Conformational Free Energy Surfaces Research Articles

Molecular Determinants of EphA2 and EphB2 Antagonism Enable the Design of Ligands with Improved Selectivity.

With the aim of identifying novel antagonists selective for the EphA receptor family, a combined experimental and computational approach was taken to investigate the molecular basis of the recognition between a prototypical Eph-ephrin antagonist (UniPR1447) and two representative receptors of the EphA and EphB subfamilies, namely, EphA2 and EphB2 receptors. The conformational free-energy surface (FES) of the binding state of UniPR1447 within the ligand binding domain of EphA2 and EphB2, reconstructed from molecular dynamics (MD) simulations performed on the microsecond time scale, was exploited to drive the design and synthesis of a novel antagonist selective for EphA2 over the EphB2 receptor. The availability of compounds with this pharmacological profile will help discriminate the importance of these two receptors in the insurgence and progression of cancer.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces.

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Molecular Origin of the Stability Difference in Four Shark IgNAR Constant Domains

Improving the stability of antibodies for manufacture and shelf life is one of the main focuses of antibody engineering. One stabilization strategy is to perform specific mutations in human antibodies based on highly stable antibodies in other species. To identify the key residues for mutagenesis, it is necessary to understand the roles of these residues in stabilizing the antibody. Here, we use molecular dynamics simulations to study the molecular origin of the four shark immunoglobulin new antigen receptors constant domains (C1–C4). According to the unfolding pathways and the conformational free energy surfaces in 8 M urea at 380 K, the C2 domain is the most stable, followed by C4, C1, and C3, which agrees with the experimental findings. The C1 and C3 domains follow a common unfolding pathway in which the unfolding starts from the edge strands, particularly strand g, and then gradually progresses to the inner strands. Detailed structural analysis of the C2 domain reveals a “sandwich-like” R339-E322-R341 salt-bridge cluster on strand g, which grants ultrahigh stability to the C2 domain. We further design two sets of mutations by mutating E322 to alanine or setting all atomic charges in E322 to zero to break the salt-bridge cluster in the C2 domain, which confirms the importance of the salt bridges in stability. In the C4 domain, the D80-K104 salt bridge on strand g also strengthens the stability. On the other hand, in the C1 and C3 domains, there is no salt bridge on strand g. In addition to the salt bridges, the overall hydrophobicity score of the hydrophobic core is also positively correlated with the domain stability. Our findings provide a detailed microscopic picture of the molecular origin of the four shark immunoglobulin new antigen receptors constant domains that not only explains the differences in their structural stability but also provides important insights into future antibody design.

Prediction of the Crystal Morphology of β-HMX using a Generalized Interfacial Structure Analysis Model

At sufficiently low supersaturations such that the spiral growth mechanism dominates, β-cyclotetramethylenetetranitramine (HMX) grows from acetone into a polyhedron surrounded mainly by the (020) and (011) faces. In order to elucidate the morphology, a generalized form of the interfacial structure analysis model is suggested. In this method, the molecular order parameters of crystals are defined to identify the orientation and conformation of the adsorbed growth unit at the interface. This presents a robust method to calculate the orientational and conformational free energy surfaces that are utilized for the spiral growth model of centrosymmetric growth units with polygonal spiral edges. From the metadynamics simulation using these order parameters as collective variables, the free energy surfaces with respect to the collective variables revealed that high conformational free energy of the chair conformation discouraged preordering of the growth units into crystal-like orientation and conformation. The r...

Identification of Rare Lewis Oligosaccharide Conformers in Aqueous Solution Using Enhanced Sampling Molecular Dynamics.

Determining the conformations accessible to carbohydrate ligands in aqueous solution is important for understanding their biological action. In this work, we evaluate the conformational free-energy surfaces of Lewis oligosaccharides in explicit aqueous solvent using a multidimensional variant of the swarm-enhanced sampling molecular dynamics (msesMD) method; we compare with multi-microsecond unbiased MD simulations, umbrella sampling, and accelerated MD approaches. For the sialyl Lewis A tetrasaccharide, msesMD simulations in aqueous solution predict conformer landscapes in general agreement with the other biased methods and with triplicate unbiased 10 μs trajectories; these simulations find a predominance of closed conformer and a range of low-occupancy open forms. The msesMD simulations also suggest closed-to-open transitions in the tetrasaccharide are facilitated by changes in ring puckering of its GlcNAc residue away from the 4C1 form, in line with previous work. For sialyl Lewis X tetrasaccharide, msesMD simulations predict a minor population of an open form in solution corresponding to a rare lectin-bound pose observed crystallographically. Overall, from comparison with biased MD calculations, we find that triplicate 10 μs unbiased MD simulations may not be enough to fully sample glycan conformations in aqueous solution. However, the computational efficiency and intuitive approach of the msesMD method suggest potential for its application in glycomics as a tool for analysis of oligosaccharide conformation.

Conformational free energy surfaces of non-ionized glycine in aqueous solution

Ab initio calculations on glycine and quantum mechanical/molecular mechanical molecular dynamics simulations (QM/MM-MD) on solvated non-ionized glycine were performed to explore the free energy landscapes of non-ionic glycine conformers in aqueous solution. Among nine different conformers of glycine, QM/MM-MD simulations found ttc and gtc conformers stable in addition to ttt, ccc, gtt, tct and gct which were well known as stable isomers in pure QM calculation. The stabilities of ttc and gtc come from a strong solvation at their carboxylic group side (–COOH) in solution. The preferred rotation along C–C (φ) as compared to C–O (θ) in both pure QM calculations and QM/MM-MD indicates the importance of intramolecular effects in determining relative free energies. On the other hand, the existence of stable ttc and gtc conformers only in solution phase clearly shows the importance of intermolecular interaction by explicit solvents. The same intermolecular interactions have a mixed effect on the free energy barriers. They reduced the barriers of A (ccc) → B (gtc) and A (ccc) → C (gct) isomerizations as compared to the ab initio or PCM results. At the same time, they also increased the barriers of B (ttc, gtc) → D (ttt, gtt). In short, the conformational free energy surfaces of non-ionized glycine in solution are largely different from the corresponding potential energy surfaces of gas phase. The fact that the initial conformer for tautomerization ccc is stable makes the N → Z tautomerization facile. However, concurrently, diverse conformational isomerizations to ccc make the tautomerization dependent on the isomerizations.

Hidden regularity and universal classification of fast side chain motions in proteins.

Proteins display characteristic dynamical signatures that appear to be universal across all proteins regardless of topology and size. Here, we systematically characterize the universal features of fast side chain motions in proteins by examining the conformational energy surfaces of individual residues obtained using enhanced sampling molecular dynamics simulation (618 free energy surfaces obtained from 0.94 μs MD simulation). The side chain conformational free energy surfaces obtained using the adaptive biasing force (ABF) method for a set of eight proteins with different molecular weights and secondary structures are used to determine the methyl axial NMR order parameters (O(axis)(2)), populations of side chain rotamer states (ρ), conformational entropies (S(conf)), probability fluxes, and activation energies for side chain inter-rotameric transitions. The free energy barriers separating side chain rotamer states range from 0.3 to 12 kcal/mol in all proteins and follow a trimodal distribution with an intense peak at ~5 kcal/mol and two shoulders at ~3 and ~7.5 kcal/mol, indicating that some barriers are more favored than others by proteins to maintain a balance between their conformational stability and flexibility. The origin and the influences of the trimodal barrier distribution on the distribution of O(axis)(2) and the side chain conformational entropy are discussed. A hierarchical grading of rotamer states based on the conformational free energy barriers, entropy, and probability flux reveals three distinct classes of side chains in proteins. A unique nonlinear correlation is established between O(axis)(2) and the side chain rotamer populations (ρ). The apparent universality in O(axis)(2) versus ρ correlation, trimodal barrier distribution, and distinct characteristics of three classes of side chains observed among all proteins indicates a hidden regularity (or commonality) in the dynamical heterogeneity of fast side chain motions in proteins.

Structures and Free Energy Landscapes of the A53T Mutant-Type α-Synuclein Protein and Impact of A53T Mutation on the Structures of the Wild-Type α-Synuclein Protein with Dynamics

The A53T genetic missense mutation of the wild-type α-synuclein (αS) protein was initially identified in Greek and Italian families with familial Parkinson's disease. Detailed understanding of the structures and the changes induced in the wild-type αS structure by the A53T mutation, as well as establishing the direct relationships between the rapid conformational changes and free energy landscapes of these intrinsically disordered fibrillogenic proteins, helps to enhance our fundamental knowledge and to gain insights into the pathogenic mechanism of Parkinson's disease. We employed extensive parallel tempering molecular dynamics simulations along with thermodynamic calculations to determine the secondary and tertiary structural properties as well as the conformational free energy surfaces of the wild-type and A53T mutant-type αS proteins in an aqueous solution medium using both implicit and explicit water models. The confined aqueous volume effect in the simulations of disordered proteins using an explicit model for water is addressed for a model disordered protein. We also assessed the stabilities of the residual secondary structure component interconversions in αS based on free energy calculations at the atomic level with dynamics using our recently developed theoretical strategy. To the best of our knowledge, this study presents the first detailed comparison of the structural properties linked directly to the conformational free energy landscapes of the monomeric wild-type and A53T mutant-type α-synuclein proteins in an aqueous solution environment. Results demonstrate that the β-sheet structure is significantly more altered than the helical structure upon A53T mutation of the monomeric wild-type αS protein in aqueous solution. The β-sheet content close to the mutation site in the N-terminal region is more abundant while the non-amyloid-β component (NAC) and C-terminal regions show a decrease in β-sheet abundance upon A53T mutation. Obtained results utilizing our new theoretical strategy show that the residual secondary structure conversion stabilities resulting in α-helix formation are not significantly affected by the mutation. Interestingly, the residual secondary structure conversion stabilities show that secondary structure conversions resulting in β-sheet formation are influenced by the A53T mutation and the most stable residual transition yielding β-sheet occurs directly from the coil structure. Long-range interactions detected between the NAC region and the N- or C-terminal regions of the wild-type αS disappear upon A53T mutation. The A53T mutant-type αS structures are thermodynamically more stable than those of the wild-type αS protein structures in aqueous solution. Overall, the higher propensity of the A53T mutant-type αS protein to aggregate in comparison to the wild-type αS protein is related to the increased β-sheet formation and lack of strong intramolecular long-range interactions in the N-terminal region in comparison to its wild-type form. The specific residual secondary structure component stabilities reported herein provide information helpful for designing and synthesizing small organic molecules that can block the β-sheet forming residues, which are reactive toward aggregation.

Combined Computational and Experimental NMR Study of Calix[4]arene Derivatives

A combined computational and experimental study of a complex supramolecular system constituted by calix[4]arene derivatives that dimerize upon CO2 binding is presented. The theoretical investigation includes ab initio density functional theory, molecular dynamics, and metadynamics analysis of both monomers and dimers. The ab initio calculation of the dimerization energy demonstrates the exergonic character of the process, due to the formation of a strong hydrogen bond network between ammonium and carbamate groups. The dimerization is driven by −31.1 kcal/mol in the case of the fully outward orientation of the carbamic hydrogens, while it results in a weaker process when different carbamic orientations are considered. The molecular dynamics simulations show the critical conformational degrees of freedom driving monomers and dimers toward common structures. These conformations show tilted orientations of the carbamic groups highlighting the fundamental role of dynamics in evaluating the most stable configurations. Metadynamics simulations describe, in agreement with the other computational tools, the conformational free energy surface of these calix[4]arenes defining three stable conformational families. ROESY and variable temperature 1H NMR experiments are in agreement with our simulations. The presented approach aims to be the reference for investigating complex supramolecular systems.

Reconstruction of Protein Side-Chain Conformational Free Energy Surfaces From NMR-Derived Methyl Axis Order Parameters

An analytical approach is developed for reconstructing site-specific methyl-bearing protein side-chain conformational energy surfaces from NMR methyl axis order parameters (O(axis)(2)). Application of an enhanced sampling algorithm (adaptive biasing force) to molecular dynamics simulation of a protein, calcium-bound calmodulin, reveals a nonlinear correlation between O(axis)(2) and the populations of rotamer states of protein side-chains, permitting the rotamer populations to be extracted directly from O(axis)(2). The analytical approach yields side-chain conformational distributions that are in excellent agreement with those obtained from the enhanced-sampling MD results.

Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap

Atomic motions in molecules are not linear. This infers that nonlinear dimensionality reduction methods can outperform linear ones in analysis of collective atomic motions. In addition, nonlinear collective motions can be used as potentially efficient guides for biased simulation techniques. Here we present a simulation with a bias potential acting in the directions of collective motions determined by a nonlinear dimensionality reduction method. Ad hoc generated conformations of trans,trans-1,2,4-trifluorocyclooctane were analyzed by Isomap method to map these 72-dimensional coordinates to three dimensions, as described by Brown and co-workers [J. Chem. Phys. 129, 064118 (2008)]. Metadynamics employing the three-dimensional embeddings as collective variables was applied to explore all relevant conformations of the studied system and to calculate its conformational free energy surface. The method sampled all relevant conformations (boat, boat-chair, and crown) and corresponding transition structures inaccessible by an unbiased simulation. This scheme allows to use essentially any parameter of the system as a collective variable in biased simulations. Moreover, the scheme we used for mapping out-of-sample conformations from the 72D to 3D space can be used as a general purpose mapping for dimensionality reduction, beyond the context of molecular modeling.

Dynamics in the Active Site of β-Secretase: A Network Analysis of Atomistic Simulations

The aspartic protease β-secretase (BACE) catalyzes the hydrolysis of the amyloid precursor protein (APP) which leads to amyloid-β aggregation and, ultimately, the perilous Alzheimer's disease. The conformational dynamics and free energy surfaces of BACE at three steps of the catalytic cycle are studied here by explicit solvent molecular dynamics simulations (multiple runs for a total of 2.2 μs). The overall plasticity of BACE is essentially identical for the three states of the substrate: the octapeptide reactant, gem-diol intermediate, and cleavage products. In contrast, the network of hydrogen bonds in the active site is more stable in the complex of BACE with the gem-diol intermediate than the other two states of the substrate. The spontaneous release of the C-terminal (P1'-P4') fragment of the product follows a single-exponential time dependence with a time constant of 50 ns and does not require the opening of the flap. The fast dissociation of the C-terminal fragment is consistent with the transmembrane location and orientation of APP and its further processing by γ-secretase. On the other hand, the N-terminal (P4-P1) fragment of the product does not exit the BACE active site within the simulation time scale of 80 ns. A unified network analysis of the complexes of BACE with the three states of the substrate provides an estimation of the activation free energy associated with the structural rearrangements that involve only noncovalent interactions. The estimated rearrangement barriers are not negligible (up to 3 kcal/mol) but are significantly smaller than the barrier of the peptide bond hydrolysis reaction.

Comparing the Efficiency of Biased and Unbiased Molecular Dynamics in Reconstructing the Free Energy Landscape of Met-Enkephalin

All-atom unbiased molecular dynamics simulations are now able to explore the microsecond to millisecond time scale for simple biological macromolecules in an explicit solvent. This allows for a careful comparison of the efficiency and accuracy of enhanced sampling methods versus long unbiased molecular dynamics in reconstructing conformational free energy surfaces. Here, we use an equilibrium microsecond-long molecular dynamics simulation as a reference to analyze the convergence properties of well-tempered metadynamics with two different sets of collective variables. In the case of the small and very diffusive Met-enkephalin pentapeptide, we find that the performance strongly depends on the choice of the collective variables (CVs). Using a set of principal component analysis derived eigenvectors, the convergence of the FES is faster than with both hand-picked CVs and unbiased molecular dynamics.

The Conformational Free-Energy Landscape of β-d-Mannopyranose: Evidence for a 1S5 → B2,5 → OS2 Catalytic Itinerary in β-Mannosidases

The mechanism of glycosidic bond cleavage by glycosidases involves substrate ring distortions in the Michaelis complex that favor catalysis. Retaining β-mannosidases bind the substrate in a (1)S(5) conformation, and recent experiments have proposed an unusual substrate conformational pathway ((1)S(5) → B(2,5) → (O)S(2)) for the hydrolysis reaction. By means of Car-Parrinello metadynamics simulations, we have obtained the conformational free-energy surface (FES) of a β-d-mannopyranose molecule associated with the ideal Stoddart conformational diagram. We have found that (1)S(5) is among the most stable conformers and simultaneously is the most preactivated conformation in terms of elongation/shortening of the C1-O1/C1-O5 bonds, C1-O1 orientation, and charge development at the anomeric carbon. Analysis of the computed FES gives support to the proposed (1)S(5) → B(2,5) → (O)S(2) catalytic itinerary, showing that the degree of preactivation of the substrate in glycoside hydrolases (GHs) is related to the properties of an isolated sugar ring. We introduce a simple preactivation index integrating several structural, electronic, and energetic properties that can be used to predict the conformation of the substrate in the Michaelis complex of any GH.

Metadynamics modelling of the solvent effect on primary hydroxyl rotamer equilibria in hexopyranosides

Accurate modelling of rotamer equilibria for the primary hydroxyl groups of monosaccharides continues to be a great challenge of computational glycochemistry. The metadynamics technique was applied to study the conformational free energy surfaces of methyl α- d-glucopyranoside and methyl α- d-galactopyranoside, employing the glycam06 force field. For both molecules, seven to eight conformational free-energy minima, differing in the ω (O-5–C-5–C-6–O-6) and χ (C-3–C-4–O-4–HO-4) dihedral angles, were identified in vacuum or in a water environment. The calculated rotamer equilibrium of the primary hydroxyl group is significantly different in vacuum than in water. The major effect of a water environment is the destabilisation of a hydrogen bond between O-4–HO-4 and O-6–HO-6 groups. It was possible to calculate the free-energy differences of individual rotamers with an accuracy of better than 2 kJ/mol. The calculated gg, gt and tg rotamer populations in water are in close agreement with experimental measurements, and therefore support the theoretical background of metadynamics.

Conformational Free Energy Surface of α-N-Acetylneuraminic Acid: An Interplay Between Hydrogen Bonding and Solvation

The conformational free energy surface of alpha-N-acetylneuraminic acid (Neu5Ac, sialic acid) in the space of ring-puckering coordinates was calculated using the metadynamics method. Free energy surfaces in vacuum and with an explicit solvent were calculated in GLYCAM 06 force field. In vacuum three structures are almost equivalently populated, namely, the (2)C(5) chair and the B(3,6)/(2)S(6) and (O)S(3) boat/skew-boat conformations. The B(3,6)/(2)S(6) structure is stabilized by an ionic hydrogen bond between the amide N-H bond and the carboxylic group. However, this structure is unfavorable in a water environment in which the experimentally observed (2)C(5) chair conformation is predicted to be more stable than the other structures. These results indicate that environment significantly influences conformation of Neu5Ac and that Neu5Ac-processing enzymes might modify a conformation of their substrates solely by a changing polarity of the environment. The structure of Neu5Ac bound in influenza neuraminidase ((4)S(2)/B(2,5)) belongs to conformations preferred in a water environment. The free energy penalty of this conformational change was calculated (relative to (2)C(5)) as 10.2 +/- 2.0 and 17.3 +/- 2.0 kJ/mol for (4,O)B/(O)S(3) and (4)S(2), respectively. This result indicates that mimicking of the enzyme-bound conformation is likely to be a viable strategy for the design of neuraminidase inhibitors.

Insights into Stability and Toxicity of Amyloid-Like Oligomers by Replica Exchange Molecular Dynamics Analyses

Deposition of insoluble amyloid plaques is frequently associated with a large variety of neurodegenerative diseases. However, data collected in the last decade have suggested that the neurotoxic action is exerted by prefibrillar, soluble assemblies of amyloid-forming proteins and peptides. The scarcity of structural data available for both amyloid-like fibrils and soluble oligomers is a major limitation for the definition of the molecular mechanisms linked to the onset of these diseases. Recently, the structural characterization of GNNQQNY and other peptides has shown a general feature of amyloid-like fibers, the so-called steric zipper motif. However, very little is known still about the prefibrillar oligomeric forms. By using replica exchange molecular dynamics we carried out extensive analyses of the properties of several small and medium GNNQQNY aggregates arranged through the steric zipper motif. Our data show that the assembly formed by two sheets, each made of two strands, arranged as in the crystalline states are highly unstable. Conformational free energy surfaces indicate that the instability of the model can be ascribed to the high reactivity of edge backbone hydrogen bonding donors/acceptors. On the other hand, data on larger models show that steric zipper interactions may keep small oligomeric forms in a stable state. These models simultaneously display two peculiar structural motifs: a tightly packed steric zipper interface and a large number of potentially reactive exposed strands. The presence of highly reactive groups on these assemblies likely generates two distinct evolutions. On one side the reactive groups quickly lead, through self-association, to the formation of ordered fibrils, on the other they may interfere with several cellular components thereby generating toxic effects. In this scenario, fiber formation propensity and toxicity of oligomeric states are two different manifestations of the same property: the hyper-reactivity of the exposed strands.

A Hamiltonian Replica Exchange Approach and Its Application to the Study of Side-Chain Type and Neighbor Effects on Peptide Backbone Conformations.

We presented a Hamiltonian replica exchange approach and applied it to investigate the effects of various factors on the conformational equilibrium of peptide backbone. In different replicas, biasing potentials of varying strengths are applied to all backbone (φ,ψ) torsional angle pairs to overcome sampling barriers. A general form of constructing biasing potentials based on a reference free energy surface is employed to minimize sampling in physically irrelevant parts of the conformational space. An extension of the weighted histogram analysis formulation allows for conformational free energy surfaces to be computed using all replicas, including those with biased Hamiltonians. This approach can significantly reduce the statistical uncertainties in computed free energies. For the peptide systems considered, it allows for effects of the order of 0.5-1 kJ/mol to be quantified using explicit solvent simulations. We applied this approach to capped peptides of 2-5 peptide units containing Ala, Phe, or Val in explicit water solvent and focused on how the conformational equilibrium of a single pair of backbone angles are influenced by changing the residue types of the same and neighboring residues as well as conformations of neighboring residues. For the effects of changing side-chain types of the same residue, our results consistently showed increased preference of β for Phe and Val relative to Ala. As for neighbor effects, our results not only indicated that they can be as large as the effects of changing the side-chain type of the same residue but also led to several new insights. We found that for the N-terminal neighbors, their conformations seem to have large effects. Relative to the β conformer of an N-terminal neighbor, its α conformer stabilizes the β conformer of its next Ala disregarding the residue type of the neighbor. For C-terminal neighbors, their chemical identities seem to play more important roles. Val as the C-terminal neighbor significantly increases the PII propensity of its previous Ala disregarding its own conformational state. These results are in good accordance with reported statistics of protein coil structure libraries, proving the persistent presence of such effects in short peptides as well as in proteins. We also observed other side-chain identity and neighbor effects which have been consistently reproduced in our simulations of different small peptide systems but not displayed by coil library statistics.

Consistent free energy landscapes and thermodynamic properties of small proteins based on a single all-atom force field employing an implicit solvation

We have attempted to improve the PARAM99 force field in conjunction with the generalized Born (GB) solvation model with a surface area correction for more consistent protein folding simulations. For this purpose, using an extended alphabeta training set of five well-studied molecules with various folds (alpha, beta, and betabetaalpha), a previously modified version of PARAM99/GBSA is further refined, such that all native states of the five training species correspond to their lowest free energy minimum states. The resulting modified force field (PARAM99MOD5/GBSA) clearly produces reasonably acceptable conformational free energy surfaces of the training set with correct identifications of their native states in the free energy minimum states. Moreover, due to its well-balanced nature, this new force field is expected to describe secondary structure propensities of diverse folds in a more consistent manner. Remarkably, temperature dependent behaviors simulated with the current force field are in good agreement with the experiment. This agreement is a significant improvement over the existing standard all-atom force fields. In addition, fundamentally important thermodynamic quantities, such as folding enthalpy (DeltaH) and entropy (DeltaS), agree reasonably well with the experimental data.

Theoretical Characterization of α-Helix and β-Hairpin Folding Kinetics

By means of the conformational free energy surface and corresponding diffusion coefficients, as obtained by long time scale atomistic molecular dynamics simulations (mus time scale), we model the folding kinetics of alpha-helix and beta-hairpin peptides as a diffusive process over the free energy surface. The two model systems studied in this paper (the alpha-helical temporin L and the beta-hairpin prion protein H1 peptide) exhibit a funnel-like almost barrierless free energy profile, leading to nonexponential folding kinetics matching rather well the available experimental data. Moreover, using the free energy profile provided by Muñoz et al. [Muñoz et al. Nature 1997, 390: 196-199], this model was also applied to reproduce the two-state folding kinetics of the C-terminal beta-hairpin of protein GB1, yielding an exponential folding kinetics with a time constant (approximately 5 micros) in excellent agreement with the experimentally observed one (approximately 6 micros). Finally, the folding kinetics obtained by solving the diffusion equation, considering either a one-dimensional or a two-dimensional free energy surface, are also compared in order to understand the relevance of the possible kinetic coupling between conformational degrees of freedom in the folding process.