Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers

Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary $q \times q$ matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur

Is Heteropolymer Freezing Well Described by the Random Energy Model?

It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over disorder, is violated in different ways for models commonly employed in heteropolymer freezing studies. The implications for proteins are also discussed.Comment: 4 pages, 3 eps figures To appear in Physical Review Letters, May 199

Gunrock: A High-Performance Graph Processing Library on the GPU

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs have been two significant challenges for developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We evaluate Gunrock on five key graph primitives and show that Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives, and better performance than any other GPU high-level graph library.Comment: 14 pages, accepted by PPoPP'16 (removed the text repetition in the previous version v5

Random walks in the space of conformations of toy proteins

Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as a random walk in an abstract (discrete) space of conformations. To test the geometry of this space, we examine the return probability $P(T)$, which is the probability to find the polymer in the native state after $T$ Monte Carlo steps, provided that it starts from the native state at the initial moment. Comparing computational data with the theoretical expressions for $P(T)$ for random walks in a variety of different spaces, we show that conformational spaces of polymer loops may have non-trivial dimensions and exhibit negative curvature characteristic of Lobachevskii (hyperbolic) geometry.Comment: 4 pages, 3 figure

Two State Behavior in a Solvable Model of β\beta-hairpin folding

Understanding the mechanism of protein secondary structure formation is an essential part of protein-folding puzzle. Here we describe a simple model for the formation of the $\beta$-hairpin, motivated by the fact that folding of a $\beta$-hairpin captures much of the basic physics of protein folding. We argue that the coupling of ``primary'' backbone stiffness and ``secondary'' contact formation (similar to the coupling between the ``secondary'' and ``tertiary'' structure in globular proteins), caused for example by side-chain packing regularities, is responsible for producing an all-or-none 2-state $\beta$-hairpin formation. We also develop a recursive relation to compute the phase diagram and single exponential folding/unfolding rate arising via a dominant transition state.Comment: Revised versio

Microbial community management in aquaculture

Microbial community management in aquaculture creates benefits at the nutritional as well as at health level for cultured species. In addition, in case of biofloc application, it allows to link species at different trophic levels, making bioflocs the potential link in integrated multispecies aquaculture

Effect of Collagen type-I on the rate of osseointegration of Ca-containing biodegradable Mg-Zr based alloys

Mg-Zr based biodegradable implants alloyed with Ca were investigated to assess their biocompatibility and efficacy in bone formation and osseointegration. Bare alloys, containing Ca, exhibited low surface energy, poor corrosion-resistance, reduced osteoinduction and bone integration activity. Upon coating with Collagen type-I, these alloys demonstrated enhanced performance as an implant material that are suitable for rapid and efficient new bone tissue induction with optimal mineral content and cellular properties

Femoral Neck Shaft Angle in Men with Fragility Fractures

Introduction. Femoral neck shaft angle (NSA) has been reported to be an independent predictor of hip fracture risk in men. We aimed to assess the role of NSA in UK men. Methods. The NSA was measured manually from the DXA scan printout in men with hip (62, 31 femoral neck and 31 trochanteric), symptomatic vertebral (91), and distal forearm (67) fractures and 389 age-matched control subjects. Age, height, weight, and BMD (g/cm2: lumbar spine, femoral neck, and total femur) measurements were performed. Results. There was no significant difference in mean NSA between men with femoral neck and trochanteric hip fractures, so all further analyses of hip fractures utilised the combined data. There was no difference in NSA between those with hip fractures and those without (either using the combined data or analysing trochanteric and femoral neck shaft fractures separately), nor between fracture subjects as a whole and controls. Mean NSA was smaller in those with vertebral fractures (129.2° versus 131°: P = 0.001), but larger in those with distal forearm fractures (129.8° versus 128.5°: P = 0.01). Conclusions. The conflicting results suggest that femoral NSA is not an important determinant of hip fracture risk in UK men

The Phase Diagram of Random Heteropolymers

We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered.Comment: 4 pages, 3 figures; published versio