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.     

Enhanced crystal packing due to solvent reorganization through reductive methylation of lysine residues in oxidoreductase from <Emphasis Type="Italic">Streptococcus pneumoniae</Emphasis>

Protein crystallization is in part driven by the changes in the entropy of the system, but opinions differ as to whether the solute (protein) or solvent (water) molecules make more of a contribution to the overall entropic change. Methylation of lysine residues in proteins has been used to enhance protein crystallization. We investigated using molecular dynamics simulations with explicit solvent molecules, the behavior of several native proteins and their methylated counterparts chosen from an earlier large-scale study. Methylated lysines are capable of making a variety of interactions including H-bonds with protein residues and solvent. We demonstrate that methylation on the lysine slightly increases its side chain conformational entropy by about 3.5 J mol⁻¹ K⁻¹. Analysis of the radial and spatial distributions of the water molecules around the methylated lysine surface in oxidoreductase from Streptococcus pneumoniae revealed a larger sphere of water molecules with low entropy, as compared with solvent associated with unmethylated lysine. If methylated lysine were to make interactions at the protein–protein interface, the low-entropy water molecules associated with methylated lysines would be released, resulting in a gain of entropy. We show that this gain more than compensates for the loss of protein entropy. Therefore, we propose that lysine methylation favors the formation of crystals through solvent entropic gain.     

Optimal relationship between average conformational entropy and average energy of interactions between residues for fast protein folding

Based on the known experimental data and using the theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue, that is an entropy capacity, for fast protein folding. Statistical analysis of conformational entropy and the number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, +/-/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts and average conformational entropy per residue. These class-specific features determine the folding rates: a proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones.     

Entropy capacity determines protein folding

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates.     

Optimal ratio between the average conformational entropy and the average energy of interaction between residues for fast protein folding

Based on available experimental data and using a theoretical model of protein folding, we demonstrate that there is an optimal ratio between the average conformational entropy and the average contact energy per residue for fast protein folding. A statistical analysis of the conformational entropy and the number of contacts per residue for 5829 protein domains from four main classes (α, β, α/β, α+β) shows that each class has its own characteristic average number of contacts per residue and average conformational entropy per residue. These class-specific characteristics determine the protein folding rates: α-proteins are the fastest to fold, β-proteins are the second fastest, α+β-proteins are the third, and α/β-proteins are the last to fold.     

Molecular dynamics simulations of peptides and proteins with amplified collective motions

We present a novel method that uses the collective modes obtained with a coarse-grained model/anisotropic network model to guide the atomic-level simulations. Based on this model, local collective modes can be calculated according to a single configuration in the conformational space of the protein. In the molecular dynamics simulations, the motions along the slowest few modes are coupled to a higher temperature by the weak coupling method to amplify the collective motions. This amplified-collective-motion (ACM) method is applied to two test systems. One is an S-peptide analog. We realized the refolding of the denatured peptide in eight simulations out of 10 using the method. The other system is bacteriophage T4 lysozyme. Much more extensive domain motions between the N-terminal and C-terminal domain of T4 lysozyme are observed in the ACM simulation compared to a conventional simulation. The ACM method allows for extensive sampling in conformational space while still restricting the sampled configurations within low energy areas. The method can be applied in both explicit and implicit solvent simulations, and may be further applied to important biological problems, such as long timescale functional motions, protein folding/unfolding, and structure prediction.     

Estimates of the loss of main-chain conformational entropy of different residues on protein folding.

The average contribution of conformational entropy for individual amino acid residues towards the free energy of protein folding is not well understood. We have developed empirical scales for the loss of the main-chain (torsion angles, phi and psi) conformational entropy by taking its side-chain into account. The analysis shows that the main-chain component of the total conformational entropy loss for a residue is significant and reflects intrinsic characteristics associated with individual residues. The values have direct correlation with the hydrophobicity values and this has important bearing on the folding process. Proteins 1999;36:332-339.     

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.     

Insight into polyproline II helical bundle stability in an antifreeze protein denatured state

The use of polyproline II (PPII) helices in protein design is currently hindered by limitations in our understanding of their conformational stability and folding. Recent studies of the snow flea antifreeze protein (sfAFP), a useful model system composed of six PPII helices, suggested that a low denatured state entropy contributes to folding thermodynamics. Here, circular dichroism spectroscopy revealed minor populations of PPII like conformers at low temperature. To get atomic level information on the conformational ensemble and entropy of the reduced, denatured state of sfAFP, we have analyzed its chemical shifts and {¹H}-¹⁵N relaxation parameters by NMR spectroscopy at four experimental conditions. No significant populations of stable secondary structure were detected. The stiffening of certain N-terminal residues at neutral versus acidic pH and shifted pK_a values leads us to suggest that favorable charge-charge interactions could bias the conformational ensemble to favor the formation the C1-C28 disulfide bond during nascent folding, although no evidence for preferred contacts between these positions was detected by paramagnetic relaxation enhancement under denaturing conditions. Despite a high content of flexible glycine residues, the mobility of the sfAFP denatured ensemble is similar for denatured α/β proteins both on fast ps/ns as well as slower μs/ms timescales. These results are in line with a conformational entropy in the denatured ensemble resembling that of typical proteins and suggest that new structures based on PPII helical bundles should be amenable to protein design.     

Water's potential role: Insights from studies of the p53 core domain

Soluble proteins with amyloidogenic propensity such as the tumor suppressor protein p53 have high proportion of incompletely desolvated backbone H bonds (HB). Such bonds are vulnerable to water attack, thus potentially leading to the misfolding of these proteins. However, it is still not clear how the surrounding solvent influences the protein native states. To address this, systematic surveys by molecular dynamics simulations and entropy analysis were performed on the p53 core domain in this work. We examined seven wild/mutant X-ray structures and observed two types of water-network hydration in three "hot hydration centers" (DNA- or small molecule- binding surfaces of the p53 core domain). The "tight" water, resulting from the local collective hydrogen-bond interactions, is probably fundamental to the protein structural stability. The second type of water is highly "dynamical" and exchanges very fast within the bulk solution, which is unambiguously assisted by the local protein motions. An entropy mapping of the solvent around the protein and a temperature perturbation analysis further present the main features of the p53 hydration network. The particular environment created by different water molecules around the p53 core domain also partly explains the structural vulnerabilities of this protein.     

Are hot-spots occluded from water?

Protein–protein interactions are the basis of many biological processes and are governed by focused regions with high binding affinities, the warm- and hot-spots. It was proposed that these regions are surrounded by areas with higher packing density leading to solvent exclusion around them – “the O-ring theory.” This important inference still lacks sufficient demonstration. We have used Molecular Dynamics (MD) simulations to investigate the validity of the O-ring theory in the context of the conformational flexibility of the proteins, which is critical for function, in general, and for interaction with water, in particular. The MD results were analyzed for a variety of solvent-accessible surface area (SASA) features, radial distribution functions (RDFs), protein–water distances, and water residence times. The measurement of the average solvent-accessible surface area features for the warm- and hot-spots and the null-spots, as well as data for corresponding RDFs, identify distinct properties for these two sets of residues. Warm- and hot-spots are found to be occluded from the solvent. However, it has to be borne in mind that water-mediated interactions have significant power to construct an extensive and strongly bonded interface. We observed that warm- and hot-spots tend to form hydrogen bond (H-bond) networks with water molecules that have an occupancy around 90%. This study provides strong evidence in support of the O-ring theory and the results show that hot-spots are indeed protected from the bulk solvent. Nevertheless, the warm- and hot-spots still make water-mediated contacts, which are also important for protein–protein binding.     

Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.     

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.     

Cold unfolding of β-hairpins: a molecular-level rationalization

Isolated β-hairpins in water have a temperature dependence of their conformational stability qualitatively resembling that of globular proteins, showing both cold and hot unfolding transitions. It is shown that a molecular-level rationalization of this cold unfolding can be provided extending the approach devised for globular proteins (Graziano G. Phys Chem Chem Phys 2010; 12:14245-14252). The decrease in the solvent-excluded volume upon folding, measured by the decrease in the solvent accessible surface area, produces a gain in configurational/translational entropy of water molecules that is the main stabilizing contribution of the folded conformation. This always stabilizing Gibbs energy contribution has a parabolic-like temperature dependence in water and is exactly counterbalanced at two temperatures (i.e., the cold and hot unfolding temperatures) by the always destabilizing Gibbs energy contribution due to the loss in conformational degrees of freedom of the peptide chain.     

Probing the self-association, intermolecular contacts, and folding propensity of amelogenin

Amelogenins are an intrinsically disordered protein family that plays a major role in the development of tooth enamel, one of the most highly mineralized materials in nature. Monomeric porcine amelogenin possesses random coil and residual secondary structures, but it is not known which sequence regions would be conformationally attractive to potential enamel matrix targets such as other amelogenins (self-assembly), other matrix proteins, cell surfaces, or biominerals. To address this further, we investigated recombinant porcine amelogenin (rP172) using "solvent engineering" techniques to simultaneously promote native-like structure and induce amelogenin oligomerization in a manner that allows identification of intermolecular contacts between amelogenin molecules. We discovered that in the presence of 2,2,2-trifluoroethanol (TFE) significant folding transitions and stabilization occurred primarily within the N- and C-termini, while the polyproline Type II central domain was largely resistant to conformational transitions. Seven Pro residues (P2, P127, P130, P139, P154, P157, P162) exhibited conformational response to TFE, and this indicates these Pro residues act as folding enhancers in rP172. The remaining Pro residues resisted TFE perturbations and thus act as conformational stabilizers. We also noted that TFE induced rP172 self-association via the formation of intermolecular contacts involving P4-H6, V19-P33, and E40-T58 regions of the N-terminus. Collectively, these results confirm that the N- and C-termini of amelogenin are conformationally responsive and represent potential interactive sites for amelogenin-target interactions during enamel matrix mineralization. Conversely, the Pro, Gln central domain is resistant to folding and this may have important functional significance for amelogenin.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Dynamics of tRNA at Different Levels of Hydration

The influence of hydration on the nanosecond timescale dynamics of tRNA is investigated using neutron scattering spectroscopy. Unlike protein dynamics, the dynamics of tRNA is not affected by methyl group rotation. This allows for a simpler analysis of the influence of hydration on the conformational motions in RNA. We find that hydration affects the dynamics of tRNA significantly more than that of lysozyme. Both the characteristic length scale and the timescale of the conformational motions in tRNA depend strongly on hydration. Even the characteristic temperature of the so-called “dynamical transition” appears to be hydration-dependent in tRNA. The amplitude of the conformational motions in fully hydrated tRNA is almost twice as large as in hydrated lysozyme. We ascribe these differences to a more open and flexible structure of hydrated RNA, and to a larger fraction and different nature of hydrophilic sites. The latter leads to a higher density of water that makes the biomolecule more flexible. All-atom molecular-dynamics simulations are used to show that the extent of hydration is greater in tRNA than in lysozyme. We propose that water acts as a “lubricant” in facilitating enhanced motion in solvated RNA molecules.     

ATPase and Protease Domain Movements in the Bacterial AAA+ Protease FtsH Are Driven by Thermal Fluctuations

AAA+ proteases are essential players in cellular pathways of protein degradation. Elucidating their conformational behavior is key for understanding their reaction mechanism and, importantly, for elaborating our understanding of mutation-induced protease deficiencies. Here, we study the structural dynamics of the Thermotoga maritima AAA+ hexameric ring metalloprotease FtsH (TmFtsH). Using a single-molecule Förster resonance energy transfer approach to monitor ATPase and protease inter-domain conformational changes in real time, we show that TmFtsH—even in the absence of nucleotide—is a highly dynamic protease undergoing sequential transitions between five states on the second timescale. Addition of ATP does not influence the number of states or change the timescale of domain motions but affects the state occupancy distribution leading to an inter-domain compaction. These findings suggest that thermal energy, but not chemical energy, provides the major driving force for conformational switching, while ATP, through a state reequilibration, introduces directionality into this process. The TmFtsH A359V mutation, a homolog of the human pathogenic A510V mutation of paraplegin (SPG7) causing hereditary spastic paraplegia, does not affect the dynamic behavior of the protease but impairs the ATP-coupled domain compaction and, thus, may account for protease malfunctioning and pathogenesis in hereditary spastic paraplegia.