Integrative Modeling and Analysis of Animal-Cell Cytokinesis

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

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.