Targeted Research Initiative for Pole Organization Leveraging Experiment and Simulation (TRIPOLES). The mitotic spindle is responsible for segregating chromosomes into two identical sets prior to cell division. Errors in the process can result in daughter cells having an incorrect number of chromosomes, a disorder referred to as aneuploidy. Cells with multipolar spindles, an aberrant spindle architecture marked by three or more spindle pole bodies rather than the typical two, are particularly susceptible to making the mistakes that lead to aneuploidy. However, relatively little is known about the mechanisms involved in multipolar mitotic spindles or how cells regulate them. In this proposal, we will develop a new theoretical framework that models multipolar mitotic spindles with an unprecedented level of detail. The model will incorporate multiple centrosomes with microtubules emanating from them, explicit chromosome pairs with a severable link, and different species of motor and crosslinking proteins to generate forces. We will first use the model to recreate healthy bipolar spindles, then expand it to investigate tripolar spindle dynamics and how cells regulate excess centrosomes. Our model will use first-principle mechanisms, which will allow us to make predictions that can be tested in experiment by our collaborators. By using theory to motivate specific follow-up experiments in this way, we can uncover novel mechanisms involved in the regulation of mitotic spindles that would otherwise go unnoticed. Beyond three main research objectives, this proposal also includes measures for a two-way transfer of knowledge, effective communication and dissemination of results, and overall management of the project. The work done in this proposal has the potential to not only illuminate how cancer cells regulate their aberrant spindle geometries, but also provide fundamental insight into how healthy bipolar spindles transition into unhealthy architectures.

Systems that fail to thermalize over a long period of time are essential for both practical applications and fundamental science. For the former, such systems can serve as stable platforms for many future technologies that operate at the quantum level, such as information storage and quantum computing devices. For the latter, such systems can host exotic quantum phases of matter by suppressing thermal excitations that tend to destroy the order. One of the most famous classes of systems that resist thermalization is the class of many-body localized (MBL) systems. Until now, it has been confirmed both experimentally and theoretically that the MBL can exist in isolated one-dimensional systems, either random or quasiperiodic ones. In higher dimensions, the fate of MBL is still unclear. A famous avalanche theory predicts the instability of the MBL phase in higher dimensional random systems due to the rare regions of weak disorder. However, quasiperiodic systems do not contain rare regions, which might stabilize the higher-dimensional MBL. The main objective of this proposal is to investigate MBL in two-dimensional quasiperiodic systems. The goal is to show whether MBL in quasiperiodic systems can survive in dimensions higher than one. With a novel numerical approach, which will allow me to study the dynamics of large systems (~100 sites) and reach long times (several hundred hopping times), combined with analytical calculations, I plan to investigate the microscopic mechanisms behind the stability/instability of the MBL phase in two-dimensional quasiperiodic models. My research will (i) provide an insight into the interplay between interactions and quasiperiodicity in two dimensions, (ii) produce a new interesting range of localization phenomena, and (iii) present a highly tunable and experimentally accessible setting where slow dynamics and localization can be studied, and possibly exploited for technological applications.