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Mathematical models are indispensable to the system biology toolkit for studying the structure and behavior of intracellular signaling networks. A common approach to modeling is to develop a system of equations that encode the known biology…
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the…
New advances in nano sciences open the door for scientists to study biological processes on a microscopic molecule-by-molecule basis. Recent single-molecule biophysical experiments on enzyme systems, in particular, reveal that enzyme…
The Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar…
Networks of biochemical reactions, like cellular metabolic networks, are kept in non-equilibrium steady states by the exchange fluxes connecting them to the environment. In most cases, feasible flux configurations can be derived from…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by…
Protein synthesis is one of the most fundamental biological processes, which consumes a significant amount of cellular resources. Despite existence of multiple mathematical models of translation, varying in the level of mechanistical…
Ultrasensitive response motifs, which are capable of converting graded stimulus in binary responses, are very well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive…
We develop a thermodynamic framework for closed and open chemical networks applicable to non-elementary reactions that do not need to obey mass action kinetics. It only requires the knowledge of the kinetics and of the standard chemical…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
Various biological system models have been proposed in systems biology, which are based on the complex biological reactions kinetic of various components. These models are not practical because we lack of kinetic information. In this paper,…
In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed…
Energy conversion in nanosized devices is studied in the framework of state-space models. We use a network representation of the underlying master equation to describe the dynamics by a graph. Particular segments of this network represent…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Given a metabolic network in terms of its metabolites and reactions, our goal is to efficiently compute the minimal knock out sets of reactions required to block a given behaviour. We describe an algorithm which improves the computation of…
Network interpretation as an effort to reveal the features learned by a network remains largely visualization-based. In this paper, our goal is to tackle semantic network interpretation at both filter and decision level. For filter-level…
Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
Signal transduction, the information processing mechanism in biological cells, is carried out by a network of biochemical reactions. The dynamics of driven biochemical reactions can be studied in terms of nonequilibrium statistical physics.…