One site fits both: A model for the ternary complex of folate + NADPH in R67 dihydrofolate reductase, a D2 symmetric enzyme

R67 dihydrofolate reductase (DHFR) is a novel enzyme that confers resistance to the antibiotic trimethoprim. The crystal structure of R67 DHFR displays a toroidal structure with a central active-site pore. This homotetrameric protein exhibits 222 symmetry, with only a few residues from each chain contributing to the active site, so related sites must be used to bind both substrate (dihydrofolate) and cofactor (NADPH) in the productive R67 DHFR?NADPH?dihydrofolate complex. Whereas the site of folate binding has been partially resolved crystallographically, an interesting question remains: how can the highly symmetrical active site also bind and orient NADPH for catalysis? To model this ternary complex, we employed DOCK and SLIDE, two methods for docking flexible ligands into proteins using quite different algorithms. The bound pteridine ring of folate (Fol I) from the crystal structure of R67 DHFR was used as the basis for docking the nicotinamide-ribose-P_i (NMN) moiety of NADPH. NMN was positioned by both DOCK and SLIDE on the opposite side of the pore from Fol I, where it interacts with Fol I at the pore's center. Numerous residues serve dual roles in binding. For example, Gln 67 from both the B and D subunits has several contacts with the pteridine ring, while the same residue from the A and C subunits has several contacts with the nicotinamide ring. The residues involved in dual roles are generally amphipathic, allowing them to make both hydrophobic and hydrophilic contacts with the ligands. The result is a `hot spot' binding surface allowing the same residues to co-optimize the binding of two ligands, and orient them for catalysis.     

Regularity and asymptotic behavior of solutions of nonautonomous differential equations

The existence of a nonautonomous approximate inertial manifold is shown for problems of the formu + Au + N(t,u)=0, in whichA is a self-adjoint operator with compact resolvent in a Hilbert spaceH. The operatorN(t, u) = G(u) + F(t, u) is nonlinear withG a monotone gradient that is locally Lipschitz fromD(A ^1/2) intoH, andF:⁺×HH a Lipschitz perturbation that is Hölder continuous int. Weak solutions are shown to be uniformly locally Hölder continuous intoD(A) with equicontinuity in families of solutions with ¦u(0)¦ r.A priori estimates of ¦Au(t)¦ are also verified and used in a skew-product flow to show there is a global attractor whose component elements form a equicontinuous family of solutions.     

Angle of incidence effects in a molecular solid

We investigate the influence of the angle of incidence on the sputter yield when bombarding molecular solid, benzene, with C₆₀. Our simulations show that at normal incidence, essentially all of the projectile energy is deposited into the substrate within ∼2.5 nm of the surface. However, at 75° incident angle, only 35% of the projectile energy is deposited within a depth of less than 1.5 nm of the surface while 65% of the projectile energy is reflected. Therefore, important aspects of the collision process which are dependent upon energy deposition, such as sputter yield, ejection depth, and molecule dissociation, may change as the incident angle changes.     

Computation of Morse decompositions for semilinear elliptic PDEs

A numerical method for computing all solutions of an elliptic boundary value problem Au + g[u, λ] = 0 and their Morse indices as steady‐states of the parabolic problem u_t + Au + g[u, λ] = 0 is presented. Morse decompositions are also determined. The method uses a finite element approach that is based on the method of alternative problems. Error estimates for the finite element approximations are verified and examples are given. © John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 290–312, 2001     

An algorithm to obtain the critical values of the t, χ2 and F distributions

In this paper a simple and efficient algorithm for obtaining the critical values of t, χ² and F distributions is proposed. They depend only on a direct iterative rational function. The differences between the proposed algorithm and others are discussed.     

On the most powerful quantile test of the scale parameter

Summary The most powerful test of the null hypothesisH ₀:σ=σ ₀ versus the alternative hypothesisH ₁:σ=σ ₁ based on a few selected sample quantiles is proposed here where σ is the scale parameter of the distribution and the location parameter μ is known. The quantiles are chosen from a large sample that is either complete or censored (singly-censored or doubly-censored). The relationship between the proposed test and the asymptotically best linear unbiased estimate (ABLUE) of the scale parameter is discussed.     

Combined simulations and analytical model for predicting trends in cluster bombardment

A series of computational investigations has been performed to examine the mesoscale energy dynamics of cluster bombardment events on a variety of systems. Through the development and application of the mesoscale energy deposition footprint (MEDF) model, we have successfully predicted the yield trends exhibited by a variety of projectiles and incident energies. The details of this model, dynamics of the damaged region, and comparison to experimental SIMS results are presented. The general cluster behavior which is revealed by this study is also discussed.