Gibson W G, Robinson J, Bennett M R
Department of Applied Mathematics, University of Sydney, New South Wales, Australia.
Philos Trans R Soc Lond B Biol Sci. 1991 Jun 29;332(1264):199-220. doi: 10.1098/rstb.1991.0050.
The implications of probabilistic secretion of quanta for the functioning of neural networks in the central nervous system have been explored. A model of stochastic secretion at synapses in simple networks, consisting of large numbers of granule cells and a relatively small number of inhibitory interneurons, has been analysed. Such networks occur in the input to the cerebellum Purkinje cells as well as to hippocampal CA3 pyramidal cells and to pyramidal cells in the visual cortex. In this model the input axons terminate on granule cells as well as on an inhibitory interneuron that projects to the granule cells. Stochastic secretion at these synapses involves both temporal variability in secretion at single synapses in the network as well as spatial variability in the secretion at different synapses. The role of this stochastic variability in controlling the size of the granule cell output to a level independent of the size of the input and in separating overlapping inputs has been determined analytically as well as by simulation. The regulation of granule-cell output activity to a reasonably constant value for different size inputs does not occur in the absence of an inhibitory interneuron when both spatial and temporal stochastic variability occurs at the remaining synapses; it is still very poor in the presence of such an interneuron but in the absence of stochastic variability. However, quite good regulation is achieved when the inhibitory interneuron is present with spatial and temporal stochastic variability of secretion at synapses in the network. Excellent regulation is achieved if, in addition, allowance is made for the nonlinear behaviour of the input-output characteristics of inhibitory interneurons. The capacity of granule-cell networks to separate overlapping patterns of activity on their inputs is adequate, with spatial variability in the secretion at synapses, but is improved if there is also temporal variability in the stochastic secretion at individual synapses, although this is at the expense of reliability in the network. Other factors which improve pattern separation are control of the output to very low activity levels, and a restriction on the cumulative size of the excitatory input terminals of each granule cell. Application of the theory to the input neural networks of the cerebellum and the hippocampus shows the role of stochastic variability in quantal transmission in determining the capacity of these networks for pattern separation and activity regulation.
人们已经探讨了量子概率性分泌对中枢神经系统神经网络功能的影响。对由大量颗粒细胞和相对少量抑制性中间神经元组成的简单网络中突触的随机分泌模型进行了分析。此类网络存在于小脑浦肯野细胞、海马CA3锥体细胞以及视觉皮层锥体细胞的输入中。在该模型中，输入轴突终止于颗粒细胞以及投射到颗粒细胞的抑制性中间神经元上。这些突触处的随机分泌涉及网络中单个突触分泌的时间变异性以及不同突触分泌的空间变异性。这种随机变异性在将颗粒细胞输出大小控制到与输入大小无关的水平以及分离重叠输入方面的作用已通过分析和模拟确定。当其余突触同时存在空间和时间随机变异性时，在没有抑制性中间神经元的情况下，颗粒细胞输出活动不会针对不同大小的输入调节到合理恒定的值；在存在这种中间神经元但没有随机变异性时，调节效果仍然很差。然而，当网络中突触存在分泌的空间和时间随机变异性且有抑制性中间神经元时，可实现相当好的调节。此外，如果考虑到抑制性中间神经元输入 - 输出特性的非线性行为，则可实现极佳的调节。颗粒细胞网络分离输入上重叠活动模式的能力在突触分泌存在空间变异性时是足够的，但如果单个突触的随机分泌也存在时间变异性，尽管这是以网络可靠性为代价的，其能力会得到提高。其他改善模式分离的因素包括将输出控制在非常低的活动水平，以及限制每个颗粒细胞兴奋性输入终端的累积大小。将该理论应用于小脑和海马的输入神经网络，显示了量子传递中的随机变异性在决定这些网络的模式分离和活动调节能力方面的作用。
