Biomathematical analysis of cell invasion: migration of neural crest cells to form the enteric nervous system

将科学研究扩展到数学层面是产生深刻理解和控制的方法。数学应用于生物学，特别是发育生物学，不如应用于其他科学分支，无疑是因为观察和测量实际发生的事情具有先天的复杂性和技术难度。用于可视化生物过程的标记、成像和计算工具直到现在才变得可用。为了在胚胎发育期间建立我们的身体，细胞必须移动；这称为细胞迁移。在伤口修复的一生中，同样的过程也会发生。不受控制的迁移是恶性肿瘤的标志，在那里它被称为侵袭性。细胞中允许它们移动的分子机制才刚刚开始被理解。然而，决定移民一般规则的大问题更难解决。以下是这类问题的一些例子。什么时候迁移？要迁移到哪里？哪条小路？要迁移多少细胞？多远？多快？怎样才能停下来？这些简单的问题仍然没有答案。我们正在开创一种新颖而独特的方法，将真实组织中真实细胞迁移的成像(数字延时电影)与数学模型相结合，以了解细胞迁移-入侵的驱动力。这项技术被应用于细胞迁移的一个特殊例子，在细胞迁移的早期，前体神经细胞沿着胃肠道的长度迁移。这一过程会导致与迁移失败相关的致命出生缺陷。肠道神经系统的发育与所有其他迁徙和入侵具有共同的特征，无论是正常的还是病理性的。生物学实验和数学模型的结合将使人们对细胞迁移-入侵过程的发展和临床关键过程有更深刻的了解。

Extending scientific studies to a mathematical level is the way to produce deep understanding and control. Mathematics has been applied less to biology, particularly the biology of development, than to other branches of science, no doubt due to the innate complexity and technical difficulties of seeing and measuring what is actually going on. Labelling, imaging and computational tools to visualise biological processes are only now becoming available. To build our bodies during embryonic development, cells must move; this is called cell migration. The same process occurs throughout life in wound repair. Uncontrolled migration is the hallmark of malignant cancers, where it is called invasion. The molecular mechanisms in cells that allow them to move are just beginning to be understood. However, the big questions determining the general rules of migration are more difficult to approach. Here are some examples of such questions. When to migrate? Where to migrate to? Which pathways? How many cells to migrate? How far? How fast? How to stop? Such simple questions are still unanswered. We are pioneering a novel and unique approach combining imaging of real cells migrating in real tissues (digital time-lapse movies) with mathematical modelling to understand the driving forces of cell migration-invasion. This technology is here applied to a particular example of cell migration where precursor nerve cells migrate all the way along the length of the gastro-intestinal tract in early development. This process gives rise to fatal birth defects associated with migration failure. The development of the nervous system in the gut has features in common with all other migrations and invasions, normal and pathological. A much more profound knowledge of the big picture of the developmentally and clinically crucial process of cell migration-invasion will emerge from this marriage of biological experimentation and mathematical modelling.