Mathematical modelling of mammalian pigmentation patterns: Stochastic modelling of melanoblast neural crest cells.

哺乳动物色素沉着模式的数学建模：成黑细胞神经嵴细胞的随机建模。

基本信息

批准号：
2282147
负责人：
金额：
--
依托单位：
University of Bath
依托单位国家：
英国
项目类别：
Studentship
财政年份：
2019
资助国家：
英国
起止时间：
2019 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=studentship-2282147
关键词：
Mathematical modelling mammalian pigmentation patterns

项目摘要

Embryogenesis defines the early stages of embryonic development. Many such developments are attained via afamily of cells called the neural crest cells. Neural crest cells play a vital role in many biological developments in theearly stages of the growing embryo, e.g. formation of bones, cartilage & pigmentation of hair & skin.Epidermal pigmentation is a product of melanogenesis which is achieved via melanocytes. Melanoblasts, the earlyprecursors of melanocytes, are the pigment-producing cells responsible for producing melanin. Melanoblastsoriginate in the trunk region of the neural crest from which they delaminate & migrate dorsoventrally along theirmigratory pathway to colonise the developing epidermis. They then differentiate into melanocytes & start producingmelanin. Survival of melanoblasts is dependent on signalling between the receptor Kit & its ligand Kitl. Mutations inthe Kit gene can alter the signalling mechanism causing melanoblasts to behave erroneously which ultimately leadsto incomplete colonisation of the epidermis. Recent research suggests that the melanoblasts of Kit mutant miceexhibit longer cell-cycle times, leaving parts of the epidermis deprived of these pigment-producing cells. The resultingneurocristopathy is called piebaldism. A piebald mouse shows a white spot on the belly. Erroneous behaviour ofother neural crest cells leads to more serious conditions such as Neurofibromatosis & Hirschsprung's disease.Larger mammals also show piebaldism, e.g. patches of unpigmented skin in cows.My project will concern modelling melanoblast behaviour using mathematical models. So far, using experimentallyparameterised stochastic agent-based models I have been able to replicate the white belly spots in mice on agrowing domain. We also showed that varying the parameter values our model can produce patch-like patterns oflarger mammals such as those seen in some cow species. We would now like to expand on this work along the following key linesPattern formation in larger mammals: Although the on-lattice agent-based model could seemingly successfullyreplicate patches in cows, our work lacks mathematical analysis to accompany these results. We will be developing amore mathematically rigorous continuum model to accompany the simulation algorithm which will quantify the patchformation in cows. It has been observed that cow patches have sharper & well-defined boundaries in contrast tothe belly spots in mice. We will develop hybrid deterministic-continuum models which exploit Turing's theory ofdiffusion-driven pattern formation in order to investigate this phenomenon.Localisation of mesenchyme dermal cells to hair follicles: Mesenchymal dermal cells play a key role in hair folliclemorphogenesis. Responding to certain signalling pathways the mesenchymal cells aggregate & form a periodicpattern of dermal condensates. The locations of these condensates mark the positions of future hair follicles. In thisstrand of the project, we are interested in the mechanisms which drive this periodic pattern. We will use simulationmodels to understand this patterning.Realistic cell-cycle time distribution: Much of the stochastic modelling during this PhD will employ the GillespieStochastic Simulation Algorithm. The Gillespie algorithm assumes that cell-cycle times are exponentially distributed& exhibit the memoryless property. However, it is well-known that cells-cycle times are not drawn from thisdistribution in reality. It has been shown previously that cell-cycle times of certain cells in mice are more accuratelymodelled using an Erlang distribution. We will be developing models to realistically model cell-cycle time data formelanoblasts. Evidence from existing work suggests correlations between cell cycle times of daughter cells & theirmore distant relatives. We would like to expand on the existing models to incorporate the effects of correlationbetween generations of

胚胎发生定义了胚胎发育的早期阶段。许多这样的发育是通过称为神经嵴细胞的细胞家族实现的。神经嵴细胞在胚胎生长早期阶段的许多生物发育中发挥着至关重要的作用，例如胚胎发育。骨骼、软骨的形成以及头发和皮肤的色素沉着。表皮色素沉着是通过黑素细胞实现的黑素生成的产物。黑素细胞是黑素细胞的早期前体，是负责产生黑色素的色素产生细胞。黑色素母细胞起源于神经嵴的躯干区域，它们从神经嵴的躯干区域分层并沿着其迁移路径向背腹迁移，以定殖发育中的表皮。然后它们分化成黑色素细胞并开始产生黑色素。成黑细胞的存活依赖于受体Kit与其配体Kit1之间的信号传导。 Kit基因的突变可以改变信号机制，导致成黑细胞行为错误，最终导致表皮不完全定植。最近的研究表明，Kit 突变小鼠的黑色素细胞表现出更长的细胞周期时间，导致部分表皮失去了这些产生色素的细胞。由此产生的神经脊椎病称为花斑症。花斑鼠的腹部有一个白点。其他神经嵴细胞的错误行为会导致更严重的病症，例如神经纤维瘤病和先天性巨结肠症。较大的哺乳动物也表现出花斑现象，例如花斑症。牛身上未着色的皮肤斑块。我的项目将涉及使用数学模型对黑素细胞行为进行建模。到目前为止，使用基于实验参数化随机代理的模型，我已经能够在生长区域复制小鼠的白腹部斑点。我们还表明，改变模型的参数值可以产生大型哺乳动物的斑块状图案，例如在某些奶牛物种中看到的图案。现在，我们希望沿着以下关键路线扩展这项工作：大型哺乳动物的模式形成：尽管基于格子代理的模型似乎可以成功地在牛身上复制斑块，但我们的工作缺乏数学分析来配合这些结果。我们将开发一个数学上更严格的连续体模型，以配合模拟算法，该算法将量化奶牛的斑块形成。据观察，与小鼠腹部斑点相比，牛斑块具有更清晰和明确的边界。我们将开发混合确定性连续体模型，利用图灵的扩散驱动模式形成理论来研究这一现象。间充质真皮细胞对毛囊的定位：间充质真皮细胞在毛囊形态发生中起着关键作用。响应某些信号通路，间充质细胞聚集并形成真皮凝聚物的周期性模式。这些凝结物的位置标志着未来毛囊的位置。在该项目的这一部分中，我们对驱动这种周期性模式的机制感兴趣。我们将使用模拟模型来理解这种模式。现实的细胞周期时间分布：本博士期间的大部分随机建模将采用 GillespieStochastic 模拟算法。 Gillespie 算法假设细胞周期时间呈指数分布并表现出无记忆特性。然而，众所周知，细胞周期时间实际上并不是从这种分布中得出的。先前已经表明，使用 Erlang 分布可以更准确地模拟小鼠某些细胞的细胞周期时间。我们将开发模型来真实地模拟成黑细胞的细胞周期时间数据。现有工作的证据表明子细胞及其更远亲的细胞周期时间之间存在相关性。我们希望扩展现有模型，以纳入各代之间相关性的影响