Polar and nonpolar atomic environments in the protein core: Implications for folding and binding

Hydrophobic interactions are believed to play an important role in protein folding and stability. Semi-empirical attempts to estimate these interactions are usually based on a model of solvation, whose contribution to the stability of proteins is assumed to be proportional to the surface area buried upon folding. Here we propose an extension of this idea by defining an environment free energy that characterizes the environment of each atom of the protein, including solvent, polar or nonpolar atoms of the same protein or of another molecule that interacts with the protein. In our model, the difference of this environment free energy between the folded state and the unfolded (extended) state of a protein is shown to be proportional to the area buried by nonpolar atoms upon folding. General properties of this environment free energy are derived from statistical studies on a database of 82 well-refined protein structures. This free energy is shown to be able to discriminate misfolded from correct structural models, to provide an estimate of the stabilization due to oligomerization, and to predict the stability of mutants in which hydrophobic residues have been substituted by site-directed mutagenesis, provided that no large structural modifications occur. © 1994 Wiley-Liss, Inc.     

Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

Protein folding in high-dimensional spaces: hypergutters and the role of nonnative interactions

We explore the consequences of very high dimensionality in the dynamical landscape of protein folding. Consideration of both typical range of stabilizing interactions, and folding rates themselves, leads to a model of the energy hypersurface that is characterized by the structure of diffusive "hypergutters" as well as the familiar "funnels". Several general predictions result: 1), intermediate subspaces of configurations will always be visited; 2), specific but nonnative interactions may be important in stabilizing these low-dimensional diffusive searches on the folding pathway, as well as native interactions; 3), sequential barriers will commonly be found, even in "two-state" proteins; 4), very early times will show characteristic departures from single-exponential kinetics; and 5), contributions of nonnative interactions to Phi-values and "Chevron plots" are calculable, and may be significant. The example of a three-helix bundle is treated in more detail as an illustration. The model also shows that high-dimensional structures provide conceptual relations between different models of protein folding. It suggests that kinetic strategies for fast folding may be encoded rather generally in nonnative as well as in native interactions. The predictions are related to very recent findings in experiment and simulation.     

Hammond behavior versus ground state effects in protein folding: evidence for narrow free energy barriers and residual structure in unfolded states

Apparent transition state movement upon mutation or changes in solvent conditions is frequently observed in protein folding and is often interpreted in terms of Hammond behavior. This led to the conclusion that barrier regions in protein folding are broad maxima on the free energy landscape. Here, we use the concept of self-interaction and cross-interaction parameters to test experimental data of 21 well-characterized proteins for Hammond behavior. This allows us to characterize the origin of transition state movements along different reaction coordinates. Only one of the 21 proteins shows a small but coherent transition state movement in agreement with the Hammond postulate. In most proteins the structure of the transition state is insensitive to changes in protein stability. The apparent change in the position of the transition state upon mutation, which is frequently observed in phi-value analysis, is in most cases due to ground-state effects caused by structural changes in the unfolded state. This argues for significant residual structure in unfolded polypeptide chains of many proteins. Disruption of these residual interactions by mutation often leads to decreased folding rates, which implies that these interactions are still present in the transition state. The failure to detect Hammond behavior shows that the free energy barriers encountered by a folding polypeptide chain are generally rather narrow and robust maxima for all experimentally explorable reaction coordinates.     

Minimizing frustration by folding in an aqueous environment

Although life as we know it evolved in an aqueous medium, the properties of water are not completely understood. In this review, we focus on the role of water in guiding protein folding and stability. Specifically, we discuss the mechanisms of protein folding in an aqueous environment, the effects of water on the folding energy landscape as well as the transition state ensemble, and interactions of water with the folded state. We show that water cannot be viewed as a passive solvent, but rather, plays a very active role in the life of a protein.     

Multiscale simulations of protein folding: application to formation of secondary structures

A multiscale simulation method of protein folding is proposed, using atomic representation of protein and solvent, combing genetic algorithms to determine the key protein structures from a global view, with molecular dynamic simulations to reveal the local folding pathways, thus providing an integrated landscape of protein folding. The method is found to be superior to previously investigated global search algorithms or dynamic simulations alone. For secondary structure formation of a selected peptide, RN24, the structures and dynamics produced by this method agree well with corresponding experimental results. Three most populated conformations are observed, including hairpin, β-sheet and α-helix. The energetic barriers separating these three structures are comparable to the kinetic energy of the atoms of the peptide, implying that the transition between these states can be easily triggered by kinetic perturbations, mainly through electrostatic interactions between charged atoms. Transitions between α-helix and β-sheet should jump over at least two energy barriers and may stay in the energetic trap of hairpin. It is proposed that the structure of proteins should be jointly governed by thermodynamic and dynamic factors; free energy is not the exclusive dominant for stability of proteins.     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

The cytochrome c folding landscape revealed by electron-transfer kinetics

We have investigated the folding energy landscape of cytochrome c by exploiting the widely different electron-transfer (ET) reactivities of buried and exposed Zn(II)-substituted hemes. An electronically excited Zn-porphyrin in guanidine hydrochloride denatured Zn-substituted cytochrome c (Zn-cyt c) reduces ruthenium(III) hexaammine about ten times faster than when embedded in the fully folded protein. Measurements of ET kinetics during Zn-cyt c folding reveal a burst intermediate in which one-third of the ensemble has a protected Zn-porphyrin and slow ET kinetics; the remaining fraction exhibits fast ET characteristic of a solvent-exposed redox cofactor. The ET data show that, under solvent conditions favoring the folded protein, collapsed non-native structures are not substantially more stable than extended conformations, and that the two populations interchange rapidly. Most of the folding free energy, then, is released when compact structures evolve into the native fold.     

Computational protein design with electrostatic focusing: Experimental characterization of a conditionally folded helical domain with a reduced amino acid alphabet

Automated methodologies to design synthetic proteins from first principles use energy computations to estimate the ability of the sequences to adopt a targeted structure. This approach is still far from systematically producing native-like sequences, due, most likely, to inaccuracies when modeling the interactions between the protein and its aqueous environment. This is particularly challenging when engineering small protein domains (with less polar pair interactions than with the solvent). We have re-designed a three-helix bundle, domain B, using a fixed backbone and a four amino acid alphabet. We have enlarged the rotamer library with conformers that increase the weight of electrostatic interactions within the design process without altering the energy function used to compute the folding free energy. Our synthetic sequences show less than 15% similarity to any Swissprot sequence. We have characterized our sequences in different solvents using circular dichroism and nuclear magnetic resonance. The targeted structure achieved is dependent on the solvent used. This method can be readily extended to larger domains. Our method will be useful for the engineering of proteins that become active only in a given solvent and for designing proteins in the context of hydrophobic solvents, an important fraction of the situations in the cell.     

154 Protein folding and binding funnels: a common driving force and a common mechanism

Under the free energy landscape theory, both the protein-folding and protein–ligand binding processes are driven by the decrease in total Gibbs free energy of the protein-solvent or protein–ligand-solvent system, which involves the non-complementary changes between the entropy and enthalpy, ultimately leading to a global free energy minimization of these thermodynamic systems (Ji & Liu, 2011; Liu et al., 2012; Yang, Ji & Liu, 2012). In the case of protein folding, the lowering of the system free energy coupled with the gradual reduction in conformational degree of freedom of the folding intermediates determines that the shape of the free energy landscape for protein folding must be funnel-like (Dill & Chan, 1997), rather than non-funneled shapes (Ben-Naim, 2012). In the funnel-like free energy landscape, protein folding can be viewed as going down the hill via multiple parallel routes from a vast majority of individual non-native states on surface outside the funnel to the native states located around the bottom of the funnel. The first stage of folding, i.e. the rapid hydrophobic collapse process, is driven by the solvent entropy maximization. Concretely, the water molecules squeeze and sequestrate the hydrophobic amino acid side chains within the interior of the folding intermediates while exposing the polar and electrostatically charged side chains on the intermediate surface so as to minimize the solvent-accessible surface area of the solute and thus, the minimal contacts between the folding intermediates and the water molecules. This will maximize the entropy of the solvent, thus contributing substantially to lowering of the system free energy due to an absolute advantage of the solvent in both quantity and mass (Yang, Ji & Liu, 2012). The resulting molten globule states (Ohgushi & Wada, 1983), within which a few transient secondary structural components and tertiary contacts have been formed but many native contacts or close residue–residue interactions has yet to form, need to be further sculptured into the native states. This is a relatively slow “bottleneck” process because the competitive interactions between protein residues within the folding intermediates and between residues and water molecules may repeat many rounds to accumulate a large enough number of stable noncovalent bonds capable of counteracting the conformational entropy loss of the intermediates, thus putting this bottleneck stage under the enthalpy control (i.e. negative enthalpy change), contributing further to the lowering of the system free energy. Although the protein–ligand association occurs around the rugged bottom of the free energy landscape, the exclusion of water from the binding interfaces and the formation of noncovalent bonds between the two partners can still lower the system free energy. In conjunction with the loss of the rotational and translational degrees of freedom of the two partners as well as the loss of the conformational entropy of the protein, these processes could merge, downwards expand, and further narrow the free energy wells within which the protein–ligand binding process takes place, thereby making them look like a funnel, which we term the binding funnel. In this funnel, the free energy downhill process follows a similar paradigm to the protein-folding process. For example, if the initial collisions/contacts occur between the properly complementary interfaces of the protein and ligand, a large amount of water molecules (which usually form a water network around the solute surface) will be displaced to suit the need for maximizing the solvent entropy. This process is similar to that of the hydrophobic collapse during protein folding, resulting in a loosely associated protein–ligand complex that needs also to be further adapted into a tight complex, i.e. the second step which is mainly driven by the negative enthalpy change through intermolecular competitive interactions to gradually accumulate the noncovalent bonds and ultimately, to stabilize the complex at a tightly bound state. Taken together, we conclude that whether in the protein-folding or in the protein–ligand binding process, both the entropy-driven first step and the enthalpy-driven second step contribute to the lowering of the system free energy, resulting in the funnel-like folding or binding free energy landscape.     

The effects of nonnative interactions on protein folding rates: theory and simulation

Proteins are minimally frustrated polymers. However, for realistic protein models, nonnative interactions must be taken into account. In this paper, we analyze the effect of nonnative interactions on the folding rate and on the folding free energy barrier. We present an analytic theory to account for the modification on the free energy landscape upon introduction of nonnative contacts, added as a perturbation to the strong native interactions driving folding. Our theory predicts a rate-enhancement regime at fixed temperature, under the introduction of weak, nonnative interactions. We have thoroughly tested this theoretical prediction with simulations of a coarse-grained protein model, by using an off-lattice C(alpha)model of the src-SH3 domain. The strong agreement between results from simulations and theory confirm the nontrivial result that a relatively small amount of nonnative interaction energy can actually assist the folding to the native structure.     

SIMPLE estimate of the free energy change due to aliphatic mutations: superior predictions based on first principles

The bioinformatics revolution of the last decade has been instrumental in the development of empirical potentials to quantitatively estimate protein interactions for modeling and design. Although computationally efficient, these potentials hide most of the relevant thermodynamics in 5-to-40 parameters that are fitted against a large experimental database. Here, we revisit this longstanding problem and show that a careful consideration of the change in hydrophobicity, electrostatics, and configurational entropy between the folded and unfolded state of aliphatic point mutations predicts 20-30% less false positives and yields more accurate predictions than any published empirical energy function. This significant improvement is achieved with essentially no free parameters, validating past theoretical and experimental efforts to understand the thermodynamics of protein folding. Our first principle analysis strongly suggests that both the solute-solute van der Waals interactions in the folded state and the electrostatics free energy change of exposed aliphatic mutations are almost completely compensated by similar interactions operating in the unfolded ensemble. Not surprisingly, the problem of properly accounting for the solvent contribution to the free energy of polar and charged group mutations, as well as of mutations that disrupt the protein backbone remains open.     

Protein folding ‐ seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical–chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α‐helices and strands of β‐sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen‐bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of “frustration” is largely eliminated and the Levinthal paradox is resolved. Putting the “bottom line” at the top: it is likely that hydrogen‐bond satisfaction represents a largely under‐appreciated parameter in protein folding models.     

The effect of increasing the stability of non-native interactions on the folding landscape of the bacterial immunity protein Im9

How stabilising non-native interactions influence protein folding energy landscapes is currently not well understood: such interactions could speed folding by reducing the conformational search to the native state, or could slow folding by increasing ruggedness. Here, we examine the influence of non-native interactions in the folding process of the bacterial immunity protein Im9, by exploiting our ability to manipulate the stability of the intermediate and rate-limiting transition state (TS) in the folding of this protein by minor alteration of its sequence or changes in solvent conditions. By analysing the properties of these species using Phi-value analysis, and exploration of the structural properties of the TS ensemble using molecular dynamics simulations, we demonstrate the importance of non-native interactions in immunity protein folding and demonstrate that the rate-limiting step involves partial reorganisation of these interactions as the TS ensemble is traversed. Moreover, we show that increasing the contribution to stability made by non-native interactions results in an increase in Phi-values of the TS ensemble without altering its structural properties or solvent-accessible surface area. The data suggest that the immunity proteins fold on multiple, but closely related, micropathways, resulting in a heterogeneous TS ensemble that responds subtly to mutation or changes in the solvent conditions. Thus, altering the relative strength of native and non-native interactions influences the search to the native state by restricting the pathways through the folding energy landscape.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

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.     

Atomistic molecular simulations of protein folding

Theory and experiment have provided answers to many of the fundamental questions of protein folding; a remaining challenge is an accurate, high-resolution picture of folding mechanism. Atomistic molecular simulations with explicit solvent are the most promising method for providing this information, by accounting more directly for the physical interactions that stabilize proteins. Although simulations of folding with such force fields are extremely challenging, they have become feasible as a result of recent advances in computational power, accuracy of the energy functions or 'force fields', and methods for improving sampling of folding events. I review the recent progress in these areas, and highlight future challenges and questions that we may hope to address with these methods. I also attempt to place atomistic models into the context of the energy landscape view of protein folding, and coarse-grained simulations.     

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.