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Many theories of neural network function assume linear summation. This is in apparent conflict with several known forms of non-linearity in real neurons. Furthermore, key network properties depend on the summation parameters, which are themselves subject to modulation and plasticity in real neurons. We tested summation responses as measured by spiking activity in small groups of CA1 pyramidal neurons using permutations of inputs delivered on an electrode array. We used calcium dye recordings as a readout of the summed spiking response of cell assemblies in the network. Each group consisted of 2–10 cells, and the calcium signal from each cell correlated with individual action potentials. We find that the responses of these small cell groups sum linearly, despite previously reported dendritic non-linearities and the thresholded responses of individual cells. This linear summation persisted when input strengths were reduced. Blockage of inhibition shifted responses up toward saturation, but did not alter the slope of the linear region of summation. Long-term potentiation of synapses in the slice also preserved the linear fit, with an increase in absolute response. However, in this case the summation gain decreased, suggesting a homeostatic process for preserving overall network excitability. Overall, our results suggest that cell groups in the CA3-CA1 network robustly follow a consistent set of linear summation and gain-control rules, notwithstanding the intrinsic non-linearities of individual neurons. Cell-group responses remain linear, with well-defined transformations following inhibitory modulation and plasticity. Our measures of these transformations provide useful parameters to apply to neural network analyses involving modulation and plasticity.

frontiers in computational neuroscience

Summation in the Hippocampal CA3-CA1 Network Remains Robustly Linear Following Inhibitory Modulation and Plasticity, but Undergoes Scaling and Offset Transformations