Mathematical analysis of neural networks for chemotaxis in
T. C. Ferrée and S. R. Lockery
Institute of Neuroscience, University of Oregon, Eugene, OR 97403.
C. elegans moves up a gradient of chemical attractant (chemotaxis) using chemosensory neurons at the tip of the nose. Laser ablations[1,2] and anatomical data indicate that chemosensory information is processed by a highly interconnected neural network of sensory neurons, interneurons and motor neurons. Patch-clamp recordings from neurons in the nerve ring show that graded potentials, rather than action potentials, are the main kind of electrical signal. To determine how a network of graded-potential neurons steers worms up gradients, we constructed an idealized model chemotaxis network of linear neurons (the simplest kind of graded-potential neurons), which controls the behavior of a simulated worm. Analyzing the model network using linear systems theory, we found that the model produced chemotaxis by altering neck angle, and thus rate of turning R, as a function of chemosensory input, according to the equation R = k1 + k2 C + k3 dC/dt, where k1, k2 and k3 are constants, and C is the chemical concentration at the tip of the nose. Thus, the model predicts that in real worms, chemotaxis may be controlled by turning in response to absolute concentration and its time derivative. We are testing this prediction by tracking worms in measured concentration gradients. We are also testing the robustness of the model network by asking whether it can control taxis behavior in a freely moving robot.
Supported by NIMH MH11373, NIMH MH51383, NSF IBN 9458102, ONR N00014-94-1-0642, the Sloan Foundation, and the Searle Scholars Program.