Analysis of a microscopic stochastic model of microtubule dynamic instability

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 tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates/frequencies of larger-scale changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady state concentration of free tubulin, and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between microscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Lastly, we use a computational Monte Carlo model to provide an explanation for non-exponential MT length distributions observed in experiments. In particular, we show that appearance of such non-exponential distributions in the experiments can occur because the true steady state has not been reached, and/or due to the presence of a cell edge.Comment: 14 pages, 7 figure

Efficiency of Organelle Capture by Microtubules as a Function of Centrosome Nucleation Capacity: General Theory and the Special Case of Polyspermia

Transport of organelles along microtubules is essential for the cell metabolism and morphogenesis. The presented analysis derives the probability that an organelle of a given size comes in contact with the microtubule aster. The question is asked how this measure of functionality of the microtubule aster is controlled by the centrosome. A quantitative model is developed to address this question. It is shown that for the given set of cellular parameters, such as size and total tubulin content, a centrosome nucleation capacity exists that maximizes the probability of the organelle capture. The developed general model is then applied to the capture of the female pronucleus by microtubules assembled on the sperm centrosome, following physiologically polyspermic fertilization. This application highlights an unintuitive reflection of nonlinearity of the nucleated polymerization of the cellular pool of tubulin. The prediction that the sperm centrosome should lower its nucleation capacity in the face of the competition from the other sperm is a stark illustration of the new optimality principle. Overall, the model calls attention to the capabilities of the centrosomal pathway of regulation of the transport-related functionality of the microtubule cytoskeleton. It establishes a quantitative and conceptual framework that can guide experiment design and interpretation

The mechanisms of microtubule catastrophe and rescue: implications from analysis of a dimer-scale computational model.

Microtubule (MT) dynamic instability is fundamental to many cell functions, but its mechanism remains poorly understood, in part because it is difficult to gain information about the dimer-scale events at the MT tip. To address this issue, we used a dimer-scale computational model of MT assembly that is consistent with tubulin structure and biochemistry, displays dynamic instability, and covers experimentally relevant spans of time. It allows us to correlate macroscopic behaviors (dynamic instability parameters) with microscopic structures (tip conformations) and examine protofilament structure as the tip spontaneously progresses through both catastrophe and rescue. The model's behavior suggests that several commonly held assumptions about MT dynamics should be reconsidered. Moreover, it predicts that short, interprotofilament "cracks" (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks influence both catastrophe and rescue. We conclude that experimentally observed microtubule behavior can best be explained by a "stochastic cap" model in which tubulin subunits hydrolyze GTP according to a first-order reaction after they are incorporated into the lattice; catastrophe and rescue result from stochastic fluctuations in the size, shape, and extent of lateral bonding of the cap

Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis.

The concept of critical concentration (CC) is central to understanding the behavior of microtubules (MTs) and other cytoskeletal polymers. Traditionally, these polymers are understood to have one CC, measured in multiple ways and assumed to be the subunit concentration necessary for polymer assembly. However, this framework does not incorporate dynamic instability (DI), and there is work indicating that MTs have two CCs. We use our previously established simulations to confirm that MTs have (at least) two experimentally relevant CCs and to clarify the behavior of individuals and populations relative to the CCs. At free subunit concentrations above the lower CC (CCElongation), growth phases of individual filaments can occur transiently; above the higher CC (CCNetAssembly), the population's polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CCNetAssembly, meaning that "typical" DI occurs below the concentration traditionally considered necessary for polymer assembly. We report that [free tubulin] at steady state does not equal CCNetAssembly, but instead approaches CCNetAssembly asymptotically as [total tubulin] increases, and depends on the number of stable MT nucleation sites. We show that the degree of separation between CCElongation and CCNetAssembly depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations

Genome-wide analysis reveals novel molecular features of mouse recombination hotspots.

International audienceMeiotic recombination predominantly occurs at discrete genomic loci called recombination hotspots, but the features defining these areas are still largely unknown (reviewed in refs 1-5). To allow a comprehensive analysis of hotspot-associated DNA and chromatin characteristics, we developed a direct molecular approach for mapping meiotic DNA double-strand breaks that initiate recombination. Here we present the genome-wide distribution of recombination initiation sites in the mouse genome. Hotspot centres are mapped with approximately 200-nucleotide precision, which allows analysis of the fine structural details of the preferred recombination sites. We determine that hotspots share a centrally distributed consensus motif, possess a nucleotide skew that changes polarity at the centres of hotspots and have an intrinsic preference to be occupied by a nucleosome. Furthermore, we find that the vast majority of recombination initiation sites in mouse males are associated with testis-specific trimethylation of lysine 4 on histone H3 that is distinct from histone H3 lysine 4 trimethylation marks associated with transcription. The recombination map presented here has been derived from a homogeneous mouse population with a defined genetic background and therefore lends itself to extensive future experimental exploration. We note that the mapping technique developed here does not depend on the availability of genetic markers and hence can be easily adapted to other species with complex genomes. Our findings uncover several fundamental features of mammalian recombination hotspots and underline the power of the new recombination map for future studies of genetic recombination, genome stability and evolution

The mechanisms of microtubule catastrophe and rescue: implications from analysis of a dimer-scale computational model

ETOC: The behavior of a dimer-scale computational model predicts that short interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks govern both catastrophe and rescue