Rapid calculation of first and second derivatives of conformational energy with respect to dihedral angles for proteins general recurrent equations

Hormones Nanofiltration in Carbon Nanotubes and Boron Nitride Nanotubes Using Uniform External Electric Field Through Molecular Dynamics

Hormones are a dangerous group of molecules that can cause harm to humans. This study based on classical molecular dynamics proposes the nanofiltration of wastewater contaminated by hormones from a computer simulation study, in which the water and the hormone were filtered in two single-walled nanotube compositions. The calculations were carried out by changing the intensities of the electric field that acted as a force exerting pressure on the filtration along the nanotube, in the simulation time of 100 ps. The hormones studied were estrone, estradiol, estriol, progesterone, ethinylestradiol, diethylbestrol, and levonorgestrel in carbon nanotubes (CNTs) and boron nitride (BNNTs). The most efficient nanofiltrations were for fields with low intensities in the order of 10-8 au and 10-7 au. The studied nanotubes can be used in membranes for nanofiltration in water treatment plants due to the evanescent field potential caused by the action of the electric field inside. Our data showed that the action of EF in conjunction with the van der Walls forces of the nanotubes is sufficient to generate the attractive potential. Evaluating the transport of water molecules in CNTs and BNNTs, under the influence of the electric field, a sequence of simulations with the same boundary conditions was carried out, seeking to know the percentage of water molecules filtered in the nanotubes.

Current directions in combining simulation-based macromolecular modeling approaches with deep learning

Introduction: Structure-guided drug discovery relies on accurate computational methods for modeling macromolecules. Simulations provide means of predicting macromolecular folds, of discovering function from structure, and of designing macromolecules to serve as drugs. Success rates are limited for any of these tasks, however. Recently, deep neural network-based methods have greatly enhanced the accuracy of predictions of protein structure from sequence, generating excitement about the potential impact of deep learning.Areas covered: This review introduces biologists to deep neural network architecture, surveys recent successes of deep learning in structure prediction, and discusses emerging deep learning-based approaches for structure-function analysis and design. Particular focus is given to the interplay between simulation-based and neural network-based approaches.Expert opinion: As deep learning grows integral to macromolecular modeling, simulation- and neural network-based approaches must grow more tightly interconnected. Modular software architecture must emerge allowing both types of tools to be combined with maximal versatility. Open sharing of code under permissive licenses will be essential. Although experiments will remain the gold standard for reliable information to guide drug discovery, we may soon see successful drug development projects based on high-accuracy predictions from algorithms that combine simulation with deep learning - the ultimate validation of this combination's power.

A Consistent Scheme for Gradient-Based Optimization of ProteinLigand Poses

Scoring and numerical optimization of protein-ligand poses is an integral part of docking tools. Although many scoring functions exist, many of them are not continuously differentiable and they are rarely explicitly analyzed with respect to their numerical optimization behavior. Here, we present a consistent scheme for pose scoring and gradient-based pose optimization. It consists of a novel variant of the BFGS algorithm enabling step-length control, named LSL-BFGS (limited step length BFGS), and the empirical JAMDA scoring function designed for pose prediction and good numerical optimizability. The JAMDA scoring function shows a high pose prediction performance in the CASF-2016 docking power benchmark, top-ranking a pose with an RMSD of ≤2 Å in about 89% of the cases. The combination of JAMDA scoring with the LSL-BFGS algorithm shows a significantly higher optimization locality (i.e., no excessive movement of poses) than with the classical BFGS algorithm while retaining the characteristically low number of scoring function evaluations. The JAMDA scoring and optimization scheme is freely available for noncommercial use and academic research.

Efficient minimization of multipole electrostatic potentials in torsion space

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom.

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5-7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.

3D flexible alignment using 2D maximum common substructure: dependence of prediction accuracy on target-reference chemical similarity

A protein-bound conformation of a target molecule can be predicted by aligning the target molecule on the reference molecule obtained from the 3D structure of the compound-protein complex. This strategy is called "similarity-based docking". For this purpose, we develop the flexible alignment program fkcombu, which aligns the target molecule based on atomic correspondences with the reference molecule. The correspondences are obtained by the maximum common substructure (MCS) of 2D chemical structures, using our program kcombu. The prediction performance was evaluated using many target-reference pairs of superimposed ligand 3D structures on the same protein in the PDB, with different ranges of chemical similarity. The details of atomic correspondence largely affected the prediction success. We found that topologically constrained disconnected MCS (TD-MCS) with the simple element-based atomic classification provides the best prediction. The crashing potential energy with the receptor protein improved the performance. We also found that the RMSD between the predicted and correct target conformations significantly correlates with the chemical similarities between target-reference molecules. Generally speaking, if the reference and target compounds have more than 70% chemical similarity, then the average RMSD of 3D conformations is <2.0 Å. We compared the performance with a rigid-body molecular alignment program based on volume-overlap scores (ShaEP). Our MCS-based flexible alignment program performed better than the rigid-body alignment program, especially when the target and reference molecules were sufficiently similar.

Modeling symmetric macromolecular structures in Rosetta3

Symmetric protein assemblies play important roles in many biochemical processes. However, the large size of such systems is challenging for traditional structure modeling methods. This paper describes the implementation of a general framework for modeling arbitrary symmetric systems in Rosetta3. We describe the various types of symmetries relevant to the study of protein structure that may be modeled using Rosetta's symmetric framework. We then describe how this symmetric framework is efficiently implemented within Rosetta, which restricts the conformational search space by sampling only symmetric degrees of freedom, and explicitly simulates only a subset of the interacting monomers. Finally, we describe structure prediction and design applications that utilize the Rosetta3 symmetric modeling capabilities, and provide a guide to running simulations on symmetric systems.

Improved molecular replacement by density- and energy-guided protein structure optimization

Molecular replacement procedures, which search for placements of a starting model within the crystallographic unit cell that best account for the measured diffraction amplitudes, followed by automatic chain tracing methods, have allowed the rapid solution of large numbers of protein crystal structures. Despite extensive work, molecular replacement or the subsequent rebuilding usually fail with more divergent starting models based on remote homologues with less than 30% sequence identity. Here we show that this limitation can be substantially reduced by combining algorithms for protein structure modelling with those developed for crystallographic structure determination. An approach integrating Rosetta structure modelling with Autobuild chain tracing yielded high-resolution structures for 8 of 13 X-ray diffraction data sets that could not be solved in the laboratories of expert crystallographers and that remained unsolved after application of an extensive array of alternative approaches. We estimate that the new method should allow rapid structure determination without experimental phase information for over half the cases where current methods fail, given diffraction data sets of better than 3.2 Å resolution, four or fewer copies in the asymmetric unit, and the availability of structures of homologous proteins with >20% sequence identity.

ROSETTA3: an object-oriented software suite for the simulation and design of macromolecules

We have recently completed a full re-architecturing of the ROSETTA molecular modeling program, generalizing and expanding its existing functionality. The new architecture enables the rapid prototyping of novel protocols by providing easy-to-use interfaces to powerful tools for molecular modeling. The source code of this rearchitecturing has been released as ROSETTA3 and is freely available for academic use. At the time of its release, it contained 470,000 lines of code. Counting currently unpublished protocols at the time of this writing, the source includes 1,285,000 lines. Its rapid growth is a testament to its ease of use. This chapter describes the requirements for our new architecture, justifies the design decisions, sketches out central classes, and highlights a few of the common tasks that the new software can perform.

A proposed interaction mechanism between elastin-derived peptides and the elastin/laminin receptor-binding domain

Elastin-derived peptides (EDPs) have been intensively studied in view of their widely diverse biological activities. These are triggered both in normal and tumor cells, through peptide anchoring at the surface of the elastin-binding protein (EBP), a subunit of the elastin/laminin receptor. In this study, we investigated both the structure of the Sgal peptide, representing the elastin-binding domain of EBP, and its interaction with EDPs, through a combination of experimental and theoretical methods. Although the conformation of the Sgal peptide is highly flexible, we detected a type I beta-turn at the QDEA sequence. This represents the best structured motif in the entire Sgal peptide, which might therefore contribute to its binding activity. We further propose a novel three-dimensional model for the interaction between the Sgal peptide and EDPs; folding of the EDPs at the GXXP motif, in a conformation close to a type VIII beta-turn, provides the efficient contact of the protein with the Q residue of the Sgal peptide. This residue is exposed to the peptide surface, because of the beta-turn structure of the QDEA residues in the peptide sequence. We further show that this complex is stabilized by three hydrogen bonds involving EDPs backbone atoms.

Refinement of protein structures into low-resolution density maps using rosetta

We describe a method based on Rosetta structure refinement for generating high-resolution, all-atom protein models from electron cryomicroscopy density maps. A local measure of the fit of a model to the density is used to directly guide structure refinement and to identify regions incompatible with the density that are then targeted for extensive rebuilding. Over a range of test cases using both simulated and experimentally generated data, the method consistently increases the accuracy of starting models generated either by comparative modeling or by hand-tracing the density. The method can achieve near-atomic resolution starting from density maps at 4-6 A resolution.

Binless estimation of the potential of mean force

For a system in thermal equilibrium, described by classical statistical mechanics, we derive an unbiased estimator for the marginal probability distribution of a coordinate of interest, rho( x). This result provides a "binless" method for estimating the potential of mean force, Phi = -beta (-1) ln rho, eliminating the need to construct histograms or perform numerical thermodynamic integration. In our method, the distribution that we seek to compute is expressed as the sum of a reference distribution, rho 0(x)essentially an initial guess or estimate of rho( x)and a correction term. While the method is valid for arbitrary rho 0, we speculate that an accurate choice of the reference distribution improves the convergence of the method. Using a model molecule, simulated both in vacuum and in solvent, we validate our proposed approach and compare its performance with the histogram and thermodynamic integration methods. We also discuss and validate an extension in which our approach is used in combination with a biasing force, meant to improve uniform sampling of the coordinate of interest.

Damped-dynamics flexible fitting

In fitting atomic structures into EM maps, it often happens that the map corresponds to a different conformation of the structure. We have developed a new methodology to handle these situations that preserves the covalent geometry of the structure and allows the modeling of large deformations. The first goal is achieved by working in generalized coordinates (positional and internal coordinates), and the second by avoiding harmonic potentials. Instead, we use dampers (shock absorbers) between every pair of atoms, combined with a force field that attracts the atomic structure toward incompletely occupied regions of the EM map. The trajectory obtained by integrating the resulting equations of motion converges to a conformation that, in our validation cases, was very close to the target atomic structure. Compared to current methods, our approach is more efficient and robust against wrong solutions and to overfitting, and does not require user intervention or subjective decisions. Applications to the computation of transition pathways between known conformers, homology and loop modeling, as well as protein docking, are also discussed.

Protein–Protein Docking with Backbone Flexibility

Computational protein-protein docking methods currently can create models with atomic accuracy for protein complexes provided that the conformational changes upon association are restricted to the side chains. However, it remains very challenging to account for backbone conformational changes during docking, and most current methods inherently keep monomer backbones rigid for algorithmic simplicity and computational efficiency. Here we present a reformulation of the Rosetta docking method that incorporates explicit backbone flexibility in protein-protein docking. The new method is based on a "fold-tree" representation of the molecular system, which seamlessly integrates internal torsional degrees of freedom and rigid-body degrees of freedom. Problems with internal flexible regions ranging from one or more loops or hinge regions to all of one or both partners can be readily treated using appropriately constructed fold trees. The explicit treatment of backbone flexibility improves both sampling in the vicinity of the native docked conformation and the energetic discrimination between near-native and incorrect models.

A comparative study of molecular dynamics in Cartesian and in internal coordinates: dynamical instability in the latter caused by nonlinearity of the equations of motion

The stability of a general molecular dynamics (MD) integration scheme is examined for simulations in generalized (internal plus external) coordinates (GCs). An analytic expression is derived for the local error in energy during each integration time step. This shows that the explicit dependence of the mass-matrix on GCs, which makes the system's Lagrange equations of motion nonlinear, causes MD simulations in GCs to be less stable than those in Cartesian coordinates (CCs). In terms of CCs, the corresponding mass-matrix depends only on atomic masses and thus atomistic motion is subject to the linear Newton equations, which makes the system more stable. Also investigated are two MD methods in GCs that utilize nonzero elements of the vibrational spectroscopic B-matrices. One updates positions and velocities in GCs that are iteratively adjusted so as to conform to the velocity Verlet equivalent in GCs. The other updates positions in GCs and velocities in CCs that are adjusted to satisfy the internal constraints of the new constrained WIGGLE MD scheme. The proposed methods are applied to an isolated n-octane molecule and their performances are compared with those of several CCMD schemes. The simulation results are found to be consistent with the analytic stability analysis. Finally, a method is presented for computing nonzero elements of B-matrices for external rotations without imposing the Casimir-Eckart conditions.

Emergence of protein fold families through rational design

Diverse proteins with similar structures are grouped into families of homologs and analogs, if their sequence similarity is higher or lower, respectively, than 20%–30%. It was suggested that protein homologs and analogs originate from a common ancestor and diverge in their distinct evolutionary time scales, emerging as a consequence of the physical properties of the protein sequence space. Although a number of studies have determined key signatures of protein family organization, the sequence-structure factors that differentiate the two evolution-related protein families remain unknown. Here, we stipulate that subtle structural changes, which appear due to accumulating mutations in the homologous families, lead to distinct packing of the protein core and, thus, novel compositions of core residues. The latter process leads to the formation of distinct families of homologs. We propose that such differentiation results in the formation of analogous families. To test our postulate, we developed a molecular modeling and design toolkit, Medusa, to computationally design protein sequences that correspond to the same fold family. We find that analogous proteins emerge when a backbone structure deviates only 1–2 Å root-mean-square deviation from the original structure. For close homologs, core residues are highly conserved. However, when the overall sequence similarity drops to ~25%–30%, the composition of core residues starts to diverge, thereby forming novel families of protein homologs. This direct observation of the formation of protein homologs within a specific fold family supports our hypothesis. The conservation of amino acids in designed sequences recapitulates that of the naturally occurring sequences, thereby validating our computational design methodology.

Studies of known proteins have revealed intriguing co-organization of their sequences and structures. Proteins with sequence similarity higher than 25%–30% usually adopt a similar structure and are called homologs, whereas those with low sequence similarity (<20%) can share the same structure and are referred as analogs. The origin of such co-organization has been a topic of extensive discussions among protein folding, design, and evolution research communities, because understanding of the emergence of homologs and analogs in the protein universe has broad implications for our ability to rationally manipulate proteins. In this study, the authors developed a molecular modeling and design method, Medusa, to computationally design diversified protein sequences that correspond to similar backbone structures, which determine a protein fold family. Using Medusa, the authors directly demonstrated the formation of distinct protein homologs within a specific fold family when the structure deviates only 1–2 Å away from the original structure. The study suggests that subtle structural changes, which appear due to accumulating mutations in the families of homologs, lead to a distinct packing of the protein core and, thus, novel compositions of core residues. The latter process leads to the formation of distinct families of homologs.

Recapitulation of protein family divergence using flexible backbone protein design

We use flexible backbone protein design to explore the sequence and structure neighborhoods of naturally occurring proteins. The method samples sequence and structure space in the vicinity of a known sequence and structure by alternately optimizing the sequence for a fixed protein backbone using rotamer based sequence search, and optimizing the backbone for a fixed amino acid sequence using atomic-resolution structure prediction. We find that such a flexible backbone design method better recapitulates protein family sequence variation than sequence optimization on fixed backbones or randomly perturbed backbone ensembles for ten diverse protein structures. For the SH3 domain, the backbone structure variation in the family is also better recapitulated than in randomly perturbed backbones. The potential application of this method as a model of protein family evolution is highlighted by a concerted transition to the amino acid sequence in the structural core of one SH3 domain starting from the backbone coordinates of an homologous structure.

Efficient minimization of angle-dependent potentials for polypeptides in internal coordinates

Angular potentials play an important role in the refinement of protein structures through angle-dependent restraints (e.g., those determined by cross-correlated relaxations, residual dipolar couplings, and hydrogen bonds). Analytic derivatives of such angular potentials with respect to the dihedral angles of proteins would be useful for optimizing such restraints and other types of angular potentials (i.e., such as we are now introducing into protein structure prediction) but have not been described. In this article, analytic derivatives are calculated for four types of angular potentials and integrated with the efficient recursive derivative calculation methods of Gō and coworkers. The formulas are implemented in publicly available software and illustrated by refining a low-resolution protein structure with idealized vector-angle, dipolar-coupling, and hydrogen-bond restraints. The method is now being used routinely to optimize hydrogen-bonding potentials in ROSETTA.

Algorithm for normal mode analysis with general internal coordinates

A technique for performing normal vibrational analysis for biological macromolecules using general internal coordinates is proposed. The technique is based on the conventional algorithm for calculating the second derivatives of potential and kinetic energies using intramolecular dihedral angles, intermolecular translation, and rotation as variables [Braun, W. et al., J Phys Soc Jpn 1984, 53, 3269]. We extend the algorithm to include more general internal coordinates, bond stretching, angle bending, and so forth, without assuming two-body interactions. The essential point is the separation of the variables for potential functions and vibrational analysis. With our technique, we can arbitrarily choose any combination of internal coordinates as variables, free from the functional form of potential energy. We can analyze complex systems such as a multiple molecular system including solvents or a transition state of chemical reactions. In addition, mixed use of the potentials of molecular mechanics and quantum chemistry is possible.

Structure-function analysis of decay-accelerating factor: identification of residues important for binding of the Escherichia coli Dr adhesin and complement regulation

Decay-accelerating factor (DAF), a complement regulatory protein, also serves as a receptor for Dr adhesin-bearing Escherichia coli. The repeat three of DAF was shown to be important in Dr adhesin binding and complement regulation. However, Dr adhesins do not bind to red blood cells with the rare polymorphism of DAF, designated Dr(a(-)); these cells contain a point mutation (Ser165-Leu) in DAF repeat three. In addition, monoclonal antibody IH4 specific against repeat three was shown to block both Dr adhesin binding and complement regulatory functions of DAF. Therefore, to identify residues important in binding of Dr adhesin and IH4 and in regulating complement, we mutated 11 amino acids-predominantly those in close proximity to Ser165 to alanine-and expressed these mutations in Chinese hamster ovary cells. To map the mutations, we built a homology model of repeat three based on the poxvirus complement inhibitory protein, using the EXDIS, DIAMOD, and FANTOM programs. We show that perhaps Ser155, and not Ser165, is the key amino acid that interacts with the Dr adhesin and amino acids Gly159, Tyr160, and Leu162 and also aids in binding Dr adhesin. The IH4 binding epitope contains residues Phe148, Ser155, and L171. Residues Phe123 and Phe148 at the interface of repeat 2-3, and also Phe154 in the repeat three cavity, were important for complement regulation. Our results show that residues affecting the tested functions are located on the same loop (148 to 171), at the same surface of repeat three, and that the Dr adhesin-binding and complement regulatory epitopes of DAF appear to be distinct and are approximately 20 A apart.

New method for parallel computation of Hessian matrix of conformational energy function in internal coordinates

A new algorithm for parallel calculation of the second derivatives (Hessian) of the conformational energy function of biomolecules in internal coordinates is proposed. The basic scheme of this algorithm is the division of the entire calculation of the Hessian matrix (called "task") into subtasks and the optimization of the assignment of processors to each subtask by considering both the load balancing and reduction of the communication cost. A genetic algorithm is used for this optimization considering the dependencies between subtasks. We applied this method to a glutaminyl transfer RNA (Gln-tRNA) molecule for which the scalability of our previously developed parallel algorithm was significantly decreased when the large number of processors was used. The speedup for the calculation was 32.6 times with 60 processors, which is considerably better than the speedup for our previously reported parallel algorithm. The elapsed time for the calculation of subtasks, data sending, and data receiving was analyzed, and the effect of the optimization using the genetic algorithm is discussed.

Aplysia attractin: biophysical characterization and modeling of a water-borne pheromone

Attractin, a 58-residue protein secreted by the mollusk Aplysia californica, stimulates sexually mature animals to approach egg cordons. Attractin from five different Aplysia species are approximately 40% identical in sequence. Recombinant attractin, expressed in insect cells and purified by reverse-phase high-performance liquid chromatography (RP-HPLC), is active in a bioassay using A. brasiliana; its circular dichroism (CD) spectrum indicates a predominantly alpha-helical structure. Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) characterization of proteolytic fragments identified disulfide bonds between the six conserved cysteines (I-VI, II-V, III-IV, where the Roman numeral indicates the order of occurrence in the primary sequence). Attractin has no significant similarity to any other sequence in the database. The protozoan Euplotes pheromones were selected by fold recognition as possible templates. These diverse proteins have three alpha-helices, with six cysteine residues disulfide-bonded in a different pattern from attractin. Model structures with good stereochemical parameters were prepared using the EXDIS/DIAMOD/FANTOM program suite and constraints based on sequence alignments with the Euplotes templates and the attractin disulfide bonds. A potential receptor-binding site is suggested based on these data. Future structural characterization of attractin will be needed to confirm these models.

Homology modeling and characterization of IgE binding epitopes of mountain cedar allergen Jun a 3

The Jun a 3 protein from mountain cedar (Juniperus ashei) pollen, a member of group 5 of the family of plant pathogenesis-related proteins (PR-proteins), reacts with serum IgE from patients with cedar hypersensitivity. We used the crystal structures of two other proteins of this group, thaumatin and an antifungal protein from tobacco, both approximately 50% identical in sequence to Jun a 3, as templates to build homology models for the allergen. The in-house programs EXDIS and FANTOM were used to extract distance and dihedral angle constraints from the Protein Data Bank files and determine energy-minimized structures. The mean backbone deviations for the energy-refined model structures from either of the templates is <1 A, their conformational energies are low, and their stereochemical properties (determined with PROCHECK) are acceptable. The circular dichroism spectrum of Jun a 3 is consistent with the postulated beta-sheet core. Tryptic fragments of Jun a 3 that reacted with IgE from allergic patients all mapped to one helical/loop surface of the models. The Jun a 3 models have features common to aerosol allergens from completely different protein families, suggesting that tertiary structural elements may mediate the triggering of an allergic response.

Dynamic structure of subtilisin-eglin c complex studied by normal mode analysis

Normal mode analysis of subtilisin-eglin c complex was performed to investigate the dynamics at the interface between the enzyme and the inhibitor. The internal motions of the complex calculated from the normal modes were divided into three parts: the internal motions changing the shape of each molecule, the external rigid-body motions changing their mutual dispositions, and the coupling between the internal and external motions. From the results of the analysis, the following characteristic features were found in the dynamics at the interface regions: 1) negative correlation between the internal and external motions within each molecule, and 2) positive correlation between the external motions of the two molecules. The former decreases the apparent amplitudes of motions at the interface. The latter minimizes the interference between individual motions of the two molecules. These dynamic characteristics allow the enzyme and the inhibitor to move as freely as possible. This finding suggests that the experimental evidence of the large entropy gain on binding should be attributed not only to strong hydrophobic interactions, but also to the dynamic structure of the complex, which is found to minimize an unavoidable loss of the conformational entropy on binding.

Torsion angle dynamics for NMR structure calculation with the new program DYANA

The new program DYANA (DYnamics Algorithm for Nmr Applications) for efficient calculation of three-dimensional protein and nucleic acid structures from distance constraints and torsion angle constraints collected by nuclear magnetic resonance (NMR) experiments performs simulated annealing by molecular dynamics in torsion angle space and uses a fast recursive algorithm to integrate the equations of motions. Torsion angle dynamics can be more efficient than molecular dynamics in Cartesian coordinate space because of the reduced number of degrees of freedom and the concomitant absence of high-frequency bond and angle vibrations, which allows for the use of longer time-steps and/or higher temperatures in the structure calculation. It also represents a significant advance over the variable target function method in torsion angle space with the REDAC strategy used by the predecessor program DIANA. DYANA computation times per accepted conformer in the "bundle" used to represent the NMR structure compare favorably with those of other presently available structure calculation algorithms, and are of the order of 160 seconds for a protein of 165 amino acid residues when using a DEC Alpha 8400 5/300 computer. Test calculations starting from conformers with random torsion angle values further showed that DYANA is capable of efficient calculation of high-quality protein structures with up to 400 amino acid residues, and of nucleic acid structures.

Prediction of polyelectrolyte polypeptide structures using Monte Carlo conformational search methods with implicit solvation modeling

Many interesting proteins possess defined sequence stretches containing negatively charged amino acids. At present, experimental methods (X-ray crystallography, NMR) have failed to provide structural data for many of these sequence domains. We have applied the dihedral probability grid-Monte Carlo (DPG-MC) conformational search algorithm to a series of N- and C-capped polyelectrolyte peptides, (Glu)20, (Asp)20, (PSer)20, and (PSer-Asp)10, that represent polyanionic regions in a number of important proteins, such as parathymosin, calsequestrin, the sodium channel protein, and the acidic biomineralization proteins. The atomic charges were estimated from charge equilibration and the valence and van der Waals parameters are from DREIDING. Solvation of the carboxylate and phosphate groups was treated using sodium counterions for each charged side chain (one Na+ for COO-; two Na for CO(PO3)-2) plus a distance-dependent (shielded) dielectric constant, epsilon = epsilon 0 R, to simulate solvent water. The structures of these polyelectrolyte polypeptides were obtained by the DPG-MC conformational search with epsilon 0 = 10, followed by calculation of solvation energies for the lowest energy conformers using the protein dipole-Langevin dipole method of Warshel. These calculations predict a correlation between amino acid sequence and global folded conformational minima: 1. Poly-L-Glu20, our structural benchmark, exhibited a preference for right-handed alpha-helix (47% helicity), which approximates experimental observations of 55-60% helicity in solution. 2. For Asp- and PSer-containing sequences, all conformers exhibited a low preference for right-handed alpha-helix formation (< or = 10%), but a significant percentage (approximately 20% or greater) of beta-strand and beta-turn dihedrals were found in all three sequence cases: (1) Aspn forms supercoil conformers, with a 2:1:1 ratio of beta-turn:beta-strand:alpha-helix dihedral angles; (2) PSer20 features a nearly 1:1 ratio of beta-turn:beta-sheet dihedral preferences, with very little preference for alpha-helical structure, and possesses short regions of strand and turn combinations that give rise to a collapsed bend or hairpin structure; (3) (PSer-Asp)10 features a 3:2:1 ratio of beta-sheet:beta-turn:alpha-helix and gives rise to a superturn or C-shaped structure.

Local moves: an efficient algorithm for simulation of protein folding

We have enhanced genetic algorithms and Monte Carlo methods for simulation of protein folding by introducing "local moves" in dihedral space. A local move consists of changes in backbone dihedral angles in a sequential window while the positions of all atoms outside the window remain unchanged. We find three advantages of local moves: (1) For some energy functions, protein conformations of lower energy are found; (2) these low energy conformations are found in fewer steps; and (3) the simulations are less sensitive to the details of the annealing protocol. To distinguish the effectiveness of local move algorithm from the complexity of the energy function, we have used several different energy functions. These energy functions include the Profile score (Bowie et al., Science 253:164-170, 1991), the knowledge-based energy function used by Bowie and Eisenberg 1994 (Proc. Natl. Acad. Sci. U.S.A. 91:4434-4440, 1994), two energy terms developed as suggested by Sippl and coworkers (Hendlich et al., J. Mol. Biol. 216:167-180, 1990), and AMBER (Weiner and Kollman, J. Comp. Chem. 2:287-303, 1981). Besides these energy functions we have used three energy functions that include knowledge of the native structures: the RMSD from the native structure, the distance matrix error, and an energy term based on the distance between different residue types called DBIN. In some of these simulations the main advantage of local moves is the reduced dependence on the details of the annealing schedule. In other simulations, local moves are superior to other algorithms as structures with lower energy are found.

De novo prediction of polypeptide conformations using dihedral probability grid Monte Carlo methodology

We tested the dihedral probability grid Monte Carlo (DPG-MC) methodology to determine optimal conformations of polypeptides by applying it to predict the low energy ensemble for two peptides whose solution NMR structures are known: integrin receptor peptide (YGRGDSP, Type II beta-turn) and S3 alpha-helical peptide (YMSEDEL KAAEAAFKRHGPT). DPG-MC involves importance sampling, local random stepping in the vicinity of a current local minima, and Metropolis sampling criteria for acceptance or rejection of new structures. Internal coordinate values are based on side-chain-specific dihedral angle probability distributions (from analysis of high-resolution protein crystal structures). Important features of DPG-MC are: (1) Each DPG-MC step selects the torsion angles (phi, psi, chi) from a discrete grid that are then applied directly to the structure. The torsion angle increments can be taken as S = 60, 30, 15, 10, or 5 degrees, depending on the application. (2) DPG-MC utilizes a temperature-dependent probability function (P) in conjunction with Metropolis sampling to accept or reject new structures. For each peptide, we found close agreement with the known structure for the low energy conformational ensemble located with DPG-MC. This suggests that DPG-MC will be useful for predicting conformations of other polypeptides.

A variable target intensity-restrained global optimization (VARTIGO) procedure for determining three-dimensional structures of polypeptides from NOESY data: application to gramicidin-S

A global optimization method for intensity-restrained structure refinement, based on variable target function (VTF) analysis, is illustrated using experimental data on a model peptide, gramicidin-S (GS) dissolved in DMSO. The method (referred to as VARTIGO for variable target intensity-restrained global optimization) involves minimization of a target function in which the range of NOE contacts is gradually increased in successive cycles of optimization in dihedral angle space. Several different starting conformations (including all-trans) have been tested to establish the validity of the method. Not all optimizations were successful, but these were readily identifiable from their large NOE R-factors. We also show that it is possible to simultaneously optimize the rotational correlation time along with the dihedral angles. The structural features of GS thus obtained from the successful optimizations are in excellent agreement with the available experimental data. A comparison is made with structures generated from an intensity-restrained single target function (STF) analysis. The results on GS suggest that VARTIGO refinement is capable of yielding better quality structures. Our work also underscores the need for a simultaneous analysis of different NOE R-factors in judging the quality of optimized structures. The NOESY data on GS in DMSO appear to provide evidence for the presence of two orientations for the ornithine side chain, in fast exchange. The NOESY spectra for this case were analyzed using a relaxation rate matrix which is a weighted average of the relaxation rate matrices for the individual conformations.