Develop new mathematical and computational tools for modeling

数学和计算工具（聂青，主题负责人） 在主题A-C中处理的过程和相互作用都是时空动态的，通常是多尺度的，并且可能受到大的随机效应的影响。这种系统的定量数学和计算分析面临着巨大的挑战，至少使用传统的方法。例如，模型探索所需的大参数空间的有效探索受到快速、准确模拟方法的缺陷的阻碍。在Aim Dia中，我们建议开发新的稳态快速方法 连续模型，涉及多个空间尺度;在目标DiB，我们提出了一个方便和强大的计算框架，一个新的有效算法，用于解决系统，涉及时间演变的空间域-一种类型的连续模型，特别是相关的组织生长（例如，在主题B）时空随机效应提出了特殊的挑战。虽然非空间随机建模和模拟提供了许多最近的见解生化反应，空间随机方法需要 更进一步的发展。在Aim D2a中，我们提出了一种新的混合空间模型和算法，将连续随机偏微分方程与离散随机反应扩散过程耦合;在Aim D2b中，我们提出了一种多尺度混合模型和算法，该模型和算法考虑了单个细胞，形态发生素的连续描述，细胞内调控网络和可能的机械效应。在Aim D2a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”生物网络的拓扑结构和参数。定义复杂的基因调控网络对于理解驱动空间现象（如模式和形态发生）的系统尤为重要。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完成的，而不是连续的空间信息。我们建议开始解决这一缺陷，在目标D3中开始制定方法， 从时空数据推断时空模型。这种方法首先开发正则化框架，以将不同类型的数据纳入推理算法，并继续开发在网络推理中使用成像数据的方法。 我们在开发计算工具的主要目标之一是鲁棒性。为了满足大规模模型探索的需要，我们必须创建在大范围的参数空间、初始和/或边界条件以及模型架构上工作良好的方法。 虽然我们总是可以期望在计算鲁棒性和速度之间进行权衡，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.