Andrea Amadei

On the convergence of the conformational coordinates basis set obtained by the essential dynamics analysis of proteins' molecular dynamics simulations

In this article we present a quantitative evaluation of the convergence of the conformational coordinates of proteins, obtained by the Essential Dynamics method. Using a detailed analysis of long molecular dynamics trajectories in combination with a statistical assessment of the significance of the measured convergence, we obtained that simulations of a few hundreds of picoseconds are in general sufficient to provide a stable and statistically reliable definition of the essential and near constraints subspaces, at least within the nanoseconds time range. Proteins 1999;36:419–424.

Molecular dynamics simulations with constrained roto-translational motions: Theoretical basis and statistical mechanical consistency

From a specific definition of the roto-translational (external) and intramolecular (internal) coordinates, a constrained dynamics algorithm is derived for removing the roto-translational motions during molecular dynamics simulations, within the leap-frog integration scheme. In the paper the theoretical basis of this new method and its statistical mechanical consistency are reported, together with two applications.

The consistency of large concerted motions in proteins in molecular dynamics simulations

A detailed investigation is presented into the effect of limited sampling time and small changes in the force field on molecular dynamics simulations of a protein. Thirteen independent simulations of the B1 IgG-binding domain of streptococcal protein G were performed, with small changes in the simulation parameters in each simulation. Parameters studied included temperature, bond constraints, cut-off radius for electrostatic interactions, and initial placement of hydrogen atoms. The essential dynamics technique was used to reveal dynamic differences between the simulations. Similar essential dynamics properties were found for all simulations, indicating that the large concerted motions found in the simulations are not particularly sensitive to small changes in the force field. A thorough investigation into the stability of the essential dynamics properties as derived from a molecular dynamics simulation of a few hundred picoseconds is provided. Although the definition of the essential modes of motion has not fully converged in these short simulations, the subspace in which these modes are confined is found to be reproducible.

A first-principles method to model perturbed electronic wavefunctions : the effect of an external homogeneous electric field

In this Letter, we show that with the use of matrix notation to express the time-independent Schroedinger equation, it is possible to model perturbed electronic wavefunctions. Such a method makes use of first principles of the quantum mechanical theory and hence is rigorous within the only approximation due to the truncation of the perturbed Hamiltonian matrix used. Results show that for three different molecules in vacuo under an electric field, the proposed method provides reliable perturbed electronic wavefunctions at a low computational costs.

Dehydration-driven solvent exposure of hydrophobic surfaces as a driving force in peptide folding

Recent work has shown that the nature of hydration of pure hydrophobic surfaces changes with the length scale considered: water hydrogen-bonding networks adapt to small exposed hydrophobic species, hydrating or “wetting” them at relatively high densities, whereas larger hydrophobic areas are “dewetted” [Chandler D (2005), Nature 29:640–647]. Here we determine whether this effect is also present in peptides by examining the folding of a β-hairpin (the 14-residue amyloidogenic prion protein H1 peptide), using microsecond time-scale molecular dynamics simulations. Two simulation models are compared, one explicitly including the water molecules, which may thus adapt locally to peptide configurations, and the other using a popular continuum approximation, the generalized Born/surface area implicit solvent model. The results obtained show that, in explicit solvent, peptide conformers with high solvent-accessible hydrophobic surface area indeed also have low hydration density around hydrophobic residues, whereas a concomitant higher hydration density around hydrophilic residues is observed. This dewetting effect stabilizes the fully folded β-hairpin state found experimentally. In contrast, the implicit solvent model destabilizes the fully folded hairpin, tending to cluster hydrophobic residues regardless of the size of the exposed hydrophobic surface. Furthermore, the rate of the conformational transitions in the implicit solvent simulation is almost doubled with respect to that of the explicit solvent. The results suggest that dehydration-driven solvent exposure of hydrophobic surfaces may be a significant factor determining peptide conformational equilibria.

Towards an exhaustive sampling of the configurational spaces of the two forms of the peptide hormone guanylin

The recently introduced Essential Dynamics sampling method is extended such that an exhaustive sampling of the available (backbone) configurational space can be achieved. From an initial Molecular Dynamics simulation an approximated definition of the essential subspace is obtained. This subspace is used to direct subsequent simulations by means of constraint forces. The method is applied to the peptide hormone guanylin, solvated in water, of which the structure was determined recently. The peptide exists in two forms and for both forms, an extensive sampling was produced. The sampling algorithm fills the available space (of the essential coordinates used in the procedure) at a rate that is approximately six to seven times larger than that for traditional Molecular Dynamics. The procedure does not cause any significant perturbation, which is indicated by the fact that free Molecular Dynamics simulations started at several places in the space defined by the Essential Dynamics sample that complete space. Moreover, analyses of the average free Molecular Dynamics step have shown that nowhere except close to the edge of the available space, there are regions where the system shows a drift in a particular direction. This result also shows that in principle, the essential subspace is a constant free energy surface, with well-defined and steep borders, in which the system moves diffusively. In addition, a comparison between two independent essential dynamics sampling runs, of one form of the peptide, shows that the obtained essential subspaces are virtually identical.

A kinetic model for the internal motions of proteins: Diffusion between multiple harmonic wells

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics.

Molecular dynamics simulation of the aggregation of the core-recognition motif of the islet amyloid polypeptide in explicit water

The formation of amyloid fibrils is associated with major human diseases. Nevertheless, the molecular mechanism that directs the nucleation of these fibrils is not fully understood. Here, we used molecular dynamics simulations to study the initial self‐assembly stages of the NH2‐NFGAIL‐COOH peptide, the core‐recognition motif of the type II diabetes associated islet amyloid polypeptide. The simulations were performed using multiple replicas of the monomers in explicit water, in a confined box starting from a random distribution of the peptides at T = 300 K and T = 340 K. At both temperatures the formation of unique clusters was observed after a few nanoseconds. Structural analysis of the clusters clearly suggested the formation of “flat” ellipsoid‐shaped clusters through a preferred locally parallel alignment of the peptides. The unique assembly is facilitated by a preference for an extended conformation of the peptides and by intermolecular aromatic interactions. Taken together, our results may provide a description of the molecular recognition determinants involved in fibril formation, in terms of the atomic detailed structure of nascent aggregates. These observations may yield information on new ways to control this process for either materials development or drug design. Proteins 2005.

Theoretical characterization of electronic states in interacting chemical systems

In this article we characterize, by means of the perturbed matrix method, the response of the electronic states of a chemical system to the perturbing environment. In the theory section we describe in detail the basic derivations and implications of the method, extending its theoretical framework to treat possible excitonic effects, and we show how to characterize the perturbed electronic states. Finally, by using a set of chemical systems interacting with complex atomic-molecular environments, we describe the nature and general features of the electronic state mixing and transitions as caused by atomic and molecular interactions.

Molecular Dynamics Simulation of Protein Folding by Essential Dynamics Sampling: Folding Landscape of Horse Heart Cytochrome c

A new method for simulating the folding process of a protein is reported. The method is based on the essential dynamics sampling technique. In essential dynamics sampling, a usual molecular dynamics simulation is performed, but only those steps, not increasing the distance from a target structure, are accepted. The distance is calculated in a configurational subspace defined by a set of generalized coordinates obtained by an essential dynamics analysis of an equilibrated trajectory. The method was applied to the folding process of horse heart cytochrome c, a protein with approximately 3000 degrees of freedom. Starting from structures, with a root-mean-square deviation of approximately 20 A from the crystal structure, the correct folding was obtained, by utilizing only 106 generalized degrees of freedom, chosen among those accounting for the backbone carbon atoms motions, hence not containing any information on the side chains. The folding pathways found are in agreement with experimental data on the same molecule.