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Register a new userNoise reduction by coupling of stochastic processes and canalization in biology
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Added by
Alexandre Ferreira Ramos
Publication date
2013
fields
Biology
and research's language is
English
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Randomness is an unavoidable feature of the intracellular environment due to chemical reactants being present in low copy number. That phenomenon, predicted by Delbruck long ago cite{delbruck40}, has been detected in both prokaryotic cite{elowitz02,cai06} and eukaryotic cite{blake03} cells after the development of the fluorescence techniques. On the other hand, developing organisms, e.g. {em D. melanogaster}, exhibit strikingly precise spatio-temporal patterns of protein/mRNA concentrations cite{gregor07b,manu09a,manu09b,boettiger09}. Those two characteristics of living organisms are in apparent contradiction: the precise patterns of protein concentrations are the result of multiple mutually interacting random chemical reactions. The main question is to establish biochemical mechanisms for coupling random reactions so that canalization, or fluctuations reduction instead of amplification, takes place. Here we explore a model for coupling two stochastic processes where the noise of the combined process can be smaller than that of the isolated ones. Such a canalization occurs if, and only if, there is negative covariance between the random variables of the model. Our results are obtained in the framework of a master equation for a negatively self-regulated -- or externally regulated -- binary gene and show that the precise control due to negative self regulation cite{becskei00} is because it may generate negative covariance. Our results suggest that negative covariance, in the coupling of random chemical reactions, is a theoretical mechanism underlying the precision of developmental processes.
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Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic approximations on the timescale of interest. One of the rigorous and popular approaches is the multiscale approximation method for continuous time Markov processes. In this approach, by scaling species abundances and reaction rates, a family of processes parameterized by a scaling parameter is defined. The limiting process of this family is then used to approximate the original process. However, we find that such approximations become inaccurate when combinations of species with disparate abundances either constitute conservation laws or form virtual slow auxiliary species. To obtain more accurate approximation in such cases, we propose here an appropriate modification of the original method.
Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper and safer. But this requires mathematical models of cellular systems. And for these models we then have to determine if they can meet our intended target behaviour. Here we develop two complementary approaches that allow us to determine whether a given molecular circuit, represented by a mathematical model, is capable of fulfilling our design objectives. We discuss algebraic methods that are capable of identifying general principles guaranteeing desired behaviour; and we provide an overview over Bayesian design approaches that allow us to choose from a set of models, that model which has the highest probability of fulfilling our design objectives. We discuss their uses in the context of biochemical adaptation, and then consider how robustness can and should affect our design approach.
Biology offers many examples of large-scale, complex, concurrent systems: many processes take place in parallel, compete on resources and influence each others behavior. The scalable modeling of biological systems continues to be a very active field of research. In this paper we introduce a new approach based on Event-B, a state-based formal method with refinement as its central ingredient, allowing us to check for model consistency step-by-step in an automated way. Our approach based on functions leads to an elegant and concise modeling method. We demonstrate this approach by constructing what is, to our knowledge, the largest ever built Event-B model, describing the ErbB signaling pathway, a key evolutionary pathway with a significant role in development and in many types of cancer. The Event-B model for the ErbB pathway describes 1320 molecular reactions through 242 events.
We present a new experimental-computational technology of inferring network models that predict the response of cells to perturbations and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is measured in terms of levels of proteins and phospho-proteins and of cellular phenotype such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, belief propagation, which is three orders of magnitude more efficient than Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in Skmel-133 melanoma cell lines, which are resistant to the therapeutically important inhibition of Raf kinase. The resulting network models reproduce and extend known pathway biology. They can be applied to discover new molecular interactions and to predict the effect of novel drug perturbations, one of which is verified experimentally. The technology is suitable for application to larger systems in diverse areas of molecular biology.
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