Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

<p>Abstract</p> <p>Background</p> <p>Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements.</p> <p>Results</p> <p>We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer-approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in <it>Saccharomyces cerevisiae</it>. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast <it>Saccharomyces cerevisiae </it>to heat shock</p> <p>Conclusion</p> <p>Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.</p

Mathematical Identification of Critical Reactions in the Interlocked Feedback Model

Dynamic simulations are necessary for understanding the mechanism of how biochemical networks generate robust properties to environmental stresses or genetic changes. Sensitivity analysis allows the linking of robustness to network structure. However, it yields only local properties regarding a particular choice of plausible parameter values, because it is hard to know the exact parameter values in vivo. Global and firm results are needed that do not depend on particular parameter values. We propose mathematical analysis for robustness (MAR) that consists of the novel evolutionary search that explores all possible solution vectors of kinetic parameters satisfying the target dynamics and robustness analysis. New criteria, parameter spectrum width and the variability of solution vectors for parameters, are introduced to determine whether the search is exhaustive. In robustness analysis, in addition to single parameter sensitivity analysis, robustness to multiple parameter perturbation is defined. Combining the sensitivity analysis and the robustness analysis to multiple parameter perturbation enables identifying critical reactions. Use of MAR clearly identified the critical reactions responsible for determining the circadian cycle in the Drosophila interlocked circadian clock model. In highly robust models, while the parameter vectors are greatly varied, the critical reactions with a high sensitivity are uniquely determined. Interestingly, not only the per-tim loop but also the dclk-cyc loop strongly affect the period of PER, although the dclk-cyc loop hardly changes its amplitude and it is not potentially influential. In conclusion, MAR is a powerful method to explore wide parameter space without human-biases and to link a robust property to network architectures without knowing the exact parameter values. MAR identifies the reactions critically responsible for determining the period and amplitude in the interlocked feedback model and suggests that the circadian clock intensively evolves or designs the kinetic parameters so that it creates a highly robust cycle

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

Protein sequestration generates a flexible ultrasensitive response in a genetic network

Ultrasensitive responses are crucial for cellular regulation. Protein sequestration, where an active protein is bound in an inactive complex by an inhibitor, can potentially generate ultrasensitivity. Here, in a synthetic genetic circuit in budding yeast, we show that sequestration of a basic leucine zipper transcription factor by a dominant-negative inhibitor converts a graded transcriptional response into a sharply ultrasensitive response, with apparent Hill coefficients up to 12. A simple quantitative model for this genetic network shows that both the threshold and the degree of ultrasensitivity depend upon the abundance of the inhibitor, exactly as we observed experimentally. The abundance of the inhibitor can be altered by simple mutation; thus, ultrasensitive responses mediated by protein sequestration are easily tuneable. Gene duplication of regulatory homodimers and loss-of-function mutations can create dominant negatives that sequester and inactivate the original regulator. The generation of flexible ultrasensitive responses is an unappreciated adaptive advantage that could explain the frequent evolutionary emergence of dominant negatives

Global organization of metabolic fluxes in the bacterium, Escherichia coli

Cellular metabolism, the integrated interconversion of thousands of metabolic substrates through enzyme-catalyzed biochemical reactions, is the most investigated complex intercellular web of molecular interactions. While the topological organization of individual reactions into metabolic networks is increasingly well understood, the principles governing their global functional utilization under different growth conditions pose many open questions. We implement a flux balance analysis of the E. coli MG1655 metabolism, finding that the network utilization is highly uneven: while most metabolic reactions have small fluxes, the metabolism's activity is dominated by several reactions with very high fluxes. E. coli responds to changes in growth conditions by reorganizing the rates of selected fluxes predominantly within this high flux backbone. The identified behavior likely represents a universal feature of metabolic activity in all cells, with potential implications to metabolic engineering.Comment: 15 pages 4 figure

Modular cell biology: retroactivity and insulation

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input–output dynamic characteristics of transcriptional components, focusing on a property, which we call ‘retroactivity', that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter-binding sites, or when the affinity of such binding sites is high. To attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation–dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast timescales of the phosphorylation and dephosphorylation reactions

Automated smoother for the numerical decoupling of dynamics models

<p>Abstract</p> <p>Background</p> <p>Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure.</p> <p>Results</p> <p>In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from <it>in-vivo </it>NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations.</p> <p>Conclusion</p> <p>The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.</p

Identification of neutral biochemical network models from time series data

<p>Abstract</p> <p>Background</p> <p>The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, <it>i.e</it>., if it is constructed according to strict guidelines.</p> <p>Results</p> <p>In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.</p> <p>Conclusion</p> <p>The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium <it>Lactococcus lactis </it>and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.</p

Optimisation of the Schizosaccharomyces pombe urg1 expression system

The ability to study protein function in vivo often relies on systems that regulate the presence and absence of the protein of interest. Two limitations for previously described transcriptional control systems that are used to regulate protein expression in fission yeast are: the time taken for inducing conditions to initiate transcription and the ability to achieve very low basal transcription in the "OFF-state". In previous work, we described a Cre recombination-mediated system that allows the rapid and efficient regulation of any gene of interest by the urg1 promoter, which has a dynamic range of approximately 75-fold and which is induced within 30-60 minutes of uracil addition. In this report we describe easy-to-use and versatile modules that can be exploited to significantly tune down P urg1 "OFF-levels" while maintaining an equivalent dynamic range. We also provide plasmids and tools for combining P urg1 transcriptional control with the auxin degron tag to help maintain a null-like phenotype. We demonstrate the utility of this system by improved regulation of HO-dependent site-specific DSB formation, by the regulation Rtf1-dependent replication fork arrest and by controlling Rhp18(Rad18)-dependent post replication repair