Collaborative Project: Analysis of Pattern Formation in Drosophila by Importance Sampling on Parallel Processors

邓9727177 调查员与约翰雷尼茨的山。西奈医学院和他们的同事研究了大规模优化方法，应用于果蝇基因网络和模式形成的问题。 这些优化问题出现在一种被称为“基因电路”的方法中，该方法是由一位主要研究人员和他的同事开发的。 该方法的本质是一组非线性常微分方程的数值反演，通过最小二乘拟合方程的轨迹到通过荧光显微镜获得的基因表达数据。 在过去，这些拟合是在Lam冷却时间表的控制下使用大都会算法在串行计算机上通过模拟退火来执行的。 它们是计算密集型的，并且可以考虑的问题的范围受到可用串行处理器的速度的限制。 研究人员正在开发新的计算方法来解决这些问题的并行处理器。 重要性抽样是最有效的，或最重要的，成分的算法在处理复杂的连续优化问题，如模式形成分析在这里进行。 模拟退火是重要性抽样的一种方法，研究人员正在开发一种通用的方法来并行模拟退火不可分离的问题。 其他重要性抽样方法来自于利用手头问题的连续属性的方法，例如牛顿方法。 研究人员开发了一系列平行的重要性抽样方法，然后协同联合收割机。 这一系列的方法包括遗传算法，连续方法，拉格朗日重新制定的拟合问题，和模拟退火。 相互作用的基因网络是生物学家和生物技术学家在21世纪面临的核心问题。 从胚胎发育到细胞分裂和细胞死亡的过程都是由基因网络控制的。 为了理解这些网络是如何工作的，有必要了解它们的内部“接线图”。 尤其重要的是，要知道基因是如何相互开启和关闭的。 现代分子生物学使研究人员能够看到在特定时刻哪些基因处于开启或关闭状态，但为了了解基因之间的“接线”，必须分析基因活性随时间的变化，并通过计算机进行分析。 分析的方法可以简化为一个“优化”问题，其中寻求一个复杂函数的最小值。 在这个项目中，研究人员正在寻找新的方法来解决大规模并行高性能计算机上的优化问题。 特别强调的是放在模拟退火，一个非常强大的优化方法的并行方法。 这项研究对基因网络以外的许多领域都很重要。 模拟退火和相关方法用于结构生物学和与药物发现相关的其他生物技术领域。 它也用于集成电路的设计。 这些领域和其他领域可能会从这项工作中受益。 该项目的资金由MPS的计算数学计划和多学科活动办公室以及BIO的发育生物学计划提供。

Deng 9727177 The investigator with John Reinitz of Mt. Sinai School of Medicine and their colleagues study large scale optimization methods applied to problems concerning gene networks and pattern formation in the fruit fly Drosophila. These optimization problems arise in a method known as "gene circuits", which was developed by one of the principal investigators and his coworkers. The essence of this method is the numerical inversion of a set of nonlinear ordinary differential equations by least squares fits of the trajectories of the equations to gene expression data obtained by fluorescence microscopy. In the past, these fits were performed by simulated annealing on serial computers using the Metropolis algorithm under the control of the Lam cooling schedule. They are computationally intensive, and the range of problems that can be considered was limited by the speed of available serial processors. The investigators are developing new computational methods for the solution of these problems on parallel processors. Importance sampling is the most efficient, or the most important, ingredient of an algorithm in treating complex continuum optimization problems such as the pattern formation analysis undertaken here. Simulated annealing is one method for importance sampling; the investigators are developing a general method for parallel simulated annealing on nonseparable problems. Other importance sampling methods are derived from methods that make use of the continuum properties of the problem at hand, such as Newton's method. The investigators develop a family of parallel importance sampling methods and then synergistically combine them. This family of methods includes genetic algorithms, continuum methods, a Lagrangian reformulation of the fitting problem, and simulated annealing. Networks of interacting genes lie at the heart of the problems that will face biologists and biotechnologists in the twenty first century. Processes ranging from e mbryonic development to cell division and cell death are controlled by networks of genes. In order to understand how these networks work, it is necessary to understand their internal "wiring diagrams". In particular, it is important to know how genes turn each other on and off. Modern molecular biology allows investigators to see which genes are on or off at a given moment, but in order to understand the "wiring" between genes, it is necessary to analyze changes in gene activity over time and analyze them by computer. The method of analysis can be reduced to an "optimization" problem, in which the smallest value of a complicated function is sought. In this project, the investigators are finding new ways to solve optimization problems on large scale parallel high-performance computers. Particular emphasis is placed on parallel methods for simulated annealing, an exceptionally powerful optimization method. This research is important to many areas beyond gene networks. Simulated annealing and related methods are used in structural biology and other biotechnology areas related to drug discovery. It is also used in the design of integrated circuits. These and other areas are likely to benefit from this work. Funding for the project is provided by the program of Computational Mathematics and the Office of Multidisciplinary Activities in MPS and by the Developmental Biology program in BIO.