Maya Mincheva

Maya Mincheva
Northern Illinois University · Department of Mathematical Sciences

PhD University of Waterloo Canada

About

33
Publications
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486
Citations

Publications

Publications (33)
Preprint
Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for delay stability, i.e., linear stability independent of both rate constants and delay parameters. In particular, the result applies when the system has no delay, implying asymptotic...
Article
Full-text available
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the...
Preprint
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the...
Article
Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and d...
Preprint
Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and d...
Article
Full-text available
This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for phosphorylation is processive, while the one for dephosphorylation is distributive (or vice versa). The fact th...
Preprint
This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely, the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for phosphorylation is processive while the one for dephosphorylation is distributive (or vice-versa). The fact th...
Article
Full-text available
A parametric sensitivity analysis for periodic solutions of delay differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the ex-trema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to m...
Data
Proof of mathematical statements and examples. In this document we first prove the claims of the main text. Next, we provide details on how to check the steps of the procedure. Finally, we give details of the examples in Table 1 and include an extra example which is a PTM network. (PDF)
Article
Full-text available
Biochemical mechanisms with mass action kinetics are usually modeled as systems of ordinary differential equations (ODE) or bipartite graphs. We present a software module for the numerical analysis of ODE models of biochemical mechanisms of chemical species and elementary reactions (BMCSER) within the programming environment of CAS Mathemat-ica. Th...
Article
Full-text available
A common feature of pattern formation in both space and time is the destabilization of a stable equilibrium solution of an ordinary differential equation by adding diffusion or delay, or both. Here we study linear stability of general reaction–diffusion systems with off-diagonal time delays. We show that a delay-stable system cannot be destabilized...
Article
Full-text available
Biochemical mechanisms with mass action kinetics are usually modeled as systems of ordinary differential equations (ODE) or bipartite graphs. We present a software module for the numerical analysis of ODE models of biochemical mechanisms of chemical species and elementary reactions (BMCSER) within the programming environment of CAS Mathemat-ica. Th...
Article
Full-text available
Mathematical modeling has become an established tool for studying biological dynamics. Current applications range from building models that reproduce quantitative data to identifying models with predefined qualitative features, such as switching behavior, bistability or oscillations. Mathematically, the latter question amounts to identifying parame...
Article
Full-text available
Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems, since they are large, nonlinear and contain many unknown parameters. Mass action biochemical mechanisms can be...
Article
Full-text available
Dual phosphorylation of proteins is a principal component of intracellular signalling. Bistability is considered an important property of such systems and its origin is not yet completely understood. Theoretical studies have established parameter values for multistationarity and bistability for many types of proteins. However, up to now no formal c...
Article
Full-text available
A biochemical mechanism with mass action kinetics can be represented as a directed bipartite graph (bipartite digraph), and modeled by a system of differential equations. If the differential equations (DE) model can give rise to some instability such as multistability or Turing instability, then the bipartite digraph contains a structure referred t...
Article
Full-text available
We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite gr...
Article
Full-text available
Systems biologists increasingly use network representations to investigate biochemical pathways and their dynamic behaviours. In this critical review, we discuss four commonly used network representations of chemical and biochemical pathways. We illustrate how some of these representations reduce network complexity but result in the ambiguous repre...
Article
Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of sp...
Article
Full-text available
It is well known that oscillations in models of biochemical reaction networks can arise as a result of a single negative cycle. On the other hand, methods for finding general network conditions for potential oscillations in large biochemical reaction networks containing many cycles are not well developed. A biochemical reaction network with any num...
Article
Full-text available
Biochemical reaction models show a variety of dynamical behaviors, such as stable steady states, multistability, and oscillations. Biochemical reaction networks with generalized mass action kinetics are represented as directed bipartite graphs with nodes for species and reactions. The bipartite graph of a biochemical reaction network usually contai...
Article
Full-text available
We represent interactions among biochemical species using a directed multigraph, which is a generalization of a more commonly used digraph. We show that network properties that are known to lead to multistability or oscillations, such as the existence of a positive feedback cycle, can be generalized to ldquocritical subnetworksrdquo that can contai...
Article
We show that solutions of a mass action chemical kinetics reaction–diffusion system are nonnegative. Conditions for components of the solution to be strictly positive or identically zero are given, based on an indexing procedure due to A. I. Volpert [Mat. Sb. (Russian) 88, 578–588 (1972); Math. USSR Sb. (English) 17, 571–582]. The results are illus...
Article
Full-text available
A chemical mechanism is a model of a chemical reaction network consisting of a set of elementary reactions that express how molecules react with each other. In classical mass-action kinetics, a mechanism implies a set of ordinary differential equations (ODEs) which govern the time evolution of the concentrations. In this article, ODE models of chem...
Article
Full-text available
Delay-differential equations are commonly used to model genetic regulatory systems with the delays representing transcription and translation times. Equations with delayed terms can also be used to represent other types of chemical processes. Here we analyze delayed mass-action systems, i.e. systems in which the rates of reaction are given by mass-...
Article
Full-text available
We show that solutions of a mass action chemical kinetics reaction–diffu-sion system are nonnegative. Conditions for components of the solution to be strictly positive or identically zero are given, based on an indexing procedure due to A. I. Vol-pert [Mat. Sb. (Russian) 88, 578–588 (1972); Math. USSR Sb. (English) 17, 571–582]. The results are ill...
Article
Full-text available
The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Mo...
Article
Full-text available
Results on stability of two types of chemical reactions, one represented by an acyclic graph and the other as a reversible reaction have been extended to the case of reaction–diffusion systems. Lyapunov functions are used as the major method for showing asymptotic stability of spatially homogeneous equilibria. Some examples are considered for illus...
Article
Conditions on the Jacobian of the reaction term and the diffusion matrix are described such that the difference of solutions of a reaction-diffusion system remains in a cone if the corresponding difference of initial and boundary conditions is in the same cone. A further condition on the Jacobian implies that the difference of solutions stays in th...
Article
Full-text available
Conditions on the Jacobian of the reaction term and the diffusion matrix are described such that the difference of solutions of a reaction-diffusion system remains in a cone if the corresponding difference of initial and boundary conditions is in the same cone. A further condition on the Jacobian implies that the difference of solutions stays in th...
Article
Full-text available
We represent interactions among biochemical species using a directed multigraph, which is a generalization of a more commonly used digraph. We show that network properties that are known to lead to multistability or oscillations, such as the existence of a positive feedback cycle, can be generalized to Bcritical subnetworks( that can contain severa...

Projects

Projects (2)
Project
Delays often appear in coarse-grained models of gene expression, typically to represent transcription and translation times. One of the key areas of my research program is to provide tools for the analysis of systems with delays.
Project
Algebraic methods for stability analysis can be difficult to apply for systems of even modest dimension. Graphical methods can sometimes help us prove that a model is incapable of certain behaviours (oscillations, multistability, Turing patterns), or conversely to rapidly identify regimes in which these behaviours are likely to be found.