Models and Algorithms for Beta-Barrel Membrane Proteins and Stochastic Networks

总结 我们的项目解决蛋白质分子的结构和机制的基本问题 和他们的互动网络。在蛋白质水平上，我们将继续支持我们的NIGMS 研究和重点是A）桶膜蛋白（BMPs）。我们将开发模型， 计算工具，用于预测其结构，了解其机制， 新的微生物制剂的配方设计。在网络层面，我们将探索一项新的研究， 方向我们将B）通过求解离散化学方程组来开发模型和精确算法。 主方程（dCME）计算精确概率景观和离散概率 研究细胞行为的随机控制的网络通量。此外，我们将 研究表型转换是如何在网络中出现的，从通常发生的 网络图案，并全面表征其多稳定性的宇宙。 在项目A）中，我们将重点关注在革兰氏阴性菌的外膜中发现的CMPs， 真核线粒体和外毒素中。CIMPs参与基本过程， 如转运、易位、能量代谢和凋亡诱导。他们也是 重要的治疗靶点。此外，还有重要的 在开发生物纳米孔作为单分子检测的生物纳米孔方面的工程兴趣， 其他生物技术应用。尽管最近取得了一些进展，但我们对CMPs的了解仍然有限： 已知的非同源的CMPs的结构只有几十种。重要的是，我们缺乏一般 了解基层党组织的组织原则及其运行机制。我们 建议开发模型和算法，用于A1）预测CMPs的结构，A2） 破译OmpG中的门控机制，以及A3）设计具有期望的 几何形状和稳定性，以实现广泛的生物技术应用。 我们的方法将基于我们开发的简化状态模型，MHIP经验模型， 我们通过广泛的组合分析得到的势函数，（m）DiSGro环 结构预测和采样算法，具有重大的新发展。 在项目B）中，我们将着重于构造精确随机 相互作用分子网络的概率景观。许多重要的生物反应 只涉及少量的分子拷贝。这种低拷贝事件产生的随机性 以及罕见的事件对于基本过程如胚胎发育是重要的， 干细胞分化和非遗传异质性。虽然离散化学大师 方程（dCME）提供了一个生成框架，用于理解中观的随机性 制度上，许多基础性问题依然存在。尽管取得了重大进展，但确切的时间- 许多感兴趣的网络的演化概率景观在计算上是不可访问的， 除了一些简单的玩具问题（例如，具有<4个节点的问题）。一个人必须依靠吉莱斯皮 Langevin/Fokker-Planck公式的模拟或近似，误差较大 未经检查我们建议发展B1）计算概率的理论模型和工具 在任意微观状态和任意反应的离散状态空间上的通量，所以 通道、瞬态和关键路径对于表征表型 可以识别开关。我们还将进行计算分析，以破译B2） 随机切换的常见机制，以及相位的全面映射 在最常见的生物图案中出现的多稳定性的图表。 我们的方法将基于我们最近的算法和理论发展的多有限 缓冲网络结构分析，角点单纯形最优状态枚举算法， 用于精确计算时间演化概率景观的ACME方法，以及 误差界分析基于我们的商矩阵和随机排序技术。

Summary Our project address fundamental problems of structures and mechanisms of protein molecules and their interaction networks. At the protein level, we will continue our NIGMS supported studies and focus on A) -Barrel Membrane Proteins (MPs). We will develop models and computational tools for predicting their structure, understanding their mechanism, and formulating design of novel MPs. At the network level, we will explore a new research direction. We will B) develop models and exact algorithms by solving the discrete chemical master equation (dCME) to compute exact probability landscape and discrete probability flux of networks for studying stochastic control of cellular behavior. Furthermore, we will examine how phenotype switching arise in networks, starting from commonly occurring network motifs and comprehensively characterize the universe of their multistabilities. In Project A), we will focus on MPs found in the outer membrane of gram-negative bacteria, eukaryotic mitochondria, and in exotoxins. MPs are involved in fundamental processes such as transport, translocation, energy metabolism, and apoptosis induction. They are also important therapeutic targets against infectious diseases. In addition, there are significant engineering interests in developing MPs as bionanopores for single molecule detection and other biotech applications. Despite recent progress, our knowledge of MPs is limited: only a few dozens of structures of non-homologous MPs are known. Importantly, we lack general understanding of the organizing principles of MPs and their functioning mechanism. We propose to develop models and algorithms for A1) predicting structures of MPs, A2) deciphering the mechanism of gating in OmpG, and A3) designing novel MPs with desired geometry and stability towards broad biotech applications. Our approach will be based on the reduced state model we developed, the MHIP empirical potential function we obtained through extensive combinatorial analysis, the (m)DiSGro loop structure prediction and sampling algorithms, with significant new development. In Project B), we will focus on the fundamental problem of constructing exact stochastic probability landscape of networks of interacting molecules. Many important biological reactions involve only a small copy number of molecules. Stochasticity arising from such low copy events as well as rare events are important for fundamental processes such as embryonic development, stem cell differentiation and nongenetic heterogeneity. While the discrete chemical master equation (dCME) provides a generate framework for understanding stochasticity in mesocopic systems, many foundational problems remain. Despite significant progress, the exact time- evolving probability landscapes for many networks of interests are computationally inaccessible, except for a few simple toy problems (e.g. those with <4 nodes). One has to rely on Gillespie simulation or approximation of Langevin/Fokker-Planck formulations, with errors largely unexamined. We propose to develop B1) theoretical model and tools for computing probability fluxes on discrete state space at arbitrary microstate and for arbitrary reactions, so passageways, transient states, and critical paths important for characterizing phenotypical switches can be identified. We will also carried out computational analysis to decipher B2) common mechanisms of stochastic switching, as well as comprehensive mapping of phase diagrams of emerging multistabilities in the most widely encountered common biological motifs. Our approach will be based on our recent algorithm and theoretical development of multi-finite buffer network structure analysis, the corner simplex optimal state enumeration algorithm, and the ACME method for exact computation of time-evolving probability landscape, as well as error-bound analysis based our quotient matrix and the technique of stochastic ordering.