James Hofrichter

Folding dynamics and mechanism of Beta-hairpin formation

Protein chains coil into α-helices and β-sheet structures. Knowing the timescales and mechanism of formation of these basic structural elements is essential for understanding how proteins fold. For the past 40 years, α-helix formation has been extensively investigated in synthetic and natural peptides, including by nanosecond kinetic studies. In contrast, the mechanism of formation of β structures has not been studied experimentally. The minimal β-structure element is the β-hairpin, which is also the basic component of antiparallel β-sheets. Here we use a nanosecond laser temperature-jump apparatus to study the kinetics of folding a β-hairpin consisting of 16 amino-acid residues. Folding of the hairpin occurs in 6 µs at room temperature, which is about 30 times slower than the rate of α-helix formation. We have developed a simple statistical mechanical model that provides a structural explanation for this result. Our analysis also shows that folding of a β-hairpin captures much of the basic physics of protein folding, including stabilization by hydrogen bonding and hydrophobic interactions, two-state behaviour, and a funnel-like, partially rugged energy landscape.

Sickle Cell Hemoglobin Polymerization

Publisher Summary The chapter describes the understanding of the physics and physical chemistry of sickle cell hemoglobin polymerization in solutions and in red cells. The polymerization of sickle cell hemoglobin has probably become the best understood of all protein self-assembly systems. The structure of the hemoglobin S molecule, the structure of the various aggregated forms of hemoglobin S, and the structural analysis of the polymers are discussed in the chapter. The chapter discusses the thermodynamics of hemoglobin S polymerization, and includes a description of the nonideal behavior of concentrated hemoglobin S solutions and the effects of physiologically relevant variables, especially oxygen, and the presence of non-S hemoglobins on the polymerization process. Understanding the polymerization process is not only important for understanding the pathophysiology of sickle cell disease, but is critical to the major problem of developing a specific therapy that could be used in the treatment of patients. The kinetic and thermodynamic studies have played a major role by providing relevant and sensitive assays for potential therapeutic agents. The results of the thermodynamic and kinetic studies of solutions are used to explain various properties of cells, including morphological and rheological properties.

Kinetics of sickle hemoglobin polymerization: II. A double nucleation mechanism

A double nucleation mechanism for the polymerization of sickle hemoglobin is described. The mechanism accounts for all of the major kinetic observations: the appearance of a delay, the high concentration dependence of the delay time, and the stochastic behavior of slowly polymerizing samples in small volumes. The mechanism postulates that there are two pathways for polymer formation: polymerization is initiated by homogeneous nucleation in the solution phase, followed by nucleation of additional polymers on the surface of existing ones. This second pathway is called heterogeneous nucleation. Since the surface of polymers is continuously increasing with time, heterogeneous nucleation provides a mechanism for the extreme autocatalysis that is manifested as an apparent delay in the kinetic progress curves. In this mechanism, each spherulitic domain of polymers is considered to be initiated by a single homogeneous nucleation event. The mechanism explains the irreproducibility of the delay time for single domain formation as arising from stochastic fluctuations in the time at which the homogeneous nucleus for the first polymer is formed. Integration of the linearized rate equations that describe this model results in a simple kinetic form: A[cosh(Bt)-1] (Bishop & Ferrone, 1984). In the accompanying paper (Ferrone et al., 1985) it was shown that the initial 10 to 15% of progress curves, with delay times varying from a few milliseconds to over 10(5) seconds, is well fit by this equation. In this paper, we present an approximate statistical thermodynamic treatment of the equilibrium nucleation processes that shows how the nucleus sizes and nucleation equilibrium constants depend on monomer concentration. The equilibrium model results in expressions for B and B2A as a function of monomer concentration in terms of five adjustable parameters: the bimolecular addition rate of a monomer to the growing aggregate, the fraction of polymerized monomers that serve as heterogeneous nucleation sites, the free energy of intermolecular bonding within the polymer, and two parameters that describe the free energy change as a function of size for the bonding of the heterogeneous nucleus to a polymer surface. This model provides an excellent fit to the data for B and B2A as a function of concentration using physically reasonable parameters. The model also correctly predicts the time regime in which stochastic behavior is observed for polymerization in small volumes.

Kinetics of sickle hemoglobin polymerization. I. Studies using temperature-jump and laser photolysis techniques.

Using a combination of laser photolysis and temperature-jump techniques, the kinetics of hemoglobin S polymerization have been studied over a wide range of delay times (10(-3) to 10(5)s), concentrations (0.2 to 0.4 g/cm3) and temperatures (5 to 50 degrees C). A slow temperature-jump technique was used to induce polymerization in samples with delay times between 10(2) seconds and 10(5) seconds by heating a solution of completely deoxygenated hemoglobin S. For samples with shorter delay times, polymerization was induced by photodissociating the carbon monoxide complex in small volumes (10(-9) cm3) using a microspectrophotometer equipped with a cw argon ion laser. The photolysis technique is described in some detail because of its importance in studying hemoglobin S polymerization at physiological concentrations and temperatures. In order, to establish conditions for complete photodissociation with minimal laser heating, a series of control experiments on normal human hemoglobin was performed and theoretically modeled. The concentration dependence of the tenth time is found to decrease with increasing hemoglobin S concentration. In the range 0.2 to 0.3 g/cm3, the tenth time varies as the 36th power of the hemoglobin S concentration, while in the range 0.3 to 0.4 g/cm3 it decreases to 16th power. As the tenth times become shorter, the progress curves broaden, with the onset of polymerization becoming less abrupt. For tenth times greater than about 30 seconds, measurements with the laser photolysis technique on small volumes yield highly irreproducible tenth times, but superimposable progress curves, indicating stochastic behavior. The initial part of the progress curves from both temperature-jump and laser photolysis experiments is well fit with an equation for the concentration of polymerized monomer, delta (t) = A[cosh (Bt) -1], which results from integration of the linearized rate equations for the double nucleation mechanism described in the accompanying paper (Ferrone et al., 1985). The dependence of the parameters A and B on temperature and concentration is obtained from fitting over 300 progress curves. The rate B has a large concentration dependence, varying at 25 degrees C from about 10(-4) S-1 at 0.2 g/cm3 to about 100 s-1 at 0.4 g/cm3.

Is cooperative oxygen binding by hemoglobin really understood

The enormous success of structural biology challenges the physical scientist. Can biophysical studies provide a truly deeper understanding of how a protein works than can be obtained from static structures and qualitative analysis of biochemical data? We address this question in a case study by presenting the key concepts and experimental results that have led to our current understanding of cooperative oxygen binding by hemoglobin, the paradigm of structure function relations in multisubunit proteins. We conclude that the underlying simplicity of the two-state allosteric mechanism could not have been demonstrated without novel physical experiments and a rigorous quantitative analysis.

Experimental tests of villin subdomain folding simulations.

We have used laser temperature-jump to investigate the kinetics and mechanism of folding the 35 residue subdomain of the villin headpiece. The relaxation kinetics are biphasic with a sub-microsecond phase corresponding to a helix-coil transition and a slower microsecond phase corresponding to overall unfolding/refolding. At 300 K, the folding time is 4.3(+/-0.6) micros, making it the fastest folding, naturally occurring protein, with a rate close to the theoretical speed limit. This time is in remarkable agreement with the prediction of 5 (+11,-3) micros by Zagrovic et al. from atomistic molecular dynamics simulations using an implicit solvent model. We test their prediction that replacement of the C-terminal phenylalanine residue with alanine will increase the folding rate by removing a transient non-native interaction. We find that the alanine substitution has no effect on the folding rate or on the equilibrium constant. Implications of this result for the validity of the simulated folding mechanism are discussed.

Geminate recombination of carbon monoxide to myoglobin.

Transient absorption spectra of myoglobin, following photolysis of the carbon monoxide complex at room temperature, were measured using a newly developed, sensitive nanosecond absorption spectrometer. The Soret spectrum of the immediate photoproduct is almost identical to that of deoxymyoglobin at equilibrium, suggesting that the heme group has changed from a planar to a domed structure in less than about 3 ns. About 4% of the photodissociated carbon monoxide molecules rebind to the hemes to which they were initially bound, with a relaxation time of 180 ns. Duddell et al. (1980) observed a geminate yield of 27% and a relaxation time of approximately 55 ns for the photolysis of oxymyoglobin. Comparison of the two results using the simplest kinetic model suggests that the 30-fold more rapid overall association rate for the reaction of oxygen with myoglobin compared to carbon monoxide results mainly from faster binding at the heme, with a small contribution from more rapid entry of oxygen into the protein from the solvent. The data on carbon monoxide are also compared with predictions from low-temperature studies of Frauenfelder and co-workers. This comparison points to the need for further experiments to demonstrate the correspondence between the ligand rebinding processes observed at high and low temperatures.

Submillisecond kinetics of protein folding

New experimental methods permit observation of protein folding and unfolding on the previously inaccessible nanosecond-microsecond timescale. These studies are beginning to establish times for the elementary motions in protein folding - secondary structure and loop formation, local hydrophobic collapse, and global collapse to the compact denatured state. They permit an estimate of about one microsecond for the shortest time in which a protein can possibly fold.

Protein reaction kinetics in a room-temperature glass

Protein reaction kinetics in aqueous solution at room temperature are often simplified by the thermal averaging of conformational substates. These substates exhibit widely varying reaction rates that are usually exposed by trapping in a glass at low temperature. Here, it is shown that the solvent viscosity, rather than the low temperature, is primarily responsible for the trapping. This was demonstrated by placement of myoglobin in a glass at room temperature and subsequent observation of inhomogeneous reaction kinetics. The high solvent viscosity slowed the rate of crossing the energy barriers that separated the substates and also suppressed any change in the average protein conformation after ligand dissociation.

[16] Polarized absorption and linear dichroism spectroscopy of hemoglobin

Publisher Summary This chapter is concerned with polarized absorption and linear dichroism spectroscopy of hemoglobin. Polarized absorption and linear dichroism are techniques that are used to study the optical properties of oriented systems. Unlike solutions, where light polarized in any direction is absorbed equally because the molecules are randomly oriented, the absorption of plane-polarized light by oriented molecules is dependent on the polarization direction of the incident light beam. Anisotropic absorption occurs because molecules fixed in space exhibit maximum absorption when the electric vector of the light is parallel to well-defined directions in the molecule. A polarized absorption experiment in which the spectra are measured in each of three orthogonal directions on a sample of known molecular orientation—such as a crystal of known structure—yields both the complete spectrum and the molecular direction of the transition moment for each absorption band. If, on the other hand, the transition moment directions are already established, the polarized absorption experiment along three orthogonal axes yields the molecular orientation. In a linear dichroism experiment, the difference between the optical densities in two directions is measured directly.