Olfactory Processing: Massive Convergence onto Sparse Codes Sparse neural coding provides numerous computational advantages. A recent analysis of the locust olfactory system has revealed a surprising circuit solution for achieving remarkably sparse and specific neural representations of odors. Mark Stopfer Sparse coding, a neural information processing strategy featuring minimal, broadly distributed spiking activity, appears to be common across brain areas and species. How is sparse coding achieved by neural circuitry? In the locust olfactory system, olfactory receptor neurons project to the antennal lobe (analogous to the vertebrate olfactory bulb), where they synapse upon a population of excitatory projection and inhibitory local neurons. Odor-driven circuit interactions coordinate these neurons into widespread oscillatory synchrony , and transform representations of any given odor into specific, reliable, exuberant and temporally complex patterns of action potentials [2,3] distributed across the majority of the 830 or so projection neurons (analogous to the vertebrate mitral cells). Projection neurons, in turn, synapse upon a group of about 50,000 follower neurons, the Kenyon cells, within the mushroom body (Figure 1), a structure analogous to the vertebrate piriform cortex. Interestingly, Kenyon cells are nearly silent. They respond to odors rarely and barely, often with just a spike or two, but reliably and with remarkable specificity . In the course of an experiment, a given Kenyon cell is likely to fire not at all, or only when the animal’s antenna encounters a particular odorant, or even a particular concentration of an odorant . Thus, there is sparse coding: for a given stimulus, very few of the huge population of Kenyon cells respond at all, and the response consists of very few spikes. A recent paper by Jortner et al.  examined how this sparse coding arises from the
fundamental circuit properties of connectivity and response threshold. How to characterize the connectivity matrix linking 830 projection neurons to 50,000 Kenyon cells? Jortner et al.  first considered the branching patterns of these neurons. In confocal images of the locust brain they noted very extensive spatial overlaps between dye-filled projection neuron axons and Kenyon cell dendrites such that large numbers of projection neurons appeared to contact each Kenyon cell. But were these apparent contacts functional? The authors devised an elegant physiology experiment: they systematically made extracellular ‘tetrode’ recordings from groups of projection neurons to monitor their spontaneous spiking while making an intracellular recording from a Kenyon cell to monitor its excitatory post-synaptic potentials (EPSPs). Although these individual EPSPs were tiny, typically buried in the noise that is characteristic of such recordings, the authors revealed them by averaging many traces that had been aligned with respect to spikes in projection neurons. A convincing series of control measures indicated that these EPSPs were most likely elicited monosynaptically by the spikes in the projection neurons. This analysis showed, remarkably, that each Kenyon cell received direct input from about half of the projection neurons tested — extrapolating from the dataset suggested every Kenyon cell sampled the output of about 415 of the 830 projection neurons. This seems paradoxical: how can such massively convergent input from so many rapid-fire projection
neurons result in the sparse and highly selective responses observed in Kenyon cells? Jortner et al.  note that three mechanisms sharply constrain the ability of Kenyon cells to spike unless odor-driven conditions are met. First, projection neurons respond to odors with temporally complex firing patterns that include periods of inhibition, so, of all projection neurons converging upon a Kenyon cell, only an odor-specific subset is active at any given time. Second, individual EPSPs triggered by projection neuron spikes are very tiny — two orders of magnitude smaller than the firing threshold of Kenyon cells — so many projection neurons need to fire together to trigger a Kenyon cell spike. And third, shutter-like, rhythmic feed-forward inhibition onto the Kenyon cells, driven indirectly by the oscillatory output of projection neurons, prohibits Kenyon cells from firing during a portion of each oscillatory cycle; projection neurons rarely fire more than once per cycle. These conditions ensure Kenyon cells spike rarely and specifically; Jortner et al.’s  analysis of these conditions is quantitative, and the numbers work out. Massively convergent wiring seems an odd way to construct a sparse representation. Yet, Jortner et al.  used the simple binomial coefficient equation to demonstrate that this arrangement is, in fact, optimal: 50% connectivity maximizes the unique projection neuron combinations Kenyon cells could sample. The resulting number of potential combinations vastly exceeds the actual number of Kenyon cells; thus, there is essentially no chance that any two Kenyon cells will sample the same group of projection neurons. This dense connectivity matrix, therefore, optimizes the differences between inputs, leading to well-separated, sparse representations of odors. Odor representations in Kenyon cells have less overlap with each other than representations in projection neurons, with attendant advantages for
Current Biology Vol 17 No 10 R364
coding. As these recent publications show, it will be essential and interesting to understand the anatomical and physiological features that make sparse codes possible.
PNs: 830 Current Biology
Figure 1. The locust olfactory system. In the locust olfactory system, 50% of the 830 projection neurons (PNs) synapse upon each of the 50,000 Kenyon cells (KCs). A simple combinatorial analysis shows that this scheme maximizes the number of potential projection neuron–Kenyon cell connection patterns, ensuring Kenyon cells can generate unique and well-separated responses to odors.
comparing stimuli with one another, and for forming memories. This decorrelation is achieved by the circuitry of the antennal lobe and its surprisingly dense connectivity to the Kenyon cells. To what extent do the principles of connectivity and response sparseness determined in the locust olfactory system apply in other systems and species? To date, no other preparation has been subject to the sort of physiological analysis provided by Jortner et al. , but there are some indications that different systems may be organized along different lines. For example, in the fruit fly Drosophila, as in the locust, odor representations in the Kenyon cells appear to be sparse , particularly compared to representations in the projection neurons [8,9]. Yet, a series of anatomical studies indicates that, in Drosophila, projection neuron to Kenyon cell connectivity is far less dense than that observed in the locust: Drosophila projection neurons and Kenyon cells are much less extensively branched than their locust counterparts [10,11] and appear to make many fewer synaptic contacts . Thus, in Drosophila, sparse coding may be achieved by a mechanism somewhat different from that of the locust.
Recent work in a vertebrate may point toward a different mechanism, as well. In an elegant study, Franks and Isaacson  recorded from layer II/III pyramidal cells from slices of rat piriform cortex while using focal electrodes to electrically stimulate the lateral olfactory tract, the pathway provided by mitral and tufted cells from the olfactory bulb. By controlling the location and intensity of the electrical stimuli, and by using various pharmacological tools, the authors found they could activate individual axons synapsing upon the pyramidal cells they were monitoring, and could thus measure the amplitudes of individual inputs. This approach revealed a range of input intensities, including some single-fiber inputs sufficiently powerful to permit only a handful of co-active mitral and tufted cells to cause their piriform follower cells to fire. This result suggests a balance of input convergence and follower threshold rather different from that of the projection neurons and Kenyon cells of the locust. Although it’s too soon to generalize about the prevalence and utility of different underlying mechanisms, it appears there is more than one way to achieve sparse
1. Laurent, G., and Davidowitz, H. (1994). Encoding of olfactory information with oscillating neural assemblies. Science 265, 1872–1875. 2. Wehr, M., and Laurent, G. (1996). Odour encoding by temporal sequences of firing in oscillating neural assemblies. Nature 384, 162–166. 3. Mazor, O., and Laurent, G. (2005). Transient dynamics versus fixed points in odor representations by locust antennal lobe projection neurons. Neuron 48, 661–673. 4. Perez-Orive, J., Mazor, O., Turner, G.C., Cassenaer, S., Wilson, R.I., and Laurent, G. (2002). Oscillations and sparsening of odor representations in the mushroom body. Science 297, 359–365. 5. Stopfer, M., Jayaraman, V., and Laurent, G. (2003). Intensity versus identity coding in an olfactory system. Neuron 39, 991–1004. 6. Jortner, R.A., Farivar, S.S., and Laurent, G. (2007). A simple connectivity scheme for sparse coding in an olfactory system. J. Neurosci. 27, 1659–1669. 7. Wang, Y., Guo, H.-F., Pologruto, T.A., Hannan, T.F., Hakker, I., Svoboda, K., and Zhong, Y. (2004). Stereotyped odor-evoked activity in the mushroom body of Drosophila revealed by green fluorescent protein-based Ca2+ imaging. J. Neurosci. 24, 6507–6514. 8. Wilson, R.I., Turner, G.C., and Laurent, G. (2004). Transformation of olfactory representations in the Drosophila antennal lobe. Science 303, 366–370. 9. Turner, G.C., and Laurent, G. (2005). Odor representations in the Drosophila mushroom body. Soc. Neurosci. Abstr. Prog. Num. 278.15. 10. Ito, K., Suzuki, K., Estes, P., Ramaswami, M., Yamamoto, D., and Strausfeld, N.J. (1998). The organization of extrinsic neurons and their implications in the functional roles of the mushroom bodies in Drosophila melanogaster Meigen. Learn Mem. 5, 52–77. 11. Tanaka, N.K., Awasaki, T., Shimada, T., and Ito, K. (2004). Integration of chemosensory pathways in the Drosophila second-order olfactory centers. Curr. Biol. 14, 449–457. 12. Wong, A.M., Wang, J.W., and Axel, R. (2002). Spatial representation of the glomerular map in the Drosophila protocerebrum. Cell 109, 229–241. 13. Franks, K.M., and Isaacson, J.S. (2006). Strong single-fiber sensory inputs to olfactory cortex: implications for olfactory coding. Neuron 49, 357–363.
NIH-NICHD, 35 Lincoln Drive, Rm 3A-102, msc 3715, Bethesda, Maryland 20892, USA. E-mail: [email protected]