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.

Predicting Important Residues and Interaction Pathways in Proteins Using Gaussian Network Model: Binding and Stability of HLA Proteins

A statistical thermodynamics approach is proposed to determine structurally and functionally important residues in native proteins that are involved in energy exchange with a ligand and other residues along an interaction pathway. The structure-function relationships, ligand binding and allosteric activities of ten structures of HLA Class I proteins of the immune system are studied by the Gaussian Network Model. Five of these models are associated with inflammatory rheumatic disease and the remaining five are properly functioning. In the Gaussian Network Model, the protein structures are modeled as an elastic network where the inter-residue interactions are harmonic. Important residues and the interaction pathways in the proteins are identified by focusing on the largest eigenvalue of the residue interaction matrix. Predicted important residues match those known from previous experimental and clinical work. Graph perturbation is used to determine the response of the important residues along the interaction pathway. Differences in response patterns of the two sets of proteins are identified and their relations to disease are discussed

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

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

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

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.

GCK gene mutations are a common cause of childhood-onset MODY (maturity-onset diabetes of the young) in Turkey.

Inactivating heterozygous mutations in the GCK gene are a common cause of MODY and result in mild fasting hyperglycaemia, which does not require treatment. We aimed to identify the frequency, clinical and molecular features of GCK mutations in a Turkish paediatric cohort.This article is freely available via PubMed Central, click on the Additional Link above to access the full-text

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

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