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Register a new userChemomechanical simulation of microtubule dynamics with explicit lateral bond dynamics
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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 lateral bonds, bending at longitudinal junctions, and the possibility of lateral bond rupture and formation. The model is computationally efficient such that we reach sufficiently long simulation times to observe repeated catastrophe and rescue events at realistic tubulin concentrations and hydrolysis rates, which allows us to deduce catastrophe and rescue rates. The chemomechanical model also allows us to gain insight into microscopic features of the GTP-tubulin cap structure and microscopic structural features triggering microtubule catastrophes and rescues. Dilution simulations show qualitative agreement with experiments. We also explore the consequences of a possible feedback of mechanical forces onto the hydrolysis process and the GTP-tubulin cap structure.
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The interaction between actin filaments and microtubules is crucial for many eukaryotic cellular processes, such as, among others, cell polarization, cell motility and cellular wound healing. The importance of this interaction has long been recognised, yet very little is understood about both the underlying mechanisms and the consequences for the spatial (re)organization of the cellular cytoskeleton. At the same time, understanding the causes and the consequences of the interaction between different biomolecular components are key questions for emph{in vitro} research involving reconstituted biomolecular systems, especially in the light of current interest in creating minimal synthetic cells. In this light, recent emph{in vitro} experiments have shown that the actin-microtubule interaction mediated by the cytolinker TipAct, which binds to actin lattice and microtubule tip, causes the directed transport of actin filaments. We develop an analytical theory of dynamically unstable microtubules, nucleated from the center of a spherical cell, in interaction with actin filaments. We show that, depending on the balance between the diffusion of unbound actin filaments and propensity to bind microtubules, actin is either concentrated in the center of the cell, where the density of microtubules is highest, or becomes localized to the cell cortex.
Several independent observations have suggested that catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent {it in vitro} observations by Gardner et al.[ M. K. Gardner et al., Cell {bf147}, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here, we investigate, via numerical simulations and mathematical calculations, some of the consequences of age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically and purely linear growth. The boundary demarcating the steady state and non-steady state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to non-exponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.
Kinesin-8 motor proteins destabilize microtubules. Their absence during cell division is associated with disorganized mitotic chromosome movements and chromosome loss. Despite recent work studying effects of kinesin 8s on microtubule dynamics, it remains unclear whether the kinesin-8 mitotic phenotypes are consequences of their effect on microtubule dynamics, their well-established motor activity, or additional unknown functions. To better understand the role of kinesin-8 proteins in mitosis, we have studied the effects of deletion of the fission-yeast kinesin-8 proteins Klp5 and Klp6 on chromosome movements and spindle length dynamics. Aberrant microtubule-driven kinetochore pushing movements and tripolar mitotic spindles occurred in cells lacking Klp5 but not Klp6. Kinesin-8 deletion strains showed large fluctuations in metaphase spindle length, suggesting a disruption of spindle length stabilization. Comparison of our results from light microscopy with a mathematical model suggests that kinesin-8 induced effects on microtubule dynamics, kinetochore attachment stability, and sliding force in the spindle can explain the aberrant chromosome movements and spindle length fluctuations seen.
Mitochondrial DNA (mtDNA) mutations cause severe congenital diseases but may also be associated with healthy aging. MtDNA is stochastically replicated and degraded, and exists within organelles which undergo dynamic fusion and fission. The role of the resulting mitochondrial networks in the time evolution of the cellular proportion of mutated mtDNA molecules (heteroplasmy), and cell-to-cell variability in heteroplasmy (heteroplasmy variance), remains incompletely understood. Heteroplasmy variance is particularly important since it modulates the number of pathological cells in a tissue. Here, we provide the first wide-reaching theoretical framework which bridges mitochondrial network and genetic states. We show that, under a range of conditions, the (genetic) rate of increase in heteroplasmy variance and de novo mutation are proportionally modulated by the (physical) fraction of unfused mitochondria, independently of the absolute fission-fusion rate. In the context of selective fusion, we show that intermediate fusion/fission ratios are optimal for the clearance of mtDNA mutants. Our findings imply that modulating network state, mitophagy rate and copy number to slow down heteroplasmy dynamics when mean heteroplasmy is low could have therapeutic advantages for mitochondrial disease and healthy aging.
Enveloped viruses enter host cells either through endocytosis, or by direct fusion of the viral membrane envelope and the membrane of the host cell. However, some viruses, such as HIV-1, HSV-1, and Epstein-Barr can enter a cell through either mechanism, with the choice of pathway often a function of the ambient physical chemical conditions, such as temperature and pH. We develop a stochastic model that describes the entry process at the level of binding of viral glycoprotein spikes to cell membrane receptors and coreceptors. In our model, receptors attach the cell membrane to the viral membrane, while subsequent binding of coreceptors enables fusion. The model quantifies the competition between fusion and endocytotic entry pathways. Relative probabilities for each pathway are computed numerically, as well as analytically in the high viral spike density limit. We delineate parameter regimes in which fusion or endocytosis is dominant. These parameters are related to measurable and potentially controllable quantities such as membrane bending rigidity and receptor, coreceptor, and viral spike densities. Experimental implications of our mechanistic hypotheses are proposed and discussed.
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