Collective force generated by multiple biofilaments can exceed the sum of forces due to individual ones

Collective dynamics and force generation by cytoskeletal filaments are crucial in many cellular processes. Investigating growth dynamics of a bundle of N independent cytoskeletal filaments pushing against a wall, we show that chemical switching (ATP/GTP hydrolysis) leads to a collective phenomenon that is currently unknown. Obtaining force-velocity relations for different models that capture chemical switching, we show, analytically and numerically, that the collective stall force of N filaments is greater than N times the stall force of a single filament. Employing an exactly solvable toy model, we analytically prove the above result for N=2. We, further, numerically show the existence of this collective phenomenon, for N>=2, in realistic models (with random and sequential hydrolysis) that simulate actin and microtubule bundle growth. We make quantitative predictions for the excess forces, and argue that this collective effect is related to the non-equilibrium nature of chemical switching.Comment: New J. Phys., 201

The random release of phosphate controls the dynamic instability of microtubules

A simple stochastic model which describes microtubule dynamics and explicitly takes into account the relevant biochemical processes is presented. The model incorporates binding and unbinding of monomers and random phosphate release inside the polymer. It is shown that this theoretical approach provides a microscopic picture of the dynamic instability phenomena of microtubules. The cap size, the concentration dependence of the catastrophe times and the delay before observing catastrophes following a dilution can be quantitatively predicted by this approach in a direct and simple way. Furthermore, the model can be solved analytically to a large extend, thus offering a valuable starting point for more refined studies of microtubules dynamics.Comment: 26 pages, 8 figure

Non-equilibrium self-assembly of a filament coupled to ATP/GTP hydrolysis

We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: a rapidly growing phase, an intermediate phase and a bound phase. We analyze all these phases, with an emphasis on the bound phase. We also discuss how hydrolysis affects force-velocity curves. The bound phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero, i.e., (to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations.Comment: 34 page

Molecular Interpretation of ACTH-β-Endorphin Coaggregation: Relevance to Secretory Granule Biogenesis

Peptide/protein hormones could be stored as non-toxic amyloid-like structures in pituitary secretory granules. ACTH and β-endorphin are two of the important peptide hormones that get co-stored in the pituitary secretory granules. Here, we study molecular interactions between ACTH and β-endorphin and their colocalization in the form of amyloid aggregates. Although ACTH is known to be a part of ACTH-β-endorphin aggregate, ACTH alone cannot aggregate into amyloid under various plausible conditions. Using all atom molecular dynamics simulation we investigate the early molecular interaction events in the ACTH-β-endorphin system, β-endorphin-only system and ACTH-only system. We find that β-endorphin and ACTH formed an interacting unit, whereas negligible interactions were observed between ACTH molecules in ACTH-only system. Our data suggest that ACTH is not only involved in interaction with β-endorphin but also enhances the stability of mixed oligomers of the entire system

Role of diffusion and reaction of the constituents in spreading of histone modification marks.

Cells switch genes ON or OFF by altering the state of chromatin via histone modifications at specific regulatory locations along the chromatin polymer. These gene regulation processes are carried out by a network of reactions in which the histone marks spread to neighboring regions with the help of enzymes. In the literature, this spreading has been studied as a purely kinetic, non-diffusive process considering the interactions between neighboring nucleosomes. In this work, we go beyond this framework and study the spreading of modifications using a reaction-diffusion (RD) model accounting for the diffusion of the constituents. We quantitatively segregate the modification profiles generated from kinetic and RD models. The diffusion and degradation of enzymes set a natural length scale for limiting the domain size of modification spreading, and the resulting enzyme limitation is inherent in our model. We also demonstrate the emergence of confined modification domains without the explicit requirement of a nucleation site. We explore polymer compaction effects on spreading and show that single-cell domains may differ from averaged profiles. We find that the modification profiles from our model are comparable with existing H3K9me3 data of S. pombe

Statistical mechanics provides novel insights into microtubule stability and mechanism of shrinkage.

Microtubules are nano-machines that grow and shrink stochastically, making use of the coupling between chemical kinetics and mechanics of its constituent protofilaments (PFs). We investigate the stability and shrinkage of microtubules taking into account inter-protofilament interactions and bending interactions of intrinsically curved PFs. Computing the free energy as a function of PF tip position, we show that the competition between curvature energy, inter-PF interaction energy and entropy leads to a rich landscape with a series of minima that repeat over a length-scale determined by the intrinsic curvature. Computing Langevin dynamics of the tip through the landscape and accounting for depolymerization, we calculate the average unzippering and shrinkage velocities of GDP protofilaments and compare them with the experimentally known results. Our analysis predicts that the strength of the inter-PF interaction (E(s)(m)) has to be comparable to the strength of the curvature energy (E(b)(m)) such that E(s)(m) - E(b)(m) ≈ 1kBT, and questions the prevalent notion that unzippering results from the domination of bending energy of curved GDP PFs. Our work demonstrates how the shape of the free energy landscape is crucial in explaining the mechanism of MT shrinkage where the unzippered PFs will fluctuate in a set of partially peeled off states and subunit dissociation will reduce the length

Spatiotemporal organization of chromatin domains: role of interaction energy and polymer entropy

Chromatin is known to be organised into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction strength parameters from experimentally known contact maps, and use it to predict chromatin organization and dynamics. Taking $\alpha$-globin domain as an example, we investigate its 3D organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Perturbing the interaction strengths systematically, we quantify how epigenetic changes can alter the spatio-temporal nature of the domains. Computing distance-distributions and relaxation times for different chromatin states, we show that weak and strong interactions cooperatively determine the organization of the domains and how the solid-like and liquid-like nature of chromatin gets altered as we vary epigenetic states. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops.Comment: 17 pages, 5 figures, supplementary material include