  This report proposes a novel framework for a rigorous robustness analysis of
stochastic biochemical systems. The technique is based on probabilistic model
checking. 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.
  The framework is applied 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 succeeded to extend previous studies performed on
deterministic models (ODE) and show 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.
