Recent studies, using unbiased sampling of neuronal activity in vivo, indicate the existence of sparse codes in the brain. These codes are characterized by highly specific, associative (i.e., dependent on combinations of features) and often invariant neuronal responses. Sparse representations present many advantages for memory storage and are, thus, of wide interest in sensory physiology. Here, we study the statistics of connectivity in an olfactory network that contributes to the generation of such codes: Kenyon cells (KCs), the intrinsic neurons of the mushroom body (a structure involved in learning and memory in insects) receive inputs from a small population of broadly tuned principal neurons; from these inputs, KCs generate exquisitely selective responses and, thus, sparse representations. We find, surprisingly, that KCs are on average each connected to about 50% of their input population. Simple analysis indicates that such connectivity indeed maximizes the difference between input vectors to KCs and helps to explain their high specificity.

One of the most basic and general tasks faced by all nervous systems is extracting relevant information from the organism's surrounding world. While physical signals available to sensory systems are often continuous, variable, overlapping, and noisy, high-level neuronal representations used for decision-making tend to be discrete, specific, invariant, and highly separable. This study addresses the question of how neuronal specificity is generated. Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties. For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated. In particular, connection probability ½, as found in the locust antennal-lobe–mushroom-body circuit, serves to maximize separation of neuronal representations across the target Kenyon cells (KCs), and explains their specific and reliable responses. This analysis yields a function expressing response specificity in terms of lower network parameters; together with appropriate gain control this leads to a simple neuronal algorithm for generating arbitrarily sparse and selective codes and linking network architecture and neural coding. I suggest a straightforward way to construct ecologically meaningful representations from this code.

Olfactory systems operate in a balancing-act between two contrasting requirements. On the one hand, dealing with the bewildering repertoire of natural odors requires them to be extremely broad and versatile. At the same time, recognizing odors reliably, discriminating between similar compounds and overlapping mixtures, and detecting odorants in miniscule concentrations all require exquisite precision and specificity. How can a single system satisfy such opposite requirements?There are of course specialized odorants (such as pheromones) which have highly specific receptor-proteins (and thus, highly specific receptor-neurons) tailored to them. In these cases the receptor-ligand pair implements a lock-and-key fit and downstream signaling proceeds via labeled-lines. Such specialized signaling channels, however, do not reflect the general case, and the designated hardware they require sharply limits the number of odorants which can be managed. General odorantsprocessed by general-purpose receptor neurons-pose a much bigger challenge, in that the very same hardware needs to allow both broadness and specificity.Here I discuss how simple neuronal hardware can solve this complex task: generating arbitrarily odorspecific cells from an arbitrarily large odor input space. Experimental findings on network architecture in the olfactory system of the locust [1] were the inspiration for a highly simplified theoretical framework, key properties of which can be analytically solved [2]. I prove that an intermediate range of connectivity values between source-and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated. In particular, connection probability ½, as found in the locust antennal-lobe-mushroom-body circuit, maximizes separation of neuronal representations across the target Kenyon cells, explaining their specific and reliable odor-responses. I show that combining such connectivity matrix with a suitable firing threshold generates arbitrarily odor-specific target cells: this forms a simple neuronal algorithm which is applicable to the general case of chemical sensing and may be found in other olfactory systems: it generates arbitrarily sparse and selective codes and allows to construct ecologically-meaningful representations from them.