Irene Otero-Muras

Local dissipative Hamiltonian description of reversible reaction networks

In this letter we show that closed reversible chemical reaction networks with independent elementary reactions admit a global pseudo-Hamiltonian structure which is at least locally dissipative around any equilibrium point. The structure matrix of the Hamiltonian description reflects the graph topology of the reaction network and it is a smooth function of the concentrations of the chemical species in the positive orthant. The physical interpretation of the description is briefly explained and two illustrative examples are presented for global and local dissipative Hamiltonian description, respectively.

Multicriteria global optimization for biocircuit design

BackgroundOne of the challenges in Synthetic Biology is to design circuits with increasing levels of complexity. While circuits in Biology are complex and subject to natural tradeoffs, most synthetic circuits are simple in terms of the number of regulatory regions, and have been designed to meet a single design criterion.ResultsIn this contribution we introduce a multiobjective formulation for the design of biocircuits. We set up the basis for an advanced optimization tool for the modular and systematic design of biocircuits capable of handling high levels of complexity and multiple design criteria. Our methodology combines the efficiency of global Mixed Integer Nonlinear Programming solvers with multiobjective optimization techniques. Through a number of examples we show the capability of the method to generate non intuitive designs with a desired functionality setting up a priori the desired level of complexity.ConclusionsThe methodology presented here can be used for biocircuit design and also to explore and identify different design principles for synthetic gene circuits. The presence of more than one competing objective provides a realistic design setting where every solution represents an optimal trade-off between different criteria.

Characterizing multistationarity regimes in biochemical reaction networks.

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.

Exploring multiplicity conditions in enzymatic reaction networks.

In this work, a novel algorithmic approach to detect multiplicity of steady states in enzymatic reaction networks is presented. The method exploits the structural properties of networks derived from the Chemical Reaction Network Theory. In first instance, the space of parameters is divided in different regions according to the qualitative behavior induced by the parameters in the long term dynamics of the network. Once the regions are identified, a condition for the appearance of multiplicities is checked in the different regions by solving a given optimization problem. In this way, the method allows the characterization of the whole parameter space of biochemical networks in terms of the appearance or not of multistability. The approach is illustrated through a well‐known case of enzymatic catalysis with substrate inhibition.

Dynamic analysis and control of biochemical reaction networks

In the present work, we combine the concepts and tools from Irreversible Thermodynamics and Control Theory in a contribution to unravel the origin of complex nonlinear behaviour in biochemical networks. Regarding cells as thermodynamic systems, we can consider dynamic evolution of intracellular processes in terms of the combined action of an endogenous entropy production and the entropy flux associated to chemicals passing through the control volume. Based on a generalized description of biochemical systems, a physically motivated storage function is constructed and used for stability analysis. In this way, the entropy flux of open systems can be meaningfully modified by efficient nonlinear control schemes capable of network stabilization, and irreversible thermodynamics provide us with the physical insight to further interpret the controlled response.

Stochastic modeling and numerical simulation of gene regulatory networks with protein bursting

Gene expression is inherently stochastic. Advanced single-cell microscopy techniques together with mathematical models for single gene expression led to important insights in elucidating the sources of intrinsic noise in prokaryotic and eukaryotic cells. In addition to the finite size effects due to low copy numbers, translational bursting is a dominant source of stochasticity in cell scenarios involving few short lived mRNA transcripts with high translational efficiency (as is typically the case for prokaryotes), causing protein synthesis to occur in random bursts. In the context of gene regulation cascades, the Chemical Master Equation (CME) governing gene expression has in general no closed form solution, and the accurate stochastic simulation of the dynamics of complex gene regulatory networks is a major computational challenge. The CME associated to a single gene self regulatory motif has been previously approximated by a one dimensional time dependent partial integral differential equation (PIDE). However, to the best of our knowledge, multidimensional versions for such PIDE have not been developed yet. Here we propose a multidimensional PIDE model for regulatory networks involving multiple genes with self and cross regulations (in which genes can be regulated by different transcription factors) derived as the continuous counterpart of a CME with jump process. The model offers a reliable description of systems with translational bursting. In order to provide an efficient numerical solution, we develop a semilagrangian method to discretize the differential part of the PIDE, combined with a composed trapezoidal quadrature formula to approximate the integral term. We apply the model and numerical method to study sustained stochastic oscillations and the development of competence, a particular case of transient differentiation attained by certain bacterial cells under stress conditions. We found that the resulting probability distributions are distinguishable from those characteristic of other transient differentiation processes. In this way, they can be employed as markers or signatures that identify such phenomena from bacterial population experimental data, for instance. The computational efficiency of the semilagrangian method makes it suitable for purposes like model identification and parameter estimation from experimental data or, in combination with optimization routines, the design of gene regulatory networks under molecular noise.

Generic parameterization for a pharmacokinetic model to predict Cd concentrations in several tissues of different fish species

In the present work, a set of generic parameters was proposed for a pharmacokinetic model, with the objective of predicting Cd concentration in the tissues of diverse fish species under different environmental conditions. Cd concentrations in a number of tissues of Oncorhynchus mykiss and Cyprinus carpio were estimated by a structurally identifiable multicompartmental model (unique solution). The 13 generic parameters of the model comprised exchange rates, tissue-blood partition coefficients, and weight-corrected elimination rate constants accounting for the routes of water respiration, excretion and egestion. On the other hand, absorption efficiencies from water and food were considered to be condition-specific and estimated for each experiment. These two parameters reflected the differences in fish exposure to diet (food type and metal concentration) or water (water chemistry and bioavailable metal concentration). A data set of 27 experiments of Cd bioaccumulation in fish tissues was compiled for model calibration. The selected dynamics on trout and carp were performed under very different experimental conditions, involving water and/or food exposure, different fish weights and exposure concentrations and the presence/absence of depuration periods. Model predicted, for most compartments and experiments, the tendency of Cd dynamics. However, accumulation in liver and kidney was underestimated in approximately a half of the experiments, due mainly to a rapid metallothionein (MT) sequestration phenomena and subsequent saturation on liver and kidney produced under high exposure concentrations. On the other hand, both generic and condition-specific parameter values were in accordance with the values reported in literature when available. Therefore, the results obtained in this work are an initial step indicating that a generic global input parameter set could be applied to physiology-based pharmacokinetic (PBPK) models for estimating Cd accumulation in fish in different types of scenarios.

Dynamic analysis and control of chemical and biochemical reaction networks

Abstract Metabolic or cell signalling pathways are examples of biochemical networks exhibiting possible complex dynamics in the form of steady-state multiplicity, sustained oscillations or even deterministic chaos. The origin of these nonlinear phenomena is not always well understood, nor it can be systematically predicted beyond a case by case basis. Despite considerable progress in dynamic aspects, efforts are still needed to develop efficient and robust methods of stabilization and control of reaction networks. In this work, we combine concepts and tools from irreversible thermodynamics and systems theory to explore the underlying dynamic properties of a general class of chemical and biochemical networks. Lyapunov and passivity based methods are given for the systematic design of globally stabilizing feedback controllers in both the concentration space and a novel minimal description of the kinetic networks dynamics: the reaction space.

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

From cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systems.

SELANSI: a toolbox for simulation of stochastic gene regulatory networks

Motivation Gene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort. Results This work presents SELANSI (SEmi‐LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi‐lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options. Availability and implementation SELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi. Contact antonio@iim.csic.es