Research Article

Mathematical modeling of microtubule dynamic instability: new insight into the link between gtp-hydrolysis and microtubule aging^⋆

¹ Aix Marseille University, CNRS, Centrale Marseille Institut de Mathématiques de Marseille, Marseille, France.
² Clarkson University, Department of Mathematics Potsdam, New York, USA
³ Aix-Marseille University, INSERM, Center of Research in Oncobiology and Oncopharmacology, Marseille, France

^* Corresponding author: florence.hubert@univ-amu.fr

Received: 17 September 2016
Accepted: 26 April 2017

Abstract

Microtubules (MTs) are protein polymers that exhibit a unique type of behavior referred to as dynamic instability. That is, they undergo periods of growth (through the addition of GTP-tubulin) and shortening (through the subtraction of GDP-tubulin). Shortening events are very fast, where this transition is referred to as a catastrophe. There are many processes that regulate MT dynamic instability, however, recent experiments show that MT dynamics may be highly regulated by a MTs age, where young MTs are less likely to undergo shortening events than older ones. In this paper, we develop a novel modeling approach to describe how the age of a MT affects its dynamic properties. In particular, we extend on a previously developed model that describes MT dynamics, by proposing a new concept for GTP-tubulin hydrolysis (the process by which newly incorporated GTP-tubulin is hydrolyzed to lower energy GDP-tubulin). In particular, we assume that hydrolysis is mainly vectorial, age-dependent and delayed according to the GTP-tubulin incorporation into the MT. Through numerical simulation, we are able to show how MT age affects certain properties that define MT dynamics. For example, simulations illustrate how the aging process leads to an increase in the rate of GTP-tubulin hydrolysis for older MTs, as well as increases in catastrophe frequency. Also, since it has been found that MT dynamic instability is affected by chemotherapy microtubule-targeting agents (MTAs), we highlight the fact that our model can be used to investigate the action of MTAs on MT dynamics by varying certain model parameters.