Influence of Josephson current second harmonic on stability of magnetic flux in long junctions

We study the long Josephson junction (LJJ) model which takes into account the second harmonic of the Fourier expansion of Josephson current. The dependence of the static magnetic flux distributions on parameters of the model are investigated numerically. Stability of the static solutions is checked by the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. New solutions which do not exist in the traditional model, have been found. Investigation of the influence of second harmonic on the stability of magnetic flux distributions for main solutions is performed.Comment: 4 pages, 6 figures, to be published in Proc. of Dubna-Nano2010, July 5-10, 2010, Russi

EFFECT OF FLUNARIZINE ON CONTRACTILE ACTIVITY OF ANTRUM AND FUNDUS OF GUINEA PIG STOMACH

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Pseudo-plateau bursting and mixed-mode oscillations in a model of developing inner hair cells

This is the final version. Available on open access from Elsevier via the DOI in this recordInner hair cells (IHCs) are excitable sensory cells in the inner ear that encode acoustic information. Before the onset of hearing IHCs fire calcium-based action potentials that trigger transmitter release onto developing spiral ganglion neurones. There is accumulating experimental evidence that these spontaneous firing patterns are associated with maturation of the IHC synapses and hence involved in the development of hearing. The dynamics organising the IHCs’ electrical activity are therefore of interest. Building on our previous modelling work we propose a three-dimensional, reduced IHC model and carry out non-dimensionalisation. We show that there is a significant range of parameter values for which the dynamics of the reduced (three-dimensional) model map well onto the dynamics observed in the original biophysical (four-dimensional) IHC model. By estimating the typical time scales of the variables in the reduced IHC model we demonstrate that this model could be characterised by two fast and one slow or one fast and two slow variables depending on biophysically relevant parameters that control the dynamics. Specifically, we investigate how changes in the conductance of the voltage-gated calcium channels as well as the parameter corresponding to the fraction of free cytosolic calcium concentration in the model affect the oscillatory model bahaviour leading to transition from pseudo-plateau bursting to mixed-mode oscillations. Hence, using fast-slow analysis we are able to further our understanding of this model and reveal a path in the parameter space connecting pseudo-plateau bursting and mixed-mode oscillations by varying a single parameter in the model.Engineering and Physical Sciences Research Council (EPSRC

Entrainment and Control of Bacterial Populations: An in Silico Study over a Spatially Extended Agent Based Model

This is the author accepted manuscript. The final version is available from American Chemical Society via the DOI in this record.We extend a spatially explicit agent based model (ABM) developed previously to investigate entrainment and control of the emergent behavior of a population of synchronized oscillating cells in a microfluidic chamber. Unlike most of the work in models of control of cellular systems which focus on temporal changes, we model individual cells with spatial dependencies which may contribute to certain behavioral responses. We use the model to investigate the response of both open loop and closed loop strategies, such as proportional control (P-control), proportional-integral control (PI-control) and proportional-integral-derivative control (PID-control), to heterogeinities and growth in the cell population, variations of the control parameters and spatial effects such as diffusion in the spatially explicit setting of a microfluidic chamber setup. We show that, as expected from the theory of phase locking in dynamical systems, open loop control can only entrain the cell population in a subset of forcing periods, with a wide variety of dynamical behaviors obtained outside these regions of entrainment. Closed-loop control is shown instead to guarantee entrainment in a much wider region of control parameter space although presenting limitations when the population size increases over a certain threshold. In silico tracking experiments are also performed to validate the ability of classical control approaches to achieve other reference behaviors such as a desired constant output or a linearly varying one. All simulations are carried out in BSim, an advanced agent-based simulator of microbial population which is here extended ad hoc to include the effects of control strategies acting onto the population.The authors declare no competing interests. We thank Dr. Nigel J. Savery at the University of Bristol for useful discussions around the subject of GRNs and for his help in developing the original ABM model. We also wish to thank Dr Gianfranco Fiore at the University of Bristol and the anonymous reviewers for reading the revised manuscript carefully and providing insightful comments that led to a consistent revision of the original manuscript. P.M. was supported by EPSRC Grant EP/E501214/1 and K.T.-A. by EPSRC Grant EP/I018638/1. The funders had no role in study design, data collection, and analysis, decision to publish, or preparation of the manuscript. This work was carried out using the computational facilities of the Advanced Computing Research Centre, University of Bristol, http://www.bris.ac.uk/acrc/

Modeling judgment of sequentially presented categories using weighting and sampling without replacement

In a series of experiments, Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874–1886, 2011) studied relative-frequency judgments of items drawn from two distinct categories. The experiments showed that the judged frequencies of categories of sequentially encountered stimuli are affected by the properties of the experienced sequences. Specifically, a first-run effect was observed, whereby people overestimated the frequency of a given category when that category was the first repeated category to occur in the sequence. Here, we (1) interpret these findings as reflecting the operation of a judgment heuristic sensitive to sequential patterns, (2) present mathematical definitions of the sequences used in Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874–1886, 2011), and (3) present a mathematical formalization of the first-run effect—the judgments-relative-to-patterns model—to account for the judged frequencies of sequentially encountered stimuli. The model parameter w accounts for the effect of the length of the first run on frequency estimates, given the total sequence length. We fitted data from Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874–1886, 2011) to the model parameters, so that with increasing values of w, subsequent items in the first run have less influence on judgments. We see the role of the model as essential for advancing knowledge in the psychology of judgments, as well as in other disciplines, such as computer science, cognitive neuroscience, artificial intelligence, and human–computer interaction

Spatiotemporal dynamics of insulitis in human Type 1 diabetes

This is the final version of the article. Available from the publisher via the DOI in this record.Type 1 diabetes (T1D) is an auto-immune disease characterised by the selective destruction of the insulin secreting beta cells in the pancreas during an inflammatory phase known as insulitis. Patients with T1D are typically dependent on the administration of externally provided insulin in order to manage blood glucose levels. Whilst technological developments have significantly improved both the life expectancy and quality of life of these patients, an understanding of the mechanisms of the disease remains elusive. Animal models, such as the NOD mouse model, have been widely used to probe the process of insulitis, but there exist very few data from humans studied at disease onset. In this manuscript, we employ data from human pancreases collected close to the onset of type 1 diabetes and propose a spatio-temporal computational model for the progression of insulitis in human T1D, with particular focus on the mechanisms underlying the development of insulitis in pancreatic islets. This framework allows us to investigate how the time-course of insulitis progression is affected by altering key parameters, such as the number of the CD20+ B cells present in the inflammatory infiltrate, which has recently been proposed to influence the aggressiveness of the disease. Through the analysis of repeated simulations of our stochastic model which track the number of beta cells within an islet, we find that increased numbers of B cells in the peri-islet space lead to faster destruction of the beta cells. We also find that the balance between the degradation and repair of the basement membrane surrounding the islet is a critical component in governing the overall destruction rate of the beta cells and their remaining number. Our model provides a framework for continued and improved spatio-temporal modelling of human T1D.This work was generously supported by the Wellcome Trust Institutional Strategic Support Award (WT105618MA). KT gratefully acknowledges the financial support of the EPSRC via grant EP/N014391/1. We are also pleased to acknowledge financial support from the European Unions Seventh Framework Programme PEVNET [FP7/2007-2013] under grant agreement number 261441 to NM. The participants of the PEVNET consortium are described at http://www.uta.fi/med/pevnet/ publications.html. Additional support was from a JDRF Career Development Award (5-CDA-2014-221-A-N) to SR and project grant 15/0005156 from Diabetes UK (to NM and SR)

Wavelet transform-based de-noising for two-photon imaging of synaptic Ca2+ transients.

PublishedJournal ArticleResearch Support, Non-U.S. Gov'tThis is an open access article.Postsynaptic Ca(2+) transients triggered by neurotransmission at excitatory synapses are a key signaling step for the induction of synaptic plasticity and are typically recorded in tissue slices using two-photon fluorescence imaging with Ca(2+)-sensitive dyes. The signals generated are small with very low peak signal/noise ratios (pSNRs) that make detailed analysis problematic. Here, we implement a wavelet-based de-noising algorithm (PURE-LET) to enhance signal/noise ratio for Ca(2+) fluorescence transients evoked by single synaptic events under physiological conditions. Using simulated Ca(2+) transients with defined noise levels, we analyzed the ability of the PURE-LET algorithm to retrieve the underlying signal. Fitting single Ca(2+) transients with an exponential rise and decay model revealed a distortion of τ(rise) but improved accuracy and reliability of τ(decay) and peak amplitude after PURE-LET de-noising compared to raw signals. The PURE-LET de-noising algorithm also provided a ∼30-dB gain in pSNR compared to ∼16-dB pSNR gain after an optimized binomial filter. The higher pSNR provided by PURE-LET de-noising increased discrimination accuracy between successes and failures of synaptic transmission as measured by the occurrence of synaptic Ca(2+) transients by ∼20% relative to an optimized binomial filter. Furthermore, in comparison to binomial filter, no optimization of PURE-LET de-noising was required for reducing arbitrary bias. In conclusion, the de-noising of fluorescent Ca(2+) transients using PURE-LET enhances detection and characterization of Ca(2+) responses at central excitatory synapses.C.M.T. and J.R.M. were supported by the Wellcome Trust, and K.T.-A. was supported by grant No. EP/I018638/1 from the Engineering and Physical Sciences Research Council

Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells.

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The entorhinal cortex is a crucial component of our memory and spatial navigation systems and is one of the first areas to be affected in dementias featuring tau pathology, such as Alzheimer's disease and frontotemporal dementia. Electrophysiological recordings from principle cells of medial entorhinal cortex (layer II stellate cells, mEC-SCs) demonstrate a number of key identifying properties including subthreshold oscillations in the theta (4-12 Hz) range and clustered action potential firing. These single cell properties are correlated with network activity such as grid firing and coupling between theta and gamma rhythms, suggesting they are important for spatial memory. As such, experimental models of dementia have revealed disruption of organised dorsoventral gradients in clustered action potential firing. To better understand the mechanisms underpinning these different dynamics, we study a conductance based model of mEC-SCs. We demonstrate that the model, driven by extrinsic noise, can capture quantitative differences in clustered action potential firing patterns recorded from experimental models of tau pathology and healthy animals. The differential equation formulation of our model allows us to perform numerical bifurcation analyses in order to uncover the dynamic mechanisms underlying these patterns. We show that clustered dynamics can be understood as subcritical Hopf/homoclinic bursting in a fast-slow system where the slow sub-system is governed by activation of the persistent sodium current and inactivation of the slow A-type potassium current. In the full system, we demonstrate that clustered firing arises via flip bifurcations as conductance parameters are varied. Our model analyses confirm the experimentally suggested hypothesis that the breakdown of clustered dynamics in disease occurs via increases in AHP conductance.The contribution of MG, KTR and JB was generously supported by a Wellcome Trust Institutional Strategic Support Award (WT105618MA). MG and KT gratefully acknowledge the financial support of the EPSRC via grant EP/N014391/1. LT’s doctoral studentship is supported by the Alzheimer’s Society in partnership with the Garfield Weston Foundation (grant reference 231). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Dynamical systems analysis of spike-adding mechanisms in transient bursts

Transient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism

Acetylcholine modulates gamma frequency oscillations in the hippocampus by activation of muscarinic M1 receptors

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1111/ejn.13582 This article is protected by copyright. All rights reserved.Modulation of gamma oscillations is important for the processing of information and the disruption of gamma oscillations is a prominent feature of schizophrenia and Alzheimer’s disease. Gamma oscillations are generated by the interaction of excitatory and inhibitory neurons where their precise frequency and amplitude are controlled by the balance of Accepted Article This article is protected by copyright. All rights reserved. excitation and inhibition. Acetylcholine enhances the intrinsic excitability of pyramidal neurons and supresses both excitatory and inhibitory synaptic transmission but the net modulatory effect on gamma oscillations is not known. Here, we find that the power, but not frequency, of optogenetically -induced gamma oscillations in the CA3 region of mouse hippocampal slices is enhanced by low concentrations of the broad spectrum cholinergic agonist carbachol but reduced at higher concentrations. This bidirectional modulation of gamma oscillations is replicated within a mathematical model by neuronal depolarization, but not by reducing synaptic conductances, mimicking the effects of muscarinic M1 receptor activation. The predicted role for M1 receptors was supported experimentally; bidirectional modulation of gamma oscillations by acetylcholine was replicated by a selective M1 receptor agonist and prevented by genetic deletion of M1 receptors. These results reveal that acetylcholine release in CA3 of the hippocampus modulates gamma oscillation power but not frequency in a bidirectional and dose -dependent manner by acting primarily through muscarinic M1 receptorsThis work was supported by the Wellcome Trust Neural Dynamics PhD programme (RTB) and the Wellcome Trust (JRM). We thank Eli Lilly and Co. for gifts of GSK -5 and M1 receptor knockout mice. We thank members of the Mellor lab for helpful discussions and J. Brown for comments on previous versions of the manuscript. The authors declare no competing financial interests