Dynamics of genetic, biochemical and analog electronic networks

同时测量细胞中许多基因的表达和许多蛋白质的浓度的技术(基因组学和蛋白质组学)的发展导致了大量的数据，但也非常需要基因调控和细胞生物化学的系统理论来提供一个框架来理解表达和蛋白质活性的动态。参数(如反应速率和降解速率)通常是不精确的，确定它们的实验可能是困难和昂贵的，所以事实证明，开发不包括所有生理细节但保留相互作用结构的定性数学模型是有用的。其中一种方法使用分段线性微分方程，其中相互作用项被粗略地建模为阶跃函数。这些“玻璃网络”允许进行大量的分析(通过将相空间划分为“盒子”)，但由于方程中的不连续性，导致了额外的数学困难，并且过于简化，无法捕捉到一些重要的生化细节。我的研究的一个主要目的是提高我们对这些网络的理解，但也要扩大它们的范围，弥合数学可控性和生物化学现实主义之间的差距。基因调控是由细胞中的蛋白质执行的，这些蛋白质本身受到外部信号的影响，通过生化反应的“路径”。我正在致力于一个大大扩展的定性框架，它应该允许对广泛的生化反应网络的行为进行基本的洞察，包括但不限于基因调控过程。另一方面，这些信号通路的更详细的数学模型可以帮助对干预措施的效果做出定量预测，我正在调查：使用“嵌合蛋白”将细胞增殖通路与细胞死亡通路联系起来，目的是杀死癌细胞；药物鸡尾酒在肿瘤中的扩散，以及它们通过触发适当的信号通路杀死肿瘤细胞的能力；以及神经组织在“支架”上的生长，最终用于修复脊髓损伤。数学技术有时适用于非常不同的领域，基因网络定性模型中使用的方程被证明是与描述模拟电子电路的方程类型相同的，这些方程被用作“真随机数生成器”(TRNG)，这在网络安全的加密系统中至关重要。黑客攻击这些TRNG的可能性需要开发更具弹性的设计，而基因网络系统中可能的混沌行为，加上所有电子电路中的固有噪声，为生产有效的新电路设计提供了极好的手段。这些分段线性方程的数学可控性允许通过巧妙的构造实现(并证明)混沌行为。

The development of technology for simultaneously measuring expression of many genes and concentrations of many proteins in cells (genomics and proteomics) has led to a profusion of data, but also a great need for a 'systems theory' of gene regulation and cell biochemistry to provide a framework for understanding dynamics of expression and protein activity. Parameters (such as reaction rates and degradation rates) are typically not known with any precision, and experiments to pin them down can be difficult and expensive, so it has proven useful to develop qualitative mathematical models that do not include all physiological details, but retain interaction structure. One such approach uses piecewise-linear differential equations in which interaction terms are modelled crudely as step functions. These 'Glass networks' allow a considerable amount of analysis (by a division of phase space into 'boxes'), but lead to additional mathematical difficulties because of the discontinuities in the equations, and simplify things too much to catch some important biochemical details. One main thrust of my research is to improve our understanding of these networks, but also to expand their scope, to bridge the gap between mathematical tractability and biochemical realism. Gene regulation is carried out by proteins in cells, which are themselves influenced by external signals via 'pathways' of biochemical reactions. I am working on a much-expanded qualitative framework that should allow fundamental insights into the behaviour of a wide range of biochemical reaction networks, including but not limited to gene regulation processes. On the other hand, more detailed mathematical models of these signalling pathways can help to make quantitative predictions about effects of interventions, and I am investigating: the use of 'chimeric proteins' to link cell proliferation pathways to cell death pathways, with the aim of killing cancer cells; the diffusion of drug cocktails through tumours and their ability to kill tumour cells by triggering appropriate signalling pathways; and the growth of neural tissue on 'scaffolds,' ultimately for use in repairing spinal chord injuries. Mathematical techniques sometimes apply in very different fields, and the equations used in qualitative models of gene networks turn out to be of the same type as the equations that describe analog electronic circuits used as 'true random number generators' (TRNGs), crucial in encryption systems for cyber security. The possibility of hacking these TRNGs necessitates development of more resilient designs, and the chaotic behaviour possible in the gene network systems, combined with intrinsic noise in all electronic circuits, provides an excellent means to produce effective new circuit designs. The mathematical tractability of these piecewise-linear equations allows chaotic behaviour to be achieved (and proved) by clever construction.