Statistical interpretation of enthalpy–entropy compensation

Krug, R. R.; Hunter, William G.; Grieger, R. A.

doi:10.1038/261566a0

Cited by 198 publications

(164 citation statements)

References 11 publications

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“…These locations correspond to the low orientational entropy locations seen above, indicating water molecules that are low in both energy and entropy, as might be expected, given the common, though debated, phenomenon of entropy-enthalpy compensation. [66][67][68][69][70][71] Second, there is a shell around the entire host comprising water molecules that have unfavorable energies because of their interactions with the host's repulsive Lennard-Jones wall. However, this shell is lightly populated, so water molecules in this region do not significantly contribute to the overall energy of solvation.…”

Section: Regular Host a Translational Entropy And Water Densitymentioning

confidence: 99%

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Nguyen

Young²,

Gilson³

2012

The Journal of Chemical Physics

302

506

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The displacement of perturbed water upon binding is believed to play a critical role in the thermodynamics of biomolecular recognition, but it is nontrivial to unambiguously define and answer questions about this process. We address this issue by introducing grid inhomogeneous solvation theory (GIST), which discretizes the equations of inhomogeneous solvation theory (IST) onto a threedimensional grid situated in the region of interest around a solute molecule or complex. Snapshots from explicit solvent simulations are used to estimate localized solvation entropies, energies, and free energies associated with the grid boxes, or voxels, and properly summing these thermodynamic quantities over voxels yields information about hydration thermodynamics. GIST thus provides a smoothly varying representation of water properties as a function of position, rather than focusing on hydration sites where solvent is present at high density. It therefore accounts for full or partial displacement of water from sites that are highly occupied by water, as well as for partly occupied and water-depleted regions around the solute. GIST can also provide a well-defined estimate of the solvation free energy and therefore enables a rigorous end-states analysis of binding. For example, one may not only use a first GIST calculation to project the thermodynamic consequences of displacing water from the surface of a receptor by a ligand, but also account, in a second GIST calculation, for the thermodynamics of subsequent solvent reorganization around the bound complex. In the present study, a first GIST analysis of the molecular host cucurbit [7]uril is found to yield a rich picture of hydration structure and thermodynamics in and around this miniature receptor. One of the most striking results is the observation of a toroidal region of high water density at the center of the host's nonpolar cavity. Despite its high density, the water in this toroidal region is disfavored energetically and entropically, and hence may contribute to the known ability of this small receptor to bind guest molecules with unusually high affinities. Interestingly, the toroidal region of high water density persists even when all partial charges of the receptor are set to zero. Thus, localized regions of high solvent density can be generated in a binding site without strong, attractive solute-solvent interactions.

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Section: Regular Host a Translational Entropy And Water Densitymentioning

confidence: 99%

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Nguyen

Young²,

Gilson³

2012

The Journal of Chemical Physics

302

506

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“…This possibility was originally discussed by Lumry and Rajender (1970) in a detailed review of compensation. A concise discussion of this was presented by Krug et al (1976), who showed that a simple statistical test can be used to determine the significance of such ⌬S versus ⌬H plots. The confidence interval for Tc is determined from a linear regression analysis of this plot and we ask whether the experimental temperature T (or harmonic mean experimental temperature if data are obtained at different temperatures) lies outside this confidence interval.…”

Section: Discussionmentioning

confidence: 99%

Entropy—enthalpy compensation: Fact or artifact?

2001

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The phenomenon of entropy-enthalpy (S-H) compensation is widely invoked as an explanatory principle in thermodynamic analyses of proteins, ligands, and nucleic acids. It has been suggested that this compensation is an intrinsic property of either complex, fluctuating, or aqueous systems. The questions examined here are whether the observed compensation is extra-thermodynamic (i.e., reflects anything more than the wellknown laws of statistical thermodynamics) and if so, what does it reveal about the system? Compensation is rather variably defined in the literature and different usages are discussed. The most precise and interesting one, which is considered here, is a linear relationship between ⌬H and ⌬S for some series of perturbations or changes in experimental variable. Some recent thermodynamic data on proteins purporting to show compensation is analyzed and shown to be better explained by other causes. A general statistical mechanical model of a complex system is analyzed to explore whether and under what conditions extrathermodynamic compensation can occur and what it reveals about the system. This model shows that the most likely behavior to be seen is linear S-H compensation over a rather limited range of perturbations with a compensation temperature Tc ‫ס‬ d⌬H/d⌬S within 20% of the experimental temperature. This behavior is insensitive to the details of the model, thus revealing little extra-thermodynamic or causal information about the system. In addition, it will likely be difficult to distinguish this from more trivial forms of compensation in real experimental systems. Keywords: Entropy-enthalpy compensation; protein thermodynamicsThe phenomenon of entropy-enthalpy compensation (referred to hereafter as compensation) is widely invoked as an explanatory principle in thermodynamic analyses of proteins, ligands, and nucleic acids. A far-from-exhaustive literature search in biological and chemical databases using the keywords entropy, enthalpy, and compensation yields >200 references to date. The term entropy-enthalpy compensation, however, is applied variably in this literature. The phenomena described by this term can be grouped into four categories, as follows:(1) The concomitant increase in S and H with temperature, basically, a restatement of the thermodynamic definitionswhere H, S, and T are the enthalpy, entropy, and absolute temperatures, respectively, and the derivatives are taken at constant pressure. Depending on whether Cp is temperature dependent or not and the range of temperatures examined, a plot of H versus S for a series of experiments at different temperatures may appear linear.(2) For some series of perturbations or changes in experimental variable other than temperature, ⌬S and ⌬H have the same sign. This is referred to here as the weak form of compensation. Examination of the statistical mechanical definitions of S and H in terms of the partition function (e.g., Hill 1986) shows that they depend in the same qualitative way on the distribution of the system among different en...

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“…[48] Sharp recently pointed out how the significance of a plot of DH versus DS could be evaluated. [49d] A statistical test that was developed more than 25 years ago [50] shows that a DH versus DS correlation has no statistical significance (at 95 % confidence level) if the average experimental temperature of the experiments T lies within the 95 % confidence level (AE 2s) of T C , where T C is the slope of the DH versus DS plot. In other words, if T C is within 20 % of the average temperature of measurement, the correlation is unlikely to be significant.…”

Section: Angewandte Chemiementioning

confidence: 99%

Binding Affinities of Host–Guest, Protein–Ligand, and Protein–Transition‐State Complexes

et al. 2003

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The affinities of hosts—ranging from small synthetic cavitands to large proteins—for organic molecules are well documented. The average association constants for the binding of organic molecules by cyclodextrins, synthetic hosts, and albumins in water, as well as of catalytic antibodies or enzymes for substrates are 103.5±2.5 M−1. Binding affinities are elevated to 108±2 M−1 for the complexation of transition states and biological antigens by antibodies or inhibitors by enzymes, and to 1016±4 M−1 for transition states with enzymes. The origins of the distributions of association constants observed for the broad range of host–guest systems are explored in this Review, and typical approaches to compute and analyze host–guest binding in solution are discussed. In many classes of complexes a rough correlation is found between the binding affinity and the surface area that is buried upon complexation. Enzymes transcend this effect and achieve transition‐state binding much greater than is expected from the surface areas.

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Statistical interpretation of enthalpy–entropy compensation

Cited by 198 publications

References 11 publications

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Entropy—enthalpy compensation: Fact or artifact?

Binding Affinities of Host–Guest, Protein–Ligand, and Protein–Transition‐State Complexes

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