Braun H A, Huber M T, Anthes N, Voigt K, Neiman A, Pei X, Moss F
Institute of Physiology, University of Marburg, Deutschhausstr. 2, D-35037 Marburg, Germany.
Biosystems. 2001 Sep-Oct;62(1-3):99-112. doi: 10.1016/s0303-2647(01)00140-x.
We used a minimal Hodgkin-Huxley type model of cold receptor discharges to examine how noise interferes with the non-linear dynamics of the ionic mechanisms of neuronal stimulus encoding. The model is based on the assumption that spike-generation depends on subthreshold oscillations. With physiologically plausible temperature scaling, it passes through different impulse patterns which, with addition of noise, are in excellent agreement with real experimental data. The interval distributions of purely deterministic simulations, however, exhibit considerable differences compared to the noisy simulations especially at the bifurcations of deterministically period-one discharges. We, therefore, analyzed the effects of noise in different situations of deterministically regular period-one discharges: (1) at high-temperatures near the transition to subthreshold oscillations and to burst discharges, and (2) at low-temperatures close to and more far away from the bifurcations to chaotic dynamics. The data suggest that addition of noise can considerably extend the dynamical behavior of the system with coexistence of different dynamical situations at deterministically fixed parameter constellations. Apart from well-described coexistence of spike-generating and subthreshold oscillations also mixtures of tonic and bursting patterns can be seen and even transitions to unstable period-one orbits seem to appear. The data indicate that cooperative effects between low- and high-dimensional dynamics have to be considered as qualitatively important factors in neuronal encoding.
我们使用了一个关于冷感受器放电的最小霍奇金-赫胥黎类型模型,来研究噪声如何干扰神经元刺激编码离子机制的非线性动力学。该模型基于这样一个假设,即动作电位的产生取决于阈下振荡。通过生理上合理的温度缩放,它呈现出不同的脉冲模式,在加入噪声后,这些模式与实际实验数据高度吻合。然而,纯确定性模拟的间隔分布与有噪声模拟相比存在显著差异,特别是在确定性周期一放电的分岔处。因此,我们分析了在确定性规则周期一放电的不同情况下噪声的影响:(1)在接近阈下振荡转变和爆发放电的高温下,以及(2)在接近和远离向混沌动力学分岔的低温下。数据表明,加入噪声可以显著扩展系统的动力学行为,在确定性固定参数组合下不同动力学情况共存。除了描述清晰的动作电位产生和阈下振荡共存外,还可以看到紧张性和爆发性模式的混合,甚至似乎出现了向不稳定周期一轨道的转变。数据表明,低维和高维动力学之间的协同效应必须被视为神经元编码中定性重要的因素。