Multicriteria global optimization for biocircuit design

One 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. In 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. The presence of more than one competing objective provides a realistic design setting where every design solution represents a trade-off between different criteria. The tool can be useful to explore and identify different design principles for synthetic gene circuits

El modelado matemático en el estudio de mecanismos de señalización celular: apoptosis inducida por interferón de tipo I

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

26 páginas, 10 figuras, 1 tabla.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedFrom 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 systemsThis work was supported by MINECO (and the European Regional Development Fund) project ªSYNBIOFACTORYº (grant number DPI2014-55276-C5-2-R).Peer reviewe

First passage times as a measure of hysteresis in stochastic gene regulatory circuits

GAIN Oportunius Grant from Xunta de Galicia.[Abstract]: In the context of phenotype switching and cell fate determination, numerousexperimental studies report hysteresis, despite the fact that the (forward) Chemical Master Equation governing the inherently stochastic underlying gene regulatory networks has a unique steady state (precluding memory effects and hysteresis). In previous works, we demonstrate thathysteresis is a transient phenomenon in systems far from the thermodynamic limit, using the convergence rates of the partial integro-differential equation associated to the forward master equation governing the stochastic process. Here, we make use of the backward master equationto quantify hysteresis and irreversibility based on First Passage Times. First, we derive the backward master equation for a gene regulatory network with protein production in bursts. Solving this equation, we obtain the probability distributions of the first times to reach some fixed final state from one starting state. The mean first passage time provides a measure to quantify how hysteresis and irreversibility in gene regulation at the singlecell level are transient effects that vanish at steady state. In addition, we provide a theoretical basis that reconciles phenotype coexistence and prevalence far from the thermodynamic limit. In fact, we substitute the notion of pseudo-potential (the so-called Waddington landscape) by a time evolving landscape built upon the Chemical Master Equation (CME) in which phenotypes,rather than prevail, persist with different intensities.Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación; FJC2019-041397-

Feedback control of stochastic gene switches using PIDE models

[Abstract]: Achieving control of gene regulatory circuits is one of the goals of synthetic biology, as a way to regulate cellular functions for useful purposes (in biomedical, environmental or industrial applications). The inherent stochastic nature of gene expression makes it challenging to control the behavior of gene regulatory networks, and increasing efforts are being devoted in the field to address different control problems. In this work, we combine the efficient modeling of stochastic gene regulatory networks by means of Partial Integro-Differential Equations with feedback control, in order to keep protein levels at the target (pre-defined) stationary probability distribution. In particular, we achieve the closedloop stabilization of bi-modal toggle-switches in the stochastic regime within the region of low probability (around the minimum located between the two modes of the uncontrolled system).GAIN Oportunius Grant Xunta de Galici

A systematic approach to plant-wide control based on thermodynamics

Abstract In this work, a systematic approach to plant-wide control design is proposed. The method combines ingredients from process networks, thermodynamics and systems theory to derive robust decentralized controllers that will ensure complete plant stability. As a first step, the considered process system is decomposed into abstract mass and energy inventory networks. In this framework, conceptual inventory control loops are then designed for the mass and energy layers to guarantee that the states of the plant, both in terms of extensive and intensive properties, will converge to a compact convex region defined by constant inventories. This result by itself does not ensure the convergence of intensive variables to a desired operation point as complex dynamic phenomena such as multiplicities may appear in the invariant set. In order to avoid these phenomena, thermodynamics naturally provides the designer, in these convex regions, with a legitimate storage or Lyapunov function candidate, the entropy, that can be employed to ensure global stability. Based on this, the control structure design procedure is completed with the realization of the conceptual inventory and intensive variable control loops over the available degrees of freedom in the system. To that purpose, both PI and feedback linearization control are employed. The different aspects of the proposed methodology will be illustrated on a non-isothermal chemical reaction network

Automated Design of Synthetic Biology Circuits

Gordon Research Conference: Biological Modeling, Directed Evolution and Complexity from Design to Application, July 14 - 19, 2019Peer reviewe

Engineering complexity in biochemical networks: methods and tools for the automated design of biochemical bistable switches and limit cycle oscillators

Bio-Inspired Analysis of Dynamical Systems International Workshop, 10-12 January 2019, Esztergom, HungaryPeer reviewe

Inferring design principles in systems and synthetic biology through optimization-based methods

Advanced Lecture Course on Computational Systems Biology CompSysBio 2019, March 31 - April 6, Aussois (France)Peer reviewe

A method for inverse bifurcation of biochemical switches: inferring parameters from dose response curves

16 páginas, 8 figuras, 4 tablas.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited[Background] Within cells, stimuli are transduced into cell responses by complex networks of biochemical reactions. In many cell decision processes the underlying networks behave as bistable switches, converting graded stimuli or inputs into all or none cell responses. Observing how systems respond to different perturbations, insight can be gained into the underlying molecular mechanisms by developing mathematical models. Emergent properties of systems, like bistability, can be exploited to this purpose. One of the main challenges in modeling intracellular processes, from signaling pathways to gene regulatory networks, is to deal with high structural and parametric uncertainty, due to the complexity of the systems and the difficulty to obtain experimental measurements. Formal methods that exploit structural properties of networks for parameter estimation can help to overcome these problems.[Results] We here propose a novel method to infer the kinetic parameters of bistable biochemical network models. Bistable systems typically show hysteretic dose response curves, in which the so called bifurcation points can be located experimentally. We exploit the fact that, at the bifurcation points, a condition for multistationarity derived in the context of the Chemical Reaction Network Theory must be fulfilled. Chemical Reaction Network Theory has attracted attention from the (systems) biology community since it connects the structure of biochemical reaction networks to qualitative properties of the corresponding model of ordinary differential equations. The inverse bifurcation method developed here allows determining the parameters that produce the expected behavior of the dose response curves and, in particular, the observed location of the bifurcation points given by experimental data.[Conclusions] Our inverse bifurcation method exploits inherent structural properties of bistable switches in order to estimate kinetic parameters of bistable biochemical networks, opening a promising route for developments in Chemical Reaction Network Theory towards kinetic model identification.We gratefully acknowledge financial support from the EU FP7 project IFNAction (contract 223608)Peer reviewe