Predicting peptide structures using NMR data and deterministic global optimization

Abstract

The ability to analyze large molecular structures by NMR techniques requires efficient methods for structure calculation. Currently, there are several widely available methods for tackling these problems, which, in general, rely on the optimization of penalty-type target functions to satisfy the conformational restraints. Typically, these methods combine simulated annealing protocols with molecular dynamics and local minimization, either in distance or torsional angle space. In this work, both a novel formulation and algorithmic procedure for the solution of the NMR structure prediction problem is outlined. First, the unconstrained, penalty-type structure prediction problem is reformulated using nonlinear constraints, which can be individually enumerated for all, or subsets, of the distance restraints. In this way, the violation can be controlled as a constraint, in contrast to the usual penalty-type restraints. In addition, the customary simplified objective function is replaced by a full atom force field in the torsional angle space. This guarantees a better description of atomic interactions, which dictate the native structure of the molecule along with the distance restraints. The second novel portion of this work involves the solution method. Rather than pursue the typical simulated annealing procedure, this work relies on a deterministic method, which theoretically guarantees that the global solution can be located. This branch and bound technique, based on the ␣BB algorithm, has already been successfully applied to the identification of global minimum energy structures of peptides modeled by full atom force

Improvement of the anti-C3 activity of compstatin using rational and combinatorial approaches

“…This algorithm selects and ranks several potential sequences compatible with a structural template that provides (but is not limited to) the Cα-Cα inter-atomic backbone distances. (ii) The foundation of the second step is a global optimization algorithm based on the use of a full-atom force field [17][18][19]. This algorithm calculates ensemble probabilities for the selected sequences applied on flexible structural templates [15].…”

“…The flexibility of compstatin in solution was shown by analysis of NMR parameters such as spin-spin coupling constants, chemical shifts, the temperature dependence of chemical shifts and NOEs [2]. The structure of a major conformer of compstatin was determined using NMR data and computational modelling [2,19].…”

“…MD simulations of the entire NMR ensemble of 21 structures, the average minimized structure and the global optimization structure [2,19] have revealed the presence of five families of inter-converting conformers at 1 ns simulation time [23]. The major population of these conformers was a coil conformation with a Type I β-turn, which had a probability of 44% [23].…”

Rigid versus unique determination of protein structures with geometric buildup

“…The determination of rigid or unique protein structures with a given set of interatomic or inter-residual distances has potential applications in NMR protein modeling [19][20][21] or modeling with residue contact distances [22,23]. However, in these applications, the distances can only be estimated within certain ranges, while the algorithms we have described apply only to exact distances.…”

Novel formulations for the sequence selection problem in de novo protein design with flexible templates

“…The probability for a sequence to fold into the template would be given by the Boltzmann-type distribution for those low energy conformers from the free folding calculation that fell into the overlap between the template-constrained conformers and the free folding conformers on an energy-versus-rmsd plot. Structure prediction was done with the aid of the αBB deterministic global optimization solver [26][27][28][29][30][31][32] with an objective function of a full-atomistic force field over the set of independent dihedral angles which can be used to describe any possible configuration of the system.…”