标题： 结构化Fisher方程的研究及其在生物化学中的应用 显示英文标题

标题： Investigation of a Structured Fisher's Equation with Applications in Biochemistry

摘要： 近期的生物研究致力于理解生化信号通路（如丝裂原活化蛋白激酶（MAPK）家族）如何影响伤口愈合过程中细胞群体的迁移。 由于Fisher方程具有简单的性质和已知的行波解，因此广泛用于建模实验性伤口愈合测定。 然而，这个以时间和空间为独立变量的部分微分方程无法解释生化活动对伤口愈合的影响。 为此，我们推导了一个以时间、空间和生化通路活性水平为独立变量的结构化Fisher方程，并证明了该方程存在自相似行波解。 我们还考虑了一个基于MAPK激活的不同表型的更复杂模型，并数值探讨了不同的生化活动时间模式如何导致群体迁移速度的增加和减少。 显示英文摘要

摘要： Recent biological research has sought to understand how biochemical signaling pathways, such as the mitogen-activated protein kinase (MAPK) family, influence the migration of a population of cells during wound healing. Fisher's Equation has been used extensively to model experimental wound healing assays due to its simple nature and known traveling wave solutions. This partial differential equation with independent variables of time and space cannot account for the effects of biochemical activity on wound healing, however. To this end, we derive a structured Fisher's Equation with independent variables of time, space, and biochemical pathway activity level and prove the existence of a self-similar traveling wave solution to this equation. We also consider a more complicated model with different phenotypes based on MAPK activation and numerically investigate how various temporal patterns of biochemical activity can lead to increased and decreased rates of population migration.