MODELING CORE

B2.模型芯 导演M.Covert和K.C.Huang；支持J.Ferrell和C.Tomlin Ariel Jaimovich(博士后)的参与。Jaimovich博士是帕特·布朗和托拜厄斯·迈耶实验室之间的系统工程师，他将就建模方法提供建议，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的模型作为一种工具来研究支撑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后果。这类实验方法的动力学和定量性质都是至关重要的。该中心的教职员工在对单个细胞的反应进行建模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，以便分析和理解细胞的集体行为。 在单细胞级别，有许多可能的建模方法，从像布尔建模这样的过程粒度方法到基于详细主方程的随机建模[121]。可以说，最成功的方法是那些基于化学动力学理论的方法，特别是常微分方程(ODE)模型。ODE模型依赖于这样一种假设，即细胞，或者至少是细胞内的特定隔室，就像搅拌良好的系统一样；当这一假设受到质疑时，ODE模型最多只能被认为是了解系统的第一步。ODE建模中的挑战包括决定分子描述的详细程度。例如，细胞周期调节因子APC/C至少有71个位点被磷酸化[122]，因此对APC/C调节的详细的ODE描述可能包括第二个不同的磷酸异构体，这是一个不切实际的大数字。另一方面，对APC/C对CDK1的响应的定量研究表明，它的行为类似于数字开关(Yang和Ferrell，未发表)，这为将这种复杂的调节近似为两态系统提供了理论基础。有时，在复杂的过程中产生的总体时间滞后，如转录，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(DDES)可能是合适的，尽管在DDES中假设的离散时间滞后可能导致不切实际的建模行为。我们使用了DDE模型、详细的ODE模型和简化的ODE模型，旨在捕获流程的本质。每种类型的建模都可能非常有用。 单细胞建模的下一个复杂级别是纳入空间考虑因素。有时，为了达到这个目的，划分的颂歌就足够了。例如，在Ferrell和Meyer实验室最近发表的关于有丝分裂触发中的空间正反馈的研究中，我们使用了分区的ODE，因为似乎Cyclin B1-CDK1在细胞质或细胞核内扩散混合的时间尺度(秒)明显快于细胞质和细胞核之间平衡的时间尺度(分钟)[29]。在其他时候，考虑空间状态的完整连续体是必要的，PDE建模是合适的。出于这些原因，在AIM 1.1中描述的有丝分裂触发波的分析中使用了PDE建模。 一旦获得了令人满意的单细胞模型，下一步的复杂程度是耦合这些模型，以允许对集体细胞行为进行建模和分析：当考虑到定义几何形状的少量细胞时-例如，在分析早期非洲爪哇胚胎时-耦合ODE是可行的。在其他情况下，例如Axelrod和Tomlin实验室对上皮片的分化进行的建模，或者对于涉及生化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提供了另一种接近细胞集体行为的方法，其中每次交互作用都会改变重要参数的输出向量，如位置、应变、速度或分泌。 所有这些建模方法都面临着许多挑战。这些问题包括使用常微分方程组和偏微分方程组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，系统的网络拓扑也可能是不完整的，部分可能是不正确的。模型参数值通常没有很好地定义。然而，参数的估计是通过了解潜在的生化机制来帮助的，这强调了定量生物学家和模型师之间密切互动的重要性。以最好的方式将随机性和噪声引入模型也是具有挑战性的。方法包括直接蒙特卡里奥模拟和将噪声函数纳入常微分方程组模型。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。

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.