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Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very…
Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in…
Dynamic instability of microtubules is considered using frameworks of non-linear thermodynamics and non-equilibrium reaction-diffusion systems. Stochastic assembly/disassembly phases in the polymerization dynamics of microtubules are…
A novel theoretical model of dynamic instability of a system of linear (1D) microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of…
Certain regulatory proteins influence the polymerization dynamics of microtubules by inducing catastrophe with a rate that depends on the microtubule length. Using a discrete formulation, here we show that, for a catastrophe rate…
This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model…
We investigate the microtubule polymerization dynamics with catastrophe and rescue events for three different confinement scenarios, which mimic typical cellular environments: (i) The microtubule is confined by rigid and fixed walls, (ii)…
If the dynamic instability of microtubules follows a gamma distribution then one can associate to it a Cantor set
Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the $Z$-ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a…
Here we study a driven lattice gas model for microtubule depolymerizing molecular motors, where traffic jams of motors induce stochastic switching between microtubule growth and shrinkage. We term this phenomenon \enquote{traffic dynamic…
The intermittent transition between slow growth and rapid shrinkage in polymeric assemblies is termed dynamic instability, a feature observed in a variety of biochemically distinct assemblies including microtubules, actin and their…
The disappearance of the guanosine triphosphate (GTP)-tubulin cap is widely believed to be the forerunner event for the growth-shrinkage transition (`catastrophe') in microtubule filaments in eukaryotic cells. We study a discrete version of…
Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of…
We propose a stochastic model that accounts for the growth, catastrophe and rescue processes of steady state microtubules assembled from MAP-free tubulin. Both experimentally and theoretically we study the perturbation of microtubule…
An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic…
Microtubules capture chromosomes during mitosis by stochastically switching between growth and shrinkage at catastrophe events. They display strikingly rich biochemistry and dynamics, regulated by a stabilizing cap with distinct…
We introduce and parameterize a chemomechanical model of microtubule dynamics on the dimer level, which is based on the allosteric tubulin model and includes attachment, detachment and hydrolysis of tubulin dimers as well as stretching of…
The reliability of any day-to-day material is critically dictated by its properties. One factor which governs the behaviour of a material, under a given condition, is the microstructure. Despite the absence of any phase transformation, a…
We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…