Person:

Gaudet, Suzanne

Stochastic fluctuations in gene expression give rise to cell-to-cell variability in protein levels which can potentially cause variability in cellular phenotype. For TRAIL (TNF-related apoptosis-inducing ligand) variability manifests itself as dramatic differences in the time between ligand exposure and the sudden activation of the effector caspases that kill cells. However, the contribution of individual proteins to phenotypic variability has not been explored in detail. In this paper we use feature-based sensitivity analysis as a means to estimate the impact of variation in key apoptosis regulators on variability in the dynamics of cell death. We use Monte Carlo sampling from measured protein concentration distributions in combination with a previously validated ordinary differential equation model of apoptosis to simulate the dynamics of receptor-mediated apoptosis. We find that variation in the concentrations of some proteins matters much more than variation in others and that precisely which proteins matter depends both on the concentrations of other proteins and on whether correlations in protein levels are taken into account. A prediction from simulation that we confirm experimentally is that variability in fate is sensitive to even small increases in the levels of Bcl-2. We also show that sensitivity to Bcl-2 levels is itself sensitive to the levels of interacting proteins. The contextual dependency is implicit in the mathematical formulation of sensitivity, but our data show that it is also important for biologically relevant parameter values. Our work provides a conceptual and practical means to study and understand the impact of cell-to-cell variability in protein expression levels on cell fate using deterministic models and sampling from parameter distributions.

Receptor-mediated apoptosis proceeds via two pathways: one requiring only a cascade of initiator and effector caspases (type I behavior) and the second requiring an initiator–effector caspase cascade and mitochondrial outer membrane permeabilization (type II behavior). Here, we investigate factors controlling type I versus II phenotypes by performing Lyapunov exponent analysis of an ODE-based model of cell death. The resulting phase diagrams predict that the ratio of XIAP to pro-caspase-3 concentrations plays a key regulatory role: type I behavior predominates when the ratio is low and type II behavior when the ratio is high. Cell-to-cell variability in phenotype is observed when the ratio is close to the type I versus II boundary. By positioning multiple tumor cell lines on the phase diagram we confirm these predictions. We also extend phase space analysis to mutations affecting the rate of caspase-3 ubiquitylation by XIAP, predicting and showing that such mutations abolish all-or-none control over activation of effector caspases. Thus, phase diagrams derived from Lyapunov exponent analysis represent a means to study multi-factorial control over a complex biochemical pathway.

Background: Mathematical modeling is being applied to increasingly complex biological systems and datasets; however, the process of analyzing and calibrating against experimental data is often challenging and a rate limiting step in model development. To address this problem, we developed a systematic methodology for calibrating quantitative models of dynamic biological processes and illustrate its utility by validating a model of TRAIL (Tumor necrosis factor Related Apoptosis-Inducing Ligand)-induced cell death. Results: We propose a serial framework integrating analysis and calibration modules and we compare various methods for global sensitivity analysis and global parameter estimation. First, adequacy of the network structure is checked by global sensitivity analysis to changes in concentrations of molecular species, validating that the model can reproduce qualitative features of the system behavior derived from experiments or literature surveys. Second, rate parameters are ranked by importance using gradient-based and variance-based sensitivity indices, and we systematically determine the optimal number of parameters to include in model calibration. Third, deterministic, stochastic and hybrid algorithms for global optimization are applied to estimate the values of the most important parameters by fitting to time series data. We compare the performance of these three optimization algorithms. Conclusions: Our proposed framework covers the entire process from validating a proto-model to establishing a realistic model for in silico experiments and thereby provides a generalized workflow for the construction of predictive models of complex network systems.