Exploring conformational space using a mean field technique with MOLS sampling

The computational identification of all the low energy structures of a peptide given only its sequence is not an easy task even for small peptides, due to the multiple-minima problem and combinatorial explosion. We have developed an algorithm, called the MOLS technique, that addresses this problem, and have applied it to a number of different aspects of the study of peptide and protein structure. Conformational studies of oligopeptides, including loop sequences in proteins have been carried out using this technique. In general the calculations identified all the folds determined by previous studies, and in addition picked up other energetically favorable structures. The method was also used to map the energy surface of the peptides. In another application, we have combined the MOLS technique, using it to generate a library of low energy structures of an oligopeptide, with a genetic algorithm to predict protein structures. The method has also been applied to explore the conformational space of loops in protein structures. Further, it has been applied to the problem of docking a ligand in its receptor site, with encouraging results.     

Exploring the conformational space of protein loops using a mean field technique with MOLS sampling

We have recently developed a computational technique that uses mutually orthogonal Latin square sampling to explore the conformational space of oligopeptides in an exhaustive manner. In this article, we report its use to analyze the conformational spaces of 120 protein loop sequences in proteins, culled from the PDB, having the length ranging from 5 to 10 residues. The force field used did not have any information regarding the sequences or structures that flanked the loop. The results of the analyses show that the native structure of the loop, as found in the PDB falls at one of the low energy points in the conformational landscape of the sequences. Thus, a large portion of the structural determinants of the loop may be considered intrinsic to the sequence, regardless of either adjacent sequences or structures, or the interactions that the atoms of the loop make with other residues in the protein or in neighboring proteins.     

Optimization methods for conformational sampling using a Boltzmann-weighted mean field approach

An optimization protocol is proposed that combines a mean field simulation approach with Boltzmann-weighted sampling. This is done by including Boltzmann probabilities of multiple conformations in the optimization procedure. The method is demonstrated on a simple model system and on the side-chain conformations of phenylalanines in a small hexapeptide. For comparison, calculations were performed using classical stochastic dynamics simulations [M. Saunders, K. N. Houk, Y. Wu, C. Still, M. Lipton, G. Chang, and W. C. Guida (1990), Journal of the American Chemical Society, Vol. 12, pp. 1419], iterative optimization of probabilities on a fixed set of basis conformations [P. Koehl and M. Delaure (1994), Journal of Molecular Biology, Vol. 239, pp. 249–275], and simulations with locally enhanced sampling [A. Roitberg and R. Elber (1991), Journal of Chemical Physics, Vol. 95, pp. 9277–9287]. Although approximations are used in our method, the results may be more physically meaningful than those of the other procedures discussed. Furthermore, the approximate Boltzmann distribution allows generalization of the results. © 1996 John Wiley & Sons, Inc.     

Exploring c-Met kinase flexibility by sampling and clustering its conformational space

It is now widely recognized that the flexibility of both partners has to be considered in molecular docking studies. However, the question how to handle the best the huge computational complexity of exploring the protein binding site landscape is still a matter of debate. Here we investigate the flexibility of c-Met kinase as a test case for comparing several simulation methods. The c-Met kinase catalytic site is an interesting target for anticancer drug design. In particular, it harbors an unusual plasticity compared with other kinases ATP binding sites. Exploiting this feature may eventually lead to the discovery of new anticancer agents with exquisite specificity. We present in this article an extensive investigation of c-Met kinase conformational space using large-scale computational simulations in order to extend the knowledge already gathered from available X-ray structures. In the process, we compare the relevance of different strategies for modeling and injecting receptor flexibility information into early stage in silico structure-based drug discovery pipeline. The results presented here are currently being exploited in on-going virtual screening investigations on c-Met.     

Conformational studies on enkephalins using the MOLS technique

Conformational studies of two linear enkephalin molecules, Met-enkephalin and Leu-enkephalin, have been carried using the mutually orthogonal Latin squares (MOLS) technique with the ECEPP/3 force field. This technique was developed recently in our laboratory to perform an unbiased search of the conformational space of peptides and to locate low energy conformations. The present study identified all the folds predicted by other studies, and in addition picked up other energetically favorable structures. The results suggest that the peptide backbone exists as a mixture of folded and unfolded forms (approximately 50% each). The study also provides information on the distribution of the low energy conformations that we have classified on the basis of structural motifs, backbone hydrogen-bonding patterns, and root mean square deviations in atomic positions.     

Exploring the conformational space of amorphous cellulose using NMR chemical shifts

(13)C-labeled amorphous cellulose and (13)C NMR chemical shifts by 2D (13)C-(13)C correlation spectroscopy were obtained in the regenerated solid-state from ionic liquids. On the basis of the assigned chemical shifts, combined with information from molecular dynamics and quantum chemistry computer simulations a twisted structure for amorphous cellulose is proposed exposing more hydrophilic surface than that of extended crystalline cellulose.     

Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm

We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed. Proteins 33:227–239, 1998. © 1998 Wiley-Liss, Inc.     

Exploring the conformational space of membrane protein folds matching distance constraints

Herein we present a computational technique for generating helix-membrane protein folds matching a predefined set of distance constraints, such as those obtained from NMR NOE, chemical cross-linking, dipolar EPR, and FRET experiments. The purpose of the technique is to provide initial structures for local conformational searches based on either energetic considerations or ad-hoc scoring criteria. In order to properly screen the conformational space, the technique generates an exhaustive list of conformations within a specified root-mean-square deviation (RMSD) where the helices are positioned in order to match the provided distances. Our results indicate that the number of structures decreases exponentially as the number of distances increases, and increases exponentially as the errors associated with the distances increases. We also found the number of solutions to be smaller when all the distances share one helix in common, compared to the case where the distances connect helices in a daisy-chain manner. We found that for 7 helices, at least 15 distances with errors up to 8 A are needed to produce a number of solutions that is not too large to be processed by local search refinement procedures. Finally, without energetic considerations, our enumeration technique retrieved the transmembrane domains of Bacteriorhodopsin (PDB entry1c3w), Halorhodopsin (1e12), Rhodopsin (1f88), Aquaporin-1 (1fqy), Glycerol uptake facilitator protein (1fx8), Sensory Rhodopsin (1jgj), and a subunit of Fumarate reductase flavoprotein (1qlaC) with Calpha level RMSDs of 3.0 A, 2.3 A, 3.2 A, 4.6 A, 6.0 A, 3.7 A, and 4.4 A, respectively.     

Study of protein-protein interaction using conformational space annealing

We apply conformational space annealing (CSA), an efficient global optimization method, to the study of protein-protein interaction. The CSA is incorporated into the Tinker molecular modeling package along with a B-spline method for CAPRI Round 5 experiments. We have used an energy function for the protein-protein interaction that consists of electrostatic interaction, van der Waals interaction, and solvation energy terms represented by the occupancy desolvation method. The parameters of the AMBER94 all-atom empirical force field are used. Each energy term is calculated by precalculated grid potentials and B-spline method approximation. The ligand protein is placed inside a sphere of 50 A radius centered at an appropriate location, and the CSA rigid docking studies are carried out to find stable complexes. Up to 10 complexes are selected using the K-mean clustering method and biological information when available. These complexes are energy-minimized for further refinement by considering the flexibility of interacting proteins. The results show that the CSA method has a potential for the study of protein-protein interaction.     

Exploring conformational changes coupled to ionization states using a hybrid Rosetta-MCCE protocol

A hybrid protocol combining Rosetta fullatom refinement and Multi-Conformation Continuum Electrostatics (MCCE) to estimate pK(a) is applied to the blind prediction of 94 mutated residues in Staphylococcal nuclease (SNase), as part of the pK(a)-cooperative benchmark test. The standard MCCE method is limited to sidechain conformational changes. The Rosetta refinement protocol is used to add the backbone conformational changes in pK(a) calculations. The non-electrostatic energy component from Rosetta and the electrostatic energy from MCCE are combined to weight the calculated ionization states. Of 63 measured pK(a)s, the root mean squared deviation (RMSD) between the calculated pK(a)s and the measured values is 4.3, showing an improvement compared to the RMSD of 6.6 in the standard MCCE calculations, using a low protein dielectric constant of 4. The breakdown of pK(a) shift from the solution values (ΔpK(a)) shows that the desolvation energy contributes the most in the standard MCCE calculations. Lowering desolvation penalties and optimizing electrostatic interactions with the Rosetta/MCCE protocol reduces the ΔpK(a) to favor the charged states. Analysis also showed that the Rosetta/MCCE protocol samples conformations with pK(a)s close to the solution values. The question remains whether the correct conformational changes coupled to the ionization changes are found here. Nevertheless, a challenge emerges to accurately estimate the reorganization energy, which is not directly measured from the electrostatic environment of the site of interest. Possible improvements to the protocol are also discussed.     

Exploring the sequence space of a DNA aptamer using microarrays

The relationship between sequence and binding properties of an aptamer for immunoglobulin E (IgE) was investigated using custom DNA microarrays. Single, double and some triple mutations of the aptamer sequence were created to evaluate the importance of specific base composition on aptamer binding. The majority of the positions in the aptamer sequence were found to be immutable, with changes at these positions resulting in more than a 100-fold decrease in binding affinity. Improvements in binding were observed by altering the stem region of the aptamer, suggesting that it plays a significant role in binding. Results obtained for the various mutations were used to estimate the information content and the probability of finding a functional aptamer sequence by selection from a random library. For the IgE-binding aptamer, this probability is on the order of 10⁻¹⁰ to 10⁻⁹. Results obtained for the double and triple mutations also show that there are no compensatory mutations within the space defined by those mutations. Apparently, at least for this particular aptamer, the functional sequence space can be represented as a rugged landscape with sharp peaks defined by highly constrained base compositions. This makes the rational optimization of aptamer sequences using step-wise mutagenesis approaches very challenging.     

Exploring protein sequence space using knowledge-based potentials

Knowledge-based potentials can be used to decide whether an amino acid sequence is likely to fold into a prescribed native protein structure. We use this idea to survey the sequence-structure relations in protein space. In particular, we test the following two propositions which were found to be important for efficient evolution: the sequences folding into a particular native fold form extensive neutral networks that percolate through sequence space. The neutral networks of any two native folds approach each other to within a few point mutations. Computer simulations using two very different potential functions, M. Sippl's PROSA pair potential and a neural network based potential, are used to verify these claims.     

Leap-dynamics: efficient sampling of conformational space of proteins and peptides in solution

Glucose-6-phosphate dehydrogenase (G6PD) plays an important role in cellular redox homeostasis, which is crucial for cell survival. In the present study, we found that G6PD status determines the response of cells exposed to nitric oxide (NO) donor. Treatment with NO donor, sodium nitroprusside (SNP), caused apoptosis in G6PD-deficient human foreskin fibroblasts (HFF1), whereas it was growth stimulatory in the normal counterpart (HFF3). Such effects were abolished by NO scavengers like hemoglobin. Ectopic expression of G6PD in HFF1 cells switched the cellular response to NO from apoptosis to growth stimulation. Experiments with 1H-?1,2,4?xadiazolo?4, 3-aquinoxalin-1-one and 8-bromo-cGMP showed that the effects of NO on HFF1 and HFF3 cells were independent of cGMP signalling pathway. Intriguingly, trolox prevented the SNP-induced apoptosis in HFF1 cells. These data demonstrate that G6PD plays a critical role in regulation of cell growth and survival.     

Leap-dynamics: efficient sampling of conformational space of proteins and peptides in solution

A molecular simulation scheme, called Leap-dynamics, that provides efficient sampling of protein conformational space in solution is presented. The scheme is a combined approach using a fast sampling method, imposing conformational 'leaps' to force the system over energy barriers, and molecular dynamics (MD) for refinement. The presence of solvent is approximated by a potential of mean force depending on the solvent accessible surface area. The method has been successfully applied to N-acetyl-L-alanine-N-methylamide (alanine dipeptide), sampling experimentally observed conformations inaccessible to MD alone under the chosen conditions. The method predicts correctly the increased partial flexibility of the mutant Y35G compared to native bovine pancreatic trypsin inhibitor. In particular, the improvement over MD consists of the detection of conformational flexibility that corresponds closely to slow motions identified by nuclear magnetic resonance techniques.     

LMProt: an efficient algorithm for Monte Carlo sampling of protein conformational space

A new and efficient Monte Carlo algorithm for sampling protein configurations in the continuous space is presented; the efficiency of this algorithm, named Local Moves for Proteins (LMProt), was compared to other alternative algorithms. For this purpose, we used an intrachain interaction energy function that is proportional to the root mean square deviation (rmsd) with respect to alpha-carbons from native structures of real proteins. For phantom chains, the LMProt method is approximately 10(4) and 20 times faster than the algorithms Thrashing (no local moves) and Sevenfold Way (local moves), respectively. Additionally, the LMProt was tested for real chains (excluded-volume all-atoms model); proteins 5NLL (138 residues) and 1BFF (129 residues) were used to determine the folding success xi as a function of the number eta of residues involved in the chain movements, and as a function of the maximum amplitude of atomic displacement delta r(max). Our results indicate that multiple local moves associated with relative chain flexibility, controlled by appropriate adjustments for eta and delta r(max), are essential for configurational search efficiency.     

Estimating biomass of submersed vegetation using a simple rake sampling technique

We evaluated the use of a simple rake sampling technique for predicting the biomass of submersed aquatic vegetation. Vegetation sampled from impounded areas of the Mississippi River using a rake sampling technique, was compared with vegetation harvested from 0.33-m² quadrats. The resulting data were used to model the relationship between rake indices and vegetation biomass (total and for individual species). We constructed linear regression models using log-transformed biomass data for sites sampled in 1999 and 2000. Data collected in 2001 were used to validate the resulting models. The coefficient of determination (R ²) for predicting total biomass was 0.82 and ranged from 0.59 (Potamogeton pectinatus) to 0.89 (Ceratophyllum demersum) for individual species. Application of the model to estimate total submersed aquatic vegetation is illustrated using data collected independent of this study. The accuracy and precision of the models tested indicate that the rake method data may be used to predict total vegetation biomass and biomass of selected species; however, the method should be tested in other regions, in other plant communities, and on other species. Handling editor: S. M. Thomaz     

A computational tool for designing FRET protein biosensors by rigid-body sampling of their conformational space

Biosensors relying on the fluorescence resonance energy transfer (FRET) between fluorescent proteins have been used for live-cell imaging of cellular events including Ca(2+) signaling. The efficiency of energy transfer between the donor and acceptor fluorescent proteins depends on the relative distance and orientation between them, which become altered by conformational changes of a fused sensory protein caused by a cellular event. In this way, changes in FRET efficiency of Ca(2+) biosensors can be correlated with Ca(2+) concentrations. The design of these FRET biosensors can be improved by modeling conformational changes before and after a cellular event. Hence, a computational tool called FPMOD was developed to predict FRET efficiency changes by constructing FRET biosensors and sampling their conformational space through rigid-body rotation. We showed with FPMOD that our computational modeling approach can qualitatively predict the FRET efficiencies of a range of biosensors, which had strong agreement with experimental results.     

Extensive conformational sampling in a ternary electron transfer complex

Here we report the crystal structures of a ternary electron transfer complex showing extensive motion at the protein interface. This physiological complex comprises the iron-sulfur flavoprotein trimethylamine dehydrogenase and electron transferring flavoprotein (ETF) from Methylophilus methylotrophus. In addition, we report the crystal structure of free ETF. In the complex, electron density for the FAD domain of ETF is absent, indicating high mobility. Positions for the FAD domain are revealed by molecular dynamics simulation, consistent with crystal structures and kinetic data. A dual interaction of ETF with trimethylamine dehydrogenase provides for dynamical motion at the protein interface: one site acts as an anchor, thereby allowing the other site to sample a large range of interactions, some compatible with rapid electron transfer. This study establishes the role of conformational sampling in multi-domain redox systems, providing insight into electron transfer between ETFs and structurally distinct redox partners.