Logarithmic compression of sensory signals within the dendritic tree of a collision-sensitive neuron

Neurons in a variety of species, both vertebrate and invertebrate, encode the kinematics of objects approaching on a collision course through a time-varying firing rate profile that initially increases, then peaks, and eventually decays as collision becomes imminent. In this temporal profile, the peak firing rate signals when the approaching object's subtended size reaches an angular threshold, an event which has been related to the timing of escape behaviors. In a locust neuron called the lobula giant motion detector (LGMD), the biophysical basis of this angular threshold computation relies on a multiplicative combination of the object's angular size and speed, achieved through a logarithmic-exponential transform. To understand how this transform is implemented, we modeled the encoding of angular velocity along the pathway leading to the LGMD based on the experimentally determined activation pattern of its presynaptic neurons. These simulations show that the logarithmic transform of angular speed occurs between the synaptic conductances activated by the approaching object onto the LGMD's dendritic tree and its membrane potential at the spike initiation zone. Thus, we demonstrate an example of how a single neuron's dendritic tree implements a mathematical step in a neural computation important for natural behavior.