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Parameter sensitivity analysis for a stochastic model of mitochondrial apoptosis pathway.

ABSTRACT: Understanding how gene alterations induce oncogenesis plays an important role in cancer research and may be instructive for cancer prevention and treatment. We conducted a parameter sensitivity analysis to the mitochondrial apoptosis model. Both a nonlinear bifurcation analysis of the deterministic dynamics and energy barrier analysis of the corresponding stochastic models were performed. We found that the parameter sensitivity ranking according to the change of the bifurcation-point locations in deterministic models and the change of the barrier heights from a living to death state of the cell in stochastic models are highly correlated. For the model we considered, in combination with previous knowledge that the parameters significantly affecting the system's bifurcation point are strongly associated with frequently mutated oncogenic genes, we conclude that the energy barrier height can be used as indicator of oncogenesis as well as bifurcation point. We provide a possible mechanism that may help elucidate the logic of cancer initiation from the view of stochastic dynamics and energy landscape. And we show the equivalence of energy barrier height and bifurcation-point location in determining the parameter sensitivity spectrum for the first time.

SUBMITTER: Chen X

PROVIDER: S-EPMC6005494 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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Parameter sensitivity analysis for a stochastic model of mitochondrial apoptosis pathway.

Chen Xianli X Li Xiaoguang X Zhao Wei W Li Tiejun T Ouyang Qi Q

PloS one 20180618 6

Understanding how gene alterations induce oncogenesis plays an important role in cancer research and may be instructive for cancer prevention and treatment. We conducted a parameter sensitivity analysis to the mitochondrial apoptosis model. Both a nonlinear bifurcation analysis of the deterministic dynamics and energy barrier analysis of the corresponding stochastic models were performed. We found that the parameter sensitivity ranking according to the change of the bifurcation-point locations i ...[more]

PMID: 29912904

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Project description:BackgroundStochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.ResultsWe propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models.ConclusionsThe SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sgd.

Project description:Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in "sloppy" systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the number of the sensitive parameters.

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Parameter sensitivity analysis for a stochastic model of mitochondrial apoptosis pathway.

Publications

Parameter sensitivity analysis for a stochastic model of mitochondrial apoptosis pathway.

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