Axonal Anatomy Optimizes Spatial Encoding in the Rat Entorhinal-Dentate System: A Computational Study

Abstract

Objective: The network architecture connecting neural regions is defined by the organization and anatomical properties of the projecting axons, but its contributions to neural encoding and system function are difficult to study experimentally.

Methods: Using a large-scale, spiking neuronal network model of rat dentate gyrus, the role of the anatomy of the entorhinal-dentate axonal projection was evaluated in the context of spatial encoding by incorporating grid cell activity to provide physiological, spatially-correlated input. The dorso-ventral extents of the entorhinal axon terminal fields were varied to generate different feedforward architectures, and the resulting spatial representations and spatial information scores of the network were evaluated. Position was decoded from the population activity using a point process filter to investigate the contributions of network architecture on spatial encoding.

Results: The model predicted the emergence of anatomical gradients within the dentate gyrus for place field size and spatial information along its dorso-ventral axis, which were dependent on the extents of the entorhinal axon terminal fields. The decoding results revealed an optimal performance at an axon terminal field extent of 2 mm that lies within the biological range.

Conclusion: The axonal anatomy mediates a tradeoff between encoding multiple place field sizes or achieving a high spatial information score, and the combination of both properties is necessary to maximize spatial encoding by a network.

Significance: In total, this paper establishes a mechanistic neuronal network model that, in concert with information-theoretic and statistical methods, can be used to investigate how lower level properties contribute to higher level function.

Fig. 1.

Distribution of grid field parameters and generation of grid cell activity. (A) Data from Hafting et al., 2005 (left and middle) and Stensola et al., 2012 (right) were used to constrain the grid field properties. (B) The grid field properties were normalized along the dorso-ventral axis of the medial entorhinal cortex using a generalized logisitic function such that the grid field properties were represented approximately equally. (C) The gradient of grid field parameters in the medial entorhinal cortex (left) and the mapping between medial entorhinal cortex and dentate gyrus (center) determine where the grid field information is communicated to within the dentate gyrus. The final distribution of grid field parameters results in a gradient in the dentate gyrus (right). (D) An example grid field is shown with notation describing the field area, distance, and orientation properties. (E) Left: The movement of a virtual rat in white is overlaid on a grid field with a triangle and circle denoting the start and end points of the movement, respectively. Right: The firing rate (red) is determined using a grid field and the movement of the rat through the field. A non-homogeneous Poisson process is used to generate spiking activity (black) using the firing rate.

Fig. 2.

Smoothed rate maps from simulated dentate granule cells at different locations along the dorso-ventral axis. A dorso-ventral gradient for the size of the place fields was observed. Ventrally-located granule cells exhibited larger place fields, and dorsally-located granule cells exhibited smaller place fields. The color scale denotes high firing rates in red and low firing rates in blue.

Fig. 3.

Raster plots of the spiking activity due to different axon terminal field extents. (A) Spiking activity is represented using black dots which represent the time and position along the longitudinal extent at which an action potential was generated. Clustered activity is apparent with smaller axon terminal field sizes and organizes into vertical bands at larger axon terminal field sizes. (B) A conceptual representation of the consequences of changing the axon terminal field have on connectivity is depicted. As the axon terminal field grows larger, a larger area of neurons can be contacted, and the input is more dispersed spatially. At smaller axon terminal fields, the area in which neurons can be contacted becomes restricted.

Fig. 4.

The effect of axon field terminal extent on granule cell place field properties and suprapyramidal-infrapyramidal differences. (A) The mean place field area within 0.5 mm bins along the dorso-ventral axis were plotted as a scatter plot with the corresponding linear fits. The mean values within a bin were plotted for visual clarity, but the regressions were performed using the raw data. (B) The magnitude of the slope between place field area and dorso-ventral position decreased log-linearly with the axon terminal field extent. The error bars denote the standard error of the estimates of slope. (C) The mean place field areas of the populations were weakly correlated with the axon terminal field extent. The error bars denote standard error. N_supra=65,000 and N_infra=55,000 for each field extent.

Fig. 5.

The effect of axon terminal field extent on spatial information score and the effect of multi-resolution input on spatial information score. (A) The mean spatial information score within 0.1 mm bins along the dorso-ventral axis were plotted with the corresponding linear fits. The mean values within a bin were plotted for visual clarity, but the regressions were performed using the raw data. (B) The magnitude of the slope between the spatial information score and dorso-ventral position decreased exponentially with the axon terminal field extent. The error bars denote the standard error for the estimates for slope. (C) The mean spatial information increases exponentially with axon field extent. The error bars denote standard deviation. (D) The standard deviation of the grid field areas that a granule cell received were plotted against the corresponding spatial information score. (E) The standard deviation of grid field areas in the input is correlated with the axon terminal field extent. A larger axon terminal field results in a granule cell receiving a total input with a larger variety of grid field sizes.

Fig. 6.

Decoding performance as a function of axon terminal field extent. (A) The position decoding estimates under different axon terminal field conditions are plotted over the actual positions. (B) The average error, represented by the Euclidean distance between the predicted and actual position, is plotted against axon terminal field extent (black). A linear regression was used to predict decoding performance using two variables: place field area slope and spatial information score (red). The p-values of the regressions were ≪ 0.001 for both blades. The coefficients to Eq. 17 and the effect sizes are listed within each figure. (C) The estimated lower bound of the mutual information between position and the spiking of the neural population is plotted as a function of axon terminal field extent.