Noise and prediction in molecular systems

Living systems are inherently stochastic and operate in a noisy environment: in single cells, reactions that involve low numbers of molecules generate stochastic fluctuations that propagate to all dependent processes. Such a noise can be a disturbance, for example by disrupting cell cycle control, or could be advantageous by enabling probabilistic strategies when favourable. Unfortunately, the underlying principles behind these probabilistic phenomena are still not well understood. This also limits our capacity to engineer reliable synthetic biological circuits. In this thesis we study Chemical Reaction Networks (CRNs) with a stochastic semantics as a probabilistic model for biochemical systems. In the first part of the thesis we consider probabilistic model checking of CRNs, which enables rigorous quantitative analysis of stochastic CRNs against a fragment of Continuous Stochastic Logic (CSL) with reward operators. Classical numerical algorithms for CSL model checking are hindered by the state space explosion problem. Here, we employ a continuous-space approximation of the stochastic model of a CRN in terms of a Gaussian process through the Central Limit Approximation (CLA). We then develop efficient and scalable approximate model checking algorithms on the resulting Gaussian process, where we restrict the probabilistic reachability problem to convex target regions. This allows us to derive an abstraction in terms of a time-inhomogeneous discrete-time Markov chain (DTMC), whose dimension is independent of the number of species on which model checking is performed, thus alleviating the state space explosion problem. We prove the correctness of our approach by demonstrating the convergence in distribution of our algorithms. In the second part of the thesis we employ mathematical analysis and the previously developed model checking techniques to reverse engineer molecular systems. We investigate how CRNs propagate and reduce the noise. Inspired by the concept of low-pass filters in electronics, we introduce the concept of molecular filter, which is a CRN that can reduce the noise of an input signal while still maintaining certain features of its time evolution. We investigate three different molecular noise filtering mechanisms, study their noise reduction capabilities and limitations, and show that non-linear dynamics, such as complex formation, are necessary for efficientcient noise reduction. We further suggest that the derived molecular filters are widespread in gene expression and regulation and, particularly, that microRNAs can serve as such noise filters.