Biomedical subjects

Ken A Dill

Publications and source records attributed to Ken A Dill.

At least 19 recordsLinked to original sources

PubMed2007

Exploring zipping and assembly as a protein folding principle.

It has been proposed that proteins fold by a process called "Zipping and Assembly" (Z&A). Zipping refers to the growth of local substructures within the chain, and assembly refers to the coming together of already-formed pieces. Our interest here is in whether Z&A is a general method that can fold most of sequence space, to global minima, efficiently. Using the HP model, we can address this question by enumerating full conformation and sequence spaces. We find that Z&A reaches the global energy minimum native states, even though it searches only a very small fraction of conformational space, for most sequences in the full sequence space. We find that Z&A, a mechanism-based search, is more efficient in our tests than the replica exchange search method. Folding efficiency is increased for chains having: (a) small loop-closure steps, consistent with observations by Plaxco et al. 1998;277;985-994 that folding rates correlate with contact order, (b) neither too few nor too many nucleation sites per chain, and (c) assembly steps that do not occur too early in the folding process. We find that the efficiency increases with chain length, although our range of chain lengths is limited. We believe these insights may be useful for developing faster protein conformational search algorithms.

Algorithms↗

PubMed2007

Routes are trees: the parsing perspective on protein folding.

An important puzzle in structural biology is the question of how proteins are able to fold so quickly into their unique native structures. There is much evidence that protein folding is hierarchic. In that case, folding routes are not linear, but have a tree structure. Trees are commonly used to represent the grammatical structure of natural language sentences, and chart parsing algorithms efficiently search the space of all possible trees for a given input string. Here we show that one such method, the CKY algorithm, can be useful both for providing novel insight into the physical protein folding process, and for computational protein structure prediction. As proof of concept, we apply this algorithm to the HP lattice model of proteins. Our algorithm identifies all direct folding route trees to the native state and allows us to construct a simple model of the folding process. Despite its simplicity, our model provides an account for the fact that folding rates depend only on the topology of the native state but not on sequence composition.

Algorithms↗

PubMed2006

Transition-states in protein folding kinetics: the structural interpretation of Phi values.

Phi values are experimental measures of the effects of mutations on the folding kinetics of a protein. A central question is what structural information Phi values give about the transition-state of folding. Traditionally, a Phi value is interpreted as representing the "nativeness" of a mutated residue in the transition-state. However, this interpretation is often problematic. We present here a better structural interpretation of Phi values for mutations within a given helix. Our interpretation is based on a simple physical model that distinguishes between secondary and tertiary free energy contributions of helical residues. From a linear fit of the model to experimental data, we obtain two structural parameters: the extent of helix formation in the transition-state, and the nativeness of tertiary interactions in the transition-state. We apply the model to all proteins with well-characterized helices for which more than 10 Phi values are available: protein A, CI2, and protein L. The model is simple to apply to experimental data, captures nonclassical Phi values <0 or >1 in these helices, and explains how different mutations at a given site can lead to different Phi values.

DNA-Binding Proteins↗

PubMed2006

On the use of orientational restraints and symmetry corrections in alchemical free energy calculations.

Alchemical free energy calculations are becoming a useful tool for calculating absolute binding free energies of small molecule ligands to proteins. Here, we find that the presence of multiple metastable ligand orientations can cause convergence problems when distance restraints alone are used. We demonstrate that the use of orientational restraints can greatly accelerate the convergence of these calculations. However, even with this acceleration, we find that sufficient sampling requires substantially longer simulations than are used in many published protocols. To further accelerate convergence, we introduce a new method of configuration space decomposition by orientation which reduces required simulation lengths by at least a factor of 5 in the cases examined. Our method is easily parallelizable, well suited for cases where a ligand cocrystal structure is not available, and can utilize initial orientations generated by docking packages.

Biophysics↗

PubMed2006

Folding very short peptides using molecular dynamics.

Peptides often have conformational preferences. We simulated 133 peptide 8-mer fragments from six different proteins, sampled by replica-exchange molecular dynamics using Amber7 with a GB/SA (generalized-Born/solvent-accessible electrostatic approximation to water) implicit solvent. We found that 85 of the peptides have no preferred structure, while 48 of them converge to a preferred structure. In 85% of the converged cases (41 peptides), the structures found by the simulations bear some resemblance to their native structures, based on a coarse-grained backbone description. In particular, all seven of the beta hairpins in the native structures contain a fragment in the turn that is highly structured. In the eight cases where the bioinformatics-based I-sites library picks out native-like structures, the present simulations are largely in agreement. Such physics-based modeling may be useful for identifying early nuclei in folding kinetics and for assisting in protein-structure prediction methods that utilize the assembly of peptide fragments.

Biophysical Phenomena↗

PubMed2005

Surfaces affect ion pairing.

In water, positive ions attract negative ions. That attraction can be modulated if a hydrophobic surface is present near the two ions in water. Using computer simulations with explicit and implicit water, we study how an ion embedded on a hydrophobic surface interacts with another nearby ion in water. Using hydrophobic surfaces with different curvatures, we find that the contact interaction between a positive and negative ion is strongly affected by the curvature of an adjacent surface, either stabilizing or destabilizing the ion pair. We also find that the solvent-separated ion pair (SSIP) can be made more stable than the contacting ion pair by the presence of a surface. This may account for why bridging waters are often found in protein crystal structures. We also note that implicit solvent models do not account for SSIPs. Finally, we find that there are charge asymmetries: an embedded positive charge attracting a negative ion is different than an embedded negative charge attracting a positive ion. Such asymmetries are also not predicted by implicit solvent models. These results may be useful for improving computational models of solvation in biology and chemistry.

Computer Simulation↗

PubMed2005

Water's hydrogen bonds in the hydrophobic effect: a simple model.

We propose a simple analytical model to account for water's hydrogen bonds in the hydrophobic effect. It is based on computing a mean-field partition function for a water molecule in the first solvation shell around a solute molecule. The model treats the orientational restrictions from hydrogen bonding, and utilizes quantities that can be obtained from bulk water simulations. We illustrate the principles in a 2-dimensional Mercedes-Benz-like model. Our model gives good predictions for the heat capacity of hydrophobic solvation, reproduces the solvation energies and entropies at different temperatures with only one fitting parameter, and accounts for the solute size dependence of the hydrophobic effect. Our model supports the view that water's hydrogen bonding propensity determines the temperature dependence of the hydrophobic effect. It explains the puzzling experimental observation that dissolving a nonpolar solute in hot water has positive entropy.

Algorithms↗

PubMed2005

Rotational superposition and least squares: the SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller.

We clarify once again that Kabsch's method and the Quaternion method are mathematically equivalent methods, that is, that they contain identical information and, when properly understood and applied, lead to identical answers to any questions regarding least-squares rotational superposition, either by proper rotations or by rotation-reflections. We also provide the correct bounds for the eigenvalue spectrum.

Algorithms↗

PubMed2005

Folding a nonbiological polymer into a compact multihelical structure.

The only molecules that are currently known to fold into unique three-dimensional conformations and perform sophisticated functions are biological polymers - proteins and some RNA molecules. Our aim is to create a nonbiological sequence-specific polymer that folds in aqueous solution. Toward that end, we synthesized sequence-specific 30mer, 45mer, and 60mer peptoid oligomers (N-substituted glycine polymers) consisting of 15mer units we chained together by disulfide and oxime linkages to mimic the helical bundle structures commonly found in proteins. Because these 15mer sequences were previously shown to form defined helical structures that aggregate together at submillimolar concentrations, we expected that by covalently linking multiple 15mers together, they might fold as helical bundles. To probe whether they folded, we used fluorescence resonance energy transfer (FRET) reporter groups. We found that certain constructs fold up with a hydrophobic core and have cooperative folding transitions. Such molecules may ultimately provide a platform for designing specific functions resembling those of proteins.

Chromatography, High Pressure Liquid↗

PubMed2005

Phi values in protein-folding kinetics have energetic and structural components.

Phi values are experimental measures of how the kinetics of protein folding is changed by single-site mutations. Phi values measure energetic quantities, but they are often interpreted in terms of the structures of the transition-state ensemble. Here, we describe a simple analytical model of the folding kinetics in terms of the formation of protein substructures. The model shows that Phi values have both structural and energetic components. It also provides a natural and general interpretation of "nonclassical" Phi values (i.e., < 0 or > 1). The model reproduces the Phi values for 20 single-residue mutations in the alpha-helix of the protein CI2, including several nonclassical Phi values, in good agreement with experiments.

Kinetics↗

PubMed2005

Comprehensive analysis of protein folding activation thermodynamics reveals a universal behavior violated by kinetically stable proteases.

Alpha-lytic protease (alpha LP) and Streptomyces griseus protease B (SGPB) are two extracellular serine proteases whose folding is absolutely dependent on the existence of their companion pro regions. Moreover, the native states of these proteins are, at best, marginally stable, with the apparent stability resulting from being kinetically trapped in the native state by large barriers to unfolding. Here, in an effort to understand the physical properties that distinguish kinetically and thermodynamically stable proteins, we study the temperature-dependences of the folding and unfolding kinetics of alpha LP and SGPB without their pro regions, and compare their behavior to a comprehensive set of other proteins. For the folding activation thermodynamics, we find some remarkable universal behaviors in the thermodynamically stable proteins that are violated dramatically by alpha LP. Despite significant variations in deltaC(P,F)++, the maximal folding speed occurs within the narrow biological temperature range for all proteins, except for alpha LP, with its maximal folding speed shifted lower by 200 K. This implies evolutionary pressures on folding speed for typical proteins, but not for alpha LP. In addition, the folding free energy barrier in the biological temperature range for most proteins is predominantly enthalpic, but purely entropic for alpha LP. The unfolding of alpha LP and SGPB is distinguished by three properties: a remarkably large deltaC(P,U)++, a very high deltaG(U)++, and a maximum deltaG(u)++ at the optimal growth temperature for the organism. While other proteins display each of these traits to some approximation, the simultaneous optimization of all three occurs only in the kinetically stable proteins, and appears to be required to maximize their unfolding cooperativity, by suppressing local unfolding events, and slowing the rate of global unfolding. Together, these properties extend the lifetime of these enzymes in the highly proteolytic extracellular environment. Attaining such functional properties seems possible only through the gross perturbation of the folding thermodynamics, which in turn has required the co-evolution of pro regions as folding catalysts.

Bacterial Proteins↗

PubMed2005

The flexibility in the proline ring couples to the protein backbone.

In proteins, the proline ring exists predominantly in two discrete states. However, there is also a small but significant amount of flexibility in the proline ring of high-resolution protein structures. We have found that this side-chain flexibility is coupled to the backbone conformation. To study this coupling, we have developed a model that is simply based on geometric and steric factors and not on energetics. We show that the coupling between phi and chi1 torsions in the proline ring can be described by an analytic equation that was developed by Bricard in 1897, and we describe a computer algorithm that implements the equation. The model predicts the observed coupling very well. The strain in the C(gamma)-C(delta)-N angle appears to be the principal barrier between the UP and DOWN pucker. This strain is relaxed to allow the proline ring to flatten in the rare PLANAR conformation.

Algorithms↗

PubMed2005

Modeling water, the hydrophobic effect, and ion solvation.

Water plays a central role in the structures and properties of biomolecules--proteins, nucleic acids, and membranes--and in their interactions with ligands and drugs. Over the past half century, our understanding of water has been advanced significantly owing to theoretical and computational modeling. However, like the blind men and the elephant, different models describe different aspects of water's behavior. The trend in water modeling has been toward finer-scale properties and increasing structural detail, at increasing computational expense. Recently, our labs and others have moved in the opposite direction, toward simpler physical models, focusing on more global properties-water's thermodynamics, phase diagram, and solvation properties, for example-and toward less computational expense. Simplified models can guide a better understanding of water in ways that complement what we learn from more complex models. One ultimate goal is more tractable models for computer simulations of biomolecules. This review gives a perspective from simple models on how the physical properties of water-as a pure liquid and as a solvent-derive from the geometric and hydrogen bonding properties of water.

Biophysics↗

PubMed2004

Using quaternions to calculate RMSD.

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well-known formula due to Kabsch. We analyze the various cases that may arise, and give a complete enumeration of the special cases in terms of the arrangement of the eigenvalues of a traceless, 4 x 4 symmetric matrix. A key result here is an expression for the gradient of the RMSD as a function of model parameters. This can be useful, for example, in finding the minimum energy path of a reaction using the elastic band methods or in optimizing model parameters to best fit a target structure.

Algorithms↗

PubMed2004

A kinematic view of loop closure.

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.

Journal Article↗

PubMed2004

Cooperativity in two-state protein folding kinetics.

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.

Algorithms↗

PubMed2003

Structural and spectroscopic studies of peptoid oligomers with alpha-chiral aliphatic side chains.

Substantial progress has been made in the synthesis and characterization of various oligomeric molecules capable of autonomous folding to well-defined, repetitive secondary structures. It is now possible to investigate sequence-structure relationships and the driving forces for folding in these systems. Here, we present detailed analysis by X-ray crystallography, NMR, and circular dichroism (CD) of the helical structures formed by N-substituted glycine (or "peptoid") oligomers with alpha-chiral, aliphatic side chains. The X-ray crystal structure of a N-(1-cyclohexylethyl)glycine pentamer, the first reported for any peptoid, shows a helix with cis-amide bonds, approximately 3 residues per turn, and a pitch of approximately 6.7 A. The backbone dihedral angles of this pentamer are similar to those of a polyproline type I peptide helix, in agreement with prior modeling predictions. This crystal structure likely represents the major solution conformers, since the CD spectra of analogous peptoid hexamers, dodecamers, and pentadecamers, composed entirely of either (S)-N-(1-cyclohexylethyl)glycine or (S)-N-(sec-butyl)glycine monomers, also have features similar to those of the polyproline type I helix. Furthermore, this crystal structure is similar to a solution NMR structure previously described for a peptoid pentamer comprised of chiral, aromatic side chains, which suggests that peptoids containing either aromatic or aliphatic alpha-chiral side chains adopt fundamentally similar helical structures in solution, despite distinct CD spectra. The elucidation of detailed structural information for peptoid helices with alpha-chiral aliphatic side chains will facilitate the mimicry of biomolecules, such as transmembrane protein domains, in a distinctly stable form.

Circular Dichroism↗

PubMed2003

Fast protein folding kinetics.

Proteins are complex molecules, yet their folding kinetics is often fast (microseconds) and simple, involving only a single exponential function of time (called two-state kinetics). The main model for two-state kinetics has been transition-state theory, where an energy barrier defines a slow step to reach an improbable structure. But how can barriers explain fast processes, such as folding? We study a simple model with rigorous kinetics that explains the high speed instead as a result of the microscopic parallelization of folding trajectories. The single exponential results from a separation of timescales; the parallelization of routes is high at the start of folding and low thereafter. The ensemble of rate-limiting chain conformations is different from in transition-state theory; it is broad, overlaps with the denatured state, is not aligned along a single reaction coordinate, and involves well populated, rather than improbable, structures.

Kinetics↗