Gain Control Network Conditions in Early Sensory Coding

Gain control is essential for the proper function of any sensory system. However, the precise mechanisms for achieving effective gain control in the brain are unknown. Based on our understanding of the existence and strength of connections in the insect olfactory system, we analyze the conditions that lead to controlled gain in a randomly connected network of excitatory and inhibitory neurons. We consider two scenarios for the variation of input into the system. In the first case, the intensity of the sensory input controls the input currents to a fixed proportion of neurons of the excitatory and inhibitory populations. In the second case, increasing intensity of the sensory stimulus will both, recruit an increasing number of neurons that receive input and change the input current that they receive. Using a mean field approximation for the network activity we derive relationships between the parameters of the network that ensure that the overall level of activity of the excitatory population remains unchanged for increasing intensity of the external stimulation. We find that, first, the main parameters that regulate network gain are the probabilities of connections from the inhibitory population to the excitatory population and of the connections within the inhibitory population. Second, we show that strict gain control is not achievable in a random network in the second case, when the input recruits an increasing number of neurons. Finally, we confirm that the gain control conditions derived from the mean field approximation are valid in simulations of firing rate models and Hodgkin-Huxley conductance based models.Author Summary: Neural networks in the brain can classify objects as being the same thing regardless of the stimulus intensity, which is referred to as gain control. This intensity invariance occurs during pattern recognition in any sensory modality. We evaluate whether it is possible to design stable neural circuits made of excitatory and inhibitory neurons that are capable of controlling the internal representation of a stimulus using network properties alone. Gain control is important because if the activity gets out of control neurons can die or be damaged by hyper-excitation. It is known that one can control the internal representation by the saturating responses of neurons. However, we show that there also is a precise relationship of network parameters that can account for gain control regardless of the external stimulus without such saturation. The most important network parameters are the connections from the inhibitory population to the rest of the network. This is consistent with experimental findings. We also show that the connections from the excitatory to the inhibitory population do not play an important role in gain control, suggesting that they can be freed for encoding purposes without leaving the operating range of the network when levels of stimulation increase.