Schwemmer Michael A, Lewis Timothy J
Program in Applied and Computational Mathematics and Princeton Neuroscience Institute, Princeton University, Princeton, NJ, 08544, USA,
J Math Biol. 2014 Jan;68(1-2):303-40. doi: 10.1007/s00285-012-0635-5. Epub 2012 Dec 22.
We examine the effects of dendritic filtering on the existence, stability, and robustness of phase-locked states to heterogeneity and noise in a pair of electrically coupled ball-and-stick neurons with passive dendrites. We use the theory of weakly coupled oscillators and analytically derived filtering properties of the dendritic coupling to systematically explore how the electrotonic length and diameter of dendrites can alter phase-locking. In the case of a fixed value of the coupling conductance (gc) taken from the literature, we find that repeated exchanges in stability between the synchronous and anti-phase states can occur as the electrical coupling becomes more distally located on the dendrites. However, the robustness of the phase-locked states in this case decreases rapidly towards zero as the distance between the electrical coupling and the somata increases. Published estimates of gc are calculated from the experimentally measured coupling coefficient (CC) based on a single-compartment description of a neuron, and therefore may be severe underestimates of gc. With this in mind, we re-examine the stability and robustness of phase-locking using a fixed value of CC, which imposes a limit on the maximum distance the electrical coupling can be located away from the somata. In this case, although the phase-locked states remain robust over the entire range of possible coupling locations, no exchanges in stability with changing coupling position are observed except for a single exchange that occurs in the case of a high somatic firing frequency and a large dendritic radius. Thus, our analysis suggests that multiple exchanges in stability with changing coupling location are unlikely to be observed in real neural systems.
我们研究了树突滤波对一对具有被动树突的电耦合球-棒神经元中锁相状态的存在性、稳定性以及对异质性和噪声的鲁棒性的影响。我们运用弱耦合振荡器理论以及解析得出的树突耦合滤波特性，系统地探究树突的电长度和直径如何改变锁相。在采用文献中给出的固定耦合电导值（gc）的情况下，我们发现随着电耦合在树突上的位置向更远端移动，同步态和反相态之间的稳定性会反复交换。然而，在这种情况下，随着电耦合与胞体之间的距离增加，锁相状态的鲁棒性会迅速降至零。已发表的gc估计值是根据基于神经元单室描述的实验测量耦合系数（CC）计算得出的，因此可能严重低估了gc。考虑到这一点，我们使用固定的CC值重新审视锁相的稳定性和鲁棒性，这对电耦合与胞体之间的最大距离施加了限制。在这种情况下，尽管锁相状态在所有可能的耦合位置范围内都保持鲁棒，但除了在高胞体放电频率和大树突半径情况下发生的一次交换外，未观察到随着耦合位置变化的稳定性交换。因此，我们的分析表明，在实际神经系统中不太可能观察到随着耦合位置变化的多次稳定性交换。
