Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

Hydrophobic sequence minimization of the α-lactalbumin molten globule

The molten globule, a widespread protein-folding intermediate, can attain a native-like backbone topology, even in the apparent absence of rigid side-chain packing. Nonetheless, mutagenesis studies suggest that molten globules are stabilized by some degree of side-chain packing among specific hydrophobic residues. Here we investigate the importance of hydrophobic side-chain diversity in determining the overall fold of the α-lactalbumin molten globule. We have replaced all of the hydrophobic amino acids in the sequence of the helical domain with a representative amino acid, leucine. Remarkably, the minimized molecule forms a molten globule that retains many structural features characteristic of a native α-lactalbumin fold. Thus, nonspecific hydrophobic interactions may be sufficient to determine the global fold of a protein.

Studies on the role of the hydrophobic domain of Ost4p in interactions with other subunits of yeast oligosaccharyl transferase

In the yeast, Saccharomyces cerevisiae, oligosaccharyl transferase (OT), which catalyzes the transfer of dolichol-linked oligosaccharide chains to nascent polypeptides in the endoplasmic reticulum, consists of nine nonidentical membrane protein subunits. Genetic and biochemical evidence indicated these nine proteins exist in three subcomplexes. Three of the OT subunits (Ost4p, Ost3p, and Stt3p) have been proposed to exist in one subcomplex. To investigate the interaction of these three membrane proteins, initially we carried out a mutational analysis of Ost4p, which is an extraordinarily small membrane protein containing only 36 amino acid residues. This analysis indicated that when single amino acid residues in a region close to the luminal face of the putative transmembrane domain of Ost4p were changed into an ionizable amino acid such as Lys or Asp, growth at 37°C and OT activity measured in vitro were impaired. In addition, using immunoprecipitation techniques and Western blot analysis, we found that with these mutations the interaction between Ost4p, Ost3p, and Stt3p was disrupted. Introduction of Lys or Asp residues at other positions in the putative transmembrane domain or at the N or C terminus of Ost4p had no effect on disrupting subunit interactions or impairing the activity of OT. These findings suggest that a localized region of the putative transmembrane domain of Ost4p mediates in stabilization of the interaction with the two other OT subunits (Ost3p and Stt3p) in a subcomplex in the endoplasmic reticulum membrane.

Specificity of native-like interhelical hydrophobic contacts in the apomyoglobin intermediate

On exposure to mildly acidic conditions, apomyoglobin forms a partially folded intermediate, I. The A, B, G, and H helices are significantly structured in this equilibrium intermediate, whereas the remainder of the protein is largely unfolded. We report here the effects of mutations at helix pairing sites on the stability of I in three classes of mutants that: (i) truncate hydrophobic side chains in native helix packing sites, (ii) truncate hydrophobic side chains not involved in interhelical contacts, and (iii) extend hydrophobic side chains at residues not involved in interhelical contacts. Class I mutants significantly decrease the stability and cooperativity of folding of the intermediate. Class II and III mutants show smaller effects on stability and have little effect on cooperativity. Qualitatively similar results to those found in I were obtained for all three classes of mutants in native myoglobin (N), demonstrating that hydrophobic burial is fairly specific to native helix packing sites in I as well as in N. These results suggest that hydrophobic burial along native-like interhelical contacts is important for the formation of the cooperatively folded intermediate.

Temperature and length scale dependence of hydrophobic effects and their possible implications for protein folding

The Lum–Chandler–Weeks theory of hydrophobicity [Lum, K., Chandler, D. & Weeks, J. D. (1999) J. Phys. Chem. 103, 4570–4577] is applied to treat the temperature dependence of hydrophobic solvation in water. The application illustrates how the temperature dependence for hydrophobic surfaces extending less than 1 nm differs significantly from that for surfaces extending more than 1 nm. The latter is the result of water depletion, a collective effect, that appears at length scales of 1 nm and larger. Because of the contrasting behaviors at small and large length scales, hydrophobicity by itself can explain the variable behavior of entropies of protein folding.

Free energy of burying hydrophobic residues in the interface between protein subunits

We have obtained an experimental estimate of the free energy change associated with variations at the interface between protein subunits, a subject that has raised considerable interest since the concept of accessible surface area was introduced by Lee and Richards [Lee, B. & Richards, F. M. (1971) J. Mol. Biol. 55, 379–400]. We determined by analytical ultracentrifugation the dimer–tetramer equilibrium constant of five single and three double mutants of human Hb. One mutation is at the stationary α1β1 interface, and all of the others are at the sliding α1β2 interface where cleavage of the tetramer into dimers and ligand-linked allosteric changes are known to occur. A surprisingly good linear correlation between the change in the free energy of association of the mutants and the change in buried hydrophobic surface area was obtained, after corrections for the energetic cost of losing steric complementarity at the αβ dimer interface. The slope yields an interface stabilization free energy of −15 ± 1.2 cal/mol upon burial of 1 Å2 of hydrophobic surface, in very good agreement with the theoretical estimate given by Eisenberg and McLachlan [Eisenberg, D. & McLachlan, A. D. (1986) Nature (London) 319, 199–203].

Designed protein tetramer zipped together with a hydrophobic Alzheimer homology: A structural clue to amyloid assembly

Limited solubility and precipitation of amyloidogenic sequences such as the Alzheimer peptide (β-AP) are major obstacles to a molecular understanding of protein fibrillation and deposition processes. Here we have circumvented the solubility problem by stepwise engineering a β-AP homology into a soluble scaffold, the monomeric protein S6. The S6 construct with the highest β-AP homology crystallizes as a tetramer that is linked by the β-AP residues forming intermolecular antiparallel β-sheets. This construct also shows increased coil aggregation during refolding, and a 14-mer peptide encompassing the engineered sequence forms fibrils. Mutational analysis shows that intermolecular association is linked to the overall hydrophobicity of the sticky sequence and implies the existence of “structural gatekeepers” in the wild-type protein, that is, charged side chains that prevent aggregation by interrupting contiguous stretches of hydrophobic residues in the primary sequence.

Mode matches and their locations in the hydrophobic free energy sequences of peptide ligands and their receptor eigenfunctions

Patterns in sequences of amino acid hydrophobic free energies predict secondary structures in proteins. In protein folding, matches in hydrophobic free energy statistical wavelengths appear to contribute to selective aggregation of secondary structures in “hydrophobic zippers.” In a similar setting, the use of Fourier analysis to characterize the dominant statistical wavelengths of peptide ligands’ and receptor proteins’ hydrophobic modes to predict such matches has been limited by the aliasing and end effects of short peptide lengths, as well as the broad-band, mode multiplicity of many of their frequency (power) spectra. In addition, the sequence locations of the matching modes are lost in this transformation. We make new use of three techniques to address these difficulties: (i) eigenfunction construction from the linear decomposition of the lagged covariance matrices of the ligands and receptors as hydrophobic free energy sequences; (ii) maximum entropy, complex poles power spectra, which select the dominant modes of the hydrophobic free energy sequences or their eigenfunctions; and (iii) discrete, best bases, trigonometric wavelet transformations, which confirm the dominant spectral frequencies of the eigenfunctions and locate them as (absolute valued) moduli in the peptide or receptor sequence. The leading eigenfunction of the covariance matrix of a transmembrane receptor sequence locates the same transmembrane segments seen in n-block-averaged hydropathy plots while leaving the remaining hydrophobic modes unsmoothed and available for further analyses as secondary eigenfunctions. In these receptor eigenfunctions, we find a set of statistical wavelength matches between peptide ligands and their G-protein and tyrosine kinase coupled receptors, ranging across examples from 13.10 amino acids in acid fibroblast growth factor to 2.18 residues in corticotropin releasing factor. We find that the wavelet-located receptor modes in the extracellular loops are compatible with studies of receptor chimeric exchanges and point mutations. A nonbinding corticotropin-releasing factor receptor mutant is shown to have lost the signatory mode common to the normal receptor and its ligand. Hydrophobic free energy eigenfunctions and their transformations offer new quantitative physical homologies in database searches for peptide-receptor matches.

Hydrophobic moments of protein structures: Spatially profiling the distribution

It is generally accepted that globular proteins fold with a hydrophobic core and a hydrophilic exterior. Might the spatial distribution of amino acid hydrophobicity exhibit common features? The hydrophobic profile detailing this distribution from the protein interior to exterior has been examined for 30 relatively diverse structures obtained from the Protein Data Bank, for 3 proteins of the 30S ribosomal subunit, and for a simple set of 14 decoys. A second-order hydrophobic moment has provided a simple measure of the spatial variation. Shapes of the calculated spatial profiles of all native structures have been found to be comparable. Consequently, profile shapes as well as particular profile features should assist in validating predicted protein structures and in discriminating between different protein-folding pathways. The spatial profiles of the 14 decoys are clearly distinguished from the profiles of their native structures.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.

Direct evidence for modified solvent structure within the hydration shell of a hydrophobic amino acid.

Neutron scattering experiments are used to determine scattering profiles for aqueous solutions of hydrophobic and hydrophilic amino acid analogs. Solutions of hydrophobic solutes show a shift in the main diffraction peak to smaller angle as compared with pure water, whereas solutions of hydrophilic solutes do not. The same difference for solutions of hydrophobic and hydrophilic side chains is also predicted by molecular dynamics simulations. The neutron scattering curves of aqueous solutions of hydrophobic amino acids at room temperature are qualitatively similar to differences between the liquid molecular structure functions measured for ambient and supercooled water. The nonpolar solute-induced expansion of water structure reported here is also complementary to recent neutron experiments where compression of aqueous solvent structure has been observed at high salt concentration.

An information theory model of hydrophobic interactions.

A molecular model of poorly understood hydrophobic effects is heuristically developed using the methods of information theory. Because primitive hydrophobic effects can be tied to the probability of observing a molecular-sized cavity in the solvent, the probability distribution of the number of solvent centers in a cavity volume is modeled on the basis of the two moments available from the density and radial distribution of oxygen atoms in liquid water. The modeled distribution then yields the probability that no solvent centers are found in the cavity volume. This model is shown to account quantitatively for the central hydrophobic phenomena of cavity formation and association of inert gas solutes. The connection of information theory to statistical thermodynamics provides a basis for clarification of hydrophobic effects. The simplicity and flexibility of the approach suggest that it should permit applications to conformational equilibria of nonpolar solutes and hydrophobic residues in biopolymers.

Active barnase variants with completely random hydrophobic cores.

The central structural feature of natural proteins is a tightly packed and highly ordered hydrophobic core. If some measure of exquisite, native-like core packing is necessary for enzymatic function, this would constitute a significant obstacle to the development of novel enzymes, either by design or by natural or experimental evolution. To test the minimum requirements for a core to provide sufficient structural integrity for enzymatic activity, we have produced mutants of the ribonuclease barnase in which 12 of the 13 core residues have together been randomly replaced by hydrophobic alternatives. Using a sensitive biological screen, we find that a strikingly high proportion of these mutants (23%) retain enzymatic activity in vivo. Further substitution at the 13th core position shows that a similar proportion of completely random hydrophobic cores supports enzyme function. Of the active mutants produced, several have no wild-type core residues. These results imply that hydrophobicity is nearly a sufficient criterion for the construction of a functional core and, in conjunction with previous studies, that refinement of a crudely functional core entails more stringent sequence constraints than does the initial attainment of crude core function. Since attainment of crude function is the critical initial step in evolutionary innovation, the relatively scant requirements contributed by the hydrophobic core would greatly reduce the initial hurdle on the evolutionary pathway to novel enzymes. Similarly, experimental development of novel functional proteins might be simplified by limiting core design to mere specification of hydrophobicity and using iterative mutation-selection to optimize core structure.