The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distrib...The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles,with period ε.The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem,with an extra zero-order term that captures the effect of the enzymatic reactions.展开更多
The regulatory mechanisms in cellular signaling systems have been studied intensively from the viewpoint that the malfunction of the regulation is thought to be one of the substantial causes of cancer formation. On th...The regulatory mechanisms in cellular signaling systems have been studied intensively from the viewpoint that the malfunction of the regulation is thought to be one of the substantial causes of cancer formation. On the other hand, it is rather difficult to develop the theoretical framework for investigation of the regulatory mechanisms due to their complexity and nonlinearity. In this study, more general approach is proposed for elucidation of characteristics of the stability in cellular signaling systems by construction of mathematical models for a class of cellular signaling systems and stability analysis of the models over variation of the network architectures and the parameter values. The model system is formulated as regulatory network in which every node represents a phosphorylation-dephosphorylation cyclic reaction for respective constituent enzyme. The analysis is performed for all variations of the regulatory networks comprised of two nodes with multiple feedback regulation loops. It is revealed from the analysis that the regulatory networks become mono-stable, bi-stable, tri-stable, or oscillatory and that the negative mutual feedback or positive mutual feedback is favorable for multi-stability, which is augmented by a negatively regulated node with a positive auto-regulation. Furthermore, the multi-stability or the oscillation is more likely to emerge in the case of low value of the Michaelis constant than in the case of high value, implying that the condition of higher saturation levels induces stronger nonlinearity in the networks. The analysis for the parameter regions yielding the multi-stability and the oscillation clarified that the stronger regulation shifts the systems toward multi-stability.展开更多
The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distrib...The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles,with period ε.The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem,with an extra zero-order term that captures the effect of the enzymatic reactions.展开更多
文摘The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles,with period ε.The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem,with an extra zero-order term that captures the effect of the enzymatic reactions.
文摘The regulatory mechanisms in cellular signaling systems have been studied intensively from the viewpoint that the malfunction of the regulation is thought to be one of the substantial causes of cancer formation. On the other hand, it is rather difficult to develop the theoretical framework for investigation of the regulatory mechanisms due to their complexity and nonlinearity. In this study, more general approach is proposed for elucidation of characteristics of the stability in cellular signaling systems by construction of mathematical models for a class of cellular signaling systems and stability analysis of the models over variation of the network architectures and the parameter values. The model system is formulated as regulatory network in which every node represents a phosphorylation-dephosphorylation cyclic reaction for respective constituent enzyme. The analysis is performed for all variations of the regulatory networks comprised of two nodes with multiple feedback regulation loops. It is revealed from the analysis that the regulatory networks become mono-stable, bi-stable, tri-stable, or oscillatory and that the negative mutual feedback or positive mutual feedback is favorable for multi-stability, which is augmented by a negatively regulated node with a positive auto-regulation. Furthermore, the multi-stability or the oscillation is more likely to emerge in the case of low value of the Michaelis constant than in the case of high value, implying that the condition of higher saturation levels induces stronger nonlinearity in the networks. The analysis for the parameter regions yielding the multi-stability and the oscillation clarified that the stronger regulation shifts the systems toward multi-stability.
文摘The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles,with period ε.The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem,with an extra zero-order term that captures the effect of the enzymatic reactions.
