In computational studies, progress has been achieved in understanding of how sparse codes can

be generated by neural networks. It was shown that the recurrent network of inhibitory neurons can represent its inputs by sparse codes (Rozell et al., 2008). Understanding of these behaviors has become possible due to the approach based on Lyapunov function (Seung et al., 1998). While these models (Rozell et al., 2008) may provide neuronal mechanisms for sparse codes, they rely on the assumption that feedforward and feedback synaptic weights should satisfy a specific relationship. It is not clear how this condition is implemented biologically. While MCs form the representation of odorants, their number is significantly smaller buy Venetoclax than the number of local inhibitory interneurons, granule cells (GCs), which play an important role in the network interactions. These cells are thought to implement lateral www.selleckchem.com/products/Rapamycin.html inhibition

between MCs through a mechanism based on dendrodendritic reciprocal synapses (Figure 1) (Shepherd et al., 2004). Such interactions facilitate discrimination between similar stimuli and mediate competition between coactive neurons (Arevian et al., 2008). In agreement with this idea, facilitating inhibition between MCs and GCs improves performance in complex but not in simple discrimination tasks (Abraham et al., 2010). In this paper, we study the mathematical model of olfactory bulb. Using this model, we address a series of questions about the responses of MCs to odorants. How can sparse combinatorial code emerge as a result of network activity in the olfactory bulb? That is, how can MCs disregard the inputs from receptor neurons? How can transient (i.e., temporally sparse) activity be generated all by the same network? What is the role of network architecture of the olfactory bulb based on dendrodendritic synapses? How can olfactory code be state dependent, and is there a way to control the responses of MCs in a task-dependent manner? To answer these questions, we propose a novel role for olfactory bulb GCs. We show that GCs can form representations of olfactory

stimuli in the inhibitory inputs that they return to the MCs. MCs transmit to the olfactory cortex the errors of these representations. An exact balance between excitation from receptor neurons and inhibition from the GCs eliminates odorant responses for some MCs; however, other MCs retain the ability to respond to odors due to the incompleteness of the GCs’ representations. This function is facilitated by the network architecture based on dendrodendritic reciprocal synapses between the MCs and the GCs. In this architecture, both feedforward and recurrent connections for the GCs are mediated by the same synapses, thus making biologically plausible the specific relationship between feedforward and feedback synaptic weights necessary for the existence of sparse coding in the current mathematical models (Rozell et al., 2008).