Collaborative Research: Integrative Modeling and Analysis of Animal-Cell Cytokinesis

分子细胞生物学的一个主要挑战是阐明细胞生长和分裂的生化机制。考虑到所涉及的复杂性，毫无疑问，数学建模将在应对这一挑战方面发挥越来越重要的作用。该研究小组最近开发了一个全细胞建模框架，其中细胞生化动力学和细胞形态变化是相互依赖的，并利用它构建了一个简单的自我复制细胞模型，其中包含了一个已建立的真核细胞周期调节机制。所得到的系统可以产生稳定的自我复制行为，细胞质体积和膜表面积与组分浓度的周期性同步倍增。由于可以模拟体内影响细胞形态变化的生化动力学过程，因此可以探索生长和分裂细胞在分裂过程（细胞质分裂）中“夹紧”的体内机制。为此，该项目的目标是模拟动物细胞中发生的细胞动力学，并将这些模型与真实细胞的已知细胞动力学行为进行比较。细胞质分裂发生在有丝分裂末期，涉及位于细胞赤道的与膜相关的肌动球蛋白环的快速组装和收缩。细胞质分裂与其他有丝分裂事件是精心编排的，例如，当后期开始时，染色体环组装，子染色单体开始分离。染色单体分离时，染色环收缩，分离完成后，染色环很快完成收缩。有丝分裂的这些最终事件的编排将被建模。生化反应和动力学参数将根据已知的实验假设。一旦开发，细胞分裂模型将被安装到现有的全细胞模型中，其中细胞周期调节被明确处理。通过这种方式，可以在体内环境中模拟细胞分裂。通过最小化膜弯曲能，还可以估计细胞生长和分裂过程中细胞形态的变化。在真实细胞中，在细胞分裂过程中，膜的组成在分裂沟处发生改变，这方面将被建模并分析其促进细胞分裂的能力。这些方面将被整合到一个自我复制的全细胞模型中，以观察细胞分裂时其赤道的“挤压”行为。所有这些都将由一个明确的生化机制驱动，并与其他细胞周期事件同步。模型的复杂性将与实验已知的内容成比例，这样它们将与现实紧密相连，具有预测能力，因此对实验家很有用。将分析模型以评估细胞骨架收缩环与膜组成局部变化在影响细胞质分裂中的重要性。这种综合方法产生了一个数学模型，该模型耦合了一个带有约束最小化问题（与细胞形状的确定有关）的常微分方程和偏微分方程系统。主要的数学挑战来自于需要在物理实际范围内确定系统参数，以便数学模型的解具有物理上合理、稳定的自我复制行为。该项目意义重大，因为在生物化学/机械水平上以及在体外和体内环境下模拟动物细胞动力学是新颖的。从广义上讲，该项目将通过在体外设计单个细胞“模块”，并在观察到适当的体外行为后将其安装到整个细胞框架中，来评估构建综合细胞模型的可行性。最终将需要一个全面的分子水平细胞模型来探索许多人类疾病，特别是癌症的发病机制，并测试新药的预期和非预期代谢作用。活细胞可以简单地看作是充满水、盐和分子（如DNA和蛋白质）的小囊。这些细胞最基本的特征之一是它们的自我复制能力。要做到这一点，细胞必须生长到原来的两倍大小，制造第二个DNA副本，将每个DNA副本移动到细胞的不同末端，最后围绕其中间分裂形成两个细胞。在这个过程的最后一部分（技术上称为“细胞质分裂”），细胞在它的中间构造一个小带，但是在细胞内部，这样从细胞外部就看不到这个带。这个内部带是由许多相同类型的蛋白质单位组成的，端到端连接在一起，就像一组堆叠的粘性块。此外，皮带被绑在细胞的表面（称为膜）上。当细胞向这条带子发出信号时，这条带子就开始在细胞的腹部收紧（通过一次一个地移除阻塞物），并将膜拉进去。这种挤压一直持续到带被压缩到一个非常小的周长，膜被完全挤压，两个细胞就形成了。研究人员最近开发了一种新的数学方法来模拟分子反应水平上的细胞生长和分裂。在这个项目中，这种方法将被用来研究这个带是如何组装的细节（在分子水平上）以及它是如何挤压的。另一个有助于这种挤压过程发生的因素似乎与膜上分子的类型有关，这些分子就在带子附着的地方。实验表明，这一区域的分子与膜其他部分的分子不同，但没有人知道它们为什么不同。这个项目的第二个方面将是调查这个问题。一般来说，当膜是平的而不是弯曲的时候是最稳定的。细胞分裂过程中的挤压过程需要它们大量弯曲，这表明挤压可能需要大量能量。人们怀疑，在这个区域发现的不同分子帮助膜弯曲，而不需要那么多的能量。同样，研究人员将使用数学建模方法来研究这是否可以解释为什么在这个区域发现不同类型的分子。这些过程不仅从基本细胞生物学的角度来看是重要的，它们也涉及到理解诸如癌症之类的疾病。癌细胞的生长和分裂是不受控制的——上面描述的细胞分裂过程出了问题。使用数学和计算机对这些过程进行建模是很重要的，因为这些过程非常复杂，任何人都不可能跟踪所有因素并了解它们如何随着时间的变化而相互作用。然而，使用数学和计算机，这些因素和相互作用可以被追踪，这允许对以前简单的基于文字的解释进行仔细的测试。通过这种仔细的测试，我们有可能更好地了解细胞是如何生长和分裂的，以及如何重新控制不受控制的癌细胞生长。

A major challenge of molecular cell biology is to elucidate the biochemical mechanisms by which cells grow and divide. Given the complexities involved, there is no doubt that mathematical modeling will play an increasingly important role in meeting this challenge. The assembled team of investigators has recently developed a whole-cell modeling framework in which cellular biochemical dynamics and changes in cell morphology are inter-dependent, and have used it to construct a simple self-replicating cell model in which an established mechanism of eukaryotic cell cycle regulation is incorporated. The resulting system can produce stable self-replicating behavior, with cytoplasm volume and membrane surface area doubling in synchrony with the periodicity in component concentrations. Because the biochemical dynamics of processes that affect changes in cell morphology in vivo can be modeled, exploring in vivo mechanisms by which growing and dividing cells "pinch" during the division process (cytokinesis) is possible. Towards this end, the objective of the proposed project is to model cytokinesis as it occurs in animal cells and to compare such models to the known cytokinetic behavior of real cells. Cytokinesis occurs near the end of mitosis, and involves the rapid assembly and contraction of a membrane-associated actomyosin ring located at the cell equator. Cytokinesis is exquisitely choreographed with other mitotic events, such that the ring assembles as anaphase begins and daughter chromatids begin to separate. The ring contracts as the chromatids separate, and the ring completes contraction soon after separation is complete. The choreography of these terminal events of mitosis will be modeled. Biochemical reactions and kinetic parameters will be assumed based on what is known experimentally. Once developed, cytokinesis models will be installed into the existing whole-cell model in which cell cycle regulation is treated explicitly. In this way, cytokinesis can be modeled within an in vivo setting. Cell morphology changes involved in cell growth and division will also be estimated by minimizing membrane bending energies. In real cells, membrane composition is altered at the cleavage furrow during cytokinesis, and this aspect will be modeled and analyzed for its ability to promote cell division. These aspects will be integrated into a self-replicating whole-cell model to observe "pinching" behavior about its equator as the cell divides. All of this will be driven by an explicit biochemical mechanism and synchronized with other cell cycle events. The complexity of the models will be scaled in proportion to what is known experimentally, such that they will be closely connected to reality, possess predictive ability, and thus be useful to experimentalists. Models will be analyzed to assess the importance of a cytoskeletal contractile ring vs. local changes in membrane composition in effecting cytokinesis. This integrative approach results in a mathematical model which couples a system of ordinary and partial differential equations with a constrained minimization problem (associated with the determination of cell shape). The primary mathematical challenges stem from the need to determine system parameters within physically realistic ranges so that the solution to the mathematical model exhibits physically reasonable, stable self-replicating behavior. The project is significant because of the novelty of modeling animal-cell cytokinetics on the biochemical/mechanistic level and under both in vitro and in vivo settings. In the broadest sense, the project will assess the feasibility of building a comprehensive cell model piecemeal by designing individual cellular "modules" in vitro and installing them into a whole-cell frame once appropriate in vitro behavior is observed. Ultimately a comprehensive molecular-level cell model will be required to explore the pathogenesis of many human diseases, especially cancer, and to test the intended and unintended metabolic effects of new pharmaceuticals.Living cells can be simplistically viewed as tiny sacs filled with water, salts and molecules such as DNA and proteins. One of the most fundamental aspects of such cells is their ability to self-replicate. To do this, a cell must grow to twice its original size, make a second copy of its DNA, move each copy of the DNA to different ends of the cell, and finally divide around its middle to form two cells. During the last part of this process (technically called "cytokinesis"), the cell constructs a little belt around its middle, but on the inside of itself such that the belt cannot be seen from the outside of the cell. This internal belt is constructed of many protein units of the same type, linked end-to-end like a stacked set of sticky blocks. Also, the belt is tied to the surface (called a membrane) of the cell. When the cell sends a signal to this belt, the belt starts to tighten around the belly of the cell (by removing blocks, one at a time) and it pulls the membrane in with it. This squeezing doesn't stop until the belt has constricted to a very small circumference, the membrane has pinched completely and two cells are made. The investigators have recently developed a new mathematical approach to modeling cell growth and division at the level of molecules reacting. In this project, this approach will be used to investigate the fine details (at the molecular level) of how this belt is assembled and how it squeezes. Another factor that appears to help this pinching process occur has to do with the types of molecules in the membrane right at the region where the belt is attached. Experiments have shown that the molecules in this region are different from those in the rest of the membrane, but no one understands why they are different. A second aspect of this project will be to investigate this question. Membranes are generally most stable when they are flat rather then bent. This pinching process during cell division requires that they bend a lot, which suggests that pinching might require a lot of energy. It is suspected that the different molecules found in this region help the membrane bend without requiring so much energy. Again, using a mathematical modeling approach, the researchers will investigate whether this might explain why different types of molecules are found in this region. These processes are not only significant from the perspective of basic cell biology, they are also involved in understanding diseases such as cancer. Cancerous cells grow and divide uncontrollably--something has gone awry with the cell division process described above. Modeling these processes using mathematics and computers is important because these processes are so complicated that it is literally impossible for any person to keep track of all the factors and understand how they interact as time changes. However, using mathematics and computers, these factors and interactions can be tracked, which permits the careful testing of what had previously been simply word-based explanations. By such careful testing, it might be possible to understand better how cells grow and divide, and how to reestablish control of uncontrolled cancerous cell growth.