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

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

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

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

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

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

Managerial delegation in a dynamic renewable resource oligopoly

I propose a differential oligopoly game of resource extraction under (quasi-static) open-loop and nonlinear feedback strategies, where firms are managerial and two alternative types of delegation contract are considered. Under open-loop information, delegation expands the residual steady state resource stock. Conversely, under nonlinear feedback information the outcome depends on the structure of managerial incentives. If sales are used, once again delegation favours resource preservation. On the contrary, if market shares are included in the delegation contract, this combines with an underlying voracity effect in shrinking the steady state volume of the resource

DYT1 dystonia patient-derived fibroblasts have increased deformability and susceptibility to damage by mechanical forces

DYT1 dystonia is a neurological movement disorder that is caused by a loss-of-function mutation in the DYT1 / TOR1A gene, which encodes torsinA, the luminal ATPase-associated (AAA+) protein. TorsinA is required for the assembly of functional linker of nucleoskeleton and cytoskeleton (LINC) complexes, and consequently the mechanical integration of the nucleus and the cytoskeleton. Despite the potential implications of altered mechanobiology in dystonia pathogenesis, the role of torsinA in regulating cellular mechanical phenotype, or mechanotype, in DYT1 dystonia remains unknown. Here, we define the mechanotype of mouse fibroblasts lacking functional torsinA as well as human fibroblasts isolated from DYT1 dystonia patients. We find that the deletion of torsinA or the expression of torsinA containing the DYT1 dystonia-causing ΔE302/303 (ΔE) mutation results in a more deformable cellular mechanotype. We observe a similar increased deformability of mouse fibroblasts that lack lamina-associated polypeptide 1 (LAP1), which interacts with and stimulates the ATPase activity of torsinA in vitro ; as well as with depletion of the LINC complex proteins, Sad1/UNC-84 (SUN)1 and SUN2, lamin A/C, or lamin B1. Moreover, we report that DYT1 dystonia patient-derived fibroblasts are more compliant than fibroblasts isolated from unafflicted individuals. DYT1 fibroblasts also exhibit increased nuclear strain and decreased viability following mechanical stretch. Taken together, our results support a model where the physical connectivity between the cytoskeleton and nucleus contributes to cellular mechanotype. These findings establish the foundation for future mechanistic studies to understand how altered cellular mechanotype may contribute to DYT1 dystonia pathogenesis; this may be particularly relevant in the context of how neurons sense and respond to mechanical forces during traumatic brain injury, which is known to be a major cause of acquired dystonia

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