The mitotic spindle is a molecular machine that segregates chromosomes prior to cell division. The traditional picture is that the spindle assembles as a result of microtubules (long dynamic polymers) randomly capturing chromosomes. After this, the spindle length is maintained by a balance of inward tension exerted by molecular motors on the microtubules connecting spindle poles and chromosomes, and outward compression generated by other motors on the overlapping microtubules connecting the spindle poles. This picture is being challenged by mounting evidence indicating that spindle assembly and maintenance rely on much more complex interconnected networks of microtubules, molecular motors, chromosomes and regulatory proteins. From an engineering point of view, three design principles of this molecular machine are especially important: the spindle assembles rapidly, it assembles accurately, and it is mechanically robust, yet malleable. How is this design achieved with randomly interacting and impermanent molecular parts? How does the spindle self-assemble? What determines its mechanical properties? Mathematical and computational modeling will be used to examine quantitatively the process of the capture of chromosomes by dynamically unstable microtubules. Kinetics of the assembly are coupled with mechanical forces, and interplay between forces, movements, chromosome capture and assembly error correction will be investigated. Then a coarse grained hydrodynamic-like model of a gel of short microtubules and molecular motors is developed to elucidate the self-organization principles for meiotic and in vitro spindles. The models are tested and refined by comparison of their predictions with quantitative data.

This project uses a novel combination of mathematical analysis, computer simulations and model-driven experiments to develop a novel quantitative model of the mitotic spindle-dynamic molecular machine that the cell uses to segregate chromosomes prior to cell division. Predictions of this model help reveal the mechanisms the cell uses to segregate the chromosomes fast, accurately and in a mechanically robust way. The assembly, error correction, and mechanics of the mitotic spindle are simulated simultaneously, generating testable predictions for the experiment. Such models are crucial for understanding not only the fundamental question of basic cell biology, but also to fine-tune drug design strategies for numerous diseases that stem from aneuploidy, i.e., an abnormal number of chromosomes.

Project Report

Cell movement and division are fundamental cell biological phenomena underlying many processes in health and disease. These phenomena rely on self-assembling molecular machines. Dynamic polymers and molecular motors are essential components of these machines. Basic principles of these components assembly and function are only beginning to become clear. By modeling two basic machines – lamellipodia (engine of motile cell) and mitotic spindle (segregating chromosomes before the division) – mathematically and computationally and by testing the models experimentally, we understood a few key principles. First, the balance of pulling and pushing forces determines the size, shape and movements of these machines. Second, interplay between these forces and geometries of essential organelles ensure both rapid and accurate self-assembly. Third, polymer-motor pattern formation can play both positive and negative roles in force generation. We also achieved a few specific important outcomes, such as understanding how the force balance mechanism regulates the blood platelet size; how dynamic kinetochore shape accelerates and corrects the mitotic spindle assembly; and that multiple redundant mechanisms can all explain the observed shapes and movements of the molecular machines. These findings were published in 13 papers in prestigious peer-reviewed journals and cited very well. Plus, three papers are submitted. Three reviews were published and are widely read. Six postdocs and two students were trained in interdisciplinary research. Lectures to high-school students were given. Two new courses were developed; new numerical codes available for the public were developed.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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University of California Davis
United States
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