Complex fluids are materials that are driven out of their equilibrium structure by means of internally generated, or externally imposed forces. The coupling of microstructure and the macroscopic behavior is the hallmark of complex fluids, and the origin of many intriguing behaviors of these materials. I am interested in studying complex fluids and complex assemblies from a microscopic perspective using theories and simulations. My goal is to bridge the gap between micro-scale dynamics and the collective behavior in these systems; such findings potentially provide the blueprint for design and control of novel materials in microscopic scales. One fascinating example of complex fluids is the cell cytoskeleton which is the primary machinery for performing many vital cellular processes such as motility, intracellular transport, and cell division. My postdoctoral research concerns the positioning and dynamics of the mitotic spindle apparatus during cell division which is crucial to the accurate segregation of chromosomes and the subsequent development of the organism. I use biophysical models to describe the interactions of microscopic tubular polymers of spindle structure, i.e. microtubules (MTs), with the molecular motors, the other organelles, and the cell boundaries; these models are then used as inputs in the dynamic simulations of this highly active cellular assembly.
The dynamics of mitotic spindle is regulated by several factors including the growth and shrinking of MTs, their interactions with molecular motors, and their flexibility and strong hydrodynamic coupling. In part, I will talk about the numerical toolbox I have developed that incorporates all these physical variables. Our method is unparalleled in a number of aspects; most notably it is the first technique to include many-body hydrodynamic interactions and the resulting cytoplasmic flows in cellular assemblies. I use boundary integral methods in Stokes flow for describing the hydrodynamic interactions between the MTs and other bodies, coupled with the state-of-the-art technology on fast summation techniques for Stokes flow. The deformation of the fibers is described by Euler-Bernoulli theory for flexible rods and their polymerization is modeled by reparametrization of the dynamic equations in the appropriate Lagrangian frame. The use of pseudo-spectral spatial discretization and implicit time-stepping makes this method highly accurate and efficient. The entire method is parallelized and scalable which allows simulating assemblies composed on thousands of fibers.
We use simulations to study the migration dynamics of pronuclear complex (PNC) in early stages of cell division of C-elegans embryo. We find that although the proposed force transduction mechanisms properly position and align the PNC, each mechanism leaves its unique fingerprint on the generated cytoplasmic flows. This feature can be utilized to differentiate between, and identify the mechanisms more relevant to the migration process. Considering that these flow signatures are generic features of each model, they can equally be applied to identifying the active mechanisms involved in other stages of cell division, as well as other organisms.
I will also talk about an ongoing collaborative work on studying the mechanics of mitotic spindle in C-elegans using a 3D reconstruction of spindle structure with electron tomography. In short, the results of the tomography show that the distribution of length and curvature of the MTs attached to chromosomes, i.e. kinetochore MTs, are different from the non-kinetochore MTs. Based on these observations we propose models that delineate the dynamics of the kinetochore MTs; we corroborate these models with detailed simulations.
Finally, I will showcase a few applications of the developed numerical framework in studying other problems in complex fluids and soft materials which I will be pursuing as a faculty member.
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