Wilson M T, Steyn-Ross Moira L, Steyn-Ross D A, Sleigh J W
Department of Engineering, University of Waikato, Hamilton 3240, New Zealand.
J Biol Phys. 2007 Jun;33(3):213-46. doi: 10.1007/s10867-008-9056-5. Epub 2008 Mar 18.
Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the "up" and "down" states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories.
皮质的平均场模型已成功用于解释睡眠、麻醉和癫痫发作等情况下脑电图特征的起源。在平均场方案中，可以通过基于波动的赫布学习规则来考虑突触权重的动态变化。然而，由于此类实现处理的是群体平均特性，它们不太适合个体突触权重可能很重要的记忆和学习应用。我们证明，通过扩展方程组，平均场模型可以进一步发展以研究高阶统计量，特别是皮质柱内突触权重的分布。这使我们能够通过平均场方案对记忆得出一些一般性结论。具体而言，我们预计当平均体细胞电位波动较大时，例如在慢波睡眠的“上”和“下”状态之间转换期间，突触权重分布的标准差会有很大变化。此外，神经元连接结构较低的皮质相对于均值的平方，其兴奋性到兴奋性突触权重的标准差最有可能减小，而连接模式强烈的皮质最有可能增加这一指标。这表明波动被用于将强（大概是有用的）记忆的编码压缩到更少但动态的神经元连接中，同时去除较弱（不太有用）的记忆。
