Spatial learning and action planning in a prefrontal cortical network model

Abstract

The interplay between hippocampus and prefrontal cortex (PFC) is fundamental to spatial cognition. Complementing hippocampal place coding, prefrontal representations provide more abstract and hierarchically organized memories suitable for decision making. We model a prefrontal network mediating distributed information processing for spatial learning and action planning. Specific connectivity and synaptic adaptation principles shape the recurrent dynamics of the network arranged in cortical minicolumns. We show how the PFC columnar organization is suitable for learning sparse topological-metrical representations from redundant hippocampal inputs. The recurrent nature of the network supports multilevel spatial processing, allowing structural features of the environment to be encoded. An activation diffusion mechanism spreads the neural activity through the column population leading to trajectory planning. The model provides a functional framework for interpreting the activity of PFC neurons recorded during navigation tasks. We illustrate the link from single unit activity to behavioral responses. The results suggest plausible neural mechanisms subserving the cognitive "insight" capability originally attributed to rodents by Tolman & Honzik. Our time course analysis of neural responses shows how the interaction between hippocampus and PFC can yield the encoding of manifold information pertinent to spatial planning, including prospective coding and distance-to-goal correlates.

Figure 1. Overview of the model architecture and connectivity.

(A) Model hippocampal place (HP) cells are selective to allocentrically-encoded positions. The prefrontal cortex (PFC) columnar network takes HP cell activities as input to learn a sparse state-action code reflecting the topological organization of the environment. The model employs recurrent excitatory collaterals between minicolumns of two subpopulations ( and ) to implement multilevel spatial processing capturing morphological regularities of the environment. (B) Each model column uses three units and a population of minicolumns, each of which is composed of two units and . Neurons receive inputs from HP cells through synapses to encode spatial locations. Forward and backward associations between locations are encoded by and connections, respectively, so that the minicolumn corresponding to the execution of an action in a given place is linked to the place visited after movement. The model uses a motivational signal conveyed by synapses to encode goal information. The population of neurons projects to motor output, where a winner-take-all competition takes place to select actions locally. Collateral projections between columns (, , and ) together with a proprioceptive signal allow the model to implement multilevel spatial processing.

Figure 2. Spatial navigation tasks used to test the capability of inferring detours.

The Tolman & Honzik's maze (adapted from [4]) consists of three pathways (Path 1, Path 2 and Path 3) with different lengths. The original maze fits approximately within a rectangle of 1.20×1.55 m. Two blocks can be introduced to prevent animals from navigating through Path 1 (Block A) or both Path 1 and Path 2 (Block B). The gate near the second intersection prevents rats from going from right to left.

Figure 3. Spatial behavior performance in the Tolman & Honzik's detour task.

Simulation results. Day 1: left column; Day 2–14: central column; Day 15: right column. (A) Occupancy grids representing path selection results qualitatively. (B) Mean path selection rate (averaged over 40 simulated animals) in the 1∶1 scale version of the maze. Note that similar to Tolman & Honzik we ignored P1 in Day 2–14 and Day 15 analyses because blocked. (C) Performance of “control” vs. “no ” animals in the 4∶1 version of Tolman & Honzik's maze.

Figure 4. Single cell response analysis.

Simulation results and relation to electrophysiological PFC recordings. (A) Examples of receptive fields of model hippocampal place (HP) cells (left), cortical neurons in (center) and in (right) when the simulated animals were solving the 4∶1 version of Tolman & Honzik's maze. White regions denote large firing rates whereas black regions correspond to silent activity. (B) Mean size of the receptive fields for each neural population, measured in pixels (i.e. 5×5 cm square regions). (C) Mutual information between single unit responses and spatial input for each population. (D) Location-selective responses of model single neurons functions of the normalized distance traveled along a section of the linearized trajectory P3 (top row) and medial PFC pyramidal cells recorded from navigating rats (bottom row).

Figure 5. Population place coding analysis.

Simulation results. (A) Examples of distributions of place field centroids for the populations of model HP cells (left), cortical neurons in (center) and in (right), when simulated rats were solving the 1∶1 version of Tolman & Honzik's maze. (B) Mean number of active neurones (average over 40 animals) when learning the 4∶1 Tolman & Honzik's maze (left). Evolution of the number of active neurons during the first 12 trials, i.e. Day 1 (right). (C) Mean spatial density (averaged over 40 animals) of receptive fields for each neural population. (D) Mutual information between population responses and spatial input states.

Figure 6. Coding of distance-to-goal and task-related information.

Simulation results and relation to experimental PFC recordings. (A) Relation between the shortest distance of a place to the goal and the firing rate of the neuron in belonging to the column representing that location. Each cross corresponds to one neuron . Beyond a certain distance, the intensity of the back-propagated goal signal reaches the noise level. As a consequence, neurons discharges become uncorrelated with the distance to the goal, and random decisions are made. (B) Frequency-selective responses of model single neurons (top row) and of medial PFC pyramidal cells recorded from navigating rats (bottom row). (C) Relation between task-related information (Day 1 Trial 12: end of “no block” phase, Day 14 Trial 12: end of “block A” phase and Day 15 Trial 7: end of “block B” phase) and firing rate of the neuron in belonging to the column representing the first intersection point. Inset: mutual information between the phase of the task and single unit responses of in vs. in .

Figure 7. Time course analysis of action-reward contingency changes.

Simulation results. Left column: Day 2 Trial 1 with block at A. Right column: Day 15 Trial 1 with block at B. (A, D) Examples of trajectories performed by simulated animals when encountering either block A or block B (distinct colors illustrate distinct actions). (B, E) Time course profile of firing rates of three neurons , and belonging to the column encoding the first intersection (and, in particular, to the minicolumns representing the actions , and , respectively). Vertical dotted lines indicate decision-making events (according to colored arrows at the bottom). (C, F) Time course profile of neural activity of three neurons , and belonging to the column representing the first intersection and to the minicolumns representing the actions , and , respectively.

Figure 8. Coding of prospective place sequences.

Simulation results and relation to experimental PFC recordings. (A) Comparison of time course shapes of the responses of four pairs of neurons and belonging to the same column (). Inset: correlation between the position of a given column within a planned path (measured as the path length from the starting column to that given column) and the skewness of the time course profile of its neuron p activity (black crosses) or its neuron s activity (gray dots). (B) Asymmetric responses of model single neurons (top row) and of pyramidal cells recorded from the PFC of navigating rats (bottom row). (C) Sequence order coding carried out by a population of monkey PFC neurons (left; data courtesy of Averbeck et al. [65]). Each curve denotes the strength of the neural activity encoding a specific segment of a planned drawing sequence (the peak of each curve corresponds to the time when the segment is actually being drawn). Similarly, a sequence order coding property was observed when recording neurons in of the model (right). Each curve measures the activity of a neuron belonging to a planned trajectory. The peaks of activity represent the times when places are actually visited.

Figure 9. Principal component analysis of simulated neuronal activities.

(A) Simulated neurons represented within the space defined by the first three principal components. (B) Spatial information per spike averaged over each neural population of the model. (C) Mean firing rate averaged over each neural population. (D) Mean absolute skewness average over each population. The color code is the same used in (A).

Figure 10. Principal component analysis and unsupervised clustering of simulated and real neuronal activities.

(A) Clustering of model activities within the PCA space. The same color scheme (used to discriminate clusters) is applied throughout the entire figure. (B) Blind clustering of real PFC recordings represented in the three first principal components space. (C, D, E) Mean information per spike, firing rate and skewness for real vs. model subpopulations (i.e. clusters).