Scale-free topology of the CA3 hippocampal network: a novel method to analyze functional neuronal assemblies

Abstract

Cognitive mapping functions of the hippocampus critically depend on the recurrent network of the CA3 pyramidal cells. However, it is still not known in detail how network activity patterns emerge, or how they encode information. By using functional multineuron calcium imaging, we simultaneously recorded the activity of >100 neurons in the CA3 region of hippocampal slice cultures. We utilized a novel computational method to analyze the multichannel spike trains and to depict functional neuronal assemblies. By means of event synchronization and the correlation matrix analysis method, we found that: 1), the average functional neuronal cluster consists of 23 neurons, and neurons could be part of multiple assemblies; 2), the clustering strength, size, and mean distance among cells in neuronal assemblies follow a power-law-like distribution; 3), the clustering strength and size of neuronal assemblies are not correlated with the total number of neurons and their physical distance; and 4), the clustering distance of neuronal assemblies is weakly correlated with the total number of neurons and their physical distance. These findings suggest that the functional organization of the spontaneously firing CA3 hippocampal network is a scale-free structure in slice culture.

Figure 1

Comparison of spike trains obtained by intercellular recordings and Ca²⁺ transient signals recorded by fMCI. The timing of the Ca²⁺ transients are correlated with the actual neural spike trains indicated below the Ca²⁺ signals. The decay of a Ca²⁺ transient is illustrated.

Figure 2

Illustration of spike train, correlation matrix, and synchronization index of the hippocampal neuronal network. (A) Confocal image of a slice loaded with Oregon Green 488 BAPTA-1. Bright signal indicates active neurons in the CA3 pyramidal cell layer. Scale: 50 μm. (B) The raster plot of the spike trains of 127 neurons is reconstructed from the Ca²⁺ imaging. (C) Correlation matrix of spontaneous activities using event synchronization at the maximal time delay of 50 ms. (D) Synchronization index of four neuronal assemblies based on the random matrix theory and surrogate techniques.

Figure 3

Details of the functional organization of neuronal assemblies depicted in Fig. 1. The bottom plot in each figure shows the elements of neuronal assembly. (Open circles) Neurons with Ca²⁺ signal and their physical positions in the CA3 region of the hippocampus. (Solid circles) Degree of participation of a given neuron in the neuronal assembly. The diameter of circles is proportional to the contributions to the neuronal assembly. The top plot in each figure is the contribution of neurons to neuronal assemblies (participation index). The participation index is equal to the diameter of solid circles at the bottom plot. Superconnected hub neurons belonging to more than one cluster are indicated by arrows (the different direction of arrows indicates different hub). (A) The participation index and neuronal assembly of the first cluster. (B) The participation index and neuronal assembly of the second cluster. (C) The participation index and neuronal assembly of the third cluster. (D) The participation index and neuronal assembly of the forth cluster.

Figure 4

Power-law relationship among the clustering strength, size, and distance of neuronal assemblies. (A) Log₁₀–log₁₀ graph of the clustering strength and the size of neuronal assemblies. Slope: α = 1.433; Pearson's correlation coefficient (r): r = 0.813 (confidence interval (CI) 0.746–0.864, P < 10⁻⁴). The variability by regression: VR = 66.1%. (B) Log₁₀–log₁₀ graph of the clustering strength and the distance of neuronal assemblies. Slope: α = −2.092; r = −0.610 (CI −0.707–0.491, P < 10⁻⁴); VR = 37.2%. (C) Log₁₀–log₁₀ graph of the distance and the size of neuronal assemblies. Slope: α = −1.173; r = −0.654 (CI −0.742–0.544, P < 10⁻⁴); VR = 42.7%.

Figure 5

Power-law relationship between various neuronal assembly properties and the participation indices (PIs) of neurons. The clustering strength, size, and distance of neuronal assemblies decrease with the coefficients of variation (CV) of the PI and increase with the entropy of the PI. (A–C) Log₁₀–log₁₀ graph among the clustering strength, cluster size, and cluster distances with the CV of PI. (D–F) Log₁₀–log₁₀ graph of clustering strength, size, and distances with the entropy of PI.

Figure 6

Relationships between various connectivity features of neuronal assemblies and the spatial distribution of active neurons. (A and B) The clustering strength and size of neuronal assemblies show no correlation with the number of active neurons located in the slices (|r| < 0.02). (C) The clustering distance is weakly dependent on the number of active neurons located in the organotypic slice cultures (r = 0.314). (D and E) The clustering strength and size of neuronal assemblies have no correlation with the distance of active neurons located in the slice (|r| < 0.15). (F) The distance of neuronal assemblies shows a weak relation to the distance of individual neurons (r = 0.280).