On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures

Modeling two-state cooperativity in protein folding

A protein model with the pairwise interaction energies varying as local environment changes, i.e., including some kinds of collective effect between the contacts, is proposed. Lattice Monte Carlo simulations on the thermodynamical characteristics and free energy profile show a well-defined two-state behavior and cooperativity of folding for such a model. As a comparison, related simulations for the usual G\={o} model, where the interaction energies are independent of the local conformations, are also made. Our results indicate that the evolution of interactions during the folding process plays an important role in the two-state cooperativity in protein folding.Comment: 5 figure

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ‘delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Cosmological model of the interaction between dark matter and dark energy

In this paper, we test the dark matter-dark energy interacting cosmological model with a dynamic equation of state $w_{DE}(z)=w_{0}+w_{1}z/(1+z)$, using type Ia supernovae (SNe Ia), Hubble parameter data, baryonic acoustic oscillation (BAO) measurements, and the cosmic microwave background (CMB) observation. This interacting cosmological model has not been studied before. The best-fitted parameters with $1 \sigma$ uncertainties are $\delta=-0.022 \pm 0.006$, $\Omega_{DM}^{0}=0.213 \pm 0.008$, $w_0 =-1.210 \pm 0.033$ and $w_1=0.872 \pm 0.072$ with $\chi^2_{min}/dof = 0.990$. At the $1 \sigma$ confidence level, we find $\delta<0$, which means that the energy transfer prefers from dark matter to dark energy. We also find that the SNe Ia are in tension with the combination of CMB, BAO and Hubble parameter data. The evolution of $\rho_{DM}/\rho_{DE}$ indicates that this interacting model is a good approach to solve the coincidence problem, because the $\rho_{DE}$ decrease with scale factor $a$. The transition redshift is $z_{tr}=0.63 \pm 0.07$ in this model.Comment: 6 pages, 6 figures, published in A&