反应扩散系统中的基因表达时滞
Gene Expression Time Delays in Reaction-Diffusion Systems
摘要：
基因表达时间延迟，模拟基因转录和翻译的复杂生物过程，已被证明在细胞动力学中起着重要作用。由基因表达过程引起的时滞也会极大地影响反应扩散系统的行为。在这篇论文中，我们探讨了它们对图灵模式机制的影响。通过将时间延迟，建模为一个固定的参数和作为一个连续的分布，到经典的反应扩散系统，表现出图灵不稳定性，我们调查这些系统的变化行为。我们发现，增加时间延迟的引入增加了空间不均匀图案稳定所需的时间，并且两者线性相关。我们还提出的结果表明，通过线性稳定性分析，增加的时间延迟可以采取行动扩大或缩小图灵空间的某个反应扩散机制，这取决于时间延迟项的位置。值得注意的是，我们发现，作为一个连续分布的建模时间延迟的定性或定量方面的结果相比，一个固定的时间延迟的平均分布的影响可以忽略不计。这些发现突出了在模拟生物模式事件时考虑基因表达时间延迟的重要性，以及在试图应用图灵机制解释生物现象之前需要完全理解细胞动力学。结果还表明，至少在本论文中考虑的分布，固定延迟和分布延迟模型具有几乎相同的动态。这允许使用更简单的固定延迟模型，而不是更复杂的分布式延迟变量。
英文摘要：
Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also greatly affect the behaviour of reaction-diffusion systems. In this dissertation, we explore their effects on Turing pattern mechanisms. By incorporating time delays, modelled as both a fixed parameter and as a continuous distribution, into classical reaction-diffusion systems that exhibit Turing instabilities, we investigate the changing behaviour of these systems. We find that an introduction of increasing time delay increases the time taken for spatially inhomogeneous patterns to stabilise, and the two are related linearly. We also present results to show, through a linear stability analysis, that an increasing time delay can act both to expand or shrink the Turing space of a certain reaction-diffusion mechanism, depending on the placement of time-delayed terms. Significantly, we find that modelling time delays as a continuous distribution has a negligible impact on qualitative or quantitative aspects of the results seen compared with a fixed time delay of the mean of the distribution. These findings serve to highlight the importance of considering gene expression time delays when modelling biological patterning events, as well as requiring a complete understanding of the cellular dynamics before attempting to apply Turing mechanisms to explain biological phenomena. The results also suggest, at least for the distributions considered in this dissertation, that fixed delay and distributed delay models have almost identical dynamics. This allows one to use simpler fixed delay models rather than the more complicated distributed delay variants.
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