Homeostatic and gain control mechanisms in a developmental model of orientation map formation in V1

Numerous studies have shown that cortical neurons can self-regulate their response gain (i.e., their output in response to an input). Theoretical studies of such gain control have primarily considered single cells or small networks of neurons in the adult brain. However, gain control is likely to be particularly important during development, because the amount and distribution of input activity can change dramatically between neurogenesis and adulthood. For instance, the developing visual system at first receives intrinsically generated input, such as retinal waves or spontaneous cortical activity, and in later stages (after eye opening) receives direct visual stimulation from the environment. In this study we examine how gain control can interact with basic homeostatic mechanisms to reproduce the experimentally observed patterns of development in a large scale model of an orientation map in the primary visual cortex (V1). Using this model, we have identified a small set of mathematical rules that can reproduce the following experimentally observed phenomena: stable orientation map development (Chapman et al. J. Neurosci., 1996, 16:6443--6453), contrast independent orientation tuning (Alitto et al. J Neurophysiol., 2004 91:2797--2808), and orientation map development that is robust against changes in the levels or distributions of input activity over time (Crair et al. Science, 1998, 279:566--570). We show that the above constraints can be met by using a simple but plausible gain control mechanism at the level of the Lateral Geniculate Nucleus (LGN) or retina, plus a mechanism that maintains a constant ratio between the strength of different input types (afferent vs. feedback, and excitatory vs. inhibitory) to each individual neuron. By directly maintaining these specific interaction ratios, it is sufficient to use a simple threshold adjustment rule for each neuron, rather than the more complex intrinsic excitability adjustment rules previously designed for more abstract networks (Triesch ICANN, 2005, 65--70). This model thus highlights the benefit of studying these phenomena in neural models whose architecture is constrained by the known connectivity of neural structures (such as V1).