Two-dimensional Cell Motility Model

许多动物细胞具有在表面上长距离爬行或滑行的能力。几十年来，科学家们一直试图了解这种运动的机制。这一点很重要，因为细胞运动是许多重要生物过程的基础，如胚胎的形成和发育、伤口愈合和免疫系统的正常功能。研究者和他的同事们根据公认的物理和生物学原理建立了一个细胞运动的数学模型。有了这样一个模型，就可以对正在建模的细胞运动的任何特定方面进行可测试的预测。人们还可以通过改变模型中适当的参数来检查细胞运动的每个子过程的贡献，这是不可能通过实验做到的。一个好的数学模型可以帮助细胞生物学家更好地理解细胞运动的原理，这将反过来帮助医生和医学领域的人们改善他们对某些疾病的治疗。现有的细胞运动模型要么是一维的，这意味着它们只关注细胞中间的垂直带，要么是空间离散的模型。一维模型是不够的，因为细胞只能有长度而不能有形状。我们还知道，某些交联形成细胞骨架的蛋白丝负责细胞运动，它们在细胞的不同部位定向不同。由于涉及到大量的方程，空间离散模型很难用数学方法进行分析。研究者和他的同事开发的模型是一个二维连续体模型，需要更复杂的分析和计算技术。研究方法包括生物实验来确定细胞边界的运动，利用力学原理建立数学模型，对所得方程进行分析和数值研究，并对分析、数值和实验结果进行比较和协调。

Many animal cells have the ability to crawl or glide overlong distance on a surface. For decades, scientists have beentrying to understand the mechanics of such movement. This isimportant because cell movement is fundamental to many importantbiological processes such as the formation and development of anembryo, wound healing, and proper functioning of the immunesystem. The investigator and colleagues develop a mathematicalmodel of cell movement based on well established physical andbiological principles. With such a model, testable predictionabout any particular aspect of cell movement that is beingmodeled can be made. One can also examine the contribution ofeach sub-process of cell movement by altering the appropriateparameters in the model, something which is not possible to do byexperiments. A good mathematical model can help cell biologistsbetter understand the principles of cell movement which will inturn help doctors and people in the medical field improve theirtreatment of certain types of diseases. Existing models of cell motility are either one-dimensional,meaning that they only focus on a vertical strip in the middle ofthe cell, or they are spatially discrete models. Aone-dimensional model is inadequate because the cell can onlyhave length but no shape. It is also known that certain proteinfilaments, which are cross-linked to form the cytoskeleton of thecell that is responsible for cell movement, are orienteddifferently at different parts of the cell. A spatially discretemodel is difficult to analyze mathematically because of the largenumber of equations involved. The model the investigator and hiscolleagues develop is a two-dimensional continuum model thatrequires more sophisticated analytical and computationaltechniques. Methods of study involve biological experiments todetermine the movement of cell boundary, development of themathematical model using mechanics principles, analytical andnumerical studies of the resulting equations, and comparisons andreconciliations of the analytical, numerical and experimentalresults.