Protein‐protein docking by shape‐complementarity and property matching

We present a computational approach to protein‐protein docking based on surface shape complementarity (“ProBinder”). Within this docking approach, we implemented a new surface decomposition method that considers local shape features on the protein surface. This new surface shape decomposition results in a deterministic representation of curvature features on the protein surface, such as “knobs,” “holes,” and “flats” together with their point normals. For the actual docking procedure, we used geometric hashing, which allows for the rapid, translation‐, and rotation‐free comparison of point coordinates. Candidate solutions were scored based on knowledge‐based potentials and steric criteria. The potentials included electrostatic complementarity, desolvation energy, amino acid contact preferences, and a van‐der‐Waals potential. We applied ProBinder to a diverse test set of 68 bound and 30 unbound test cases compiled from the Dockground database. Sixty‐four percent of the protein‐protein test complexes were ranked with an root mean square deviation (RMSD) < 5 Å to the target solution among the top 10 predictions for the bound data set. In 82% of the unbound samples, docking poses were ranked within the top ten solutions with an RMSD < 10 Å to the target solution. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Predicting olfactory receptor neuron responses from odorant structure

Background  

Olfactory receptors work at the interface between the chemical world of volatile molecules and the perception of scent in the brain. Their main purpose is to translate chemical space into information that can be processed by neural circuits. Assuming that these receptors have evolved to cope with this task, the analysis of their coding strategy promises to yield valuable insight in how to encode chemical information in an efficient way.     

Comparison principles applied to obstacle problems with penalties

Penalty methods form a well known technique to embed elliptic variational inequality problems into a family of variational equations (cf. [6], [13], [17]). Using the specific inverse monotonicity properties of these problems L _∞-bounds for the convergence can be derived by means of comparison solutions. Lagrange duality is applied to estimate parameters involved.

For piecewise linear finite elements applied on weakly acute triangulations in combination with mass lumping the inverse monotonicity of the obstacle problems can be transferred to its discretization. This forms the base of similar error estimations in the maximum norm for the penalty method applied to the discrete problem.

The technique of comparison solutions combined with the uniform boundedness of the Lagrange multipliers leads to decoupled convergence estimations with respect to the discretization and penalization parameters.     

Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.     

A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms

A new deterministic branch and bound algorithm is presented in this paper for the global optimization of continuous problems that involve concave univariate, bilinear and linear fractional terms. The proposed algorithm, the branch and contract algorithm, relies on the use of a bounds-contraction subproblem that aims at reducing the size of the search region by eliminating portions of the domain in which the objective function takes only values above a known upper bound. The solution of contraction subproblems at selected branch and bound nodes is performed within a finite contraction operation that helps reducing the total number of nodes in the branch and bound solution tree. The use of the proposed algorithm is illustrated with several numerical examples.     

On the Existence of a Generalized Solution to a Three-Dimensional Elliptic Equation with Radiation Boundary Condition

For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent q which is greater than for the fourth power law.     

Quantification of regional intrapulmonary oxygen partial pressure evolution during apnea by (3)He MRI

We present a new method to determine in vivo the temporal evolution of intrapulmonary oxygen concentrations by functional lung imaging with hyperpolarized (3)Helium ((3)He-->). Single-breath, single-bolus visualization of (3)He--> administered to the airspaces is used to analyze nuclear spin relaxation caused by the local oxygen partial pressure p(O(2))(t). We model the dynamics of hyperpolarization in the lung by rate equations. Based hereupon, a double acquisition technique is presented to separate depolarization by RF pulses and oxygen induced relaxation. It permits the determination of p(O(2)) with a high accuracy of up to 3% with simultaneous flip angle calibration using no additional input parameters. The time course of p(O(2)) during short periods of breathholding is found to be linear in a pig as well as in a human volunteer. We also measured the wall relaxation time in the lung and deduced a lower limit of 4.3 min.     

Partial inner product spaces. II. Operators

We study linear operators between nondegenerate partial inner product spaces and their relationships to selfadjoint operators in a “middle” Hilbert space.     

Ultimate turbulent Taylor-Couette flow

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re(i)=2×10(6) of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Re(w) of the turbulent Taylor-vortex flow is found to scale as Re(w)∝Ta(1/2), exactly as predicted by Grossmann and Lohse [Phys. Fluids 23, 045108 (2011).] for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu(ω)∝Ta(0.38), also in correspondence with turbulence in the ultimate regime. The scaling of Nu(ω) is confirmed by local angular velocity flux measurements extracted from high-speed PIV measurements: though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global torque measurements.