Holliday junction resolvase in Schizosaccharomyces pombe has identical endonuclease activity to the CCE1 homologue YDC2

A novel Holliday junction resolving activity has been identified in fractionated cell extracts of the fission yeast Schizosaccharomyces pombe . The enzyme catalyses endonucleolytic cleavage of Holliday junction-containing chi DNA and synthetic four-way DNA junctions. The activity cuts with high specificity a synthetic four-way junction containing a 12 bp core of homologous sequences but has no activity on another four-way junction (with a fixed crossover point), a three-way junction, linear duplex DNA or duplex DNA containing six mismatched nucleotides in the centre. The major cleavage sites map as single nicks in the vicinity of the crossover point, 3' of a thymidine residue. These data indicate that the activity has a strong DNA structure selectivity as well as a limited sequence preference; features similar to the Holliday junction resolving enzymes RuvC of Escherichia coli and the mitochondrial CCE1 (cruciform-cuttingenzyme 1) of Saccharomyces cerevisiae. A putative homologue of CCE1 in S.pombe (YDC2_SCHPO) has been identified through a search of the sequence database. The open reading frame of this gene has been cloned and the encoded protein, YDC2, expressed in E.coli . The purified recombinant YDC2 exhibits Holliday junction resolvase activity and is, therefore, a functional S.pombe homologue of CCE1. The resolvase YDC2 shows the same substrate specificity and produces identical cleavage sites as the activity obtained from S. pombe cells. Both YDC2 and the cellular activity cleave Holliday junctions in both orientations to give nicks that can be ligated in vitro. The partially purified Holliday junction resolving enzyme in fission yeast is biochemically indistinguishable from recombinant YDC2 and appears to be the same protein

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

Dynamics of plateau bursting in dependence on the location of its equilibrium

We present a mathematical analysis, based on numerical explorations, of the bursting patterns that arise in plateau-bursting models of endocrine cells as the position of the equilibrium varies. We consider both square-wave and pseudo-plateau bursting. Within the framework of systems with multiple time scales, it is well known how the underlying fast subsystem organises the behaviour of the model, but such results are valid only in a small enough neighbourhood of the singular limit that defines the fast subsystem. Hence, the slow variable (intracellular calcium concentration) must be very slow, while the physiologically realistic range is moderately slow. Furthermore, the theoretical predictions are also only valid for parameter values such that the equilibrium is close to a homoclinic bifurcation that occurs in the fast subsystem. In this paper, we discuss what happens outside this theoretically known neighbourhood of parameter space. Our results complement our earlier work, in collaboration with Riess and Sherman (Journal of Theoretical Biology 2010, in press), which focussed on how the bursting patterns vary with the rate of change epsilon of the slow variable: we fix epsilon and move the equilibrium over the full range of the bursting regime

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

Bifurcation Analysis of a Two-Compartment Hippocampal Pyramidal Cell Model

The Pinsky-Rinzel model is a non-smooth 2-compartmental CA3 pyramidal cell model that has been used widely within the field of neuroscience. Here we propose a modified (smooth) system that captures the qualitative behaviour of the original model, while allowing the use of available, numerical continuation methods to perform full-system bifurcation and fastslow analysis. We study the bifurcation structure of the full system as a function of the applied current and the maximal calcium conductance. We identify the bifurcations that shape the transitions between resting, bursting and spiking behaviours, and which lead to the disappearance of bursting when the calcium conductance is reduced. Insights gained from this analysis, are then used to firstly illustrate how the irregular spiking activity found between bursting and stable spiking states, can be influenced by phase differences in the calcium and dendritic voltage, which lead to corresponding changes in the calcium-sensitive potassium current. Furthermore, we use fast-slow analysis to investigate the mechanisms of bursting and show that bursting in the model is dependent on the intermediately slow variable, calcium, while the other slow variable, the activation gate of the afterhyperpolarisation current, does not contribute to setting the intraburst dynamics but participates in setting the interburst interval. Finally, we discuss how some of the described bifurcations affect spiking behaviour, during sharp-wave ripples, in a larger network of Pinsky-Rinzel cells.LAA is supported by the Engineering and Physical Sciences Research Council (EPSRC) and Eli Lilly & Company; LYP is supported by the Wellcome Trust; and KT-A is supported by grant EP/N014391/1 of the EPSRC

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

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