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。许多这样的发展是通过称为神经rest细胞的细胞的。神经rest细胞在生长胚胎的阶段的许多生物学发展中起着至关重要的作用，例如骨骼的形成，软骨和皮肤的色素沉着。表皮色素沉着是黑色素生成的产物，是通过黑素细胞实现的。黑素细胞是黑素细胞的早期原则，是产生色素的细胞，负责产生黑色素。黑素细胞在神经rest的树干区域中溶解它们，它们从中分层并沿着他们的移民途径迁移，以殖民表皮殖民。然后，他们分化为黑素细胞并开始产生梅拉素。黑素细胞的存活取决于受体试剂盒与其配体kitl之间的信号传导。套件基因中的突变会改变导致黑素细胞行为的信号传导机制，最终使表皮的不完整定植。最近的研究表明，试剂盒突变体的黑素细胞会延长细胞周期，使一部分表皮剥夺了这些产生色素的细胞。由此产生的神经疗法被称为piebaldism。一只Piebald鼠标在腹部显示一个白色斑点。其他神经rest细胞的错误行为会导致更严重的疾病，例如神经纤维瘤病和Hirschsprung氏病。LARARGER哺乳动物也表现出Piebaldism，例如我的项目将涉及使用数学模型对黑素细胞行为进行建模的项目。到目前为止，使用实验参数化的随机剂模型，我已经能够在小鼠的小鼠上复制在劳动域中的白色腹部斑点。我们还表明，改变参数值我们的模型可以产生像哺乳动物的斑块一样的图案，例如在某些牛种类中看到的哺乳动物。现在，我们想在较大的哺乳动物中沿着以下关键线板的形成扩展这项工作：尽管基于现代代理的模型似乎可以成功地将牛的补丁取代，但我们的工作缺乏数学分析，无法伴随这些结果。我们将开发数学上严格的连续模型，以伴随仿真算法，该算法将量化牛中的斑块形成。已经观察到，牛斑块在小鼠的腹部斑点上具有更清晰且定义明确的边界。我们将开发混合确定性核模型，这些模型利用Turing的扩散驱动的模式形成理论，以研究这种现象。间质真皮细胞对毛囊的局部化：间充质皮细胞在毛囊中起关键作用。为了响应某些信号通路，间充质细胞聚集并形成真皮冷凝物的周期性图案。这些冷凝水的位置标志着未来毛囊的位置。在该项目的The strand中，我们对推动这种周期性模式的机制感兴趣。我们将使用仿真模型来理解这种模式。真实的细胞周期时间分布：该博士学位期间的许多随机建模将采用Gillespiestochastic模拟算法。 Gillespie算法假设细胞周期时间是指数分布的并表现出无内存的属性。但是，众所周知，细胞循环时间并不是从现实中得出的。先前已经证明，使用ERLANG分布对小鼠某些细胞的细胞周期时间更精确。我们将开发模型，以现实地对细胞周期时间数据forelanolanoblasts进行建模。现有工作的证据表明，子细胞的细胞周期时间及其更远的亲戚之间的相关性。我们想扩展现有模型，以结合几代人之间的相关性影响