Improved Pruning algorithms and Divide-and-Conquer strategies for Dead-End Elimination, with application to protein design

MOTIVATION: Structure-based protein redesign can help engineer proteins with desired novel function. Improving computational efficiency while still maintaining the accuracy of the design predictions has been a major goal for protein design algorithms. The combinatorial nature of protein design results both from allowing residue mutations and from the incorporation of protein side-chain flexibility. Under the assumption that a single conformation can model protein folding and binding, the goal of many algorithms is the identification of the Global Minimum Energy Conformation (GMEC). A dominant theorem for the identification of the GMEC is Dead-End Elimination (DEE). DEE-based algorithms have proven capable of eliminating the majority of candidate conformations, while guaranteeing that only rotamers not belonging to the GMEC are pruned. However, when the protein design process incorporates rotameric energy minimization, DEE is no longer provably-accurate. Hence, with energy minimization, the minimized-DEE (MinDEE) criterion must be used instead. RESULTS: In this paper, we present provably-accurate improvements to both the DEE and MinDEE criteria. We show that our novel enhancements result in a speedup of up to a factor of more than 1000 when applied in redesign for three different proteins: Gramicidin Synthetase A, plastocyanin, and protein G. AVAILABILITY: Contact authors for source code.     

Conformational analysis of the 20-residue membrane-bound portion of melittin by conformational space annealing

The conformational space of the 20-residue membrane-bound portion of melittin has been investigated extensively with the conformational space annealing (CSA) method and the ECEPP/3 (Empirical Conformational Energy Program for Peptides) algorithm. Starting from random conformations, the CSA method finds that there are at least five different classes of conformations, within 4 kcal/mol, which have distinct backbone structures. We find that the lowest energy conformation of this peptide from previous investigations is not the global minimum-energy conformation (GMEC); but it belongs to the second lowest energy class of the five classes found here. In four independent runs, one conformation is found repeatedly as the lowest energy conformation of the peptide (two of the four lowest energy conformations are identical; the other two have essentially identical backbone conformations but slightly different side-chain conformations). We propose this conformation, whose energy is lower than that found previously by 1.9 kcal/mol, as the GMEC of the ECEPP/3 force field. The structure of the proposed GMEC is less helical and more compact than the previous one. It appears that the CSA method can find several classes of conformations of a 20-residue peptide starting from random conformations utilizing only its amino acid sequence information. The proposed GMEC has also been found with a modified electrostatically driven Monte Carlo method [D. R. Ripoll, A. Liwo, and H.A. Scheraga (1998) “New Developments of the Electrostatically Driven Monte Carlo Method: Test on the Membrane-Bound Portion of Melittin,” Biopolymers, Vol. 46, pp. 117–126]. © 1998 John Wiley & Sons, Inc. Biopoly 46: 103–115, 1998     

Dead-end elimination with backbone flexibility

MOTIVATION: Dead-End Elimination (DEE) is a powerful algorithm capable of reducing the search space for structure-based protein design by a combinatorial factor. By using a fixed backbone template, a rotamer library, and a potential energy function, DEE identifies and prunes rotamer choices that are provably not part of the Global Minimum Energy Conformation (GMEC), effectively eliminating the majority of the conformations that must be subsequently enumerated to obtain the GMEC. Since a fixed-backbone model biases the algorithm predictions against protein sequences for which even small backbone movements may result in a significantly enhanced stability, the incorporation of backbone flexibility can improve the accuracy of the design predictions. If explicit backbone flexibility is incorporated into the model, however, the traditional DEE criteria can no longer guarantee that the flexible-backbone GMEC, the lowest-energy conformation when the backbone is allowed to flex, will not be pruned. RESULTS: We derive a novel DEE pruning criterion, flexible-backbone DEE (BD), that is provably accurate with backbone flexibility, guaranteeing that no rotamers belonging to the flexible-backbone GMEC are pruned; we also present further enhancements to BD for improved pruning efficiency. The results from applying our novel algorithms to redesign the beta1 domain of protein G and to switch the substrate specificity of the NRPS enzyme GrsA-PheA are then compared against the results from previous fixed-backbone DEE algorithms. We confirm experimentally that traditional-DEE is indeed not provably-accurate with backbone flexibility and that BD is capable of generating conformations with significantly lower energies, thus confirming the feasibility of our novel algorithms. AVAILABILITY: Contact authors for source code.     

Dead‐end elimination with perturbations (DEEPer): A provable protein design algorithm with continuous sidechain and backbone flexibility

Computational protein and drug design generally require accurate modeling of protein conformations. This modeling typically starts with an experimentally determined protein structure and considers possible conformational changes due to mutations or new ligands. The DEE/A* algorithm provably finds the global minimum‐energy conformation (GMEC) of a protein assuming that the backbone does not move and the sidechains take on conformations from a set of discrete, experimentally observed conformations called rotamers. DEE/A* can efficiently find the overall GMEC for exponentially many mutant sequences. Previous improvements to DEE/A* include modeling ensembles of sidechain conformations and either continuous sidechain or backbone flexibility. We present a new algorithm, DEEPer (D ead‐E nd E limination with Per turbations), that combines these advantages and can also handle much more extensive backbone flexibility and backbone ensembles. DEEPer provably finds the GMEC or, if desired by the user, all conformations and sequences within a specified energy window of the GMEC. It includes the new abilities to handle arbitrarily large backbone perturbations and to generate ensembles of backbone conformations. It also incorporates the shear, an experimentally observed local backbone motion never before used in design. Additionally, we derive a new method to accelerate DEE/A*‐based calculations, indirect pruning, that is particularly useful for DEEPer. In 67 benchmark tests on 64 proteins, DEEPer consistently identified lower‐energy conformations than previous methods did, indicating more accurate modeling. Additional tests demonstrated its ability to incorporate larger, experimentally observed backbone conformational changes and to model realistic conformational ensembles. These capabilities provide significant advantages for modeling protein mutations and protein–ligand interactions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Generalized dead-end elimination algorithms make large-scale protein side-chain structure prediction tractable: implications for protein design and structural genomics

The dead-end elimination (DEE) theorems are powerful tools for the combinatorial optimization of protein side-chain placement in protein design and homology modeling. In order to reach their full potential, the theorems must be extended to handle very hard problems. We present a suite of new algorithms within the DEE paradigm that significantly extend its range of convergence and reduce run time. As a demonstration, we show that a total protein design problem of 10(115) combinations, a hydrophobic core design problem of 10(244) combinations, and a side-chain placement problem of 10(1044) combinations are solved in less than two weeks, a day and a half, and an hour of CPU time, respectively. This extends the range of the method by approximately 53, 144 and 851 log-units, respectively, using modest computational resources. Small to average-sized protein domains can now be designed automatically, and side-chain placement calculations can be solved for nearly all sizes of proteins and protein complexes in the growing field of structural genomics.     

A Monte Carlo sampling method of amino acid sequences adaptable to given main-chain atoms in the proteins

We have developed a computational method of protein design to detect amino acid sequences that are adaptable to given main-chain coordinates of a protein. In this method, the selection of amino acid types employs a Metropolis Monte Carlo method with a scoring function in conjunction with the approximation of free energies computed from 3D structures. To compute the scoring function, a side-chain prediction using another Metropolis Monte Carlo method was performed to select structurally suitable side-chain conformations from a side-chain library. In total, two layers of Monte Carlo procedures were performed, first to select amino acid types (1st layer Monte Carlo) and then to predict side-chain conformations (2nd layers Monte Carlo). We applied this method to sequence design for the entire sequence on the SH3 domain, Protein G, and BPTI. The predicted sequences were similar to those of the wild-type proteins. We compared the results of the predictions with and without the 2nd layer Monte Carlo method. The results revealed that the two-layer Monte Carlo method produced better sequence similarity to the wild-type proteins than the one-layer method. Finally, we applied this method to neuraminidase of influenza virus. The results were consistent with the sequences identified from the isolated viruses.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. I. Backbone structure of enkephalin

A new methodology for theoretically predicting the native, three-dimensional structure of a polypeptide is presented. Based on equilibrium statistical mechanics, an algorithm has been designed to determine the probable conformation of a polypeptide by calculating conditional free-energy maps for each residue of the macromolecule. The conditional free-energy map of each residue is computed from a set of probability integrals, obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. By locating the region(s) of lowest free energy for each map, the probable conformation for each residue can be identified. The native structure of the polypeptide is assumed to be the combination of the probable conformations of the individual residues. All multidimensional probability integrals are evaluated by an adaptive Monte Carlo algorithm (SMAPPS —Statistical-Mechanical Algorithm for Predicting Protein Structure). The Monte Carlo algorithm searches the entire conformational space, adjusting itself automatically to concentrate its sampling in regions where the magnitude of the integrand is largest (“importance sampling”). No assumptions are made about the native conformation. The only prior knowledge necessary for the prediction of the native conformation is the amino acid sequence of the polypeptide. To test the effectiveness of the algorithm, SMAPPS was applied to the prediction of the native conformation of the backbone of Met-enkephalin, a pentapeptide. In the calculations, only the backbone dihedral angles (? and ψ) were allowed to vary; all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to the alleged global minimum energy previously determined by direct energy minimization. For each conformation generated randomly by the Monte Carlo algorithm, the total conformational energy of the polypeptide was obtained from established empirical potential energy functions. Solvent effects were not included in the computations. With this initial application of SMAPPS , three distinct low-free-energy β-bend structures of Met-enkephalin were found. In particular, one of the structures has a conformation remarkably similar to the one associated with the previously alleged global minimum energy. The two additional structures of the pentapeptide have conformational energies lower than the previously computed low-energy structure. However, the Monte Carlo results are in agreement with an improved energy-minimization procedure. These initial results on the backbone structure of Met-enkephalin indicate that an equilibrium statistical-mechanical procedure, coupled with an adaptive Monte Carlo algorithm, can overcome many of the problems associated with the standard methods of direct energy minimization.     

Protein design using continuous rotamers

Optimizing amino acid conformation and identity is a central problem in computational protein design. Protein design algorithms must allow realistic protein flexibility to occur during this optimization, or they may fail to find the best sequence with the lowest energy. Most design algorithms implement side-chain flexibility by allowing the side chains to move between a small set of discrete, low-energy states, which we call rigid rotamers. In this work we show that allowing continuous side-chain flexibility (which we call continuous rotamers) greatly improves protein flexibility modeling. We present a large-scale study that compares the sequences and best energy conformations in 69 protein-core redesigns using a rigid-rotamer model versus a continuous-rotamer model. We show that in nearly all of our redesigns the sequence found by the continuous-rotamer model is different and has a lower energy than the one found by the rigid-rotamer model. Moreover, the sequences found by the continuous-rotamer model are more similar to the native sequences. We then show that the seemingly easy solution of sampling more rigid rotamers within the continuous region is not a practical alternative to a continuous-rotamer model: at computationally feasible resolutions, using more rigid rotamers was never better than a continuous-rotamer model and almost always resulted in higher energies. Finally, we present a new protein design algorithm based on the dead-end elimination (DEE) algorithm, which we call iMinDEE, that makes the use of continuous rotamers feasible in larger systems. iMinDEE guarantees finding the optimal answer while pruning the search space with close to the same efficiency of DEE. Availability: Software is available under the Lesser GNU Public License v3. Contact the authors for source code.     

Branch-and-terminate: a combinatorial optimization algorithm for protein design.

BACKGROUND: Several deterministic and stochastic combinatorial optimization algorithms have been applied to computational protein design and homology modeling. As structural targets increase in size, however, it has become necessary to find more powerful methods to address the increased combinatorial complexity. RESULTS: We present a new deterministic combinatorial search algorithm called 'Branch-and-Terminate' (B&T), which is derived from the Branch-and-Bound search method. The B&T approach is based on the construction of an efficient but very restrictive bounding expression, which is used for the search of a combinatorial tree representing the protein system. The bounding expression is used both to determine the optimal organization of the tree and to perform a highly effective pruning procedure named 'termination'. For some calculations, the B&T method rivals the current deterministic standard, dead-end elimination (DEE), sometimes finding the solution up to 21 times faster. A more significant feature of the B&T algorithm is that it can provide an efficient way to complete the optimization of problems that have been partially reduced by a DEE algorithm. CONCLUSIONS: The B&T algorithm is an effective optimization algorithm when used alone. Moreover, it can increase the problem size limit of amino acid sidechain placement calculations, such as protein design, by completing DEE optimizations that reach a point at which the DEE criteria become inefficient. Together the two algorithms make it possible to find solutions to problems that are intractable by either algorithm alone.     

Dead-End Based Modeling Tools to Explore the Sequence Space That Is Compatible with a Given Scaffold

The dead-end elimination algorithm has proven to be a powerful tool in protein homology modeling since it allows one to determine rapidly the global minimum-energy conformation (GMEC) of an arbitrarily large collection of side chains, given fixed backbone coordinates. After introducing briefly the necessary background, we focus on logic arguments that increase the efficacy of the dead-end elimination process. Second, we present new theoretical considerations on the use of the dead-end elimination method as a tool to identify sequences that are compatible with a given scaffold structure. Third, we initiate a search for properties derived from the computed GMEC structure to predict whether a given sequence can be well packed in the core of a protein. Three properties will be considered: the nonbonded energy, the accessible surface area, and the extent by which the GMEC side-chain conformations deviate from a locally optimal conformation.     

Protein design simulations suggest that side-chain conformational entropy is not a strong determinant of amino acid environmental preferences

Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein.     

Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).     

PLUG (Pruning of Local Unrealistic Geometries) removes restrictions on biophysical modeling for protein design

Protein design algorithms must search an enormous conformational space to identify favorable conformations. As a result, those that perform this search with guarantees of accuracy generally start with a conformational pruning step, such as dead-end elimination (DEE). However, the mathematical assumptions of DEE-based pruning algorithms have up to now severely restricted the biophysical model that can feasibly be used in protein design. To lift these restrictions, I propose to prune local unrealistic geometries (PLUG) using a linear programming-based method. PLUG's biophysical model consists only of well-known lower bounds on interatomic distances. PLUG is intended as preprocessing for energy-based protein design calculations, whose biophysical model need not support DEE pruning. Based on 96 test cases, PLUG is at least as effective at pruning as DEE for larger protein designs—the type that most require pruning. When combined with the LUTE protein design algorithm, PLUG greatly facilitates designs that account for continuous entropy, large multistate designs with continuous flexibility, and designs with extensive continuous backbone flexibility and advanced nonpairwise energy functions. Many of these designs are tractable only with PLUG, either for empirical reasons (LUTE's machine learning step achieves an accurate fit only after PLUG pruning), or for theoretical reasons (many energy functions are fundamentally incompatible with DEE).     

Applications of simulated annealing to peptides

We report the application of a new conformation searching algorithm called simulated annealing to the location of the global minimum energy conformation of peptides. Simulated annealing is a Metropolis Monte Carlo approach to conformation generation in which both the energy and temperature dependence of the Boltzmann distribution guides the search for the global minimum. Both uphill and downhill moves are possible, which allows the molecule to escape from local minima. Applications to the 20 natural amino acid "dipeptide models" as well as to polyalanines up to Ala80 are very successful in finding the lowest energy conformation. A history file of the simulated annealing process allows reconstruction and examination of the random walk around conformation space. A separate program, Conf-Gen, reads the history file and extracts all low-energy conformations visited during the run.     

Automatic protein design with all atom force-fields by exact and heuristic optimization

A fully automatic procedure for predicting the amino acid sequences compatible with a given target structure is described. It is based on the CHARMM package, and uses an all atom force-field and rotamer libraries to describe and evaluate side-chain types and conformations. Sequences are ranked by a quantity akin to the free energy of folding, which incorporates hydration effects. Exact (Branch and Bound) and heuristic optimisation procedures are used to identifying highly scoring sequences from an astronomical number of possibilities. These sequences include the minimum free energy sequence, as well as all amino acid sequences whose free energy lies within a specified window from the minimum. Several applications of our procedure are illustrated. Prediction of side-chain conformations for a set of ten proteins yields results comparable to those of established side-chain placement programs. Applications to sequence optimisation comprise the re-design of the protein cores of c-Crk SH3 domain, the B1 domain of protein G and Ubiquitin, and of surface residues of the SH3 domain. In all calculations, no restrictions are imposed on the amino acid composition and identical parameter settings are used for core and surface residues. The best scoring sequences for the protein cores are virtually identical to wild-type. They feature no more than one to three mutations in a total of 11-16 variable positions. Tests suggest that this is due to the balance between various contributions in the force-field rather than to overwhelming influence from packing constraints. The effectiveness of our force-field is further supported by the sequence predictions for surface residues of the SH3 domain. More mutations are predicted than in the core, seemingly in order to optimise the network of complementary interactions between polar and charged groups. This appears to be an important energetic requirement in absence of the partner molecules with which the SH3 domain interacts, which were not included in the calculations. Finally, a detailed comparison between the sequences generated by the heuristic and exact optimisation algorithms, commends a note of caution concerning the efficiency of heuristic procedures in exploring sequence space.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Computational analysis of two similar neuropeptides yields distinct conformational ensembles

Conformational states and thermodynamic properties for two similar neuropeptides, GDPFLRF-NH(2) and GYPFLRF-NH(2), have been computed by Monte Carlo simulated annealing (MCSA) conformational searches and Metropolis Monte Carlo (MMC) calculations. These peptides were recently shown to have dramatically different conformations in solution by NMR [Edison et al., J Neuroscience 1999;19:6318-6326]. Final conformations of multiple independent MCSA runs were the starting points for MMC calculations, and conformations saved at intervals during MMC runs were characterized in terms of total energy, configuration entropy, side-chain fraction population, and ensemble average inter-nuclear distances. Without the use of any NMR data-generated pseudo-potentials, the present calculations were in excellent qualitative agreement with all previous NMR experimental data and provided a foundation by which to more quantitatively interpret the experimental NMR results. Proteins 2000;40:367-377.     

ROSETTALIGAND: protein-small molecule docking with full side-chain flexibility

Protein-small molecule docking algorithms provide a means to model the structure of protein-small molecule complexes in structural detail and play an important role in drug development. In recent years the necessity of simulating protein side-chain flexibility for an accurate prediction of the protein-small molecule interfaces has become apparent, and an increasing number of docking algorithms probe different approaches to include protein flexibility. Here we describe a new method for docking small molecules into protein binding sites employing a Monte Carlo minimization procedure in which the rigid body position and orientation of the small molecule and the protein side-chain conformations are optimized simultaneously. The energy function comprises van der Waals (VDW) interactions, an implicit solvation model, an explicit orientation hydrogen bonding potential, and an electrostatics model. In an evaluation of the scoring function the computed energy correlated with experimental small molecule binding energy with a correlation coefficient of 0.63 across a diverse set of 229 protein- small molecule complexes. The docking method produced lowest energy models with a root mean square deviation (RMSD) smaller than 2 A in 71 out of 100 protein-small molecule crystal structure complexes (self-docking). In cross-docking calculations in which both protein side-chain and small molecule internal degrees of freedom were varied the lowest energy predictions had RMSDs less than 2 A in 14 of 20 test cases.     

New Monte Carlo algorithms for protein folding.

Over the past three decades, a number of powerful simulation algorithms have been introduced to the protein folding problem. For many years, the emphasis has been placed on how to both overcome the multiple minima problem and find the conformation with the global minimum potential energy. Since the new view of the protein folding mechanism (based on the free energy landscape of the protein system) arose in the past few years, however, it is now of interest to obtain a global knowledge of the phase space, including the intermediate and denatured states of proteins. Monte Carlo methods have proved especially valuable for these purposes. As well as new, powerful optimization techniques, novel algorithms that can sample much a wider phase space than conventional methods have been established.     

Electronic and vibrational circular dichroism of aromatic amino acids by density functional theory

Structures of model compounds mimicking aromatic amino acid residues in proteins are optimized by density functional theory (DFT), assuming that the main-chain conformation was a random coil. Excitation energies and dipole and rotational strengths for the optimized structures were calculated based on time-dependent DFT (TD-DFT). The electronic circular dichroism (ECD) bands of the models were significantly affected by side-chain conformations. Hydration models of the aromatic residues were also subjected to TD-DFT calculations, and the ECD bands of these models were found to be highly perturbed by the hydration of the main-chain amide groups. In addition to calculating the random-coil conformation, we also performed TD-DFT calculations of the aromatic residue models, assuming that the main-chain conformation was an alpha-helix or beta-strand. As expected, the overall feature of the ECD bands was also perturbed by the main-chain conformations. Moreover, vibrational circular dichroism (VCD) spectra of the hydration models in a random-coil structure were simulated by DFT, which showed that the VCD spectra are more sensitive to the side-chain conformations than the ECD spectra. The present results show that analyses combining ECD and VCD spectroscopy and using DFT calculations can elucidate the main- and side-chain conformations of aromatic residues in proteins.