Analysis and generic properties of gene regulatory networks with graded response functions

A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter variations and robustness issues. Different mathematical frameworks have been proposed to derive such models. In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model the dynamics of the concentrations of mRNAs and proteins. These models are usually characterized by the presence of highly nonlinear Hill function terms. A typical simplification is to reduce the number of equations by means of a quasi-steady-state assumption on the mRNA concentrations. This yields a class of simplified ODE models. A radically different approach is to replace the Hill functions by piecewise-linear approximations [5]. A further modelling approach is the use of discretetime maps [7] where the evolution of the system is modelled in discrete, rather than continuous, time. The aim of this paper is to discuss and compare these different modelling approaches, using a representative gene regulatory network. We will show that different models often lead to conflicting conclusions concerning the existence and stability of equilibria and stable oscillatory behaviours. Moreover, we shall discuss, where possible, the viability of making certain modelling approximations (e.g. quasi-steady-state mRNA dynamics or piecewise-linear approximations of Hill functions) and their effects on the overall system dynamics.

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“…In particular, in the work originated by Plahte et al [36], and also in [3,4,19] the following PWL function for activation is used:…”

Section: Ordinary Differential Equationsmentioning

confidence: 99%

“…In [36] Plahte et al described two problems when the PWL step function are being used to model gene regulatory networks. One problem is to define a continuous solution across the threshold hyperplanes when the model includes self-regulation.…”

Section: Dynamics Of the Spwlmmentioning

confidence: 99%

Comparing different ODE modelling approaches for gene regulatory networks

Polynikis

Hogan

Bernardo

2009

Journal of Theoretical Biology

150

103

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“…(1) could be applied to GRNs of any size and complexity, and the generic analysis developed in [7,14] is fully applicable to networks of any size. However, as the network becomes large, there is a combinatorial explosion of phase-space domains and parameter combinations that need to be investigated, and a computerized, algorithmic approach becomes a necessity.…”

Section: A Modeling Framework For the Study Of Grn Dynamicsmentioning

confidence: 99%

“…(5,6) taken together approximate the exact solution in D S for q close to zero, i.e. for steep sigmoids [7]. One just has to express x s by the solution Z s,sj (τ ) and replace τ by t/q.…”

Section: A Modeling Framework For the Study Of Grn Dynamicsmentioning

confidence: 99%

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An Algorithm for Qualitative Simulation of Gene Regulatory Networks with Steep Sigmoidal Response Functions

Self Cite

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Abstract. A specific class of ODEs has been shown to be adequate to describe the essential features of the complex dynamics of Gene-Regulatory Networks (GRN). But, the effective exploitation of such models to predict the dynamics of specific GRNs by classical numerical schemes is greatly hampered by the current lack of precise and quantitative information on regulation mechanisms and kinetic parameters. Due to the size and complexity of large GRNs, classical qualitative analysis could be very hard, or even impracticable, to be carried out by hand, and conventional qualitative simulation approaches rapidly lead to an exponential growth of the generated behavior tree that, besides all possible sound behaviors, may also contain spurious ones. This paper discusses the work-in-progress of a research effort aiming at the design and implementation of a computational framework for qualitative simulation of the dynamics of a class of ODE models of GRNs. The algorithm we propose results from a set of symbolic computation algorithms that carry out the integration of qualitative reasoning techniques with singular perturbation analysis methods. The former techniques allow us to cope with uncertain and incomplete knowledge whereas the latter ones lay the mathematical groundwork for a sound and complete algorithm capable to deal with regulation processes that occur at different time scales.

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Embedded control of cell growth using tunable genetic systems

Fusco

Salzano

Fiore

et al. 2022

Intl J Robust & Nonlinear

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We present an embedded feedback control strategy to control the density of a bacterial population, allowing cells to self-regulate their growth rate so as to reach a desired density at steady state. We consider a static culture condition, where cells are provided with a limited amount of space and nutrients. The control strategy is built using a tunable expression system (TES), which controls the production of a growth inhibitor protein, complemented with a quorum sensing mechanism for the sensing of the population density. We show on a simplified population-level model that the TES endows the control system with additional flexibility by allowing the set-point to be changed online. Finally, we validate the effectiveness of the proposed control strategy by means of realistic in silico experiments conducted in BSim, an agent-based simulator explicitly designed to simulate bacterial populations, and we test the robustness of our design to disturbances and parameters' variations due, for instance, to cell-to-cell variability.

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Analysis and generic properties of gene regulatory networks with graded response functions

Cited by 98 publications

References 57 publications

Comparing different ODE modelling approaches for gene regulatory networks

Comparing different ODE modelling approaches for gene regulatory networks

An Algorithm for Qualitative Simulation of Gene Regulatory Networks with Steep Sigmoidal Response Functions

Embedded control of cell growth using tunable genetic systems

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