Elucidating Cellular Population Dynamics by Molecular Density Function Perturbations

Studies performed at single-cell resolution have demonstrated the physiological significance of cell-to-cell variability. Various types of mathematical models and systems analyses of biological networks have further been used to gain a better understanding of the sources and regulatory mechanisms of such variability. In this work, we present a novel sensitivity analysis method, called molecular density function perturbation (MDFP), for the dynamical analysis of cellular heterogeneity. The proposed analysis is based on introducing perturbations to the density or distribution function of the cellular state variables at specific time points, and quantifying how such perturbations affect the state distribution at later time points. We applied the MDFP analysis to a model of a signal transduction pathway involving TRAIL (tumor necrosis factor-related apoptosis-inducing ligand)-induced apoptosis in HeLa cells. The MDFP analysis shows that caspase-8 activation regulates the timing of the switch-like increase of cPARP (cleaved poly(ADP-ribose) polymerase), an indicator of apoptosis. Meanwhile, the cell-to-cell variability in the commitment to apoptosis depends on mitochondrial outer membrane permeabilization (MOMP) and events following MOMP, including the release of Smac (second mitochondria-derived activator of caspases) and cytochrome c from mitochondria, the inhibition of XIAP (X-linked inhibitor of apoptosis) by Smac, and the formation of the apoptosome.

[1]  A. Boettiger.  Analytic approaches to stochastic gene expression in multicellular systems. , 2013, Biophysical journal.

[2]  Muruhan Rathinam,et al.  Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks. , 2010, The Journal of chemical physics.

[3]  D. Kirschner,et al.  A methodology for performing global uncertainty and sensitivity analysis in systems biology. , 2008, Journal of theoretical biology.

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

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

[6]  Rudiyanto Gunawan,et al.  Ensemble Kinetic Modeling of Metabolic Networks from Dynamic Metabolic Profiles , 2012, Metabolites.

[7]  Deborah A. Flusberg,et al.  Surviving apoptosis: life-death signaling in single cells. , 2015, Trends in cell biology.

[8]  Rudiyanto Gunawan,et al.  Reduction of kinetic models using dynamic sensitivities , 2013, Comput. Chem. Eng..

[9]  R. Braatz,et al.  Parameter Sensitivity Analysis Applied to Modeling Transient Enhanced Diffusion and Activation of Boron in Silicon , 2003 .

[10]  D. Tranchina,et al.  Stochastic mRNA Synthesis in Mammalian Cells , 2006, PLoS biology.

[11]  M. A. Henson.  Dynamic modeling of microbial cell populations. , 2003, Current opinion in biotechnology.

[12]  A. Oudenaarden,et al.  Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences , 2008, Cell.

[13]  Keijo Ruohonen,et al.  Developing Itô stochastic differential equation models for neuronal signal transduction pathways , 2006, Comput. Biol. Chem..

[14]  Vahid Shahrezaei,et al.  Analytical distributions for stochastic gene expression , 2008, Proceedings of the National Academy of Sciences.

[15]  Marc S. Sherman,et al.  Cell-to-cell variability in the propensity to transcribe explains correlated fluctuations in gene expression. , 2015, Cell systems.

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

[17]  D. Peter,et al.  Kernel estimation of a distribution function , 1985 .

[18]  P. Cahan,et al.  Origins and implications of pluripotent stem cell variability and heterogeneity , 2013, Nature Reviews Molecular Cell Biology.

[19]  Rudiyanto Gunawan,et al.  Understanding dynamics using sensitivity analysis: caveat and solution , 2011, BMC Systems Biology.

[20]  Suresh Kumar Poovathingal,et al.  Stochastic Drift in Mitochondrial DNA Point Mutations: A Novel Perspective Ex Silico , 2009, PLoS Comput. Biol..

[21]  Michail Stamatakis,et al.  Cell population balance and hybrid modeling of population dynamics for a single gene with feedback , 2013, Comput. Chem. Eng..

[22]  Peter K. Sorger,et al.  Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis , 2012, PLoS Comput. Biol..

[23]  Michael P H Stumpf,et al.  Sensitivity, robustness, and identifiability in stochastic chemical kinetics models , 2011, Proceedings of the National Academy of Sciences.

[24]  David F. Anderson,et al.  An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains , 2011, SIAM J. Numer. Anal..

[25]  Z Zi,et al.  Sensitivity analysis approaches applied to systems biology models. , 2011, IET systems biology.

[26]  Marco Ratto,et al.  Global Sensitivity Analysis , 2008 .

[27]  Rudiyanto Gunawan,et al.  Dynamical analysis of cellular networks based on the Green's function matrix. , 2009, Journal of theoretical biology.

[28]  E. Cox,et al.  Real-Time Kinetics of Gene Activity in Individual Bacteria , 2005, Cell.

[29]  Heinz Koeppl,et al.  ‘Glocal’ Robustness Analysis and Model Discrimination for Circadian Oscillators , 2009, PLoS Comput. Biol..

[30]  Hua Wu,et al.  Parametric sensitivity in chemical systems , 1999 .

[31]  S. Gaudet,et al.  Cell-to-cell variability in cell death: can systems biology help us make sense of it all? , 2014, Cell Death and Disease.

[32]  J. Hasty,et al.  Noise-based switches and amplifiers for gene expression. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Rudiyanto Gunawan,et al.  Phase Sensitivity Analysis of Circadian Rhythm Entrainment , 2007, Journal of biological rhythms.

[34]  Brian Ingalls,et al.  Sensitivity analysis: from model parameters to system behaviour. , 2008, Essays in biochemistry.

[35]  H. Najm,et al.  Spectral methods for parametric sensitivity in stochastic dynamical systems. , 2007, Biophysical journal.

[36]  Muruhan Rathinam,et al.  A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems. , 2012, The Journal of chemical physics.

[37]  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 .

[38]  Adam P. Arkin,et al.  Efficient stochastic sensitivity analysis of discrete event systems , 2007, J. Comput. Phys..

[39]  Adam P Arkin,et al.  Deviant effects in molecular reaction pathways , 2006, Nature Biotechnology.

[40]  Constantinos C. Pantelides,et al.  Monte Carlo evaluation of derivative-based global sensitivity measures , 2009, Reliab. Eng. Syst. Saf..

[41]  Yang Cao,et al.  Sensitivity analysis of discrete stochastic systems. , 2005, Biophysical journal.

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

[43]  Marc Hafner,et al.  Fractional killing arises from cell-to-cell variability in overcoming a caspase activity threshold , 2015, Molecular Systems Biology.