1,435 research outputs found
Critical Transitions In a Model of a Genetic Regulatory System
We consider a model for substrate-depletion oscillations in genetic systems,
based on a stochastic differential equation with a slowly evolving external
signal. We show the existence of critical transitions in the system. We apply
two methods to numerically test the synthetic time series generated by the
system for early indicators of critical transitions: a detrended fluctuation
analysis method, and a novel method based on topological data analysis
(persistence diagrams).Comment: 19 pages, 8 figure
Gene regulated car driving: using a gene regulatory network to drive a virtual car
This paper presents a virtual racing car controller based on an artificial gene regulatory network. Usually used to control virtual cells in developmental models, recent works showed that gene regulatory networks are also capable to control various kinds of agents such as foraging agents, pole cart, swarm robots, etc. This paper details how a gene regulatory network is evolved to drive on any track through a three-stages incremental evolution. To do so, the inputs and outputs of the network are directly mapped to the car sensors and actuators. To make this controller a competitive racer, we have distorted its inputs online to make it drive faster and to avoid opponents. Another interesting property emerges from this approach: the regulatory network is naturally resistant to noise. To evaluate this approach, we participated in the 2013 simulated racing car competition against eight other evolutionary and scripted approaches. After its first participation, this approach finished in third place in the competition
Mathematical modelling plant signalling networks
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This sub-cellular analysis paves the way for more comprehensive mathematical studies of hormonal transport and signalling in a multi-scale setting
The impact of cellular characteristics on the evolution of shape homeostasis
The importance of individual cells in a developing multicellular organism is
well known but precisely how the individual cellular characteristics of those
cells collectively drive the emergence of robust, homeostatic structures is
less well understood. For example cell communication via a diffusible factor
allows for information to travel across large distances within the population,
and cell polarisation makes it possible to form structures with a particular
orientation, but how do these processes interact to produce a more robust and
regulated structure? In this study we investigate the ability of cells with
different cellular characteristics to grow and maintain homeostatic structures.
We do this in the context of an individual-based model where cell behaviour is
driven by an intra-cellular network that determines the cell phenotype. More
precisely, we investigated evolution with 96 different permutations of our
model, where cell motility, cell death, long-range growth factor (LGF),
short-range growth factor (SGF) and cell polarisation were either present or
absent. The results show that LGF has the largest positive impact on the
fitness of the evolved solutions. SGF and polarisation also contribute, but all
other capabilities essentially increase the search space, effectively making it
more difficult to achieve a solution. By perturbing the evolved solutions, we
found that they are highly robust to both mutations and wounding. In addition,
we observed that by evolving solutions in more unstable environments they
produce structures that were more robust and adaptive. In conclusion, our
results suggest that robust collective behaviour is most likely to evolve when
cells are endowed with long range communication, cell polarisation, and
selection pressure from an unstable environment
Perfect Sampling of the Master Equation for Gene Regulatory Networks
We present a Perfect Sampling algorithm that can be applied to the Master
Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's
Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo
methods and combines it with the Dominated Coupling From The Past (DCFTP)
algorithm to provide guaranteed sampling from the stationary distribution. We
show how the DCFTP-SSA can be generically applied to genetic networks with
feedback formed by the interconnection of linear enzymatic reactions and
nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the
error and convergence of the DCFTP-SSA, as compared to the standard SSA,
through a set of increasingly complex examples. Once the building blocks for
GRNs have been introduced, the algorithm is applied to study properly averaged
dynamic properties of two experimentally relevant genetic networks: the toggle
switch, a two-dimensional bistable system, and the repressilator, a
six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa
Evolving Sensitivity Balances Boolean Networks
We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman’s Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. Insilico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks
Quantifying the Dynamics of Coupled Networks of Switches and Oscillators
Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems
Gene regulated car driving: using a gene regulatory network to drive a virtual car
This paper presents a virtual racing car controller based on an artificial gene regulatory network. Usually used to control virtual cells in developmental models, recent works showed that gene regulatory networks are also capable to control various kinds of agents such as foraging agents, pole cart, swarm robots, etc. This paper details how a gene regulatory network is evolved to drive on any track through a three-stages incremental evolution. To do so, the inputs and outputs of the network are directly mapped to the car sensors and actuators. To make this controller a competitive racer, we have distorted its inputs online to make it drive faster and to avoid opponents. Another interesting property emerges from this approach: the regulatory network is naturally resistant to noise. To evaluate this approach, we participated in the 2013 simulated racing car competition against eight other evolutionary and scripted approaches. After its first participation, this approach finished in third place in the competition
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