Figure 1: Morphology of the principal neurons of the antennal lobe (functional analogs of vertebrate mitral cells of the olfactory bulb). Two projection neurons (of a total of 830) in the locust antennal lobe, viewed en face (left) or normal to that view (right). Each neuron samples 10-16 glomeruli among about 1,000 in each antennal lobe. The glomeruli sampled by a single PN are organized in a circle confined to a plane. PNs all lie in parallel planes, occupying a sphere. Within one plane, many PNs co-exists, with a range of radii. Intracellular stains and confocal stacks by S. Sarah Farivar (PhD 2005). Movies of PNs in situ are shown in Movie 1 and Movie 2

Figure 2: Morphology of Kenyon cells (KCs), the principal neurons of the mushroom body, a structure involved in olfactory memory. The mushroom body is post-synaptic to the antennal lobe; Kenyon cells thus receive direct excitatory input from the antennal lobe projection neurons. In locust, there are 50,000 Kenyon cells per mushroom body. Three KCs are shown, in the input neuropil of the mushroom body (calyx, here shown in gold). KCs are spiny neurons, with small somata (6-8 microns) and fine dendrites and axons (100-200nm diameter). Movies of segmented KCs in situ are shown in Movie 3.

Figure 3: Contrast between odor responses of PNs (Figure 1) and KCs (Figure 2). PNs have high baseline discharge rates (3-4 spikes/s) and respond promiscuously to odors (about 50% of odors, as measured over 1s post-stimulus delivery). PN responses are complex (generally patterned in time), but odor- and PN-specific. By contrast. KCs have very low discharge rates (1 sp/30s on average, though most KCs remain silent for many minutes) and extremely rare responses to odors. Those responses are brief (2.3 spikes on average) and time-specific for a given KC-odor combination. That is, each odor evokes a response in a set of KCs, but the respective responses of those KCs are spread in time over the duration of the stimulus or its immediate aftermath. Odors are thus represented by highly distributed (in space and in time) patterns of PN activity but by very sparse sets of KCs in the mushroom body. A major focus of this lab has been (and remains) to understand the computational purposes and underlying mechanisms of this transformation. Some of these basic features are described further below.

Figure 4: Decoding of PN population output by KCs.

Bottom: Because odor-evoked activity is distributed in time and across PNs, we can describe those patterns as trajectories in PN phase space. Imagine that we plotted the firing activity of all PNs when odor X is presented. Following odor onset, many PNs fire, at times determined by the stimulus and PN identity. Thus, at any one time (we typically chose a 50 ms long time window as our time step, for reasons explained later), only a subset of these PNs is active; they define a vector of PN activity at that time. Fifty ms later, activity across the PN population has evolved some, such that the state of the PN population is described by a new vector of PN activity. Over a long time interval (e.g., one second or so), the PN population response (and thus the representation of odor X by PNs) can be described as a trajectory defined by the corresponding time series of PN activity vectors. By using dimensionality reduction techniques, we can project those trajectories in 2 or 3 dimensions, and visualize them. This is what is shown in the bottom right figure (also schematized in Movie 4) . The three trajectories shown in this figure represent the behavior of 99 PNs in response to one odor presented in pulses of three different durations (0.3s, 1s, 3s). B represents the rest state (baseline), and FP represents a fixed point, reached by the PNs only after 1.5 to 3 s. Upon odor offset, the population relaxes back to baseline, following a new trajectory, also odor specific (see Mazor and Laurent, 2005, for details). Each odor can thus be represented by a trajectory (in fact, a family of trajectories, see Stopfer, Jayaraman and Laurent, 2003) and a fixed point, only visited for long-lasting stimuli.

Top: These patterns are then decoded by KCs in the mushroom body by a process that is starting to be well understood (Perez-Orive et al., 2002 and 2004; Mazor and Laurent, 2005) (see also Movie 5). Each KC connects to a subset of PNs (the size of that subset is the object of studies presently under way) and carries out a pattern matching operation between its connection vector and the PN population activity vector. This operation is carried out discretely in time, once per oscillation cycle. Indeed, the PN output is periodic (~20Hz) and transiently synchronized (see local field potential oscillations in top diagram). The oscillation period serves as the time unit over which each KC in the mushroom body is given the opportunity to fire: a KC fires if the set of PNs active at that time (i.e., the instantaneous location of the population in PN phase space) is sufficiently close the subset of PNs that that KC is connected to. Given appropriate connectivity and firing thresholds, only very few KCs respond to any odor, and different KCs can respond to the same odor, but at different times, a consequence of the dynamics of PN responses. The main mechanisms ensuring that KCs carry out a discrete decoding of PN input (i.e., once per oscillation cycle) are explained in Movie 5).

Figure 5: Basic computations accomplished by the antennal lobe-mushroom body circuit.

a. The overall consequences of antennal lobe dynamics are to increase the separability of odor representations, spreading them in representation space.

b. This appears to be accomplished in several concurrent stages: dynamics in the antennal lobe causes the separation of representation vectors. Optima are reached during the transient phases (on and off) of PN activity, and paradoxically not when PNs reach their fixed point (Mazor and Laurent, 2005). This emphasizes the inappropriateness of mean -rates descriptions of activity. We describe this operation as a temporal  decorrelation, first observed in the zebrafish olfactory bulb (Friedrich and Laurent, 2001; Friedrich et al., 2004). The PN population output is then “classified” by KCs, such that each PN vector is recognized by a very small number of KCs. The representations are thus specific, and sparse in the mushroom body, a site for memory. This operation further decreases the overlap between representations, and thus also contributes to stimulus decorrelation (over odors). This basic optimization design was proposed by David Marr in his theoretical studies of cerebellar architecture (Marr, 1969) and has been studied in more detail for idealized systems of binary units by Pentti Kanerva (1989, MIT press).