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Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
Stochastic modeling of reaction networks is a framework used to describe the time evolution of many natural and artificial systems, including, biochemical reactive systems at the molecular level, viral kinetics, the spread of epidemic…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…
Numerous aqueous systems host elements in multiple redox states, with wide ranging implications such as their influence on the formation/dissolution of minerals, water toxicity, and nutrient cycling. To uncover governing mechanisms and…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
The in silico exploration of chemical, physical and biological systems requires accurate and efficient energy functions to follow their nuclear dynamics at a molecular and atomistic level. Recently, machine learning tools gained a lot of…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these…
An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…
Understanding the set of elementary steps and kinetics in each reaction is extremely valuable to make informed decisions about creating the next generation of catalytic materials. With physical and mechanistic complexity of industrial…
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…
In this paper, we present a study on how to develop an efficient multiscale simulation strategy for the dynamics of chemically active systems on low-dimensional supports. Such reactions are encountered in a wide variety of situations,…
Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
Chemical reactions are often associated with an energy barrier along the reaction pathway which hinders the spontaneity of the reaction. Changing the energy barrier along the reaction pathway allows one to modulate the performance of a…
We present a computational procedure to characterize the signs of sensitivities of steady states to parameter perturbations in chemical reaction networks.
The recrossing correction to the transition state theory estimate of a thermal rate can be difficult to calculate when the energy barrier is flat. This problem arises, for example, in polymer escape if the polymer is long enough to stretch…
We discuss a method to describe the qualitative dynamics of chemical reaction networks in terms of symbolic dynamics. The method, that can be applied to mass-action reaction networks with separated timescales, uses solutions of the partial…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…