Biomedical subjects

Michael Levitt

Publications and source records attributed to Michael Levitt.

18 recordsLinked to original sources

PubMed2004

Diffusion of nucleoside triphosphates and role of the entry site to the RNA polymerase II active center.

Nucleoside triphosphates (NTPs) diffuse to the active center of RNA polymerase II through a funnel-shaped opening that narrows to a negatively charged pore. Computer simulation shows that the funnel and pore reduce the rate of diffusion by a factor of approximately 2 x 10(-7). The resulting limitation on the rate of RNA synthesis under conditions of low NTP concentration may be overcome by NTP binding to an entry site adjacent to the active center. Binding to the entry site greatly enhances the lifetime of an NTP in the active center region, and it prevents "backtracking" and the consequent occlusion of the active site.

Binding Sites↗

PubMed2004

Improved protein structure selection using decoy-dependent discriminatory functions.

BACKGROUND: A key component in protein structure prediction is a scoring or discriminatory function that can distinguish near-native conformations from misfolded ones. Various types of scoring functions have been developed to accomplish this goal, but their performance is not adequate to solve the structure selection problem. In addition, there is poor correlation between the scores and the accuracy of the generated conformations. RESULTS: We present a simple and nonparametric formula to estimate the accuracy of predicted conformations (or decoys). This scoring function, called the density score function, evaluates decoy conformations by performing an all-against-all Calpha RMSD (Root Mean Square Deviation) calculation in a given decoy set. We tested the density score function on 83 decoy sets grouped by their generation methods (4state_reduced, fisa, fisa_casp3, lmds, lattice_ssfit, semfold and Rosetta). The density scores have correlations as high as 0.9 with the Calpha RMSDs of the decoy conformations, measured relative to the experimental conformation for each decoy. We previously developed a residue-specific all-atom probability discriminatory function (RAPDF), which compiles statistics from a database of experimentally determined conformations, to aid in structure selection. Here, we present a decoy-dependent discriminatory function called self-RAPDF, where we compiled the atom-atom contact probabilities from all the conformations in a decoy set instead of using an ensemble of native conformations, with a weighting scheme based on the density scores. The self-RAPDF has a higher correlation with Calpha RMSD than RAPDF for 76/83 decoy sets, and selects better near-native conformations for 62/83 decoy sets. Self-RAPDF may be useful not only for selecting near-native conformations from decoy sets, but also for fold simulations and protein structure refinement. CONCLUSIONS: Both the density score and the self-RAPDF functions are decoy-dependent scoring functions for improved protein structure selection. Their success indicates that information from the ensemble of decoy conformations can be used to derive statistical probabilities and facilitate the identification of near-native structures.

Computational Biology↗

PubMed2004

Funnel-like organization in sequence space determines the distributions of protein stability and folding rate preferred by evolution.

To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.

Biological Evolution↗

PubMed2004

The ASTRAL Compendium in 2004.

The ASTRAL Compendium provides several databases and tools to aid in the analysis of protein structures, particularly through the use of their sequences. Partially derived from the SCOP database of protein structure domains, it includes sequences for each domain and other resources useful for studying these sequences and domain structures. The current release of ASTRAL contains 54,745 domains, more than three times as many as the initial release 4 years ago. ASTRAL has undergone major transformations in the past 2 years. In addition to several complete updates each year, ASTRAL is now updated on a weekly basis with preliminary classifications of domains from newly released PDB structures. These classifications are available as a stand-alone database, as well as integrated into other ASTRAL databases such as representative subsets. To enhance the utility of ASTRAL to structural biologists, all SCOP domains are now made available as PDB-style coordinate files as well as sequences. In addition to sequences and representative subsets based on SCOP domains, sequences and subsets based on PDB chains are newly included in ASTRAL. Several search tools have been added to ASTRAL to facilitate retrieval of data by individual users and automated methods. ASTRAL may be accessed at http://astral.stanford. edu/.

Animals↗

PubMed2004

Simulating protein evolution in sequence and structure space.

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.

Algorithms↗

PubMed2003

Funnel sculpting for in silico assembly of secondary structure elements of proteins.

We present a method for designing a funnel-shaped free-energy surface that reproducibly assembles secondary structure elements of proteins into their native conformations from a random extended configuration. Assuming a priori knowledge of secondary structure, our method can design a funnel-shaped surface for folding of alpha, beta, and alphabeta structures individually. We design energy surfaces that fold up to five unrelated sequences with the same energy parameters. We develop a measure of the foldability of an energy landscape in silico and present an alternative way to view energy landscapes.

Algorithms↗

PubMed2003

A major role for carbon monoxide as an endogenous hyperpolarizing factor in the gastrointestinal tract.

Carbon monoxide (CO) is proposed as a physiological messenger. CO activates cGMP and has a direct effect on potassium channels. Both actions of CO lead to hyperpolarization of a cell's resting membrane potential, suggesting that CO may function as a hyperpolarizing factor, although direct evidence is still lacking. Here we take advantage of the known membrane potential gradient that exists in the muscle layers of the gastrointestinal tract to determine whether CO is an endogenous hyperpolarizing factor. We find that heme oxygenase-2-null mice have depolarized smooth muscle cells and that the membrane potential gradient in the gut is abolished. Exogenous CO hyperpolarizes the membrane potential. Regions of the canine gastrointestinal tract that are more hyperpolarized generate more CO and have higher heme oxygenase activity than more depolarized regions. Our results suggest that CO is a critical hyperpolarizing factor required for the maintenance of intestinal smooth muscle membrane potential and gradient.

Animals↗

PubMed2003

A novel approach to decoy set generation: designing a physical energy function having local minima with native structure characteristics.

We suggest a new approach to the generation of candidate structures (decoys) for ab initio prediction of protein structures. Our method is based on random sampling of conformation space and subsequent local energy minimization. At the core of this approach lies the design of a novel type of energy function. This energy function has local minima with native structure characteristics and wide basins of attraction. The current work presents our motivation for deriving such an energy function and also tests the derived energy function. Our approach is novel in that it takes advantage of the inherently rough energy landscape of proteins, which is generally considered a major obstacle for protein structure prediction. When local minima have wide basins of attraction, the protein's conformation space can be greatly reduced by the convergence of large regions of the space into single points, namely the local minima corresponding to these funnels. We have implemented this concept by an iterative process. The potential is first used to generate decoy sets and then we study these sets of decoys to guide further development of the potential. A key feature of our potential is the use of cooperative multi-body interactions that mimic the role of the entropic and solvent contributions to the free energy. The validity and value of our approach is demonstrated by applying it to 14 diverse, small proteins. We show that, for these proteins, the size of conformation space is considerably reduced by the new energy function. In fact, the reduction is so substantial as to allow efficient conformational sampling. As a result we are able to find a significant number of near-native conformations in random searches performed with limited computational resources.

Animals↗

PubMed2002

Evidence of turn and salt bridge contributions to beta-hairpin stability: MD simulations of C-terminal fragment from the B1 domain of protein G.

We ran and analyzed a total of eighteen, 10 ns molecular dynamics simulations of two C-terminal beta-hairpins from the B1 domain of Protein G: twelve runs for the last 16 residues and six runs for the last 15 residues, G41-E56 and E42-E56, respectively. Based on their CalphaRMS deviation from the starting structure and the pattern of stabilizing interactions (hydrogen bonds, hydrophobic contacts, and salt bridges), we were able to classify the twelve runs on G41-E56 into one of three general states of the beta-hairpin ensemble: 'Stable', 'Unstable', and 'Unfolded'. Comparing the specific interactions between these states, we find that on average the stable beta-hairpin buries 287 A(2) of hydrophobic surface area, makes 13 hydrogen bonds, and forms 3 salt-bridges. We find that the hydrophobic core prefers to make some specific contacts; however, this core does not require optimal packing. Side-chain hydrogen bonds stabilize the beta-hairpin turn with strong stabilizing interactions primarily due to the carboxyl of D46 with contributions from T49 hydroxyl. Buoyed by the strength of the hydrophobic core, other hydrogen bonds, primarily main-chain, guide the beta-hairpin into registration by forming a loose network of interactions, making an approximately constant number of hydrogen bonds from a pool of possible candidates. In simulations on E42-E56, where the salt bridge closing the termini is not favored, we observe that all the simulations show no 'Stable' behavior, but are 'Unstable' or 'Unfolded'. We can estimate that the salt-bridge between the termini provides approximately 1.3 kcal/mol. Altogether, the results suggest that the beta-hairpin folds beginning at the turn, followed by hydrophobic collapse, and then hydrogen bond formation. Salt bridges help to stabilize the folded conformations by inhibiting unfolded states.

Hydrogen Bonding↗

PubMed2002

Sequence variations within protein families are linearly related to structural variations.

It is commonly believed that similarities between the sequences of two proteins infer similarities between their structures. Sequence alignments reliably recognize pairs of protein of similar structures provided that the percentage sequence identity between their two sequences is sufficiently high. This distinction, however, is statistically less reliable when the percentage sequence identity is lower than 30% and little is known then about the detailed relationship between the two measures of similarity. Here, we investigate the inverse correlation between structural similarity and sequence similarity on 12 protein structure families. We define the structure similarity between two proteins as the cRMS distance between their structures. The sequence similarity for a pair of proteins is measured as the mean distance between the sequences in the subsets of sequence space compatible with their structures. We obtain an approximation of the sequence space compatible with a protein by designing a collection of protein sequences both stable and specific to the structure of that protein. Using these measures of sequence and structure similarities, we find that structural changes within a protein family are linearly related to changes in sequence similarity.

Amino Acid Sequence↗

PubMed2002

Small libraries of protein fragments model native protein structures accurately.

Prediction of protein structure depends on the accuracy and complexity of the models used. Here, we represent the polypeptide chain by a sequence of rigid fragments that are concatenated without any degrees of freedom. Fragments chosen from a library of representative fragments are fit to the native structure using a greedy build-up method. This gives a one-dimensional representation of native protein three-dimensional structure whose quality depends on the nature of the library. We use a novel clustering method to construct libraries that differ in the fragment length (four to seven residues) and number of representative fragments they contain (25-300). Each library is characterized by the quality of fit (accuracy) and the number of allowed states per residue (complexity). We find that the accuracy depends on the complexity and varies from 2.9A for a 2.7-state model on the basis of fragments of length 7-0.76A for a 15-state model on the basis of fragments of length 5. Our goal is to find representations that are both accurate and economical (low complexity). The models defined here are substantially better in this regard: with ten states per residue we approximate native protein structure to 1A compared to over 20 states per residue needed previously. For the same complexity, we find that longer fragments provide better fits. Unfortunately, libraries of longer fragments must be much larger (for ten states per residue, a seven-residue library is 100 times larger than a five-residue library). As the number of known protein native structures increases, it will be possible to construct larger libraries to better exploit this correlation between neighboring residues. Our fragment libraries, which offer a wide range of optimal fragments suited to different accuracies of fit, may prove to be useful for generating better decoy sets for ab initio protein folding and for generating accurate loop conformations in homology modeling.

Models, Molecular↗

PubMed2002

A comprehensive analysis of 40 blind protein structure predictions.

BACKGROUND: We thoroughly analyse the results of 40 blind predictions for which an experimental answer was made available at the fourth meeting on the critical assessment of protein structure methods (CASP4). Using our comparative modelling and fold recognition methodologies, we made 29 predictions for targets that had sequence identities ranging from 50% to 10% to the nearest related protein with known structure. Using our ab initio methodologies, we made eleven predictions for targets that had no detectable sequence relationships. RESULTS: For 23 of these proteins, we produced models ranging from 1.0 to 6.0 A root mean square deviation (RMSD) for the Calpha atoms between the model and the corresponding experimental structure for all or large parts of the protein, with model accuracies scaling fairly linearly with respect to sequence identity (i.e., the higher the sequence identity, the better the prediction). We produced nine models with accuracies ranging from 4.0 to 6.0 A Calpha RMSD for 60-100 residue proteins (or large fragments of a protein), with a prediction accuracy of 4.0 A Calpha RMSD for residues 1-80 for T110/rbfa. CONCLUSIONS: The areas of protein structure prediction that work well, and areas that need improvement, are discernable by examining how our methods have performed over the past four CASP experiments. These results have implications for modelling the structure of all tractable proteins encoded by the genome of an organism.

Amino Acid Sequence↗

PubMed2002

Roles of mutation and recombination in the evolution of protein thermodynamics.

We present a comprehensive study of the evolutionary origin of the thermodynamic behavior of proteins. With the use of a simplified model, we exhaustively enumerate the space of all sequences and the space of all structures, simulate the evolutionary relationship between sequences and structures, and characterize the steady-state sequence distribution for all structures in terms of several thermodynamic variables. We assess the effects of two major forces of evolution: mutation and recombination. Three simplifications are made. First, a two-dimensional lattice model is used to represent protein sequences and structures. Second, proteins undergo neutral evolution so that the fitness landscape has a flat allowed region inside of which all sequences are equally fit. Third, we ignore otherwise important factors such as finite population size and evolutionary time. Two scenarios emerge from our study. The first occurs when evolution is dominated by mutation events. Even though the prototype sequence that is most mutationally robust is preferred by evolution, the preference is not strong enough to offset the huge size of sequence space. Most native sequences are located near the boundary of the fitness region and are marginally compatible with the native structure. The second scenario occurs when evolution is dominated by recombination events. Now evolutionary preference for prototype sequence is strong enough to overcome the size of sequence space so that most native sequences are located near the center of sequence-structure compatibility. We conclude that the relative frequency of mutation and recombination events is a major determinant of how optimal protein sequences are for their structures.

Evolution, Molecular↗

PubMed2002

Within the twilight zone: a sensitive profile-profile comparison tool based on information theory.

This paper presents a novel approach to profile-profile comparison. The method compares two input profiles (like those that are generated by PSI-BLAST) and assigns a similarity score to assess their statistical similarity. Our profile-profile comparison tool, which allows for gaps, can be used to detect weak similarities between protein families. It has also been optimized to produce alignments that are in very good agreement with structural alignments. Tests show that the profile-profile alignments are indeed highly correlated with similarities between secondary structure elements and tertiary structure. Exhaustive evaluations show that our method is significantly more sensitive in detecting distant homologies than the popular profile-based search programs PSI-BLAST and IMPALA. The relative improvement is the same order of magnitude as the improvement of PSI-BLAST relative to BLAST. Our new tool often detects similarities that fall within the twilight zone of sequence similarity.

Algorithms↗

PubMed2002

Protein topology and stability define the space of allowed sequences.

We describe a new approach to explore and quantify the sequence space associated with a given protein structure. A set of sequences are optimized for a given target structure, using all-atom models and a physical energy function. Specificity of the sequence for its target is ensured by using the random energy model, which keeps the amino acid composition of the sequence constant. The designed sequences provide a multiple sequence alignment that describes the sequence space compatible with the structure of interest; here the size of this space is estimated by using an information entropy measure. In parallel, multiple alignments of naturally occurring sequences can be derived by using either sequence or structure alignments. We compared these 3 independent multiple sequence alignments for 10 different proteins, ranging in size from 56 to 310 residues. We observed that the subset of the sequence space derived by using our design procedure is similar in size to the sequence spaces observed in nature. These results suggest that the volume of sequence space compatible with a given protein fold is defined by the length of the protein as well as by the topology (i.e., geometry of the polypeptide chain) and the stability (i.e., free energy of denaturation) of the fold.

Amino Acid Sequence↗

PubMed2002

Improved recognition of native-like protein structures using a family of designed sequences.

The goal of the inverse protein folding problem is to identify amino acid sequences that stabilize a given target protein conformation. Methods that attempt to solve this problem have proven useful for protein sequence design. Here we show that the same methods can provide valuable information for protein fold recognition and for ab initio protein structure prediction. We present a measure of the compatibility of a test sequence with a target model structure, based on computational protein design. The model structure is used as input to design a family of low free energy sequences, and these sequences are compared with the test sequence by using a metric in sequence space based on nearest-neighbor connectivity. We find that this measure is able to recognize the native fold of a myoglobin sequence among different globin folds. It is also powerful enough to recognize near-native protein structures among non-native models.

Amino Acid Sequence↗

PubMed2002

ASTRAL compendium enhancements.

The ASTRAL compendium provides several databases and tools to aid in the analysis of protein structures, particularly through the use of their sequences. It is partially derived from the SCOP database of protein domains, and it includes sequences for each domain as well as other resources useful for studying these sequences and domain structures. Several major improvements have been made to the ASTRAL compendium since its initial release 2 years ago. The number of protein domain sequences included has doubled from 15 190 to 30 867, and additional databases have been added. The Rapid Access Format (RAF) database contains manually curated mappings linking the biological amino acid sequences described in the SEQRES records of PDB entries to the amino acid sequences structurally observed (provided in the ATOM records) in a format designed for rapid access by automated tools. This information is used to derive sequences for protein domains in the SCOP database. In cases where a SCOP domain spans several protein chains, all of which can be traced back to a single genetic source, a 'genetic domain' sequence is created by concatenating the sequences of each chain in the order found in the original gene sequence. Both the original-style library of SCOP sequences and a new library including genetic domain sequences are available. Selected representative subsets of each of these libraries, based on multiple criteria and degrees of similarity, are also included. ASTRAL may be accessed at http://astral.stanford.edu/.

Amino Acid Sequence↗

PubMed2002

Design of an optimal Chebyshev-expanded discrimination function for globular proteins.

We describe the construction of a scoring function designed to model the free energy of protein folding. An optimization technique is used to determine the best functional forms of the hydrophobic, residue-residue and hydrogen-bonding components of the potential. The scoring function is expanded by use of Chebyshev polynomials, the coefficients of which are determined by minimizing the score, in units of standard deviation, of native structures in the ensembles of alternate decoy conformations. The derived effective potential is then tested on decoy sets used conventionally in such studies. Using our scoring function, we achieve a high level of discrimination between correct and incorrect folds. In addition, our method is able to represent functions of arbitrary shape with fewer parameters than the usual histogram potentials of similar resolution. Finally, our representation can be combined easily with many optimization methods, because the total energy is a linear function of the parameters. Our results show that the techniques of Z-score optimization and Chebyshev expansion work well.

Amino Acids↗