Related papers: Variable elimination in post-translational modific…
The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and…
Post-translational modification (PTM) of proteins plays a key role in signal transduction, and hence significant effort has gone toward understanding how PTM networks process information. This involves, on the theory side, analyzing the…
Chemical kinetics plays an important role in governing the thermal evolution in reactive flows problems. The possible interactions between chemical species increase drastically with the number of species considered in the system. Various…
Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
Gaining insights from realistic dynamical models of biochemical systems can be challenging given their large number of state variables. Model reduction techniques can mitigate this by decreasing complexity by mapping the model onto a…
This paper analyses of a stochastic model of a chemical reaction network with three types of chemical species ${\cal R}$, ${\cal M}$ and ${\cal U}$ that interact to transform a flow of external resources, the chemical species ${\cal Q}$, to…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in…
In this work we present new scalable, information theory-based variational methods for the efficient model reduction of high-dimensional deterministic and stochastic reaction networks. The proposed methodology combines, (a) information…
Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…
Multistationary chemical reaction networks are of interest to scientists and mathematicians alike. While some criteria for multistationarity exist, obtaining explicit reaction rates and steady states that exhibit multistationarity for a…
Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with…