Related papers: Log-Linear Reaction Quotient Dynamics
Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and…
We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a…
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…
We investigate the thermodynamic implications of two control mechanisms of open chemical reaction networks. The first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange…
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…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
Chemical equilibrium is fully characterized by thermodynamics, while the rates of chemical reactions can be calculated for ideal solutions by using mass-action equations. The evaluation of the rates of reactions in a non-ideal system is…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
The molecular network in an organism consists of transcription/translation regulation, protein-protein interactions/modifications and a metabolic network, together forming a system that allows the cell to respond sensibly to the multiple…
Predicting how systems respond to external perturbations far from equilibrium remains a fundamental challenge across physics, chemistry, and biology. We present a unified response framework for stochastic Markov dynamics that integrates…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
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…
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between…
A dynamic logic method was developed to analyze molecular networks of cells by combining Kauffman and Thomas's logic operations with molecular interaction parameters. The logic operations characterize the discrete interactions between…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
We propose a kinetic relaxation-model to describe a generation-recombination reaction of two species. The decay to equilibrium is studied by two recent methods for proving hypocoercivity of the linearized equations. Exponential decay of…
Since molecular energy transformations are responsible for chemical reaction rates at the most fundamental level, chemical kinetics should provide some information about molecular energies. This is the premise and objective of this note. We…
Unlike fluids at thermal equilibrium, biomolecular mixtures in living systems can sustain nonequilibrium steady states, in which active processes modify the conformational states of the constituent molecules. Despite qualitative…