Computational methods for stochastic models of biochemical reaction systems

该研究项目的目标是开发和分析下一代生物化学模型的随机模拟方法。 这些模型包括基因调控网络、神经网络以及病毒感染和生长的模型。 具体而言，两个主要的研究课题被认为是有效的计算的期望和有效的计算参数的敏感性。 该项目的数学重点将是蒙特卡罗估计的发展是公正的，但数量级更有效的比目前的最先进的状态。为了实现这样的效率，新颖的耦合程序，有时结合使用的多层次蒙特卡罗框架，将在两个项目领域。 部分由于新技术的出现，特别是荧光蛋白，现在有大量文献表明，分子相互作用的有效随机性所产生的波动可能会产生重大后果，包括表型结果的随机化和非遗传群体异质性。 在这种情况下，随机模型，结合分析和计算工具，是必不可少的，如果他们要很好地理解。 本计画所要解决的问题，往往是系统生物学计算实验的瓶颈。 因此，该研究将使许多超出现有技术范围的逼真建模和仿真场景成为可能。 由于相关模型包括基因网络和病毒生长的模型，该项目通过大大提高这些模型的预测能力，在改善长期人类健康方面发挥作用。

The objective of this research project is to develop and analyze next generation stochastic simulation methods for the models found in biochemistry. Such models include gene regulatory networks, neural networks, and models of viral infection and growth. Specifically, the two main research topics considered are the efficient computation of expectations and the efficient computation of parametric sensitivities. The mathematical focus of the project will the development of Monte Carlo estimators that are unbiased, yet orders of magnitude more efficient than the current state of the art. To achieve such efficiency, novel coupling procedures, sometimes used in conjunction with the multi-level Monte Carlo framework, will be employed in both project areas. Due in part to the appearance of new technologies, most notably fluorescent proteins, there is now a large literature demonstrating that the fluctuations arising from the effective randomness of molecular interactions can have significant consequences, including a randomization of phenotypic outcomes and non-genetic population heterogeneity. In such cases, stochastic models, combined with both analytical and computational tools, are essential if they are to be well understood. The problems that will be addressed in this project often form the bottleneck in computational experiments in systems biology. Hence, the research will make possible many realistic modeling and simulation scenarios that are beyond the range of existing techniques. As the relevant models include those for both gene networks and viral growth, this project plays a role in improving long-term human health by greatly improving the predictive power of such models.