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.

Two amyloid precursor protein transgenic mouse models with Alzheimer disease-like pathology

Mutations in the amyloid precursor protein (APP) gene cause early-onset familial Alzheimer disease (AD) by affecting the formation of the amyloid β (Aβ) peptide, the major constituent of AD plaques. We expressed human APP751 containing these mutations in the brains of transgenic mice. Two transgenic mouse lines develop pathological features reminiscent of AD. The degree of pathology depends on expression levels and specific mutations. A 2-fold overexpression of human APP with the Swedish double mutation at positions 670/671 combined with the V717I mutation causes Aβ deposition in neocortex and hippocampus of 18-month-old transgenic mice. The deposits are mostly of the diffuse type; however, some congophilic plaques can be detected. In mice with 7-fold overexpression of human APP harboring the Swedish mutation alone, typical plaques appear at 6 months, which increase with age and are Congo Red-positive at first detection. These congophilic plaques are accompanied by neuritic changes and dystrophic cholinergic fibers. Furthermore, inflammatory processes indicated by a massive glial reaction are apparent. Most notably, plaques are immunoreactive for hyperphosphorylated tau, reminiscent of early tau pathology. The immunoreactivity is exclusively found in congophilic senile plaques of both lines. In the higher expressing line, elevated tau phosphorylation can be demonstrated biochemically in 6-month-old animals and increases with age. These mice resemble major features of AD pathology and suggest a central role of Aβ in the pathogenesis of the disease.

Mapping sites of interaction of p47-phox and flavocytochrome b with random-sequence peptide phage display libraries.

During assembly of the phagocyte NADPH oxidase, cytosolic p47-phox translocates to the plasma membrane and binds to flavocytochrome b, and binding domains for p47-phox have been identified on the C-terminal tails of both flavocytochrome b subunits. In the present report, we further examine the interaction of these two oxidase components by using random-sequence peptide phage display library analysis. Screening p47-phox with the peptide libraries identified five potential sites of interaction with flavocytochrome b, including three previously reported regions of interaction and two additional regions of interaction of p47-phox with gp91-phox and p22-phox. The additional sites were mapped to a domain on the first predicted cytosolic loop of gp91-phox encompassing residues S86TRVRRQL93 and to a domain near the cytosolic C-terminal tail of gp91-phox encompassing residues F450EWFADLL457. The mapping also confirmed a previously reported binding domain on gp91-phox (E554SGPRGVHFIF564) and putative Src homology 3 domain binding sites on p22-phox (P156PRPP160 and G177GPPGGP183). To demonstrate that the additional regions identified were biologically significant, peptides mimicking the gp91-phox sequences F77LRGSSACCSTRVRRQL93 and E451WFADLLQLLESQ463 were synthesized and assayed for their ability to inhibit NADPH oxidase activity. These peptides had EC50 values of 1 microM and 230 microM, respectively, and inhibited activation when added prior to assembly but did not affect activity of the preassembled oxidase. Our data demonstrate the usefulness of phage display library analysis for the identification of biologically relevant sites of protein-protein interaction and show that the binding of p47-phox to flavocytochrome b involves multiple binding sites along the C-terminal tails of both gp91- and p22-phox and other regions of gp91-phox nearer to the N terminus.

Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.