAkWSJElqsQAZoQKlqs5oPn4N2G267S1QJEmSpJYbpVe8ktyfzropu9BVb1TV3/TT3gJlSN54zRXDDmEgf/+ovYcdwiz44bADaKV/XXvxsEMYyJE7PWnYIQzkmrpg2CG00uevv2zYIQzk8KX7DzuEWfCjYQfQSituWDnsEAZy6MP3GXYIs2D1sAPozwj1oACfA24DLqNrJfl+WaBIkiRJbTbgSvJzYKeqOmymjZ1mWJIkSWq5VO9tnl2UpO9phcezB0WSJElquVHoQUnyXTovm90PeGmSNXRe8QpQVdXXGAELFEmSJKnNRmea4cNn4yYWKJIkSVKLhdHoQQF+BqyrqnUASR4LPAu4tqrO7fcmjkGRJEmSWi4bquc2T75Is2J8kkcD36CzDsork/x9vzexQJEkSZLarPrYppDksCRXJVmd5MQJzr8gyRXNdlGSJ0xwm+2q6urm84uBT1TVq4BnMo3XvyxQJEmSpJbLht5bz7bJYuA0OoXEnsAxSfYcd9mPgKc1A93/Fjh9glt1l0LPAL4MUFV3A32/hOYYFEmSJKnlBpxK+EBgdVWtAUhyDnAEcOXGC6rqoq7rLwZ2muA+VyQ5GbgeeDTwpeZ+204nGHtQJEmSpDarwXpQgKXAdV37a5tjk3k58IUJjr8CuJnOOJTfq6o7muN7Aif38SSAPSiSJElS+03dg7IkyaVd+6dX1cbXtNLvHZMcTKdAOeg+DaruBN4+7vr9mt6Xi8ZfPxkLFEmSJKnFOtMMT1mh3FxVyyY5txZ4RNf+TsAN9/meZG/gDOCZVXVLn+GdAezX57WAr3hJkiRJ7Tb4K16XALsn2TXJ5sDRwHndFyR5JHAu8KKq+uE0opuod6Yne1AkSZKklhtkocaqWp/kBGAFsBj4cFWtSnJ8c3458GbgIcD7kwCs79Ej0+2k6cZjgSJJkiS13KAryVfV+cD5444t7/r8J8Cf9B1PshTYGbg1yVObe1zYT1sLFEmSJKnNCqh5Wy1+SkneARxFZ5riseZwARYokiRJ0kIwaA/KLHsO8NiqumsmjS1QJEmSpBYLAy/UONvWAJsBFiiSJEnSglPVzzTD8+kOYGWSC+gqUqrq1f00tkCRJEmSWm7EXvE6j3HTFE+HBYokSZLUZgWMUA9KVZ2VZEvgkVV11XTbT7lQY5JK8u6u/dcleeu4ay5P8olxx85MckeSrbuOvbe535JmfyzJyiSrmnv8ZRIXj5QkSZKmYcCFGmc3luTZwErgi83+Pkn67lHppxi4C3jexqJiggAe19znqUm2Gnd6NXBEc90i4GDg+q7zd1bVPlX1eOAQ4FnAW/oNXpIkSRKdaYZ7bfPrrcCBwM87odVKYNd+G/dToKwHTgdeO8n5Y4GzgS8BfzDu3CfozIEM8HTgv5r73UdV3QQcB5yQZnlKSZIkSVOo0epBobPK/G33jbI//b5OdRrwgiQPmuDcUcAn6RQjx4w7dzWwfZLtmnPn9PqSqlrTxLTD+HNJjktyaZJLf3bL2H0bSyPK3FUbmbdqK3NXC1FnmuHquc2z7yU5FlicZPck/whc1G/jvgqUqrod+Chwr6nBkhwA/KyqrgUuAPZripFu5wJHA08Evt7H103Ye1JVp1fVsqpatv1DFvcTtjQSzF21kXmrtjJ3tVBlrHpu8+xVwOPpDBX5BHA78Jp+G09nFq9TgG8DH+k6dgywR5IfN/vbAEcCZ3Rdc07T7qyq2tDr7a0kuwFjwE3TiEuSJElauKpGbRavO4A3AW9KshjYqqp+3W/7vmfMqqpbgU8BL4d7Br3/IbB3Ve1SVbvQGRB/zLh2P2kCfH+v+yfZHlgOnFo1//1QkiRJUlulem/zGkvy8STbNBNorQKuSvL6fttPd0rfdwMbZ/N6KnB9VXXPynUhsGeSh3U3qqoPVtU1E9xvy43TDANfoTPQ/qRpxiRJkiQtXDVyr3jt2QwReQ5wPvBI4EX9Np7yFa+qemDX5xuBB3SdftK4a8eAjcXJSya53y5dn305VJIkSRrUaL2AtFmSzegUKKdW1bqk/34cF0WUJEmSWi4bquc2ZfvksCRXJVmd5MQJzu+R5BtJ7kryuilu90Hgx8BWwIVJdqYzUL4v0xkkL0mSJGkUDdCD0gxkP43OwulrgUuSnFdVV3ZddiudGX2fM3Uo9T7gfV2Hrk1ycL/xWKBIkiRJLZYaeJzJgcDqZk1CkpxDZ/KrewqUZlH1m5L8/pTxJPenM7PvLty73vibfoKxQJEkSZLabsOUy8UvSXJp1/7pVXV683kpcF3XubV01jCcqc8BtwGX0VkLZVosUCRJkqQ2K2DK+oSbq2rZJOcmWqhwkC6ZnarqsJk2dpC8JEmS1HLZsKHnNoW1wCO69ncCbhggnIuS/NZMG9uDIkmSJLVaDTrN8CXA7kl2Ba4HjgaOHeB+BwEvSfIjOq94Baiq2rufxhYokiRJUpsVMMAg+apan+QEYAWwGPhwVa1KcnxzfnmSHYFLgW2ADUlew28WZBzvmTMOBgsUSZIkqfUy4EKNVXU+nVXfu48t7/r8UzqvfvVzr2uTHATsXlUfSbI98MCp2m1kgSJJkiS1WQFjU4+Sny9J3gIsAx4LfATYDPgY8Nv9tLdAkSRJklqt+plmeD49F9gX+DZAVd2QZOt+G1ugSJIkSW034Ctes+zuqqokBZBkq+k0tkCRJEmS2qwKxsaGHUW3TyX5ILBtklcALwfO6LexBYokSZLUdiPUg1JVJyc5BLgdeAzwf6rqK/22t0CRJEmS2mxEBskn+QW/WYG+e3X645P8GrgGeFNVXdDrPhYokiRJUtuNQA9KVU06ED7JYmAv4J+bPydlgSJJkiS12eiNQbmPqhoDLk/yj1Nda4EiSZIktd1oTTM8qar64FTXpEagO2i6kvwMuHYOv2IJcPMc3n8+tP0Z5iP+natq+zn+jnsxd6fU9vhh7p9hU8xbaP9/+7bHD+buTPjfffg2yX8vTNeDNtu+nrLtkT2v+eLNH7ysqpbNU0gDaWUPylwnSZJL2/IfcDJtf4a2xz8Zc7e3tscPm8YzjDcf/2Nu+8+t7fHDpvEM4/l37tTa/gxtj3/WFNSIv+I1Ha0sUCRJkiR1aeFbUZOxQJEkSZLarAWD5KfDAmVipw87gFnQ9mdoe/zD0vafW9vjh03jGYah7T+3tscPm8YzzLdN4WfW9mdoe/yzploySL4frRwkL0mSJKnjQYseUk+6/7N6XvOlX3+sNYPkFw07AEmSJEkDqg29tykkOSzJVUlWJzlxgvNJ8r7m/BVJ9puT58BXvCRJkqRWq6qBZvFqVnk/DTgEWAtckuS8qrqy67JnArs32xOBDzR/zroF1YOSZCzJyiSrklye5C+TLOo6f2CSC5vq8QdJzkjygCQvSfKzJN9JcnWSFUme0uaYk7yruf6KJJ9Jsu0cxV9J3t21/7okbx13zeVJPjHu2JlJ7kiyddex9zb3W9Ls9/zZbErMXXO3jdqYt3MZ93zkrnk7O9qYu23O2+Z7zN0B1dhYz20KBwKrq2pNVd0NnAMcMe6aI4CPVsfFwLZJHjb7T0JTcS2QDfhl1+cdgK8AJzX7D6WzmNOTm/0Az2+OvwQ4tavtwcBPgce1NWbg94D7NZ/fAbxjjuL/NfAjYEmz/zrgrV3nHwd8F7ge2Krr+JnAFcALm/1Fzf7arntN+rPZ1DZz19xt49bGvG177pq3o50DbYx5PvLW3J2Vn98XgUun2L43bv+4rvbPB87o2n9Rd140xz4PHNS1fwGwbC6eZ5OrHvtVVTcBxwEnJAnwSuCsqvpGc76q6tNVdeMEbb9KZ9aI49oac1V9qarWN6cvBnaao7DXN9/72j/YNQsAAALqSURBVEnOHwucDXwJ+INx5z4BHNV8fjrwX8397mOCn80my9w1d9uojXnbfHfbcte8nWVtzN0W5i2YuwOpqsOqatkU217j9rtnQJvoZzF+Jq1+rpkVC7ZAAaiqNXR+BjsAewGXTaP5t4E95iKuXuYo5pcBXxg8ukmdBrwgyYMmOHcU8Ek6f7kcM+7c1cD2SbZrzp3T60vG/Ww2aebuPczdFmlj3kIrc9e8nWVtzN0W5i2Yu8O0FnhE1/5OwA0zuGZWLOgCpTHT6nmYVfesxZzkTXR+y/DPA0XUQ1XdDnwUePW47z4A+FlVXUunm3C/5i+XbucCR9MZhPX1Pr5uk/ltSB/MXXO3jdqYt4N8/7znrnk7Z9qYu63JWzB3h+wSYPckuybZnM7P8rxx15wH/HE6ngTcVlX/PRfBLOgCJcluwBhwE7AK2H8azfcFvj8XcfUymzEneTFwOPCCqprrBXFOAV4ObNV17BhgjyQ/Bq4BtgGOHNfuHOBvgS9X9Z4jb9zPZpNm7pq7bdTGvIXW5q55O4vamLstzVswd4eieY3vBGAFnf/2n6qqVUmOT3J8c9n5wBpgNfAh4M/nMqAFs3HvQVLb03mPcfwAsid2XfNCYEfuO4DsaQxn0NusxQwcBlwJbD+P8b8T+AnwVjrF8XXA0q7zBwMXNJ/PBJ7ffP5T4FHN5x8z8aC3e/1sNrXN3DV327i1MW/bnrvm7WjnQBtjno+8NXfdxm8LbR2ULZOsBDaj0015NvAegKq6McnRwMlJdgA2ABfS6TIEOCrJQcAD6MwycWRVzcdvROYq5lOB+wNfbsaIXVxVGyvkufJuOtU5wFOB66vq+q7zFwJ7jp+yrqo+OMn9Jv3ZbILMXXO3jdqYt3MZ93znrnk7c23M3U0lb8HcXfBSNdc9dZIkSZLUnwU9BkWSJEnSaLFAkSRJkjQyLFAkSZIkjQwLFEmSJEkjwwJFkiRJ0siwQJEkSZI0MixQJEmSJI2M/w+VVSqlNkqfIAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "titles = ['Dim = {}'.format(n) for n in range(1, 5)]\n", "fig2, axes = plt.subplots(1, 4, sharey=True, figsize=(15, 3))\n", "for i, (data, title) in enumerate(zip(dres2, titles)):\n", " imi = axes[i].imshow(data, vmax=np.log(2), vmin=0)\n", " axes[i].set_xticks(np.arange(3))\n", " axes[i].set_xticklabels(labels)\n", " axes[i].set_title(title)\n", "plt.yticks(np.arange(3), labels)\n", "cbar2 = fig2.colorbar(imi, ax=axes.ravel().tolist())\n", "cbar2.set_label('Jensen-Shannon divergence')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, adding more dimensions to the principal component analysis has little difference in how similar each ensemble is over its resulting probability distribution (i.e. not similar at all!)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "rd_p1, rd_p2, rd_p3, _ = details2['reduced_coordinates']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot how the trajectories vary on one dimension with a violin plot, we can see that DCD is indeed very distant from DCD2 and NAMD on the first principal component." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0, 0, 'DCD'), Text(0, 0, 'DCD2'), Text(0, 0, 'NAMD')]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rd_p1_fig, rd_p1_ax = plt.subplots(figsize=(4, 8))\n", "split_data = [x[0].reshape((-1,)) for x in zip_data_with_labels(rd_p1)]\n", "rd_p1_ax.violinplot(split_data, showextrema=False)\n", "rd_p1_ax.set_xticks(np.arange(1, 4))\n", "rd_p1_ax.set_xticklabels(labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expanding out to the second principal component shows that DCD2 and NAMD mainly vary on the second axis." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rd_p2_fig, rd_p2_ax = plt.subplots()\n", "for data, label in zip_data_with_labels(rd_p2):\n", " rd_p2_ax.scatter(*data, label=label)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting over the top three principal components gives quite a different result to the reduced coordinates given by stochastic proximity embedding." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rd_p3_fig = plt.figure(figsize=(8, 6))\n", "rd_p3_ax = rd_p3_fig.add_subplot(111, projection='3d')\n", "for data, label in zip_data_with_labels(rd_p3):\n", " rd_p3_ax.scatter(*data, label=label)\n", "rd_p3_ax.set_xlabel('PC 1')\n", "rd_p3_ax.set_ylabel('PC 2')\n", "rd_p3_ax.set_zlabel('PC 3')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating the error in a dimension reduction ensemble similarity analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`encore.dres` also allows for error estimation using a bootstrapping method. This returns the average Jensen-Shannon divergence, and standard deviation over the samples. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "avgs, stds = encore.dres([u1, u2, u3],\n", " selection='name CA',\n", " dimensionality_reduction_method=dim_red_method,\n", " estimate_error=True,\n", " ncores=4)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.24044451, 0.59424151],\n", " [0.24044451, 0. , 0.58874337],\n", " [0.59424151, 0.58874337, 0. ]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "avgs" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.06175088, 0.05114253],\n", " [0.06175088, 0. , 0.05259189],\n", " [0.05114253, 0.05259189, 0. ]])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] Oliver Beckstein, Elizabeth J. Denning, Juan R. Perilla, and Thomas B. Woolf.\n", "Zipping and Unzipping of Adenylate Kinase: Atomistic Insights into the Ensemble of OpenClosed Transitions.\n", "Journal of Molecular Biology, 394(1):160–176, November 2009.\n", "00107.\n", "URL: https://linkinghub.elsevier.com/retrieve/pii/S0022283609011164, doi:10.1016/j.jmb.2009.09.009.\n", "\n", "[2] Richard J. Gowers, Max Linke, Jonathan Barnoud, Tyler J. E. Reddy, Manuel N. Melo, Sean L. Seyler, Jan Domański, David L. Dotson, Sébastien Buchoux, Ian M. Kenney, and Oliver Beckstein.\n", "MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations.\n", "Proceedings of the 15th Python in Science Conference, pages 98–105, 2016.\n", "00152.\n", "URL: https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html, doi:10.25080/Majora-629e541a-00e.\n", "\n", "[3] Naveen Michaud-Agrawal, Elizabeth J. Denning, Thomas B. Woolf, and Oliver Beckstein.\n", "MDAnalysis: A toolkit for the analysis of molecular dynamics simulations.\n", "Journal of Computational Chemistry, 32(10):2319–2327, July 2011.\n", "00778.\n", "URL: http://doi.wiley.com/10.1002/jcc.21787, doi:10.1002/jcc.21787.\n", "\n", "[4] Matteo Tiberti, Elena Papaleo, Tone Bengtsen, Wouter Boomsma, and Kresten Lindorff-Larsen.\n", "ENCORE: Software for Quantitative Ensemble Comparison.\n", "PLOS Computational Biology, 11(10):e1004415, October 2015.\n", "00031.\n", "URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004415, doi:10.1371/journal.pcbi.1004415." ] } ], "metadata": { "kernelspec": { "display_name": "Python (mdanalysis)", "language": "python", "name": "mdanalysis" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }