Overview

Although there has been a lot of previous work focusing on the in vitro assembly of microtubules and flagellar filaments, no attempt has been made to assemble them on a cell’s surface. Therefore, we developed mathematical models to explore the possible dynamics of this process and to guide the experiments in wet lab.

One key problem in both the microtubule part and flagellar filament part of our design is the competition between the assembly of monomers on the yeast surface and that in the solution. How can we adjust our experimental parameters such as initial monomer concentration to promote the polymerization on the yeast surface as much as possible and avoid the same process in the solution? Will we be able to obtain enough polymers on the yeast surface to satisfy our needs? Our models gave a positive answer and also provided guidance to optimize the outcome in experiments.

There are differences between these two kinds of polymers as well. The most significant one is that depolymerization is prominent in the assembly of microtubule, but does not play an important role in the assembly of flagellar filaments. This led us to use different models to describe them. To capture the dynamic instability of microtubules, we used the stochastic chemical reaction model combined with Monte Carlo simulation method. The polymerization of flagellar filaments can be described with the law of mass action and Michaelis-Menten kinetics, so we chose ordinary differential equations to model it.

Another key difference between the two polymers is our purpose. We want to use the displayed microtubules to screen microtubule-stabilizing agents (which inhibit microtubule depolymerization by curbing GTP hydrolysis), so we closely examined the effect of different GTP hydrolysis rate on microtubule assembly. We plan to use flagellar filaments to expand the yeasts’ capacity to display enzymes, so we used our model to predict the possible magnitude of this expansion.

Please click on the sidebar to the left to view our modeling work of microtubules and flagellar filaments.

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Team:BNU-China/Model

Overview