A mathematical model of negative covariability of inter-columnar excitatory synaptic actions caused by presynaptic inhibition.

We previously showed that a positive covariability between intracortical excitatory synaptic actions onto the two layer three pyramidal cells (PCs) located in mutually adjacent columns is changed into a negative covariability by column-wise presynaptic inhibition of intracortical inputs, implicated as a basis for the desynchronization of inter-columnar synaptic actions. Here we investigated how the inter-columnar desynchronization is modulated by the strength of presynaptic inhibition or other factors, by using a mathematical model. Based on our previous findings on the paired-pulse depression (PPD) of intracortical excitatory postsynaptic currents (EPSCs) evoked in PCs located in the stimulated home column (HC) but no PPD in PCs located in the adjacent column (AC), a mathematical model of synaptic connections between PCs and inhibitory interneurons was constructed. When the paired-pulse ratio (PPR) was decreased beyond 0.80, the correlation coefficient between the two second EPSC amplitudes in the paired PCs located in the HC and AC and that in the paired PCs located in the same HC exhibited opposite changes, and reached a global negative maximum and local positive maximum, respectively, at almost the same PPR (0.40). At this PPR, the desynchronization between the two cell assemblies in mutually adjacent columns would be maximized. These positive and negative covariabilities were not produced without background oscillatory synchronization across columns and were enhanced by increasing the synchronization magnitude, indicating that the synchronization leads to the desynchronization. We propose that a slow oscillatory synchronization across columns may emerge following the liberation from the column-wise presynaptic inhibition of inter-columnar synaptic inputs.