Medvedev G S, Wilson C J, Callaway J C, Kopell N
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544-1000, USA.
J Comput Neurosci. 2003 Jul-Aug;15(1):53-69. doi: 10.1023/a:1024422802673.
Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.
中脑多巴胺能神经元自发放电率的短暂增加被认为可作为奖励预测误差信号。先前提出的一种机制涉及神经元各部分的阈下钙依赖性振荡。在该机制中，振荡的固有频率随细胞突起的直径而变化，因此细胞上的固有频率存在很大差异，但强电压耦合在静息条件下强制产生单一振荡频率。在先前的工作中，对一个更简单的振荡器系统进行数学分析表明，振荡器链可以产生瞬态动力学，其中耦合系统的频率会暂时增加，这在多巴胺能神经元的生物物理模型中可以看到。瞬态动力学被证明是沿着相空间不变子集缓慢漂移的结果，漂移速率由李雅普诺夫函数给出。在本文中，我们表明完整的生物物理模型存在相同的数学结构，赋予了缓慢漂移和李雅普诺夫函数生理意义，该函数被证明可描述细胞不同部位细胞内钙浓度的差异。瞬态的持续时间很长，与钙处置的时间常数相当。这些结果表明，多巴胺能神经元输入的短暂变化可产生持久的放电率瞬变，其形式由细胞固有特性决定。
