Counterion density profiles at charged flexible membranes

Counterion distributions at charged soft membranes are studied using perturbative analytical and simulation methods in both weak coupling (mean-field or Poisson-Boltzmann) and strong coupling limits. The softer the membrane, the more smeared out the counterion density profile becomes and counterions pentrate through the mean-membrane surface location, in agreement with anomalous scattering results. Membrane-charge repulsion leads to a short-scale roughening of the membrane.Comment: 4 pages, 4 figure

Computing Slow Manifolds of Saddle Type

Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both stable and unstable fast manifolds. We present two examples of bifurcation problems where these manifolds play a key role and a third example in which saddle-type slow manifolds are part of a traveling wave profile of a partial differential equation. Initial value solvers are incapable of computing trajectories on saddle-type slow manifolds, so the slow manifold of saddle type (SMST) algorithm presented here is formulated as a boundary value method. We take an empirical approach here to assessing the accuracy and effectiveness of the algorithm.Comment: preprint version - for final version see journal referenc

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

A voice for change? Trust relationships between ombudsmen, individuals and public service providers

There has been a debate for years about what the role of the ombudsman is. This article examines a key component of the role, to promote trust in public services and government. To be able to do this, however, an ombudsman needs to be perceived as legitimate and be trusted by a range of stakeholders, including the user. This article argues that three key relationships in a person’s complaint journey can build trust in an institution, and must therefore be understood as a system. The restorative justice framework is adapted to conceptualize this trust model as a novel approach to understanding the institution from the perspective of its users. Taking two public sector ombudsmen as examples, the article finds that voice and trust need to be reinforced through the relationships in a consumer journey to manage individual expectations, prevent disengagement, and thereby promote trust in the institution, in public service providers, and in government

Nuclear Envelope Composition Determines The Ability Of Neutrophil-Type Cells To Passage Through Micron-Scale Constrictions

Neutrophils are characterized by their distinct nuclear shape, which is thought to facilitate the transit of these cells through pore spaces less than one-fifth of their diameter. We used human promyelocytic leukemia (HL-60) cells as a model system to investigate the effect of nuclear shape in whole cell deformability. We probed neutrophil-differentiated HL-60 cells lacking expression of lamin B receptor, which fail to develop lobulated nuclei during granulopoiesis and present an in vitro model for Pelger-Huët anomaly; despite the circular morphology of their nuclei, the cells passed through micron-scale constrictions on similar timescales as scrambled controls. We then investigated the unique nuclear envelope composition of neutrophil-differentiated HL-60 cells, which may also impact their deformability; although lamin A is typically down-regulated during granulopoiesis, we genetically modified HL-60 cells to generate a subpopulation of cells with well defined levels of ectopic lamin A. The lamin A-overexpressing neutrophil-type cells showed similar functional characteristics as the mock controls, but they had an impaired ability to pass through micron-scale constrictions. Our results suggest that levels of lamin A have a marked effect on the ability of neutrophils to passage through micron-scale constrictions, whereas the unusual multilobed shape of the neutrophil nucleus is less essential

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

The SOS Pilot Study: a RCT of routine oxygen supplementation early after acute stroke—effect on recovery of neurological function at one week

Mild hypoxia is common after stroke and associated with poor long-term outcome. Oxygen supplementation could prevent hypoxia and improve recovery. A previous study of routine oxygen supplementation showed no significant benefit at 7 and 12 months. This pilot study reports the effects of routine oxygen supplementation for 72 hours on oxygen saturation and neurological outcomes at 1 week after a stroke

A large displacement, high frequency, underwater microelectromechanical systems actuator

Here, we demonstrate an in situ electrostatic actuator that can operate underwater across a wide range of displacements and frequencies, achieving a displacement of approximately 10-μm at 500-Hz and 1-μm at 5-kHz; this performance surpasses that of existing underwater physical actuators. To attain these large displacements at such high speeds, we optimized critical design parameters using a computationally efficient description of the physics of low quality (Q) factor underwater electrostatic actuators. Our theoretical model accurately predicts actuator motion profiles as well as limits of bandwidth and displacement