Topology of globular proteins. II.

This paper continues the inquiry into the likelihood of occurrence of protein structures which are “knotted”. The probability of knotted con formations is calculated by a simple Monte Carlo method for the proteins lysozyme and ribonuclease and for an elementary bicyclic polymer. Ribonuclease shows no measurable inclination towards tangling, but some 10%. of the lysozyme conformations are knotted. The implications of this result for the role of disulfide bridge formation in protein renaturation are discussed.     

A structural basis for the interaction of urea with lysozyme.

The effect of urea on the crystal structure of hen egg-white lysozyme has been investigated using X-ray crystallography. High resolution structures have been determined from crystals grown in the presence of 0, 0.7, 2, 3, 4, and 5 M urea and from crystals soaked in 9 M urea. All the forms are essentially isomorphous with the native type II crystals, and the derived structures exhibit excellent geometry and RMS differences from ideality in bond distances and angles. Comparison of the urea complex structures with the native enzyme (type II form, at 1.5 A resolution) indicates that the effect of urea is minimal over the concentration range studied. The mean difference in backbone conformation between the native enzyme and its urea complexes varies from 0.18 to 0.49 A. Conformational changes are limited to flexible surface loops (Thr 69-Asn 74, Ser 100-Asn 103), the active site loop (Asn 59-Cys 80), and the C-terminus (Cys 127-Leu 129). Urea molecules are bound to distinct sites on the surface of the protein. One molecule is bound to the active site cleft's C subsite, at all concentrations, in a fashion analogous to that of the N-acetyl substituent of substrate and inhibitor sugars normally bound to this site. Occupation of this subsite by urea alone does not appear to induce the conformational changes associated with inhibitor binding.     

The chiroptical properties of proteins. II. Near-ultraviolet circular dichroism of lysozyme

A study of the near-uv CD spectrum of lysozyme was carried out in the presence and absence of the inhibitor tri-N-acetylglucosamine, and theoretical chiroptical calculations based on the tetragonal crystal structure of the enzyme and the enzyme-inhibitor complex were performed. The results of these calculations indicate that the near-uv CD spectrum of lysozyme can be adequately explained in terms of negative rotatory strengths arising from the tryptophan ¹L_a (293–300 nm) and the disulfide n-σ* bands (250 rm), and positive rotatory strength contributions from the tryptophan ¹L_b bands (291 nm) and the tyrosine ¹L_b bands (275 nm). Contributions to the rotatory strength of each band were approximated in terms of specific interactions between chromophores. It was found that the rotatory strength of most of the near-uv transitions arises primarily from coupling interactions involving other side-chain chromophores and amide groups which are in close proximity. Changes which are observed in the lysozyme CD spectrum on binding of tri-N-acetylglucosamine may be explained in terms of changes in the rotatory strength which result from interactions of the ¹L_a transitions of the active-site tryptophans with the acetamide groups of the inhibitor. The reasonable agreement which is found between the experimental and calculated rotatory strengths implies that the crystal conformation of lysozyme must resemble the solution conformation.     

Study of thermal denaturation of lysozyme and other globular proteins by light-scattering spectroscopy

The technique of intensity correlation light-scattering spectroscopy has been used to accurately determine the extent of physical swelling of lysozyme, ribonuclease, and chymotrypsinogen produced by thermal denaturation. The change in hydrodynamic radius is deduced from direct measurements of the diffusion coefficient, carried out in the temperature range 20° to 70°C at various values of pH in the range 1.0 to 3.0 at ionic strengths of from 0.01 M to 0.2 M. An average radius increase of 18% is observed for lysozyme and ribonuclease, with an estimate of 26% for chymotrypsinogen. Analysis of the pH dependence of the transition temperature leads to the conclusion that the lysozyme charge increases by approximately +2e during unfolding. We have applied this value of the charge increase along with the 18% average radius increase to estimate the electrostatic contribution to the free-energy change for denaturation of lysozyme. The results are consistent with the experimental observation that the transition temperature is nearly independent of ionic strength.     

Structural changes and fluctuations of proteins. II. Analysis of the denaturation of globular proteins.

The statistical thermodynamic model of protein structure proposed in paper I is developed with special attention to the hydrophobic interaction. Calorimetric measurements of the thermal denaturation of five globular proteins, ribonuclease A, lysozyme, alpha-chymotrypsin, cytochrome c, and myoglobin, are quantitatively analyzed using the model. The thermodynamic parameters obtained by the least squares method reflect the global, average properties of proteins and are in good agreement with the expected values estimated from experimental and theoretical studies for model peptides. The average bond energy epsilon is well related to the tertiary structure of each protein. However, the difference in the parameters between different proteins is not observed for the cooperative energy ZJ and the chain entropy alpha. The individuality of a protein as far as its structural stability is concerned, is mainly reflected by the parameter gamma specifying the hydrophobic nature of a protein. The model is further applied in the analysis of several aspects of the structural stability of globular proteins. Denaturation induced by denaturants, salts, and pH are also explained by the model in a unified manner.     

The adsorption of globular proteins

A series of experiments is suggested to elucidate further the nature of the adsorption of globular proteins on polar solid surfaces. Two ratios of surface energies and the total protein volume are used to characterize the expected form of the adsorbed species. A simple model calculation illustrates the approach.     

On the computation of the tertiary structure of globular proteins II.

The semi-empirical approach proposed earlier (Y?as et al., 1978) to compute the tertiary structures of globular proteins is here amplified and developed further. Using, as input, information on sequence and certain averages of interatomic distances which can be semi-empirically estimated, structures have been computed for pancreatic trypsin inhibitor, lysozyme and staphylococcal nuclease which resemble those determined by X-ray diffraction methods. The approach used is compared and contrasted with others proposed recently.     

The nature of folded states of globular proteins.

We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.