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Nucleosomes are the fundamental building blocks of chromatin that not only help in the folding of chromatin, but also in carrying epigenetic information. It is known that nucleosome sliding is responsible for dynamically organizing chromatin structure and the resulting gene regulation. Since sliding can move two neighboring nucleosomes physically close or away, can it play a role in the spreading of histone modifications? We investigate this by simulating a stochastic model that couples nucleosome dynamics with the kinetics of histone modifications. We show that the sliding of nucleosomes can affect the modification pattern as well as the time it takes to modify a given region of chromatin. Exploring different nucleosome densities and modification kinetic parameters, we show that nucleosome sliding can be important for creating histone modification domains. Our model predicts that nucleosome density coupled with sliding dynamics can create an asymmetric histone modification profile around regulatory regions. We also compute the probability distribution of modified nucleosomes and relaxation kinetics of modifications. Our predictions are comparable with known experimental results.

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is reversible at stall. Conversely, we show that this additive property typically does not hold true when the system is irreversible at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

We investigate collective dynamics of branched actin networks growing against a rigid movable wall constrained by a resistive force. Computing the force velocity relations, we show that the stall force of such networks depends not only on the average number of filaments touching the wall, but also on the amount of fluctuation of the leading edge of the network. These differences arise due to differences in the network architecture, namely, distance between two adjacent branching points and the initial distance of the starting filament from the wall, with their relative magnitudes influencing the nature of the force velocity curves (convex versus concave). We also show that the introduction of branching results in nonmonotonic diffusion constant, a quantity that measures the growth in length fluctuation of the leading edge of the network, as a function of externally applied force. Together our results demonstrate how the collective dynamics of a branched network differs from that of a parallel filament network.

Microtubules consist of 13 protofilaments arranged in the form of a cylinder. The protofilaments are composed of longitudinally attached tubulin dimers that can exist in either a less curved state [GTP-bound tubulin (T)] or a more curved state [GDP-bound tubulin (D)]. Hydrolysis of T into D leaves the straight and laterally attached protofilaments of the microtubule in a mechanically stressed state, thus leading to their unzipping. The elastic energy in the unzipping protofilaments can be harnessed by a force transducer such as the Dam1-kinetochore ring complex in order to exert pulling force on chromosomes during cell division. In the present paper we develop a simple continuum model to obtain this pulling force as a function of the mechanical properties of protofilaments and the size of the Dam1-kinetochore ring. We also extend this model to investigate the role played by the T subunits found at the plus end of the microtubule (the T cap) on the mechanical stability of microtubules.