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.

An all-atom protein force field, CHARMM36m, offers improved accuracy for simulating intrinsically disordered peptides and proteins. The all-atom additive CHARMM36 protein force field is widely used in molecular modeling and simulations. We present its refinement, CHARMM36m (
 http://mackerell.umaryland.edu/charmm_ff.shtml
 ), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.

/pdf/charmm36m-an-improved-force-field-for-folded-and-hi2fge7lt7.pdf

CHARMM36m: An improved force field for folded and intrinsically disordered proteins

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

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

The protein folding 'speed limit'.

Publisher Summary The chapter describes the understanding of the physics and physical chemistry of sickle cell hemoglobin polymerization in solutions and in red cells. The polymerization of sickle cell hemoglobin has probably become the best understood of all protein self-assembly systems. The structure of the hemoglobin S molecule, the structure of the various aggregated forms of hemoglobin S, and the structural analysis of the polymers are discussed in the chapter. The chapter discusses the thermodynamics of hemoglobin S polymerization, and includes a description of the nonideal behavior of concentrated hemoglobin S solutions and the effects of physiologically relevant variables, especially oxygen, and the presence of non-S hemoglobins on the polymerization process. Understanding the polymerization process is not only important for understanding the pathophysiology of sickle cell disease, but is critical to the major problem of developing a specific therapy that could be used in the treatment of patients. The kinetic and thermodynamic studies have played a major role by providing relevant and sensitive assays for potential therapeutic agents. The results of the thermodynamic and kinetic studies of solutions are used to explain various properties of cells, including morphological and rheological properties.

Sickle cell hemoglobin polymerization.

Publisher Summary This chapter summarizes the properties of the singular value decomposition, which are relevant for data analysis. The chapter describes the way in which the singular value decomposition (SVD) of a noise-free data set for which the spectra, f , and concentration, c , vectors are known can be calculated from consideration of the integrated overlaps of these components. Because data analysis necessarily begins with matrices, which are “noisy” at some level of precision, the chapter describes some of the properties of the SVD of matrices, which contain noise. It describes the SVD of random matrices (that is, matrices containing only noise). The chapter explores the way the random amplitudes are distributed in the SVD output when noise is added to a data matrix by using perturbation theory. The chapter discusses the significant advantages that result from the application of SVD and complementary processing techniques for the analysis of large sets of experimental data.

[8] Singular value decomposition: Application to analysis of experimental data

Nanosecond lasers were used to measure the rate of conformational changes in myoglobin after ligand dissociation at ambient temperatures. At low solvent viscosities the rate is independent of viscosity, but at high viscosities it depends on approximately the inverse first power of the viscosity. Kramers theory for unimolecular rate processes can be used to explain this result if the friction term is modified to include protein as well as solvent friction. The theory and experiment suggest that the dominant factor in markedly reducing the rate of conformational changes in myoglobin at low temperatures (less than 200 K) is the very high viscosity (greater than 10(7) centipoise) of the glycerol-water solvent. That is, at low temperatures conformational substates may not be "frozen" so much as "stuck."

https://science.sciencemag.org/content/sci/256/5065/1796.full.pdf

James Hofrichter

Papers

Folding dynamics and mechanism of β-hairpin formation

The protein folding 'speed limit'.

Sickle cell hemoglobin polymerization.

[8] Singular value decomposition: Application to analysis of experimental data

The role of solvent viscosity in the dynamics of protein conformational changes