Biomedical subjects

Adam Liwo

Publications and source records attributed to Adam Liwo.

At least 19 recordsLinked to original sources

PubMed2007

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

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

Biophysics↗

PubMed2007

Molecular dynamics with the United-residue force field: ab initio folding simulations of multichain proteins.

The implementation of molecular dynamics with the united-residue (UNRES) force field is extended to treat multichain proteins. Constant temperature was maintained in the simulations with Berendsen or Langevin thermostats. The method was tested on three alpha-helical proteins (1G6U and GCN4-p1, each with two chains, and 1C94, with four chains). Simulations were carried out for both the isolated single chains and the multichain complexes. The proteins were folded by starting from the extended conformation with random initial velocities and with the chains parallel to each other. No symmetry constraints or structure information were included for the single chains or the multichain complexes. In the case of single-chain simulations, a high percentage of the trajectories (100% for 1G6U, 90% for GCN4-p1, and 80% for 1C94) converged to nativelike structures (assumed as the experimental structure of a monomer in the multichain complex), showing that, for the proteins studied in this work with the UNRES force field, the interactions between chains are not critical for stabilization of the individual chains. In the case of multichain simulations, the native structures of the 1G6U and GCN4-p1 complexes, but not that of 1C94, are predicted successfully. The association of the subunits does not follow a unique mechanism; the monomers were observed to fold both before and simultaneously with their association.

Biophysics↗

PubMed2007

Protein-folding dynamics: overview of molecular simulation techniques.

Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study protein-folding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.

Algorithms↗

PubMed2006

Implementation of a symplectic multiple-time-step molecular dynamics algorithm, based on the united-residue mesoscopic potential energy function.

A symplectic multiple-time-step (MTS) algorithm has been developed for the united-residue (UNRES) force field. In this algorithm, the slow-varying forces (which contain most of the long-range interactions and are, therefore, expensive to compute) are integrated with a larger time step, termed the basic time step, and the fast-varying forces are integrated with a shorter time step, which is an integral fraction of the basic time step. Based on the split operator formalism, the equations of motion were derived. Separation of the fast- and slow-varying forces leads to stable molecular dynamics with longer time steps. The algorithms were tested with the Ala(10) polypeptide chain and two versions of the UNRES force field: the current one in which the energy components accounting for the energetics of side-chain rotamers (U(rot)) can lead to numerically unstable forces and a modified one in which the the present U(rot) was replaced by a numerically stable expression which, at present, is parametrized only for polyalanine chains. With the modified UNRES potential, stable trajectories were obtained even when extending the basic time step to 15 fs and, with the original UNRES potentials, the basic time step is 1 fs. An adaptive multiple-time-step (A-MTS) algorithm is proposed to handle instabilities in the forces; in this method, the number of substeps in the basic time step varies depending on the change of the magnitude of the acceleration. With this algorithm, the basic time step is 1 fs but the number of substeps and, consequently, the computational cost are reduced with respect to the MTS algorithm. The use of the UNRES mesoscopic energy function and the algorithms derived in this work enables one to increase the simulation time period by several orders of magnitude compared to conventional atomic-resolution molecular dynamics approaches and, consequently, such an approach appears applicable to simulating protein-folding pathways, protein functional dynamics in a real molecular environment, and dynamical molecular recognition processes.

Algorithms↗

PubMed2006

Assessment of two theoretical methods to estimate potentiometric titration curves of peptides: comparison with experiment.

We compared the ability of two theoretical methods of pH-dependent conformational calculations to reproduce experimental potentiometric titration curves of two models of peptides: Ac-K5-NHMe in 95% methanol (MeOH)/5% water mixture and Ac-XX(A)7OO-NH2 (XAO) (where X is diaminobutyric acid, A is alanine, and O is ornithine) in water, methanol (MeOH), and dimethyl sulfoxide (DMSO), respectively. The titration curve of the former was taken from the literature, and the curve of the latter was determined in this work. The first theoretical method involves a conformational search using the electrostatically driven Monte Carlo (EDMC) method with a low-cost energy function (ECEPP/3 plus the SRFOPT surface-solvation model, assumming that all titratable groups are uncharged) and subsequent reevaluation of the free energy at a given pH with the Poisson-Boltzmann equation, considering variable protonation states. In the second procedure, molecular dynamics (MD) simulations are run with the AMBER force field and the generalized Born model of electrostatic solvation, and the protonation states are sampled during constant-pH MD runs. In all three solvents, the first pKa of XAO is strongly downshifted compared to the value for the reference compounds (ethylamine and propylamine, respectively); the water and methanol curves have one, and the DMSO curve has two jumps characteristic of remarkable differences in the dissociation constants of acidic groups. The predicted titration curves of Ac-K5-NHMe are in good agreement with the experimental ones; better agreement is achieved with the MD-based method. The titration curves of XAO in methanol and DMSO, calculated using the MD-based approach, trace the shape of the experimental curves, reproducing the pH jump, while those calculated with the EDMC-based approach and the titration curve in water calculated using the MD-based approach have smooth shapes characteristic of the titration of weak multifunctional acids with small differences between the dissociation constants. Nevertheless, quantitative agreement between theoretically predicted and experimental titration curves is not achieved in all three solvents even with the MD-based approach, which is manifested by a smaller pH range of the calculated titration curves with respect to the experimental curves. The poorer agreement obtained for water than for the nonaqueous solvents suggests a significant role of specific solvation in water, which cannot be accounted for by the mean-field solvation models.

Algorithms↗

PubMed2006

Polyproline II conformation is one of many local conformational states and is not an overall conformation of unfolded peptides and proteins.

The alanine-based peptide Ac-XX(A)7OO-NH2, referred to as XAO (where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively), has recently been proposed to possess a well defined polyproline II (P(II)) conformation at low temperatures. Based on the results of extensive NMR and CD investigations combined with theoretical calculations, reported here, we present evidence that, on the contrary, this peptide does not have any significant amount of organized P(II) structure but exists in an ensemble of conformations with a distorted bend in the N- and C-terminal regions. The conformational ensemble was obtained by molecular dynamics/simulated annealing calculations using the amber suite of programs with time-averaged distance and dihedral-angle restraints obtained from rotating-frame nuclear Overhauser effect (ROE) volumes and vicinal coupling constants 3J(HN Eta alpha), respectively. The computed ensemble-averaged radius of gyration Rg (7.4 +/- 1.0) A is in excellent agreement with that measured by small-angle x-ray scattering (SAXS) whereas, if the XAO peptide were in the P(II) conformation, Rg would be 11.6 A. Depending on the pH, peptide concentration, and temperature, the CD spectra of XAO do or do not possess the maximum with positive ellipticity in the 217-nm region, which is characteristic of the P(II) structure, reflecting a shifting conformational equilibrium rather than an all-or-none transition. The "P(II) conformation" should, therefore, be considered as one of the accessible conformational states of individual amino acid residues in peptides and proteins rather than as a structure of most of the chain in the early stage of folding.

Alanine↗

PubMed2006

Molecular dynamics study of amyloid formation of two Abl-SH3 domain peptides.

Molecular dynamics (MD) simulations were carried out for two-strand and ten-strand beta-sheets constructed from two peptides corresponding to the diverging turn of two homologous Abl-SH3 domains, DLSFMKGE (MK; from Drosophila) and DLSFKKGE (KK; from man), in explicit water at the temperatures of 30, 170/190 and 300 K. It was found that the 2 x MK beta-sheet is more stable than the 2 x KK beta-sheet, and that the 10 x MK beta-sheet is more stable than the 10 x KK beta-sheet; this suggests that the MK systems are fibril-creating and the KK systems are not. These results might explain why most SH3 domains possess two conserved basic residues at the diverging turn, which may act as gatekeepers in order to avoid aggregation.

Amino Acid Sequence↗

PubMed2005

Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains.

Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.

Computer Simulation↗

PubMed2005

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems.

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.

Algorithms↗

PubMed2005

Molecular dynamics with the united-residue model of polypeptide chains. I. Lagrange equations of motion and tests of numerical stability in the microcanonical mode.

The Lagrange formalism was implemented to derive the equations of motion for the physics-based united-residue (UNRES) force field developed in our laboratory. The C(alpha)...C(alpha) and C(alpha)...SC (SC denoting a side-chain center) virtual-bond vectors were chosen as variables. The velocity Verlet algorithm was adopted to integrate the equations of motion. Tests on the unblocked Ala(10) polypeptide showed that the algorithm is stable in short periods of time up to the time step of 1.467 fs; however, even with the shorter time step of 0.489 fs, some drift of the total energy occurs because of momentary jumps of the acceleration. These jumps are caused by numerical instability of the forces arising from the U(rot) component of UNRES that describes the energetics of side-chain-rotameric states. Test runs on the Gly(10) sequence (in which U(rot) is not present) and on the Ala(10) sequence with U(rot) replaced by a simple numerically stable harmonic potential confirmed this observation; oscillations of the total energy were observed only up to the time step of 7.335 fs, and some drift in the total energy or instability of the trajectories started to appear in long-time (2 ns and longer) trajectories only for the time step of 9.78 fs. These results demonstrate that the present U(rot) components (which are statistical potentials derived from the Protein Data Bank) must be replaced with more numerically stable functions; this work is under way in our laboratory. For the purpose of our present work, a nonsymplectic variable-time-step algorithm was introduced to reduce the energy drift for regular polypeptide sequences. The algorithm scales down the time step at a given point of a trajectory if the maximum change of acceleration exceeds a selected cutoff value. With this algorithm, the total energy is reasonably conserved up to a time step of 2.445 fs, as tested on the unblocked Ala(10) polypeptide. We also tried a symplectic multiple-time-step reversible RESPA algorithm and achieved satisfactory energy conservation for time steps up to 7.335 fs. However, at present, it appears that the reversible RESPA algorithm is several times more expensive than the variable-time-step algorithm because of the necessity to perform additional matrix multiplications. We also observed that, because Ala(10) folds and unfolds within picoseconds in the microcanonical mode, this suggests that the effective (event-based) time unit in UNRES dynamics is much larger than that of all-atom dynamics because of averaging over the fast-moving degrees of freedom in deriving the UNRES potential.

Alanine↗

PubMed2005

Molecular origin of anticooperativity in hydrophobic association.

The structuring of water molecules in the vicinity of nonpolar solutes is responsible for hydrophobic hydration and association thermodynamics in aqueous solutions. Here, we studied the potential of mean force (PMF) for the formation of a dimer and trimers of methane molecules in three specific configurations in explicit water to explain multibody effects in hydrophobic association on a molecular level. We analyzed the packing and orientation of water molecules in the vicinity of the solute to explain the effect of ordering of the water around nonpolar solutes on many-body interactions. Consistent with previous theoretical studies, we observed cooperativity, manifested as a reduction of the height of the desolvation barrier for the trimer in an isosceles triangle geometry, but for linear trimers, we observed only anticooperativity. A simple mechanistic picture of hydrophobic association is drawn. The free energy of hydrophobic association depends primarily on the difference in the number of water molecules in the first solvation shell of a cluster and that in the monomers of a cluster; this can be approximated by the molecular surface area. However, there are unfavorable electrostatic interactions between the water molecules from different parts of the solvation shell of a trimer because of their increased orientation induced by the nonpolar solute. These electrostatic interactions make an anticooperative contribution to the PMF, which is clearly manifested for the linear trimer where the multibody contribution due to changes in the molecular surface area is equal to zero. The information theory model of hydrophobic interactions of Hummer et al. also explains the anticooperativity of hydrophobic association of the linear trimers; however, it predicts anticooperativity with a qualitatively identical distance dependence for nonlinear trimers, which disagrees with the results of simulations.

Hydrophobic and Hydrophilic Interactions↗

PubMed2005

Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains.

We report the application of Langevin dynamics to the physics-based united-residue (UNRES) force field developed in our laboratory. Ten trajectories were run on seven proteins [PDB ID codes 1BDD (alpha; 46 residues), 1GAB (alpha; 47 residues), 1LQ7 (alpha; 67 residues), 1CLB (alpha; 75 residues), 1E0L (beta; 28 residues), and 1E0G (alpha+beta; 48 residues), and 1IGD (alpha+beta; 61 residues)] with the UNRES force field parameterized by using our recently developed method for obtaining a hierarchical structure of the energy landscape. All alpha-helical proteins and 1E0G folded to the native-like structures, whereas 1IGD and 1E0L yielded mostly nonnative alpha-helical folds although the native-like structures are lowest in energy for these two proteins, which can be attributed to neglecting the entropy factor in the current parameterization of UNRES. Average folding times for successful folding simulations were of the order of nanoseconds, whereas even the ultrafast-folding proteins fold only in microseconds, which implies that the UNRES time scale is approximately three orders of magnitude larger than the experimental time scale because the fast motions of the secondary degrees of freedom are averaged out. Folding with Langevin dynamics required 2-10 h of CPU time on average with a single AMD Athlon MP 2800+ processor depending on the size of the protein. With the advantage of parallel processing, this process leads to the possibility to explore thousands of folding pathways and to predict not only the native structure but also the folding scenario of a protein together with its quantitative kinetic and thermodynamic characteristics.

Biophysical Phenomena↗

PubMed2005

Interplay of charge distribution and conformation in peptides: comparison of theory and experiment.

We assessed the correlation between charge distribution and conformation of flexible peptides by comparing the theoretically calculated potentiometric-titration curves of two model peptides, Ac-Lys5-NHMe (a model of poly-L-lysine) and Ac-Lys-Ala11-Lys-Gly2-Tyr-NH2 (P1) in water and methanol, with the experimental curves. The calculation procedure consisted of three steps: (i) global conformational search of the peptide under study using the electrostatically driven Monte Carlo (EDMC) method with the empirical conformational energy program for peptides (ECEPP)/3 force field plus the surface-hydration (SRFOPT) or the generalized Born surface area (GBSA) solvation model as well as a molecular dynamics method with the assisted model building and energy refinement (AMBER)99/GBSA force field; (ii) reevaluation of the energy in the pH range considered by using the modified Poisson-Boltzmann approach and taking into account all possible protonation microstates of each conformation, and (iii) calculation of the average degree of protonation of the peptide at a given pH value by Boltzmann averaging over conformations. For Ac-Lys5-NHMe, the computed titration curve agrees qualitatively with the experimental curve of poly-L-lysine in 95% methanol. The experimental titration curves of peptide P1 in water and methanol indicate a remarkable downshift of the first pK(a) value compared to the values for reference compounds (n-butylamine and phenol, respectively), suggesting the presence of a hydrogen bond between the tyrosine hydroxyl oxygen and the H(epsilon) proton of a protonated lysine side chain. The theoretical titration curves agree well with the experimental curves, if conformations with such hydrogen bonds constitute a significant part of the ensemble; otherwise, the theory predicts too small a downward pH shift.

Electrochemistry↗

PubMed2005

Theoretical calculations of homoconjugation equilibrium constants in systems modeling acid-base interactions in side chains of biomolecules using the potential of mean force.

The potentials of mean force (PMFs) were determined for systems forming cationic and anionic homocomplexes composed of acetic acid, phenol, isopropylamine, n-butylamine, imidazole, and 4(5)-methylimidazole, and their conjugated bases or acids, respectively, in three solvents with different polarity and hydrogen-bonding propensity: acetonitrile (AN), dimethyl sulfoxide (DMSO), and water (H(2)O). For each pair and each solvent a series of umbrella-sampling molecular dynamics simulations with the AMBER force field, explicit solvent, and counterions added to maintain a zero net charge of a system were carried out and the PMF was calculated by using the Weighted Histogram Analysis Method (WHAM). Subsequently, homoconjugation-equilibrium constants were calculated by numerical integration of the respective PMF profiles. In all cases but imidazole stable homocomplexes were found to form in solution, which was manifested as the presence of contact minima corresponding to hydrogen-bonded species in the PMF curves. The calculated homoconjugation constants were found to be greater for complexes with the OHO bridge (acetic acid and phenol) than with the NHN bridge and they were found to decrease with increasing polarity and hydrogen-bonding propensity of the solvent (i.e., in the series AN > DMSO > H(2)O), both facts being in agreement with the available experimental data. It was also found that interactions with counterions are manifested as the broadening of the contact minimum or appearance of additional minima in the PMF profiles of the acetic acid-acetate, phenol/phenolate system in acetonitrile, and the 4(5)-methylimidazole/4(5)-methylimidzole cation conjugated base system in dimethyl sulfoxide.

Acid-Base Equilibrium↗

PubMed2004

Towards gelsolin amyloid formation.

Amyloid diseases result from protein misfolding and aggregation into fibrils. Some features of gelsolin amyloidogenic fragments comprised of residues 173-243 (G173-243) and residues 173-202 (G173-202) were investigated by the method of molecular dynamics (MD). The alpha-helical structure of G173-243 present in the whole protein unwinds during the course of MD simulation of the fragment G173-243, suggesting that the G173-243 structure is not stable and could unfold before becoming involved in gelsolin amyloid fibril formation. Twelve fragments of G173-202 were used to build a possible beta-fibril. During the course of the simulation, G173-202 fragments formed hydrogen bonds and tended to turn by an angle of 10 degrees -20 degrees towards each other.

Amyloid↗

PubMed2004

Prediction of the structures of proteins with the UNRES force field, including dynamic formation and breaking of disulfide bonds.

The presence of disulfide bonds is essential for maintaining the structure and function of many proteins. The disulfide bonds are usually formed dynamically during folding. This process is not accounted for in present algorithms for protein-structure prediction, which either deduce the possible positions of disulfide bonds only after the structure is formed or assume fixed disulfide bonds during the course of simulated folding. In this work, the conformational space annealing (CSA) method and the UNRES united-residue force field were extended to treat dynamic formation of disulfide bonds. A harmonic potential is imposed on the distance between disulfide-bonded cysteine side-chain centroids to describe the energetics of bond distortion and an energy gain of 5.5 kcal/mol is added for disulfide-bond formation. Formation, breaking and rearrangement of disulfide bonds are included in the CSA search by introducing appropriate operations; the search can also be carried out with a fixed disulfide-bond arrangement. The algorithm was applied to four proteins: 1EI0 (alpha), 1NKL (alpha), 1L1I (beta-helix) and 1ED0 (alpha + beta). For 1EI0, a low-energy structure with correct fold was obtained both in the runs without and with disulfide bonds; however, it was obtained as the lowest in energy only with the native disulfide-bond arrangement. For the other proteins studied, structures with the correct fold were obtained as the lowest (1NKL and 1L1I) or low-energy structures (1ED0) only in runs with disulfide bonds, although the final disulfide-bond arrangement was non-native. The results demonstrate that, by including the possibility of formation of disulfide bonds, the predictive power of the UNRES force field is enhanced, even though the disulfide-bond potential introduced here rarely produces disulfide bonds in native positions. To the best of our knowledge, this is the first algorithm for energy-based prediction of the structure of disulfide-bonded proteins without any assumption as to the positions of native disulfides or human intervention. Directions for improving the potentials and the search method are suggested.

Algorithms↗

PubMed2004

A united residue force-field for calcium-protein interactions.

United-residue potentials are derived for interactions of the calcium cation with polypeptide chains in energy-based prediction of protein structure with a united-residue (UNRES) force-field. Specific potentials were derived for the interaction of the calcium cation with the Asp, Glu, Asn, and Gln side chains and the peptide group. The analytical expressions for the interaction energies for each of these amino acids were obtained by averaging the electrostatic interaction energy, expressed by a multipole series over the dihedral angles not considered in the united-residue model, that is, the side-chain dihedral angles chi and the dihedral angles lambda for the rotation of peptide groups about the C(alpha)...C(alpha) virtual-bond axes. For the side-chains that do not interact favorably with calcium, simple excluded-volume potentials were introduced. The parameters of the potentials were obtained from ab initio quantum mechanical calculations of model systems at the Restricted Hartree-Fock (RHF) level with the 6-31G(d,p) basis set. The energy surfaces of pairs consisting of Ca(2+)-acetate, Ca(2+)-propionate, Ca(2+)-acetamide, Ca(2+)-propionamide, and Ca(2+)-N-methylacetamide systems (modeling the Ca(2+)-Asp(-), Ca(2+)-Glu(-), Ca(2+)-Asn, Ca(2+)-Gln, and Ca(2+)-peptide group interactions) at different distances and orientations were calculated. For each pair, the restricted free energy (RFE) surfaces were calculated by numerical integration over the degrees of freedom lost when switching from the all-atom model to the united-residue model. Finally, the analytical expressions for each pair were fitted to the RFE surfaces. This force-field was able to distinguish the EF-hand motif from all potential binding sites in the crystal structures of bovine alpha-lactalbumin, whiting parvalbumin, calbindin D9K, and apo-calbindin D9K.

Animals↗

PubMed2004

Use of NMR and fluorescence spectroscopy as well as theoretical conformational analysis in conformation-activity studies of cyclic enkephalin analogues.

In this review the conformational studies of natural enkephalins (H-Tyr-Gly-Gly-Phe-Met-OH; the [Met(5)]enkephalin and H-Tyr-Gly-Gly-Phe-Leu-OH; the [Leu(5)]enkephalin), their acyclic and cyclic analogues, including those carried out in our laboratory, performed by experimental and theoretical methods and their combination, are described. Emphasis is given on the role of conformational constraints introduced by cyclization on activity at the micro and delta opioid receptors. Comparison of the conformations of cyclic enkephalin analogues with high delta-receptor activity with those of potent rigid non-peptide delta-receptor agonists indicates that the proximity of the aromatic side chains in positions 1 and 4 as well as the N-terminal amino group is desirable for the activity at the delta opioid receptors; early conformational studies also suggested that spatial separation of the aromatic side chains and rigidity of the cyclic backbone is desirable for micro-receptor activity. The results of our recent conformational studies performed with the use of fluorescence and NMR spectroscopy as well as theoretical calculations indicate, however, that these structural features are not necessary for activity at the micro opioid receptors. Methods applied to the determination of the conformation of flexible peptides, such as Nuclear Magnetic Resonance (NMR), fluorescence spectroscopy, and theoretical conformational analysis are also discussed briefly.

Enkephalins↗