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ABSTRACT: Thermodynamic analysis of brittle fracture specimens near the threshold developed by Rice (Thermodynamics of quasi-static
growth of Griffith cracks, J Mech Phys Solid 26:61–78, 1978) is extended to specimens undergoing microstructural changes.
The proposed extension gives rise to a generalization of the threshold concept that mirrors the way the resistance curve generalizes
the fracture toughness. In the absence of experimental data, the resistance curve near the threshold is constructed using
a basic lattice model.
KeywordsSub-critical crack growth–Threshold–Resistance curve
International Journal of Fracture 05/2012; 167(2):147-155. · 1.49 Impact Factor
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ABSTRACT: Self-assembly of a binary monolayer of charged particles is modeled using molecular dynamics and statistical mechanics. The equilibrium phase diagram for the system has three distinct phases: an ionic crystal; a geometrically ordered crystal with disordered charges; and a fluid. We show that self-assembly occurs near the phase transition between the ionic crystal and the fluid, and that the rate of ordering is sensitive to the applied pressure. By assuming an Arrhenius form for the rate of ordering, an optimality condition for the temperature and pressure is derived that maximizes the rate. Using the Clausius-Clapeyron equation, the optimal point on the phase boundary is expressed in terms of the thermodynamic changes in state variables across the boundary. The predicted optimal temperature and pressure conditions are in good agreement with numerical simulations and result in self-organization rates five times that of a simulation without applied pressure.
The Journal of chemical physics 10/2011; 135(15):154501. · 3.09 Impact Factor
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ABSTRACT: Reduced-dimensionality, coarse-grained models are commonly employed to describe the structure and dynamics of large molecular systems. In those models, the dynamics is often described by Langevin equations of motion with phenomenological parameters. This paper presents a rigorous coarse-graining method for the dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes.
The Journal of chemical physics 08/2011; 135(5):054107. · 3.09 Impact Factor
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ABSTRACT: In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.
Physical Biology 02/2008; 5(2):026008. · 2.60 Impact Factor
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ABSTRACT: We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each cross-link increases until it ruptures. The stochastic cross-link rupture process is assumed to be governed by first order kinetics with a rate that depends exponentially on the transmitted force. We have performed random searches to identify optimal cross-link configurations whose unfolding requires a large applied force (measure of strength) and/or large dissipated energy (measure of toughness). We found that such optimal chains always involve cross-links arranged to form parallel strands. The location of those optimal strands generally depends on the loading rate. Optimal chains with a small number of cross-links were found to be almost as strong and tough as optimal chains with a large number of cross-links. Furthermore, optimality of chains with a small number of cross-links can be easily destroyed by adding cross-links at random. The present findings are relevant for the interpretation of single molecule force probe spectroscopy studies of the mechanical unfolding of "load-bearing" proteins, whose native topology often involves parallel strand arrangements similar to the optimal configurations identified in the study.
Physical Review E 03/2005; 71(2 Pt 1):021904. · 2.26 Impact Factor
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ABSTRACT: Proteins that perform mechanical functions in living organisms often exhibit exceptionally high strength and elasticity. Recent studies of the unfolding of single protein molecules under mechanical loading showed that their strength is mostly determined by their native topology rather than by thermodynamic stability. To identify the topologies of polymer molecules that maximize their resistance to unfolding, we have simulated the response of cross-linked polymer chains under tensile loading and have found that chain configurations that maximize the unfolding work and force involve parallel strands. Chains with such optimal topologies tend to unfold in an all-or-none fashion, in contrast to randomly cross-linked chains, most of which exhibit low mechanical resistance and tend to unfold sequentially. These findings are consistent with AFM studies and molecular mechanics simulations of the unfolding of -sheet proteins. In particular, parallel strands give rise to the high strength of the immunoglobulin-like domains in the muscle protein titin.
The Journal of Physical Chemistry B 08/2003; 107:8730-8733. · 3.70 Impact Factor
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ABSTRACT: We discuss the statistical mechanical properties of a single polymer chain that forms cross links among its monomers. Models of this type have served as prototypes in theories of RNA and protein folding. The chain is allowed to form pseudoknots and its monomers can each participate in multiple cross links. We demonstrate that the conformational free energy of such a chain can be estimated by using an algorithm that scales as a power of the number of cross links N(N1-N3, depending on the problem). Straightforward exact evaluation of the chain partition function via multidimensional integration scales exponentially with N and often is computationally prohibitive. Our approach can also be used to compute the "entropic force" generated by a cross-linked chain when it is stretched at its ends. Such forces can be directly measured by atomic force microscopy or by laser optical trap experiments performed on single RNA, DNA, and protein molecules.
Physical Review E 08/2002; 66(1 Pt 1):011908. · 2.26 Impact Factor
