Evaluating the energetics of empty cavities and internal mutations in proteins.

The energetics of cavity formation in proteins is evaluated with two different approaches and results are analyzed and compared to experimental data. In the first approach, free energy of cavity formation is extracted by RMS fitting from the distribution of numbers of cavities, N, with different volumes, Vcav, in 80 high-resolution protein structures. It is assumed that the distribution of number of cavities according to their volume follows the Boltzmann law, N(Vcav) = exp [(-a.Vcav-b)/kT], or its simplified form. Specific energy cost of cavity formation, a, extracted by RMS fitting from these distributions is compared to a values extracted from experimental free energies of cavity formation in T4 lysozyme fitted to similar expressions. It is found that fitting of both sets of data leads to similar magnitudes and uncertainties in the calculated free energy values. It is shown that Boltzmann-like distribution of cavities can be derived for a simple model of an equilibrium interconversion between mutants in an extracellular system. We, however, suggest that a partitioning into cavity-dependent and cavity-independent terms may lose meaning when one attempts to describe mutation effects on protein stability in terms of specific free energy contributions. As an alternative approach, a direct molecular mechanics evaluation is attempted of T4 lysozyme destabilization by five single cavity-creating mutations. The calculations are based on the approach used in calculations of the energetics of packing defects in crystals. For all mutations calculated destabilizations agree with the corresponding experimental values within +/-0.6 kcal/mol. A computational relaxation of the mutant was most difficult to achieve for the mutation producing the smallest cavity. However, calculations do not always reproduce crystallographically observed contraction/expansion of cavities. It is suggested that this may be related to usually observed large RMS differences (> 1 A) between crystallographic and energy-minimized protein structures, and thus correct energetics might be easier to calculate than the correct geometry.

A view of thermodynamics of hydration emerging from continuum studies.

Main physical-chemical features of hydration found in continuum studies and possible limitations of the method are analyzed. Particular attention is given to: the choice of thermodynamic observables to be compared to the calculations; representations of the solute polarizability; compensation between the loss of hydration enthalpy and gain in Coulomb interactions upon a complex formation; two minima in interaction potentials between polar groups in solution; similarities and dissimilarities between interaction potentials in solution from continuum and molecular theories; continuum calculations of entropies of hydration; and evaluation of a temperature dependence of thermodynamic characteristics of hydration with continuum methods.

Quantitative evaluation of hydration thermodynamics with a continuum model.

We attempt to analyze whether experimental entropies, enthalpies and free energies of hydration of small uncharged molecules can be quantitatively rationalized with a continuum model including a classical reaction field formalism. We find that a simple proportionality to accessible surface with five different atom types allows satisfactory (within 1-1.5 kcal/mol) reproduction of hydration entropies (T delta S) of over 40 solutes. The agreement with experiment can possibly be improved if proximity effects and configurational contributions to transfer entropies are taken into account. In calculations of hydration enthalpies a reasonable agreement with experimental data can be obtained only when solute polarizability is taken into account. Electrostatic contributions to calculated hydration enthalpies exhibit strong dependencies on both the magnitude and the direction of molecular dipole moments. We demonstrate that for 20 molecules with experimentally measured vacuum dipole moments density functional calculations with DZVPD basis set including diffuse functions on d-orbitals allows prediction of experimental dipole moments within 0.1 D. At a fixed direction of the molecular dipole moment, mu, the electrostatic component of hydration enthalpy varies as mu 2. Thus an uncertainty of 0.1 D corresponds to uncertainties of 0.5-0.7 kcal/mol in hydration enthalpies of most small dipolar solutes. A 30 degree change in the direction of the molecular dipole together with the corresponding change in the quadrupole moment can result in a change of hydration enthalpy of 3 kcal/mol. Changes in the quadrupole moment alone can result in hydration enthalpy changes of over 1 kcal/mol. Representations of multipole expansions by point charges on nuclei fitted to molecular electrostatic potentials cannot accurately reproduce all these factors. Use of such point charges in calculations of hydration enthalpies predictably leads to discrepancies with experiment of approximately 3 kcal/mol for some solutes. However, errors in hydration enthalpies and hydration entropies are usually compensating leading in most cases to agreement between calculated and experimental free energies of hydration within 1.5 kcal/mol.

Continuum electrostatics of the C-peptide: anatomy of the problem.

A computational study of the role of all ionizable groups of the C-peptide in its helix-coil transition is performed within the framework of continuum electrostatics. The method employed in our computations involves a numeric solution of the Poisson equation with the Boundary Element Method. Our calculations correctly predict the experimentally observed trends in the helix-coil equilibrium of the C-peptide, and suggest that the mechanisms involved are more complex than usually presumed in the literature. Our results suggest that electrostatic interactions in the unfolded conformation are often more important than in the helix, total electrostatic contribution to the helix-coil transition due to the side chains of the C-peptide destabilizes the helix, changes in the helix stability produced by the changes in the ionization state of the side chains are dominated by side chain effects, the effect of the helix dipole on the energetics of the helix-coil transition of the C-peptide is either minor or similar to other contributions in magnitude; while the formation of a salt bridge is electrostatically favorable, formation of the hydrogen bond between a charged and a polar side chains is not. Factors limiting the accuracy of the computations are discussed.

Criteria that discriminate between native proteins and incorrectly folded models.

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.

Correlation between calculated local stability and hydrogen exchange rates in proteins.

The attempt is made to find new correlations between local structural characteristics of proteins and the hydrogen exchange rates of their individual main-chain amides, and to relate such correlations to possible mechanisms of hydrogen exchange. It is found that in bovine pancreatic trypsin inhibitor (BPTI) the surface area buried by a particular residue and its neighbors correlates with the exchange rate of the main-chain amide of that residue. As the area buried by a particular fragment can be associated with the stabilization of the protein structure by this fragment, the correlation suggests a role for the energetics of the local unfolding in the mechanism of hydrogen exchange. Calculations based on the assumption that the exchange mechanism involves local unfolding lead to quantitative agreement between the calculated and experimentally measured exchange rates for 80% of the amides of BPTI that are buried or hydrogen bonded to the main-chain or to internal water molecules. The same degree of correlation is found between the calculated exchange rates and partial exchange data for ribonuclease S, hen lysozyme and cytochrome c. A similarly strong correlation is found between calculated exchange rates and the exchange rates of ribonuclease A determined by neutron diffraction in the crystal. The criteria of correlation are, however, less stringent in this case because of the experimental errors, which are larger than for solution data. It is suggested that the observed correlation be used for predictions of hydrogen exchange rates in proteins.

Internal cavities and buried waters in globular proteins.

A fast algorithm that detects internal cavities in proteins and predicts the positions of buried water molecules is described. The cavities are characterized in terms of volume, surface area, polarity, and the presence of bound waters. The algorithm is applied to 12 proteins whose structures are known to high resolution and successfully predicts the locations of over 80% of internal water molecules. Most proteins are found to have a number of internal cavities ranging in volume from 10 to 180 A3. Some of these cavities contain water and some do not, with the probability of containing a buried water increasing with cavity size. However, many large cavities are found to be empty (i.e., they do not contain a crystallographically determined water). For multidomain proteins over half of the total cavity volume is at the interdomain interface. Possible implications for the energetics of cavity formation and for the functional role of internal cavities are discussed.

Independent folding of the carboxyl-terminal fragment 228-316 of thermolysin.

The COOH-terminal fragment 206-316 of thermolysin was shown previously to maintain a stable folded structure in aqueous solution comparable to that of the corresponding region in native thermolysin and thus to possess protein domain characteristics [Fontana, A., Vita, C., & Chaiken, I. M. (1983) Biopolymers 22, 69-78]. In order to study the effect of polypeptide chain length on folding and stability of an isolated domain, the 111 amino acid residue fragment was shortened on the NH2-terminal side by removal of a 22-residue segment. Treatment of fragment 206-316 with hydroxylamine under alkaline conditions permitted selective cleavage of the Asn227-Gly228 peptide bond, and from the reaction mixture fragment 228-316 was isolated in homogeneous form. This fragment appeared to attain in aqueous solution the folding properties of the corresponding segment in the intact protein, as indicated by quantitative analysis of secondary structure from far-ultraviolet circular dichroism spectra and immunological properties. Thus, double-immunodiffusion analyses showed that fragment 228-316 is able to recognize and precipitate anti-thermolysin antibodies raised in rabbits with native thermolysin as immunogen. The fragment displayed fully reversible and cooperative conformational transitions mediated by pH, heat, and guanidine hydrochloride (Gdn.HCl), as expected for a globular protein species. Thermal denaturation of the fragment in aqueous solution at pH 7.8 showed a Tm of 66 degrees C and the Gdn.HCl-mediated unfolding a midpoint transition at 2.2 M denaturant concentration.(ABSTRACT TRUNCATED AT 250 WORDS)

On the environment of ionizable groups in globular proteins.

The environment of ionizable groups in 36 proteins is characterized in terms of solvent-accessibility, salt-bridge formation and hydrogen-bonding. Possible implications of our results as to the protonation state of buried ionizable groups are considered and patterns useful for model building studies on proteins are derived. The most interesting finding is that there are on average two completely buried ionizable groups per protein of which at least 20% do not form salt-bridges. However, all buried ionizable groups form hydrogen bonds with neutral polar groups.

Location of domains in globular proteins.

Although it has become widely accepted that domains are the basic units of structure, function and evolution in proteins and it is thought that proteins with complex functions evolve by fusion of genes coding for individual domains, the domains are not uniformly defined. Most commonly, domains are simply the compact and more or less loosely connected areas apparent from a visual inspection of protein models; to avoid subjectivity and ambiguities inherent in visual inspection, certain computer algorithms for location of these 'structural' domains have recently been proposed. An alternative interpretation is that domains are stable protein fragments found in biochemical experiments. I regard them as 'globular fragments' which may refold autonomously and carry specific functions, and I propose here a method for location of these globular fragments based on surface area measurements. Applied to several proteins the globular fragments found often coincide with structural domains or are contained within them. In particular the globular fragments found in globins correlate with the two structural domains proposed previously, and do not correlate with the three coding sequences separated by introns in the haemoglobin genes.

[Role of surface distribution of hydrophobic groups in the assembly of protein quaternary structure]. / Rol' poverkhnostnogo raspredeleniia gidrofobnykh grupp v samosborke chetvertichnoi struktury belkov

The method for two-dimensional representation of protein surfaces, based on the analogy with geographic map, and the algorithm for the search of the most favourable regions of izologous intermolecular interactions are proposed. It is assumed that the most favourable izologous interaction corresponds to an izologous contact of subunits which maximally dehydrates surface hydrophobic groups. The subunits are approximated by ellipsoids of revolution. The hydrophobic groups are assumed to be dehydrated if their C beta-atoms are inside the surface regions of the contacting ellipsoids inaccessible for contact with the sphere representing a water molecule. Using the proposed methods it is shown that for all izologous structures, known to atomic resolution, general shape of the molecule and distribution of hydrophobic groups on its surface: 1) provide a rough intersubunit recognition during assembly (deviation of the center of the experimentally localized contact region from the center of one of two-three regions obtained by us does not exceed 6--7 A); 2) choose only a few most favourable mutual orientations of the contacting regions; 3) can determine the pathway of the assembly.

[High time resolution x-ray study of the dynamics of a single muscle contraction]. / Rentgenograficheskoe issledovanie dinamiki odinochnogo myshechnogo sokrashcheniia s vysokim vremennym razresheniem.

A method of the diffraction cinema which enables to study the time-course of structural changes during twitch contraction is described. The method is based on using synchrotron radiation, position-sensitive counter and small-angle focusing X-ray camera. Only 0.1 s is required to record a good muscle X-ray diagram: meridional diagram contains all layer-lines beginning with the 429 A; the equatorial diagram contains 5 reflections including very weak alpha-reflection. The method allows to record 64 sequent diffraction patterns with different duration (1--2000 ms). The experiment is handled by a computer. Some tens of the films of isometric twitch contraction with time resolution of 3--20 ms have been obtained. During isometric contraction considerable changes in the intensity of both meridional and equatorial reflections were found. The changes were interpreted as indicating movement of cross-bridges toward the thin filaments. During the latent phase there are no visible changes in the intensity of the reflections; the result indicates that during this phase there are no structural changes in position and configuration of cross-bridges.

[Calculation of the quaternary structure of the alpha--beta-dimer of hemoglobin]. / Raschet chetvertichnoi struktury alpha--beta-dimera gemoglobina.

The calculation of the structure of haemoglobin alpha--beta-dimer is performed. Calculation is divided into two steps: at the first step highly hydrophobic regions of the subunit surfaces which can provide the stability of the complex are found; at the second--the fitting of this surface regions is carried out. The calculation has resulted in finding three most stable structures. R. m. s. deviation of the positions of C beta-atoms of one of these structures from those in the native one is 3.5 A.

A model of myoglobin self-organization.

The self-organization of helical regions of myoglobin into a compact tertiary structure is considered on the basis of the hypothesis on the step-wise mechanism of self-organization of protein molecules. It is assumed that the self-organization begins with the formation of "centers of crystallization" and proceeds with the growth of on such center or by a sequential collapse of two or more grown centers. Different pathways of self-organization of myoglobin are considered; the most favourable structures corresponding to the greatest number of dehydrated bulky hydrophobic groups and to all the strongly hydrophilic groups exposed to water are selected at every stage of the given pathway and the others are neglected. One of the two most favourable structures obtained in such a way coincides in rough resolution with the native tertiary structure of protein.