A bulk water-dependent desolvation energy model for analyzing the effects of secondary solutes on biological equilibria

A new phenomenological model for interpreting the effects of solutes on biological equilibria is presented. The model attributes changes in equilibria to differences in the desolvation energy of the reacting species that, in turn, reflect changes in the free energy of the bulk water upon addition of secondary solutes. The desolvation approach differs notably from that of other solute models by treating the free energy of bulk water as a variable and by not ascribing the observed shifts in reaction equilibria to accumulation or depletion of solutes next to the surfaces of the reacting species. On the contrary, the partitioning of solutes is viewed as a manifestation of the different subpopulations of water that arise in response to the surface boundary conditions. A thermodynamic framework consistent with the proposed model is used to derive a relationship for a specific reaction, an aqueous solubility equilibrium, in two or more solutions. The resulting equation reconciles some potential issues with the transfer free energy model of Tanford. Application of the desolvation energy model to the analysis of a two-state protein folding equilibrium is discussed and contrasted to the application of two other solute models developed by Timasheff and by Parsegian. Future tabulation of solvation energies and bulk water energies may allow biophysical chemists to confirm the mechanism by which secondary solutes influence binding and conformational equilibria and may provide a common ground on which experimentalists and theoreticians can compare and evaluate their results.     

Calculation of the free energy and cooperativity of protein folding

Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design.     

A desolvation barrier to hydrophobic cluster formation may contribute to the rate-limiting step in protein folding.

To gain insight into the free energy changes accompanying protein hydrophobic core formation, we have used computer simulations to study the formation of small clusters of nonpolar solutes in water. A barrier to association is observed at the largest solute separation that does not allow substantial solvent penetration. The barrier reflects an effective increase in the size of the cavity occupied by the expanded but water-excluding cluster relative to both the close-packed cluster and the fully solvated separated solutes; a similar effect may contribute to the barrier to protein folding/unfolding. Importantly for the simulation of protein folding without explicit solvent, we find that the interactions between nonpolar solutes of varying size and number can be approximated by a linear function of the molecular surface, but not the solvent-accessible surface of the solutes. Comparison of the free energy of cluster formation to that of dimer formation suggests that the assumption of pair additivity implicit in current protein database derived potentials may be in error.     

Free energy surfaces of miniproteins with a betabetaalpha motif: replica exchange molecular dynamics simulation with an implicit solvation model

Designed miniproteins with a betabetaalpha motif, such as BBA5, 1FSD, and 1PSV can serve as a benchmark set to test the validity of all-atom force fields with computer simulation, because they contain all the basic structural elements in protein folding. Unfortunately, it was found that the standard all-atom force fields with the generalized Born (GB) implicit solvation model tend to produce distorted free energy surfaces for the betabetaalpha proteins, not only because energetically those proteins need to be described by more balanced weights of the alpha- and beta-strands, but also because the GB implicit solvation model suffers from overestimated salt bridge effects. In an attempt to resolve these problems, we have modified one of the standard all-atom force fields in conjunction with the GB model, such that each native state of the betabetaalpha proteins is in its free energy minimum state with reasonable energy barriers separating local minima. With this modified energy model, the free energy contour map in each protein was constructed from the replica exchange molecular dynamics REMD simulation. The resulting free energy surfaces are significantly improved in comparison with previous simulation results and consistent with general views on small protein folding behaviors with realistic topology and energetics of all three proteins.     

Differences in hydration coupled to specific and nonspecific competitive binding and to specific DNA Binding of the restriction endonuclease BamHI

Using the osmotic stress technique together with a self-cleavage assay we measure directly differences in sequestered water between specific and nonspecific DNA-BamHI complexes as well as the numbers of water molecules released coupled to specific complex formation. The difference between specific and nonspecific binding free energy of the BamHI scales linearly with solute osmolal concentration for seven neutral solutes used to set water activity. The observed osmotic dependence indicates that the nonspecific DNA-BamHI complex sequesters some 120-150 more water molecules than the specific complex. The weak sensitivity of the difference in number of waters to the solute identity suggests that these waters are sterically inaccessible to solutes. This result is in close agreement with differences in the structures determined by x-ray crystallography. We demonstrate additionally that when the same solutes that were used in competition experiments are used to probe changes accompanying the binding of free BamHI to its specific DNA sequence, the measured number of water molecules released in the binding process is strikingly solute-dependent (with up to 10-fold difference between solutes). This result is expected for reactions resulting in a large change in a surface exposed area.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

Docking enzyme-inhibitor complexes using a preference-based free-energy surface

We present a docking scheme that utilizes both a surface complementarity screen as well as an energetic criterion based on surface area burial. Twenty rigid enzyme/inhibitor complexes with known coordinate sets are arbitrarily separated and reassembled to an average all-atom rms (root mean square) deviation of 1.0 Å from the native complexes. Docking is accomplished by a hierarchical search of geometrically compatible triplets of surface normals on each molecule. A pruned tree of possible bound configurations is built up using successive consideration of larger and larger triplets. The best scoring configurations are then passed through a free-energy screen where the lowest energy member is selected as the predicted native state. The free energy approximation is derived from observations of surface burial by atom pairs across the interface of known enzyme/inhibitor complexes. The occurrence of specific atom-atom surface burial, for a set of complexes with well-defined secondary structure both in the bound and unbound states, is parameterized to mimic the free energy of binding. The docking procedure guides the inhibitor into its native state using orientation and distance-dependent functions that reproduce the ideal model of free energies with an average rms deviation of 0.9 kcal/mol. For all systems studied, this docking procedure identifies a single, unique minimum energy configuration that is highly compatible with the native state. © 1996 Wiley-Liss, Inc.     

Progress in protein-protein docking: atomic resolution predictions in the CAPRI experiment using RosettaDock with an improved treatment of side-chain flexibility

RosettaDock uses real-space Monte Carlo minimization (MCM) on both rigid-body and side-chain degrees of freedom to identify the lowest free energy docked arrangement of 2 protein structures. An improved version of the method that uses gradient-based minimization for off-rotamer side-chain optimization and includes information from unbound structures was used to create predictions for Rounds 4 and 5 of CAPRI. First, large numbers of independent MCM trajectories were carried out and the lowest free energy docked configurations identified. Second, new trajectories were started from these lowest energy structures to thoroughly sample the surrounding conformation space, and the lowest energy configurations were submitted as predictions. For all cases in which there were no significant backbone conformational changes, a small number of very low-energy configurations were identified in the first, global search and subsequently found to be close to the center of the basin of attraction in the free energy landscape in the second, local search. Following the release of the experimental coordinates, it was found that the centers of these free energy minima were remarkably close to the native structures in not only the rigid-body orientation but also the detailed conformations of the side-chains. Out of 8 targets, the lowest energy models had interface root-mean-square deviations (RMSDs) less than 1.1 A from the correct structures for 6 targets, and interface RMSDs less than 0.4 A for 3 targets. The predictions were top submissions to CAPRI for Targets 11, 12, 14, 15, and 19. The close correspondence of the lowest free energy structures found in our searches to the experimental structures suggests that our free energy function is a reasonable representation of the physical chemistry, and that the real space search with full side-chain flexibility to some extent solves the protein-protein docking problem in the absence of significant backbone conformational changes. On the other hand, the approach fails when there are significant backbone conformational changes as the steric complementarity of the 2 proteins cannot be modeled without incorporating backbone flexibility, and this is the major goal of our current work.     

Evaluation of free energy landscape for base-amino acid interactions using ab initio force field and extensive sampling

Structural data of protein-DNA complex show redundancy and flexibility in base-amino acid interactions. To understand the origin of the specificity in protein-DNA recognition, we calculated the interaction free energy, enthalpy, entropy, and minimum energy maps for AT-Asn, GC-Asn, AT-Ser, and GC-Ser by means of a set of ab initio force field with extensive conformational sampling. We found that the most preferable interactions in these pairs are stabilized by hydrogen bonding, and are mainly enthalpy driven. However, minima in the free energy maps are not necessarily the same as those in the minimum energy map or enthalpy maps, due to the entropic effect. The effect of entropy is particularly important in the case of GC-Asn. Experimentally observed structures of base-amino acid interactions are within preferable regions in the calculated free energy maps, where there are many different interaction configurations with similar energy. The full geometry optimization procedure using ab initio molecular orbital method was applied to get the optimal interaction geometries for AT-Asn, GC-Asn, AT-Ser, and GC-Ser. We found that there are various base-amino acid combinations with similar interaction energies. These results suggest that the redundancy and conformational flexibility in the base-amino acid interactions play an important role in the protein-DNA recognition.     

The free energy of a liquid when viewed as a population of overlapping clusters

The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural fluctuations arises from the local athermal constraints imposed by the overlap of adjacent coordination shells. In the context of the recently developed Favoured Local Structure model [Soft Matt. 11, 3322 (2015)], we derive explicit expressions for the structural energy and entropy in the high-temperature limit, compare this approximation with simulation data and consider the extension of this free energy to the case of spatial inhomogeneity in the distribution of local structures.     

Compatible solute biosynthesis in cyanobacteria

Compatible solutes are a functional group of small, highly soluble organic molecules that demonstrate compatibility in high amounts with cellular metabolism. The accumulation of compatible solutes is often observed during the acclimation of organisms to adverse environmental conditions, particularly to salt and drought stress. Among cyanobacteria, sucrose, trehalose, glucosylglycerol and glycine betaine are used as major compatible solutes. Interestingly, a close correlation has been discovered between the final salt tolerance limit and the primary compatible solute in these organisms. In addition to the dominant compatible solutes, many strains accumulate mixtures of these compounds, including minor compounds such as glucosylglycerate or proline as secondary or tertiary solutes. In particular, the accumulation of sucrose and trehalose results in an increase in tolerance to general stresses such as desiccation and high temperatures. During recent years, the biochemical and molecular basis of compatible solute accumulation has been characterized using cyanobacterial model strains that comprise different salt tolerance groups. Based on these data, the distribution of genes involved in compatible solute synthesis among sequenced cyanobacterial genomes is reviewed, and thereby, the major compatible solutes and potential salt tolerance of these strains can be predicted. Knowledge regarding cyanobacterial salt tolerance is not only useful to characterize strain-specific adaptations to ecological niches, but it can also be used to generate cells with increased tolerance to adverse environmental conditions for biotechnological purposes.     

Evaluation of second osmotic virial coefficients from molecular simulation following scaled-particle theory

ABSTRACT

We report a scaled particle theory-based method for evaluation of second osmotic virial coefficients from molecular simulations of dilute species in solution. In this method, we evaluate the work associated with growing a cavity in solution that is perfectly permeable to the solvent but is completely impermeable to the solutes, thereby establishing an osmotic stress between the cavity interior and exterior. Extrapolating our results to determine the solute concentration in contact with a cavity with an infinite radius, we are able to evaluate the solute osmotic pressure and second osmotic virial coefficient. A finite size correction is introduced to account for the impact of effectively concentrating the solutes in the periphery of the simulation box with increasing cavity size. We demonstrate the utility of the proposed method by evaluating second osmotic virial coefficients for methane in water as a function of temperature. The approach proposed here provides a physically transparent route for calculation of second osmotic virial coefficients by direct interrogation of simulation configurations without having to explicitly evaluate the long-range integral over solute-solute correlations required following McMillan-Mayer theory.     

The molecular structure of the IsiA-Photosystem I supercomplex, modelled from high-resolution, crystal structures of Photosystem I and the CP43 protein

We present the molecular structure of the IsiA-Photosystem I (PSI) supercomplex, inferred from high-resolution, crystal structures of PSI and the CP43 protein. The structure of iron-stress-induced A protein (IsiA) is similar to that of CP43, albeit with the difference that IsiA is associated with 15 chlorophylls (Chls), one more than previously assumed. The membrane-spanning helices of IsiA contain hydrophilic residues many of which bind Chl. The optimal structure of the IsiA-PSI supercomplex was inferred by systematically rearranging the IsiA monomers and PSI trimer in relation to each other. For each of the 6,969,600 structural configurations considered, we counted the number of optimal Chl-Chl connections (i.e., cases where Chl-bound Mg atoms are ≤ 25 Å apart). Fifty of these configurations were found to have optimal energy-transfer potential. The 50 configurations could be divided into three variants; one of these, comprising 36 similar configurations, was found to be superior to the other configurations in terms of its potential to transfer excitation energy to the reaction centres under low-light conditions and its potential to dissipate excess energy under high-light conditions. Compared to the assumed model [Biochemistry 42 (2003) 3180-3188], the new Chl increases by 7% the ability of IsiA to harvest sunlight while the rearrangement of the constituent components of the IsiA-PSI supercomplex increases by 228% the energy-transfer potential. In conclusion, our model allows us to explain how the IsiA-PSI supercomplex may act as an efficient light-harvesting structure under low-light conditions and as an efficient dissipater of excess energy under high-light conditions.     

A probabilistic method for calculating the energy of hydrophobic interactions

A theoretical approach is developed for estimating the hydrophobic interaction energy on the molecular level. The underlying idea of the model is the fundamental relationship between the probability of the appearance of a solvent-excluded volume in fluid water as a result of density fluctuations, on one hand, and the free energy of primitive hydrophobic solutes, on the other. This probability is estimated basing on an information theory model in combination with experimental data on the distribution density and radial distribution function. The free energy of hydrophobic interactions is determined for a complex that consists of several hard spheres. The critical number of particles in the complex is estimated.     

Modeling Free Energy Availability from Hadean Hydrothermal Systems to the First Metabolism

Off-axis Hydrothermal Systems (HSs) are seen as the possible setting for the emergence of life. As the availability of free energy is a general requirement to drive any form of metabolism, we ask here under which conditions free energy generation by geologic processes is greatest and relate these to the conditions found at off-axis HSs. To do so, we present a conceptual model in which we explicitly capture the energetics of fluid motion and its interaction with exothermic reactions to maintain a state of chemical disequilibrium. Central to the interaction is the temperature at which the exothermic reactions take place. This temperature not only sets the equilibrium constant of the chemical reactions and thereby the distance of the actual state to chemical equilibrium, but these reactions also shape the temperature gradient that drives convection and thereby the advection of reactants to the reaction sites and the removal of the products that relate to geochemical free energy generation. What this conceptual model shows is that the positive feedback between convection and the chemical kinetics that is found at HSs favors a greater rate of free energy generation than in the absence of convection. Because of the lower temperatures and because the temperature of reactions is determined more strongly by these dynamics rather than an external heat flux, the conditions found at off-axis HSs should result in the greatest rates of geochemical free energy generation. Hence, we hypothesize from these thermodynamic considerations that off-axis HSs seem most conducive for the emergence of protometabolic pathways as these provide the greatest, abiotic generation rates of chemical free energy.     

On the osmoregulation in Atriplex hymenelytra (Torr.) Wats. (Chenopodiaceae)

Summary Aspects of osmoregulation were studied in leaves of irrigated and nonirrigated plants of Atriplex hymenelytra (Torr.) Wats. (Chenopodiaceae) from their natural habitat in Death Valley, California. Using a set of several data concentrations of inorganic electrolytes (Na⁺, K⁺, Cl^-) and of oxalate in the mesophyll of this salt secreting species were calculated. The osmotic potential resulting from these solutes (under consideration of an empirically estimated osmotic coefficient) is in good agreement with field measurements of the overall osmotic potential in the leaf mesophyll as determined by pressure-volume curves. This indicates that these 4 electrolytes are the main osmotically active solutes. Oxalate is present in comparably high concentrations and is used to achieve ion balance.Organic solutes analyzed include soluble carbohydrates (mono-, di- and oligosaccharides), amino- and organic acids as well as glycinebetaine. Of these, organic- and amino acids (including proline) contribute only little to osmoregulation. Soluble carbohydrates and especially glycinebetaine exhibit concentrations high enough for generating considerable osmotic potentials, at least if these compounds are regarded to be restricted to the cytoplasm acting as compatible solutes.