Biomedical subjects

Ron Elber

Publications and source records attributed to Ron Elber.

13 recordsLinked to original sources

PubMed2006

SSALN: an alignment algorithm using structure-dependent substitution matrices and gap penalties learned from structurally aligned protein pairs.

In template-based modeling of protein structures, the generation of the alignment between the target and the template is a critical step that significantly affects the accuracy of the final model. This paper proposes an alignment algorithm SSALN that learns substitution matrices and position-specific gap penalties from a database of structurally aligned protein pairs. In addition to the amino acid sequence information, secondary structure and solvent accessibility information of a position are used to derive substitution scores and position-specific gap penalties. In a test set of CASP5 targets, SSALN outperforms sequence alignment methods such as a Smith-Waterman algorithm with BLOSUM50 and PSI_BLAST. SSALN also generates better alignments than PSI_BLAST in the CASP6 test set. LOOPP server prediction based on an SSALN alignment is ranked the best for target T0280_1 in CASP6. SSALN is also compared with several threading methods and sequence alignment methods on the ProSup benchmark. SSALN has the highest alignment accuracy among the methods compared. On the Fischer's benchmark, SSALN performs better than CLUSTALW and GenTHREADER, and generates more alignments with accuracy >50%, >60% or >70% than FUGUE, but fewer alignments with accuracy >80% than FUGUE. All the supplemental materials can be found at http://www.cs.cornell.edu/ approximately jianq/research.htm.

Algorithms↗

PubMed2005

Atomically detailed potentials to recognize native and approximate protein structures.

Atomically detailed potentials for recognition of protein folds are presented. The potentials consist of pair interactions between atoms. One or three distance steps are used to describe the range of interactions between a pair. Training is carried out with the mathematical programming approach on the decoy sets of Baker, Levitt, and some of our own design. Recognition is required not only for decoy-native structural pairs but also for pairs of decoy and homologous structures. Performance is tested on the targets of CASP5 using templates from the Protein Data Bank, on two test ab initio decoy sets from Skolnick's laboratory, and on decoy sets from Moult's laboratory. We conclude that the newly derived potentials have significant recognition capacity, comparable to the best models derived from other techniques. The new potentials require a significantly smaller number of parameters. The enhanced recognition capacity extends primarily to the identification of structures generated by ab initio simulation and less to the recognition of approximate shapes created by homology.

Computational Biology↗

PubMed2005

Long-timescale simulation methods.

The outstanding challenges in computer simulations of biological macromolecules are related to their complexity. Part of the complexity of biological systems concerns their physical size. Enumerating atoms ranging from a few in small signal molecules to the millions of particles in biological complexes is an obvious example of biological hierarchy. Another aspect is the extremely broad range of timescales of life science processes (many orders of magnitude); this adds another dimension of complexity. This extended range of timescales may even be observed for a single biomolecular process. Consider, for example, the R to T transition in hemoglobin. The complete conformational change occurs in tens of microseconds. However, the system has more than one timescale. Considerable activity occurs on a range of timescales before the final event (heme relaxation, picoseconds; tertiary relaxation, nanoseconds; ligand escape from the protein matrix and rebinding, hundreds of nanoseconds and so on). Whereas the basic time-step of atomically detailed simulations is about a femtosecond, it is not difficult to find molecular processes in biology that span more than ten orders of magnitude of relevant times, making the straightforward simulation of these events very difficult. Several techniques have been developed in recent years to address these problems.

Algorithms↗

PubMed2004

Computing time scales from reaction coordinates by milestoning.

An algorithm is presented to compute time scales of complex processes following predetermined milestones along a reaction coordinate. A non-Markovian hopping mechanism is assumed and constructed from underlying microscopic dynamics. General analytical analysis, a pedagogical example, and numerical solutions of the non-Markovian model are presented. No assumption is made in the theoretical derivation on the type of microscopic dynamics along the reaction coordinate. However, the detailed calculations are for Brownian dynamics in which the velocities are uncorrelated in time (but spatial memory remains).

Computer Simulation↗

PubMed2004

Enriching the sequence substitution matrix by structural information.

A fundamental step in homology modeling is the comparison of two protein sequences: a probe sequence with an unknown structure and function and a template sequence for which the structure and function are known. The detection of protein similarities relies on a substitution matrix that scores the proximity of the aligned amino acids. Sequence-to-sequence alignments use symmetric substitution matrices, whereas the threading protocols use asymmetric matrices, testing the fitness of the probe sequence into the structure of the template protein. We propose a linear combination of threading and sequence-alignment scoring function, to produce a single (mixed) scoring table. By fitting a single parameter (which is the relative contribution of the BLOSUM 50 matrix and the threading energy table of THOM2) we obtain a significant increase in prediction capacity in the twilight zone of homology modeling (detecting sequences with <25% sequence identity and with very similar structures). For a difficult test of 176 homologous pairs, with no signal of sequence similarity, the mixed model makes it possible to detect between 40 and 100% more protein pairs than the number of pairs that are detected by pure threading. Surprisingly, the linear combination of the two models is performing better than threading and than sequence alignment when the percentage of sequence identity is low. We finally suggest that further enrichment of substitution matrices, combing more structural descriptors such as exposed surface area, or secondary structure is expected to enhance the signal as well.

Algorithms↗

PubMed2004

Computational analysis of sequence selection mechanisms.

Mechanisms leading to gene variations are responsible for the diversity of species and are important components of the theory of evolution. One constraint on gene evolution is that of protein foldability; the three-dimensional shapes of proteins must be thermodynamically stable. We explore the impact of this constraint and calculate properties of foldable sequences using 3660 structures from the Protein Data Bank. We seek a selection function that receives sequences as input, and outputs survival probability based on sequence fitness to structure. We compute the number of sequences that match a particular protein structure with energy lower than the native sequence, the density of the number of sequences, the entropy, and the "selection" temperature. The mechanism of structure selection for sequences longer than 200 amino acids is approximately universal. For shorter sequences, it is not. We speculate on concrete evolutionary mechanisms that show this behavior.

Computer Simulation↗

PubMed2003

Kinetics of cytochrome C folding: atomically detailed simulations.

The vast range of time scales (from nanoseconds to seconds) during protein folding is a challenge for experiments and computations. To make concrete predictions on folding mechanisms, atomically detailed simulations of protein folding, using potentials derived from chemical physics principles, are desired. However, due to their computational complexity, straightforward molecular dynamics simulations of protein folding are impossible today. An alternative algorithm is used that makes it possible to compute approximate atomically detailed long time trajectories (the Stochastic Difference Equation in Length). This algorithm is used to compute 26 atomically detailed folding trajectories of cytochrome c (a millisecond process). The early collapse of the protein chain (with marginal formation of secondary structure), and the earlier formation of the N and C helices (compare to the 60's helix) are consistent with the experiment. The existence of an energy barrier upon entry to the molten globule is examined as well. In addition to (favorable) comparison to experiments, we show that non-native contacts drive the formation of the molten globule. In contrast to popular folding models, the non-native contacts do not form off-pathway kinetic traps in cytochrome c.

Algorithms↗

PubMed2003

Ion permeation through the gramicidin channel: atomically detailed modeling by the Stochastic Difference Equation.

Atomically detailed descriptions of ionic solution, membrane, and the gramicidin channel are used to compute molecular dynamics trajectories of ion permeation. The microsecond trajectories are calculated with the Stochastic Difference Equation (SDE), which provides approximate solutions to the equations of motions (with filtered high-frequency modes) of extended timescales. The relative permeations of lithium, sodium, and potassium are estimated by using a novel, kinetic cycle protocol and are compared with experiment. The transport through native gramicidin and one fluoro-valine variant is considered as well. Qualitative agreement between theory and experiment is obtained. The faster permeation rate of sodium compared to lithium is reproduced in the calculations. The calculations also reproduce the slower diffusion through a gramicidin with fluorinated valine compared to native gramicidin. The calculations are inconclusive about the relative rates of potassium and sodium. The experiment suggests that potassium permeates more quickly. We directly probe the kinetics of a biophysical process at a relevant time window without reducing the atomically detailed description of the system. The calculations were able to capture subtle balances between binding and diffusion that determine permeation rates. The same model gave the correct ordering of diffusion rates for cases in which electrostatic binding has opposite effects and must be supplemented by dynamic factors. Diffusion rates are faster when favorable electrostatic interactions of ions in the channel (compared to the solvent) are observed. Studies of a gramicidin variant suggest an opposite effect, in which permeation is faster for the less polar channel, indicating dynamic effects. Although both trends can be explained qualitatively, it is not possible to predict (before doing the SDE calculations) which factor is more important.

Computational Biology↗

PubMed2003

The dominant interaction between peptide and urea is electrostatic in nature: a molecular dynamics simulation study.

The conformational equilibrium of a blocked valine peptide in water and aqueous urea solution is studied using molecular dynamics simulations. Pair correlation functions indicate enhanced concentration of urea near the peptide. Stronger hydrogen bonding of urea-peptide compared to water-peptide is observed with preference for helical conformation. The potential of mean force, computed using umbrella sampling, shows only small differences between urea and water solvation that are difficult to quantify. The changes in solvent structure around the peptide are explained by favorable electrostatic interactions (hydrogen bonds) of urea with the peptide backbone. There is no evidence for significant changes in hydrophobic interactions in the two conformations of the peptide in urea solution. Our simulations suggest that urea denatures proteins by preferentially forming hydrogen bonds to the peptide backbone, reducing the barrier for exposing protein residues to the solvent, and reaching the unfolded state.

Computer Simulation↗

PubMed2003

Atomically detailed simulations of helix formation with the stochastic difference equation.

An algorithm is described to compute approximate classical trajectories as a boundary value problem with an integration step in the arc length. High-frequency motions are filtered out when a large integration step is used, maintaining the stability of the algorithm. At the limit of high filtering (large steps), but still offering an accurate description of the continuous path, the trajectory approaches the steepest descent path (SDP). The steepest descent path is widely used as a reaction coordinate in chemical systems. At intermediate step sizes, some inertial motions remain, interpolating between reaction coordinates and exact classical trajectories. Numerical studies of spatial and energetic properties of meta-trajectories are carried out. Two systems are considered here: valine dipeptide and the folding of a small helical protein. Although thermodynamic properties of meta-trajectories are affected by the filtering, the ordering of events remains similar for substantial differences in trajectory resolution.

Algorithms↗

PubMed2002

An atomically detailed study of the folding pathways of protein A with the stochastic difference equation.

An algorithm is applied here to compute folding pathways of staphylococcal protein A, fragment B. Emphasis is on studies of the complete process, starting from an ensemble of fully denatured conformations and ending at the folded state. The stochastic difference equation algorithm is based on optimization of an action that makes it possible to use a large integration step. Motions with typical displacements that change rapidly on the size scale of the step are filtered out, providing numerically stable and approximate solutions. The present approach is unique in maintaining an atomically detailed picture while providing a systematic, controlled approximation to the classical equations of motion. Analysis of 130 trajectories suggests the following folding mechanism for protein A: At an early precollapse phase of the process, a few native hydrogen bonds form near the C terminus of the protein. The hydrogen bonds are formed mostly within the third helix. The next step is chain collapse that occurs in parallel to additional growth of secondary structure seeds. Therefore, the present study does not support a pure hydrophobic collapse, or substantial early formation of secondary structure. At the last step, native tertiary contacts are formed at the same time as the completion of the secondary structure elements. To a large extent, the process is parallel and not sequential. The early formation of the third helix of protein A, fragment B (in the calculation), is consistent with experimental data.

Algorithms↗

PubMed2002

Maximum feasibility guideline in the design and analysis of protein folding potentials.

Protein folding potentials are expected to have the lowest energy for the native shape. The Linear Programming (LP) approach achieves exactly that goal for a training set, or indicates that this goal is impossible to obtain. If a solution cannot be found (i.e., the problem is infeasible) two possible routes are possible: (a) choosing a new functional form for the potential, (b) finding the best potential with a feasible subset of the data, and (or) detecting inconsistent subset of the data in the training set. Here, we explore option (b). A simple heuristic for finding an approximate solution to an infeasible set of linear inequalities is outlined. An approximately feasible solution is obtained iteratively, starting from a certain initial guess, by computing a series of analytic centers of the polyhedra defined by all the inequalities satisfied at the subsequent iterations. Standard interior point algorithms for Linear Programming can be used to compute efficiently the analytic center of a polyhedron. We demonstrate how this procedure can be used for the design of folding potentials that are linear in their parameters. The procedure shows an improvement in the quality of the potentials and sometimes points to flaws in the original data.

Algorithms↗

PubMed2002

Long time dynamics of complex systems.

Molecular dynamics trajectories of large biological molecules are restricted to nanoseconds. We describe a computational method, based on optimization of a functional, to extend the time of molecular simulations by orders of magnitude. Variants of our technique have already produced microsecond and millisecond trajectories. The large steps enable feasible computations of atomically detailed approximate trajectories. Numerical examples are provided: (i) a conformational change in blocked glycine peptide and (ii) helix formation of an alanine-rich peptide.

Computer Simulation↗