Structural characterization of flexible proteins using small-angle X-ray scattering

Structural analysis of flexible macromolecular systems such as intrinsically disordered or multidomain proteins with flexible linkers is a difficult task as high-resolution techniques are barely applicable. A new approach, ensemble optimization method (EOM), is proposed to quantitatively characterize flexible proteins in solution using small-angle X-ray scattering (SAXS). The flexibility is taken into account by allowing for the coexistence of different conformations of the protein contributing to the experimental scattering pattern. These conformers are selected using a genetic algorithm from a pool containing a large number of randomly generated models covering the protein configurational space. Quantitative criteria are developed to analyze the EOM selected models and to determine the optimum number of conformers in the ensemble. Simultaneous fitting of multiple scattering patterns from deletion mutants, if available, provides yet more detailed local information about the structure. The efficiency of EOM is demonstrated in model and practical examples on completely or partially unfolded proteins and on multidomain proteins interconnected by linkers. In the latter case, EOM is able to distinguish between rigid and flexible proteins and to directly assess the interdomain contacts.     

A global optimization algorithm for generalized semi-infinite,continuous minimax with coupled constraints and bi-level problems

We propose an algorithm for the global optimization of three problem classes: generalized semi-infinite, continuous coupled minimax and bi-level problems. We make no convexity assumptions. For each problem class, we construct an oracle that decides whether a given objective value is achievable or not. If a given value is achievable, the oracle returns a point with a value better than or equal to the target. A binary search is then performed until the global optimum is obtained with the desired accuracy. This is achieved by solving a series of appropriate finite minimax and min-max-min problems to global optimality. We use Laplace’s smoothing technique and a simulated annealing approach for the solution of these problems. We present computational examples for all three problem classes.     

Silicon nanowire photodetector enhanced by a bow-tie antenna

Properties of surface plasmon polaritons can be exploited for the miniaturisation of photonic circuits below the optical wavelength scale. Smaller and more sensitive photodetectors can be made by using sub-wavelength semiconductor elements such as germanium or silicon nanowires in combination with nanometer-scale antennas. The proposed nanowire photodetector enables on-chip optical sensing applications with increased sensitivity and reduced size.     

New oxorhenium(V) complexes from the widely used diaminedithiol (DADT) ligand system

Synthesis of the 2,9-dimethyl-4,7-diaza-4-alkyl-2,9-decanedithiol (1, alkyl = morpholinylethyl in a, and alkyl = pyrrolidinylethyl in b), following a widely used synthetic scheme for diaminedithiol (DADT) ligands, led to the isolation of 1-alkyl-2-(1'-methyl-1'-sulfanylethyl)-3-(2' '-methyl-2' '-sulfanylpropyl)diazolidine (3) as the major product. Both ligands 1 and 2 gave complexes with the oxorhenium ReO(V) core. Ligand 1 gave the expected ReO[SNNS] complex (2) with the side chain on nitrogen in the syn configuration. Ligand 3 gave, in the presence of a monodentate aromatic thiol, complexes of the ReO[SNN][S][S] (4) and ReO[SNN][S] type (5), respectively, in which the diazolidine ring has rearranged to a thiazolidine ring. Crystallographic analysis showed that in 4 the coordination geometry about the metal is distorted octahedral where the equatorial plane is defined by the sulfur and one of the nitrogen atoms of the ligand and the two sulfurs of the aromatic thiols, while the axial positions are occupied by the oxygen of the ReO core and the second nitrogen of the ligand. Specifically, complex 4a crystallizes in space group P2(1)/c, a = 15.63(1) A, b = 15.28(2) A, c = 16.07(1) A, beta = 113.78(2) degrees, V = 3512(5) A(3), Z = 4. Complex 4b crystallizes in space group P2(1)/n, a = 14.560(9) A, b = 14.804(9) A, c = 19.85(1) A, beta = 90.94(2) degrees, V = 4278(1) A(3), Z = 4. In 5b, the coordination geometry is distorted square pyramidal with the SNN donor atom of the ligand and the aromatic thiol defining the equatorial plane and the doubly bonded oxygen occupying the apex of the pyramid. Complex 5b crystallizes in space group P(-)1, a = 9.387(5) A, b = 11.306(5) A, c = 14.040(6) A, alpha = 84.51(1) degrees, beta = 84.45(2) degrees, gamma = 87.17(1) degrees, V = 1475(1) A(3), Z = 2. All isolated complexes are neutral and lipophilic. Complete assignments of (1)H and (13)C NMR resonances are reported.     

Evidence of reciprocal reorientation of the catalytic and hemopexin-like domains of full-length MMP-12

The proteolytic activity of matrix metalloproteinases toward extracellular matrix components (ECM), cytokines, chemokines, and membrane receptors is crucial for several homeostatic and pathological processes. Active MMPs are a family of single-chain enzymes (23 family members in the human genome), most of which constituted by a catalytic domain and by a hemopexin-like domain connected by a linker. The X-ray structures of MMP-1 and MMP-2 suggest a conserved and well-defined spatial relationship between the two domains. Here we present structural data for MMP-12, suitably stabilized against self-hydrolysis, both in solution (NMR and SAXS) and in the solid state (X-ray), showing that the hemopexin-like and the catalytic domains experience conformational freedom with respect to each other on a time scale shorter than 10(-8) s. Hints on the probable conformations are also obtained. This experimental finding opens new perspectives for the often hypothesized active role of the hemopexin-like domain in the enzymatic activity of MMPs.     

A branch and bound method for the solution of multiparametric mixed integer linear programming problems

In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch and bound strategy that involves the solution of a multiparametric linear programming sub-problem at leaf nodes and appropriate comparison procedures to update the tree. McCormick relaxation procedures are employed to overcome the presence of bilinear terms in the model. The algorithm generates an envelope of parametric profiles, containing the optimal solution of the mp-MILP problem. The parameter space is partitioned into polyhedral convex critical regions. Two examples are presented to illustrate the steps of the proposed algorithm.     

Linearly Constrained Global Optimization and Stochastic Differential Equations

A stochastic algorithm is proposed for the global optimization of nonconvex functions subject to linear constraints. Our method follows the trajectory of an appropriately defined Stochastic Differential Equation (SDE). The feasible set is assumed to be comprised of linear equality constraints, and possibly box constraints. Feasibility of the trajectory is achieved by projecting its dynamics onto the set defined by the linear equality constraints. A barrier term is used for the purpose of forcing the trajectory to stay within the box constraints. Using Laplace’s method we give a characterization of a probability measure (Π) that is defined on the set of global minima of the problem. We then study the transition density associated with the projected diffusion process and show that its weak limit is given by Π. Numerical experiments using standard test problems from the literature are reported. Our results suggest that the method is robust and applicable to large-scale problems.     

Possible observation of “string excitations” of a hole in a quantum antiferromagnet

We argue that recently reported high resolution angle-resolved photoelectron spectra from cuprates, where an anomalous high-energy dispersion was identified, reveal the internal structure of the hole quasiparticle in quantum antiferromagnets and more importantly it is evidence for the existence of “string-excitations” which validate early predictions based on the t–J model. Their energy–momentum dispersion, the manner in which the spectral weight is transfered to higher energy string excitations, and the vanishing of the quasiparticle spectral weight near the Γ point, are all in agreement with predictions without adjusting any parameters.     

On the Logistic Equation in the Complex Plane

The famous logistic differential equation is studied in the complex plane. The method used is based on a functional analytic technique which provides a unique solution of the ordinary differential equation (ODE) under consideration in H ₂(𝔻) or H ₁(𝔻) and gives rise to an equivalent difference equation for which a unique solution is established in ?₂ or ?₁. For the derivation of the solution of the logistic differential equation this discrete equivalent equation is used. The obtained solution is analytic in {z ∈ ?: |z| <T}, T > 0. Numerical experiments were also performed using the classical 4th order Runge–Kutta method. The obtained results were compared for real solutions as well as for solutions of the form y(t) = u(t) + iv(t), t ∈ ?. For t ∈ ? the solution derived by the present method, seems to have singularities, that is, points where it ceases to be analytic, in certain sectors of the complex plane. These sectors, depending on the values of the involved parameters, can move at different directions, join forming common sectors, or pass through each other and continue moving independently. Moreover, the real and imaginary part of the solution seem to exhibit oscillatory behavior near these sectors.     

Flexible long-term capacity planning in closed-loop supply chains with remanufacturing

We deal with long-term demand-driven capacity planning policies in the reverse channel of closed-loop supply chains (CLSCs) with remanufacturing, under high capacity acquisition cost coupled with uncertainty in actual demand, sales patterns, quality and timing of end-of-use product returns. The objective is to facilitate the decision-making when the management faces the dilemma of implementing either a strategy of early large-scale investments to benefit from economies of scale and capacity readiness, or a flexible strategy of low volume but more frequent capacity expansions. We consider a CLSC with two sequential product-types. We study the system’s response in terms of transient flows, actual/desired capacity level, capacity expansions/contractions and total supply chain profit, employing a simulation-based system dynamics optimization approach. Extensive numerical investigation covers a broad range of real-world remanufacturable products under alternative scenarios in relation to the market preference over product-types. The key findings propose flexible policies as improved alternatives to large-scale capacity expansions/contractions in terms of adaptability to the actual pattern of end-of-use product returns and involved risk in the investments’ turnover. Flexible policies are also proposed as practices to avoid overcapacity phenomena in collection and remanufacturing capacity and as robust policies to product demand. Their implementation is revealed to be even more important for the case of remanufacturing, when a high capacity acquisition unit-cost ratio (remanufacturing/collection) is coupled with strong economies of scale. Finally, results under different information sharing structures show changes in remanufacturing policies, thus justifying the importance of coordination between the decision-maker and the distributor.