Improved sampling for simulations of interfacial membrane proteins: application of generalized shadow hybrid Monte Carlo to a peptide toxin/bilayer system

The computational costs associated with performing molecular dynamics (MD) simulations are still somewhat prohibitive and therefore limit the time and length scales that can be currently achieved. One approach to overcoming the limited size and duration of a simulation is to reduce the amount of detail when representing a system of interest, generally termed "coarse-graining". An alternative approach is via more efficient sampling methods that offer an enhanced search of a complex multidimensional energy landscape. One could also combine enhanced sampling methods with a coarse-grained (CG) force field. Here, we apply generalized shadow hybrid Monte Carlo (GSHMC), a recently proposed simulation protocol, to a biomolecular system of moderate size and show that GSHMC offers improved sampling compared to standard MD simulation. Our test system is a CG representation of a small peptide toxin interacting with a phospholipid bilayer. Specifically, we show that GSHMC allows for a quicker localization of the toxin to its equilibrium location of interaction at the headgroup/water interface of the bilayer. GSHMC therefore potentially allows for future exploration of larger and more complex systems over longer periods, which would otherwise be impractical to perform using conventional simulation methodology.     

New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings

Numerical Algorithms - We propose and study new projection-type algorithms for solving pseudomonotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of...     

Sensitive redox speciation of neptunium by CE–ICP–MS

Capillary electrophoresis (CE) was used to separate the neptunium oxidation states Np(IV) and Np(V), which are the only oxidation states of Np that are stable under environmental conditions. The CE setup was coupled to an inductively coupled plasma mass spectrometer (Agilent 7500ce) using a Mira Mist CE nebulizer and a Scott-type spray chamber. The combination of the separation capacity of CE with the detection sensitivity of inductively coupled plasma mass spectrometry (ICP-MS) allows identification and quantification of Np(IV) and Np(V) at the trace levels expected in the far field of a nuclear waste repository. Limits of detection of 1?×?10^-9 and 5?×?10^-10 mol L^-1 for Np(IV) and Np(V), respectively, were achieved, with a linear range from 10^-9 to 10^-6 mol L^-1. The method was applied to study the redox speciation of the Np remaining in solution after interaction of 5?×?10^-7 mol L^-1 Np(V) with Opalinus Clay. Under mildly oxidizing conditions, a Np sorption of 31% was found, with all the Np remaining in solution being Np(V). A second sorption experiment performed in the presence of Fe²⁺ led to complete sorption of the Np onto the clay. After desorption with HClO₄, a mixture of Np(IV) and Np(V) was found in solution by CE–ICP–MS, indicating that some of the sorbed Np had been reduced to Np(IV) by Fe²⁺.     

Abstract convex optimal antiderivatives

Having studied families of antiderivatives and their envelopes in the setting of classical convex analysis, we now extend and apply these notions and results in settings of abstract convex analysis. Given partial data regarding a c-subdifferential, we consider the set of all c-convex c-antiderivatives that comply with the given data. Under a certain assumption, this set is not empty and contains both its lower and upper envelopes. We represent these optimal antiderivatives by explicit formulae. Some well known functions are, in fact, optimal c-convex c-antiderivatives. In one application, we point out a natural minimality property of the Fitzpatrick function of a c-monotone mapping, namely that it is a minimal antiderivative. In another application, in metric spaces, a constrained Lipschitz extension problem fits naturally the convexity notions we discuss here. It turns out that the optimal Lipschitz extensions are precisely the optimal antiderivatives. This approach yields explicit formulae for these extensions, the most particular case of which recovers the well known extensions due to McShane and Whitney.     

Isotropic-nematic interface and wetting in suspensions of colloidal platelets

We study interfacial phenomena in a colloidal dispersion of sterically stabilized gibbsite platelets, exhibiting coexisting isotropic and nematic phases separated by a sharp horizontal interface. The nematic phase wets a vertical glass wall and polarized light micrographs reveal homeotropic surface anchoring both at the free isotropic-nematic interface and at the wall. On the basis of complete wetting of the wall by the nematic phase, as found in our density functional calculations and computer simulations, we analyze the balance between Frank elasticity and surface anchoring near the contact line. Because of weak surface anchoring, the director field in the capillary rise region is uniform. From the measured rise (6 microm) of the meniscus at the wall we determine the isotropic-nematic surface tension to be 3 nN/m, in quantitative agreement with our theoretical and simulation results.     

Detecting K-Theory by Cyclic Homology

We discuss which part of the rationalized algebraic K-theoryof a group ring is detected via trace maps to Hochschild homology,cyclic homology, periodic cyclic or negative cyclic homology.2000 Mathematics Subject Classification 19D55.     

Anisotropic Operator Symbols Arising From Multivariate Jump Processes

It is shown that infinitesimal generators of certain multivariate pure jump Lévy copula processes give rise to a class of anisotropic symbols that extends the well-known classes of pseudo differential operators of H?rmander-type. In addition, we provide minimal regularity convergence analysis for a sparse tensor product finite element approximation to solutions of the corresponding stationary Kolmogorov equations . The computational complexity of the presented approximation scheme is essentially independent of the underlying state space dimension.      

Local analytic solutions of the generalized Dhombres functional equation II

We study local analytic solutions f of the generalized Dhombres functional equation f(zf(z))=φ(f(z)), where φ is holomorphic at w₀≠0, f is holomorphic in some open neighborhood of 0, depending on f, and f(0)=w₀. After deriving necessary conditions on φ for the existence of nonconstant solutions f with f(0)=w₀ we describe, assuming these conditions, the structure of the set of all formal solutions, provided that w₀ is not a root of 1. If |w₀|≠1 or if w₀ is a Siegel number we show that all formal solutions yield local analytic ones. For w₀ with 0<|w₀|<1 we give representations of these solutions involving infinite products.     

Radiation curable materials – principles and new perspectives

Increasing environmental concerns and the ensuing legislation to cut emissions of volatile organic compounds (VOCs) have been major driving forces behind the development of radiation cured coatings over the past 25 years. Today radiation cured coatings are known for their good overall performance and their excellent resistance against chemical and physical surface damages. Advanced photoinitiator systems allow the light stabilisation of UV‐curable formulations and the outdoor application of the coating. The rapid curing, combined with the possibility of immediate processing of the coated objects opens the way for radiation curing – in 100%‐, water based‐, and dual cure systems as well as for radiation curable powder coatings – for a wide variety of application.     

Affine-Invariant Ensemble Transform Methods for Logistic Regression

We investigate the application of ensemble transform approaches to Bayesian inference of logistic regression problems. Our approach relies on appropriate extensions of the popular ensemble Kalman filter and the feedback particle filter to the cross entropy loss function and is based on a well-established homotopy approach to Bayesian inference. The arising finite particle evolution equations as well as their mean-field limits are affine-invariant. Furthermore, the proposed methods can be implemented in a gradient-free manner in case of nonlinear logistic regression and the data can be randomly subsampled similar to mini-batching of stochastic gradient descent. We also propose a closely related SDE-based sampling method which again is affine-invariant and can easily be made gradient-free. Numerical examples demonstrate the appropriateness of the proposed methodologies.