Exploring the effect of end-binding proteins and microtubule targeting chemotherapy drugs on microtubule dynamic instability.

Microtubules (MTs) play a key role in normal cell development and are a primary target for many cancer chemotherapy MT targeting agents (MTAs). As such, understanding MT dynamics in the presence of such agents, as well as other proteins that alter MT dynamics, is extremely important. In general, MTs grow relatively slowly and shorten very fast (almost instantaneously), an event referred to as a catastrophe. These dynamics, referred to as dynamic instability, have been studied in both experimental and theoretical settings. In the presence of MTAs, it is well known that such agents work by suppressing MT dynamics, either by promoting MT polymerization or promoting MT depolymerization. However, recent in vitro experiments show that in the presence of end-binding proteins (EBs), low doses of MTAs can increase MT dynamic instability, rather than suppress it. Here, we develop a novel mathematical model, to describe MT and EB dynamics, something which has not been done in a theoretical setting. Our MT model is based on previous modeling efforts, and consists of a pair of partial differential equations to describe length distributions for growing and shortening MT populations, and an ordinary differential equation (ODE) system to describe the time evolution for concentrations of GTP- and GDP-bound tubulin. A new extension of our approach is the use of an integral term, rather than an advection term, to describe very fast MT shortening events. Further, we introduce an ODE system to describe the binding and unbinding of EBs with MTs. To compare simulation results with experiment, we define novel mathematical expressions for time- and distance-based catastrophe frequencies. These quantities help to define MT dynamics in in vivo and in vitro settings. Simulation results show that increasing concentrations of EBs work to increase time-based catastrophe while distance-based catastrophe is less affected by changes in EB concentration, a result that is consistent with experiment. We further describe how EBs and MTAs alter MT dynamics. In the context of this modeling framework, we show that it is likely that MTAs and EBs do not work independently from one another. Thus, we propose a mechanism for how EBs can work synergistically with MTAs to promote MT dynamic instability at low MTA dose.