MODELING CORE

B2.建模核心 董事M.隐蔽和K。C.作者声明：by J. Tomlin Ariel Jaimovich（Postdoc）. Jaimovich博士是Pat Brown和Tobias Meyer实验室之间的系统工程师，他将提供建模方法的建议，并帮助协调该中心的夏季外展研讨会。 建模核心的首要目标是使用细胞系统模型作为工具来研究支持细胞集体反应的遗传和分子网络。然后可以使用化学，光或机械扰动对这些见解进行实验测试，然后尽可能通过实时单细胞显微镜和定量图像分析来评估结果。这类实验方法的动力学和定量性质都是至关重要的。该中心的教师在模拟单个细胞的反应以及将这些模型与定量实验相结合方面拥有丰富的经验和成功。下一个挑战是将单细胞模型耦合在一起，以允许分析和理解细胞的集体行为。 在单细胞水平上，有许多可能的建模方法，从过程粒度方法（如布尔建模）到详细的基于主方程的随机建模[121]。可以说，最成功的方法是那些基于化学动力学理论，特别是常微分方程（ODE）模型。ODE模型依赖于这样的假设，即细胞，或者至少是细胞内的特定区域，就像搅拌良好的系统一样;当这个假设受到怀疑时，ODE模型最多应该被认为是理解系统的第一步。ODE建模的挑战包括决定分子描述的详细程度。例如，细胞周期调控因子APC/C至少有71个位点被磷酸化[122]，因此APC/C调控的详细ODE描述可能包括第二种不同的磷酸异构体，这是一个不切实际的大数字。另一方面，APC/C对CDK 1的响应的定量研究表明，它的行为就像一个数字开关（Yang和Ferrell，未发表），这为将这种复杂的调节近似为双态系统提供了理论基础。有时，转录等复杂过程中产生的总体时间滞后比过程中间步骤的细节更重要。在这些情况下，延迟微分方程模型（DDE）可能是适当的，虽然离散时间滞后DDE中假设可能会导致不切实际的建模行为。我们已经使用了DDE模型、详细的ODE模型和简化的ODE模型来捕捉过程的本质。每种类型的建模都可能是有用的。 单细胞建模的下一个复杂程度是纳入空间考虑。有时，划分的ODE就足以达到这个目的。例如，在Ferrell和Meyer实验室最近发表的有丝分裂触发中的空间正反馈研究中，我们使用了区室化ODE，因为细胞质或细胞核内细胞周期蛋白B1-CDK 1扩散混合的时间尺度（秒）似乎比细胞质和细胞核之间平衡的时间尺度（分钟）快得多[29]。在其他时候，考虑一个完整的连续空间状态是必要的，PDE建模是适当的。出于这些原因，PDE建模用于分析目标1.1中描述的有丝分裂触发波。 一旦获得了令人满意的单细胞模型，下一个层次的复杂性是耦合这些模型，以允许集体细胞行为进行建模和分析：当被认为是在定义的几何形状的细胞数量很少，例如，在分析早期非洲爪蟾胚胎耦合常微分方程是可行的。在其他情况下，例如Axelrod和Tomlin实验室对上皮层分化进行的建模，或者涉及生物化学和机械相互作用的过程，混合模型可能更合适。离散和基于代理的建模，其中每个相互作用都会改变位置，应变，速度或分泌等重要参数的输出向量，提供了接近细胞集体行为的另一种方式。 所有这些建模方法都面临着许多挑战。这些包括使用ODE和PDE表示单个细胞的不确定性。即使在研究得很好的过程中，如细胞周期调节，系统的网络拓扑结构也可能不完整，部分可能不正确。模型参数值通常没有很好的定义。然而，参数的估计有助于了解潜在的生化机制，这强调了定量生物学家和建模者之间密切互动的重要性。以最佳方式将随机性和噪声引入模型也具有挑战性。方法包括直接Monte Cario模拟和纳入ODE模型的噪声函数。在任何情况下，所有模型都会产生需要识别和表示/可视化的高置信度和低置信度预测的混合。

B2. MODELING CORE Directors M. Covert and K. C. Huang; supporting participation by J. Ferrell and C. Tomlin Ariel Jaimovich (Postdoc). Dr. Jaimovich is a systems engineer between Pat Brown and Tobias Meyer's laboratory who will provide advise on modeling approaches and also help in coordinating the summer outreach workshop of the center. The overarching aim of the Modeling Core is to use models of cellular systems as a tool to investigate the genetic and molecular networks that underpin the collective responses of cells. These insights can then be tested experimentally using chemical, light, or mechanical perturbations, and then assessing the consequences, whenever possible, through real-time, single cell microscopy and quantitative image analysis. Both the dynamical and quantitative natures of this type of experimental approach are of critical importance. The Center's faculty members have extensive experience and success in modeling the responses of individual cells, and in integrating these models with quantitative experimentation. The next challenge is to couple single cell models together to allow the collective behaviors of cells to be analyzed and understood. At the single cell level there are many possible approaches to modeling, ranging from course-grained methods like Boolean modeling through detailed master equation-based stochastic modeling [121]. Arguably the most successful approaches have been those based chemical kinetic theory, particularly ordinary differential equation (ODE) models. ODE models rely upon the assumption that cells, or at least specific compartments within cells, act like well-stirred systems; when this assumption is in doubt, ODE models should be considered at best a first step toward an understanding of the system. Challenges in ODE modeling include deciding how detailed the molecular description is to be. For example, the cell cycle regulator APC/C is phosphorylated at least 71 sites [122], and so a detailed ODE description of APC/C regulation could include 2nd distinct phosphoisomers, an impractically large number. On the other hand, quantitative studies of the response of APC/C to CDK1 have shown that it behaves like a digital switch (Yang and Ferrell, unpublished), which provides a rationale for approximating this complex regulation as a two-state system. Sometimes the overall time lags produced in complex processes, like transcription, are more important than the details of the intermediate steps of the process. In these cases delay differential equation models (DDEs) may be appropriate, although the discrete time lags assumed in DDEs can lead to unrealistic modeled behaviors. We have made use of DDE models, detailed ODE models, and simplified ODE models designed to capture the essence of a process. Each type of modeling has can be useful. The next level of complexity in single cell modeling is to incorporate spatial considerations. Sometimes compartmentalized ODEs are sufficient for this purpose. For example, in the studies of spatial positive feedback in the mitotic trigger recently published by the Ferrell and Meyer labs, we made use of compartmentalized ODEs because it seemed likely that the time scale for diffusive mixing of cyclin B1-CDK1 within the cytoplasm or nucleus (seconds) was substantially faster than the time scale for equilibration between the cytoplasm and nucleus (minutes) [29]. At other times, considering a full continuum of spatial states is essential and PDE modeling is appropriate. For these reasons, PDE modeling was used in the analysis of mitotic trigger waves described in Aim 1.1. Once satisfactory single cell models have been obtained, the next level of complexity is to couple these models to allow collective cellular behaviors to be modeled and analyzed: When small numbers of cells in defined geometries are being considered-for example, in analyzing early Xenopus embryos-coupled ODEs are feasible. In other cases, such as the modeling carried out by the Axelrod and Tomlin labs on differentiation in epithelial sheets, or for processes involving both biochemical and mechanical interactions, hybrid models may be more appropriate. Discrete and agent-based modeling, where each interaction changes an output vector of important parameters like location, strain, velocity, or secretion, provide another way of approaching the collective behavior of cells. All of these modeling approaches share a number of challenges. These include uncertainties in the representation of individual cells using ODEs and PDEs. Even in well-studied processes, like cell cycle regulation, the network topology of system is likely incomplete and parts might be incorrect. Model parameter values are often not well defined. However, estimation of parameters is helped by understanding the underlying biochemical mechanisms, which emphasizes the importance of close interaction between quantitative biologists and modelers. It is also challenging to introduce stochasticity and noise into a model in the best way. Approaches include direct Monte Cario simulations and the inclusion into ODE models of noise functions. In any case, all models yield a mix of high and low confidence predictions that need to be identified and represented/visualized.