Biomedical subjects

Ken A Dill

Publications and source records attributed to Ken A Dill.

16 recordsLinked to original sources

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↗

PubMed2003

Folding kinetics of two-state proteins: effect of circularization, permutation, and crosslinks.

Protein folding kinetics has recently been probed by clever experiments using circular permutants and other topological mutations. A circular permutant is created from a wild-type protein by covalently linking together the chain ends and cleaving elsewhere in the chain. An interesting puzzle is why circular permutation causes no apparent change in the folding mechanism of CI2, but dramatic changes in the folding mechanisms of S6 and of an SH3 domain, as determined by Phi-value experiments. Here, we use a computational model to predict the folding routes of topological variants, based on a measure (effective contact order) of the chain entropy loss at each folding step. The predictions are consistent with the experiments, leading to insights into the folding routes and into the meaning of Phi-values in general. We find that Phi-values do not always describe time sequences of folding events, or positions along a single reaction coordinate; rather, Phi reflects only the degree of rate control. For example, the circular permutant P(40-41) of CI2 is predicted to reverse the time sequence of the formation of beta(1)beta(4) relative to beta(2)beta(3), without changing the diffuse Phi-value distribution, while the circular permutant P(13-14) of S6 switches the rate-limiting step from the formation of beta(1)beta(4) to beta(1)beta(3), changing the Phi-value distribution from diffuse to strongly polarized. As a test of the model, we propose mutations that should reverse these outcomes.

Entropy↗

PubMed2003

Folding rates and low-entropy-loss routes of two-state proteins.

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.

Animals↗

PubMed2003

MOPED: method for optimizing physical energy parameters using decoys.

We present a method called MOPED for optimizing energetic and structural parameters in computational models, including all-atom energy functions, when native structures and decoys are given. The present method goes beyond previous approaches in treating energy functions that are nonlinear in the parameters and continuous in the degrees of freedom. We illustrate the method by improving solvation parameters in the energy function EEF1, which consists of the CHARMM19 polar hydrogen force field augmented by a Gaussian solvation term. Although the published parameters for EEF1 correctly discriminate the native from decoys in the decoy sets of Levitt et al., they fail on several of the more difficult decoy sets of Baker et al. MOPED successfully finds improved parameters that allow EEF1 to discriminate native from decoy structures on all protein structures that do not have metals or prosthetic groups.

Algorithms↗

PubMed2003

Computing the transition state populations in simple protein models.

We describe the master equation method for computing the kinetics of protein folding. We illustrate the method using a simple Go model. Presently most models of two-state fast-folding protein folding kinetics invoke the classical idea of a transition state to explain why there is a single exponential decay in time. However, if proteins fold via funnel-shaped energy landscapes, as predicted by many theoretical studies, then it raises the question of what is the transition state. Is it a specific structure, or a small ensemble of structures, as is expected from classical transition state theory? Or is it more like the denatured states of proteins, a very broad ensemble? The answer that is usually obtained depends on the assumptions made about the transition state. The present method is a rigorous way to find transition states, without assumptions or approximations, even for very nonclassical shapes of energy landscapes. We illustrate the method here, showing how the transition states in two-state protein folding can be very broad ensembles.

Kinetics↗

PubMed2003

A simple analytical model of water.

Water is an unusual liquid. It expands upon freezing, has minima in its volume, heat capacity, and isothermal compressibility with temperature, and shows signs of a first-order phase transition when supercooled. These anomalies disappear at high pressures. We review a recent analytical theory that predicts water's thermal properties and the main features of its phase diagram, including multiple crystalline phases and a fluid-fluid transition in the supercooled liquid. It also predicts a fragile-to-strong crossover in supercooled water's temperature-dependent relaxation processes. The theory is based on a simplified model for how triplets of waters interact via hydrogen bonds, steric repulsions, and dispersion attractions. It is designed to give simple insights into the microscopic origins of water's properties.

Hydrogen Bonding↗

PubMed2003

Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures.

We investigate a novel approach for studying the kinetics of protein folding. Our framework has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMs) that have been applied in many diverse fields with great success. In our previous work, we presented our PRM-based technique and obtained encouraging results studying protein folding pathways for several small proteins. In this paper, we describe how our motion planning framework can be used to study protein folding kinetics. In particular, we present a refined version of our PRM-based framework and describe how it can be used to produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap which is computed in a few hours on a desktop PC. Results are presented for 14 proteins. Our ability to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics, such as proteins that exhibit both two-state and three-state kinetics that are not captured by other theoretical techniques.

Computational Biology↗

PubMed2003

A path planning-based study of protein folding with a case study of hairpin formation in protein G and L.

We investigate a novel approach for studying protein folding that has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMS). Our focus is to study issues related to the folding process, such as the formation of secondary and tertiary structure, assuming we know the native fold. A feature of our PRM-based framework is that the large sets of folding pathways in the roadmaps it produces, in a few hours on a desktop PC, provide global information about the protein's energy landscape. This is an advantage over other simulation methods such as molecular dynamics or Monte Carlo methods which require more computation and produce only a single trajectory in each run. In our initial studies, we obtained encouraging results for several small proteins. In this paper, we investigate more sophisticated techniques for analyzing the folding pathways in our roadmaps. In addition to more formally revalidating our previous results, we present a case study showing our technique captures known folding differences between the structurally similar proteins G and L.

Bacterial Proteins↗

PubMed2002

Potential of mean force between two hydrophobic solutes in water.

We study the potential of mean force between two nonpolar solutes in the Mercedes Benz model of water. Using NPT Monte Carlo simulations, we find that the solute size determines the relative preference of two solute molecules to come into contact ('contact minimum') or to be separated by a single layer of water ('solvent-separated minimum'). Larger solutes more strongly prefer the contacting state, while smaller solutes have more tendency to become solvent-separated, particularly in cold water. The thermal driving forces oscillate with solute separation. Contacts are stabilized by entropy, whereas solvent-separated solute pairing is stabilized by enthalpy. The free energy of interaction for small solutes is well-approximated by scaled-particle theory.

Monte Carlo Method↗

PubMed2002

How ions affect the structure of water.

We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.

Computer Simulation↗

PubMed2002

The elastic net algorithm and protein structure prediction.

Predicting protein structures from their amino acid sequences is a problem of global optimization. Global optima (native structures) are often sought using stochastic sampling methods such as Monte Carlo or molecular dynamics, but these methods are slow. In contrast, there are fast deterministic methods that find near-optimal solutions of well-known global optimization problems such as the traveling salesman problem (TSP). But fast TSP strategies have yet to be applied to protein folding, because of fundamental differences in the two types of problems. Here, we show how protein folding can be framed in terms of the TSP, to which we apply a variation of the Durbin-Willshaw elastic net optimization strategy. We illustrate using a simple model of proteins with database-derived statistical potentials and predicted secondary structure restraints. This optimization strategy can be applied to many different models and potential functions, and can readily incorporate experimental restraint information. It is also fast; with the simple model used here, the method finds structures that are within 5-6 A all-Calpha-atom RMSD of the known native structures for 40-mers in about 8 s on a PC; 100-mers take about 20 s. The computer time tau scales as tau approximately n, where n is the number of amino acids. This method may prove to be useful for structure refinement and prediction.

Algorithms↗

PubMed2002

Fast-folding protein kinetics, hidden intermediates, and the sequential stabilization model.

Do two-state proteins fold by pathways or funnels? Native-state hydrogen exchange experiments show discrete nonnative structures in equilibrium with the native state. These could be called hidden intermediates (HI) because their populations are small at equilibrium, and they are not detected in kinetic experiments. HIs have been invoked as disproof of funnel models, because funnel pictures appear to indicate (1) no specific sequences of events in folding; (2) a continuum, rather than a discrete ladder, of structures; and (3) smooth landscapes. In the present study, we solve the exact dynamics of a simple model. We find, instead, that the present microscopic model is indeed consistent with HIs and transition states, but such states occur in parallel, rather than along the single pathway predicted by the sequential stabilization model. At the microscopic level, we observe a huge multiplicity of trajectories. But at the macroscopic level, we observe two pathways of specific sequences of events that are relatively traditional except that they are in parallel, so there is not a single reaction coordinate. Using singular value decomposition, we show an accurate representation of the shapes of the model energy landscapes. They are highly complex funnels.

Hydrogen-Ion Concentration↗

PubMedDate not supplied

Incorporation of chemoselective functionalities into peptoids via solid-phase submonomer synthesis.

A simple route to the introduction of a number of chemoselective functional groups into peptoids (oligo(N-substituted glycines)) by an extension of the standard solid-phase submonomer method is reported. The following groups were introduced: aminooxyacetamide, N-(carbamoylmethyl)acetohydrazide, mercaptoacetamide, 2-pyridinesulfenylmercaptoacetamide, and aldehyde-terminated peptoids. The method uses commercially available reagents, is fully compatible with standard peptoid submonomer synthesis conditions, is easily automated, and generates the desired functionalized peptoid in high yield and purity. Peptoids with suitable pairs of chemoselective ligation groups were joined in high yield.

Chromatography, High Pressure Liquid↗