Characterising complex kinetics of non-equilibrium self-assembly of bio-filaments is of general interest. Dynamic instability in microtubules, consisting of successive catastrophes and rescues, is observed to occur as a result of the non-equilibrium conversion of GTP-tubulin to GDP-tubulin. We study this phenomenon using a model for microtubule kinetics with GTP/GDP state-dependent polymerisation, depolymerisation and hydrolysis of subunits. Our results reveal a sharp switch-like transition in the mean velocity of the filaments, from a growth phase to a shrinkage phase, with an associated co-existence of the two phases. This transition is reminiscent of the discontinuous phase transition across the liquid-gas boundary. We probe the extent of discontinuity in the transition quantitatively using characteristic signatures such as bimodality in velocity distribution, variance and Binder cumulant, and also hysteresis behaviour of the system. We further investigate ageing behaviour in catastrophes of the filament, and find that the multi-step nature of catastrophes is intensified in the vicinity of the switching transition. This assumes importance in the context of Microtubule Associated Proteins which have the potential of altering kinetic parameter values.

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This study investigates the effect of spatial patterns of acetylation on the disassembly dynamics of microtubule filaments using a multi-protofilament model.

Microtubules (MTs) are bio-polymers, composed of tubulin proteins, involved in several functions such as cell division, transport of cargoes within cells, maintaining cellular structures etc. Their kinetics are often affected by chemical modifications on the filament known as Post Translational Modifications (PTMs). Acetylation is a PTM which occurs on the luminal surface of the MT lattice and has been observed to reduce the lateral interaction between tubulins on adjacent protofilaments. Depending on the properties of the acetylase enzyme αTAT1 and the structural features of MTs, the patterns of acetylation formed on MTs are observed to be quite diverse. In this study, we present a multi-protofilament model with spatially heterogenous patterns of acetylation, and investigate how the local kinetic differences arising from heterogeneity affect the global kinetics of MT filaments. From the computational study we conclude that a filament with spatially uniform acetylation is least stable against disassembly, while ones with more clustered acetylation patterns may provide better resistance against disassembly. The increase in disassembly times for clustered pattern as compared to uniform pattern can be upto fifty percent for identical amounts of acetylation. Given that acetylated MTs affect several cellular functions as well as diseases such as cancer, our study indicates that spatial patterns of acetylation need to be focussed on, apart from the overall amount of acetylation. Author SummaryMicrotubules (MTs) form a crucial part of the cytoskeletal machinery which regulates several cellular processes. The basic building block of MTs are tubulin proteins. These proteins assemble in lateral and longitudinal directions to form a hollow cylindrical structure of a MT. There are chemical modifications on tubulin, known as Post Translational Modifications (PTMs), which affect the stability and dynamics of MT filaments. We computationally study how one such PTM, namely acetylation, affects the kinetics of disassembly of a MT filament. We propose a model which incorporates spatially heterogeneous patterns of acetylation on MT filament and study how they may regulate the disassembly times and velocities, a factor hitherto unexplored in studies. We conclude that there are significant differences of disassembly velocities and their fluctuations depending on the differnces in spatial patterns of acetylation. PLOS1/22 1 Microtubules constitute an important class of bio-polymers that are essential for cell 2 division, transport of vesicles, cell motility and for maintaining the structure and shape 3 of the cell [1][2][3][4][5]. In order to fulfil certain cellular functions, during the corresponding 4 stage of the cell cycle, MTs may have to polymerise and maintain stable structures. 5However, at other times, certain other cellular functions call for these filaments to 6 depolymerise into free protein subunits, before entering into another period of stable 7 assembly or bout of rapid dynamics. How MTs regulate the dynamics in these ...

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