Computational methods for stochastic models of biochemical reaction systems

本研究项目的目的是为生物化学中发现的模型开发和分析下一代随机模拟方法。这些模型包括基因调控网络、神经网络和病毒感染和生长模型。具体来说，考虑的两个主要研究课题是期望的有效计算和参数灵敏度的有效计算。该项目的数学重点将是开发蒙特卡罗估计器，它是无偏的，但比目前的艺术状态更有效的数量级。为了达到这种效率，将在两个项目领域采用新颖的耦合程序，有时与多层蒙特卡罗框架结合使用。部分由于新技术的出现，尤其是荧光蛋白的出现，现在有大量文献表明，分子相互作用的有效随机性引起的波动可能产生重大后果，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，如果要很好地理解随机模型，就必须将其与分析和计算工具相结合。在这个项目中将要解决的问题往往构成了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现实建模和仿真场景成为可能。由于相关模型既包括基因网络模型，也包括病毒生长模型，本项目通过大大提高这些模型的预测能力，对改善人类的长期健康起到了作用。

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.