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.

Recurrent excitatory postsynaptic potentials induced by synchronized fast cortical oscillations

Gamma frequency (about 20–70 Hz) oscillations occur during novel sensory stimulation, with tight synchrony over distances of at least 7 mm. Synchronization in the visual system has been proposed to reflect coactivation of different parts of the visual field by a single spatially extended object. We have shown that intracortical mechanisms, including spike doublet firing by interneurons, can account for tight long-range synchrony. Here we show that synchronous gamma oscillations in two sites also can cause long-lasting (>1 hr) potentiation of recurrent excitatory synapses. Synchronous oscillations lasting >400 ms in hippocampal area CA1 are associated with an increase in both excitatory postsynaptic potential (EPSP) amplitude and action potential afterhyperpolarization size. The resulting EPSPs stabilize and synchronize a prolonged beta frequency (about 10–25 Hz) oscillation. The changes in EPSP size are not expressed during non-oscillatory behavior but reappear during subsequent gamma-oscillatory events. We propose that oscillation-induced EPSPs serve as a substrate for memory, whose expression either enhances or blocks synchronization of spatially separated sites. This phenomenon thus provides a dynamical mechanism for storage and retrieval of stimulus-specific neuronal assemblies.

Calcium electrogenesis in distal apical dendrites of layer 5 pyramidal cells at a critical frequency of back-propagating action potentials

Action potentials in juvenile and adult rat layer-5 neocortical pyramidal neurons can be initiated at both axonal and distal sites of the apical dendrite. However, little is known about the interaction between these two initiation sites. Here, we report that layer 5 pyramidal neurons are very sensitive to a critical frequency of back-propagating action potentials varying between 60 and 200 Hz in different neurons. Bursts of four to five back-propagating action potentials above the critical frequency elicited large regenerative potentials in the distal dendritic initiation zone. The critical frequency had a very narrow range (10–20 Hz), and the dendritic regenerative activity led to further depolarization at the soma. The dendritic frequency sensitivity was suppressed by blockers of voltage-gated calcium channels, and also by synaptically mediated inhibition. Calcium-fluorescence imaging revealed that the site of largest transient increase in intracellular calcium above the critical frequency was located 400–700 μm from the soma at the site for initiation of calcium action potentials. Thus, the distal dendritic initiation zone can interact with the axonal initiation zone, even when inputs to the neuron are restricted to regions close to the soma, if the output of the neuron exceeds a critical frequency.

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.

Proline Accumulation in Maize (Zea mays L.) Primary Roots at Low Water Potentials. II. Metabolic Source of Increased Proline Deposition in the Elongation Zone1

The proline (Pro) concentration increases greatly in the growing region of maize (Zea mays L.) primary roots at low water potentials (ψw), largely as a result of an increased net rate of Pro deposition. Labeled glutamate (Glu), ornithine (Orn), or Pro was supplied specifically to the root tip of intact seedlings in solution culture at high and low ψw to assess the relative importance of Pro synthesis, catabolism, utilization, and transport in root-tip Pro deposition. Labeling with [3H]Glu indicated that Pro synthesis from Glu did not increase substantially at low ψw and accounted for only a small fraction of the Pro deposition. Labeling with [14C]Orn showed that Pro synthesis from Orn also could not be a substantial contributor to Pro deposition. Labeling with [3H]Pro indicated that neither Pro catabolism nor utilization in the root tip was decreased at low ψw. Pro catabolism occurred at least as rapidly as Pro synthesis from Glu. There was, however, an increase in Pro uptake at low ψw, which suggests increased Pro transport. Taken together, the data indicate that increased transport of Pro to the root tip serves as the source of low-ψw-induced Pro accumulation. The possible significance of Pro catabolism in sustaining root growth at low ψw is also discussed.

Root Xylem Embolisms and Refilling. Relation to Water Potentials of Soil, Roots, and Leaves, and Osmotic Potentials of Root Xylem Sap1

Embolism and refilling of vessels was monitored directly by cryomicroscopy of field-grown corn (Zea mays L.) roots. To test the reliability of an earlier study showing embolism refilling in roots at negative leaf water potentials, embolisms were counted, and root water potentials (Ψroot) and osmotic potentials of exuded xylem sap from the same roots were measured by isopiestic psychrometry. All vessels were full at dawn (Ψroot −0.1 MPa). Embolisms were first seen in late metaxylem vessels at 8 am. Embolized late metaxylem vessels peaked at 50% at 10 am (Ψroot −0.1 MPa), fell to 44% by 12 pm (Ψroot −0.23 MPa), then dropped steadily to zero by early evening (Ψroot −0.28 MPa). Transpiration was highest (8.5 μg cm−2 s−1) between 12 and 2 pm when the percentage of vessels embolized was falling. Embolized vessels were refilled by liquid moving through their lateral walls. Xylem sap was very low in solutes. The mechanism of vessel refilling, when Ψroot is negative, requires further investigation. Daily embolism and refilling in roots of well-watered plants is a normal occurrence and may be a component of an important hydraulic signaling mechanism between roots and shoots.

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.

Event-related brain potentials in the study of visual selective attention

Event-related brain potentials (ERPs) provide high-resolution measures of the time course of neuronal activity patterns associated with perceptual and cognitive processes. New techniques for ERP source analysis and comparisons with data from blood-flow neuroimaging studies enable improved localization of cortical activity during visual selective attention. ERP modulations during spatial attention point toward a mechanism of gain control over information flow in extrastriate visual cortical pathways, starting about 80 ms after stimulus onset. Paying attention to nonspatial features such as color, motion, or shape is manifested by qualitatively different ERP patterns in multiple cortical areas that begin with latencies of 100–150 ms. The processing of nonspatial features seems to be contingent upon the prior selection of location, consistent with early selection theories of attention and with the hypothesis that spatial attention is “special.”