A systems engineering approach to model, tune and test synthetic gene circuits

La biología sintética se define como la ingeniería de la biología: el (re)diseño y construcción de nuevas partes, dispositivos y sistemas biológicos para realizar nuevas funciones con fines útiles, que se basan en principios elucidados de la biología y la ingeniería. Para facilitar la construcción rápida, reproducible y predecible de estos sistemas biológicos a partir de conjuntos de componentes es necesario desarrollar nuevos métodos y herramientas. La tesis plantea la optimización multiobjetivo como el marco adecuado para tratar los problemas comunes que surgen en el diseño racional y el ajuste óptimo de los circuitos genéticos sintéticos. Utilizando un enfoque clásico de ingeniería de sistemas, la tesis se centra principalmente en: i) el modelado de circuitos genéticos sintéticos basado en los primeros principios, ii) la estimación de parámetros de modelos a partir de datos experimentales y iii) el ajuste basado en modelos para lograr el desempeño deseado de los circuitos. Se han utilizado dos circuitos genéticos sintéticos de diferente naturaleza y con diferentes objetivos y problemas: un circuito de realimentación de tipo 1 incoherente (I1-FFL) que exhibe la importante propiedad biológica de adaptación, y un circuito de detección de quorum sensing y realimentación (QS/Fb) que comprende dos bucles de realimentación entrelazados -uno intracelular y uno basado en la comunicación de célula a célula- diseñado para regular el nivel medio de expresión de una proteína de interés mientras se minimiza su varianza a través de la población de células. Ambos circuitos han sido analizados in silico e implementados in vivo. En ambos casos, se han desarrollado modelos de estos circuitos basado en primeros principios. Se presta especial atención a ilustrar cómo obtener modelos de orden reducido susceptibles de estimación de parámetros, pero manteniendo el significado biológico. La estimación de los parámetros del modelo a partir de los datos experimentales se considera en diferentes escenarios, tanto utilizando modelos determinísticos como estocásticos. Para el circuito I1-FFL se consideran modelos determinísticos. Aquí, la tesis plantea la utilización de modelos locales utilizando la optimización multiobjetivo para realizar la estimación de parámetros del modelo bajo escenarios con estructura de modelo incompleta. Para el circuito QS/Fb, una estructura controlada por realimentación, el problema tratado es la falta de excitabilidad de las señales. La tesis propone una metodología de estimación en dos etapas utilizando modelos estocásticos. La metodología permite utilizar datos de curso temporal promediados de la población y mediciones de distribución en estado estacionario para una sola célula. El ajuste de circuitos basado en modelos para lograr un desempeño deseado también se aborda mediante la optimización multiobjetivo. Para el circuito QS/Fb se realiza un análisis estocástico completo. La tesis aborda cómo tener en cuenta correctamente tanto el ruido intrínseco como el extrínseco, las dos principales fuentes de ruido en los circuitos genéticos. Se analiza el equilibrio entre ambas fuentes de ruido y el papel que desempeñan en el bucle de realimentación intracelular, y en la realimentación extracelular de toda la población. La principal conclusión es que la compleja interacción entre ambos canales de realimentación obliga al uso de la optimización multiobjetivo para el adecuado ajuste del circuito. En esta tesis además del uso adecuado de herramientas de optimización multiobjetivo, la principal preocupación es cómo derivar directrices para el ajuste in silico de parámetros de circuitos que puedan aplicarse de forma realista in vivo en un laboratorio estándar. Como alternativa al análisis de sensibilidad de parámetros clásico, la tesis propone el uso de técnicas de clustering a lo largo de los frentes de Pareto, relacionando el comprLa biologia sintètica es defineix com l'enginyeria de la biologia: el (re) disseny i construcció de noves parts, dispositius i sistemes biològics per a realitzar noves funcions útils que es basen a principis elucidats de la biologia i l'enginyeria. Per facilitar la construcció ràpida, reproduïble i predictible de aquests sistemes biològics a partir de conjunts de components és necessari desenvolupar nous mètodes i eines. La tesi planteja la optimització multiobjectiu com el marc adequat per a tractar els problemes comuns que apareixen en el disseny racional i l' ajust òptim dels circuits genètics sintètics. Utilitzant un enfocament clàssic d'enginyeria de sistemes, la tesi es centra principalment en: i) el modelatge de circuits genètics sintètics basat en primers principis, ii) l' estimació de paràmetres de models a partir de dades experimentals i iii) l' ajust basat en models per aconseguir el rendiment desitjat dels circuits. S'han utilitzat dos circuits genètics sintètics de diferent naturalesa i amb diferents objectius i problemes: un circuit de prealimentació de tipus 1 incoherent (I1-FFL) que exhibeix la important propietat biològica d'adaptació, i un circuit de quorum sensing i realimentació (QS/Fb) que comprèn dos bucles de realimentació entrellaçats -un intracel·lular i un basat en la comunicació de cèl·lula a cèl·lula- dis-senyat per regular el nivell mitjà d'expressió normal d'una proteïna d'interès mentre es minimitza la seua variació al llarg de la població de cèl·lules. Els dos circuits han estat analitzats in silico i implementats in vivo. En tots dos casos, s'han desenvolupat models basats en primers principis d'aquests circuits. Després es presta especial atenció a delinear com obtenir models d'ordre reduït susceptibles de estimació de paràmetres, però mantenint el significat biològic. L' estimació dels paràmetres del model a partir de les dades experimentals es considera en diferents escenaris, tant utilitzant models determinístics com estocàstics. Per al circuit I1-FFL es consideren models determinístics. La tesi planteja la utilització de models locals utilitzant la optimització multiobjectiu per realitzar l'estimació de parametres del model sota escenaris amb estructura de model incompleta (dinàmica no modelada). Per al circuit de QS/Fb, una estructura controlada per realimentació, el problema tractat és la manca d'excitabilitat dels senyals. La tesi proposa una metodologia de estimació en dues etapes utilitzant models estocàstics. La metodologia permet utilitzar dades de curs temporal promediats de la població i mesures de distribució en estat estacionari d'una sola una cèl·lula. L' ajust de circuits basat en models per aconseguir el rendiment desitjat dels circuits també s' aborda mitjançant la optimització multiobjectiu. Per al circuit QS/Fb, es fa un anàlisi estocàstic complet. La tesi aborda com tenir en compte correctament tant el soroll intrínsec com l' extrínsec, les dues principals fonts de soroll en els circuits genètics sintètics. S' analitza l'equilibri entre dues fonts de soroll i el paper que exerceixen en el bucle de realimentació intracel·lular, les i en la realimentació extracel·lular de tota la població. La principal conclusió es que la complexa interacció entre els dos canals de realimentació fa necessari l' ús de la optimització multiobjectiu per al adequat ajust del circuit. En aquesta tesi, a més de l'ús adequat d'eines d'optimització multiobjectiu, la principal preocupació és com derivar directives per al ajust in silico de paràmetres de circuits que puguin aplicar-se de forma realista en viu en un laboratori estàndard. Així, com a alternativa a l'anàlisi de sensibilitat de paràmetres clàssic, la tesi proposa l'ús de l' tècniques de l'agrupació al llarg dels fronts de Pareto, relacionant el compromís de dessempeny amb les regions en l'espai d'paràmetres.Synthetic biology is defined as the engineering of biology: the deliberate (re)design and construction of novel biological and biologically based parts, devices and systems to perform new functions for useful purposes, that draws on principles elucidated from biology and engineering. Methods and tools are needed to facilitate fast, reproducible and predictable construction of biological systems from sets of biological components. This thesis raises multi-objective optimization as the proper framework to deal with common problems arising in rational design and optimal tuning of synthetic gene circuits. Using a classical systems engineering approach, the thesis mainly addresses: i) synthetic gene circuit modeling based on first principles, ii) model parameters estimation from experimental data and iii) model-based tuning to achieve desired circuit performance. Two gene synthetic circuits of different nature and with different goals and inherent problems have been used throughout the thesis: an Incoherent type 1 feedforward circuit (I1-FFL) that exhibits the important biological property of adaptation, and a Quorum sensing/Feedback circuit (QS/Fb) comprising two intertwined feedback loops -an intracellular one and a cell-to-cell communication-based one-- designed to regulate the mean expression level of a protein of interest while minimizing its variance across the population of cells. Both circuits have been analyzed in silico and implemented in vivo. In both cases, circuit modeling based on first principles has been carried out. Then, special attention is paid to illustrate how to obtain reduced order models amenable for parameters estimation yet keeping biological significance. Model parameters estimation from experimental data is considered in different scenarios, both using deterministic and stochastic models. For the I1-FFL circuit, deterministic models are considered. In this case, the thesis raises ensemble modeling using multi-objective optimization to perform model parameters estimation under scenarios with incomplete model structure (unmodeled dynamics). For the QS/Fb gene circuit, a feedback controlled structure, the lack of excitability of the signals is the problem addressed. The thesis proposes a two-stage estimation methodology using stochastic models. The methodology allows using population averaged time-course data and steady state distribution measurements at the single-cell level. Model-based circuit tuning to achieve desired circuit performance is also addressed using multi-objective optimization. First, for the QS/Fb feedback control circuit, a complete stochastic analysis is performed. Here, the thesis addresses how to correctly take into account both intrinsic and extrinsic noise, the two main sources of noise in gene synthetic circuits. The trade-off between both sources of noise, and the role played by in the intracellular single-cell feedback loop and the extracellular population-wide feedback is analyzed. The main conclusion being that the complex interplay between both feedback channels compel the use of multi-objective optimization for proper tuning of the circuit to achieve desired performance. Thus, the thesis wraps up all the previous results and uses them to address circuit tuning for desired performance. Here, besides the proper use of multi-objective optimization tools, the main concern is how to derive guidelines for circuit parameters tuning in silico that can realistically be applied in vivo in a standard laboratory. Thus, as an alternative to classical parameters sensitivity analysis, the thesis proposes the use of clustering techniques along the optimal Pareto fronts relating the performance trade-offs with regions in the circuits parameters space.This work has been partially supported by the Spanish Government (CICYT DPI2014- 55276-C5-1) and the European Union (FEDER). The author was recipient of the grant Formación de Personal Investigador by the Universitat Politècnica de València, subprogram 1 (FPI/2013-3242). She was also recipient of the competitive grants for pre-doctoral stays Erasmus Student Placement-European Programme 2015, and FPI Mobility program 2016 of the Universitat Politècnica de València. She also received the competitive grant for a pre-doctoral stay Becas de movilidad para Jóvenes Profesores e Investigadores 2016, Programa de Becas Iberoamérica of the Santander Bank.Boada Acosta, YF. (2018). A systems engineering approach to model, tune and test synthetic gene circuits [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/112725TESI

Multiobjective Identification of a Feedback Synthetic Gene Circuit

© 2020 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Kinetic (i.e., dynamic) semimechanistic models based on the first principles are particularly important in systems and synthetic biology since they can explain and predict the functional behavior that emerges from the time-varying concentrations in cellular components. However, gene circuit models are nonlinear higher order ones and have a large number of parameters. In addition, experimental measurements are often scarce, and enough signal excitability for identification cannot always be achieved. These characteristics render the identification problem ill-posed, so most gene circuit models present incomplete parameter identifiability. Thus, parameter identification of typical biological models still appears as an open problem, where ensemble modeling approaches and multiobjective optimization arise as natural options. We address the problem of identifying the stochastic model of a closed-loop synthetic genetic circuit designed to minimize the gene expression noise. The model results from the feedback interaction between two subsystems. Besides incomplete parameter identifiability, the closed-loop dynamics cannot be directly identified due to the lack of enough input signal excitability. We apply a two-stage approach. First, the open-loop averaged time-course experimental data are used to identify a reduced-order stochastic model of the system direct chain. Then, closed-loop steady-state stochastic distributions are used to identify the remaining parameters in the feedback configuration. In both cases, multiobjective optimization is used to address the parameter identifiability, providing sets of parameters valid for different state-space regions. The methodology gives good identification results, provides clear guidelines on the effect of the parameters under different scenarios, and it is particularly useful for easily combining time-course population averaged and steady-state single-cell distribution experimental data.This work was supported by the European Union and Spanish Government, MINECO/AEI/FEDER under Grant DPI2017-82896-C2-1-R. The work of Y. Boada was supported by the Universitat Politecnica de Valencia under Grant FPI/2013-3242.Boada-Acosta, YF.; Vignoni, A.; Picó, J. (2020). Multiobjective Identification of a Feedback Synthetic Gene Circuit. IEEE Transactions on Control Systems Technology. 28(1):208-223. https://doi.org/10.1109/TCST.2018.2885694S20822328

Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise

[EN] Stochastic fluctuations in gene expression trigger both beneficial and harmful consequences for cell behavior. Therefore, achieving a desired mean protein expression level while minimizing noise is of interest in many applications, including robust protein production systems in industrial biotechnology. Here, we consider a synthetic gene circuit combining intracellular negative feed- back and cell-to-cell communication based on quorum sensing. Accounting for both intrinsic and extrinsic noise, stochastic simulations allow us to analyze the capability of the circuit to reduce noise strength as a function of its parameters. We obtain mean expression levels and noise strengths for all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in Escherichia coli. Our in silico experiments, validated by preliminary in vivo results, reveal significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback and highlight the differential role that they play in regard to intrinsic and extrinsic noise.his work was partially supported by the Spanish Government(CICYT DPI2014-55276-C5-1) and the European Union(FEDER). Y.B. thanks grant FPI/2013-3242 of UPV.Boada-Acosta, YF.; Vignoni, A.; Picó, J. (2017). Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise. ACS Synthetic Biology. 6(10):1903-1912. https://doi.org/10.1021/acssynbio.7b00087S1903191261

Extended metabolic biosensor design for dynamic pathway regulation of cell factories

[EN] Transcription factor-based biosensors naturally occur in metabolic pathways to maintain cell growth and to provide a robust response to environmental fluctua-tions. Extended metabolic biosensors, i.e., the cascading of a bio-conversion pathway and a transcription factor (TF) responsive to the downstream effector metabolite, provide sensing capabilities beyond natural effectors for implement-ing context-aware synthetic genetic circuits and bio-observers. However, the engineering of such multi-step circuits is challenged by stability and robustness issues. In order to streamline the design of TF-based biosensors in metabolic pathways, here we investigate the response of a genetic circuit combining a TF-based extended metabolic biosensor with an antithetic integral circuit, a feed-back controller that achieves robustness against environmental fluctuations. The dynamic response of an extended biosensor-based regulated flavonoid pathway is analyzed in order to address the issues of biosensor tuning of the regulated pathway under industrial biomanufacturing operating constraints.This work is partially supported by grant MINECO/AEI and EU DPI2017-82896-C2-1-R. P.C. acknowledges support from the Universitat Politecnica de Valencia Talento Programme.Boada-Acosta, YF.; Vignoni, A.; Picó, J.; Carbonell, P. (2020). Extended metabolic biosensor design for dynamic pathway regulation of cell factories. iScience. 23(7):1-25. https://doi.org/10.1016/j.isci.2020.101305S125237Agrawal, D. K., Dolan, E. M., Hernandez, N. E., Blacklock, K. M., Khare, S. D., & Sontag, E. D. (2020). Mathematical Models of Protease-Based Enzymatic Biosensors. ACS Synthetic Biology, 9(2), 198-208. doi:10.1021/acssynbio.9b00279Arnold, F. H. (2017). Directed Evolution: Bringing New Chemistry to Life. Angewandte Chemie International Edition, 57(16), 4143-4148. doi:10.1002/anie.201708408Boada, Y., Vignoni, A., & Picó, J. (2017). Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise. ACS Synthetic Biology, 6(10), 1903-1912. doi:10.1021/acssynbio.7b00087Boada, Y., Vignoni, A., & Picó, J. (2017). Multi-objective optimization for gene expression noise reduction in a synthetic gene circuit * *This work is partially supported by Spanish government and European Union (FEDER-CICYT DPI2014-55276-C5-1). Y.B. thanks grant FPI/2013-3242 of Universitat Politècnica de València, and also thanks the support from the Ayudas para movilidad dentro del Programa para la Formación de Personal Investigador (FPI) de la UPV para estancias 2016. A.V. thanks the Max Planck Society, the CSBD and the MPI-CBG. The authors are grateful to Prof. Dr. Ivo F. 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Contractivity of a genetic circuit with internal feedback and cell-to-cell communication

[EN] We consider a realistic model of the synthetic gene circuit combining cell-to-cell communication system via quorum sensing, and a synthetic repressible promoter implementing intracellular negative feedback control. The circuit has been shown to increase robustness with respect to both extrinsic and intrinsic noise elsewhere. As a first step towards an analytic analysis, in this paper we use contraction theory to perform a stability analysis. From it, we infer the components of the circuit most affecting the rate of contractivity, using biologically sensible values of the circuit parameters.This research was partially funded by grant FEDER-CICYT DPI2014-55276-C5-1-R. Yadira Boada thanks grant FPI/2013-3242 of the Universitat Politècnica de València.Picó-Marco, E.; Boada-Acosta, YF.; Picó, J.; Vignoni, A. (2016). Contractivity of a genetic circuit with internal feedback and cell-to-cell communication. IFAC-PapersOnLine. 49(26):213-218. https://doi.org/10.1016/j.ifacol.2016.12.128S213218492

Gene Expression Space Shapes the Bioprocess Trade-Offs among Titer, Yield and Productivity

[EN] Optimal gene expression is central for the development of both bacterial expression systems for heterologous protein production, and microbial cell factories for industrial metabolite production. Our goal is to fulfill industry-level overproduction demands optimally, as measured by the following key performance metrics: titer, productivity rate, and yield (TRY). Here we use a multiscale model incorporating the dynamics of (i) the cell population in the bioreactor, (ii) the substrate uptake and (iii) the interaction between the cell host and expression of the protein of interest. Our model predicts cell growth rate and cell mass distribution between enzymes of interest and host enzymes as a function of substrate uptake and the following main lab-accessible gene expression-related characteristics: promoter strength, gene copy number and ribosome binding site strength. We evaluated the differential roles of gene transcription and translation in shaping TRY trade-offs for a wide range of expression levels and the sensitivity of the TRY space to variations in substrate availability. Our results show that, at low expression levels, gene transcription mainly defined TRY, and gene translation had a limited effect; whereas, at high expression levels, TRY depended on the product of both, in agreement with experiments in the literature.This research was partially supported by grants MINECO/AEI, EU DPI2017-82896-C21-R 662 and MICINN/AEI, EU PID2020-117271RB-C21. F.N.S.-N. thanks the UPV grant number PAID-01-2017.Santos-Navarro, FN.; Boada-Acosta, YF.; Vignoni, A.; Picó, J. (2021). Gene Expression Space Shapes the Bioprocess Trade-Offs among Titer, Yield and Productivity. Applied Sciences. 11(13):1-17. https://doi.org/10.3390/app11135859S117111

RBS and Promoter Strengths Determine the Cell-Growth-Dependent Protein Mass Fractions and Their Optimal Synthesis Rates

[EN] Models of gene expression considering host-circuit interactions are relevant for understanding both the strategies and associated trade-offs that cell endogenous genes have evolved and for the efficient design of heterologous protein expression systems and synthetic genetic circuits. Here, we consider a small-size model of gene expression dynamics in bacterial cells accounting for host-circuit interactions due to limited cellular resources. We define the cellular resources recruitment strength as a key functional coefficient that explains the distribution of resources among the host and the genes of interest and the relationship between the usage of resources and cell growth. This functional coefficient explicitly takes into account lab-accessible gene expression characteristics, such as promoter and ribosome binding site (RBS) strengths, capturing their interplay with the growth-dependent flux of available free cell resources. Despite its simplicity, the model captures the differential role of promoter and RBS strengths in the distribution of protein mass fractions as a function of growth rate and the optimal protein synthesis rate with remarkable fit to the experimental data from the literature for Escherichia coli. This allows us to explain why endogenous genes have evolved different strategies in the expression space and also makes the model suitable for model-based design of exogenous synthetic gene expression systems with desired characteristics.This work was partially supported by grants MINECO/AEI, EU DPI2017-82896-C2-1-R, and MCIN/AEI/10.13039/501100011033 grant number PID2020-117271RB-C21. F.N.S.-N. is grateful to grant PAID-01-2017 (Universitat Politecnica de Valencia). The authors are very grateful to the anonymous reviewers for their comprehensive and in-depth reviews.Santos-Navarro, FN.; Vignoni, A.; Boada-Acosta, YF.; Picó, J. (2021). RBS and Promoter Strengths Determine the Cell-Growth-Dependent Protein Mass Fractions and Their Optimal Synthesis Rates. ACS Synthetic Biology. 10(12):3290-3303. https://doi.org/10.1021/acssynbio.1c0013132903303101

Optimization Alternatives for Robust Model-based Design of Synthetic Biological Circuits

[EN] Synthetic biology is reaching the situation where tuning devices by hand is no longer possible due to the complexity of the biological circuits being designed. Thus, mathematical models need to be used in order, not only to predict the behavior of the designed synthetic devices; but to help on the selection of the biological parts, i.e., guidelines for the experimental implementation. However, since uncertainties are inherent to biology, the desired dynamics for the circuit usually requires a trade-off among several goals. Hence, a multi-objective optimization design (MOOD) naturally arises to get a suitable parametrization (or range) of the required kinetic parameters to build a biological device with some desired properties. Biologists have classically addressed this problem by evaluating a set of random Monte Carlo simulations with parameters between an operation range. In this paper, We propose solving the MOOD by means of dynamic programming using both a global multi-objective evolutionary algorithm (MOLA) and a local gradient-based nonlinear programming (NLP) solver. The performance of both alternatives is then checked in the design of a well-known biological circuit: a genetic incoherent feed-forward loop showing adaptive behavior. (C) 2016, IFAC (International Federation of Antomatic Control) Hosting by Elsevier Ltd. All rights reserved.The research leading to these results has received funding from the European Union (FP7/2007-2013 under grant agreement no604068), the Spanish Government (FEDER-CICYT DPI2011-524 28112-C04-01, DPI2014-55276-C5-1-R, DPI2015-70975-P) and the National Council of Scientific and Technologic Development of Brazil (BJT-304804/2014-2). Yadira Boada thanks also grant FPI/2013-3242 of the Universitat Politecnica de ValenciaBoada-Acosta, YF.; Pitarch Pérez, JL.; Vignoni, A.; Reynoso Meza, G.; Picó, J. (2016). Optimization Alternatives for Robust Model-based Design of Synthetic Biological Circuits. IFAC-PapersOnLine. 49(7):821-826. https://doi.org/10.1016/j.ifacol.2016.07.291S82182649

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Gene expression modelling and simulation. Model reduction and noise

[ES] Este trabajo aborda metodologías de modelado para el análisis y diseño de redes sintéticas de genes. Nuestro modelo para la bacteria E. coli. incluye: i) quorum sensing como un mecanismo de comunicación entre células y, ii) un proceso de regulación o control de la expresión genética.[EN] This work deals with modelling methodologies for analysis and simulation of gene synthetic networks. Our model of the E. coli. bacteria include: i) quorum sensing as a cell-to-cell communication mechanism and ii) a regulatory or control process of the gene expression.Boada Acosta, YF. (2013). Gene expression modelling and simulation. Model reduction and noise. http://hdl.handle.net/10251/38376Archivo delegad