Mathematical modeling of variability in intracellular signaling

Cellular signaling is essential in information processing and decision making. Therefore, a variety of experimental approaches have been developed to study signaling on bulk and single-cell level. Single-cell measurements of signaling molecules demonstrated a substantial cell-to-cell variability, raising questions about its causes and mechanisms and about how cell populations cope with or exploit cellular heterogeneity. To gain insights from single-cell signaling data, analysis and modeling approaches have been introduced. This review discusses these modeling approaches, with a focus on recent advances in the development and calibration of mechanistic models. Additionally, it outlines current and future challenges.

[1]  D. Lauffenburger,et al.  Measurement and modeling of signaling at the single-cell level. , 2012, Biochemistry.

[2]  Fabian J. Theis,et al.  Meeting the Challenges of High-Dimensional Single-Cell Data Analysis in Immunology , 2019, Front. Immunol..

[3]  Frank Allgöwer,et al.  An inverse problem of tomographic type in population dynamics , 2014, 53rd IEEE Conference on Decision and Control.

[4]  M. Elowitz,et al.  Regulatory activity revealed by dynamic correlations in gene expression noise , 2008, Nature Genetics.

[5]  J. Banga,et al.  Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods , 2011, PloS one.

[6]  Jan Hasenauer,et al.  A Hierarchical, Data-Driven Approach to Modeling Single-Cell Populations Predicts Latent Causes of Cell-To-Cell Variability. , 2018, Cell systems.

[7]  Joerg Stelling,et al.  A simple and flexible computational framework for inferring sources of heterogeneity from single-cell dynamics , 2018, bioRxiv.

[8]  Gunnar Cedersund,et al.  Nonlinear mixed-effects modelling for single cell estimation: when, why, and how to use it , 2015, BMC Systems Biology.

[9]  M. Khammash,et al.  The finite state projection algorithm for the solution of the chemical master equation. , 2006, The Journal of chemical physics.

[10]  Khachik Sargsyan,et al.  Sources of Cell-to-cell Variability in Canonical Nuclear Factor-κB (NF-κB) Signaling Pathway Inferred from Single Cell Dynamic Images* , 2011, The Journal of Biological Chemistry.

[11]  Roland Eils,et al.  Intra- and Interdimeric Caspase-8 Self-Cleavage Controls Strength and Timing of CD95-Induced Apoptosis , 2014, Science Signaling.

[12]  Frank Allgöwer,et al.  A visual analytics approach for models of heterogeneous cell populations , 2012, EURASIP J. Bioinform. Syst. Biol..

[13]  J. Hasenauer,et al.  Cell-to-cell variability in JAK2/STAT5 pathway components and cytoplasmic volumes define survival threshold in erythroid progenitor cells , 2019, bioRxiv.

[14]  Roland Eils,et al.  Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model , 2009, PLoS Comput. Biol..

[15]  Bernd Bodenmiller,et al.  Influence of node abundance on signaling network state and dynamics analyzed by mass cytometry , 2017, Nature Biotechnology.

[16]  D. Sherrington Stochastic Processes in Physics and Chemistry , 1983 .

[17]  Mattias Goksör,et al.  A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast , 2015, PloS one.

[18]  M. Yaffe Why geneticists stole cancer research even though cancer is primarily a signaling disease , 2019, Science Signaling.

[19]  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 .

[20]  Hongyu Zhao,et al.  BAYESIAN HIERARCHICAL MODELING FOR SIGNALING PATHWAY INFERENCE FROM SINGLE CELL INTERVENTIONAL DATA. , 2011, The annals of applied statistics.

[21]  Jan Hasenauer,et al.  Parallelization and High-Performance Computing Enables Automated Statistical Inference of Multi-scale Models. , 2017, Cell systems.

[22]  P. Swain,et al.  Gene Regulation at the Single-Cell Level , 2005, Science.

[23]  Fabian J. Theis,et al.  Meeting the challenges of high-dimensional data analysis in immunology , 2018, bioRxiv.

[24]  Daniel Weindl,et al.  Efficient Parameter Estimation Enables the Prediction of Drug Response Using a Mechanistic Pan-Cancer Pathway Model. , 2018, Cell systems.

[25]  Lani F. Wu,et al.  Characterizing heterogeneous cellular responses to perturbations , 2008, Proceedings of the National Academy of Sciences.

[26]  Fabian J. Theis,et al.  Network plasticity of pluripotency transcription factors in embryonic stem cells , 2015, Nature Cell Biology.

[27]  A. Hoffmann,et al.  Identifying Noise Sources governing cell-to-cell variability. , 2018, Current opinion in systems biology.

[28]  Abigail K Kimball,et al.  A Beginner’s Guide to Analyzing and Visualizing Mass Cytometry Data , 2018, The Journal of Immunology.

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

[30]  Sean C. Bendall,et al.  Data-Driven Phenotypic Dissection of AML Reveals Progenitor-like Cells that Correlate with Prognosis , 2015, Cell.

[31]  Lani F. Wu,et al.  Cellular Heterogeneity: Do Differences Make a Difference? , 2010, Cell.

[32]  Jill P. Mesirov,et al.  Automated High-Dimensional Flow Cytometric Data Analysis , 2010, RECOMB.

[33]  W. Hiddemann,et al.  Characterization of Rare, Dormant, and Therapy-Resistant Cells in Acute Lymphoblastic Leukemia , 2016, Cancer cell.

[34]  Peter K. Sorger,et al.  Highly multiplexed imaging of single cells using a high-throughput cyclic immunofluorescence method , 2015, Nature Communications.

[35]  Fabian J. Theis,et al.  Multi-Experiment Nonlinear Mixed Effect Modeling of Single-Cell Translation Kinetics after Transfection , 2018 .

[36]  Chetan D. Pahlajani,et al.  Stochastic reduction method for biological chemical kinetics using time-scale separation. , 2011, Journal of theoretical biology.

[37]  Timm Schroeder,et al.  Long-term single-cell imaging of mammalian stem cells , 2011, Nature Methods.

[38]  S. Gaudet,et al.  Redefining Signaling Pathways with an Expanding Single-Cell Toolbox. , 2016, Trends in biotechnology.

[39]  Fabian J. Theis,et al.  ODE Constrained Mixture Modelling: A Method for Unraveling Subpopulation Structures and Dynamics , 2014, PLoS Comput. Biol..

[40]  David Hsu,et al.  Statistical Model Checking Based Calibration and Analysis of Bio-pathway Models , 2013, CMSB.

[41]  Jonas Wallin,et al.  BayesFlow: latent modeling of flow cytometry cell populations , 2016, BMC Bioinformatics.

[42]  Karlynn E. Neu,et al.  Single-Cell Genomics: Approaches and Utility in Immunology. , 2017, Trends in immunology.

[43]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[44]  K. Sachs,et al.  Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data , 2005, Science.

[45]  Michael P H Stumpf,et al.  An information-theoretic framework for deciphering pleiotropic and noisy biochemical signaling , 2018, Nature Communications.

[46]  J. Buhmann,et al.  Highly multiplexed imaging of tumor tissues with subcellular resolution by mass cytometry , 2014, Nature Methods.

[47]  Sang-Cheol Seok,et al.  Cell responses only partially shape cell-to-cell variations in protein abundances in Escherichia coli chemotaxis , 2013, Proceedings of the National Academy of Sciences.

[48]  Sarah Filippi,et al.  Robustness of MEK-ERK Dynamics and Origins of Cell-to-Cell Variability in MAPK Signaling , 2016, Cell reports.

[49]  D. Vitkup,et al.  Maximum Entropy Framework For Inference Of Cell Population Heterogeneity In Signaling Networks , 2017 .

[50]  Joerg Stelling,et al.  A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics. , 2019, Cell systems.

[51]  Karen Sachs,et al.  Multiplexed mass cytometry profiling of cellular states perturbed by small-molecule regulators , 2012, Nature Biotechnology.

[52]  Jan Hasenauer,et al.  Estimation of biochemical network parameter distributions in cell populations , 2009, 0905.1191.

[53]  Eric J. Deeds,et al.  Fundamental trade-offs between information flow in single cells and cellular populations , 2017, Proceedings of the National Academy of Sciences.

[54]  Sarah A Teichmann,et al.  A test metric for assessing single-cell RNA-seq batch correction , 2018, Nature Methods.

[55]  Jan Hasenauer,et al.  pyABC: distributed, likelihood-free inference , 2017, bioRxiv.

[56]  D. Kell,et al.  Flow cytometry and cell sorting of heterogeneous microbial populations: the importance of single-cell analyses. , 1996, Microbiological reviews.

[57]  Douglas A Lauffenburger,et al.  Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis , 2011, Molecular systems biology.

[58]  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.

[59]  Sean C. Bendall,et al.  Extracting a Cellular Hierarchy from High-dimensional Cytometry Data with SPADE , 2011, Nature Biotechnology.

[60]  Eugenio Cinquemani,et al.  What Population Reveals about Individual Cell Identity: Single-Cell Parameter Estimation of Models of Gene Expression in Yeast , 2016, PLoS Comput. Biol..

[61]  F. Lampariello,et al.  On the use of the Kolmogorov-Smirnov statistical test for immunofluorescence histogram comparison. , 2000, Cytometry.