An open-loop approach to study the stochastic properties

Randomness is an inevitable aspect of biological networks. It has been long accepted that variability of components in a network can propagate throughout the network. In this thesis, we introduce a method that allows us to decompose the total variability of a single component into individual contributions from the other components in a network. Our method of noise decomposition helps us investigate key parameters and their relative impact on the total normalized noise and also allows us to illustrate the importance of different
system modifications by adding or omitting biological processes. With our generally applicable noise decomposition method, we are able to determine the strength of individual correlations induced by different co-regulation processes that connect different components
of a network. In bistable systems, variability can occur through stochastic transitions from one steady state to another. Noise induced transitions between two steady states are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. We open multicomponent feedback loops at the slowest variables in order to calculate the transition rates from one steady state to another. By reclosing the feedback loop, we calculate the mean first passage time (MFPT) using the Fokker-Planck equation. It is important to emphasize that the accurate
approximation of the open-loop results is not a sufficient condition for a good prediction of the MFPT. We show that only the opening at the slowest variable warrants an accurate prediction of MFPT. Multiplicative interactions among different components can introduce correlations among noises. We show that the introduced correlations affect the mean and variance of the open loop function and consequently increase the transition rate between two steady states in the closed-loop system. Our results indicate that the open-loop approach can contribute to the theoretical prediction of the MFPT. The theoretical results are shown to be in good agreement with the results of stochastic simulation.