Related papers: Discreteness-induced Transition in Catalytic React…
We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts…
Mutation is introduced into autocatalytic reaction networks. Examples of low dimensional dynamical systems --- n = 2, 3 and 4 --- are discussed and complete qualitative analysis is presented. Error thresholds known from simple…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
We consider a general class of autocatalytic reactions, that has been shown to display stochastically switching behaviour (Discreteness Induced Transitions) in some parameter regimes. This behaviour was shown to occur when either the…
A major challenge in network science is to determine parameters governing complex network dynamics from experimental observations and theoretical models. In complex chemical reaction networks, for example, such as those describing processes…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
Over the last years, analyses performed on a stochastic model of catalytic reaction networks have provided some indications about the reasons why wet-lab experiments hardly ever comply with the phase transition typically predicted by…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…
We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or…
Stochastic chemical reaction networks (CRNs) are complex systems which combine the features of concurrent transformation of multiple variables in each elementary reaction event, and nonlinear relations between states and their rates of…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
Novel physical mechanism is proposed for explanation of temperature-independent transition reactions in molecular systems. The mechanism becomes effective in the case of conformation transitions between quasi-isoenergetic molecular states.…
The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
We investigate the catalytic reactions model used in cell modeling. The reaction kinetic is defined through the energies of different species of molecules following random independent distribution. The related statistical physics model has…
A system containing a pre-steady state standard (non-autocatalytic) reaction, with multiple paths, evolves toward a kinetic state with the minimum attainable activation free energy. Displacement of the path frequency distribution in this…
Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…