Jon M. Sorenson

What can x-ray scattering tell us about the radial distribution functions of water?

We present an analysis of the Advanced Light Source (ALS) x-ray scattering experiment on pure liquid water at ambient temperature and pressure described in the preceding article. The present study discusses the extraction of radial distribution functions from the x-ray scattering of molecular fluids. It is proposed that the atomic scattering factors used to model water be modified to include the changes in the intramolecular electron distribution caused by chemical bonding effects. Based on this analysis we present a gOO(r) for water consistent with our recent experimental data gathered at the ALS, which differs in some aspects from the gOO(r) reported by other x-ray and neutron scattering experiments. Our gOO(r) exhibits a taller and sharper first peak, and systematic shifts in all peak positions to smaller r. Based on experimental uncertainties, we discuss what features of gOO(r) should be reproduced by classical simulations of nonpolarizable and polarizable water models, as well as ab initio simulation...

A high-quality x-ray scattering experiment on liquid water at ambient conditions

We report a new, high-quality x-ray scattering experiment on pure ambient water using a synchrotron beam line at the Advanced Light Source at Lawrence Berkeley National Laboratory. Several factors contribute to the improved quality of our intensity curves including use of a highly monochromatic source, a well-characterized polarization correction, a Compton scattering correction that includes electron correlation, and more accurate intensities using a modern charge coupled device (CCD) detector. We provide a comprehensive description of the data processing that we have used for correcting systematic errors, and we provide an estimate of our remaining random errors. The resulting error estimates of our data are smaller then the discrepancies between data sets collected in past x-ray experiments. We find that the older x-ray curves support a family of gOO(r)’s that exhibit a smaller first peak (∼2.2), while the current data is better fit with a family of gOO(r)’s with a first peak height of 2.8, and systema...

Toward minimalist models of larger proteins: a ubiquitin-like protein.

Our recently developed off‐lattice bead model capable of simulating protein structures with mixed α/β content has been extended to model the folding of a ubiquitin‐like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant‐temperature Langevin dynamics simulations and sampling with the multiple multi‐histogram method over five‐order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C‐terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi‐exponential below the folding temperature, with glass‐like kinetics appearing at T/Tf ∼ 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic‐scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces. Proteins 2002;46:368–379.

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an a/~ protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multi-histogram method combined with constant-tempera ture Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--si milar to experiments on protein G, and one pathway contains no intermediates--s imilar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus non-local interactions in various fold classes, addressing the effect of sequence Permission to make dtgltal or hard copras of all or part oftlus work for pe~sonat or classroom use ~s granted without lee prm, lded that copies are not made or dmtnbutcd for profit ol eommc~cml advantage and that copras bear th~s notme and the full c~tatlon on the first page 1o copy otherwise, to repubhsh, to post on servers or to redistribute to hsts. requires prior specll]C permission and/or a tee

Differences in hydration structure near hydrophobic and hydrophilic amino acids

We use molecular dynamics to simulate recent neutron scattering experiments on aqueous solutions of N-acetyl-leucine-amide and N-acetyl-glutamine-amide, and break down the total scattering function into contributions from solute-solute, solute-water, water-water, and intramolecular correlations. We show that the shift of the main diffraction peak to smaller angle that is observed for leucine, but not for glutamine, is attributable primarily to alterations in water-water correlations relative to bulk. The perturbation of the water hydrogen-bonded network extends roughly two solvation layers from the hydrophobic side chain surface, and is characterized by a distribution of hydrogen bonded ring sizes that are more planar and are dominated by pentagons in particular than those near the hydrophilic side chain. The different structural organization of water near the hydrophobic solute that gives rise to the inward shift in the main neutron diffraction peak under ambient conditions may also provide insight into the same directional shift for pure liquid water as it is cooled and supercooled.

Protein Engineering Study of Protein L by Simulation

We examine the ability of our recently introduced minimalist protein model to reproduce experimentally measured thermodynamic and kinetic changes upon sequence mutation in the well-studied immunoglobulin-binding protein L. We have examined five different sequence mutations of protein L that are meant to mimic the same mutation type studied experimentally: two different mutations which disrupt the natural preference in the beta-hairpin #1 and beta-hairpin #2 turn regions, two different helix mutants where a surface polar residue in the alpha-helix has been mutated to a hydrophobic residue, and a final mutant to further probe the role of nonnative hydrophobic interactions in the folding process. These simulated mutations are analyzed in terms of various kinetic and thermodynamic changes with respect to wild type, but in addition we evaluate the structure-activity relationship of our model protein based on the phi-value calculated from both the kinetic and thermodynamic perspectives. We find that the simulated thermodynamic phi-values reproduce the experimental trends in the mutations studied and allow us to circumvent the difficult interpretation of the complicated kinetics of our model. Furthermore, the level of resolution of the model allows us to directly predict what experiments seek in regard to protein engineering studies of protein folding--namely the residues or portions of the polypeptide chain that contribute to the crucial step in the folding of the wild-type protein.

Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach

An off‐lattice 46‐bead model of a small all‐β protein has been recently criticized for possessing too many traps and long‐lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the β‐sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first‐passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the Tf > Tg sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics. Proteins 1999;37:582–591. Published 1999 Wiley‐Liss, Inc.

The importance of hydration for the kinetics and thermodynamics of protein folding: simplified lattice models

BACKGROUND Recent studies have proposed various sources for the origin of cooperativity in simplified protein folding models. Important contributions to cooperativity that have been discussed include backbone hydrogen bonding, sidechain packing and hydrophobic interactions. Related work has also focused on which interactions are responsible for making the free energy of the native structure a pronounced global minimum in the free energy landscape. In addition, two-flavor bead models have been found to exhibit poor folding cooperativity and often lack unique native structures. We propose a simple multibody description of hydration with expectations that it might modify the free energy surface in such a way as to increase the cooperativity of folding and improve the performance of two-flavor models. RESULTS We study the thermodynamics and kinetics of folding for designed 36-mer sequences on a cubic lattice using both our solvation model and the corresponding model without solvation terms. Degeneracies of the native states are studied by enumerating the maximally compact states. The histogram Monte Carlo method is used to obtain folding temperatures, densities of states and heat capacity curves. Folding kinetics are examined by accumulating mean first-passage times versus temperature. Sequences in the proposed solvation model are found to have more unique ground states, fold faster and fold with more cooperativity than sequences in the nonsolvation model. CONCLUSIONS We find that the addition of a multibody description of solvation can improve the poor performance of two-flavor lattice models and provide an additional source for more cooperative folding. Our results suggest that a better description of solvation will be important for future theoretical protein folding studies.

Solution X-ray scattering as a probe of hydration-dependent structuring of aqueous solutions

We report on new X-ray solution scattering experiments and molecular dynamics simulations conducted for increasing solute concentrations of N-acetyl-amino acid-amides and -methylamides in water, for the amino acids leucine, glutamine, and glycine. As the concentration increases, the main diffraction peak of pure water at Q = 2.0 A-1 shifts to smaller angle for the larger leucine and glutamine amino acids, and a new diffraction peak grows in at Q ∼ 0.8 A-1 for only the hydrophobic amino acid leucine. The unaltered value of the peak position at Q ∼ 0.8 A-1 over a large concentration range suggests that a stable and ordered leucine solute–solute distribution is sustained. Simulations of the distributions of leucines in water that reproduce the experimental observable show that mono-dispersed to small molecular aggregates of two to six hydrophobic amino acids are formed, as opposed to complete segregation of the hydrophobic solutes into one large cluster. The scattering results for the hydrophobic leucine amino acid are contrasted with experiments and simulations of the model hydrophilic side chain glutamine and the model backbone glycine. The self-assembly process of protein folding modeled with these experiments, in particular the condensation to a hydrophobic core, shares similar issues with the desolvation phenomena that are important in drug discovery.