Rinzel J, Baer S M
National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, Maryland 20892.
Biophys J. 1988 Sep;54(3):551-5. doi: 10.1016/S0006-3495(88)82988-6.
We have obtained new insights into the behavior of a class of excitable systems when a stimulus, or parameter, is slowly tuned through a threshold value. Such systems do not accommodate no matter how slowly a stimulus ramp is applied, and the stimulus value at onset of repetitive activity shows a curious, nonmonotonic dependence on ramp speed. (Jakobsson, E. and R. Guttman. Biophys. J. 1980. 31:293-298.) demonstrated this for squid axon and for the Hodgkin-Huxley (HH) model. Furthermore, they showed theoretically that for moderately slow ramps the threshold increases as the ramp speed decreases, but for much slower ramp speeds threshold decreases as the ramp speed decreases. This latter feature was found surprising and it was suggested that the HH model, and squid axon in low calcium, exhibits reverse accommodation. We have found that reverse accommodation reflects the influence of persistent random fluctuations, and is a feature of all such excitable systems. We have derived an analytic condition which yields an approximation for threshold in the case of a slow ramp when the effect of fluctuations are negligible. This condition predicts, and numerical calculations confirm, that the onset of oscillations occurs beyond the critical stimulus value which is predicted by treating the stimulus intensity as a static parameter, i.e., the dynamic aspect of a ramp leads to a delay in the onset. The condition further demonstrates a memory effect, i.e., firing threshold is dependent on the initial state of the system. For very slow ramps then, fluctuations diminish both the delay and memory effects. We characterize the class of excitable systems for which these behaviors are expected, and we illustrate the phenomena for the HH model and for a model of cAMP-receptor dynamics in Dictyostelium discoideum.
当一个刺激或参数缓慢调至阈值时，我们对一类可兴奋系统的行为有了新的认识。无论刺激斜坡施加得多么缓慢，这类系统都不会适应，并且重复活动开始时的刺激值对斜坡速度呈现出一种奇特的非单调依赖性。（雅各布松，E. 和 R. 古特曼。《生物物理学杂志》。1980 年。31:293 - 298。）对鱿鱼轴突和霍奇金 - 赫胥黎（HH）模型证明了这一点。此外，他们从理论上表明，对于适度缓慢的斜坡，阈值会随着斜坡速度的降低而增加，但对于更缓慢的斜坡速度，阈值会随着斜坡速度的降低而降低。后一个特征被发现令人惊讶，有人提出 HH 模型以及低钙环境下的鱿鱼轴突表现出反向适应。我们发现反向适应反映了持续随机波动的影响，并且是所有此类可兴奋系统的一个特征。我们推导了一个解析条件，当波动的影响可忽略不计时，该条件可在缓慢斜坡情况下给出阈值的近似值。这个条件预测，并且数值计算也证实，振荡的开始发生在将刺激强度视为静态参数时所预测的临界刺激值之后，即斜坡的动态方面会导致开始延迟。该条件还展示了一种记忆效应，即放电阈值取决于系统的初始状态。那么对于非常缓慢的斜坡，波动会减小延迟和记忆效应。我们描述了预期会出现这些行为的可兴奋系统类别，并针对 HH 模型以及盘基网柄菌中 cAMP 受体动力学模型说明了这些现象。
