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Cross-disciplinary investigation of pattern formation in Zebrafish using spatially extended mathematical models with volume exclusion

使用具有体积排除的空间扩展数学模型对斑马鱼图案形成进行跨学科研究

基本信息

批准号：
1864779
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：
2016
资助国家：
英国
起止时间：
2016 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=studentship-1864779
关键词：
Cross disciplinary investigation pattern formation

项目摘要

Considerable theoretical and experimental investigations-have prompted hypotheses that a Turing-type reaction-diffusion mechanism may be responsible for the striped pigment pattern of zebrafish. However, recent experimental studies suggest that the mechanism uses cell-cell interactions, rather than the classic pre-pattern- generating pair of interacting, diffusible ligands.Indeed, Yamanaka and Kondo (2014) have suggested that the asymmetric interactions and differential movement rates of xanthophores and melanophores - leading to escape-pursuit behaviour - can induce pattern formation. Recently a third cell type - iridophores - have also been suggested as critically important for zebrafish pattern formation. Finally, we have identified Agouti Signalling Peptide (ASIP) as a further patterning component, likely acting in parallel to the stripe-forming mechanism.Mathematical modelling has played an important role in the elucidation of zebrafish striping mechanisms. The framework typically employed to represent this phenomenon utilises deterministic continuum partial differential equations (PDEs). These two-species PDE-based models fail to capture the underlying biology appropriately for four main reasons: (i) they do not account for the fluctuations inherent in biological systems; (ii) finite cell size effects are neglected; the crucial role of (iii) iridophores and (iv) ASIP signalling are ignored.The central goal of this project is to generate a framework to investigate the effects of stochasticity and finite cell size upon pattern formation models which include iridophores and ASIP signalling, and to apply it to the study of zebrafish skin patterning.I will construct an on-lattice exclusion-process model in which cells interact with neighbours, and move to neighbouring lattice sites. A detailed investigation of the relationship between key length scales in the model, the system size and compartment size, and their impact on the patterns formed, will be carried out. Subsequently hypotheses on pigment cell interactions will be explicitly encoded in this framework to explore the potential of the model to replicate the patterns on both wild-type and mutant fish.These theoretical studies will alternate with experimental investigations. Guided by the modelling outputs, I will generate data to test the models efficacy. Data will be obtained from the literature and guided experimental studies for which our ongoing collaboration with Rotllant and Cerda-Reverter will be invaluable. Experimental studies will involve direct quantitative measurements of important properties of the pigment cell pattern, e.g. perhaps including dynamic cell-cell distances and density; pair correlation functions; gene expression (e.g. using qRT-PCR on skin samples); and RT-PCR comparing skin samples at different stages.

相当多的理论和实验研究，促使假设图灵型反应扩散机制可能是负责条纹色素模式的斑马鱼。然而，最近的实验研究表明，该机制使用细胞间的相互作用，而不是经典的预模式生成对相互作用，可扩散的配体。事实上，Yamanaka和Kondo（2014）已经提出，不对称的相互作用和不同的运动速率的黄色素细胞和黑色素细胞-导致逃避-追求行为-可以诱导模式的形成。最近，第三种细胞类型-虹膜细胞-也被认为对斑马鱼模式的形成至关重要。最后，我们已经确定Agglutinase信号肽（ASIP）作为进一步的图案化组件，可能在平行的条纹形成mechanism.Mathematical建模发挥了重要作用，在阐明斑马鱼条纹机制。通常用于表示这种现象的框架利用确定性连续偏微分方程（PDE）。这些基于两种群偏微分方程的模型未能恰当地捕捉潜在的生物学，主要有四个原因：（i）它们没有考虑生物系统中固有的波动;（ii）有限细胞尺寸效应被忽略;（iii）虹膜载体和（iv）的关键作用ASIP信号被忽略。这个项目的中心目标是产生一个框架来研究随机性和有限细胞大小的影响模式形成模型，其中包括iridophores和ASIP信号，并将其应用到斑马鱼皮肤patterning的研究。我将构建一个晶格上的排斥过程模型，其中细胞与邻居相互作用，并移动到相邻的晶格网站。将对模型中的关键长度尺度、系统大小和隔室大小之间的关系及其对形成的模式的影响进行详细调查。随后，色素细胞相互作用的假设将明确编码在这个框架中，以探索模型的潜力，复制模式的野生型和突变鱼。这些理论研究将与实验研究交替进行。在建模输出的指导下，我将生成数据来测试模型的有效性。数据将从文献和指导性实验研究中获得，我们与Rotllant和Cerda-Reverter的持续合作将是非常宝贵的。实验研究将涉及色素细胞模式的重要特性的直接定量测量，例如可能包括动态细胞-细胞距离和密度;配对相关函数;基因表达（例如在皮肤样品上使用qRT-PCR）;以及RT-PCR比较不同阶段的皮肤样品。