Size of a polymer molecule in solution. Part 1.—Excluded volume problem

Edwards, S. F.; Singh, Pooran

doi:10.1039/f29797501001

Cited by 97 publications

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“…2-4 were calculated by using ␦ ϭ 0, ⌬s ϭ 1k (29), and segments of two residues. The results were insensitive to ␦ and weakly dependent on the ln(l) part of the entropy cost [adjusting this term to account for excluded volume (36) affects mainly the size of the barrier], but neglecting the extension term r 2 /la 2 (25) can lead to more qualitative changes in the landscape (see SI Text and SI Fig. 7).…”

Section: Methodsmentioning

confidence: 99%

Folding domain B of protein A on a dynamically partitioned free energy landscape

Nelson

Grishin

2008

Proc. Natl. Acad. Sci. U.S.A.

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The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñ oz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar ␣-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.folding landscape ͉ frustration ͉ protein folding T he routes a protein travels on the way to its native ensemble are the result of a sensitive exchange between energy and entropy coupling the protein to its solvent environment. Often the basic topography of the folding landscape (1) can be understood just from what would be necessary kinetically for a protein-like molecule to organize itself into a particular native shape (2-4), but the detailed way in which a protein interacts with solvent can qualitatively affect the way it folds (5, 6). The conformation of a protein is coupled to large-scale fluctuations in solvent density (7-9), and for small globular proteins investigated in kinetics experiments, most of the change in solvent exposure (10) can occur before the protein is half folded. The rate at which a protein explores its conformational space is slaved to local solvent motions (11,12), and together these effects can have a significant influence on the time scale for folding.Recently methods have become available to simulate proteins with explicit solvent on a time scale long enough to explore folding (13-15). These simulations provide the most precise picture of protein kinetics, but are as a result less wieldy to describe variations that occur across different experiments and solvent conditions (16-18). Typically, much more simplistic ␣-carbon type models have been used to address these problems, and when guided by experiment they can provide an accurate description of...

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Section: Methodsmentioning

confidence: 99%

Folding domain B of protein A on a dynamically partitioned free energy landscape

Nelson

Grishin

2008

Proc. Natl. Acad. Sci. U.S.A.

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“…We expect δ ∼ λ/N , since the discrete monomers are separated by a distance |r i+1 − r i | ≈ λa on an average in the reference Hamiltonian, βH 1 . The cutoff is only imposed in theories that have a self-energy divergence [14,15,16,17], and is generally not required if there is no divergence, as is the case here. However, we will see that this cutoff is essential in order to reproduce the FECs obtained in simulations.…”

Section: Polymers Under Tension In a Good Solvent Theorymentioning

confidence: 99%

“…To compute the force-extension curves (FECs) and compare them to simulations, we use a self-consistent variational method, originally proposed by Edwards and Singh [14]. Following the convention in single molecule experiments, we use FEC for the extension changes upon application of force.…”

Section: Polymers Under Tension In a Good Solvent Theorymentioning

confidence: 99%

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Stretching Homopolymers

et al. 2007

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Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with N monomers, to force (f ) in good and poor solvents. In good solvents and for sufficiently large N we show, in accord with scaling predictions, that the mean extension along the f axis Z ∼ f for small f , and Z ∼ f 2 3 (the Pincus regime) for intermediate values of f . The theoretical predictions for Z as a function of f are in excellent agreement with simulations for N = 100 and 1600. However, even with N = 1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite N . We predict the Pincus scaling in a good solvent will be observed for N 10 5 . The forcedependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as f is varied. A strongly hydrophobic polymer remains globular as long as f is less than a critical value f c . Above f c , an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.1 arXiv:0705.3029v1 [cond-mat.soft]

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“…It is unclear to us whether this analysis applies for d = 3, but a variational wave function of the form (72) has been widely used in other disordered condensed matter situations 41 : vortex lattice with impurities in superconductors, interface in a random potential, amorphous solidification of vulcanized macromolecules,...…”

Section: High Dimension Approachmentioning

confidence: 99%

Protein Folding and Heteropolymers

Garel

Orland

Pitard

1997

Series on Directions in Condensed Matter Physics

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We present a statistical mechanics approach to the protein folding problem. We first review some of the basic properties of proteins, and introduce some physical models to describe their thermodynamics. These models rely on a random heteropolymeric description of these non random biomolecules. Various kinds of randomness are investigated, and the connection with disordered systems is discussed. We conclude by a brief study of the dynamics of proteins.Natural proteins have the property of folding into an (almost) unique compact native structure, which is of biological interest 1,2 . The compactness of this unique native state is largely due to the existence of an optimal amount of hydrophobic amino-acid residues 3 , since these biological objects are usually designed to work in water. The task of predicting the conformation of the three-dimensional structure from the linear primary sequence is often referred to as the protein folding problem. Already at this stage, a rigorous analytical theory appears difficult, since it amounts to study a mesoscopic system (most proteins have between 100 and 500 residues), notwithstanding the solvent's properties.This mesoscopic system is of a classical nature; the quantum mechanical valence electrons of the atoms induce interactions between the heavy "nuclei" which can then be treated as classical objects interacting through classical many-body interactions. This observation forms the basis of Molecular Dynamics, Monte Carlo, or Statistical Mechanical models.To further complicate the matter, both the compactness and the chemical heterogeneity of a given protein tend to slow down dynamical processes: the question of the kinetic control of the folding (as opposed to a thermodynamic control) is therefore periodically asked. This remark suggests that the folding process may have something in common with the physics of glassy systems, where competing interactions (frustration) and/or disorder lead to a very rugged phase space, resulting in slow dynamical processes. In this review, we will assume that the folded state of proteins is thermodynamically stable (the folded state is the state of minimal free energy).There has been a considerable amount of numerical simulations of proteins, using molecular dynamics or Monte Carlo calculations (for a review see 2,3,4 ).This promising approach will not be discussed in this review. We will use only analytical approaches throughout. Similarly, models emphasizing the micro-crystalline character of the folded proteins will not be addressed here 5 .The outline of this review is the following. In the first section, we introduce at an elementary level, some notions of the physics, chemistry and biology of proteins. In the second section, we study (using statistical physics methods) some heteropolymer models which are possibly relevant to the protein folding problem. The phase diagrams of these models bear some qualitative resemblance to the real systems.In the last section, we tackle the issues of dynamics. In view of the complexity of 1

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Size of a polymer molecule in solution. Part 1.—Excluded volume problem

Cited by 97 publications

References 0 publications

Folding domain B of protein A on a dynamically partitioned free energy landscape

Folding domain B of protein A on a dynamically partitioned free energy landscape

Stretching Homopolymers

Protein Folding and Heteropolymers

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