Universality of the collapse transition of sticky polymers

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the $\theta$ state, independent of polymer-solvent chemistry, in the crossover regime between $\theta$ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has the additional important characteristic of "functionality" $\varphi$, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, $\varphi=1$), we find a standard second-order $\theta$ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered $\theta$ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under $\theta$ conditions is found to be the same for chains with and without stickers.Comment: 13 pages, 10 figures, supplementary material (see ancillary directory), to appear in Soft Matte

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

Defining a Physical Basis for Diversity in Protein Self-Assemblies Using a Minimal Model

Self-assembly of proteins into ordered, fibrilar structures is a commonly observed theme in biology. It has been observed that diverse set of proteins (e.g., alpha-synuclein, insulin, TATA-box binding protein, Sup35, p53), independent of their sequence, native structure, or function could self-assemble into highly ordered structures known as amyloids. What are the crucial features underlying amyloidogenesis that make it so generic? Using coarse-grained simulations of peptide self-assembly, we argue that variation in two physical parameters-bending stiffness of the polypeptide and strength of intermolecular interactions-can give rise to many of the structural features typically associated with amyloid self-assembly. We show that the interplay between these two factors gives rise to a rich phase diagram displaying high diversity in aggregated states. For certain parameters, we find a bimodal distribution for the order parameter implying the coexistence of ordered and disordered aggregates. Our findings may explain the experimentally observed variability including the "off-pathway" aggregated structures. Further, we demonstrate that sequence-dependence and protein-specific signatures could be mapped to our coarse-grained framework to study self-assembly behavior of realistic systems such as the STVIIE peptide and A beta 42. The work also provides certain guiding principles that could be used to design novel peptides with desired self-assembly properties, by tuning a few physical parameters

Coupling of replisome movement with nucleosome dynamics can contribute to the parent-daughter information transfer

Positioning of nucleosomes along the genomic DNA is crucial for many cellular processes that include gene regulation and higher order packaging of chromatin. The question of how nucleosome-positioning information from a parent chromatin gets transferred to the daughter chromatin is highly intriguing. Accounting for experimentally known coupling between replisome movement and nucleosome dynamics, we propose a model that can obtain de novo nucleosome assembly similar to what is observed in recent experiments. Simulating nucleosome dynamics during replication, we argue that short pausing of the replication fork, associated with nucleosome disassembly, can be a event crucial for communicating nucleosome positioning information from parent to daughter. We show that the interplay of timescales between nucleosome disassembly (tau (p)) at the replication fork and nucleosome sliding behind the fork (tau (s)) can give rise to a rich 'phase diagram' having different inherited patterns of nucleosome organization. Our model predicts that only when tau(p) >= tau(s) the daughter chromatin can inherit nucleosome positioning of the parent

Signatures of a macroscopic switching transition for a dynamic microtubule

Characterising complex kinetics of non-equilibrium self-assembly of bio-filaments is of general interest. Dynamic instability in microtubules, consisting of successive catastrophes and rescues, is observed to occur as a result of the non-equilibrium conversion of GTP-tubulin to GDP-tubulin. We study this phenomenon using a model for microtubule kinetics with GTP/GDP state-dependent polymerisation, depolymerisation and hydrolysis of subunits. Our results reveal a sharp switch-like transition in the mean velocity of the filaments, from a growth phase to a shrinkage phase, with an associated coexistence of the two phases. This transition is reminiscent of the discontinuous phase transition across the liquid-gas boundary. We probe the extent of discontinuity in the transition quantitatively using characteristic signatures such as bimodality in velocity distribution, variance and Binder cumulant, and also hysteresis behaviour of the system. We further investigate ageing behaviour in catastrophes of the filament, and find that the multi-step nature of catastrophes is intensified in the vicinity of the switching transition. This assumes importance in the context of Microtubule Associated Proteins which have the potential of altering kinetic parameter values

Force generation and step-size fluctuations in a dynein motor

Molecular motors such as dynein are known to move by taking steps of different sizes, depending on the load. Here, we develop a simple, discrete, minimal ratchet model for a motor that can take steps of sizes delta(o) and 2 delta(o) in order to provide a bare-bones description of dynein. We obtain the force-velocity curves and diffusivity for this motor for different concentrations of ATP. We also study the mechano-chemical energy transduction and thermodynamic efficiency of the motor. Further, by investigating the statistics of step sizes for the motor, we show that the average step size and fluctuation in step sizes have a non-monotonic force dependence. We develop closed-form analytical expressions for all our results, which despite the simplicity of the model give a reasonable match with the known experiments and simulations on dynein