Multiscale modelling of cellular oscillators: applications to vertebrate segmentation and hair follicle cycling.

近年来在遗传和分子生物学方面取得的巨大进展已经导致了对许多不同空间和时间尺度上出现的许多复杂过程的详细描述。这种前所未有的数据洪流可能使我们能够很好地了解基因和蛋白质如何在细胞中共同工作，并由此了解多细胞生物是如何发展的。然而，其中存在着现代科学的一个巨大挑战：我们的知识往往停留在孤立的小口袋里，缺乏一个将碎片化的数据联系在一起的概念框架，无法产生和检验各种想法和假设。这就是数学建模和数值模拟可以发挥基本作用的地方，可以与任何研究工具相媲美；它们允许我们将多个非线性过程的影响组合成一个连贯的结构，可以用于生成假设和实验可测试的预测。我们特别感兴趣的是建模两种范例系统的生物振荡器：一个分子钟参与分割的头尾轴的脊椎动物胚胎和毛囊周期。体发育是指脊椎动物胚胎的头尾轴被分割成被称为体的重复单元，导致椎骨、肋骨和相关肌肉组织的前体形成。体体由紧密结合的细胞块组成，脊髓两侧各有一个，它们以严格的时空顺序形成：从头到尾，在明确的时间间隔内。在被并入体之前，位于头尾轴上的细胞在许多基因产物中表现出振荡。这些振荡通过细胞间的信号传导同步，导致基因表达的移动带从尾部开始，在新形成的体体中稳定下来。细胞-细胞信号的破坏导致以畸形肋骨和椎骨为特征的节段性缺陷。许多哺乳动物的皮肤上覆盖着毛囊，每个毛囊都在进行再生循环。这种循环的原因有很多：允许扩张和生长，控制头发的长度，适应不断变化的环境和社会条件，防止与快速分裂的组织相关的恶性变性。每个毛囊都要经历一系列的阶段，每个周期阶段之间的转变取决于毛囊向当地环境中分泌的化学物质。许多头发生长缺陷的特征是通过卵泡周期的不正确的进展速度，并引起脱发等疾病。该项目的主要目的是开发新的数学和计算技术，以便对先前描述的振荡生物元件系统进行建模。我们将假设每个单独的元素可以显示持续或可激发的振荡（需要一个超阈值刺激才能显示振荡），并且它与该领域的其他元素相互作用。根据相互作用的水平，系统可能在组织水平上显示同步振荡。然而，这种同步可能受到干扰，例如，来自环境的外部影响或单个元件振荡频率的变化。将发展数学技术和数值模拟来描述单个振荡器的行为和它们相互作用的不同形式。这些模型将使用目前可用的生物学假设来构建，并根据实验观察进行参数化和测试。反过来，这些模型将被用来产生假设和实验可验证的预测，这将进一步加深我们对该领域的理解。

The dramatic advances made in genetic and molecular biology in recent years have resulted in detailed descriptions of a number of complex processes that arise on many different spatial and temporal scales. This unparalleled flood of data may well enable us to understand how genes and proteins work collectively in a cell and from this how multi-cellular organisms develop. However, therein lies one of the great challenges of modern science: all too often our knowledge remains in isolated pockets, lacking a conceptual framework tying the fragmented data together and allowing ideas and hypotheses to be generated and tested. This is where mathematical modelling and numerical simulation can play a fundamental role, comparable with any research tool; they allow us to combine the effects of multiple non-linear processes into a coherent structure that can be used for the generation of hypotheses and experimentally testable predictions. In particular we will be interested in modelling two paradigm systems of biological oscillators: a molecular clock involved in segmentation of the head-tail axis of vertebrate embryos and the hair follicle cycle. Somitogenesis, segmentation of the head-tail axis of vertebrate embryos into repeated units known as somites, results in formation of precursors of the vertebrae, ribs and associated musculature. The somites consist of tightly bound blocks of cells, one of each side of the spinal chord, and they form in a strict spatio-temporal order: from head to tail, at well-defined time intervals. Before becoming incorporated into somites, cells lying along the head-tail axis exhibit oscillations in a number of gene products. These oscillations are synchronised via cell-cell signalling, resulting in travelling bands of gene expression that begin in the tail and are stabilised in the newly forming somites. Disruption of cell-cell signalling results in segmental defects that are characterised by malformed ribs and vertebrae.The skin of many mammals is covered with hair follicles, each undergoing regenerative cycling. The reasons for this cycling are plentiful: to allow for expansion and growth, to control hair length, to adapt to changing environmental and social conditions and to protect against the malignant degeneration associated with rapidly dividing tissue. Each hair follicle goes through a series of stages with the transformations between cycle stages dependent on secretion, by the follicles, of chemicals into the local environment. Many hair growth defects can be characterised by incorrect rates of progression through the follicular cycle and give rise to disorders such as alopecia. The main aim of this project is to develop novel mathematical and computational techniques in order to model the systems of oscillating biological elements described previously. We will assume each individual element can display either sustained or excitable oscillations (requires a supra-threshold stimulus in order to exhibit an oscillation) and that it interacts with other elements in the field. Depending on the level of interaction the system may display synchronised oscillations on a tissue level. However, this synchronisation can be disturbed by, for example, external influence from the environment or variation in the oscillation frequency of individual elements. Mathematical techniques will be developed and numerical simulations employed to describe the behaviour of the individual oscillators and different forms for their interaction. The models will be constructed using currently available biological hypotheses, parametrised and tested against experimental observations. In turn, the models will be used to generate hypotheses and experimentally testable predictions which will further our understanding in the area.