{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# scLVM - Accounting for cell-to-cell heterogeneity in single-cell RNA-Seq data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "scLVM requires preprocessed and normalize signle-cell RNA-Seq data as input. This example assumes that the data have already been processed appropriately. For an example of how the input file for this notebook can be generated form raw counts, see R/transform_counts_Tcells.R" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stage 1: Fitting process" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "scLVM uses the Gaussian Process Latent variable model to fit a cell-cell covariance matrix, which is induced by a specified number of hidden factor (typically low rank). This approach resembles a Principal Component Analysis on genes annotated to a hidden factor (such as cell cycle). However, instead of explicitly reconstructing PCA loadings and scores, the GPLVM approach fits a low-rank cell-to-cell covariance to the empirical covariance matrix of these genes. Moreover, scLVM accounts for the technical noise estimates during the fitting." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/matplotlib/__init__.py:855: UserWarning: text.fontsize is deprecated and replaced with font.size; please use the latter.\n", " warnings.warn(self.msg_depr % (key, alt_key))\n" ] } ], "source": [ "# activiate inline plotting\n", "%pylab inline\n", "# load modules\n", "import sys\n", "import scipy as SP\n", "import pylab as PL\n", "from matplotlib import cm\n", "import h5py\n", "import os\n", "\n", "#adjust path\n", "scLVM_BASE = './..'\n", "from scLVM import scLVM\n", "\n", "#sys.path.append(scLVM_BASE)\n", "#sys.path.append( scLVM_BASE +'..')\n", "#sys.path.append(scLVM_BASE + 'scLVM/utils') #this is not included in the github repo\n", "#sys.path.append(scLVM_BASE +'CFG')\n", "#from misc import *\n", "#from barplot import *\n", "#from default import *\n", "from scLVM.utils.barplot import *\n", "from scLVM.utils.misc import *\n", "\n", "from IPython.display import Latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, the required data have to be loaded. These include:\n", "* Normalised gene expression data: LogNcountsMmus\n", "* Technical noise (in log space): LogVar_techMmus \n", "* Gene symbols: gene_names\n", "* Heterogeneous genes (boolean vector): genes_geterogen \n", "* Cell cycle genes (vector of indices): cellcyclegenes_filter" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = os.path.join(scLVM_BASE,'data','Tcell','data_Tcells_normCounts.h5f')\n", "f = h5py.File(data,'r')\n", "Y = f['LogNcountsMmus'][:] # gene expression matrix\n", "tech_noise = f['LogVar_techMmus'][:] # technical noise\n", "genes_het_bool=f['genes_heterogen'][:] # index of heterogeneous genes\n", "geneID = f['gene_names'][:] # gene names\n", "cellcyclegenes_filter = SP.unique(f['cellcyclegenes_filter'][:].ravel() -1) # idx of cell cycle genes from GO\n", "cellcyclegenes_filterCB = f['ccCBall_gene_indices'][:].ravel() -1 # idx of cell cycle genes from cycle base ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, for the fitting process, we need the gene matrix of cell cycle genes:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# filter cell cycle genes\n", "idx_cell_cycle = SP.union1d(cellcyclegenes_filter,cellcyclegenes_filterCB)\n", "# determine non-zero counts\n", "idx_nonzero = SP.nonzero((Y.mean(0)**2)>0)[0]\n", "idx_cell_cycle_noise_filtered = SP.intersect1d(idx_cell_cycle,idx_nonzero)\n", "# subset gene expression matrix\n", "Ycc = Y[:,idx_cell_cycle_noise_filtered]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize the cell cycle matrix" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xV1EVXp53lFFbb6MosG7hap4dsxWAD8atoOfEzcaaRYTgyvX4/mYarauF0nLw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\nvymcBtwJJ5xw4m+K/wfbs9C6xe4bPAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt = PL.subplot(1,1,1)\n", "PL.imshow(Ycc,cmap=cm.RdBu,vmin=-3,vmax=+3,interpolation='None')\n", "#PL.colorbar()\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "PL.xlabel('genes')\n", "PL.ylabel('cells')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "scLVM can now be fit using the cell cycle expression matrix. The user needs to define the number of latent factors to be fitted. Initially, we fit a model assuming a large numbers of factos:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "k = 80 # number of latent factors\n", "out_dir = scLVM_BASE + 'cache' # folder where results are cached\n", "file_name = 'Kcc.hdf5' # name of the cache file\n", "recalc = True # recalculate X and Kconf\n", "use_ard = True # use automatic relevance detection\n", "sclvm = scLVM(Y)\n", "#Fit model with 80 factors\n", "X_ARD,Kcc_ARD,varGPLVM_ARD = sclvm.fitGPLVM(idx=idx_cell_cycle_noise_filtered,k=k,out_dir=out_dir,file_name=file_name,recalc=recalc, use_ard=use_ard)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to determine an appropriate number of hidden factors, it is instructive to visualize the variance contributions of the individual latent factors. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Nm4Xye4D3NzwqMzNb4pVNQGsA06uUvwEMb1w4Zma2tCibgGYCm1Up/xjwUOPC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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot variance contributions from ARD \n", "plt = PL.subplot(1,1,1)\n", "PL.title('Variance explained by latent factors')\n", "PL.scatter(SP.arange(k)+1,varGPLVM_ARD['X_ARD'])\n", "PL.xlim([0,k+1])\n", "PL.xlabel('# Factor')\n", "PL.ylabel('Variance explained')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example (and generally when considering cell cycle as the confounding factor), there is a large gap in the proportion of explained variance between the first and the second factor. This suggests, that a single latent factor underlies the variation captured by the cellcycle genes. Consequently, we choose to re-fit the scLVM mdoel with one latent factor only." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Fit model with a single factor (rank 1 covariance matrix)\n", "X,Kcc,varGPLVM = sclvm.fitGPLVM(idx=idx_cell_cycle_noise_filtered,k=1,out_dir='./cache',file_name=file_name,recalc=True, use_ard=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inferred cell to cell covaraince matrix can be visualized: " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GmGalbG0Kbf5QDacqHmD9Yhcn8TYWjodaCwa0HFXN9COhctr5re+oiodO1u20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\n0NXysw5U38d4DFwlOfTtlWTeeT5eC1w3yzBvjevXdNRmfhavaPptNt9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HJ5vMe4NySZTp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot inferred similarity matrix\n", "plt = PL.subplot(1,1,1)\n", "PL.title('Similarity matrix based on cell cycle')\n", "PL.imshow(Kcc,cmap=cm.RdBu,vmin=-3,vmax=+3,interpolation='None')\n", "PL.colorbar()\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "PL.xlabel('cells')\n", "PL.ylabel('cells')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stage 2: Variance decomposition and cell cycle correction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we use the fitted scLVM model to decompose the source of variance for each gene." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# considers only heterogeneous genes\n", "Ihet = genes_het_bool==1\n", "Y = Y[:,Ihet]\n", "tech_noise = tech_noise[Ihet]\n", "geneID = geneID[Ihet]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The computation time for the next step can be substantial. If large datasets are considerd, it may be advisable to distribute these calculations on a high performance compute cluster. In this case i0 and i1 determine the range of genes for wich this anlaysis is performed. Here, we fit the model on 1,000 genes only in order to limit computation times. Consequently, all the downstram analyses illustrated in this notebook are done on a subset of all variable genes only." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#optionally: restrict range for the analysis\n", "i0 = 0 # gene from which the analysis starts\n", "i1 = 2000 # gene at which the analysis ends \n", "\n", "# construct sclvm object\n", "sclvm = scLVM(Y,geneID=geneID,tech_noise=tech_noise)\n", "\n", "# fit the model from i0 to i1\n", "sclvm.varianceDecomposition(K=Kcc,i0=i0,i1=i1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once the contribution of cell cycle to the observed variance is estimated, cell-cycle corrected gene expression levels can be obtained. The variance component estimates calculated by scLVM are normalised such that they sum uo to 1. There may be a small number of genes where the maximum likelihood fit does not converge propperly. We suggest to remove these in downstream analyses." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(81, 2000)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "normalize=True # variance components are normalizaed to sum up to one\n", "\n", "# get variance components\n", "var, var_info = sclvm.getVarianceComponents(normalize=normalize)\n", "var_filtered = var[var_info['conv']] # filter out genes for which vd has not converged\n", "\n", "# get corrected expression levels\n", "Ycorr = sclvm.getCorrectedExpression()\n", "Ycorr.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we visualize the resulting variance component using a pie chart. Shown are the average contributions of variance (across genes) for different categories:\n", "* Hidden_0: the first hidden factor, here the the cell cycle\n", "* bio_noise: the residual biological variation\n", "* techh_noise: the technical noise level" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#calculate average variance components across all genes and visualize\n", "var_mean = var_filtered.mean(0)\n", "colors = ['Green','MediumBlue','Gray']\n", "pp=PL.pie(var_mean,labels=var_info['col_header'],autopct='%1.1f%%',colors=colors,\n", " shadow=True, startangle=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also visualize this stratifying for different levels of technical noise." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QBEFPo9QGvF2BL5vZI5KyvfKmAYv/JGDBIkE15qOLmN8gL0o1xoOBGa3kDwQW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\nP26hRtWpaJxu6Nidbsad0jFz3Bi8Ztu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H2=1-var_filtered[:,2]\n", "var_comp_fileds = SP.array([[0, 'cell cycle', 'Peru'],\n", " [1, 'biol. var', 'DarkMagenta'],\n", " [2, 'tech. var', '#92c5de']], dtype=object)\n", "var_plot(var_filtered,H2,var_comp_fileds,normalize=True, figsize=[5,4])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gene correlation analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fitted cell cycle covariance matrix can also be used in a range of other analyses. Here, we illustrate it's use to improve the estimation of pairwise correlation coefficients between genes, while accounting for the cell cycle.\n", "For each gene i, we fit a linear mixed model with a fixed effect representing the contribution of a second gene j and random effect representing the contribution of the cell cycle. Gene correlations can then be determined by testing the significance of the fixed effect. Again, the computational complexity of this analysis can be substantial, requiring distributing these analyses on a parallel compute cluster. For illustration, we here consider the gene-gene correlation network of the first 10 genes." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "i0 = 0 # gene from which the analysis starts\n", "i1 = 10 # gene to which the analysis ends\n", "\n", "# fit lmm without correction\n", "pv0,beta0,info0 = sclvm.fitLMM(K=None,i0=i0,i1=i1,verbose=False)\n", "# fit lmm with correction\n", "pv1,beta1,info1 = sclvm.fitLMM(K=Kcc,i0=i0,i1=i1,verbose=False)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(, )" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt=PL.subplot(2,2,1)\n", "PL.title('Without Correction')\n", "p=PL.imshow(beta0[:,i0:i1],cmap=cm.RdBu,vmin=-0.6,vmax=+1,interpolation='None')\n", "PL.colorbar()\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "PL.xlabel('gene'),PL.ylabel('gene')\n", "plt=PL.subplot(2,2,2)\n", "PL.title('With Correction')\n", "p=PL.imshow(beta1[:,i0:i1],cmap=cm.RdBu,vmin=-0.6,vmax=+1,interpolation='None')\n", "PL.colorbar()\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "PL.xlabel('gene'),PL.ylabel('gene')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Downstream analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cell-cycle corrected gene expression matix can used for various kinds of downstream analysis. This includes clustering, visualisation, network analysis etc. To use the correct expression matrix in other programmes, it is straightforward to export the corrected expression matrix as CSV file:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "SP.savetxt('Ycorr.txt',Ycorr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example for downstream analyses using corrected exprssion levels, we here consider GPy to fit a non-linear Bayeisan PCA model, therbey visualizing hidden substructures between cells." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "warning in stationary: failed to import cython module: falling back to numpy\n" ] } ], "source": [ "import GPy" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Model optimization\n", "Ystd = Ycorr-Ycorr.mean(0)\n", "Ystd/=Ystd.std(0)\n", "input_dim = 2 # How many latent dimensions to use\n", "kern = GPy.kern.RBF(input_dim,ARD=True) # ARD kernel\n", "m = GPy.models.BayesianGPLVM(Ystd, input_dim=input_dim, kernel=kern, num_inducing=40)\n", "m.optimize('scg', messages=0, max_iters=2000)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model assumes two principle components. Here, we visualize the relative importance of the two components." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.kern.plot_ARD()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the position of individual cells in the principal component space can be visualized. Cells are colour coded by GATA3 expression, a canonical T-cell differentiation marker gene." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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T2jmcZe2MJ0RFRXF0yyt2LXjFFwOHvrcO5cqV4+TZk1i7ZMfjZn8aLG5Gtwuf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\nBOCccxnKE4BzzmWo/wc/1OdMFZVlvAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "i_Gata3 = SP.where(geneID=='ENSMUSG00000015619')\n", "color = Ycorr[:,i_Gata3]\n", "#color = Ycorr[:,0]\n", "PL.scatter(m.X[:,0]['mean'], m.X[:,1]['mean'], 40, color)\n", "PL.xlabel('PC1')\n", "PL.ylabel('PC2')\n", "PL.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We comapre the non-linear projection to a standard principle component anlaysis:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "[S,W] = PCA(Ystd,2)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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r1WpatW7I/ftH6dzVH5UKBg/exNKlNfHy2hpuBIQQ/PLzWPr0HsDJkyexs7Oj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\niJwCXI0zCdI2oDHwGHAApwfdGGO8YyuClakcoAfwIFAT51X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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PL.scatter(S[:,0],S[:,1], 40, color)\n", "PL.xlabel('PC1')\n", "PL.ylabel('PC2')\n", "PL.colorbar()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }