Biomedical subjects

K A Dill

Publications and source records attributed to K A Dill.

At least 55 records · Page 3Linked to original sources

PubMed1995

Designing amino acid sequences to fold with good hydrophobic cores.

We present two methods for designing amino acid sequences of proteins that will fold to have good hydrophobic cores. Given the coordinates of the desired target protein or polymer structure, the methods generate sequences of hydrophobic (H) and polar (P) monomers that are intended to fold to these structures. One method designs hydrophobic inside, polar outside; the other minimizes an energy function in a sequence evolution process. The sequences generated by these methods agree at the level of 60-80% of the sequence positions in 20 proteins in the Protein Data Bank. A major challenge in protein design is to create sequences that can fold uniquely, i.e. to a single conformation rather than to many. While an earlier lattice-based sequence evolution method was shown not to design unique folders, our method generates unique folders in lattice model tests. These methods may also be useful in designing other types of foldable polymer not based on amino acids.

Amino Acid Sequence↗

PubMed1995

A simple protein folding algorithm using a binary code and secondary structure constraints.

We describe an algorithm to predict tertiary structures of small proteins. In contrast to most current folding algorithms, it uses very few energy parameters. Given the secondary structural elements in the sequence--alpha-helices and beta-strands--the algorithm searches the remaining conformational space of a simplified real-space representation of chains to find a minimum energy of an exceedingly simple potential function. The potential is based only on a single type of favorable interaction between hydrophobic residues, an unfavorable excluded volume term of spatial overlaps and, for sheet proteins, an interstrand hydrogen bond interaction. Where appropriate, the known disulfide bonds are constrained by a square-law potential. Conformations are searched by a genetic algorithm. The model predicts reasonably well the known tertiary folds of seven out of the 10 small proteins we consider. We draw two conclusions. First, for the proteins we tested, this exceedingly simple potential function is no worse than others having hundreds of energy parameters in finding the right general tertiary structures. Second, despite its simplicity, the potential function is not the weak link in this algorithm. Differences between our predicted structures and the correct targets can be ascribed to shortcomings in our search strategy. This potential function may be useful for testing other conformational search strategies.

Algorithms↗

PubMed1994

Does compactness induce secondary structure in proteins? A study of poly-alanine chains computed by distance geometry.

A few years ago, lattice model studies indicated that compactness could induce polymer chains to develop protein-like secondary structures. Subsequent off-lattice studies have found the amounts of induced structure to be relatively small. Here we use distance geometry to generate random conformations of compact poly-alanine chains of various chain lengths. The poly-alanine chains are subjected only to compactness and excluded volume constraints; no other energies or conformational propensities are included in the chain generation procedure. We find that compactness leads to considerable stabilization of secondary structure, but the absolute amount of secondary structure depends strongly on the criteria used to define helices and sheets. By loose criteria, much secondary structure arises from compactness, but by strict criteria, little does. The stabilization free energy of secondary structure provided by compactness, however, appears to be independent of criteria. Since real helices and sheets in proteins can be identified by strict criteria, we introduced small energy perturbations to compact poly-alanine chains using the AMBER force field. Small refinements produced good alpha-helices. For beta-sheets, however, larger refinements are necessary. Compactness appears to impart stability, but not much structural specificity, to secondary structures in proteins. Compactness acts more like diffusion as a force, a result of ensemble statistics, than like pair interactions such as hydrogen bonding.

Models, Chemical↗

PubMed1994

Modeling compact denatured states of proteins.

We propose a model for the conformations of compact denatured states of globular proteins: that they are broad ensembles of chain backbone conformations that involve common localized hydrophobic clustering and helical contacts, depending on the amino acid sequence. We construct representative ensembles for chain lengths up to 136 monomers on three-dimensional cubic lattices using the "hydrophobic zippers" method (Fiebig & Dill, 1993). We find that model conformations with radii of gyration about 20% larger than native conformations commonly have bimodal distributions of P(r), of the pairwise interatomic distances, r, and Kratky plots in agreement with recent small-angle X-ray scattering (Sosnick & Trewhella, 1992; Flanagan et al., 1992; Kataoka et al., 1993; Flanagan et al., 1993) experiments on three different proteins. We also find that the lattice model of the Shortle 1-136 fragment of staphylococcal nuclease does not appear capable of forming a single hydrophobic core by hydrophobic zippering, consistent with experiments.

Amino Acid Sequence↗

PubMed1994

Side-chain entropy and packing in proteins.

What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is side-chain "freezing" or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.

Drug Stability↗

PubMed1993

Aggregation and denaturation of apomyoglobin in aqueous urea solutions.

The effects of urea on apomyoglobin solubility have been investigated. Apomyoglobin precipitation was found to be a thermodynamically reversible process independent of the pathway of aggregation. A liquid-solid phase diagram was constructed for the precipitation of apomyoglobin as a function of urea and protein concentration. Apomyoglobin solubility decreases by an order of magnitude between 0 and 1.5 M urea, reaching a minimum near 2.4 M urea and increasing at higher urea concentrations (the denaturation midpoint is at approximately 2.6 M urea). This decrease in protein solubility is opposite to that expected based on amino acid solubilities, since both polar and nonpolar molecules become more soluble with increasing urea concentration. Solubility minima for proteins have been rationalized in terms of folding intermediates. However, our structural studies show no evidence for folding intermediates in apomyoglobin under the experimental conditions, apart from small predenaturation changes. Our data are consistent with an alternative hypothesis, namely, that the primary aggregating species are denatured protein molecules, rather than intermediate states. Consistent with recent thermodynamic and statistical mechanical models, the solubility minimum may be described as the result of two competing effects of urea: (1) urea denatures the protein, and (2) urea makes the solvent more favorable for the native and any denatured state. At low urea concentration, solubility decreases with increasing urea concentration due to the domination of the solubility behavior by the increase in the population of aggregation-competent (denatured) protein molecules. However, at high urea concentration, the increasingly favorable nature of the solvent dominates, resulting in increasing solubility with urea concentration. The phase diagram provides guidance for the best experimental conditions (pathway) to use to avoid aggregation during the refolding of denaturant-unfolded protein.

Animals↗

PubMed1993

Cooperativity in protein-folding kinetics.

How does a protein find its native state without a globally exhaustive search? We propose the "HZ" (hydrophobic zipper) hypothesis: hydrophobic contacts act as constraints that bring other contacts into spatial proximity, which then further constrain and zip up the next contacts, etc. In contrast to helix-coil cooperativity, HZ-heteropolymer collapse cooperativity is driven by nonlocal interactions, causes sheet and irregular conformations in addition to helices, leads to secondary structures concurrently with early hydrophobic core formation, is much more sequence dependent than helix-coil processes, and involves compact intermediate states that have much secondary--but little tertiary--structure. Hydrophobic contacts in the 1992 Protein Data Bank have the type of "topological localness" predicted by the hypothesis. The HZ paths for amino acid sequences that mimic crambin and bovine pancreatic trypsin inhibitor are quickly found by computer; the best configurations thus reached have single hydrophobic cores that are within about 3 kcal/mol of the global minimum. This hypothesis shows how proteins could find globally optimal states without exhaustive search.

Amino Acid Sequence↗

PubMed1993

Families and the structural relatedness among globular proteins.

Protein structures come in families. Are families "closely knit" or "loosely knit" entities? We describe a measure of relatedness among polymer conformations. Based on weighted distance maps, this measure differs from existing measures mainly in two respects: (1) it is computationally fast, and (2) it can compare any two proteins, regardless of their relative chain lengths or degree of similarity. It does not require finding relative alignments. The measure is used here to determine the dissimilarities between all 12,403 possible pairs of 158 diverse protein structures from the Brookhaven Protein Data Bank (PDB). Combined with minimal spanning trees and hierarchical clustering methods, this measure is used to define structural families. It is also useful for rapidly searching a dataset of protein structures for specific substructural motifs. By using an analogy to distributions of Euclidean distances, we find that protein families are not tightly knit entities.

Algorithms↗

PubMed1993

Local and nonlocal interactions in globular proteins and mechanisms of alcohol denaturation.

How important are helical propensities in determining the conformations of globular proteins? Using the two-dimensional lattice model and two monomer types, H (hydrophobic) and P (polar), we explore both nonlocal interactions, through an HH contact energy, epsilon, as developed in earlier work, and local interactions, through a helix energy, sigma. By computer enumeration, the partition functions for short chains are obtained without approximation for the full range of both types of energy. When nonlocal interactions dominate, some sequences undergo coil-globule collapse to a unique native structure. When local interactions dominate, all sequences undergo helix-coil transitions. For two different conformational properties, the closest correspondence between the lattice model and proteins in the Protein Data Bank is obtained if the model local interactions are made small compared to the HH contact interaction, suggesting that helical propensities may be only weak determinants of globular protein structures in water. For some HP sequences, varying sigma/epsilon leads to additional sharp transitions (sometimes several) and to "conformational switching" between unique conformations. This behavior resembles the transitions of globular proteins in water to helical states in alcohols. In particular, comparison with experiments shows that whereas urea as a denaturant is best modeled as weakening both local and nonlocal interactions, trifluoro-ethanol is best modeled as mainly weakening HH interactions and slightly enhancing local helical interactions.

Alcohols↗

PubMed1992

Hydrogen bonding in globular proteins.

A global census of the hydrogen bonds in 42 X-ray-elucidated proteins was taken and the following demographic trends identified: (1) Most hydrogen bonds are local, i.e. between partners that are close in sequence, the primary exception being hydrogen-bonded ion pairs. (2) Most hydrogen bonds are between backbone atoms in the protein, an average of 68%. (3) All proteins studied have extensive hydrogen-bonded secondary structure, an average of 82%. (4) Almost all backbone hydrogen bonds are within single elements of secondary structure. An approximate rule of thirds applies: slightly more than one-third (37%) form i----i--3 hydrogen bonds, almost one-third (32%) form i----i--4 hydrogen bonds, and slightly less than one-third (26%) reside in paired strands of beta-sheet. The remaining 5% are not wholly within an individual helix, turn or sheet. (5) Side-chain to backbone hydrogen bonds are clustered at helix-capping positions. (6) An extensive network of hydrogen bonds is present in helices. (7) To a close approximation, the total number of hydrogen bonds is a simple function of a protein's helix and sheet content. (8) A unique quantity, termed the reduced number of hydrogen bonds, is defined as the maximum number of hydrogen bonds possible when every donor:acceptor pair is constrained to be 1:1. This quantity scales linearly with chain length, with 0.71 reduced hydrogen bond per residue. Implications of these results for pathways of protein folding are discussed.

Algorithms↗

PubMed1992

Temperature dependence of retention in reversed-phase liquid chromatography. 2. Mobile-phase considerations.

The retention mechanism in reversed-phase liquid chromatography (RPLC) has been examined over a wide temperature range with emphasis on the role of the mobile phase. van't Hoff plot shapes were used to assess the retention mechanism, and the data showed evidence of the hydrophobic effect when water-rich and/or hydrogen-bonded mobile phases such as methanol/water were used. However, different van't Hoff plot shape was observed with acetonitrile/water mobile phases, indicating a change in the retention mechanism. These data showed that the hydrophobic effect, which had previously been proposed as the driving force for retention, is not a satisfactory explanation for the retention process in all RPLC systems.

Chromatography, High Pressure Liquid↗

PubMed1992

Inverse protein folding problem: designing polymer sequences.

We consider the question of how to design proteins. How can we find "good" amino acid sequences (i) that fold to a desired "target" structure as a native conformation of lowest accessible free energy and (ii) that will not simultaneously fold to many other conformations of the same free energy? Current protein designs often focus on helix propensities and turns. We focus here on designing the hydrophobicity. For a model of self-avoiding hydrophobic/polar chains on two-dimensional square lattices, geometric proofs and exhaustive enumerations show the following results. (i) The strategy hydrophobic residues inside/polar residues outside is not optimal. Placement of additional hydrophobic residues on the surface is often necessary. (ii) To avoid unwanted conformations, the designed sequence must have neither too many nor too few hydrophobic residues. (iii) The computational complexity of inverse folding appears to be in a different class than folding: unlike the folding problem, the design problem does not scale exponentially with chain length. Some design strategies, described here for the lattice model, produce good sequences and scale only linearly with chain length.

Drug Design↗

PubMed1992

Modeling the effects of mutations on the denatured states of proteins.

We develop a model for the reversible denaturation of proteins and for the effects of single-site mutations on the denatured states. The model is based on short chains of sequences of H (hydrophobic) and P (other) monomers configured as self-avoiding walks on the two-dimensional square lattice. The N (native) state is defined as the unique conformation of lowest contact energy, whereas the D (denatured) state is defined as the collection of all other conformations. With this model we are able to determine the exact partition function, and thus the exact native-denatured equilibrium for various solvent conditions, using the computer to exhaustively enumerate every possible configuration. Previous studies confirm that this model shows many aspects of protein-like behavior. The present study attempts to model how the denatured state (1) depends on the amino acid sequence, and (2) is changed by single-site mutations. The model accounts for two puzzling experimental results: (1) the replacement of a polar residue by a hydrophobic amino acid on the surface of a protein can destabilize a native protein, and (2) the "denaturant slope," m = partial delta G/partial c (where c is the concentration of denaturant--urea, guanidine hydrochloride), can sometimes change by as much as 30% due to a single mutation. The principal conclusion of the present study is that, under strong folding conditions, the denatured conformations that are in equilibrium with the native state are not open random configurations. Instead, they are an ensemble of highly compact conformations with a distribution that depends on the residue sequence and that can be substantially altered by single mutations. Most importantly, we conclude that mutations can exert their dominant effects on protein stability by changing the entropy of folding.

Amino Acid Sequence↗

PubMed1992

Phospholipid interactions in model membrane systems. I. Experiments on monolayers.

We study the lateral headgroup interactions among phosphatidylcholine (PC) molecules and among phosphatidylethanolamine (PE) molecules in monolayers and extend our previous models. In this paper, we present an extensive set of pressure-area isotherms and surface potential experiments on monolayers of phospholipids ranging from 14 to 22 carbons in length at the n-heptane/water interface, over a wide range of temperature, salt concentration, and pH on the acid side. The pressure data presented here are a considerable extension of previous data (1) to higher surface densities, comprehensively checked for monolayer loss, and include new data on PE molecules. We explore surface densities ranging from extremely low to intermediate, near to the main phase transition, in which range the surface pressures and potentials are found to be independent of the chain length. Thus, these data bear directly on the headgroup interactions. These interactions are observed to be independent of ionic strength. PC and PE molecules differ strongly in two respects: (a) the lateral repulsion among PC molecules is much stronger than for PE, and (b) the lateral repulsion among PC molecules increases strongly with temperature whereas PE interactions are almost independent of temperature. Similarly, the surface potential for PC is found to increase with temperature whereas for PE it does not. In this and the following paper we show that these data from dilute to semidilute monolayers are consistent with a theoretical model that predicts that, independent of coverage, for PC the P-N+ dipole is oriented slightly into the oil phase because of the hydrophobicity of the methyl groups, increasingly so with temperature, whereas for PE the P-N+ dipole is directed into the water phase.

Electrochemistry↗

PubMed1992

Phospholipid interactions in model membrane systems. II. Theory.

We describe statistical thermodynamic theory for the lateral interactions among phospholipid head groups in monolayers and bilayers. Extensive monolayer experiments show that at low surface densities, PC head groups have strong lateral repulsions which increase considerably with temperature, whereas PE interactions are much weaker and have no significant temperature dependence (see the preceding paper). In previous work, we showed that the second virial coefficients for these interactions can be explained by: (a) steric repulsions among the head groups, and (b) a tilting of the P-N+ dipole of PC so that the N+ end enters the oil phase, to an extent that increases with temperature. It was also predicted that PE interactions should be weaker and less temperature dependent because the N+ terminal of the PE head-group is hydrophilic, hence, it is tilted into the water phase, so dipolar contributions among PE's are negligible due to the high dielectric constant of water. In the present work, we broaden the theory to treat phospholipid interactions up to higher lateral surface densities. We generalize the Hill interfacial virial expansion to account for dipoles and to include the third virial term. We show that to account for the large third virial coefficients for both PC and PE requires that the short range lateral attractions among the head groups also be taken into account. In addition, the third virial coefficient includes fluctuating head group dipoles, computed by Monte Carlo integration assuming pairwise additivity of the instantaneous pair potentials. We find that because the dipole fluctuations are correlated, the average triplet interactions do not equal the sum of the average dipole pair potentials. This is important for predicting, the magnitude and the independence of temperature of the third virial coefficients for PC. The consistency of the theory with data of both the second and the third virial coefficients extends the applicability of the head-group model to semiconcentrated monolayers, in agreement with the surface potential data in the foregoing paper.

Lipid Bilayers↗

PubMed1991

Solvent denaturation and stabilization of globular proteins.

Statistical thermodynamic theory has recently been developed to account for the stabilities of globular proteins. Here we extend that work to predict the effects of solvents on protein stability. Folding is assumed to be driven by solvophobic interactions and opposed by conformational entropy. The solvent dependence of the solvophobic interactions is taken from transfer experiments of Nozaki and Tanford on amino acids into aqueous solutions of urea or guanidine hydrochloride (GuHCl). On the basis of the assumption of two pathways involving collapse and formation of a core, the theory predicts that increasing denaturant should lead to a two-state denaturation transition (i.e., there is a stable state along each path separated by a free energy barrier). The denaturation midpoint is predicted to occur at higher concentrations of urea than of GuHCl. At neutral pH, the radius of the solvent-denatured state should be much smaller than for a random-flight chain and increase with either denaturant concentration or number of polar residues in the chain. A question of interest is whether free energies of folding should depend linearly on denaturant, as is often assumed. The free energy is predicted to be linear for urea but to have some small curvature for GuHCl. Predicted slopes and exposed areas of the unfolded states are found to be in generally good agreement with experiments. We also discuss stabilizing solvents and compare thermal with solvent denaturation.

Amino Acid Sequence↗

PubMed1991

Protein stability: electrostatics and compact denatured states.

Globular proteins can be denatured by changing pH and ionic strength. Much recent evidence has led to the surprising conclusion that there are two acid-denatured states: one highly unfolded and the other more compact, sometimes called the "molten globule." Here we describe a molecular theory for electrostatic stability of globular proteins based on the properties of the constituent amino acids: oil/water partition coefficients, pK values of the titratable groups, and their temperature dependences. Predicted denaturation temperatures vs. pH are in good agreement with experiments of other workers on myoglobin. The theory also predicts two populations of denatured species, one open and the other more compact, with densities in the range found experimentally for molten globular states. In addition, it predicts a phase diagram (stability vs. pH, ionic strength) in good agreement with experiments of Goto and Fink [Goto, Y. & Fink, A. L. (1989) Biochemistry 28, 945-952; and Goto, Y. & Fink, A. L. (1990) J. Mol. Biol. 214, 803-805]. The well-known salt destabilization of myoglobin has been generally considered evidence for ion pairing, but the present theory, based on smeared charge repulsion, explains the salt destabilization at low pH without ion pairing. In addition, for myoglobin the theory predicts salt stabilization at high pH, as observed for beta-lactamase by Goto and Fink.

Drug Stability↗

PubMed1991

The three states of globular proteins: acid denaturation.

We describe statistical mechanical theory that aims to predict protein stabilities as a function of temperature, pH, and salt concentration, from the physical properties of the constituent amino acids: (1) the number of nonpolar groups, (2) the chain length, (3) the temperature-dependent free energy of transfer, (4) the pKa's (including those in the native state) and their temperature dependencies. We calculate here the phase diagrams for apomyoglobin and hypothetical variant proteins. The theory captures essential features of protein stability including myoglobin's Tm vs pH as measured by P. L. Privalov [(1979) Advances in Protein Chemistry, Vol. 33, pp. 167-241] and its ionic strength vs pH phase diagram as measured by Y. Goto and A. L. Fink [(1990) Journal of Molecular Biology, Vol. 214, pp. 803-805]. The main predictions here are the following: (1) There are three stable states, corresponding to native (N), compact denatured (C), and highly unfolded (U), with transitions between them. (2) In agreement with experiments, the compact denatured state is predicted to have enthalpy closer to U than N because even though there is considerable hydrophobic "clustering" in C, this nevertheless represents a major loss of hydrophobic contacts relative to configurations (N) that have a hydrophobic "core." (3) C becomes more prominent in the phase diagram with increasing nonpolar content or decreasing chain length, perhaps thus accounting for (a) why lysozyme and alpha-lactalbumin differ in their denatured states, and (b) why shortened Staph nuclease molecules are compact. (4) Of major importance for protein calorimetry is Privalov's observation that the enthalpy of folding, delta H (T, pH) is independent of pH. The theory accounts for this through the prediction that the main electrostatic contribution to stability is not enthalpic; the main contribution is the entropy, mainly due to the different distributions of protons and small ions in the native and denatured states.

Apoproteins↗