Mathematical modeling of microtubule dynamics: Insights into physiology and disease

Computer models of microtubule dynamics have provided the basis for many of the theories on the cellular mechanics of the microtubules, their polymerization kinetics, and the diffusion of tubulin and tau. In the three-dimensional model presented here, we include the effects of tau concentration and the hydrolysis of GTP-tubulin to GDP-tubulin and observe the emergence of microtubule dynamic instability. This integrated approach simulates the essential physics of microtubule dynamics in a cellular environment. The model captures the structure of the microtubules as they undergo steady state dynamic instabilities in this simplified geometry, and also yields the average number, length, and cap size of the microtubules. The model achieves realistic geometries and simulates cellular structures found in degenerating neurons in disease states such as Alzheimer disease. Further, this model can be used to simulate microtubule changes following the addition of antimitotic drugs which have recently attracted attention as chemotherapeutic agents.

Research highlights▶ The presented three-dimensional mathematical model simulates microtubule dynamics within cells. ▶ This model incorporates polymerization kinetics and hydrolysis of GTP to GDP, and allows the microtubules to move dynamically within a “cell” defined by a cellular membrane. ▶ The regional concentrations of tubulin and tau are also included parameters that affect microtubule polymerization and depolymerization. ▶ This model can be modified to mimic microtubule dynamics in sporadic disease systems as well as predict the effect of various treatment options that directly affect microtubules.