Related papers: Biochemical network decomposition reveals absolute…
Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this…
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…
In this paper we study how to determine if a linear biochemical network satisfies the detailed balance condition, without knowing the details of all the reactions taking place in the network. To this end, we use the formalism of response…
The flow models of complex network system are developed and main flow characteristics of its elements are defined. Those characteristics are applied for determining actual structure of the system, analyzing its development on all lifecycle…
Biochemical oscillations are prevalent in living organisms. Systems with a small number of constituents cannot sustain coherent oscillations for an indefinite time because of fluctuations in the period of oscillation. We show that the…
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…
We present a uniform method for translating an arbitrary nondeterministic finite automaton (NFA) into a deterministic mass action input/output chemical reaction network (I/O CRN) that simulates it. The I/O CRN receives its input as a…
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system…
The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…
Biological systems possess negative entropy. In them, one form of order produces another, more organized form of order. We propose a formal scheme to calculate robustness of an entire biological system by quantifying the negative entropy…
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…
We show that adding new chemical species into the reactions of a chemical reaction network (CRN) in such a way that the rank of the network remains unchanged preserves its capacity for multiple nondegenerate equilibria and/or periodic…
The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of…
We present a data-driven verification approach that determines whether or not a given chemical reaction network (CRN) satisfies a given property, expressed as a formula in a modal logic. Our approach consists of three phases, integrating…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this…
[Background] Several studies have mentioned network modularity -- that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other -- as a factor affecting metabolic…
Network analysis has revealed whole-network properties hypothesized to be general characteristics of ecosystems including pathway proliferation, and network non-locality, homogenization, amplification, mutualism, and synergism. Collectively…
The mathematical formalisms used to model biological systems induce both latent and ambiguous assumptions that can limit or distort their representational capabilities. Developing formalisms that can represent systems more precisely is…