Dynamics of genetic, biochemical and analog electronic networks

遗传、生化和模拟电子网络的动力学

• 批准号: RGPIN-2017-04042
• 负责人: Edwards, Roderick
• 金额: $ 2.19万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758955
• 关键词: Dynamics; genetic; biochemical; analog; electronic

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.

用于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”，以提供理解表达和蛋白质活性的动态的框架。参数（如反应速率和降解速率）通常不知道任何精确度，实验来确定它们可能是困难和昂贵的，所以它已被证明是有用的开发定性数学模型，不包括所有的生理细节，但保留相互作用的结构。一种这样的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额外的数学困难，并且简化了太多的事情，无法捕捉一些重要的生物化学细节。我的研究的一个主要目的是提高我们对这些网络的理解，同时也扩大它们的范围，弥合数学可处理性和生物化学现实性之间的差距。基因调控由细胞中的蛋白质进行，这些蛋白质本身通过生化反应的“途径”受到外部信号的影响。我正在研究一个大大扩展的定性框架，该框架应该允许对广泛的生化反应网络的行为进行基本的了解，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进行定量预测，我正在研究：使用“嵌合蛋白”将细胞增殖途径与细胞死亡途径联系起来，目的是杀死癌细胞;药物鸡尾酒通过肿瘤的扩散及其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与描述用作“真随机数发生器”（TRNG）的模拟电子电路的方程是同一类型的，这在网络安全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与所有电子电路中的固有噪声相结合，为产生有效的新电路设计提供了一种极好的手段。这些分段线性方程的数学易处理性允许通过巧妙的构造实现（并证明）混沌行为。