Stochastic gene expression has been implicated in a variety of cellular processes, including cell differentiation and disease. In this issue of Cell, Weinberger et al. (2005) take an integrated computational-experimental approach to study the Tat transactivation feedback loop in HIV-1 and show that fluctuations in a key regulator, Tat, can result in a phenotypic bifurcation. This phenomenon is observed in an isogenic population where individual cells display two distinct expression states corresponding to latent and productive infection by HIV-1. These findings demonstrate the importance of stochastic gene expression in molecular "decision-making."

Stochastic Gene Expression in a Lentiviral Positive Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity

Motivation: Identification of regulatory networks is typically based on deterministic models of gene expression. Increasing experimental evidence suggests that the gene regulation process is intrinsically random. To ensure accurate and thorough processing of the experimental data, stochasticity must be explicitly accounted for both at the modelling stage and in the design of the identification algorithms.

Results: We propose a model of gene expression in prokaryotes where transcription is described as a probabilistic event, whereas protein synthesis and degradation are captured by first-order deterministic kinetics. Based on this model and assuming that the network of interactions is known, a method for estimating unknown parameters, such as synthesis and binding rates, from the outcomes of multiple time-course experiments is introduced. The method accounts naturally for sparse, irregularly sampled and noisy data and is applicable to gene networks of arbitrary size. The performance of the method is evaluated on a model of nutrient stress response in Escherichia coli.

Contact: cinquemani@control.ee.ethz.ch

Supplementary information: Supplementary data are available at Bioinformatics online.

https://www.zora.uzh.ch/id/eprint/79156/1/pub1.pdf

Stochastic dynamics of genetic networks

Stochastic Hybrid Systems are probabilistic models suitable at describing the dynamics of variables presenting interleaved and interacting continuous and discrete components. 
Engineering systems like communication networks or automotive and air traffic control systems, financial and industrial processes like market and manufacturing models, and natural systems like biological and ecological environments exhibit compound behaviors arising from the compositions and interactions between their heterogeneous components. Hybrid Systems are mathematical models that are by definition suitable to describe such complex systems. The effect of the uncertainty upon the involved discrete and continuous dynamics—both endogenously and exogenously to the system—is virtually unquestionable for biological systems and often inevitable for engineering systems, and naturally leads to the employment of stochastic hybrid models. 
The first part of this dissertation introduces gradually the modeling framework and focuses on some of its features. In particular, two sequential approximation procedures are introduced, which translate a general stochastic hybrid framework into a new probabilistic model. Their convergence properties are sketched. It is argued that the obtained model is more predisposed to analysis and computations. 
The kernel of the thesis concentrates on understanding the theoretical and computational issues associated with an original notion of probabilistic reachability for controlled stochastic hybrid systems. The formal approach is based on formulating reachability analysis as a stochastic optimal control problem, which is solved via dynamic programming. A number of related and significant control problems, such as that of probabilistic safety, are reinterpreted with this approach. The technique is also computationally tested on a benchmark case study throughout the whole work. Moreover, a methodological application of the concept in the area of Systems Biology is presented: a model for the production of antibiotic as a component of the stress response network for the bacterium Bacillus subtilis is described. The model allows one to reinterpret the survival analysis for the single bacterial cell as a probabilistic safety specification problem, which is then studied by the aforementioned technique. 
In conclusion, this dissertation aims at introducing a novel concept of probabilistic reachability that is both formally rigorous, computationally analyzable and of applicative interest. Furthermore, by the introduction of convergent approximation procedures, the thesis relates and positively compares the presented approach with other techniques in the literature.

Probabilistic reachability for stochastic hybrid systems: theory, computations, and applications

The dynamics of biochemical reaction networks can be accurately described by stochastic hybrid models, where we assume that large chemical populations evolve deterministically and continuously over time while small populations change through random discrete reactions.We propose an algorithm for estimating the parameters of a given biochemical reaction network based on a stochastic hybrid model. We assume that noisy time series measurements of the chemical populations are available and follow a maximum likelihood approach to calibrate the parameters. We numerically approximate the likelihood and its derivatives for concrete values of the parameters and show that, based on this approximation, the maximization of the likelihood can be done efficiently.We substantiate the usefulness of our approach by applying it to several case studies from systems biology.

Parameter estimation for stochastic hybrid models of biochemical reaction networks

The term stochastic hybrid systems defines a class of dynamical and control systems that involve the interaction of continuous dynamics, discrete dynamics and probabilistic uncertainty. Over the last decade stochastic hybrid systems have emerged as a powerful modeling paradigm in a wide range of application areas. The talk will provide an overview of recent developments in this rapidly evolving field of research. We will introduce some of the theoretical foundations and challenges of stochastic hybrid systems and outline computational methods that can be used to analyze and control such systems, based primarily on randomized algorithms. The discussion will be motivated by several applied modeling, analysis and control problems from the areas of systems biology and air traffic management. This extended abstract provides some motivation for the talk, as well as an extensive list of references that can serve as a starting point for further reading.

Stochastic hybrid systems: Theory and applications

Parameter identification for stochastic hybrid systems using randomized optimization: A case study on subtilin production by Bacillus subtilis

Parameter Identification for Piecewise Deterministic Markov Processes: A Case Study on a Biochemical Network

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Parameter identification for stochastic hybrid systems using randomized optimization: A case study on subtilin production by Bacillus subtilis

Parameter Identification for Piecewise Deterministic Markov Processes: A Case Study on a Biochemical Network