Abstract
We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
Highlights
Robustness is one of the fundamental features of biological systems
We propose a novel framework for robustness analysis of stochastic biochemical systems
To this end, inspected systems are described by means of stochastic biochemical kinetic models, system’s functionality is defined by its logical properties, and system’s perturbation is modelled as a change in stochastic kinetic parameters or initial conditions of the model
Summary
Robustness is one of the fundamental features of biological systems. According to Kitano [1] ‘‘robustness is a property that allows a system to maintain its functions against internal and external perturbations’’. To formally analyse robustness, we must precisely define a model of a biological system, its perturbations and the notions of a system’s function. We propose a novel framework for robustness analysis of stochastic biochemical systems. To this end, inspected systems are described by means of stochastic biochemical kinetic models, system’s functionality is defined by its logical properties, and system’s perturbation is modelled as a change in stochastic kinetic parameters or initial conditions of the model. Kinetic models with parameters are used to formally capture cell dynamics. Limited knowledge of numerical parameters poses a challenge since precise values of all parameters (kinetic constants, initial concentrations, environmental conditions, etc.) may be unknown, may be known but imprecisely, or may in principle form a bounded uncertainty interval (e.g., non-homogeneous cell populations, different structural conformations of a molecule leading to multiple kinetic rates, etc.). It is necessary to take into account possible uncertainties, variance and inhomogeneities
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