Long lived transients in gene regulation

Gene expression is regulated by the set of transcription factors (TFs) that bind to the promoter. The ensuing regulating function is often represented as a combinational logic circuit, where output (gene expression) is determined by current input values (promoter bound TFs) only. However, the simultaneous arrival of TFs is a strong assumption, since transcription and translation of genes introduce intrinsic time delays and there is no global synchronisation among the arrival times of different molecular species at their targets. We present an experimentally implementable genetic circuit with two inputs and one output, which in the presence of small delays in input arrival, exhibits qualitatively distinct population-level phenotypes, over timescales that are longer than typical cell doubling times. From a dynamical systems point of view, these phenotypes represent long-lived transients: although they converge to the same value eventually, they do so after a very long time span. The key feature of this toy model genetic circuit is that, despite having only two inputs and one output, it is regulated by twenty-three distinct DNA-TF configurations, two of which are more stable than others (DNA looped states), one promoting and another blocking the expression of the output gene. Small delays in input arrival time result in a majority of cells in the population quickly reaching the stable state associated with the first input, while exiting of this stable state occurs at a slow timescale. In order to mechanistically model the behaviour of this genetic circuit, we used a rule-based modelling language, and implemented a grid-search to find parameter combinations giving rise to long-lived transients. Our analysis shows that in the absence of feedback, there exist path-dependent gene regulatory mechanisms based on the long timescale of transients. The behaviour of this toy model circuit suggests that gene regulatory networks can exploit event timing to create phenotypes, and it opens the possibility that they could use event timing to memorise events, without regulatory feedback. The model reveals the importance of (i) mechanistically modelling the transitions between the different DNA-TF states, and (ii) employing transient analysis thereof

Long lived transients in gene regulation

Gene expression is regulated by the set of transcription factors (TFs) that bind to the promoter. The ensuing regulating function is often represented as a combinational logic circuit, where output (gene expression) is determined by current input values (promoter bound TFs) only. However, the simultaneous arrival of TFs is a strong assumption, since transcription and translation of genes introduce intrinsic time delays and there is no global synchronisation among the arrival times of different molecular species at their targets. We present an experimentally implementable genetic circuit with two inputs and one output, which in the presence of small delays in input arrival, exhibits qualitatively distinct population-level phenotypes, over timescales that are longer than typical cell doubling times. From a dynamical systems point of view, these phenotypes represent long-lived transients: although they converge to the same value eventually, they do so after a very long time span. The key feature of this toy model genetic circuit is that, despite having only two inputs and one output, it is regulated by twenty-three distinct DNA-TF configurations, two of which are more stable than others (DNA looped states), one promoting and another blocking the expression of the output gene. Small delays in input arrival time result in a majority of cells in the population quickly reaching the stable state associated with the first input, while exiting of this stable state occurs at a slow timescale. In order to mechanistically model the behaviour of this genetic circuit, we used a rule-based modelling language, and implemented a grid-search to find parameter combinations giving rise to long-lived transients. Our analysis shows that in the absence of feedback, there exist path-dependent gene regulatory mechanisms based on the long timescale of transients. The behaviour of this toy model circuit suggests that gene regulatory networks can exploit event timing to create phenotypes, and it opens the possibility that they could use event timing to memorise events, without regulatory feedback. The model reveals the importance of (i) mechanistically modelling the transitions between the different DNA-TF states, and (ii) employing transient analysis thereof

Reduction of Chemical Reaction Networks with Approximate Conservation Laws

Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integrals approximate conservation laws. In order to define fast subsystems and identify approximate conservation laws, we use ideas from tropical geometry. We prove that any approximate conservation law evolves slower than all the species involved in it and therefore represents a supplementary slow variable in an extended system. By elimination of some variables of the extended system, we obtain networks without approximate conservation laws, which can be reduced by standard singular perturbation methods. The field of applications of approximate conservation laws covers the quasi-equilibrium approximation, well known in biochemistry. We discuss both two timescale reductions of fast-slow systems and multiple timescale reductions of multiscale networks. Networks with multiple timescales have hierarchical relaxation. At a given timescale, our multiple timescale reduction method defines three subsystems composed of (i) slaved fast variables satisfying algebraic equations, (ii) slow driving variables satisfying reduced ordinary differential equations, and (iii) quenched much slower variables that are constant. The algebraic equations satisfied by fast variables define chains of nested normally hyberbolic invariant manifolds. In such chains, faster manifolds are of higher dimension and contain the slower manifolds. Our reduction methods are introduced algorithmically for networks with linear, monomial or polynomial approximate conservation laws. Keywords: Model order reduction, chemical reaction networks, singular perturbations, multiple timescales, tropical geometry

Analysis of Biochemical Reaction Networks using Tropical and Polyhedral Geometry Methods

The field of systems biology makes an attempt to realise various biological functions and processes as the emergent properties of the underlying biochemical network model. The area of computational systems biology deals with the computational methods to compute such properties. In this context, the thesis primarily discusses novel computational methods to compute the emergent properties as well as to recognize the essence in complex network models. The computational methods described in the thesis are based on the computer algebra techniques, namely tropical geometry and extreme currents. Tropical geometry is based on ideas of dominance of monomials appearing in a system of differential equations, which are often used to describe the dynamics of the network model. In such differential equation based models, tropical geometry deals with identification of the metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is much slower compared to the rest of the phase space. The application of such properties in model reduction and symbolic dynamics are demonstrated in the network models obtained from a public database namely Biomodels. Extreme currents are limiting edges of the convex polyhedrons describing the admissible fluxes in biochemical networks, which are helpful to decompose a biochemical network into a set of irreducible pathways. The pathways are shown to be associated with given clinical outcomes thereby providing some mechanistic insights associated with the clinical phenotypes. Similar to the tropical geometry, the method based on extreme currents is evaluated on the network models derived from a public database namely KEGG. Therefore, this thesis makes an attempt to explain the emergent properties of the network model by determining extreme currents or metastable regimes. Additionally, their applicability in the real world network models are discussed

Modeling of chemical process systems as finite state machines for formal verification

Orientador: Roger Josef ZempTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia QuímicaResumo: A análise da segurança de processos industriais é feita primariamente com ferramentas como HAZOP e Análise de Árvore de Falhas. Esses métodos exigem conhecimentos de diversas áreas e contam com a participação de engenheiros e outros profissionais na elaboração de documentos que descrevem cenários de desastre e planos de contingência. A modelagem e simulação de processos poderia ser usada nesse sentido para auxiliar na determinação de condições operacionais que levariam ao desastre. Porém, explorar todo o espaço de estados do modelo de um processo em busca destes cenários é custoso, e frequentemente inviável, em termos de tempo computacional, pois os cenários a considerar são, usualmente, infinitos. Para resolver problemas exploratórios semelhantes, cientistas da computação desenvolveram métodos para deduzir se modelos de sistemas físicos atendem ou não certas propriedades (um programa nunca pode travar ou um processador nunca pode errar os cálculos, por exemplo). Esse conjunto de métodos, chamado de verificação formal, em geral exige modelos que os engenheiros químicos não estão acostumados a trabalhar, como as máquinas de estados finitos. Assim, o presente trabalho teve por objetivo o desenvolvimento de um método para modelagem de processos químicos como máquinas de estados finitos para que estes modelos pudessem ser utilizados em verificação formal. O método extrai informações sobre a dinâmica do processo e constrói automaticamente as máquinas. O método foi aplicado em um estudo de caso de um reator CSTR com múltiplos estados estacionários, onde o modelo resultante foi verificado a fim de descobrir rotas de partida do equipamento e alcançabilidade dos estados estacionários em termos das variáveis operacionais disponíveis. A técnica se mostrou eficaz e flexível o suficiente para construir a máquina a partir de diferentes fontes de informação da dinâmica do processo, inclusive, em princípio, de simuladores de processosAbstract: HAZOP and Fault Tree Analysis are generally used as tools for industrial safety analysis and they usually require knowledge from several different areas. Engineers and other professionals use those tools to develop documents describing hazard scenarios and contingency plans. Process modelling and simulation could help during the elaboration of this documentation by indicating operational conditions with potential to disaster. However, exhaustive exploration of the model state space to search for these scenarios is very time consuming, and frequently impracticable, because the considered scenarios are, usually, infinite. To solve similar exploratory problems, computer scientists developed several methods to prove if models of physical systems meet some specifications (e.g. a software must not have deadlock or a CPU must not miss any operation). These methods, called formal verification, sometimes require models that chemical engineers do not usually deal with, like finite state machines. This work aimed at the development of a method to model chemical processes as finite state machines for formal verification purposes. The method extracts information about the system's dynamics and builds automatically the machines. The technique was applied on a case study of a multiple steady state CSTR, where the finite state model was verified in order to find viable startup strategies and analyze reachability of stable steady states with the available operational variables. It was demonstrated that the method is effective and flexible enough to build the machines from serveral different sources of information of the process dynamics, including, in principal, from process simulatorsDoutoradoEngenharia QuímicaDoutor em Engenharia Química140590/2014-5CNP

Symbolic Dynamics of Biochemical Pathways as Finite States Machines

We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a number of states that is inferior to the number of biochemical species. For nonlinear pathways, we propose a general approach to approximate their dynamics by finite state machines working on the metastable states of the network (long life states where the system has slow dynamics). For networks with polynomial rate functions we propose to compute metastable states as solutions of the tropical equilibration problem. Tropical equilibrations are defined by the equality of at least two dominant monomials of opposite signs in the differential equations of each dynamic variable. In algebraic geometry, tropical equilibrations are tantamount to tropical prevarieties, that are finite intersections of tropical hypersurfaces