Department of Mathematics, Liaoning University, Shenyang 110036, People's Republic of China.
Phys Biol. 2011 Oct;8(5):055004. doi: 10.1088/1478-3975/8/5/055004. Epub 2011 Aug 10.
The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.
丝裂原活化蛋白激酶（MAPK）级联在细胞生长的控制中起着关键作用。该途径的失调导致许多癌症的发生。为了更好地理解其信号转导，我们构建了 MAPK 途径的反应扩散模型。我们对磷酸化-去磷酸化反应的三个层次以及从细胞膜到细胞核的扩散过程进行了建模。基于 MAPK 级联中的不同类型的反馈，引入了四种操作模式。对于这四种模式中的每一种，通过数值模拟来探索活性激酶（即 ppMAPK）的空间分布和剂量反应曲线。研究了传播长度、扩散系数和反馈强度对途径动力学的影响。我们发现，当传播长度较短时，MAPK 级联中的固有双稳性可以产生具有恒定幅度的 ppMAPK 行波。与其他所有模式相比，在这种固有双稳性模式下，ppMAPK 的衰减速度较慢，随着传播长度的增加而增加。此外，我们检查了这四种模式对 Ras-GTP 的全局和局部响应，并演示了这些剂量反应曲线的形状如何随着传播长度的增加而变化。此外，我们发现较大的扩散常数在零级时会产生更高的响应水平，并在强 Ras-GTP 刺激下使 ppMAPK 曲线变平。此外，我们观察到，在更宽的信号范围内，ppMAPK 的空间响应对负反馈比对正反馈更敏感。最后，我们展示了振荡信号如何通过激酶级联传递，并发现高频信号比低频信号衰减得更快。
