207 research outputs found
A Stochastic Analysis of Autoregulation of Gene Expression
This paper analyzes, in the context of a prokaryotic cell, the stochastic
variability of the number of proteins when there is a control of gene
expression by an autoregulation scheme. The goal of this work is to estimate
the efficiency of the regulation to limit the fluctuations of the number of
copies of a given protein. The autoregulation considered in this paper relies
mainly on a negative feedback: the proteins are repressors of their own gene
expression. The efficiency of a production process without feedback control is
compared to a production process with an autoregulation of the gene expression
assuming that both of them produce the same average number of proteins. The
main characteristic used for the comparison is the standard deviation of the
number of proteins at equilibrium. With a Markovian representation and a simple
model of repression, we prove that, under a scaling regime, the repression
mechanism follows a Hill repression scheme with an hyperbolic control. An
explicit asymptotic expression of the variance of the number of proteins under
this regulation mechanism is obtained. Simulations are used to study other
aspects of autoregulation such as the rate of convergence to equilibrium of the
production process and the case where the control of the production process of
proteins is achieved via the inhibition of mRNAs
Stochastic Gene Expression in Cells: A Point Process Approach
This paper investigates the stochastic fluctuations of the number of copies
of a given protein in a cell. This problem has already been addressed in the
past and closed-form expressions of the mean and variance have been obtained
for a simplified stochastic model of the gene expression. These results have
been obtained under the assumption that the duration of all the protein
production steps are exponentially distributed. In such a case, a Markovian
approach (via Fokker-Planck equations) is used to derive analytic formulas of
the mean and the variance of the number of proteins at equilibrium. This
assumption is however not totally satisfactory from a modeling point of view
since the distribution of the duration of some steps is more likely to be
Gaussian, if not almost deterministic. In such a setting, Markovian methods can
no longer be used. A finer characterization of the fluctuations of the number
of proteins is therefore of primary interest to understand the general economy
of the cell. In this paper, we propose a new approach, based on marked Poisson
point processes, which allows to remove the exponential assumption. This is
applied in the framework of the classical three stages models of the
literature: transcription, translation and degradation. The interest of the
method is shown by recovering the classical results under the assumptions that
all the durations are exponentially distributed but also by deriving new
analytic formulas when some of the distributions are not anymore exponential.
Our results show in particular that the exponential assumption may,
surprisingly, underestimate significantly the variance of the number of
proteins when some steps are in fact not exponentially distributed. This
counter-intuitive result stresses the importance of the statistical assumptions
in the protein production process
Models of protein production along the cell cycle: an investigation of possible sources of noise
In this article, we quantitatively study, through stochastic models, the
efects of several intracellular phenomena, such as cell volume growth, cell
division, gene replication as well as fuctuations of available RNA polymerases
and ribosomes. These phenomena are indeed rarely considered in classic models
of protein production and no relative quantitative comparison among them has
been performed. The parameters for a large and representative class of proteins
are determined using experimental measures. The main important and surprising
conclusion of our study is to show that despite the signifcant fuctuations of
free RNA polymerases and free ribosomes, they bring little variability to
protein production contrary to what has been previously proposed in the
literature. After verifying the robustness of this quite counter-intuitive
result, we discuss its possible origin from a theoretical view, and interpret
it as the result of a mean-feld efect
Modal decomposition of linearized open channel flow
Open channel flow is traditionally modeled as an hyperbolic system of conservation laws, which is an infinite dimensional system with complex dynamics. We consider in this paper an open channel represented by the Saint-Venant equations linearized around a non uniform steady flow regime. We use a frequency domain approach to fully characterize the open channel flow dynamics. The use of the Laplace transform enables us to derive the distributed transfer matrix, linking the boundary inputs to the state of the system. The poles of the system are then computed analytically, and each transfer function is decomposed in a series of eigenfunctions, where the influence of space and time variables can be decoupled. As a result, we can express the time-domain response of the whole canal pool to boundary inputs in terms of discharges. This study is first done in the uniform case, and finally extended to the non uniform case. The solution is studied and illustrated on two different canal pools
A RBA model for the chemostat modeling
A RBA model for the chemostat modeling. 58. Conference on Decision and Contro
Validation of the 3-under-2 principle of cell wall growth in Gram-positive bacteria by simulation of a simple coarse-grained model
The aim of this work is to propose a first coarse-grained model of Bacillus
subtilis cell wall, handling explicitly the existence of multiple layers of
peptidoglycans. In this first work, we aim at the validation of the recently
proposed "three under two" principle.Comment: Revised introduction, results unchange
(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis
(Im) Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis
Background: Metabolic control analysis (MCA) and supplyâdemand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supplyâdemand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect.
Results: This study integrates control engineering and classical MCA augmented with supplyâdemand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the âintegral controlâ (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of âintegral controlâ should rarely be expected to lead to the âperfect adaptationâ: although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily.
Conclusions: A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the âperfectâ regulatory structures designed by control engineering vis-Ă -vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering
Reduced Complexity Controllers for LPV Systems: Towards Incremental Synthesis
International audienceExisting synthesis methods for LPV systems often result in controllers of high complexity. So far, there is no efficient and systematic remedy to this issue as there exists no convex formulation of the problem of finding a solution of reduced complexity to the general case LPV synthesis problem. In this paper, the specific case is considered when parameter-dependent signals are measured. It is proven that these measures can be exploited so that the problem of reduced-complexity controller synthesis can be written as an LMI optimization problem. A complete procedure for the controller construction is provided. The interest of the result is discussed in relation with nonlinear methods. First, an interpretation of the controller strategy is proposed with regard to the feedback linearization method. Second, it is proven that a nonlinear controller ensuring the closed loop incremental properties can be constructed
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