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Register a new userOptimal Observation Time Points in Stochastic Chemical Kinetics
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Added by
Charalampos Kyriakopoulos Mr
Publication date
2014
fields
Biology
and research's language is
English
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Wet-lab experiments, in which the dynamics within living cells are observed, are usually costly and time consuming. This is particularly true if single-cell measurements are obtained using experimental techniques such as flow-cytometry or fluorescence microscopy. It is therefore important to optimize experiments with respect to the information they provide about the system. In this paper we make a priori predictions of the amount of information that can be obtained from measurements. We focus on the case where the measurements are made to estimate parameters of a stochastic model of the underlying biochemical reactions. We propose a numerical scheme to approximate the Fisher information of future experiments at different observation time points and determine optimal observation time points. To illustrate the usefulness of our approach, we apply our method to two interesting case studies.
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Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations, and multi-stability.
This is a short review of two common approximations in stochastic chemical and biochemical kinetics. It will appear as Chapter 6 in the book Quantitative Biology: Theory, Computational Methods and Examples of Models edited by Brian Munsky, Lev Tsimring and Bill Hlavacek (to be published in late 2017/2018 by MIT Press). All chapter references in this article refer to chapters in the aforementioned book.
Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.
In a well-stirred system undergoing chemical reactions, fluctuations in the reaction propensities are approximately captured by the corresponding chemical Langevin equation. Within this context, we discuss in this work how the Kramers escape theory can be used to predict rare events in chemical reactions. As an example, we apply our approach to a recently proposed model on cell proliferation with relevance to skin cancer [P.B. Warren, Phys. Rev. E {bf 80}, 030903 (2009)]. In particular, we provide an analytical explanation for the form of the exponential exponent observed in the onset rate of uncontrolled cell proliferation.
We investigate the protein expression pattern of the lamB gene in Escherichia coli LE392. The gene product LamB is an important membrane protein for maltose transport into cells but it is also exploited by bacteriophage lambda for infection. Although our bacterial population is clonal, stochastic gene expression leads to a majority population with a large receptor number and a minority population with a small receptor number. We find that the LamB receptor distribution p(n) of the small-n population is scale invariant with the exponent depending on growth conditions. A heuristic model is proposed that relates the observed exponent to the protein production rate.
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