The dopamine circuit as a reward-taxis navigation system

Research on certain circuits in simple organisms, such as bacterial chemotaxis, has enabled the formulation of mathematical design principles, leading to ever more precise experimental tests, catalyzing quantitative understanding. It would be important to map these principles to the far more complex case of a vertebrate behavioral circuit. Here, we provide such a mapping for the midbrain dopamine system. Dopamine transmission plays a key role in learning, motivation, and movement, but its systems-level function is not fully understood. We develop a minimal mechanistic model of the dopamine circuit based on physiological and behavioral data, and show that it can be mapped mathematically to the bacterial chemotaxis circuit. Just as chemotaxis robustly climbs attractant gradients, the dopamine circuit performs reward-taxis where the attractant is the expected value of reward. The reward-taxis mechanism is based on a circuit feature called fold-change detection, where the circuit outputs the temporal logarithmic derivative of expected reward. The model can explain the general matching law, in which the ratio of responses to concurrent rewards goes as the reward ratio to the power {beta}. It provides an accurate mechanistic value for {beta} as the average gain/baseline ratio of the dopaminergic neurons. Reward-taxis provides testable etiologies for specific dopamine-related disorders.