Reviewing the thermodynamic parameters characterizing self-association and ligand binding of proteins at 25 OC, we find AGO, AHo, AS\", and ACpo are often all of negative sign. It is thus not possible to account for the stability of association complexes of proteins on the basis of hydrophobic interactions alone. We present a conceptual model of protein association consisting of two steps: the mutual penetration of hydration layers causing disordering of the solvent followed by further short-range interactions. The net AGO for the complete association process is primarily determined by the positive entropy change accompanying the first step and the negative enthalpy change of the second step. On the basis of the thermochemical behavior of small molecule interactions, we conclude that the strengthening of hydrogen bonds in the I n the past decade, a complete thermodynamic description of the self-association of many proteins and their interactions From the Laboratory of Molecular Biology (P.D.R.) and Laboratory of Nutrition and Endocrinology (S.S.), National Institute of Arthritis, Metabolism and Digestive Diseases, National Institutes of Health, Bethesda, Maryland 20205. Received September 23, 1980. low dielectric macromolecular interior and van der Waals' interactions introduced as a consequence of the hydrophobic effect are the most important factors contributing to the observed negative values of AHo and ASo and hence to the stability of protein association complexes. The X-ray crystallographic structures of these complexes are consonant with this analysis. The tendency for protein association reactions to become entropy dominated and/or entropy-enthalpy assisted at low temperatures and enthalpy dominated at high temperatures (a consequence of the typically negative values of AC,\") arises from the diminution of the hydrophobic effect with increasing temperature which is a general property of the solvent, water. with small molecular substrates has become available. Concomitantly, X-ray crystallography has provided a detailed picture of some of these associations, and this has stimulated a number of theoretical studies (Levitt & Warshel, 1975; Gelin & Karplus, 1975; Chothia & Janin, 1975), based upon energetic considerations, to account for these structures. The This article not subject to U S . Copyright. Published 1981 by the American Chemical Society T H E R M O D Y N A M I C S O F P R O T E I N A S S O C I A T I O N V O L . 2 0 , N O . 1 1 , 1 9 8 1 3097 Table I: Thermodynamics of Protein Association' association process A G \" ~ AiY A s o , A c p o (kcal mol-') (kcal mol-l) (cal K-I mol-') (cal K-I mol-I) refb trypsin (bovine) + inhibitor (soybean) -14.6 8.6 78 -440 c, d deoxyhemoglobin S gelation -3.4 2.0 18 -200 e, f lysozyme self-association (indefinite) -3.9 -6 .4 -8.3 g glucagon trimerization -12.1 -3 1 -64 -430 h, i hemoglobin t haptoglobin -11.5 -3 3 -7 3 -940 i a-chymotrypsin dimerization -7.1 -35 -9 5 k, I S-peptide + S-protein (ribonuclease) -13 -40 -90 -1100 m, n All thermodynamic parameters expressed per mole of complex formed except the indefinite association cases of hemoglobin S and lysozyme for which the mole refers to the monomeric protein reacted. Unitary entropy and free energy are given for processes of defined stoichiometry. Standard states are hypothetical 1 M protein, pH at which the reaction was measured. All pHs were close to 7 except for trypsin, pH 5, haptoglobin, pH 5.5, and glucagon, pH 10.5. All data for 25 \"C except glucagon, T = 30 \"C. ence is to calorimetric work and the second is to X-ray crystallographic structure determination. al. (1974). e Rosset al. (1977). Wishner e t al. (1975). g Banerjee et al. (1975). Johnson et al. (1979). * Sasaki et al. (1975). For each entry, the first referSweet et Baugh & Trowbridge (1972). Lavialle et al. (1974). Shiao & Sturtevant (1969). lVandlen &Tulinsky (1973). Hearn et al. (1971). Wyckoff e t al. (1970). methodology and problems involved in such calculations have been critically reviewed by NBmethy & Scheraga (1977). In this paper we review the thermodynamics of protein association processes for the examples best characterized in terms of their chemistry and structure. From this survey we find that the thermodynamic parameters AGO, Ai?, AS\", and ACpo are predominantly of negative sign. This result poses severe difficulties for interpretations of protein association based upon the entropically driven hydrophobic effect. The aim of this paper is to attempt to account for the signs and magnitudes of these thermodynamic parameters for protein association reactions in terms of known molecular forces and the thermochemistry of small molecule interactions.

Thermodynamics of protein association reactions: forces contributing to stability

The manner in which a newly synthesized chain of amino acids transforms itself into a perfectly folded protein depends both on the intrinsic properties of the amino-acid sequence and on multiple contributing influences from the crowded cellular milieu. Folding and unfolding are crucial ways of regulating biological activity and targeting proteins to different cellular locations. Aggregation of misfolded proteins that escape the cellular quality-control mechanisms is a common feature of a wide range of highly debilitating and increasingly prevalent diseases.

Protein folding and misfolding

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

/pdf/microfluidics-fluid-physics-at-the-nanoliter-scale-4bpahtd8qa.pdf

Microfluidics: Fluid physics at the nanoliter scale

While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large number of applications, limitations in the model with respect to the equilibrium between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non Gly, Pro) backbone CMAP potential has been refined against experimental solution NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mechanical energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mechanical energy surfaces, followed by additional empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against data not used to guide parametrization: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equilibrium folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for the modeling and simulation studies of proteins, including studies of protein folding, assembly and functionally relevant conformational changes.

/pdf/optimization-of-the-additive-charmm-all-atom-protein-force-4qtc6t5kz1.pdf

Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles.

[This corrects the article on p. 100 in vol. 41.].

Energy conservation in chemotrophic anaerobic bacteria.

Protein chains coil into α-helices and β-sheet structures. Knowing the timescales and mechanism of formation of these basic structural elements is essential for understanding how proteins fold1. For the past 40 years, α-helix formation has been extensively investigated in synthetic and natural peptides2,3,4,5, including by nanosecond kinetic studies6,7. In contrast, the mechanism of formation of β structures has not been studied experimentally. The minimal β-structure element is the β-hairpin, which is also the basic component of antiparallel β-sheets. Here we use a nanosecond laser temperature-jump apparatus to study the kinetics of folding a β-hairpin consisting of 16 amino-acid residues. Folding of the hairpin occurs in 6 µs at room temperature, which is about 30 times slower than the rate of α-helix formation6,7. We have developed a simple statistical mechanical model that provides a structural explanation for this result. Our analysis also shows that folding of a β-hairpin captures much of the basic physics of protein folding, including stabilization by hydrogen bonding and hydrophobic interactions, two-state behaviour, and a funnel-like, partially rugged energy landscape.

Folding dynamics and mechanism of β-hairpin formation

Protein folding is inherently a heterogeneous process because of the very large number of microscopic pathways that connect the myriad unfolded conformations to the unique conformation of the native structure. In a first step towards the long-range goal of describing the distribution of pathways experimentally, Forster resonance energy transfer1 (FRET) has been measured on single, freely diffusing molecules2,3,4. Here we use this method to determine properties of the free-energy surface for folding that have not been obtained from ensemble experiments. We show that single-molecule FRET measurements of a small cold-shock protein expose equilibrium collapse of the unfolded polypeptide and allow us to calculate limits on the polypeptide reconfiguration time. From these results, limits on the height of the free-energy barrier to folding are obtained that are consistent with a simple statistical mechanical model, but not with the barriers derived from simulations using molecular dynamics. Unlike the activation energy, the free-energy barrier includes the activation entropy and thus has been elusive to experimental determination for any kinetic process in solution.

/pdf/probing-the-free-energy-surface-for-protein-folding-with-172shkygjx.pdf

Probing the free-energy surface for protein folding with single-molecule fluorescence spectroscopy

http://dasher.wustl.edu/bio5325/reading/curropstrbio-14-76-04.pdf

The protein folding 'speed limit'.

Protein folding studied by single-molecule FRET.

An elementary statistical mechanical model was used to calculate the folding rates for 22 proteins from their known three-dimensional structures. In this model, residues come into contact only after all of the intervening chain is in the native conformation. An additional simplifying assumption is that native structure grows from localized regions that then fuse to form the complete native molecule. The free energy function for this model contains just two contributions—conformational entropy of the backbone and the energy of the inter-residue contacts. The matrix of inter-residue interactions is obtained from the atomic coordinates of the three-dimensional structure. For the 18 proteins that exhibit two-state equilibrium and kinetic behavior, profiles of the free energy versus the number of native peptide bonds show two deep minima, corresponding to the native and denatured states. For four proteins known to exhibit intermediates in folding, the free energy profiles show additional deep minima. The calculated rates of folding the two-state proteins, obtained by solving a diffusion equation for motion on the free energy profiles, reproduce the experimentally determined values surprisingly well. The success of these calculations suggests that folding speed is largely determined by the distribution and strength of contacts in the native structure. We also calculated the effect of mutations on the folding kinetics of chymotrypsin inhibitor 2, the most intensively studied two-state protein, with some success.

https://www.pnas.org/content/pnas/96/20/11311.full.pdf

William A. Eaton

Papers

Folding dynamics and mechanism of β-hairpin formation

Probing the free-energy surface for protein folding with single-molecule fluorescence spectroscopy

The protein folding 'speed limit'.

Protein folding studied by single-molecule FRET.

A simple model for calculating the kinetics of protein folding from three-dimensional structures