A visual analytics approach for models of heterogeneous cell populations

In recent years, cell population models have become increasingly common. In contrast to classic single cell models, population models allow for the study of cell-to-cell variability, a crucial phenomenon in most populations of primary cells, cancer cells, and stem cells. Unfortunately, tools for in-depth analysis of population models are still missing. This problem originates from the complexity of population models. Particularly important are methods to determine the source of heterogeneity (e.g., genetics or epigenetic differences) and to select potential (bio-)markers. We propose an analysis based on visual analytics to tackle this problem. Our approach combines parallel-coordinates plots, used for a visual assessment of the high-dimensional dependencies, and nonlinear support vector machines, for the quantification of effects. The method can be employed to study qualitative and quantitative differences among cells. To illustrate the different components, we perform a case study using the proapoptotic signal transduction pathway involved in cellular apoptosis.

[1]  M. Zweig,et al.  Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. , 1993, Clinical chemistry.

[2]  J. Humphrey,et al.  Cancer Drug Discovery and Development , 2003 .

[3]  Alfred Inselberg,et al.  Parallel coordinates: a tool for visualizing multi-dimensional geometry , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[4]  D. Lauffenburger,et al.  Quantitative analysis of pathways controlling extrinsic apoptosis in single cells. , 2008, Molecular cell.

[5]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[6]  Bernhard Schölkopf,et al.  Comparing support vector machines with Gaussian kernels to radial basis function classifiers , 1997, IEEE Trans. Signal Process..

[7]  Lani F. Wu,et al.  Patterns of basal signaling heterogeneity can distinguish cellular populations with different drug sensitivities , 2010, Molecular systems biology.

[8]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[9]  Simon V. Avery,et al.  Microbial cell individuality and the underlying sources of heterogeneity , 2006, Nature Reviews Microbiology.

[10]  C.,et al.  Cancer Chemoprevention , 2004, Cancer Drug Discovery and Development.

[11]  Heinz Koeppl,et al.  Accounting for extrinsic variability in the estimation of stochastic rate constants , 2012 .

[12]  F. Allgöwer,et al.  Bistability Analyses of a Caspase Activation Model for Receptor-induced Apoptosis* , 2004, Journal of Biological Chemistry.

[13]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[14]  Sabrina L Spencer,et al.  Non-genetic Cell-to-cell Variability and the Consequences for Pharmacology This Review Comes from a Themed Issue on Omics Edited the Distribution of Protein Abundance and Resulting Variability in Phenotype Measuring Cell-to-cell Variation , 2022 .

[15]  Mats Jirstrand,et al.  Systems biology Systems Biology Toolbox for MATLAB : a computational platform for research in systems biology , 2006 .

[16]  Daniel Weiskopf,et al.  Progressive Splatting of Continuous Scatterplots and Parallel Coordinates , 2011, Comput. Graph. Forum.

[17]  Daniel Weiskopf,et al.  Visualization methods and support vector machines as tools for determining markers in models of heterogeneous populations: Proapoptotic signaling as a case study , 2011 .

[18]  P. Scheurich,et al.  Tumor necrosis factor signaling , 2003, Cell Death and Differentiation.

[19]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[20]  M. Elowitz,et al.  Functional roles for noise in genetic circuits , 2010, Nature.

[21]  Antonios Armaou,et al.  Fault‐tolerant process control , 2012 .

[22]  Jochen H M Prehn,et al.  Systems analysis of effector caspase activation and its control by X‐linked inhibitor of apoptosis protein , 2006, The EMBO journal.

[23]  Frank Allgöwer,et al.  Analysis of heterogeneous cell populations: A density-based modeling and identification framework , 2011 .

[24]  D. Lauffenburger,et al.  Modeling a Snap-Action, Variable-Delay Switch Controlling Extrinsic Cell Death , 2008, PLoS biology.

[25]  Vladimir Vapnik,et al.  The Nature of Statistical Learning , 1995 .

[26]  Ovidiu Ivanciuc,et al.  Applications of Support Vector Machines in Chemistry , 2007 .

[27]  Claire L. Thompson Reconnecting with family , 2010 .

[28]  Maike A. Laussmann,et al.  The Caspase-8 Dimerization/Dissociation Balance Is a Highly Potent Regulator of Caspase-8, -3, -6 Signaling* , 2010, The Journal of Biological Chemistry.

[29]  Daniel Weiskopf,et al.  Continuous Parallel Coordinates , 2009, IEEE Transactions on Visualization and Computer Graphics.

[30]  Johan Paulsson,et al.  Models of stochastic gene expression , 2005 .

[31]  B. Snijder,et al.  Origins of regulated cell-to-cell variability , 2011, Nature Reviews Molecular Cell Biology.

[32]  Rey-Huei Chen,et al.  Spindle checkpoint regulates Cdc20p stability in Saccharomyces cerevisiae. , 2004, Genes & development.

[33]  Frank Allgöwer,et al.  Live and let die - A systems biology view on cell death , 2009, Comput. Chem. Eng..

[34]  Bryan Howie Life's onslaught , 2010 .

[35]  David Feng,et al.  Matching Visual Saliency to Confidence in Plots of Uncertain Data , 2010, IEEE Transactions on Visualization and Computer Graphics.

[36]  David A. Gewirtz,et al.  Apoptosis, senescence, and cancer , 2007 .

[37]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[38]  Oliver Sawodny,et al.  ON/OFF and Beyond - A Boolean Model of Apoptosis , 2009, PLoS Comput. Biol..

[39]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[40]  V. Grantcharova,et al.  Therapeutically Targeting ErbB3: A Key Node in Ligand-Induced Activation of the ErbB Receptor–PI3K Axis , 2009, Science Signaling.

[41]  Christoph Borner,et al.  XIAP discriminates between type I and type II FAS-induced apoptosis , 2009, Nature.

[42]  P. Swain,et al.  Intrinsic and extrinsic contributions to stochasticity in gene expression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[43]  Frank Allgöwer,et al.  Identification of models of heterogeneous cell populations from population snapshot data , 2011, BMC Bioinformatics.

[44]  James J. Thomas,et al.  Defining Insight for Visual Analytics , 2009, IEEE Computer Graphics and Applications.

[45]  Ingo Röder,et al.  Stem Cell Proliferation and Quiescence—Two Sides of the Same Coin , 2009, PLoS Comput. Biol..

[46]  J. Tyson,et al.  Mathematical model of the cell division cycle of fission yeast. , 2001, Chaos.

[47]  Johan Paulsson,et al.  Non-genetic heterogeneity from stochastic partitioning at cell division , 2011, Nature Genetics.

[48]  I. Glauche,et al.  Cellular aging leads to functional heterogeneity of hematopoietic stem cells: a modeling perspective , 2011, Aging cell.

[49]  Peter K. Sorger,et al.  Measuring and Modeling Apoptosis in Single Cells , 2011, Cell.

[50]  Sergei L. Kosakovsky Pond,et al.  An Evolutionary Model-Based Algorithm for Accurate Phylogenetic Breakpoint Mapping and Subtype Prediction in HIV-1 , 2009, PLoS Comput. Biol..

[51]  P. Sorger,et al.  Non-genetic origins of cell-to-cell variability in TRAIL-induced apoptosis , 2009, Nature.