Troy Cellmer

Chemical, physical, and theoretical kinetics of an ultrafast folding protein

An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein—the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models—a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 105 possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 105 microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models.

Measuring internal friction of an ultrafast-folding protein

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.

Extracting rate coefficients from single-molecule photon trajectories and FRET efficiency histograms for a fast-folding protein.

Recently developed statistical methods by Gopich and Szabo were used to extract folding and unfolding rate coefficients from single-molecule Förster resonance energy transfer (FRET) data for proteins with kinetics too fast to measure waiting time distributions. Two types of experiments and two different analyses were performed. In one experiment bursts of photons were collected from donor and acceptor fluorophores attached to a 73-residue protein, α(3)D, freely diffusing through the illuminated volume of a confocal microscope system. In the second, the protein was immobilized by linkage to a surface, and photons were collected until one of the fluorophores bleached. Folding and unfolding rate coefficients and mean FRET efficiencies for the folded and unfolded subpopulations were obtained from a photon by photon analysis of the trajectories using a maximum likelihood method. The ability of the method to describe the data in terms of a two-state model was checked by recoloring the photon trajectories with the extracted parameters and comparing the calculated FRET efficiency histograms with the measured histograms. The sum of the rate coefficients for the two-state model agreed to within 30% with the relaxation rate obtained from the decay of the donor-acceptor cross-correlation function, confirming the high accuracy of the method. Interestingly, apparently reliable rate coefficients could be extracted using the maximum likelihood method, even at low (<10%) population of the minor component where the cross-correlation function was too noisy to obtain any useful information. The rate coefficients and mean FRET efficiencies were also obtained in an approximate procedure by simply fitting the FRET efficiency histograms, calculated by binning the donor and acceptor photons, with a sum of three-Gaussian functions. The kinetics are exposed in these histograms by the growth of a FRET efficiency peak at values intermediate between the folded and unfolded peaks as the bin size increases, a phenomenon with similarities to NMR exchange broadening. When comparable populations of folded and unfolded molecules are present, this method yields rate coefficients in very good agreement with those obtained with the maximum likelihood method. As a first step toward characterizing transition paths, the Viterbi algorithm was used to locate the most probable transition points in the photon trajectories.

Making connections between ultrafast protein folding kinetics and molecular dynamics simulations

Determining the rate of forming the truly folded conformation of ultrafast folding proteins is an important issue for both experiments and simulations. The double-norleucine mutant of the 35-residue villin subdomain is the focus of recent computer simulations with atomistic molecular dynamics because it is currently the fastest folding protein. The folding kinetics of this protein have been measured in laser temperature-jump experiments using tryptophan fluorescence as a probe of overall folding. The conclusion from the simulations, however, is that the rate determined by fluorescence is significantly larger than the rate of overall folding. We have therefore employed an independent experimental method to determine the folding rate. The decay of the tryptophan triplet-state in photoselection experiments was used to monitor the change in the unfolded population for a sequence of the villin subdomain with one amino acid difference from that of the laser temperature-jump experiments, but with almost identical equilibrium properties. Folding times obtained in a two-state analysis of the results from the two methods at denaturant concentrations varying from 1.5–6.0 M guanidinium chloride are in excellent agreement, with an average difference of only 20%. Polynomial extrapolation of all the data to zero denaturant yields a folding time of 220 (+100,-70) ns at 283 K, suggesting that under these conditions the barrier between folded and unfolded states has effectively disappeared—the so-called “downhill scenario.”

Evidence of multiple folding pathways for the villin headpiece subdomain.

The defining property of two-state models of protein folding is that the measured relaxation rates are independent of the starting conditions and only depend on the final conditions. In this work we compare the kinetics of the very fast folding villin subdomain measured after a large change in denaturant concentration using an ultrarapid microfluidic mixer with the kinetics measured after a small temperature change in a laser T-jump experiment and find a significant difference in the observed folding kinetics. The final conditions of temperature and denaturant concentration and the use of tryptophan fluorescence as a probe are the same in both experiments, while the initial conditions are very different. The slower mixing kinetics show no evidence of the faster phase in T-jump experiments, which would support models of on- or off-pathway intermediates. Rather we interpret the combined mixer and T-jump experiments as evidence of an ensemble of unfolded states, some of which are traps. The ensemble after dilution from high denaturant is more expanded than the ensemble after an increase in temperature and, on average, takes longer to reach the native state.

Kinetic assay shows that increasing red cell volume could be a treatment for sickle cell disease

Significance Sickle cell disease can be treated by preventing polymerization of the mutant hemoglobin to form fibers during the time that red cells are transiting the smallest vessels of the tissues. However, most drugs in clinical trials are aimed at reducing the sequelae of fiber formation, such as inflammation and adhesion to the vascular endothelium. Searching for drugs that increase the delay before polymerization, which allows more cells to escape the small vessels before fibers form, has been hampered by the lack of a quantitative and sensitive assay, which we describe in this work. With this assay, we show that increasing the delay time by increasing red cell volume to reduce the intracellular hemoglobin concentration is a viable approach to therapy. Although it has been known for more than 60 years that the cause of sickle cell disease is polymerization of a hemoglobin mutant, hydroxyurea is the only drug approved for treatment by the US Food and Drug Administration. This drug, however, is only partially successful, and the discovery of additional drugs that inhibit fiber formation has been hampered by the lack of a sensitive and quantitative cellular assay. Here, we describe such a method in a 96-well plate format that is based on laser-induced polymerization in sickle trait cells and robust, automated image analysis to detect the precise time at which fibers distort (“sickle”) the cells. With this kinetic method, we show that small increases in cell volume to reduce the hemoglobin concentration can result in therapeutic increases in the delay time prior to fiber formation. We also show that, of the two drugs (AES103 and GBT440) in clinical trials that inhibit polymerization by increasing oxygen affinity, one of them (GBT440) also inhibits sickling in the absence of oxygen by two additional mechanisms.

Universality of supersaturation in protein-fiber formation

The thermodynamics and kinetics of the aggregation of sickle-cell hemoglobin into fibers have been studied in great detail under a wide range of solution conditions. The stability of the fiber is measured by the solubility; the kinetics is characterized by a delay before the appearance of fibers. A review of data in the literature shows that there is no correlation of the delay time with fiber stability and only a weak correlation with the initial protein concentration. There is, however, a striking collapse of all the data onto a single universal curve when the delay time is plotted versus the supersaturation, which is the ratio of the initial protein concentration to the solubility, expressed as activities. Collapse onto the same universal curve is also obtained when using delay times calculated from the double-nucleation theoretical model.

Coarse-Grained Simulations of Protein Aggregation

Protein aggregation is believed to be responsible for a number of human diseases and limits the yields of pharmaceutical proteins during production. Computer simulations can be used to develop novel experimentally testable hypotheses pertaining to aggregation. While all-atom simulations with explicit solvent are too computationally intensive to address the multitude of relevant time scales, coarse-grained models make it possible to observe the transition of monomers to an equilibrium containing aggregates. Here, we provide the reader with background information and a list of steps for setting up, performing, and analyzing computer simulations of aggregating coarse-grained (CG) proteins.

Theoretical Simulation of Red Cell Sickling Upon Deoxygenation Based on the Physical Chemistry of Sickle Hemoglobin Fiber Formation

The polymerization of the mutant hemoglobin S upon deoxygenation to form fibers in red blood cells of patients suffering from sickle-cell anemia results in changes in cell shape and rigidity, also known as sickling, which underlie the pathology of the disease. While much has been learned about the fundamental physical chemistry of the polymerization process, transferring these insights to sickling of red cells under in vivo conditions requires being able to monitor, and ultimately predict, the time course of cellular sickling under physiological conditions of deoxygenation. To this end, we have developed an experimental technique for tracking the temporal evolution of the sickling of red blood cells under laboratory deoxygenation conditions, based on the automated analysis of sequences of microscope images and machine-learning analysis to characterize cell morphology. As an aid in the quantitative understanding of these experiments, we have developed a computational framework for simulating the time dependence of sickling in populations of red blood cells which incorporates the current theoretical and empirical understanding of the physical chemistry of the sickling process. In order to apply these techniques to our experiments, we have theoretically determined the time course of deoxygenation by solving the diffusion equation for oxygen in our experimental geometry. With this combined description, we are able to reproduce our experimentally observed kinetics of sickling, suggesting that our theoretical approach should be applicable to physiological deoxygenation scenarios.

Dynamics of Structural Elements of GB1 β-Hairpin Revealed by Tryptophan-Cysteine Contact Formation Experiments

Quenching of the triplet state of tryptophan by close contact with cysteine provides a tool for measuring the rate of intramolecular contact formation, one of the most elementary events in the folding process, in peptides and proteins using only natural probes. Here we present a study performed on a stabilized mutant of the second β-hairpin of the GB1 domain, where we combine steady-state fluorescence, laser-induced temperature-jump, and contact formation measurements to unveil the role of elementary structural components on hairpin dynamics and overall stability. In particular, our methodology provides access to the conformational dynamics of both the folded and unfolded state of the hairpin under native conditions, revealing the presence of extremely slow dynamics on the microsecond time scale in the unfolded state and coexistence of structures with partial pairing of the tails in the folded state. Comparing model peptides that mimic the turn sequence, we found that both ion pairing and hydrogen bonding due to the threonine side chain contribute to the propensity of turn formation but not to the much slower dynamics of the hydrophobic core formation. Interestingly, the dynamics of the turn region in isolation are significantly faster than the dynamics measured for the unfolded state of the complete hairpin, suggesting that non-native hydrophobic contacts slow down the reconfiguration dynamics of the unfolded state. Overall, the information extracted from these experiments provides kinetic limits on interconversions among conformational populations, hence enabling a simplified multistate free-energy landscape for the GB1 hairpin to be drawn.