170 research outputs found
Sequential noise-induced escapes for oscillatory network dynamics
It is well known that the addition of noise in a multistable system can
induce random transitions between stable states. The rate of transition can be
characterised in terms of the noise-free system's dynamics and the added noise:
for potential systems in the presence of asymptotically low noise the
well-known Kramers' escape time gives an expression for the mean escape time.
This paper examines some general properties and examples of transitions between
local steady and oscillatory attractors within networks: the transition rates
at each node may be affected by the dynamics at other nodes. We use first
passage time theory to explain some properties of scalings noted in the
literature for an idealised model of initiation of epileptic seizures in small
systems of coupled bistable systems with both steady and oscillatory
attractors. We focus on the case of sequential escapes where a steady attractor
is only marginally stable but all nodes start in this state. As the nodes
escape to the oscillatory regime, we assume that the transitions back are very
infrequent in comparison. We quantify and characterise the resulting sequences
of noise-induced escapes. For weak enough coupling we show that a master
equation approach gives a good quantitative understanding of sequential
escapes, but for strong coupling this description breaks down
Sequential escapes: onset of slow domino regime via a saddle connection
We explore sequential escape behaviour of coupled bistable systems under the
influence of stochastic perturbations. We consider transient escapes from a
marginally stable "quiescent" equilibrium to a more stable "active"
equilibrium. The presence of coupling introduces dependence between the escape
processes: for diffusive coupling there is a strongly coupled limit (fast
domino regime) where the escapes are strongly synchronised while for
intermediate coupling (slow domino regime) without partially escaped stable
states, there is still a delayed effect. These regimes can be associated with
bifurcations of equilibria in the low-noise limit. In this paper we consider a
localized form of non-diffusive (i.e pulse-like) coupling and find similar
changes in the distribution of escape times with coupling strength. However we
find transition to a slow domino regime that is not associated with any
bifurcations of equilibria. We show that this transition can be understood as a
codimension-one saddle connection bifurcation for the low-noise limit. At
transition, the most likely escape path from one attractor hits the escape
saddle from the basin of another partially escaped attractor. After this
bifurcation we find increasing coefficient of variation of the subsequent
escape times
Fast and slow domino regimes in transient network dynamics
It is well known that the addition of noise to a multistable dynamical system
can induce random transitions from one stable state to another. For low noise,
the times between transitions have an exponential tail and Kramers' formula
gives an expression for the mean escape time in the asymptotic limit. If a
number of multistable systems are coupled into a network structure, a
transition at one site may change the transition properties at other sites. We
study the case of escape from a "quiescent" attractor to an "active" attractor
in which transitions back can be ignored. There are qualitatively different
regimes of transition, depending on coupling strength. For small coupling
strengths the transition rates are simply modified but the transitions remain
stochastic. For large coupling strengths transitions happen approximately in
synchrony - we call this a "fast domino" regime. There is also an intermediate
coupling regime some transitions happen inexorably but with a delay that may be
arbitrarily long - we call this a "slow domino" regime. We characterise these
regimes in the low noise limit in terms of bifurcations of the potential
landscape of a coupled system. We demonstrate the effect of the coupling on the
distribution of timings and (in general) the sequences of escapes of the
system.Comment: 3 figure
Control of Ca2+ influx and calmodulin activation by SK-channels in dendritic spines (dataset)
A 3-dimensional model of Ca2+ and calmodulin dynamics within an idealised, but biophysically-plausible,
dendritic spine, demonstrates that SK-channels regulate calmodulin activation specifically during neurone firing patterns associated with induction of spike timing-dependent plasticity.The journal article associated with this dataset is available at: http://hdl.handle.net/10871/21745.The key trigger for Hebbian synaptic plasticity is influx of Ca2+ into postsynaptic
dendritic spines. The magnitude of [Ca2+] increase caused by NMDA-receptor
(NMDAR) and voltage-gated Ca2+ -channel (VGCC) activation is thought to determine
both the amplitude and direction of synaptic plasticity by differential activation of Ca2+
-sensitive enzymes such as calmodulin. Ca2+ influx is negatively regulated by Ca2+
-activated K+ channels (SK-channels) which are in turn inhibited by neuromodulators
such as acetylcholine. However, the precise mechanisms by which SK-channels control
the induction of synaptic plasticity remain unclear. Using a 3-dimensional model of
Ca2+ and calmodulin dynamics within an idealised, but biophysically-plausible,
dendritic spine, we show that SK-channels regulate calmodulin activation specifically
during neuron-firing patterns associated with induction of spike timing-dependent
plasticity. SK-channel activation and the subsequent reduction in Ca2+ influx through
NMDARs and L-type VGCCs results in an order of magnitude decrease in calmodulin (CaM)
activation, providing a mechanism for the effective gating of synaptic plasticity
induction. This provides a common mechanism for the regulation of synaptic plasticity
by neuromodulators
Dynamical systems analysis of spike-adding mechanisms in transient bursts
The electronic version of this article is the complete one and can be found online at: doi:10.1186/2190-8567-2-7Open Access ArticleTransient 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.Engineering and Physical Sciences Research Council (EPSRC
Bacterial secretion and the role of diffusive and subdiffusive first passage processes
Open Access ArticleBy funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events. The spatio-temporal mechanisms through which these events occur are however not fully understood, due in part to the inherent challenges in tracking single molecules moving within an intracellular medium. As a result, theoretical predictions of secretion times are still lacking. Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes. Using parameters from Shigella flexneri we are able to test the role that translocators might have to activate the needle complexes and offer semi-quantitative explanations of recent experimental observations.Engineering and Physical Sciences Research Council (EPSRC)Medical Research Council (MRC
Modeling Joint Improvisation between Human and Virtual Players in the Mirror Game
Joint improvisation is observed to emerge spontaneously among humans
performing joint action tasks, and has been associated with high levels of
movement synchrony and enhanced sense of social bonding. Exploring the
underlying cognitive and neural mechanisms behind the emergence of joint
improvisation is an open research challenge. This paper investigates the
emergence of jointly improvised movements between two participants in the
mirror game, a paradigmatic joint task example. A theoretical model based on
observations and analysis of experimental data is proposed to capture the main
features of their interaction. A set of experiments is carried out to test and
validate the model ability to reproduce the experimental observations. Then,
the model is used to drive a computer avatar able to improvise joint motion
with a human participant in real time. Finally, a convergence analysis of the
proposed model is carried out to confirm its ability to reproduce the emergence
of joint movement between the participants
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