Recent experiments, advances in theory, and analogies to other complex systems such as glasses and spin glasses yield insight into protein dynamics. The basis of the understanding is the observation that the energy landscape is complex: Proteins can assume a large number of nearly isoenergetic conformations (conformational substates). The concepts that emerge from studies of the conformational substates and the motions between them permit a quantitative discussion of one simple reaction, the binding of small ligands such as carbon monoxide to myoglobin.

https://science.sciencemag.org/content/sci/254/5038/1598.full.pdf

The energy landscapes and motions of proteins.

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.

Sickle cell hemoglobin polymerization.

Publisher Summary This chapter summarizes the properties of the singular value decomposition, which are relevant for data analysis. The chapter describes the way in which the singular value decomposition (SVD) of a noise-free data set for which the spectra, f , and concentration, c , vectors are known can be calculated from consideration of the integrated overlaps of these components. Because data analysis necessarily begins with matrices, which are “noisy” at some level of precision, the chapter describes some of the properties of the SVD of matrices, which contain noise. It describes the SVD of random matrices (that is, matrices containing only noise). The chapter explores the way the random amplitudes are distributed in the SVD output when noise is added to a data matrix by using perturbation theory. The chapter discusses the significant advantages that result from the application of SVD and complementary processing techniques for the analysis of large sets of experimental data.

[8] Singular value decomposition: Application to analysis of experimental data

Nanosecond lasers were used to measure the rate of conformational changes in myoglobin after ligand dissociation at ambient temperatures. At low solvent viscosities the rate is independent of viscosity, but at high viscosities it depends on approximately the inverse first power of the viscosity. Kramers theory for unimolecular rate processes can be used to explain this result if the friction term is modified to include protein as well as solvent friction. The theory and experiment suggest that the dominant factor in markedly reducing the rate of conformational changes in myoglobin at low temperatures (less than 200 K) is the very high viscosity (greater than 10(7) centipoise) of the glycerol-water solvent. That is, at low temperatures conformational substates may not be "frozen" so much as "stuck."

https://science.sciencemag.org/content/sci/256/5065/1796.full.pdf

The role of solvent viscosity in the dynamics of protein conformational changes

X-ray structure and refinement of carbon-monoxy (Fe II)-myoglobin at 1.5 A resolution.

Geminate recombination of carbon monoxide to myoglobin

A nanosecond absorption spectrometer has been used to measure the optical spectra of hemoglobin between 3 ns and 100 ms after photolysis of the CO complex. The data from a single experiment comprise a surface, defined by the time-ordered set of 50-100 spectra. Singular value decomposition is used to represent the observed spectra in terms of a minimal set of basis spectra and the time course of their amplitudes. Both CO rebinding and conformational changes are found to be multiphasic. Prior to the quaternary structural change, two relaxations are observed that are assigned to geminate recombination followed by a tertiary structural change. These relaxations are interpreted in terms of a kinetic model that points out their potential role in kinetic cooperativity. The rapid escape of CO from the heme pocket compared with the rate of rebinding observed for both R and T quaternary states shows that the quaternary structure controls the overall dissociation rate by changing the rate at which the Fe--CO bond is broken. A comparable description of the control of the overall association rates must await a more complete experimental description of the kinetics of the quaternary T state.

https://www.pnas.org/content/pnas/80/8/2235.full.pdf

Nanosecond absorption spectroscopy of hemoglobin: elementary processes in kinetic cooperativity.

Hybrid hemoglobins were prepared in which cobalt was substituted for the heme iron in either the alpha or beta subunits. Transient optical absorption spectra were measured at room temperature for these hybrids at time intervals between 0 and 50 ms following photodissociation of the carbon monoxide complex with 10-ns laser pulses. The cobalt porphyrins do not bind carbon monoxide, making it possible to investigate the time-resolved response of the cobalt-containing subunits to photodissociation of carbon monoxide in the iron-containing subunits. At the same time the response of the iron-containing subunits to the photolysis event can be studied, permitting an independent determination of the kinetics of ligand rebinding and conformational changes in the alpha and beta subunits of an intact tetramer. The data were analyzed by using singular-value decomposition to obtain the kinetic progress curve for ligand rebinding, the deoxyheme and cobalt porphyrin spectral changes, and the time course of these spectral changes. The geminate rebinding kinetics following photodissociation of alpha(Co)2 beta(Fe-CO)2 were very similar to those found unsubstituted hemoglobin, alpha(Fe-CO)2 beta(Fe-CO)2, indicating equivalence of the geminate kinetics for alpha and beta subunits within the R-state tetramer. The results for alpha(Fe-CO)2 beta(Co)2 were consistent with this conclusion, even though the analysis was complicated by the presence of comparable populations of R- and T-state species. Comparison of the deoxyheme spectral changes and relaxation times among the three molecules indicated that both alpha and beta subunits contribute to the deoxyheme spectral changes that signal tertiary and quaternary conformational changes in the unsubstituted tetramer. The response of the cobalt porphyrins to photodissociation was similar in the two hybrids. No structural changes were detected in the cobalt-containing subunits until the second tertiary conformational change in the iron-containing subunits observed at 1-2 microseconds. Much larger structural changes, as judged by the amplitude of the spectral changes, occurred in the cobalt-containing subunits concomitant with the R----T quaternary change at about 20 microseconds.

Nanosecond optical spectra of iron-cobalt hybrid hemoglobins: geminate recombination, conformational changes, and intersubunit communication.

The fluorescence of lima bean trypsin inhibitor is due to a single tyrosine residue at position 69. The lifetime of this tyrosine fluorescence is 620 +/- 50 ps (mean +/- SD) and is little affected by addition of 0.88 M citrate, an efficient quencher of tyrosine fluorescence. The steady-state emission intensity is also only weakly reduced by the quencher. The tyrosine is thus not accessible to the citrate and is probably located in the interior of the protein. The high pK of the tyrosine supports this conclusion. The fluorescence anisotropy decay of the inhibitor's tyrosine can be fitted to a double exponential form, with time constants of about 40 ps and greater than or equal to 3 ns. The anisotropy at time zero is 0.19 +/- 0.015 (mean +/- SD), the same as for N-acetyl-L-tyrosinamide in viscous glycerol solution. The nanosecond component of the decay is consistent with rotation of the entire protein molecule. The 40-ps component demonstrates that the tyrosine has considerable freedom to move independently of the protein as a whole. This rotational correlation time is approximately what is observed for free tyrosine in aqueous solution. Since the polypeptide chain near tyrosine-69 is anchored by several disulfide bonds, the data argue that this interior portion of the protein consists of a rigid, immobile backbone embedded in fluid, mobile amino acid side chains.

http://www.pnas.org/content/83/23/8977.full.pdf

Joseph H. Sommer

Papers

Geminate recombination of carbon monoxide to myoglobin

Nanosecond absorption spectroscopy of hemoglobin: elementary processes in kinetic cooperativity.

Nanosecond optical spectra of iron-cobalt hybrid hemoglobins: geminate recombination, conformational changes, and intersubunit communication.

Fluorescence polarization decay of tyrosine in lima bean trypsin inhibitor

Picosecond time-resolved fluorescence spectra of ethidium bromide: evidence for a nonactivated reaction