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

13C Chemical Shifts in Proteins: A Rich Source of Encoded Structural Information

Despite the formidable progress in Nuclear Magnetic Resonance (NMR) spectroscopy, quality assessment of NMR-derived structures remains as an important problem. Thus, validation of protein structures is essential for the spectroscopists, since it could enable them to detect structural flaws and potentially guide their efforts in further refinement. Moreover, availability of accurate and efficient validation tools would help molecular biologists and computational chemists to evaluate quality of available experimental structures and to select a protein model which is the most suitable for a given scientific problem. The ¹³C^α nuclei are ubiquitous in proteins, moreover, their shieldings are easily obtainable from NMR experiments and represent a rich source of encoded structural information that makes ¹³C^α chemical shifts an attractive candidate for use in computational methods aimed at determination and validation of protein structures. In this chapter, the basis of a novel methodology of computing, at the quantum chemical level of theory, the ¹³C^α shielding for the amino acid residues in proteins is described. We also identify and examine the main factors affecting the ¹³C^α-shielding computation. Finally, we illustrate how the information encoded in the ¹³C chemical shifts can be used for a number of applications, viz., from protein structure prediction of both α-helical and β-sheet conformations, to determination of the fraction of the tautomeric forms of the imidazole ring of histidine in proteins as a function of pH or to accurate detection of structural flaws, at a residue-level, in NMR-determined protein models.

Predicting hydration free energies of amphetamine-type stimulants with a customized molecular model

Amphetamine-type stimulants (ATS) are a group of incitation and psychedelic drugs affecting the central nervous system. Physicochemical data for these compounds are essential for understanding the stimulating mechanism, for assessing their environmental impacts, and for developing new drug detection methods. However, experimental data are scarce due to tight regulation of such illicit drugs, yet conventional methods to estimate their properties are often unreliable. Here we introduce a tailor-made multiscale procedure for predicting the hydration free energies and the solvation structures of ATS molecules by a combination of first principles calculations and the classical density functional theory. We demonstrate that the multiscale procedure performs well for a training set with similar molecular characteristics and yields good agreement with a testing set not used in the training. The theoretical predictions serve as a benchmark for the missing experimental data and, importantly, provide microscopic insights into manipulating the hydrophobicity of ATS compounds by chemical modifications.

How Efficient Is Replica Exchange Molecular Dynamics? An Analytic Approach

Replica exchange molecular dynamics (REMD) has become a standard technique for accelerating relaxation in biosimulations. Despite its widespread use, questions remain about its efficiency compared with conventional, constant temperature molecular dynamics (MD). An analytic approach is taken to describe the relative efficiency of REMD with respect to MD. This is applied to several simple two-state models and to several real proteins-protein L and the B domain of protein A-to predict the relative efficiency of REMD with respect to MD in actual applications. In agreement with others, we find the following: as long as there is a positive activation energy for folding, REMD is more efficient than MD; the effectiveness of REMD is strongly dependent on the activation enthalpy; and the efficiency of REMD for actual proteins is a strong function of the maximum temperature. Choosing the maximum temperature too high can result in REMD becoming significantly less efficient than conventional MD. A good rule of thumb appears to be to choose the maximum temperature of the REMD simulation slightly above the temperature at which the enthalpy for folding vanishes. Additionally, we find that the number of replicas in REMD, while important for simulations shorter than one or two relaxation times, has a minimal effect on the asymptotic efficiency of the method.

A Folding Pathway Model of Mini-Protein BBA5

We present the folding pathway model of mini-protein BBA5, a bundle of secondary structures, α-helix and β-hairpin, by using action-derived molecular dynamics (ADMD) simulations. From ten independent ADMD simulations, we extracted common features of the folding pathway of BBA5, from which we found that the early stage chain compaction was followed by the formation of C-terminal α-helix. The N-terminal β-hairpin was observed to form only after α-helix was stabilized. This result is in good agreement with the experimental observation that BBA5 mutants were moderately cooperative folders, and their C-terminal helical fragments were of higher secondary structure propensity while the N-terminal hairpin fragments were of a random coil spectrum. We found that the most flexible part of BBA5 is the N-terminal four residues. Although both are made of the identical ββα motif, the secondary structure formation sequence of BBA5 is found to be different from that of FSD-1. Finally, a description of the folding pathway in terms of principal component analysis is presented to characterize the folding dynamics in reduced dimensions. With only three principal components, we were able to describe 83.4% of the pathway.

13C Chemical Shifts in Proteins: A Rich Source of Encoded Structural Information

Despite the formidable progress in Nuclear Magnetic Resonance (NMR) spectroscopy, quality assessment of NMR-derived structures remains as an important problem. Thus, validation of protein structures is essential for the spectroscopists, since it could enable them to detect structural flaws and potentially guide their efforts in further refinement. Moreover, availability of accurate and efficient validation tools would help molecular biologists and computational chemists to evaluate quality of available experimental structures and to select a protein model which is the most suitable for a given scientific problem. The ¹³C^α nuclei are ubiquitous in proteins, moreover, their shieldings are easily obtainable from NMR experiments and represent a rich source of encoded structural information that makes ¹³C^α chemical shifts an attractive candidate for use in computational methods aimed at determination and validation of protein structures. In this chapter, the basis of a novel methodology of computing, at the quantum chemical level of theory, the ¹³C^α shielding for the amino acid residues in proteins is described. We also identify and examine the main factors affecting the ¹³C^α-shielding computation. Finally, we illustrate how the information encoded in the ¹³C chemical shifts can be used for a number of applications, viz., from protein structure prediction of both α-helical and β-sheet conformations, to determination of the fraction of the tautomeric forms of the imidazole ring of histidine in proteins as a function of pH or to accurate detection of structural flaws, at a residue-level, in NMR-determined protein models.

A second look at mini-protein stability: analysis of FSD-1 using circular dichroism, differential scanning calorimetry, and simulations

Mini-proteins that contain <50 amino acids often serve as model systems for studying protein folding because their small size makes long timescale simulations possible. However, not all mini-proteins are created equal. The stability and structure of FSD-1, a 28-residue mini-protein that adopted the betabetaalpha zinc-finger motif independent of zinc binding, was investigated using circular dichroism, differential scanning calorimetry, and replica-exchange molecular dynamics. The broad melting transition of FSD-1, similar to that of a helix-to-coil transition, was observed by using circular dichroism, differential scanning calorimetry, and replica-exchange molecular dynamics. The N-terminal beta-hairpin was found to be flexible. The FSD-1 apparent melting temperature of 41 degrees C may be a reflection of the melting of its alpha-helical segment instead of the entire protein. Thus, despite its attractiveness due to small size and purposefully designed helix, sheet, and turn structures, the status of FSD-1 as a model system for studying protein folding should be reconsidered.

Dual folding pathways of an alpha/beta protein from all-atom ab initio folding simulations

Successful ab initio folding of proteins with both alpha-helix and beta-sheet requires a delicate balance among a variety of forces in the simulation model, which may explain that the successful folding of any alpha/beta proteins to within experimental error has yet to be reported. Here we demonstrate that it is an achievable goal to fold alpha/beta proteins with a force field emphasizing the balance between the two major secondary structures. Using our newly developed force field, we conducted extensive ab initio folding simulations on an alpha/beta protein full sequence design (FSD) employing both conventional molecular dynamics and replica exchange molecular dynamics in combination with a generalized-Born solvation model. In these simulations, the folding of FSD to the native state with high population (>64.2%) and high fidelity (C(alpha)-Root Mean Square Deviation of 1.29 A for the most sampled conformation when compared to the experimental structure) was achieved. The folding of FSD was found to follow two pathways. In the major pathway, the folding started from the formation of the helix. In the minor pathway, however, folding of the beta-hairpin started first. Further examination revealed that the helix initiated from the C-terminus and propagated toward the N-terminus. The formation of the hydrophobic contacts coincided with the global folding. Therefore the hydrophobic force does not appear to be the driving force of the folding of this protein.

Bounding the electrostatic free energies associated with linear continuum models of molecular solvation

The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.

Computational approaches for the design of peptides with anti-breast cancer properties

Background: Breast cancer is the most common cancer among women. Tamoxifen is the preferred drug for estrogen receptor-positive breast cancer treatment, yet many of these cancers are intrinsically resistant to tamoxifen or acquire resistance during treatment. Therefore, scientists are searching for breast cancer drugs that have different molecular targets. Methodology: Recently, a computational approach was used to successfully design peptides that are new lead compounds against breast cancer. We used replica exchange molecular dynamics to predict the structure and dynamics of active peptides, leading to the discovery of smaller bioactive peptides. Conclusions: These analogs inhibit estrogen-dependent cell growth in a mouse uterine growth assay, a test showing reliable correlation with human breast cancer inhibition. We outline the computational methods that were tried and used along with the experimental information that led to the successful completion of this research.

Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Use of decoys to optimize an all-atom force field including hydration

A novel method of parameter optimization is proposed. It makes use of large sets of decoys generated for six nonhomologous proteins with different architecture. Parameter optimization is achieved by creating a free energy gap between sets of nativelike and nonnative conformations. The method is applied to optimize the parameters of a physics-based scoring function consisting of the all-atom ECEPP05 force field coupled with an implicit solvent model (a solvent-accessible surface area model). The optimized force field is able to discriminate near-native from nonnative conformations of the six training proteins when used either for local energy minimization or for short Monte Carlo simulated annealing runs after local energy minimization. The resulting force field is validated with an independent set of six nonhomologous proteins, and appears to be transferable to proteins not included in the optimization; i.e., for five out of the six test proteins, decoys with 1.7- to 4.0-A all-heavy-atom root mean-square deviations emerge as those with the lowest energy. In addition, we examined the set of misfolded structures created by Park and Levitt using a four-state reduced model. The results from these additional calculations confirm the good discriminative ability of the optimized force field obtained with our decoy sets.

All-atom level direct folding simulation of a betabetaalpha miniprotein

We performed ab initio folding simulation for a betabetaalpha peptide BBA5 (PDB code 1T8J) with a modified param99 force field using the generalized Born solvation model (param99MOD5/GBSA). For efficient conformational sampling, we extended a previously developed novel Q-replica exchange molecular dynamics (Q-REMD) into a multiplexed Q-REMD. Starting from a fully extended conformation, we were able to locate the nativelike structure in the global free minimum region at 280 K. The current approach, which combines the more balanced force field with the efficient sampling scheme, demonstrates a clear advantage in direct folding simulation at all-atom level.

Recent advances in implicit solvent-based methods for biomolecular simulations

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

Use of 13C(alpha) chemical shifts for accurate determination of beta-sheet structures in solution

A physics-based method, aimed at determining protein structures by using NOE-derived distance constraints together with observed and computed 13C(alpha) chemical shifts, is applied to determine the structure of a 20-residue all-beta peptide (BS2). The approach makes use of 13C(alpha) chemical shifts, computed at the density functional level of theory, to derive backbone and side-chain torsional constraints for all of the amino acid residues, without making use of information about residue occupancy in any region of the Ramachandran map. In addition, the torsional constraints are derived dynamically--i.e., they are redefined at each step of the algorithm. It is shown that, starting from randomly generated conformations, the final protein models are more accurate than existing NMR-derived models of the peptide, in terms of the agreement between predicted and observed 13C(beta) chemical shifts, and some stereochemical quality indicators. The accumulated evidence indicates that, for a highly flexible BS2 peptide in solution, it may not be possible to determine a single structure (or a small set of structures) that would satisfy all of the constraints exactly and simultaneously because the observed NOEs and 13C(alpha) chemical shifts correspond to a dynamic ensemble of conformations. Analysis of the structural flexibility, carried out by molecular dynamics simulations in explicit water, revealed that the whole peptide can be characterized as having liquid-like behavior, according to the Lindemann criterion. In summary, a beta-sheet structure of a highly flexible peptide in solution can be determined by a quantum-chemical-based procedure.

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.

Computational design and experimental discovery of an antiestrogenic peptide derived from alpha-fetoprotein

Breast cancer is the most common cancer among women, and tamoxifen is the preferred drug for estrogen receptor-positive breast cancer treatment. Many of these cancers are intrinsically resistant to tamoxifen or acquire resistance during treatment. Consequently, there is an ongoing need for breast cancer drugs that have different molecular targets. Previous work has shown that 8-mer and cyclic 9-mer peptides inhibit breast cancer in mouse and rat models, interacting with an unsolved receptor, while peptides smaller than eight amino acids did not. We show that the use of replica exchange molecular dynamics predicts the structure and dynamics of active peptides, leading to the discovery of smaller peptides with full biological activity. Simulations identified smaller peptide analogues with the same conserved reverse turn demonstrated in the larger peptides. These analogues were synthesized and shown to inhibit estrogen-dependent cell growth in a mouse uterine growth assay, a test showing reliable correlation with human breast cancer inhibition.

Two-stage folding of HP-35 from ab initio simulations

Accurate ab initio simulation of protein folding is a critical step toward elucidation of protein-folding mechanisms. Here, we demonstrate highly accurate folding of the 35 residue villin headpiece subdomain (HP35) by all-atom molecular dynamics simulations using AMBER FF03 and the generalized-Born solvation model. In a set of 20 micros long simulations, the protein folded to the native state in multiple trajectories, with the lowest C(alpha) RMSD being 0.39 A for residues 2-34 (excluding residues 1 and 35). The native state had the highest population among all sampled conformations, and the center of most populated cluster had a C(alpha) RMSD of 1.63 A. Folding of this protein can be described as a two-stage process that followed a well-defined pathway. In the first stage, formation of helices II and III as a folding intermediate constituted the rate-limiting step and was initiated at a folding nucleus around residues Phe17 and Pro21. The folding intermediate further acted as a template that facilitated the folding and docking of helix I in the second stage. Detailed descriptions of the folding kinetics and the roles of key residues are presented.

Folding free-energy landscape of villin headpiece subdomain from molecular dynamics simulations

High-accuracy ab initio folding has remained an elusive objective despite decades of effort. To explore the folding landscape of villin headpiece subdomain HP35, we conducted two sets of replica exchange molecular dynamics for 200 ns each and three sets of conventional microsecond-long molecular dynamics simulations, using AMBER FF03 force field and a generalized-Born solvation model. The protein folded consistently to the native state; the lowest C(alpha)-rmsd from the x-ray structure was 0.46 A, and the C(alpha)- rmsd of the center of the most populated cluster was 1.78 A at 300 K. ab initio simulations have previously not reached this level. The folding landscape of HP35 can be partitioned into the native, denatured, and two intermediate-state regions. The native state is separated from the major folding intermediate state by a small barrier, whereas a large barrier exists between the major folding intermediate and the denatured states. The melting temperature T(m) = 339 K extracted from the heat-capacity profile was in close agreement with the experimentally derived T(m) = 342 K. A comprehensive picture of the kinetics and thermodynamics of HP35 folding emerges when the results from replica exchange and conventional molecular dynamics simulations are combined.

Direct folding simulation of alpha-helices and beta-hairpins based on a single all-atom force field with an implicit solvation model

Recently, we have shown that a modified energy model based on the param99 force field with the generalized Born (GB) solvation model produces reliable free energy landscapes of mini-proteins with a betabetaalpha motif (BBA5, 1FSD, and 1PSV), with the native structures of the mini-proteins located in their lowest free energy minimum states. One of the main features in the modified energy model is a significant improvement for more balanced treatments of alpha and beta strands in proteins. In this study, using the replica exchange molecular dynamics (REMD) simulation method with this new force field, we have carried out extensive ab initio folding studies of several well-known peptides with alpha or beta strands (C-peptide, EK-peptide, le0q, and gbl). Starting from fully extended conformations as the initial conditions, all of the native-like structures of the target peptides were successfully identified by REMD, with reasonable representations of free energy surfaces. The present simulation results with the modified energy model are consistent with experiments, demonstrating an extended applicability of the energy model to folding studies of a variety of alpha-helices, beta-strands, and alpha/beta proteins.

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta

Determination of conformational free energies of peptides by multidimensional adaptive umbrella sampling

We improve the multidimensional adaptive umbrella sampling method for the computation of conformational free energies of biomolecules. The conformational transition between the alpha-helical and beta-hairpin conformational states of an alanine decapeptide is used as an example. Convergence properties of the weighted-histogram-analysis-based adaptive umbrella sampling can be improved by using multiple replicas in each adaptive iteration and by using adaptive updating of the bounds of the umbrella potential. Using positional root-mean-square deviations from structures of the alpha-helical and beta-hairpin reference states as reaction coordinates, we obtained well-converged free energy surfaces of both the in-vacuum and in-solution decapeptide systems. From the free energy surfaces well-converged relative free energies between the two conformational states can be derived. Advantages and disadvantages of different methods for obtaining conformational free energies as well as implications of our results in studying conformational transitions of proteins and in improving force field are discussed.