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Register a new userGeometric Path Integrals. A Language for Multiscale Biology and Systems Robustness
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In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes.
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For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing.
The stochastic simulation of large-scale biochemical reaction networks is of great importance for systems biology since it enables the study of inherently stochastic biological mechanisms at the whole cell scale. Stochastic Simulation Algorithms (SSA) allow us to simulate the dynamic behavior of complex kinetic models, but their high computational cost makes them very slow for many realistic size problems. We present a pilot service, named WebStoch, developed in the context of our StochSoCs research project, allowing life scientists with no high-performance computing expertise to perform over the internet stochastic simulations of large-scale biological network models described in the SBML standard format. Biomodels submitted to the service are parsed automatically and then placed for parallel execution on distributed worker nodes. The workers are implemented using multi-core and many-core processors, or FPGA accelerators that can handle the simulation of thousands of stochastic repetitions of complex biomodels, with possibly thousands of reactions and interacting species. Using benchmark LCSE biomodels, whose workload can be scaled on demand, we demonstrate linear speedup and more than two orders of magnitude higher throughput than existing serial simulators.
Complex biological systems are very robust to genetic and environmental changes at all levels of organization. Many biological functions of Escherichia coli metabolism can be sustained against single-gene or even multiple-gene mutations by using redundant or alternative pathways. Thus, only a limited number of genes have been identified to be lethal to the cell. In this regard, the reaction-centric gene deletion study has a limitation in understanding the metabolic robustness. Here, we report the use of flux-sum, which is the summation of all incoming or outgoing fluxes around a particular metabolite under pseudo-steady state conditions, as a good conserved property for elucidating such robustness of E. coli from the metabolite point of view. The functional behavior, as well as the structural and evolutionary properties of metabolites essential to the cell survival, was investigated by means of a constraints-based flux analysis under perturbed conditions. The essential metabolites are capable of maintaining a steady flux-sum even against severe perturbation by actively redistributing the relevant fluxes. Disrupting the flux-sum maintenance was found to suppress cell growth. This approach of analyzing metabolite essentiality provides insight into cellular robustness and concomitant fragility, which can be used for several applications, including the development of new drugs for treating pathogens.
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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