Bifurcation and resonance in a model for bursting nerve cells

In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.     

Full system bifurcation analysis of endocrine bursting models

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.     

Resetting Behavior in a Model of Bursting in Secretory Pituitary Cells: Distinguishing Plateaus from Pseudo-Plateaus

We study a recently discovered class of models for plateau bursting, inspired by models for endocrine pituitary cells. In contrast to classical models for fold-homoclinic (square-wave) bursting, the spikes of the active phase are not supported by limit cycles of the frozen fast subsystem, but are transient oscillations generated by unstable limit cycles emanating from a subcritical Hopf bifurcation around a stable steady state. Experimental time courses are suggestive of such fold-subHopf models because the spikes tend to be small and variable in amplitude; we call this pseudo-plateau bursting. We show here that distinct properties of the response to attempted resets from the silent phase to the active phase provide a clearer, qualitative criterion for choosing between the two classes of models. The fold-homoclinic class is characterized by induced active phases that increase towards the duration of the unperturbed active phase as resets are delivered later in the silent phase. For the fold-subHopf class of pseudo-plateau bursting, resetting is difficult and succeeds only in limited windows of the silent phase but, paradoxically, can dramatically exceed the native active phase duration. J.V. Stern and H.M. Osinga contributed equally.     

On the dynamics of bursting systems

The dynamics of three-variable models of bursting are studied. It is shown that under certain conditions, the dynamics on the attractor can be essentially reduced to two dimensions. The salient dynamics on the attractor can thus be completely described by the return map of a section which is a logistic interval map. Two specific bursting models from the literature are shown to fit in the general framework which is developed. Bifurcation of the full system for one case in investigated and the dynamical behavior on the attractor is shown to depend on the position of a certain nullcline.Supported in part by N.S.F.On leave at University of Maryland     

Noise induced complexity: patterns and collective phenomena in a small-world neuronal network

The effects of noise on patterns and collective phenomena are studied in a small-world neuronal network with the dynamics of each neuron being described by a two-dimensional Rulkov map neuron. It is shown that for intermediate noise levels, noise-induced ordered patterns emerge spatially, which supports the spatiotemporal coherence resonance. However, the inherent long range couplings of small-world networks can effectively disrupt the internal spatial scale of the media at small fraction of long-range couplings. The temporal order, characterized by the autocorrelation of a firing rate function, can be greatly enhanced by the introduction of small-world connectivity. There exists an optimal fraction of randomly rewired links, where the temporal order and synchronization can be optimized.     

神经起步点产生的一种新型簇放电节律———阵发周期1节律

实验中发现了神经起步点产生的一种新型的簇放电节律－－阵发周期1节律。其特征如下：连续周期1放电与休止期（quiescence）轮流出现;非周期性,连续放电持续期、连续放电次数以及休止期有较大变异性;位于周期1节律和静息状态之间。具有较长周期的伪单色噪声激励的FHN（FizHugh-Nagumo）模型可以产生类似的阵发周期1节律。模型和实验中的阵发周期1节律的统计特征、变化规律和所处的参数区间相类似。这表明：阵发周期1节律是由与伪单色噪声类似的长时程振荡激励引起的。     

线性整合放电模型的相干共振

研究了神经递质以随机点序列释放和电压门控离子通道噪声共同作用下,线性整合放电模型的相干共振现象。基于分形布朗运动和改进的欧拉方法,得到了神经元膜电压分布和神经元放电峰峰间隔的信噪比。结果表明,神经元放电的峰峰间隔是神经递质的达到强度、离子通道噪声强度的非单调函数。适当的神经递质到达强度和离子通道噪声强度使峰峰间隔的信噪比出现最大值,即出现相干共振现象。     

Sustained oscillations via coherence resonance in SIR

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.     

Qualitative validation of the reduction from two reciprocally coupled neurons to one self-coupled neuron in a respiratory network model

The pre-Bötzinger complex of the mammalian brainstem is a heterogeneous neuronal network, and individual neurons within the network have varying strengths of the persistent sodium and calcium-activated nonspecific cationic currents. Individually, these currents have been the focus of modeling efforts. Previously, Dunmyre et al. (J Comput Neurosci 1–24, 2011) proposed a model and studied the interactions of these currents within one self-coupled neuron. In this work, I consider two identical, reciprocally coupled model neurons and validate the reduction to the self-coupled case. I find that all of the dynamics of the two model neuron network and the regions of parameter space where these distinct dynamics are found are qualitatively preserved in the reduction to the self-coupled case.     

实验性神经起步点产生的整数倍簇放电节律

随机Hindmarsh-Rose模型中产生簇（bursting)放电节律是神经放电中存在随机自共振的一个重要理论证据,但是,该簇放电节律在实验中一直没有被发现。在实验性神经起步点细胞外[Ca^2 ]([Ca^2 ]o)低于周期1节律的[Ca^2 ]o时,发现了一种簇放电节律。其簇簇间期（inter-burst intervals,IBIs)呈现出与随机自共振引起的整数倍峰放电（interger multiple spiking)节律的峰峰间期类似的整数倍特征。随机Hindmarsh-Rose模型中产生的簇（bursting)放电节律也表现出类似的特征。结果验证了随机自共振簇放电的存在性,揭示该簇放电节律的统计特征。此外,该簇放电节律的参数区间以及其与整数倍峰放电节律的区别被揭示,簇放电节律的[Ca^2 ]o低于峰放电律的[Ca^2 ]o。     

Minimisation of sensitivity losses due to the use of gradient pulses in triple-resonance NMR of proteins

Summary The use of pulsed field gradients in multiple-pulse NMR experiments has many advantages, including the possibility of obtaining excellent water suppression without the need for selective presaturation. In such gradient experiments the water magnetization is dephased deliberately; exchange between the saturated protons of the solvent water and the NH protons of a protein transfers this saturation to the protein. As the solvent is in large excess and relaxes relatively slowly, the result is a reduction in the sensitivity of the experiment due to the fact that the NH proton magnetization is only partially recovered. These effects can be avoided by ensuring that the water magnetization remains intact and is returned to the +z-axis at the start of data acquisition. General procedures for achieving this aim in any triple-resonance experiment are outlined and two specific examples are given. Experimental results confirm the sensitivity advantage of the modified sequences.     

Neural dynamics of envelope coding

We consider the processing of narrowband signals that modulate carrier waveforms in sensory systems. The tuning of sensory neurons to the carrier frequency results in a high sensitivity to the amplitude modulations of the carrier. Recent work has revealed how specialized circuitry can extract the lower-frequency modulation associated with the slow envelope of a narrowband signal, and send it to higher brain along with the full signal. This paper first summarizes the experimental evidence for this processing in the context of electroreception, where the narrowband signals arise in the context of social communication between the animals. It then examines the mechanism of this extraction by single neurons and neural populations, using intracellular recordings and new modeling results contrasting envelope extraction and stochastic resonance. Low noise and peri-threshold stimulation are necessary to obtain a firing pattern that shows high coherence with the envelope of the input. Further, the output must be fed through a slow synapse. Averaging networks are then considered for their ability to detect, using additional noise, signals with power in the envelope bandwidth. The circuitry that does support envelope extraction beyond the primary receptors is available in many areas of the brain including cortex. The mechanism of envelope extraction and its gating by noise and bias currents is thus accessible to non-carrier-based coding as well, as long as the input to the circuit is a narrowband signal. Novel results are also presented on a more biophysical model of the receptor population, showing that it can encode a narrowband signal, but not its envelope, as observed experimentally. The model is modified from previous models by stimulus reducing contrast in order to make it sufficiently linear to agree with the experimental data.     

实验性神经起步点自发放电的分叉和整数倍节律

在实验性神经起步点发现了放电峰峰间期序列随细胞外[Ca^2 ]变化产生的加周期分叉和整数倍节律。并用确定性Chay模型和随机Chay模型进行数值模拟。从模拟实验结果的角度看,加周期分叉过程遵从Chay模型决定的确定性机制,随机因素对其有影响但影响较小;而在相应的参数区间,整数倍节律则是在随机因素驱动下产生,是随机共振现象,是由确定性机制和随机因素共同作用的结果。这表明,实验性神经起步点放电节律的分叉和随机共振现象的出现是必然的,受确定性机制和随机因素共同影响。但在不同参数区间,随机因素对神经放电节律的作用不同。     

NMR characterization of copper and lipid interactions of the C2B domain of synaptotagmin I—relevance to the non-classical secretion of the human acidic fibroblast growth factor (hFGF-1)

Human fibroblast growth factor (hFGF-1) is a ∼ 17 kDa heparin binding cytokine. It lacks the conventional hydrophobic N-terminal signal sequence and is secreted through non-classical secretion routes. Under stress, hFGF-1 is released as a multiprotein complex consisting of hFGF-1, S100A13 (a calcium binding protein), and p40 synaptotagmin (Syt1). Copper (Cu²⁺) is shown to be required for the formation of the multiprotein hFGF-1 release complex (Landriscina et al. ,2001; Di Serio et al., 2008). Syt1, containing the lipid binding C2B domain, is believed to play an important role in the eventual export of the hFGF-1 across the lipid bilayer. In this study, we characterize Cu²⁺ and lipid interactions of the C2B domain of Syt1 using multidimensional NMR spectroscopy. The results highlight how Cu²⁺ appears to stabilize the protein bound to pS vesicles. Cu²⁺ and lipid binding interface mapped using 2D ¹H-¹⁵N heteronuclear single quantum coherence experiments reveal that residues in β-strand I contributes to the unique Cu²⁺ binding site in the C2B domain. In the absence of metal ions, residues located in Loop II and β-strand IV contribute to binding to unilamelar pS vesicles. In the presence of Cu²⁺, additional residues located in Loops I and III appear to stabilize the protein-lipid interactions. The results of this study provide valuable information towards understanding the molecular mechanism of the Cu²⁺-induced non-classical secretion of hFGF-1.     

Isolation, expression and characterization of two single-chain variable fragment antibodies against an endo-polygalacturonase secreted by Sclerotinia sclerotiorum

Canola is a very important economic crop in the world and canola stem rot caused by Sclerotinia sclerotiorum (Lib.) de Bary, a necrotrophic, highly destructive and non-host-specific fungus, can reduce yield significantly. This fungus secretes numerous cell wall degrading enzymes including an endo-polygalacturonase, SSPG1d, which has been detected at early stages of infection. In this report we describe the isolation of two recombinant antibodies of the single-chain variable fragment (ScFv) format from RNA of mice immunized with recombinant SSPG1d (rSSPG1d) or a peptide derived from SSPG1d (peptide 3796) that was predicted to be antigenic. The ScFvs were isolated using the established phage display technology. These recombinant antibodies were expressed, purified and refolded to functional antibodies with a yield of 120–500 μg per liter of cell culture. Recombinant antibodies were characterized using various techniques including enzyme-linked immunosorbent assay (ELISA) and surface plasmon resonance (SPR). Of the two ScFvs, it appears that only ScFv-rSSPG1d is able to detect whole SSPG1d produced by the fungus. Thus our results indicate that this ScFv may have utility in the detection of the SSPG1d enzyme in an antibody-based diagnostic test for S. sclerotiorum infection.