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K A Dill

Publications and source records attributed to K A Dill.

At least 37 records · Page 2Linked to original sources
PubMed1997

Ligand binding to proteins: the binding landscape model.

Models of ligand binding are often based on four assumptions: (1) steric fit: that binding is determined mainly by shape complementarity; (2) native binding: that ligands mainly bind to native states; (3) locality: that ligands perturb protein structures mainly at the binding site; and (4) continuity: that small changes in ligand or protein structure lead to small changes in binding affinity. Using a generalization of the 2D HP lattice model, we study ligand binding and explore these assumptions. We first validate the model by showing that it reproduces typical binding behaviors. We observe ligand-induced denaturation, ANS and heme-like binding, and "lock-and-key" and "induced-fit" specific binding behaviors characterized by Michaelis-Menten or more cooperative types of binding isotherms. We then explore cases where the model predicts violations of the standard assumptions. For example, very different binding modes can result from two ligands of identical shape. Ligands can sometimes bind highly denatured states more tightly than native states and yet have Michaelis-Menten isotherms. Even low-population binding to denatured states can cause changes in global stability, hydrogen-exchange rates, and thermal B-factors, contrary to expectations, but in agreement with experiments. We conclude that ligand binding, similar to protein folding, may be better described in terms of energy landscapes than in terms of simpler mass-action models.

Hemeproteins↗
PubMed1997

Chiral N-substituted glycines can form stable helical conformations.

BACKGROUND: Short sequence-specific heteropolymers of N-substituted glycines (peptoids) have emerged as promising tools for drug discovery. Recent work on medium-length peptoids containing chiral centers in their sidechains has demonstrated the existence of stable chiral conformations in solution. In this report, we explore the conformational properties of these N alpha chiral peptoids by molecular mechanics calculations and we propose a model for the solution conformation of an octamer of (S)-N-(1-phenylethyl)glycine. RESULTS: Molecular mechanics calculations indicate that the presence of N-substituents in which the N alpha carbons are chiral centers has a dramatic impact on the available backbone conformations. These results are supported by semi-empirical quantum mechanical calculations and coincide qualitatively with simple steric considerations. They suggest that an octamer of (S)-N-(1-phenylethyl)glycine should form a right-handed helix with cis amide bonds, similar to the polyproline type I helix. This model is consistent with circular dichorism studies of these molecules. CONCLUSIONS: Peptoid oligomers containing chiral centers in their sidechains present a new structural paradigm that has promising implications for the design of stably folded molecules. We expect that their novel structure may provide a scaffold to create heteropolymers with useful functionality.

Amino Acid Substitution↗
PubMed1997

From Levinthal to pathways to funnels.

While the classical view of protein folding kinetics relies on phenomenological models, and regards folding intermediates in a structural way, the new view emphasizes the ensemble nature of protein conformations. Although folding has sometimes been regarded as a linear sequence of events, the new view sees folding as parallel microscopic multi-pathway diffusion-like processes. While the classical view invoked pathways to solve the problem of searching for the needle in the haystack, the pathway idea was then seen as conflicting with Anfinsen's experiments showing that folding is pathway-independent (Levinthal's paradox). In contrast, the new view sees no inherent paradox because it eliminates the pathway idea: folding can funnel to a single stable state by multiple routes in conformational space. The general energy landscape picture provides a conceptual framework for understanding both two-state and multi-state folding kinetics. Better tests of these ideas will come when new experiments become available for measuring not just averages of structural observables, but also correlations among their fluctuations. At that point we hope to learn much more about the real shapes of protein folding landscapes.

Kinetics↗
PubMed1997

Protein structure and energy landscape dependence on sequence using a continuous energy function.

We have recently described a new conformational search strategy for protein folding algorithms called the CGU (convex global underestimator) method. Here we use a simplified protein chain representation and a differentiable form of the Sun/Thomas/Dill energy function to test the CGU method. Standard search methods, such as Monte Carlo and molecular dynamics are slowed by kinetic traps. That is, the computer time depends more strongly on the shape of the energy landscape (dictated by the amino acid sequence) than on the number of degrees of freedom (dictated by the chain length). The CGU method is not subject to this limitation, since it explores the underside of the energy landscape, not the top. We find that the CGU computer time is largely independent of the monomer sequence for different chain folds and scales as O(n4) with chain length. By using different starting points, we show that the method appears to find global minima. Since we can currently find stable states of 36-residue chains in 2.4 hours, the method may be practical for small proteins.

Algorithms↗
PubMed1997

Solvation: how to obtain microscopic energies from partitioning and solvation experiments.

Oil-water partitioning, solubilities, and vapor pressure experiments on small-molecule compounds are often used as models to obtain energies for biomolecular modeling. For example, measured partition coefficients, K, are often inserted into the formula -RT in K to obtain quantities thought to represent microscopic contact interaction free energies. We review evidence here that this procedure does not always give microscopically meaningful free energies. Some partitioning processes, particularly involving polymeric solvents such as octanol or hexadecane, are governed not only by translational entropies and contact interactions, but also by free energies resulting from changes in the conformations of the polymer chains upon solute insertion. The Flory-Huggins theory is more suitable for these situations than is the classical approach. We discuss the physical bases for both approaches.

Molecular Conformation↗
PubMed1996

An iterative method for extracting energy-like quantities from protein structures.

We present a method (ENERGI) for extracting energy-like quantities from a data base of protein structures. In this paper, we use the method to generate pairwise additive amino acid "energy" scores. These scores are obtained by iteration until they correctly discriminate a set of known protein folds from decoy conformations. The method succeeds in lattice model tests and in the gapless threading problem as defined by Maiorov and Crippen [Maiorov, V. N. & Crippen, G. M. (1992) J. Mol. Biol. 227, 876-888]. A more challenging test of threading a larger set of test proteins derived from the representative set of Hobohm and Sander [Hobohm, U. & Sander, C. (1994) Protein Sci. 3, 522-524] is used as a "workbench" for exploring how the ENERGI scores depend on their parameter sets.

Amino Acid Sequence↗
PubMed1996

Statistical potentials extracted from protein structures: how accurate are they?

"Statistical potentials" are energies widely used in computer algorithms to fold, dock, or recognize protein structures. They are derived from: (1) observed pairing frequencies of the 20 amino acids in databases of known protein structures, and (2) approximations and assumptions about the physical process that these quantities measure. Using exact lattice models, we construct a rigorous test of those assumptions and approximations. We find that statistical potentials often correctly rank-order the relative strengths of interresidue interactions, but they do not reflect the true underlying energies because of systematic errors arising from the neglect of excluded volume in proteins. We find that complex residue-residue distance dependences observed in statistical potentials, even those among charged groups, can be largely explained as an indirect consequence of the burial of non-polar groups. Our results suggest that current statistical potentials may have limited value in protein folding algorithms and wherever they are used to provide energy-like quantities.

Algorithms↗
PubMed1996

Comparing folding codes for proteins and polymers.

Proteins fold to unique compact native structures. Perhaps other polymers could be designed to fold in similar ways. The chemical nature of the monomer "alphabet" determines the "energy matrix" of monomer interactions-which defines the folding code, the relationship between sequence and structure. We study two properties of energy matrices using two-dimensional lattice models: uniqueness, the number of sequences that fold to only one structure, and encodability, the number of folds that are unique lowest-energy structures of certain monomer sequences. For the simplest model folding code, involving binary sequences of H (hydrophobic) and P (polar) monomers, only a small fraction of sequences fold uniquely, and not all structures can be encoded. Adding strong repulsive interactions results in a folding code with more sequences folding uniquely and more designable folds. Some theories suggest that the quality of a folding code depends only on the number of letters in the monomer alphabet, but we find that the energy matrix itself can be at least as important as the size of the alphabet. Certain multi-letter codes, including some with 20 letters, may be less physical or protein-like than codes with smaller numbers of letters because they neglect correlations among inter-residue interactions, treat only maximally compact conformations, or add arbitrary energies to the energy matrix.

Models, Chemical↗
PubMed1996

A simple model of chaperonin-mediated protein folding.

Chaperonins are oligomeric proteins that help other proteins fold. They act, according to the "Anfinsen cage" or "box of infinite dilution" model, to provide private space, protected from aggregation, where a protein can fold. Recent evidence indicates, however, that proteins are often ejected from the GroEL chaperonin in nonnative conformations, and repeated cycles of binding and ejection are needed for successful folding. Some experimental evidence suggests that GroEL chaperonins can act as folding "catalysts" in an ATP-dependent manner even when no aggregation takes place. This implies that chaperonins must somehow recognize the kinetically trapped intermediate states of a protein. A central puzzle is how a chaperonin can catalyze the folding reaction of a broad spectrum of different proteins. We propose a physical mechanism by which chaperonins can flatten the energy barriers to folding in a nonspecific way. Using a lattice model, we illustrate how a chaperonin could provide a sticky surface that helps pull apart an incorrectly folded protein so it can try again to fold. Depending on the relative sizes of the protein and the chaperonin cavity, folding can proceed both inside and outside the chaperonin. Consistent with experiments, we find that the folding rate and amount of native protein can be considerably enhanced, or sometimes reduced, depending on the amino acid sequence, the chaperonin size, and the binding and ejection rates from the chaperonin.

Catalysis↗
PubMed1996

Folding proteins with a simple energy function and extensive conformational searching.

We describe a computer algorithm for predicting the three-dimensional structures of proteins using only their amino acid sequences. The method differs from others in two ways: (1) it uses very few energy parameters, representing hydrophobic and polar interactions, and (2) it uses a new "constraint-based exhaustive" searching method, which appears to be among the fastest and most complete search methods yet available for realistic protein models. It finds a relatively small number of low-energy conformations, among which are native-like conformations, for crambin (1CRN), avian pancreatic polypeptide (1PPT), melittin (2MLT), and apamin. Thus, the lowest-energy states of very simple energy functions may predict the native structures of globular proteins.

Algorithms↗
PubMed1996

A fast conformational search strategy for finding low energy structures of model proteins.

We describe a new computer algorithm for finding low-energy conformations of proteins. It is a chain-growth method that uses a heuristic bias function to help assemble a hydrophobic core. We call it the Core-directed chain Growth method (CG). We test the CG method on several well-known literature examples of HP lattice model proteins [in which proteins are modeled as sequences of hydrophobic (H) and polar (P) monomers], ranging from 20-64 monomers in two dimensions, and up to 88-mers in three dimensions. Previous nonexhaustive methods--Monte Carlo, a Genetic Algorithm, Hydrophobic Zippers, and Contact Interactions--have been tried on these same model sequences. CG is substantially better at finding the global optima, and avoiding local optima, and it does so in comparable or shorter times. CG finds the global minimum energy of the longest HP lattice model chain for which the global optimum is known, a 3D 88-mer that has only been reachable before by the CHCC complete search method. CG has the potential advantage that it should have nonexponential scaling with chain length. We believe this is a promising method for conformational searching in protein folding algorithms.

Algorithms↗
PubMed1996

Binding of ionic ligands to polyelectrolytes.

Ionic ligands can bind to polyelectrolytes such as DNA or charged polysaccharides. We develop a Poisson-Boltzmann treatment to compute binding constants as a function of ligand charge and salt concentration in the limit of low ligand concentration. For flexible chain ligands, such as oligopeptides, we treat their conformations using lattice statistics. The theory predicts the salt dependence and binding free energies, of Mg(2+) ions to polynucleotides, of hexamine cobalt(III) to calf thymus DNA, of polyamines to T7 DNA, of oligolysines to poly(U) and poly(a), and of tripeptides to heparin, a charged polysaccharide. One parameter is required to obtain absolute binding constants, the distance of closest separation of the ligand to the polyion. Some, but not all, of the binding entropies and enthalpies are also predicted accurately by the model.

Animals↗
PubMed1995

Models of cooperativity in protein folding.

What is the basis for the two-state cooperativity of protein folding? Since the 1950s, three main models have been put forward. 1. In 'helix-coil' theory, cooperativity is due to local interactions among near neighbours in the sequence. Helix-coil cooperativity is probably not the principal basis for the folding of globular proteins because it is not two-state, the forces are weak, it does not account for sheet proteins, and there is no evidence that helix formation precedes the formation of a hydrophobic core in the following pathways. 2. In the 'sidechain packing' model, cooperativity is attributed to the jigsaw-puzzle-like complementary fits of sidechains. This too is probably not the basis of folding cooperativity because exact models and experiments on homopolymers with sidechains give no evidence that sidechain freezing is two-state, sidechain complementarities in proteins are only weak trends, and the molten globule model predicted by this model is far more native-like than experiments indicate. 3. In the 'hydrophobic core collapse' model, cooperativity is due to the assembly of non-polar residues into a good core. Exact model studies show that this model gives two-state behaviour for some sequences of hydrophobic and polar monomers. It is based on strong forces. There is considerable experimental evidence for the kinetics this model predicts: the development of hydrophobic clusters and cores is concurrent with secondary structure formation. It predicts compact denatured states with sizes and degrees of disorder that are in reasonable agreement with experiments.

Kinetics↗
PubMed1995

Forces of tertiary structural organization in globular proteins.

The tertiary structures of globular proteins have remarkable and complex symmetries. What forces cause them? We find that a very simple model reproduces some of those symmetries. Proteins are modeled as copolymers of specific sequences of hydrophobic (H) and polar (P) monomers (HP model) configured as self-avoiding flights on simple three-dimensional cubic lattices. The model has no parameters; we just seek the conformations that have the global maximum number of HH contacts for any given sequence. Finding global optima for chains in this model has not been computationally possible before for chains longer than 36-mers. We report here a procedure that can find all the globally optimal conformations, the number of which defines the degeneracy of a sequence, for chains up to 88 monomers long. It is about 37 orders of magnitude faster than previous exact methods. We find that degeneracy is an important aspect of sequence design. So far, we have found that four-helix bundles, alpha/beta-barrels, and parallel beta-helices are globally optimal conformations of polar/nonpolar sequences that have minimal degeneracy.

Amino Acid Sequence↗
PubMed1995

A test of lattice protein folding algorithms.

We report a blind test of lattice-model-based search strategies for finding global minima of model protein chains. One of us (E.I.S.) selected 10 compact conformations of 48-mer chains on the three-dimensional cubic lattice and used their inverse folding algorithm to design HP (H, hydrophobic; P, polar) sequences that should fold to those "target" structures. The sequences, but not the structures, were sent to the UCSF group (K.Y., K.M.F., P.D.T., H.S.C., and K.A.D.), who used two methods to attempt to find the globally optimal conformations: "hydrophobic zippers" and a constraint-based hydrophobic core construction (CHCC) method. The CHCC method found global minima in all cases, and the hydrophobic zippers method found global minima in some cases, in minutes to hours on workstations. In 9 out of 10 sequences, the CHCC method found lower energy conformations than the 48-mers were designed to fold to. Thus the search strategies succeed for the HP model but the design strategy does not. For every sequence the global energy minimum was found to have multiple degeneracy with 10(3) to 10(6) conformations. We discuss the implications of these results for (i) searching conformational spaces of simple models of proteins and (ii) how these simple models relate to proteins.

Algorithms↗
PubMed1995

Principles of protein folding--a perspective from simple exact models.

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.

Amino Acid Sequence↗
PubMed1995

A statistical mechanical model for hydrogen exchange in globular proteins.

We develop a statistical mechanical theory for the mechanism of hydrogen exchange in globular proteins. Using the HP lattice model, we explore how the solvent accessibilities of chain monomers vary as proteins fluctuate from their stable native conformations. The model explains why hydrogen exchange appears to involve two mechanisms under different conditions of protein stability: (1) a "global unfolding" mechanism by which all protons exchange at a similar rate, approaching that of the denatured protein, and (2) a "stable-state" mechanism by which protons exchange at rates that can differ by many orders of magnitude. There has been some controversy about the stable-state mechanism: does exchange take place inside the protein by solvent penetration, or outside the protein by the local unfolding of a subregion? The present model indicates that the stable-state mechanism of exchange occurs through an ensemble of conformations, some of which may bear very little resemblance to the native structure. Although most fluctuations are small-amplitude motions involving solvent penetration or local unfolding, other fluctuations (the conformational distant relatives) can involve much larger transient excursions to completely different chain folds.

Drug Stability↗