Develop new mathematical and computational tools for modeling

数学和计算工具(聂青青，主题领袖) 主题A-C中涉及的过程和相互作用都是时空动态的，通常是多尺度的，并可能受到大的随机效应的影响。这类系统的定量数学和计算分析面临着巨大的挑战，至少使用传统方法是如此。例如，由于快速、准确的模拟方法的不足，阻碍了对模型探索所需的大参数空间的有效探索。针对这一问题，我们提出了一种新的快速稳态算法。 连续介质模型涉及多个空间尺度；在Aim DIB中，我们提出了一个方便和健壮的计算框架和一个新的高效算法来求解涉及时间演化空间域的系统--一种特别与组织生长相关的连续介质模型(例如在主题B中)时空随机效应带来了特殊的挑战。虽然非空间随机建模和模拟提供了许多关于生化反应的最新见解，但空间随机方法需要 更进一步的发展。在目标D2a中，我们提出了一个新的混合空间模型和算法，它将连续随机偏微分方程和离散随机反应扩散过程耦合起来；在目标D2B中，我们提出了一个多尺度混合模型和算法，该模型和算法考虑了单个细胞、形态原的连续描述、细胞内调节网络和可能的机械效应。在AIM D2B中开发的工具可以应用于AIM D2B中的混合方法。这些建模框架将 帮助主题A-C中的项目比目前可能的更自由、更有效地探索随机效应。 系统生物学的一个共同目标是使用大型生物数据集来“学习”生物网络的拓扑和参数。定义复杂的基因调控网络对于理解驱动空间现象的系统尤其重要，例如图案化和形态发生。然而，目前大多数网络推理都是使用扰动序列或时间序列数据进行的，而不是使用连续的空间信息。我们建议通过在目标D3中开始开发方法来开始解决这一不足之处 从时空数据推断时空模型。这种方法从开发正则化框架开始，以使不同类型的数据能够合并到推理算法中，并继续开发在网络推理中使用成像数据的方法。 我们开发计算工具的主要目标之一是健壮性。为了满足本提案中的生物学种类所需的大规模模型探索的需要，我们必须创建能够在大范围的参数空间、初始和/或边界条件以及模型体系结构中工作的方法。 尽管我们总是可以期待计算稳健性和速度之间的权衡，但需要对单个模型的细节进行最小微调的计算框架可能对本提案中的工作以及整个系统生物学社区更有用。

MATHEMATICAL AND COMPUTATIONAL TOOLS (Qing Nie, Theme Leader) The processes and interactions dealt with in Themes A-C are all spatiotemporally dynamic, typically multiscale, and potentially subject to large stochastic effects. Quantitative mathematical and computational analysis of such systems faces substantial challenges, at least using conventional methods. For example, the efficient exploration of large parameter spaces¿necessary for model exploration¿is hindered by deficiencies in methods for fast, accurate simulation. In Aim Dia, we propose to develop new fast methods for steady state continuum models that involve multiple spatial scales; In Aim Dib, we propose a convenient and robust computational framework with a new efficient algorithm for solving systems involving temporally evolving spatial domains - a type of continuum model especially relevant to tissue growth (e.g. in Theme B) Spatiotemporal stochastic effects pose special challenges. While non-spatial stochastic modeling and simulation has provided many recent insights into biochemical reactions, spatial stochastic methods need much further development. In Aim D2a, we propose a new hybrid spatial model and algorithm that couples continuum stochastic partial differential equations with discrete stochastic reaction-diffusion processes; In Aim D2b, we propose a multi-scale hybrid model and algorithm that accounts for individual cells, continuum descriptions of morphogens, intracellular regulatory networks, and possible mechanical effects. The tools developed in Aim D2a can be applied to the hybrid approach in Aim D2b. These modeling frameworks will help projects in Themes A-C explore stochastic effects more freely and efficiently than is currently possible. A common goal in Systems Biology is to use large biological data sets to "learn" the topology and parameters of biological networks. Defining complex gene regulatory networks is particularly important for understanding systems that drive spatial phenomena, such as patterning and morphogenesis. Yet, currently, most network inference is done using perturbation-series, or time-series data, but not continuous spatial information. We propose to begin to address this deficiency by starting to develop, in Aim D3, methods for inferring spatiotemporal models from spatiotemporal data. This approach begins with the development of a regularization framework to enable incorporation of different kinds of data into inference algorithms, and continues with development of approaches to use imaging data in network inference. One of our major goals in the development of computational tools is robustness. To meet the need for large scale model exploration that the kinds of biology in this proposal require, we must create methods that workwell over large ranges of parameter space, initial and/or boundary conditions, and model architecture. Although we can always expect trade-offs between computafional robustness and speed, computational frameworks that require minimal fine-tuning to the specifics of individual models are likely to be much more useful to the work in this proposal, and to the Systems Biology community in general.