Steered molecular dynamics studies of the potential of mean force of a Na+ or K+ ion in a cyclic peptide nanotube

Potential of mean force (PMF) profiles of a single Na+ or K+ ion passing through a cyclic peptide nanotube, cyclo[-(D-Ala-Glu-D-Ala-Gln)2-], in water are calculated to provide insight into ion transport and to understand the conductance difference between these two ions. The PMF profiles are obtained by performing steered molecular dynamics (SMD) simulations that are based on the Jarzynski equality. The computed PMF profiles for both ions show barriers of around 2.4 kcal/mol at the channel entrances and exits and energy wells in the middle of the tube. The energy barriers, so-called dielectric energy barriers, arise due to the desolvation of water molecules when ions move across the nanotube, and the energy wells appear as a result of attractive interactions between the cations and negatively charged carbonyl oxygens on the backbone of the tube. We find more and deeper energy wells in the PMF profile for Na+ than for K+, which suggests that Na+ ions have a longer residence time inside the nanotube and that permeation of Na+ ions is reduced compared to K+ ions. Calculations of the radial distribution functions (RDF) between the ions and oxygens in the water molecules and in carbonyl groups on the tube and an investigation of the orientations of the carbonyl groups show that, in contrast with the dynamic carbonyl groups observed in the selectivity filter of the KcsA ion channel, the carbonyl groups in the cyclic peptide nanotube are relatively rigid, with only slight reorientation of the carbonyl groups as the cations pass through. The rigidity of the carbonyl groups in the cyclic peptide nanotube can be attributed to their role in hydrogen bonding, which is responsible for the tube structure. Comparison of the PMF profiles with the electrostatic energy profiles calculated from the Poisson-Boltzmann (PB) equation, a dielectric continuum model, reveals that the dielectric continuum model breaks down in the confined region within the tube that governs ion transport.     

Controlling the energy transfer in dipole chains

Processing digital signals on the molecular scale is of great interest. In this paper, we discuss the control of pulselike energy propagation through one-dimensional arrays of dipoles. Three systems are explored. In the first system, a chain of coaxial dipoles is gated by two control dipoles. Changing the orientation of these control dipoles lets us control the transfer of energy in the chain. In the other two systems, the chain-branch system and the two-branch system, two chains are used as an input and the propagation of energy is controlled by sending one or two signals toward the junction. Both systems can operate as a logical AND port. Their geometrical configurations are key to a well-defined control and operation of the AND port.     

An Inverse Theorem for the Uniformity Seminorms Associated with the Action of {{\mathbb {F}^{\infty}_{p}}}

Let ${\mathbb {F}}Let \mathbb F{\mathbb {F}} a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra uniformity seminorm U ^k (X) for an ergodic action (T_g)_{g ? \mathbb F^w}{(T_{g})_{{g} \in \mathbb {F}^{\omega}}} of the infinite abelian group \mathbb F^w{\mathbb {F}^{\omega}} on a probability space X = (X, B, m){X = (X, \mathcal {B}, \mu)} is generated by phase polynomials f: X ? S¹{\phi : X \to S^{1}} of degree less than C(k) on X, where C(k) depends only on k. In the case where k ￡ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} we obtain the sharp result C(k) = k. This is a finite field counterpart of an analogous result for \mathbb Z{\mathbb {Z}} by Host and Kra [HK]. In a companion paper [TZ] to this paper, we shall combine this result with a correspondence principle to establish the inverse theorem for the Gowers norm in finite fields in the high characteristic case k ￡ char(\mathbb F){k \leq {\rm char}(\mathbb {F})} , with a partial result in low characteristic.     

Cellular properties and population asymptotics in the population balance equation

Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.     

Polymer surface analysis: The leadership and contributions of David Briggs

David Briggs was a surface analysis pioneer. Starting in 1970 and continuing throughout his career, Dave used his expertise, vision, and ability to quickly master new surface analysis methods and solve important industrial problems. It certainly helped that he was an outstanding fundraiser in both industrial and academic settings, which ensured he always had an impressive array of the latest, most advanced surface analysis instrumentation at his disposal. He insisted on doing surface analysis correctly, and through his publications, databases, and books, he provided the community with the needed guidelines and methods to do so. In the 1970s, Dave's research was largely focused on X-ray photoelectron spectroscopy (XPS, also known as electron spectroscopy for chemical analysis [ESCA]) characterization of polymers and catalysts. He added secondary ion mass spectrometry (SIMS) to his instrumentation arsenal in the 1980s and provided many of the key, pioneering publications that described how to use this method to characterize polymer surfaces. He also did some of the first surface analysis imaging experiments in the 1980s. In the 1990s, he continued his XPS and SIMS research on polymers and advanced the surface analysis community's ability to properly interpret surface analysis data through databases and advanced data processing methods. Dave continued to publish polymer and catalysis surface analysis papers in the 2000s, but also expanded his surface analysis studies to several other topics.     

Nonlinear response properties of ultralarge hyperpolarizability twisted pi-system donor-acceptor chromophores. Dramatic environmental effects on response

State-average complete active space self-consistent field (SA-CASSCF) calculations are performed on the energetically lowest two electronic states of a novel alkyl-substituted 4-quinopyran twisted pi-system electro-optic chromophore. In the gas phase, the ground-state electronic configuration is diradicaloid (D), and the first excited state is zwitterionic (Z). When an external dipolar field is applied to simulate polar solvation, the relative energies of D and Z are dramatically perturbed. At sufficient field strengths, the relative ordering of the states is inverted so that Z becomes the ground state. As the energy difference between the D and Z states falls, the magnitudes of the longitudinal static polarizability (alpha) and hyperpolarizability (beta) increase appreciably--in certain cases, by 2 orders of magnitude. These computational results are interpreted and supported by qualitative state correlation diagrams constructed from qualitative molecular orbital theory and are in agreement with recent experimental results on twisted pi-system electro-optic chromophores (Kang, H. et al. J. Am. Chem. Soc. 2007, 129, 3267). The computational results also suggest that changing the environmental polarity is a promising strategy for tuning alpha and beta in such types of chromophores, which experimentally exhibit large nonlinear optical response.     

Phase diagram for assembly of biologically-active peptide amphiphiles

We construct a phase diagram for self-assembling biologically active peptide amphiphiles. The structure and stability of the assemblies are studied as a function of pH and salinity of the solution. The general features of the phase diagram are predicted based on theoretical modeling of the self-assembly process, as well as experimental data, and further experiments are performed to verify and ascertain the boundary locations of the diagram. Depending on solution conditions, the amphiphiles can form cylindrical or spherical micelles, intermediate structures between these, or may not assemble at all. We also demonstrate that changing conditions may result in phase transitions among these structures. This type of phase diagram could be useful in the design of certain supramolecular nanostructures by providing information on the necessary conditions to form them.     

Differentiating calcium carbonate polymorphs by surface analysis techniques—an XPS and TOF‐SIMS study

Calcium carbonate has evoked interest owing to its use as a biomaterial, and for its potential in biomineralization. Three polymorphs of calcium carbonate, i.e. calcite, aragonite, and vaterite were synthesized. Three conventional bulk analysis techniques, Fourier transform infrared (FTIR), X‐ray diffraction (XRD), and SEM, were used to confirm the crystal phase of each polymorphic calcium carbonate. Two surface analysis techniques, X‐ray photoelectron spectroscopy (XPS) and time‐of‐flight secondary ion mass spectroscopy (TOF‐SIMS), were used to differentiate the surfaces of these three polymorphs of calcium carbonate. XPS results clearly demonstrate that the surfaces of these three polymorphs are different as seen in the Ca(2p) and O(1s) core‐level spectra. The different atomic arrangement in the crystal lattice, which provides for a different chemical environment, can explain this surface difference. Principal component analysis (PCA) was used to analyze the TOF‐SIMS data. Three polymorphs of calcium carbonate cluster into three different groups by PCA scores. This suggests that surface analysis techniques are as powerful as conventional bulk analysis to discriminate calcium carbonate polymorphs. Copyright © 2008 John Wiley & Sons, Ltd.     

Theory of three-dimensional alignment by intense laser pulses

We introduce a theoretical framework for study of three-dimensional alignment by moderately intense laser pulses and discuss it at an elementary level. Several features of formal interest are noted and clarified. Our approach is nonperturbative, treating the laser field within classical and the material system within quantum mechanics. The theory is implemented numerically using a basis set of rotational eigenstates, transforming the time-dependent Schrodinger equation to a set of coupled differential equations where all matrix elements are analytically soluble. The approach was applied over the past few years to explore different adiabatic and nonadiabatic three-dimensional alignment approaches in conjunction with experiments, but its formal details and numerical implementation were not reported in previous studies. Although we provide simple numerical examples to illustrate the content of the equations, our main goal is to complement previous reports through an introductory discussion of the underlying theory.