Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology

For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together, leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and actions must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.Comment: Topical review, 31 pages, 10 figure

Statistical Properties of Contact Maps

A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the possible configurations of a polypeptide chain of N amino acids, represented by (N-1)-step self avoiding walks on a lattice, grows exponentially with N for all dimensions D>1. We carry out exact enumerations in D=2 on the square and triangular lattices for walks of up to 20 steps and investigate various statistical properties of contact maps corresponding to such walks. We also study the exact statistics of contact maps generated by walks on a ladder.Comment: Latex file, 15 pages, 12 eps figures. To appear on Phys. Rev.

From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term

On the origin of the Boson peak in globular proteins

We study the Boson Peak phenomenology experimentally observed in globular proteins by means of elastic network models. These models are suitable for an analytic treatment in the framework of Euclidean Random Matrix theory, whose predictions can be numerically tested on real proteins structures. We find that the emergence of the Boson Peak is strictly related to an intrinsic mechanical instability of the protein, in close similarity to what is thought to happen in glasses. The biological implications of this conclusion are also discussed by focusing on a representative case study.Comment: Proceedings of the X International Workshop on Disordered Systems, Molveno (2006

Nonlinearity of Mechanochemical Motions in Motor Proteins

The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors - myosin V and kinesin KIF1A - and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode, nor a superposition of such modes yield an approximation of strongly nonlinear dynamics.Comment: 10 pages, 6 figure

Universal behavior of localization of residue fluctuations in globular proteins

Localization properties of residue fluctuations in globular proteins are studied theoretically by using the Gaussian network model. Participation ratio for each residue fluctuation mode is calculated. It is found that the relationship between participation ratio and frequency is similar for all globular proteins, indicating a universal behavior in spite of their different size, shape, and architecture.Comment: 4 pages, 3 figures. To appear in Phys. Rev.

Bi-allelic mutations in MYL1 cause a severe congenital myopathy.

OBJECTIVE: Congenital myopathies are typically characterised by early onset hypotonia, weakness and hallmark features on biopsy. Despite the rapid pace of gene discovery, approximately 50% of patients with a congenital myopathy remain without a genetic diagnosis following screening of known disease genes. METHODS: We performed exome sequencing on two consanguineous probands diagnosed with a congenital myopathy and muscle biopsy showing selective atrophy/hypotrophy or absence of type II myofibres. RESULTS: We identified variants in the gene (MYL1) encoding the skeletal muscle fast-twitch specific myosin essential light chain in both probands. A homozygous essential splice acceptor variant (c.479-2A>G, predicted to result in skipping of exon 5 was identified in Proband 1, and a homozygous missense substitution (c.488T>G, p.(Met163Arg)) was identified in Proband 2. Protein modeling of the p.(Met163Arg) substitution predicted it might impede intermolecular interactions that facilitate binding to the IQ domain of myosin heavy chain, thus likely impacting on the structure and functioning of the myosin motor. MYL1 was markedly reduced in skeletal muscle from both probands, suggesting that the missense substitution likely results in an unstable protein. Knock down of myl1 in zebrafish resulted in abnormal morphology, disrupted muscle structure and impaired touch-evoked escape responses, thus confirming that skeletal muscle fast-twitch specific myosin essential light chain is critical for myofibre development and function. INTERPRETATION: Our data implicate MYL1 as a crucial protein for adequate skeletal muscle function and that MYL1 deficiency is associated with a severe congenital myopathy

On the conservation of the slow conformational dynamics within the amino acid kinase family: NAGK the paradigm

N-Acetyl-L-Glutamate Kinase (NAGK) is the structural paradigm for examining the catalytic mechanisms and dynamics of amino acid kinase family members. Given that the slow conformational dynamics of the NAGK (at the microseconds time scale or slower) may be rate-limiting, it is of importance to assess the mechanisms of the most cooperative modes of motion intrinsically accessible to this enzyme. Here, we present the results from normal mode analysis using an elastic network model representation, which shows that the conformational mechanisms for substrate binding by NAGK strongly correlate with the intrinsic dynamics of the enzyme in the unbound form. We further analyzed the potential mechanisms of allosteric signalling within NAGK using a Markov model for network communication. Comparative analysis of the dynamics of family members strongly suggests that the low-frequency modes of motion and the associated intramolecular couplings that establish signal transduction are highly conserved among family members, in support of the paradigm sequence→structure→dynamics→function © 2010 Marcos et al

ATPase Subdomain IA Is a Mediator of Interdomain Allostery in Hsp70 Molecular Chaperones

The versatile functions of the heat shock protein 70 (Hsp70) family of molecular chaperones rely on allosteric interactions between their nucleotide-binding and substrate-binding domains, NBD and SBD. Understanding the mechanism of interdomain allostery is essential to rational design of Hsp70 modulators. Yet, despite significant progress in recent years, how the two Hsp70 domains regulate each other's activity remains elusive. Covariance data from experiments and computations emerged in recent years as valuable sources of information towards gaining insights into the molecular events that mediate allostery. In the present study, conservation and covariance properties derived from both sequence and structural dynamics data are integrated with results from Perturbation Response Scanning and in vivo functional assays, so as to establish the dynamical basis of interdomain signal transduction in Hsp70s. Our study highlights the critical roles of SBD residues D481 and T417 in mediating the coupled motions of the two domains, as well as that of G506 in enabling the movements of the α-helical lid with respect to the β-sandwich. It also draws attention to the distinctive role of the NBD subdomains: Subdomain IA acts as a key mediator of signal transduction between the ATP- and substrate-binding sites, this function being achieved by a cascade of interactions predominantly involving conserved residues such as V139, D148, R167 and K155. Subdomain IIA, on the other hand, is distinguished by strong coevolutionary signals (with the SBD) exhibited by a series of residues (D211, E217, L219, T383) implicated in DnaJ recognition. The occurrence of coevolving residues at the DnaJ recognition region parallels the behavior recently observed at the nucleotide-exchange-factor recognition region of subdomain IIB. These findings suggest that Hsp70 tends to adapt to co-chaperone recognition and activity via coevolving residues, whereas interdomain allostery, critical to chaperoning, is robustly enabled by conserved interactions. © 2014 General et al