考虑机械效应的钙信号的数学建模
Mathematical modelling of calcium signalling taking into account mechanical effects
摘要：
人体内的大部分钙都储存在骨骼中。其余的储存在其他地方，钙信号是体内信息传播的最重要机制之一。然而，许多问题仍然悬而未决。在这项工作中，我们首先考虑Atri等人提出的数学模型。\cite{ atri1993single}。省略扩散，该模型是一个系统的两个非线性常微分方程（ODE）的钙浓度，和未被钙灭活的$IP_3$受体的分数。我们详细分析了系统的$IP_3$浓度，\textit{bifurcation parameter}，增加提出了一些新的见解。我们分析渐近的弛豫振荡的模型，利用分离的时间尺度。此外，实验证据表明，细胞释放钙时，机械刺激，反过来，钙的释放会影响细胞的机械行为的动机，我们提出了一个扩展的Atri模型的三维非线性ODE机械化学模型，其中额外的方程，始终来自一个完整的粘弹性\emph{ansatz}，模型的演变细胞/组织扩张。此外，在钙动力学方程中，我们引入了一个新的“拉伸激活”源项，诱导钙释放，并涉及一个新的分叉参数，“强度”的源。改变两个分叉参数，我们详细分析了机械和化学效应的相互作用，我们发现，随着机械刺激强度的增加，出现振荡的$IP_3$参数范围减小，直到振荡最终消失在一个临界值。最后，我们分析了模型时，钙动力学假设比其他两个变量的动态更快。
英文摘要：
Most of the calcium in the body is stored in bone. The rest is stored elsewhere, and calcium signalling is one of the most important mechanisms of information propagation in the body. Yet, many questions remain open. In this work, we initially consider the mathematical model proposed in Atri et al. \cite{ atri1993single}. Omitting diffusion, the model is a system of two nonlinear ordinary differential equations (ODEs) for the calcium concentration, and the fraction of $IP_3$ receptors that have not been inactivated by the calcium. We analyse in detail the system as the $IP_3$ concentration, the \textit{bifurcation parameter}, increases presenting some new insights. We analyse asymptotically the relaxation oscillations of the model by exploiting a separation of timescales. Furthermore, motivated by experimental evidence that cells release calcium when mechanically stimulated and that, in turn, calcium release affects the mechanical behaviour of cells, we propose an extension of the Atri model to a 3D nonlinear ODE mechanochemical model, where the additional equation, derived consistently from a full viscoelastic \emph{ansatz}, models the evolution of cell/tissue dilatation. Furthermore, in the calcium dynamics equation we introduce a new "stretch-activation" source term that induces calcium release and which involves a new bifurcation parameter, the "strength" of the source. Varying the two bifurcation parameters, we analyse in detail the interplay of the mechanical and the chemical effects, and we find that as the strength of the mechanical stimulus is increased, the $IP_3$ parameter range for which oscillations emerge decreases, until oscillations eventually vanish at a critical value. Finally, we analyse the model when the calcium dynamics are assumed faster than the dynamics of the other two variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
