Charge transfer across biomembranes: A solution to the conundrum of high desolvation free energy penalty in ion transport

Charge transfer across membranes is an important problem in a wide variety of fundamental physicochemical and biological processes. Since Mitchell's concept of the ion well advanced in 1968, several models of ion translocation across biomembranes, for instance through the membrane-bound FO portion of ATP synthase have been proposed. None of these models has considered the large desolvation free energy penalty of ~500 meV incurred in transferring a protonic charge from the aqueous phase into the membrane that hinders such charge transfer processes. The difficulty has been pointed out repeatedly. However, the problem of how the adverse ∆Gdesolvation barrier is overcome in order to enable rapid ion translocation in biomembranes has not been satisfactorily resolved. Hence the fact that the self-energy of the charges has been overlooked can be regarded as a main source of confusion in the field of bioenergetics. Further, in order to consider charges of a finite size (and not just point charges), the free energy of transferring the ions from water into a membrane phase of lower dielectric εm needs to be evaluated. Here a solution to the longstanding conundrum has been proposed by including the bound anion - the second ion in Nath's two-ion theory of energy coupling and ATP synthesis - in the free energy calculations. The mechanistic importance of the H+ - A- charge pair in causing rotation and ATP synthesis by ion-protein interactions is highlighted. The ∆G calculations have been performed by using the Kirkwood-Tanford-Warshel (KTW) theory that takes into account the self-energies of the ions. The results show that the adverse ∆Gdesolvation can be almost exactly compensated by the sum of the electrostatic free energy of the charge-charge interactions and the dipole solvation energy for long-range ion pairs. Results of free energy compensation using the KTW theory have been compared with experimental data on the ∆G of ion pairs and shown to be in reasonable agreement. A general thermodynamic cycle for coupled ion transfer has been constructed to further elucidate facilitated ion permeation between water and membrane phases. Molecular interpretations of the results and their implications for various mechanisms of energy transduction have been discussed. We firmly believe that use of electrostatic theories such as the KTW theory that properly include the desolvation free energy penalty arising from the self-energy of the relevant ions are crucial for quantifying charge transfer processes in bioenergetics. Finally, the clear-cut implication is that proton-only and single-ion theories of ATP synthesis, such as the chemiosmotic theory, are grossly inadequate to comprehend energy storage and transduction in biological processes.

Probing the structural determinants for the function of intracellular loop 2 in structurally cognate G-protein-coupled receptors

Intracellular loop 2 (IL2) in G-protein-coupled receptors (GPCRs) is functionally important, e.g., in binding to G-protein and β-arrestin. Differences in secondary structure of IL2 in the crystal structures of the very similar β(1)- and β(2)-adrenergic receptors (β(1)AR and β(2)AR, respectively), i.e., an α-helix and an L-shaped strand, respectively, emphasize the need to understand the structural basis for IL2 functionality. We studied the properties of IL2 in the context of experimental data using a Monte Carlo-based ab initio method. The procedure was validated first by verifying that the IL2 structures in β(1)AR and β(2)AR crystals were correctly reproduced, even after conformational ensemble searches at >1200 K where most secondary structure had been lost. We found that IL2 in β(1)AR and β(2)AR sampled each other's conformation but adopted different energetically preferred conformations, consistent with the crystal structures. The results indicate a persistent contextual preference for the structure of IL2, which was conserved when the IL2 sequences were interchanged between the receptors. We conclude that the protein environment, more than the IL2 sequence, regulates the IL2 structures. We extended the approach to the molecular model of 5-HT(2A)R for which no crystal structure is available and found that IL2 is predominantly helical, similar to IL2 in β(1)AR. Because the P3.57A mutation in IL2 had been shown to decrease β-arrestin binding and internalization, we predicted the effects of the mutation and found that it decreased the propensity of IL2 to form helix, identifying the helical IL2 as a component of the GPCR active form.

Distance and exposure dependent effective dielectric function

In an effort to develop a dielectric screening function for molecular dynamics simulations of biomolecules in implicit solvent, effective dielectric constants (D(eff)) for a large number of atom pairs in a typical globular protein are calculated by continuum electrostatics. Plots of D(eff) versus the intercharge distance are in general sigmoidal with the characteristics of the curve depending on the distance of the two charges from the dielectric boundary and, secondarily, on the extent to which the area surrounding each charge is occupied by solvent (the "exposure"). The D(eff) values were fitted to an empirical, analytical function of these parameters that reproduces the data reasonably well, although considerable scatter exists in the range of D(eff) from 30 to 80. In the system used for parameterization, the mean square deviation of electrostatic interaction energies with this function is 0.48 kcal/mol, compared to 1.45 for an analytical Generalized Born model and 1.52 for the linear distance-dependent dielectric model. When tested in other proteins of varying size and compactness, the present function is superior to both of the above models, except for a fully unfolded polypeptide chain, where the Generalized Born model is superior.

A critical analysis of continuum electrostatics: the screened Coulomb potential--implicit solvent model and the study of the alanine dipeptide and discrimination of misfolded structures of proteins

An analysis of the screened Coulomb potential--implicit solvent model (SCP--ISM) is presented showing that general equations for both the electrostatic and solvation free energy can be derived in a continuum approach, using statistical averaging of the polarization field created by the solvent around the molecule. The derivation clearly shows how the concept of boundary, usually found in macroscopic approaches, is eliminated when the continuum model is obtained from a microscopic treatment using appropriate averaging techniques. The model is used to study the alanine dipeptide in aqueous solution, as well as the discrimination of native protein structures from misfolded conformations. For the alanine dipeptide the free energy surface in the phi--psi space is calculated and compared with recently reported results of a detailed molecular dynamics simulation using an explicit representation of the solvent, and with other available data. The study showed that the results obtained using the SCP--ISM are comparable to those of the explicit water calculation and compares favorably to the FDPB approach. Both transition states and energy minima show a high correlation (r > 0.98) with the results obtained in the explicit water analysis. The study of the misfolded structures of proteins comprised the analysis of three standard decoy sets, namely, the EMBL, Park and Levitt, and Baker's CASP3 sets. In all cases the SCP--ISM discriminated well the native structures of the proteins, and the best-predicted structures were always near-native (cRMSD approximately 2 A).

What are the dielectric "constants" of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.

Buried charged surface in proteins

BACKGROUND

The traditional picture of charged amino acids in globular proteins is that they are almost exclusively on the outside exposed to the solvent. Buried charges, when they do occur, are assumed to play an essential role in catalysis and ligand binding, or in stabilizing structure as, for instance, helix caps.

RESULTS

By analyzing the amount and distribution of buried charged surface and charges in proteins over a broad range of protein sizes, we show that buried charge is much more common than is generally believed. We also show that the amount of buried charge rises with protein size in a manner which differs from other types of surfaces, especially aromatic and polar uncharged surfaces. In large proteins such as hemocyanin, 35% of all charges are greater than 75% buried. Furthermore, at all sizes few charged groups are fully exposed. As an experimental test, we show that replacement of the buried D178 of muconate lactonizing enzyme by N stabilizes the enzyme by 4.2 degrees C without any change in crystallographic structure. In addition, free energy calculations of stability support the experimental results.

CONCLUSIONS

Nature may use charge burial to reduce protein stability; not all buried charges are fully stabilized by a prearranged protein environment. Consistent with this view, thermophilic proteins often have less buried charge. Modifying the amount of buried charge at carefully chosen sites may thus provide a general route for changing the thermophilicity or psychrophilicity of proteins.