Theoretical study of the NLO responses of some natural and unnatural amino acids used as probe molecules.

The first hyperpolarizabilities ß of the natural aromatic amino acids tryptophan and tyrosine have been investigated using several methods and basis sets. Some of the theoretical results obtained were compared to the only experimental hyper-Rayleigh scattering data available. The sensitivity of tryptophan to its local environment was analyzed by constructing two-dimensional potential energy plots around the dipeptide tryptophan-lysine. Static hyperpolarizabilities ß(0) of the found minima were calculated by a second-order Møller-Plesset (MP2) method in combination with the 6-31+G(d) basis set. Moreover, the efficiency of tryptophan and those of a series of unnatural amino acids as endogenous probe molecules were tested by calculating the nonlinear responses of some peptides. Impressive results were obtained for the amino acid ALADAN, which shows significantly improved nonlinear performance compared to other amino acids with weak nonlinear responses.

Sampling small-scale and large-scale conformational changes in proteins and molecular complexes.

Sampling of small-scale and large-scale motions is important in various computational tasks, such as protein-protein docking and ligand binding. Here, we report further development and applications of the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method generates conformational moves of any complexity and size by identifying and crossing well-defined saddle points connecting energy minima. Simulations on two all-atom proteins and three protein complexes containing between 70 and 300 amino acids indicate that ARTIST opens the door to the full treatment of all degrees of freedom in dense systems such as protein-protein complexes.

ARTIST: an activated method in internal coordinate space for sampling protein energy landscapes.

We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computer-aided drug design to supramolecular assembly.

Navigation and analysis of the energy landscape of small proteins using the activation-relaxation technique.

The resolution of the protein folding problem has been tied to the development of a detailed understanding of the configurational energy or of the free energy landscape associated with these molecules. Using the activation-relaxation technique and a simplified energy model, we present here a detailed analysis of the energy landscape of 16-residue peptide that folds into a beta-hairpin. Our results support the concept of an energy landscape with an effective topology consistent with a scale-free network.

Helix H1 of the prion protein is rather stable against environmental perturbations: molecular dynamics of mutation and deletion variants of PrP(90-231).

We need to understand the underlying factors that promote or reverse the amyloid-type structure of the prion protein (PrP). In an earlier study, we showed that mutations within the first beta strand can extend the short beta sheet in the normal protein into a larger sheet at neutral pH. To determine the impact of the point mutation P102L and the deletion of either the first or the second beta strand on PrP, we performed further long molecular explicit water dynamics simulations. The trajectories show that all mutations do not exert a uniform effect on the dynamics of the N-terminal tail. The results of the deletion of the two beta strands confirm the idea that partially unfolded conformations are involved in the structural transition. In the deletion variants, the alpha helices H2 and H3 are disordered, while helix H1 is either fully stable or partially disordered. This finding, consistent with recent spectroscopic analyses on peptides spanning helix H1 and flanking sequences, demonstrates that unfolding of the full domain containing helix H1 is not an early step in PrP interconversion. This result also raises questions regarding a current view of PrP(Sc) structure that transforms helix H1 into a beta sheet conformation.

Computer simulations aimed at structure prediction of supersecondary motifs in proteins.

It is well established that protein structures are more conserved than protein sequences. One-third of all known protein structures can be classified into ten protein folds, which themselves are composed mainly of alpha-helical hairpin, beta hairpin, and betaalphabeta supersecondary structural elements. In this study, we explore the ability of a recent Monte Carlo-based procedure to generate the 3D structures of eight polypeptides that correspond to units of supersecondary structure and three-stranded antiparallel beta sheet. Starting from extended or misfolded compact conformations, all Monte Carlo simulations show significant success in predicting the native topology using a simplified chain representation and an energy model optimized on other structures. Preliminary results on model peptides from nucleotide binding proteins suggest that this simple protein folding model can help clarify the relation between sequence and topology.

Evidence that the 127-164 region of prion proteins has two equi-energetic conformations with beta or alpha features.

Prion proteins cause neurodegenerative illnesses in humans and animals. The diseases are associated with a topological change from a predominantly alpha (PrP(C)) to beta-sheet (PrP(Sc)) structure. Many studies have focused on the minimum sequence requirements and key events for developing or transmitting disease. Here, we report on the application of molecular modeling studies to predict the lowest-energy conformations for five fragments in solution at pH 7. We show that PrP(143-158) adopts a helix, the model PrP(106-126), PrP(142-167), and PrP(143-178) peptides have a clear preference for a variety of beta-sheet structures, whereas PrP(127-164) has two iso-energetic conformations with all beta or alphabeta native-like structures. Such a finding for PrP(127-164), which explains a large body of experimental data, including the location of all mutations causing prion diseases, may have important implications for triggering or propagating the topological change.

Sampling activated mechanisms in proteins with the activation-relaxation technique.

The activated dynamics of proteins occur on time scales of milliseconds and longer. Standard all-atom molecular dynamics simulations are limited to much shorter times, of the order of tens of nanoseconds. Therefore, many activated mechanisms that are crucial for long-time dynamics will not be observed in such molecular dynamics simulation; different methods are required. Here, we describe in detail the activation-relaxation technique (ART) that generates directly activated mechanisms. The method is defined in the configurational energy landscape and defines moves in a two step fashion: (a) a configuration is first brought from a local minimum to a nearby first-order saddle point (the activation); and (b) the configuration is relaxed to a new metastable state (the relaxation). The method has already been applied to a wide range of problems in condensed matter, including metallic glasses, amorphous semiconductors and silica glass. We review the algorithm in detail, discuss some previously published results and present simulations of activated mechanisms for a two-helix bundle protein using an all-atom energy function.

Generating ensemble averages for small proteins from extended conformations by Monte Carlo simulations.

Since it is not feasible to determine the structure of every protein by experiment, algorithms delivering the folded conformation of a protein solely from its amino acid sequence are desirable. Here the diffusion-process controlled-Monte Carlo approach has been applied to generating ensemble averages for three small proteins with 31, 36, and 46 residues. Starting from extended conformations and using an energy model that was developed on other protein models, the simulations find nativelike structures deviating by 3 A rms from the experimental structures for the main chain atoms. The balance between long-range and short-range interactions is discussed briefly in the context of stability and folding.

The loop opening/closing motion of the enzyme triosephosphate isomerase.

To explore the origin of the large-scale motion of triosephosphate isomerase's flexible loop (residues 166 to 176) at the active site, several simulation protocols are employed both for the free enzyme in vacuo and for the free enzyme with some solvent modeling: high-temperature Langevin dynamics simulations, sampling by a "dynamics driver" approach, and potential-energy surface calculations. Our focus is on obtaining the energy barrier to the enzyme's motion and establishing the nature of the loop movement. Previous calculations did not determine this energy barrier and the effect of solvent on the barrier. High-temperature molecular dynamics simulations and crystallographic studies have suggested a rigid-body motion with two hinges located at both ends of the loop; Brownian dynamics simulations at room temperature pointed to a very flexible behavior. The present simulations and analyses reveal that although solute/solvent hydrogen bonds play a crucial role in lowering the energy along the pathway, there still remains a high activation barrier. This finding clearly indicates that, if the loop opens and closes in the absence of a substrate at standard conditions (e.g., room temperature, appropriate concentration of isomerase), the time scale for transition is not in the nanosecond but rather the microsecond range. Our results also indicate that in the context of spontaneous opening in the free enzyme, the motion is of rigid-body type and that the specific interaction between residues Ala176 and Tyr208 plays a crucial role in the loop opening/closing mechanism.

Long timestep dynamics of peptides by the dynamics driver approach.

Previous experience with the Langevin/implicit-Euler scheme for dynamics ("LI") on model systems (butane, water) has shown that LI is numerically stable for timesteps in the 5-20 fs range but quenches high-frequency modes. To explore applications to polypeptides, we apply LI to model systems (several dipeptides, a tetrapeptide, and a 13-residue oligoalanine) and also develop a new dynamics driver approach ("DA"). The DA scheme, based on LI, addresses the important issue of proper sampling, which is unlikely to be solved by small-timestep integration methods or implicit methods with intrinsic damping at room temperature, such as LI. Equilibrium averages, time-dependent molecular properties, and sampling trends at room temperature are reported for both LI and DA dynamics simulations, which are then compared to those generated by a standard explicit discretization of the Langevin equation with a 1 fs timestep. We find that LI's quenching effects are severe on both the fast and slow (due to vibrational coupling) frequency modes of all-atom polypeptides and lead to more restricted dynamics at moderate timesteps (40 fs). The DA approach empirically counteracts these damping effects by adding random atomic perturbations to the coordinates at each step (before the minimization of a dynamics function). By restricting the energetic fluctuations and controlling the kinetic energy, we are able with a 60 fs timestep to generate continuous trajectories that sample more of the relevant conformational space and also reproduce reasonably Boltzmann statistics. Although the timescale for transition may be accelerated by the DA approach, the transitional information obtained for the alanine dipeptide and the tetrapeptide is consistent with that obtained by several other theoretical approaches that focus specifically on the determination of pathways. While the trajectory for oligoalanine by the explicit scheme over the nanosecond timeframe remains in the vicinity of the full alpha R-helix starting structure, and a high-temperature (600 degrees K) MD trajectory departs slowly from the alpha helical structure, the DA-generated trajectory for the same CPU time exhibits unfolding and refolding and reveals a range of conformations with an intermediate helix content. Significantly, this range of states is more consistent with spectroscopic experiments on small peptides, as well as the cooperative two-state model for helix-coil transition. The good, near-Boltzmann statistics reported for the smaller systems above, in combination with the interesting oligoalanine results, suggest that DA is a promising tool for efficiently exploring conformational spaces of biomolecules and exploring folding/unfolding processes of polypeptides.

Effect of Urey-Bradley-Shimanouchi force field on the harmonic dynamics of proteins.

A normal mode analysis of bovine pancreatic trypsin inhibitor is carried out by using a Urey-Bradley-Shimanouchi potential energy function. The density of vibrational states, the magnitudes, and time scales of the atomic fluctuations are compared with experimental and theoretical results obtained by the more commonly used potential energy functions. The atomic fluctuations of Lys-15 are subject to extensive considerations as this residue is buried in the trypsin specificity pocket. It is found that Arg-17 is likely to be of importance in order to understand the way BPTI binds on trypsin.