Biomedical subjects

Burak Erman

Publications and source records attributed to Burak Erman.

7 recordsLinked to original sources

PubMed2007

Computational basis of knowledge-based conformational probabilities derived from local- and long-range interactions in proteins.

The probabilities of the various basins in Ramachandran maps are examined critically. The theoretical basis of probability calculations both from molecular computations and from protein libraries are discussed. The well-defined basins of the Ramachandran maps are treated as rotational isomeric states. Statistical independence and dependence of the states of different residues along the peptide chain are discussed. The Flory isolated pair hypothesis, near neighbor correlations, context effects, and long-range correlations are examined critically. A method of evaluating long-range correlations in helical and extended sequences is introduced in analogy with earlier polymer theory. Three different protein libraries are constructed where data is considered from residues in the (i) coiled regions, (ii) all regions, and (iii) only the helical and extended regions of proteins. Singlet and pairwise dependent probabilities calculated from these libraries are used to predict whether a given sequence is helical or extended. Predictions using pairwise dependence were not better than those using singlet probabilities. Modeling of long-range correlations improved the predictions significantly. Removal of the Chameleon sequences from the data set also improved the predictions, but to a lesser extent.

Amino Acid Sequence↗

PubMed2006

Quantum mechanical calculations of tryptophan and comparison with conformations in native proteins.

We report a detailed analysis of the potential energy surface of N-acetyl-l-tryptophan-N-methylamide, (NATMA) both in the gas phase and in solution. The minima are identified using the density-functional-theory (DFT) with the 6-31g(d) basis set. The full potential energy surface in terms of torsional angles is spanned starting from various initial configurations. We were able to locate 77 distinct L-minima. The calculated energy maps correspond to the intrinsic conformational propensities of the individual NATMA molecule. We show that these conformations are essentially similar to the conformations of tryptophan in native proteins. For this reason, we compare the results of DFT calculations in the gas and solution phases with native state conformations of tryptophan obtained from a protein library. In native proteins, tryptophan conformations have strong preferences for the beta sheet, right-handed helix, tight turn, and bridge structures. The conformations calculated by DFT, the solution-phase results in particular, for the single tryptophan residue are in agreement with native state values obtained from the Protein Data Bank.

Algorithms↗

PubMed2006

The gaussian network model: precise prediction of residue fluctuations and application to binding problems.

The single-parameter Gamma matrix of force constants proposed by the Gaussian Network Model (GNM) is iteratively modified to yield native state fluctuations that agree exactly with experimentally observed values. The resulting optimized Gamma matrix contains residue-specific force constants that may be used for an accurate analysis of ligand binding to single or multiple sites on proteins. Bovine Pancreatic Trypsin Inhibitor (BPTI) is used as an example. The calculated off-diagonal elements of the Gamma matrix, i.e., the optimized spring constants, obey a Lorentzian distribution. The mean value of the spring constants is approximately -0.1, a value much weaker than -1 of the GNM. Few of the spring constants are positive, indicating repulsion between residues. Residue pairs with large number of neighbors have spring constants around the mean, -0.1. Large negative spring constants are between highly correlated pairs of residues. The fluctuations of the distance between anticorrelated pairs of residues are subject to smaller spring constants. The importance of the number of neighbors of residue pairs in determining the elements of the Gamma matrix is pointed out. Allosteric effects of binding on a single or multiple residues of BPTI are illustrated and discussed. Comparison of the predictions of the present model with those of the standard GNM shows that the two models agree at lower modes, i.e., those relating to global motions, but they disagree at higher modes. In the higher modes, the present model points to the important contributions from specific residues whereas the standard GNM fails to do so.

Amino Acids↗

PubMed2006

Optimum folding pathways of proteins: their determination and properties.

We develop a dynamic optimization technique for determining optimum folding pathways of proteins starting from different initial configurations. A coarse-grained Go model is used. Forces acting on each bead are (i) the friction force, (ii) forces from bond length constraints, (iii) excluded volume constraints, and (iv) attractive forces between residue pairs that are in contact in the native state. An objective function is defined as the total attractive energy between nonbonded residues, which are neighbors in the native state. The objective function is minimized over all feasible paths, satisfying bond length and excluded volume constraints. The optimization problem is nonconvex and contains a large number of constraints. An augmented Lagrangian method with a penalty barrier function was used to solve the problem. The method is applied to a 36-residue protein, chicken villin headpiece. Sequences of events during folding of the protein are determined for various pathways and analyzed. The relative time scales are compared and scaled according to experimentally measured events. Formation times of the helices, turn, and the loop agree with experimental data. We obtain the overall folding time of the protein in the range of 600 ns-1.2 micros that is smaller than the experimental result of 4-5 micros, showing that the optimal folding times that we obtain may be possible lower bounds. Time dependent variables during folding and energies associated with short- and long-range interactions between secondary structures are analyzed in modal space using Karhunen-Loeve expansion.

Kinetics↗

PubMed2004

Folding dynamics of proteins from denatured to native state: principal component analysis.

Several trajectories starting from random configurations and ending in the native state for chymotrypsin inhibitor 2, CI2, are generated using a Go-type model where the backbone torsional angles execute random jumps on which a drift towards their native values is superposed. Bond lengths and bond angles are kept fixed, and the size of the backbone atoms and side groups are recognized. The large datasets obtained are analyzed using a particular type of principal component analysis known as Karhunen-Loeve expansion (KLE). Trajectories are decomposed separately into modes in residue space and time space. General features of different folding trajectories are compared in the modal space and relationships between the structure of CI2 and its folding dynamics are obtained. Dynamic scaling and order reduction of the folding trajectories are discussed. A continuous wavelet transform is used to decompose the nonstationary folding trajectories into windows exhibiting different features of folding dynamics. Analysis of correlations confirms the known two-state nature of folding of CI2. All of the conserved residues of the protein are shown to be stationary in the small modes of the residue space. The sequential nature of folding is shown by examining the slow modes of the trajectories. The present model of protein folding dynamics is compared with the simple Rouse model of polymer dynamics. Principal component analysis is shown to be a very effective tool for the characterization of the general folding features of proteins.

Computational Biology↗

PubMed2002

The elastic net algorithm and protein structure prediction.

Predicting protein structures from their amino acid sequences is a problem of global optimization. Global optima (native structures) are often sought using stochastic sampling methods such as Monte Carlo or molecular dynamics, but these methods are slow. In contrast, there are fast deterministic methods that find near-optimal solutions of well-known global optimization problems such as the traveling salesman problem (TSP). But fast TSP strategies have yet to be applied to protein folding, because of fundamental differences in the two types of problems. Here, we show how protein folding can be framed in terms of the TSP, to which we apply a variation of the Durbin-Willshaw elastic net optimization strategy. We illustrate using a simple model of proteins with database-derived statistical potentials and predicted secondary structure restraints. This optimization strategy can be applied to many different models and potential functions, and can readily incorporate experimental restraint information. It is also fast; with the simple model used here, the method finds structures that are within 5-6 A all-Calpha-atom RMSD of the known native structures for 40-mers in about 8 s on a PC; 100-mers take about 20 s. The computer time tau scales as tau approximately n, where n is the number of amino acids. This method may prove to be useful for structure refinement and prediction.

Algorithms↗

PubMed2002

Minimum energy configurations of the 2-dimensional HP-model of proteins by self-organizing networks.

We use self-organizing maps (SOM) as an efficient tool to find the minimum energy configurations of the 2-dimensional HP-models of proteins. The usage of the SOM for the protein folding problem is similar to that for the Traveling Salesman Problem. The lattice nodes represent the cities whereas the neurons in the network represent the amino acids moving towards the closest cities, subject to the HH interactions. The valid path that maximizes the HH contacts corresponds to the minimum energy configuration of the protein. We report promising results for the cases when the protein completely fills a lattice and discuss the current problems and possible extensions. In all the test sequences up to 36 amino acids, the algorithm was able to find the global minimum and its degeneracies.

Algorithms↗