Multiple pH regime molecular dynamics simulation for pK calculations

Ionisation equilibria in proteins are influenced by conformational flexibility, which can in principle be accounted for by molecular dynamics simulation. One problem in this method is the bias arising from the fixed protonation state during the simulation. Its effect is mostly exhibited when the ionisation behaviour of the titratable groups is extrapolated to pH regions where the predetermined protonation state of the protein may not be statistically relevant, leading to conformational sampling that is not representative of the true state. In this work we consider a simple approach which can essentially reduce this problem. Three molecular dynamics structure sets are generated, each with a different protonation state of the protein molecule expected to be relevant at three pH regions, and pK calculations from the three sets are combined to predict pK over the entire pH range of interest. This multiple pH molecular dynamics approach was tested on the GCN4 leucine zipper, a protein for which a full data set of experimental data is available. The pK values were predicted with a mean deviation from the experimental data of 0.29 pH units, and with a precision of 0.13 pH units, evaluated on the basis of equivalent sites in the dimeric GCN4 leucine zipper.     

Free energy of helix propagation in short polyalanine chains determined from peptide growth simulations of La3+-binding model peptides. Comparison with experimental data

Molecular dynamics (MD) is, at present, a unique tool making it possible to study, at the atomic level, conformational transitions in peptides and proteins. Nevertheless, because MD calculations are always based on a more or less approximate physical model, using a set of approximate parameters, their reliability must be tested by comparison with experimental data. Unfortunately, it is very difficult to find a peptide system in which conformational transitions can be studied both experimentally and using MD simulations so that a direct comparison of the results obtained in both ways could be made. Such a system, containing a rigid alpha-helix nucleus stabilized by La(3+) coordination to a 12-residue sequence taken from an EF-hand protein has recently been used to determine experimentally the helix propagation parameters in very short polyalanine segments (Goch et al. (2003) Biochemistry 42: 6840-6847). The same parameters were calculated here for the same peptide system using the peptide growth simulation method with, alternatively, charmm 22 and cedar potential energy functions. The calculated free energies of the helix-coil transition are about two times too large for cedar and even three times too large for charmm 22, as compared with the experimental values. We suggest that these discrepancies have their origin in the incorrect representation of unfolded peptide backbone in solution by the molecular mechanics force fields.     

All-valence-shell molecular orbital calculations on the chiroptical properties of substituted and unsubstituted 2,5-diketopiperazine structures

The chiroptical properties of L -3-methyl-2,5-diketopiperazine (L -alanylglycyl anhydride) are examined on a theoretical model in which the electronic wave functions are obtained from semi-empirical all-valence-shell molecular orbital calculations. The INDO molecular orbital model is used to perform SCF-MO calculations on the ground states of six conformation isomers of L -3-methyl-2,5-diketopiperazine and two chiral conformational isomers of unsubstituted 2,5-diketopiperazine. Excited-state wave functions are constructed in the virtual orbital-configuration interaction approximation. The rotatory strengths, dipole strengths, oscillator strengths, and dissymmetry factors of the first eight singlet–singlet transitions for each of the eight structures are calculated and reported. Additionally, ground-state dipole moments, net atomic charges, and the first four ionization potentials (calculated according to Koopman's theorem) are computed for each structure. The signs and the magnitudes of the rotatory strengths are found to be extremely sensitive to the conformation of the piperazine ring as well as to methyl substitution at the α carbon of the ring. Spectra–structure relationships based on the calculations reported here are discussed, and the available experimental CD data on dissymmetric 2,5-diketopiperazine are examined in terms of our theoretical results.     

Determination of three-dimensional structures of proteins from interproton distance data by hybrid distance geometry-dynamical simulated annealing calculations

A new hybrid distance space-real space method for determining three-dimensional structures of proteins on the basis of interproton distance restraints is presented. It involves the following steps: (i) the approximate polypeptide fold is obtained by generating a set of substructures comprising only a small subset of atoms by projection from multi-dimensional distance space into three-dimensional cartesian coordinate space using a procedure known as 'embedding'; (ii) all remaining atoms are then added by best fitting extended amino acids one residue at a time to the substructures; (iii) the resulting structures are used as the starting point for real space dynamical simulated annealing calculations. The latter involve heating the system to a high temperature followed by slow cooling in order to overcome potential barriers along the pathway towards the global minimum region. This is carried out by solving Newton's equations of motion. Unlike conventional restrained molecular dynamics, however, the non-bonded interactions are represented by a simple van der Waals repulsion term. The method is illustrated by calculations on crambin (46 residues) and the globular domain of histone H5 (79 residues). It is shown that the hybrid method is more efficient computationally and samples a larger region of conformational space consistent with the experimental data than full metric matrix distance geometry calculations alone, particularly for large systems.     

Peptide Free Energy Landscapes Calibrated by Molecular Orbital Calculations

Free energy landscapes of peptide conformations werecalibrated by ab initiomolecular orbital calculations, after enhancedconformational sampling using the multicanonical molecular dynamicssimulations. Three different potentials of mean force for an isolateddipeptide were individually obtained using the conventional force fields,AMBER parm94, AMBER parm96, and CHARMm22. Each potential ofmean force was calibrated based on the umbrella sampling algorithm fromthe adiabatic energy map that was calculated separately by the abinitiomolecular orbital method. All the calibrated potentials of mean forcecoincided well. The calibration was applied to a peptide in explicit water,and the calibrated free energy landscapes did not depend on the force fieldused in conformational sampling, as far as the conformational space waswell sampled.     

Normal mode calculations of icosahedral viruses with full dihedral flexibility by use of molecular symmetry

The study of the dynamics and thermodynamics of small icosahedral virus capsids is an active field of research. Normal mode analysis is one of the computational tools that can provide important insights into the conformational changes of the virus associated with cell entry or caused by changing of the physicochemical environment. Normal mode analysis of virus capsids has been limited due to the size of these systems, which often exceed 50,000 residues. Here we present the first normal mode calculation with full dihedral flexibility of several virus capsids, including poliovirus, rhinovirus, and cowpea chlorotic mottle virus. The calculations were made possible by applying group theoretical methods, which greatly simplified the calculations without any approximation beyond the all-atom force field representations in general use for smaller protein systems. Since a full Cartesian basis set was too large to be handled by the available computer memory, we used a basis set that includes all internal dihedral angles of the system with the exception of the peptide bonds, which were assumed rigid. The fluctuations of the normal modes are shown to correlate well with crystallographic temperature factors. The motions of the first several normal modes of each symmetry type are described. A hinge bending motion in poliovirus was found that may be involved in the mechanism by which bound small molecules inhibit conformational changes of the capsid. Fully flexible normal mode calculations of virus capsids are expected to increase our understanding of virus dynamics and thermodynamics, and can be useful in the refinement of cryo-electron microscopy structures of viruses.     

Mean-field calculations of chain packing and conformational statistics in lipid bilayers: comparison with experiments and molecular dynamics studies.

A molecular, mean-field theory of chain packing statistics in aggregates of amphiphilic molecules is applied to calculate the conformational properties of the lipid chains comprising the hydrophobic cores of dipalmitoyl-phosphatidylcholine (DPPC), dioleoyl-phosphatidylcholine (DOPC), and palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayers in their fluid state. The central quantity in this theory, the probability distribution of chain conformations, is evaluated by minimizing the free energy of the bilayer assuming only that the segment density within the hydrophobic region is uniform (liquidlike). Using this distribution we calculate chain conformational properties such as bond orientational order parameters and spatial distributions of the various chain segments. The lipid chains, both the saturated palmitoyl (-(CH2)14-CH3) and the unsaturated oleoyl (-(CH2)7-CH = CH-(CH2)7-CH3) chains are modeled using rotational isomeric state schemes. All possible chain conformations are enumerated and their statistical weights are determined by the self-consistency equations expressing the condition of uniform density. The hydrophobic core of the DPPC bilayer is treated as composed of single (palmitoyl) chain amphiphiles, i.e., the interactions between chains originating from the same lipid headgroup are assumed to be the same as those between chains belonging to different molecules. Similarly, the DOPC system is treated as a bilayer of oleoyl chains. The POPC bilayer is modeled as an equimolar mixture of palmitoyl and oleoyl chains. Bond orientational order parameter profiles, and segment spatial distributions are calculated for the three systems above, for several values of the bilayer thickness (or, equivalently, average area/headgroup) chosen, where possible, so as to allow for comparisons with available experimental data and/or molecular dynamics simulations. In most cases the agreement between the mean-field calculations, which are relatively easy to perform, and the experimental and simulation data is very good, supporting their use as an efficient tool for analyzing a variety of systems subject to varying conditions (e.g., bilayers of different compositions or thicknesses at different temperatures).     

Conformational-energy calculations for oligosaccharides: a comparison of methods and a strategy of calculation

A theoretical conformational analysis of dimethoxymethane, 2-methoxytetrahydropyran, cellobiose, and maltose has been performed. The validity of several commonly used classical approaches to conformational energy, assuming non-bonded interactions, torsional terms, and the exo-anomeric contribution, and the MM2CARB method (a modified version of the MM2 force-field program using the Jeffrey-Taylor parameters) was tested against available experimental data or previous quantum-chemical calculations. The MM2CARB method correctly reproduces the energies and the variations in bond lengths and bond angles for conformers of dimethoxymethane and 2-methoxytetrahydropyran. Prediction of the observed conformers with simple potential functions appears to be less satisfactory. In particular, calculations that take into account non-bonded interactions and the exo-anomeric contribution based on dimethoxymethane give predicted energy differences that are 2–3 times higher than the experimental values. The general shapes of the (Φ, Ψ) potential-energy surfaces for cellobiose and maltose provided by potential-function calculations suggest the presence of several minima whose energies depend, to a great extent, on the choice of molecular geometry. The MM2CARB-calculated structures of seven cellobiose and five maltose conformers demonstrate clearly the variation of disaccharide geometry with change of conformation around the glycosidic linkage. The relative energies calculated by simple methods differ from MM2CARB energies and indicate that the simple potential-functions methods give only a qualitative estimate of oligosaccharide conformers. Based on these results, we propose a general strategy and two different approaches for the investigation of conformational properties of oligosaccharides.     

Molecular orbital calculations on the conformation of polypeptides and proteins. 8. The conformational energy maps and stereochemical rotational states of the asparaginyl, glutaminyl aspartyl and glutamyl residues

Quantum-mechanical calculations on the conformational energy map and stereo-chemical rotational states of aminoacid residues by the PCILO method are extended to the asparaginyl, glutaminyl, aspartyl and glutamyl residues in their neutral form. One of the most outstanding features of the results is the occurrence of the global minimum (or of one of a few equivalent global minima) in the region of the left handed α-helix for the first three of the above mentioned residues. The results of the calculations are compared with experimental data from eight, globular proteins which confirm that these residues may exist, in fact, in this conformation. They also enable to understand the experimentally observed possibility of helix reversal in esters of poly-L -aspartic acid as a function of substitutions in the side chain.     

Conformational behaviour of the architectural units of peptides and proteins. Assessment of current understanding by ab initio quantum mechanical methods and refinement of the dipeptide energy surface.

The conformational energy surfaces of analogues of the dipeptide unit of polypeptides and proteins are calculated by ab initio methods using extended basis sets.The calculations are not particularly sensitive to the choice of (extended) basis set.The calculations are shown to support a particular empirical method parameterized with respect to crystal data. Non-hydrogen bonded conformations agree to within 3 kcal mol^?1, even for conformations in which quite considerable degrees of atomic overlap occur.Hydrogen bonded conformations, are, however, in less satisfactory agreement and it is the ab initio calculations which appear to be at fault.A simple correction is applied to the ab initio energy for hydrogen bonded conformations, and with the use of the empirical energy surface a full quantum mechanical conformational energy map is interpolated for the alanyl dipeptide.The effect of flexibility in the peptide backbone is taken into account, and supports recent empirical findings that distortions in valence angles must be considered in calculations of the conformational behaviour of peptides.     

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic–hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H–H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H–H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.     

Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings

Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.     

Continuum solvent model calculations of alamethicin-membrane interactions: thermodynamic aspects

Alamethicin is a 20-amino acid antibiotic peptide that forms voltage-gated ion channels in lipid bilayers. Here we report calculations of its association free energy with membranes. The calculations take into account the various free-energy terms that contribute to the transfer of the peptide from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the solvation free energy are calculated using continuum solvent models. The contributions from the lipid perturbation and membrane deformation effects and the entropy loss associated with peptide immobilization in the bilayer are estimated from a statistical thermodynamic model. The calculations were carried out using two classes of experimentally observed conformations, both of which are helical: the NMR and the x-ray crystal structures. Our calculations show that alamethicin is unlikely to partition into bilayers in any of the NMR conformations because they have uncompensated backbone hydrogen bonds and their association with the membrane involves a large electrostatic solvation free energy penalty. In contrast, the x-ray conformations provide enough backbone hydrogen bonds for the peptide to associate with bilayers. We tested numerous transmembrane and surface orientations of the peptide in bilayers, and our calculations indicate that the most favorable orientation is transmembrane, where the peptide protrudes approximately 4 A into the water-membrane interface, in very good agreement with electron paramagnetic resonance and oriented circular dichroism measurements. The calculations were carried out using two alamethicin isoforms: one with glutamine and the other with glutamate in the 18th position. The calculations indicate that the two isoforms have similar membrane orientations and that their insertion into the membrane is likely to involve a 2-A deformation of the bilayer, again, in good agreement with experimental data. The implications of the results for the biological function of alamethicin and its capacity to oligomerize and form ion channels are discussed.     

Strategies for dealing with conformational sampling in structural calculations of flexible or kinked transmembrane peptides.

Peptides corresponding to transmembrane (TM) segments from membrane proteins provide a potential route for the determination of membrane protein structure. We have determined that 2 functionally critical TM segments from the mammalian Na+/H+ exchanger display well converged structure in regions separated by break points. The flexibility of these break points results in conformational sampling in solution. A brief review of available NMR structures of helical membrane proteins demonstrates that there are a number of published structures showing similar properties. Such flexibility is likely indicative of kinks in the full-length protein. This minireview focuses on methods and protocols for NMR structure calculation and analysis of peptide structures under conditions of conformational sampling. The methods outlined allow the identification and analysis of structured peptides containing break points owing to conformational sampling and the differentiation between oligomerization and ensemble-averaged observation of multiple peptide conformations.     

Aggregation and conformational studies on a pentapeptide derivative

Most of the disease causing proteins such as beta amyloid, amylin, and huntingtin protein, which are natively disordered, readily form fibrils consisting of beta-sheet polymers. Though all amyloid fibrils are made up of beta-sheet polymers, not all peptides with predominant beta-sheet content in the native state develop into amyloid fibrils. We hypothesize that stable amyloid like fibril formation may require mixture of different conformational states in the peptide. We have tested this hypothesis on amyloid forming peptide namely HCl(Ile)(5)NH(CH(2)CH(2)O)(3)CH(3) (I). We show peptide I, has propensity to form self-assembled structures of beta-sheets in aqueous solutions. When incubated over a period of time in aqueous buffer, I self assembled into beta sheet like structures with diameters ranging from 30 to 60 A that bind with amyloidophilic dyes like Congo red and Thioflavin T. Interestingly peptide I developed into unstable fibrils after prolonged aging at higher concentration in contrast with the general mature fibril-forming propensity of various amyloid petides known to date.     

Identification of structured peptide segments in folding proteins.

Prediction of the structures of long polypeptides and small proteins has been carried out using conformational energy calculations. These calculations can be applied to large proteins if structured regions of their sequences can be identified. Three different approaches to identifying such sequences are presented. First, sequences of five or more contiguous hydrophobic residues tend to nucleate alpha-helices. Second, peptide sequences from parent proteins that have the same biological activities as the parent proteins are highly structured. Third, structured synthetic peptide segments from proteins inhibit the folding of the parent proteins by competing with the corresponding segment of the protein chain for associating with complementary regions. Examples of each of these approaches are presented.     

Peptide bond distortions from planarity: new insights from quantum mechanical calculations and peptide/protein crystal structures

By combining quantum-mechanical analysis and statistical survey of peptide/protein structure databases we here report a thorough investigation of the conformational dependence of the geometry of peptide bond, the basic element of protein structures. Different peptide model systems have been studied by an integrated quantum mechanical approach, employing DFT, MP2 and CCSD(T) calculations, both in aqueous solution and in the gas phase. Also in absence of inter-residue interactions, small distortions from the planarity are more a rule than an exception, and they are mainly determined by the backbone ψ dihedral angle. These indications are fully corroborated by a statistical survey of accurate protein/peptide structures. Orbital analysis shows that orbital interactions between the σ system of C(α) substituents and the π system of the amide bond are crucial for the modulation of peptide bond distortions. Our study thus indicates that, although long-range inter-molecular interactions can obviously affect the peptide planarity, their influence is statistically averaged. Therefore, the variability of peptide bond geometry in proteins is remarkably reproduced by extremely simplified systems since local factors are the main driving force of these observed trends. The implications of the present findings for protein structure determination, validation and prediction are also discussed.     

In Silico Analysis of Peptide Potential Biological Functions

Over the past decade, tools of omics technologies have generated a large amount of data in various repositories, which are of interest for meta-analysis today. Now, researchers in the field of proteomics and peptidomics focus not on sequencing, but on functions performed by molecules and metabolic interactions, in which the proteins or peptides participate. As a result of a single LC-MS/MS analysis, several thousand unique peptides can be identified, each of which may be bioactive. A classic technique for determining the peptide function is a direct experiment. Bioinformatics approaches as a preliminary analysis of potential biological functions are an important step and are able to significantly reduce time and cost of experimental verification. This article provides an overview of computational methods for predicting biological functions of peptides. Approaches based on machine learning, which are the most popular today, algorithms using structural, evolutionary, or statistical patterns, as well as methods based on molecular docking, are considered. Databases of bioactive peptides are reported, providing information necessary to construct new algorithms for predicting biological functions. Attention is paid to the characteristics of peptides, on the basis of which it is possible to draw conclusions about their bioactivity. In addition, the report provides a list of online services that may be used by researchers to analyze potential activities of peptides with which they work.     

Origins of life: conformational energy calculations on primitive tRNA nestling an amino acid

We report conformational energy calculations on our proposal of a molecular interaction theory for the origin of the nucleic acid-directed, adaptor-mediated synthesis of proteins that links the phenomena of chemical and biological evolution. A particular conformation of a pentanucleotide turns out to be a double-sided template for a primitive decoding system. It is able to neatly nestle an amino acid via hydrogen bonds, and this complex is found to be an energetically favourable conformation. The total potential energy of the complex is calculated using semi-empirical potential energy functions. A local-minimum conformation is obtained and its features are reported. The template conformation of the pentanucleotide is found to have an energy value far lower than a regular helical conformation. When the amino acid is nestled in the cleft of the template-conformation through specific hydrogen bonds, the energy is further lowered. A D-amino acid nestled into the PIT (Primitive tRNA) is found to be less stable than its L counterpart, as revealed by energy calculations.     

The binding mechanism of a novel nicotinamide isostere inhibiting with TNKSs: a molecular dynamic simulation and binding free energy calculation

Tankyrases (TNKSs), a member of human poly (ADP-ribose) polymerase (PARP) protein superfamily, plays a key role in regulation of cell proliferation. Among the representative proteins of the PARPs family, it is found that the inhibitors have high selectivity for Tankyrase1 (TNKS1). The specific binding modes are investigated between the TNKS1 protein and nicotinamide isostere (ISX) which functions as an inhibitor of TNKS1. The stabilities of ISX-TNKS1 and AVA939-TNKS1 complexes are estimated by molecular dynamics (MD) simulations and free energy calculations; a good agreement with experimental results is reached. On the basis of the calculated results of MD simulations, we found that the inhibitors influence the conformational flexibility of TNKS1 and the XAV939 binding drive the peptide Ile1228-Gly1229-Gly1230 to form a helical structure while the ISX binding drive the peptide to form a turn structure. Moreover, the formed important hydrogen bonds of Tyr1203 residue with XVA939 and WAT1551 with ISX enhance stabilities of the complexes, and the electrostatic interactions in XAV939-TNKS1 and van der Waals interactions in ISX-TNKS1 system are main driving forces for affinity. According to the results of the decomposition of binding free energy, it is obvious that the residues Try1224 and Lys1220 make the most favorable contributions to the binding in, respectively, ISX and XAV939 complexes. Taken together, the obtained results are useful for studying the binding mechanisms of TNKSs and inhibitors and for designing potent inhibitors.