Figure 1. A mechanism for endotaxis.

(A) A constrained environment of tunnels linked by intersections, with special locations offering food, water, and the exit. (1) A real odor emitted by the food source decreases with distance (shading). (2) A virtual odor tagged to the water source. (3) A virtual odor tagged to the exit. (4) Abstract representation of this environment by a graph of nodes (intersections) and edges (tunnels). (B) A neural circuit to implement endotaxis. Open circles: four populations of neurons that represent ‘resource,’ ‘point,’ ‘map,’ and ‘goal.’ Arrows: signal flow. Solid circles: synapses. Point cells have small receptive fields localized in the environment and excite map cells. Map cells excite each other (green synapses) and also excite goal cells (blue synapses). Resource cells signal the presence of a resource, for example, cheese, water, or the exit. Map synapses and goal synapses are modified by activity-dependent plasticity. A ‘mode’ switch selects among various goal signals depending on the animal’s need. They may be virtual odors (water, exit) or real odors (cheese). Another goal cell (clock) may report how recently the agent has visited a location. The output of the mode switch gets fed to the chemotaxis module for gradient ascent. Mathematical symbols used in the text: ${\displaystyle u_i}$ is the output of a point cell at location ${\displaystyle i}$, ${\displaystyle w_i}$ is the input to the corresponding map cell, ${\displaystyle v_i}$ is the output of that map cell, ${\displaystyle \mathbf{M}}$ is the matrix of synaptic weights among map cells, ${\displaystyle \mathbf{G}}$ are the synaptic weights from the map cells onto goal cells, and ${\displaystyle r_k}$ is the output of goal cell ${\displaystyle k}$.