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

ABSTRACT: 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.

SUBMITTER: Khalili M

PROVIDER: S-EPMC2286548 | biostudies-literature | 2004 Oct

REPOSITORIES: biostudies-literature

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

Khalili Mey M Saunders Jeffrey A JA Liwo Adam A Ołdziej Stanislaw S Scheraga Harold A HA

Protein science : a publication of the Protein Society 20041001 10

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 ...[more]

PMID: 15388862

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Project description:The growth mechanism of β-amyloid (Aβ) peptide fibrils was studied by a physics-based coarse-grained united-residue model and molecular dynamics (MD) simulations. To identify the mechanism of monomer addition to an Aβ(1-40) fibril, we placed an unstructured monomer at a distance of 20 Å from a fibril template and allowed it to interact freely with the latter. The monomer was not biased towards fibril conformation by either the force field or the MD algorithm. With the use of a coarse-grained model with replica-exchange molecular dynamics, a longer timescale was accessible, making it possible to observe how the monomers probe different binding modes during their search for the fibril conformation. Although different assembly pathways were seen, they all follow a dock-lock mechanism with two distinct locking stages, consistent with experimental data on fibril elongation. Whereas these experiments have not been able to characterize the conformations populating the different stages, we have been able to describe these different stages explicitly by following free monomers as they dock onto a fibril template and to adopt the fibril conformation (i.e., we describe fibril elongation step by step at the molecular level). During the first stage of the assembly ("docking"), the monomer tries different conformations. After docking, the monomer is locked into the fibril through two different locking stages. In the first stage, the monomer forms hydrogen bonds with the fibril template along one of the strands in a two-stranded β-hairpin; in the second stage, hydrogen bonds are formed along the second strand, locking the monomer into the fibril structure. The data reveal a free-energy barrier separating the two locking stages. The importance of hydrophobic interactions and hydrogen bonds in the stability of the Aβ fibril structure was examined by carrying out additional canonical MD simulations of oligomers with different numbers of chains (4-16 chains), with the fibril structure as the initial conformation. The data confirm that the structures are stabilized largely by hydrophobic interactions and show that intermolecular hydrogen bonds are highly stable and contribute to the stability of the oligomers as well.

Project description:The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring ?-carbon atoms (C?s), which serve only as geometrical points, and a united side chain (SC) attached to the respective C?. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: C?···C?···C?···SC (?(1)), SC···C?···C?···C? (?(2)), and SC···C?···C?···SC (?(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles ?(1) and ?(2) for rotation about the C?···C? virtual-bond angles and over the side-chain angles ?. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

Project description:Continuing our effort to introduce d-amino-acid residues in the united residue (UNRES) force field developed in our laboratory, in this work the Cα ··· Cα ··· Cα backbone-virtual-bond-valence-angle (θ) potentials for systems containing d-amino-acid residues have been developed. The potentials were determined by integrating the combined energy surfaces of all possible triplets of terminally blocked glycine, alanine, and proline obtained with ab initio molecular quantum mechanics at the MP2/6-31G(d,p) level to calculate the corresponding potentials of mean force (PMFs). Subsequently, analytical expressions were fitted to the PMFs to give the virtual-bond-valence potentials to be used in UNRES. Alanine represented all types of amino-acid residues except glycine and proline. The blocking groups were either the N-acetyl and N',N'-dimethyl or N-acetyl and pyrrolidyl group, depending on whether the residue next in sequence was an alanine-type or a proline residue. A total of 126 potentials (63 symmetry-unrelated potentials for each set of terminally blocking groups) were determined. Together with the torsional, double-torsional, and side-chain-rotamer potentials for polypeptide chains containing d-amino-acid residues determined in our earlier work (Sieradzan et al. J. Chem. Theory Comput., 2012, 8, 4746), the new virtual-bond-angle (θ) potentials now constitute the complete set of physics-based potentials with which to run coarse-grained simulations of systems containing d-amino-acid residues. The ability of the extended UNRES force field to reproduce thermodynamics of polypeptide systems with d-amino-acid residues was tested by comparing the experimentally measured and the calculated free energies of helix formation of model KLALKLALxxLKLALKLA peptides, where x denotes any d- or l- amino-acid residue. The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation. To test the ability of UNRES with the new potentials to reproduce the structures of polypeptides with d-amino-acid residues, an ab initio replica-exchange folding simulation of thurincin H from Bacillus thuringiensis, which has d-amino-acid residues in the sequence, was carried out. UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

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

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

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