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

大量的理论和实验研究提出了一种假设，即图灵型反应扩散机制可能是斑马鱼条纹色素图案的原因。然而，最近的实验研究表明，这种机制使用细胞-细胞相互作用，而不是经典的模式生成前相互作用的扩散配体对。事实上，Yamanaka和Kondo（2014）已经提出，黄细胞和黑细胞的不对称相互作用和不同的运动速率——导致逃避-追求行为——可以诱导模式形成。最近，第三种细胞类型——虹膜细胞——也被认为对斑马鱼的图案形成至关重要。最后，我们确定了Agouti信号肽（ASIP）作为进一步的模式组件，可能与条纹形成机制并行作用。数学建模在阐明斑马鱼条纹机制方面发挥了重要作用。通常用来表示这种现象的框架是利用确定性连续体偏微分方程（PDEs）。这些基于两种偏微分方程的模型未能适当地捕捉到潜在的生物学，主要有四个原因：(i)它们没有考虑到生物系统固有的波动；（ii）忽略有限单元尺寸效应；（iii）虹膜团和（iv） ASIP信号的关键作用被忽视了。该项目的中心目标是生成一个框架来研究随机性和有限细胞大小对图案形成模型的影响，包括虹膜团和ASIP信号，并将其应用于斑马鱼皮肤图案的研究。我将构建一个晶格上排斥过程模型，其中细胞与邻居相互作用，并移动到邻近的晶格位置。将详细研究模型中关键长度尺度、系统大小和隔室大小之间的关系，以及它们对形成的模式的影响。随后，关于色素细胞相互作用的假设将在该框架中明确编码，以探索该模型在野生型和突变型鱼身上复制模式的潜力。这些理论研究将与实验研究交替进行。在模型输出的指导下，我将生成数据来检验模型的有效性。数据将从文献和指导实验研究中获得，我们与Rotllant和Cerda-Reverter的持续合作将是非常宝贵的。实验研究将涉及对色素细胞模式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；对相关函数；基因表达（如对皮肤样本使用qRT-PCR）；和RT-PCR比较不同阶段的皮肤样本。

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.