Predicting brain organization with a computational model: 50-year perspective on lateral inhibition and oscillatory gating by dendrodendritic synapses

Abstract

The first compartmental computer models of brain neurons using the Rall method predicted novel and unexpected dendrodendritic interactions between mitral and granule cells in the olfactory bulb. We review the models from a 50-year perspective on the work that has challenged, supported, and extended the original proposal that these interactions mediate both lateral inhibition and oscillatory activity, essential steps in the neural basis of olfactory processing and perception. We highlight strategies behind the neurophysiological experiments and the Rall methods that enhance the ability of detailed compartmental modeling to give counterintuitive predictions that lead to deeper insights into neural organization at the synaptic and circuit level. The application of these methods to mechanisms of neurogenesis and plasticity are exciting challenges for the future.

INTRODUCTION

The first report using digital computers for analyzing biophysically accurate models of mammalian neurons was a study of the spread of synaptic potentials in dendrites of the spinal motor neuron (Rall 1964). In that report the basic principles of modeling with the new method were laid out. A study was then initiated to extend the method to neurons in the brain. The system chosen was interactions between mitral and granule cells in the olfactory bulb, based on Golgi-stained neurons (Fig. 1) and a variety of electrophysiological data, from single cells to local field potentials (Phillips et al. 1961, 1963; Shepherd 1962; 1963a, 1963b; Yamamoto et al. 1963). This earlier work had produced one of the first microcircuit diagrams for a brain region, where it was proposed that the anaxonic granule cell is an inhibitory interneuron for the mitral cell in processing olfactory input (Shepherd 1963b).

Fig. 1.

Neuron types and dendrodendritic synapses and actions in the mammalian olfactory bulb. Left: diagram from Cajal (1911) of the Golgi stained neurons of the olfactory bulb. G, granule cell; GL, glomeruli; M, mitral cell; T, tufted cell. A: sequence of activation of the dendrodendritic synapses. Time periods I–II: depolarization of a mitral cell dendrite (D) by an action potential spreading either actively or passively from the soma activates an excitatory synapse (E) onto a granule cell dendritic spine. Time periods II–III: depolarized spine activates feedback inhibition (J) of the mitral cell dendrite. Time period III: long-lasting hyperpolarizing inhibition. B: pathways for self- and lateral inhibition: on the right, orthodromic (OD) olfactory input or antidromic (AD) activation (arrows) both lead to invasion of the mitral cell lateral dendrites and synaptic activation of granule cells. This causes self-inhibition back onto the same mitral cell (curved arrow), and lateral inhibition onto other mitral cell dendrites (straight arrows). As the action potential sweeps through the lateral dendrite, it activates the output synapses before receiving the feedback inhibition, so that the reciprocal synapses always operate in sequence onto the same mitral cells, and only through the inhibitory synapses onto neighboring mitral cells. From Rall and Shepherd (1968).

The aim of the modeling study was for the first time to subject a proposed circuit such as this to rigorous testing for the biophysical properties of the neurons and their synaptic interactions. In addition to expected neuron properties, the simulations predicted unexpected synaptic connections: reciprocal dendrodendritic interactions between the mitral and granule cells (Fig. 1, A and B). Although unprecedented, they were soon confirmed by electron microscopy in the first report of Rall et al. (1966); see also Hirata (1964) and Andres (1965). The dendrodendritic circuit accounted for the connectivity underlying the proposed lateral inhibition of mitral cells and strongly supported it as a key element in sensory processing in olfaction. The study also proposed that the dendrodendritic circuit could generate oscillatory activity, a key property for central nervous system functions, during sensory processing.

The output synapses on the dendrites of both the mitral and granule cells overturned the classical neuron doctrine of unidirectional information flow between neurons from axons to dendrites (reviewed in Shepherd 1991, 2016). The dendrodendritic synapses became a model for similar nonclassical synaptic arrangements elsewhere in the nervous system (Shepherd 1978, 2004). The evolving concepts of the granule cell have been reviewed elsewhere (Shepherd et al. 2007). Here we focus on the computational models and the tests of the models for lateral inhibition and oscillatory activity that have taken place in the intervening half century.

By way of background, Wilfrid Rall, who led the original project, has been widely regarded as the pioneer, together with Alan Hodgkin and Andrew Huxley, in establishing the field of computational neuroscience. He was the first recipient of the Swartz Prize in 2008 for contributions to computational neuroscience. The paper to be reviewed here has been recognized as an American Physiological Society (APS) Classic Paper. In introducing this paper Idan Segev (2006) observed: “…probably the tour de force of Rall’s works (and perhaps of computational neuroscience in general) is the 1968 paper of Rall and Shepherd in the Journal of Neurophysiology.” It is timely therefore to see how the model has survived and bring it up to date.

ORIGINAL MODEL OF 1968

Rall et al. (1966) is usually cited for the first publication of the dendrodendritic circuit, but it focused mostly on evidence from electron microscopy. This has left obscured the companion paper (Rall and Shepherd 1968), which presented the critical evidence for the compartmental models of the mitral and granule cells and their functional interactions, showing in detail how they would generate self- and lateral inhibition and also oscillatory potentials involved in olfactory processing. The model of those functions, especially the lateral inhibition, has stimulated many experimental studies and theories of the neural basis of mammalian olfaction. Controversies have arisen around precise mechanisms, sometimes without sufficient attention to the original model. Now, with a 50-year perspective, it is appropriate to reemphasize the approach used in this first study and summarize the key functional predictions of the original model, the current state of experimental and computational testing, and challenges for the future.

The electrophysiological study of Phillips et al. (1961, 1963) and Shepherd (1963a, 1963b); see also Yamamoto et al. (1963), provided the data for the mitral and granule cell physiological properties used in the model (Fig. 1) (we shall use the term mitral cell to cover both mitral and middle tufted cells in most cases). At this early time the spinal motor neuron was the main model of neuron physiological properties (Eccles 1957). The key data in the olfactory bulb study showed the same sequential activation of the axon hillock and soma-dendrites in the action potential in the mitral cell, followed after a disynaptic delay by strong and long-lasting hyperpolarizing inhibition. The antidromic action potential recordings were localized to the mitral cell body layer. The synaptically evoked field potentials attributed to the granule cell dendrites peaked in the nearby external plexiform layer where the granule cell dendrites mingle with the mitral cell lateral dendrites. In a local circuit diagram, it was postulated (Shepherd 1963b: Fig. 7, p. 112) that the mitral cell inhibition was due to the granule cell acting as an inhibitory interneuron, in analogy with the Renshaw cell in the spinal cord. This suggested novel properties of inhibitory output from granule cell dendrites onto mitral cell lateral dendrites and the inhibition due to prolonged synaptic action in the absence of action potentials.

The compartmental models were built mainly on these data to test the proposed circuit. The 1960s were early in the computer era. All computations were by main frame room-filling machines, with tiny memories consisting of a few hundreds of kilobytes. Runs were overnight, which required close examination of each run to decide on the most meaningful variable to test for the next run. To test for impulse invasion of the mitral cell axon hillock and dendrites, a simulated Hodgkin-Huxley (Hodgkin and Huxley 1952) action potential was constructed by Rall that could run on the limited machines then available and was carefully matched to the Golgi anatomy and the electrophysiological data (Rall and Shepherd 1968). At a meeting on the 60th anniversary of the Hodgkin-Huxley (HH) model in 2012 it was determined that this was probably the first incorporation of a realistic HH action potential model into a simulation of a brain neuron.

The model confirmed most of the proposed olfactory bulb circuit but surprisingly showed that activation of the granule cell most likely comes not from mitral cell axon collaterals as originally proposed, but from the mitral cell dendrites that are themselves the targets of the inhibition, so that the granule cell is activated by excitatory dendrodendritic synapses and in turn brings about mitral cell inhibition through inhibitory dendrodendritic synapses (Fig. 1). Although the original model of mitral cell axon collateral activation was thus disproved, it served its purpose in forcing the realization that activation by axon collaterals of the deep dendrites of the granule cell would not fit with the extracellular potential profile of the activated granule cell dendrites at that moment in time, whereas the mitral cell lateral dendrites were at the right place and time to do so. It should be stressed that in the model the reciprocal side-by-side synapses do not conflict with or short-circuit each other, because they operate in a sequential mode of mitral-to-granule excitation followed by granule-to-mitral inhibition for self-inhibition, and by a single inhibitory granule-to-mitral mode for lateral inhibition (Fig. 1).

The experimental data and the model were immediately confirmed by Nicoll (1969) and have supported by numerous subsequent studies. The reciprocal nature of the excitation and inhibition was convincingly demonstrated by Jahr and Nicoll (1982). The full dendrodendritic mitral-granule interactions were modeled at IBM on a mainframe computer (Shepherd and Brayton 1979), still with only a megabyte of memory. Combining the two functional neuron models with their synaptic interactions thus constituted a model of an entire local circuit, what is now termed a microcircuit (Shepherd 1978).

DENDRODENDRITIC SYNAPSES AND DENDRITIC SPINES

The side-by-side reciprocal nature of the dendrodendritic synapses has been confirmed by many studies; see Fig. 2, A and B. The existence of the inhibitory synapse was early questioned (Ramon-Moliner 1977) but was confirmed by ethanolic phosphotungstic acid staining (Jackowski et al. 1978). The term “gemmule” was initially applied to the granule cell spine, but it is now recognized as a variety of dendritic spine. Suggestions were made to consider the dendritic output synapses as a special subtype, but their presence in many other brain regions indicated that they are standard type 1 excitatory and type 2 inhibitory synapses, in a reciprocal configuration that is effective for their function.

Fig. 2.

Dendrodendritic synapses as local input-output sites in the granule cell spine in the rodent olfactory bulb. A: electron micrograph of a granule (Gr) dendritic spine making dendrodendritic synapses with a mitral/tufted (M/T) cell lateral dendrite. Arrowheads indicate orientation of the mitral-to-granule cell type 1 synapse and granule-to-mitral type 2 synapse. m, Mitochondrion. B and C: this spine and others were used to develop the computational model of diffusion of Ca²⁺ from the head of the spine sp54 into the neck. As can be seen in the graph, diffusion drops off precipitously in the neck, supporting the hypothesis that granule cell spine heads are relatively isolated from the parent dendrite and can function as independent units. from Woolf and Greer (1994).

Glutamate was shown to be the transmitter at the excitatory mitral-to-granule synapse (Cotman et al. 1987) and GABA at the inhibitory granule-to-mitral synapse (Nicoll 1971). NMDA receptors on the granule cells mediate slow long-lasting excitatory postsynaptic potentials, associated with a long-lasting GABA inhibition of the mitral cells (Schoppa et al. 1998). This may be partly the basis for the experimentally recorded prolonged synaptic inhibition in the absence of action potentials (Shepherd 1963b).

The synapses became of special interest with regard to both developmental neurogenesis and adult neurogenesis, the latter a rare property which the olfactory bulb shares with the dentate gyrus. During embryonic development, GABA_A receptors have a depolarizing action due to the reversed Cl⁻ gradient, which may contribute to network synchronization (Ben-Ari 2002). AMPA receptors are expressed early, before NMDA receptors, opposite to the sequence in many other brain regions (Schoppa et al. 1998). In contrast, during adult neurogenesis, GABA-mediated inhibition may protect established circuits from disruption by the new neurons (Carleton et al. 2003). Similarly, transient voltage-gated Na⁺ channels in the granule cells are delayed until later maturation. Axodendritic synapses from the olfactory cortex onto the deep dendrites of the granule cells are made before the inhibitory output synapses appear (Whitman and Greer 2007), so that the new dendrodendritic module is integrated into central circuits before its specific sensory input and output functions. Membrane properties involved in the regulation of dendritic excitability and dendrodendritic inhibition continue to be under active investigation (e.g., Bartel et al. 2015; Thomas et al. 2005).

A critical question is the kind of microenvironment within a granule spine, which is slightly larger than a cortical pyramidal cell spine and can serve as a more accessible model for studying movement of ions and second messengers within and between spines. Computer simulations of individual spines (Woolf and Greer 1994) showed that for Ca²⁺ and other second messengers with moderate to strong binding and extrusion mechanisms, their effects will be mostly confined within their spine head of origin (Fig. 2). Thus, use-dependent changes including plasticity will bias that spine’s responses to future inputs. This adds to the evidence of individual spines acting as largely independent functional integrative units and, in the case of the dendrodendritic synapses, as largely independent input-output units. The granule cell thus appears to have been the first example of a neuron recognized as a “multiunit neural network” (cf. Poirazi and Papoutsi 2020). In addition to these second messenger effects, the close relations between the side-by-side reciprocal synapses has suggested that the Ca²⁺ flowing in through an excitatory mitral-to-granule synapse could contribute to the activation of a neighboring inhibitory granule-to-mitral synapse (Chen et al. 2000), further supporting the unitary input-output function of the granule cell spine.

Soon after the mitral-granule cell model was reported, it was found that, within the olfactory glomerulus, mitral cell dendritic tufts interact through dendrodendritic synapses with another type of interneuron, the periglomerular cell (Pinching and Powell 1971; Reese and Brightman 1970), and evidence was obtained for an inhibitory action by the periglomerular cell dendrites (Shepherd 1971). In addition to reciprocal synapses, serial patterns are frequent, indicating complex processing of the incoming sensory information. We discuss the functional significance of the two layers of olfactory processing below. Further examples of dendrodendritic synaptic interactions have been found in many regions within the nervous system (summarized in Shepherd 2004); a common pattern is dendrodendritic inhibition by an interneuron dendrite of a principal neuron dendrite, as in the original model.

ACTIVE DENDRITES

An important issue has been whether the mitral cell dendrites are passive or active. The HH model provided the opportunity to test for this. Intracellular recordings were too limited at the time for this purpose, but the extracellular field potentials around the antidromically propagating action potential provided a valuable constraint. Reconstruction of those potentials (Fig. 8 in Rall and Shepherd 1968) pointed to two possibilities: the impulse spreads either passively in large diameter electronically short dendrites (primary plus lateral) or actively in thinner dendrites. Both of these were consistent with fitting the field potentials. However, they did not differentiate between properties of primary versus lateral dendrites.

Subsequently, specific evidence was sought in many types of cortical dendrites. for active properties using patch recordings. The mitral cell provided some of the best evidence. Chen et al. (1997) showed that action potential initiation can occur at the soma-initial segment or at the distal dendritic tuft in the glomerular layer depending on the physiological conditions. With weak distal synaptic excitation in the tuft, impulse activation tends to occur at or near the axon hillock, the classical most excitable site. As tuft synaptic excitation increases, the impulse initiation site shifts to the less excitable tuft site. Inhibitory input from the granule cells onto the soma and lateral dendrites also shifts initiation toward the distal dendrite. Thus the site of action potential generation is determined dynamically, depending on the balance between excitatory inputs to the distal tuft and inhibitory inputs at the level of the soma. This puts the mitral cell among other cortical neurons with critical active properties (Chen et al. 1997).

These experimental results could be reconstructed in a computational model of the mitral cell (Shen et al. 1999), which reproduced precisely how the action potential site shifts between soma and distal dendrite as in the experiments.

It may be noted that Rall was sometimes criticized for simulations that assumed dendrites were only passive. In fact, the mitral cell was the first in which active dendrites were computationally simulated. Subsequently Segev and Rall (1988) took up the question of active properties of dendritic spines. The advent of patch recordings in the 1990s revealed the ubiquitous presence of active properties in the dendrites of many neurons, as noted above.

Active properties are also present in the anaxonal granule cell, which responds to activation with brief action potential firing (Shepherd 1963b). The original model assumed that dendrodendritic synapses could function at two activity levels: by presynaptic depolarization of individual dendritic branches or spines or by action potentials spreading from the cell body throughout the dendritic tree (Rall and Shepherd 1968). Recent studies have provided evidence for action potential initiation in the apical dendrite near the soma (Pressler and Strowbridge 2019).

Active dendritic properties are critically important to lateral inhibition in the olfactory bulb, as we shall see.

LATERAL INHIBITION

The initial interpretation of the mitral-granule cell dendrodendritic interactions was that they would provide for lateral inhibition, a fundamental property known to be present in the retina (Kuffler 1953) and other sensory systems, well recognized to mediate contrast enhancement of the retinal image (Fig. 3A). It was inferred that lateral inhibition in the olfactory bulb could by analogy enhance contrast between the patterns of activation of the mitral cells during odor stimulations. This hypothesis received strong support from Yokoi et al. (1995), who showed that a given mitral cell responds best to a specific member of a chemical series, with a kind of “lateral” inhibition repressing responses of neighboring members of the series (Fig. 3B).

Fig. 3.

A: lateral inhibition in the retina; central excitation of a retinal ganglion cell is surrounded by inhibition, a classical example of spatial contrast enhancement, a fundamental operation in processing spatial patterns in sensory systems. From Kuffler (1953). B: example showing contrast enhancement by “lateral” inhibition in the olfactory bulb, in a chemical series of aldehydes of differing carbon lengths, which heightens contrast between odor molecules by excitation of a mitral cell by one odor molecule type (n-hexylaldehyde 6CHO) and inhibiting neighboring related odor molecules (4)CHO and (8)CHO in the series. From Yokoi et al. (1995); copyright (1995) National Academy of Sciences, U.S.A.

Two questions have been raised about the mechanism for the lateral inhibition. One is the extent to which lateral inhibition is due to the mitral-granule dendrodendritic synaptic interactions or to interactions at the glomerular level. In addition to the intraglomerular dendrodendritic interactions noted above, axons of glomerular layer cells mediate lateral inhibition of cells belonging to surrounding glomeruli (Aungst et al. 2003; Shepherd 1972). These and other cells and their connections provide a rich repertoire of lateral excitatory and inhibitory actions at the glomerular level (Cleland and Linster 2012; Cleland and Sethupathy 2006; Wachowiak and Shipley 2006), in parallel with the inhibitory actions at the granule cell level. All of these mechanisms are the subject of current experimental and computational analysis (e.g., Carey et al. 2015; Cavarretta et al. 2018).

A second question has been raised by the activation pattern of glomeruli and mitral cells by odor stimulation. Some studies show a tendency for regional localization of activated glomeruli by a given odor molecule type (Mori and Yoshihara 1995), while others show a wide activation pattern over the dorsal surface (Soucy et al. 2009) or the whole olfactory bulb (Stewart et al. 1979; Xu et al. 2003). When this is combined with the fact that the odor stimuli are highly multidimensional, it has implied that the organization of the olfactory bulb must be “nontopographical”; that is, the retinal model of lateral inhibition limited to the contiguous surrounding area of an excited cell cannot apply, ruling out the participation of the dendrodendritic inhibition of mitral cells on the belief that it could inhibit only neighboring mitral cells. This interpretation was largely due to the summary diagram of Fig. 1, which was interpreted to mean that the lateral inhibition acts only on neighboring mitral cells, whereas it was meant to indicate that the extent of lateral inhibition depends on the extent of impulse invasion of lateral dendrites.

This objection has in any case been rendered moot by the experiments of Xiong and Chen (2002) (see also Lowe 2002) (see Fig. 4) which confirmed the prediction that mitral cell dendrites may be excitable and carry action potentials. They showed that an action potential can propagate the full length of a lateral dendrite (Fig. 4, Control), which may extend up to half the perimeter of the olfactory bulb. They also showed that stimulation of deeper granule cells can block the propagation at any arbitrary distance, as can local application of their neurotransmitter GABA (Fig. 4, positions 1 and 2). This means that lateral inhibition can potentially be activated at arbitrary distances from a given mitral cell, making lateral inhibition effective over an extended nontopographical odor map, as indicated in Fig. 4. The active mitral cell lateral dendrites can thus provide for dynamic and arbitrary combinations of activated mitral cell outputs within broad odor maps, conveying the high dimensionality inherent in the odor maps to the next processing stage in the olfactory cortex.

Fig. 4.

Action potential propagation in a mitral cell lateral dendrite and gating by local synaptic inhibition. Control: an action potential evoked at the soma propagates throughout the primary and lateral mitral cell dendrites, as indicated by spike-evoked Ca²⁺ signals at five different positions along the dendrite. Through this means a mitral cell can activate dendrodendritic synapses for lateral inhibition of distant mitral cells. Pipette I: propagation toward positions 4 and 5 is blocked by ejecting GABA from a micropipette at position 4. Similarly, stimulating local inhibitory synaptic inputs to the mitral cell lateral dendrite can also block spike propagation. Through this mechanism granule cells can dynamically regulate the extent of surround inhibition. Pipette II: changing the location of GABA application shifts the spike-blocking site proximally to produce a much smaller inhibitory surround. Depending on other sensory inputs and centrifugal modulation, a granule cell may feed back inhibition at a given site far away from the activated mitral cell, or closer, providing for multiple sites of lateral inhibition within an extensive odor map. From Xiong and Chen (2002).

The high dimensionality of odor space is due to the multiple ways—carbon chain length, functional end group, double bonds, aromatic ring, etc.—that odor molecules can be similar to or different from each other. A big challenge in the field is how this high dimensionality can be represented in the two-dimensional space of the olfactory glomerular layer and the mitral cells connected to them. The fact that mitral cells are only one synapse from the receptors and one synapse from the cortex indicates that in fact olfactory processing of high dimensionality must actually be quite efficient. This contrasts with the visual system, where at least four synapses are needed to get from the stimulus at the receptors to the perception in association neocortex.

How does the olfactory system enable so short a pathway to process so much complexity? A key finding is that the next step in the pathway, olfactory cortex (including the anterior olfactory nucleus: Brunjes et al. 2005), already functions as a high-level associative cortex, comparable to higher visual association areas (Haberly 1985; Wilson and Barkai 2018). How can the olfactory bulb contain all the needed processing steps?

We hypothesize that each granule cell spine functions as an integrative unit, making each granule cell not just one integrative unit but multiple integrative units. As expressed by Egger and Urban (2006), “the GC [granule cell] spine may be capable of acting like a minineuron,” a concept mentioned above in discussing the independent action of a spine. Many of these integrative actions may be subthreshold for global output from the granule cell, but above threshold for individual spines or populations of spines (Egger et al. 2005; Woolf et al. 1991). This means that there are several levels of processing within the olfactory bulb. These mechanisms are being built into simulations of the olfactory bulb microcircuit (Egger and Urban 2006; Nagayama et al. 2014; Shepherd et al. 2018).

Current work indicates that the excitatory dendrodendritic synapses are relatively weak while the excitatory synapses of centrifugal axons from the olfactory cortex are relatively strong (Pressler and Strowbridge 2017). This sets up a situation in which granule cell odor responses and the lateral inhibition they generate require summation from sufficient numbers of activated glomeruli to reach threshold for generating action potentials in their granule cell subsets, reinforced by coincidence excitation from specific subsets of pyramidal neurons in olfactory cortex. “This dual-pathway requirement likely enables the sparse mitral/granule cell interconnections to develop highly odor-specific responses that facilitate fine olfactory discrimination” (Pressler and Strowbridge 2017, p. 11774).

To achieve this ability of the olfactory bulb to send output directly to higher association olfactory cortex, we hypothesize that the high-dimensional molecular combinations in the olfactory bulb are processed through large populations of granule cell spines with broad response spectra processing at different layers; the active mitral cell lateral interactions are widespread and highly combinatorial; and there is a logical arrangement of activated glomeruli and mitral cells reflecting both chemical structure and perceptual significance (see Snitz et al. 2013). This hypothesis is being tested experimentally and in scaled-up three-dimensional models (Cavarretta et al. 2016) of mitral-granule cell processing (Fig. 5). An advantage of these models is that they can show the activity in the entire system, and enable one to access the membrane and firing properties of any specific neuron and assess its contribution to the whole system.

Fig. 5.

Full 3D model seen en face (A) and from the side (B) [glomeruli (GL) in red]. C: three typical glomerular units, formed by mitral cells (MC), middle tufted cells (mTC), and granule cells (GC). D: slice section illustrating the different spatial organizations of the dendritic arborizations of MCs and mTCs within the EPL. E: typical snapshot from a movie illustrating the response of the olfactory bulb system during an odor-simulated input of 3 glomeruli (shown in yellow), 74 ms after onset of a simulated sniff.. Purple lines simulate apical and lateral dendrites of mitral cell bodies (concealed in the network of lateral dendrites). Light lines indicate sites of action potential propagation emanating from the mitral cell bodies and propagating various distances into the lateral dendrites depending on blockage by granule cells, thus providing for targeted lateral inhibition throughout this extensive area of the olfactory bulb. Individual active dendrites can be related to a given mitral cell and their properties evaluated within the context of the population response. The model is based on experimental evidence from Vincis et al. (2012). A–D adapted from Cavarretta et al. (2018). A full high-definition version of the movie in E can be downloaded from https://senselab.med.yale.edu/modeldb/data/151681/movie1.mp4.

OSCILLATORY ACTIVITY

In addition to lateral inhibition, the original model proposed a second main function for the dendrodendritic synapses: generation of oscillatory potentials. In the same circuit of Fig. 1, slow buildup of excitation from the incoming receptor cells would activate the mitral cells (Fig. 6A), which would then be shut off by the recurrent and lateral inhibition. As the inhibition subsided the continuing excitatory input in the glomeruli would initiate the next cycle (Fig. 6A). It was pointed out (Rall and Shepherd 1968) that the resulting local field potentials would be enhanced by the synchrony of the tightly coupled mitral and granule cell populations, as well as by the radial alignment of the granule cell electric dipoles generating the potentials. The demonstration that centrifugal fibers make synapses on the granule cell spines (Price and Powell 1970) suggested that these fibers would be able to exert an important influence on the granule cells, possibly by raising or lowering their excitability.

Fig. 6.

A: the postulated mechanism for generating oscillatory activity in the olfactory bulb by the dendrodendritic synaptic interactions. Top: in a mitral cell dendritic tuft (MT) in a glomerulus, input from converging axons of olfactory receptor cells causes a prolonged EPSP. Middle: the activated mitral cells (MC) generate synchronous action potentials (ap), which activate EPSPs in the granule (Gr) cells (bottom), followed by feedback and lateral inhibitory IPSPs through the dendrodendritic synapses. EPSP, excitatory postsynaptic potential; IPSP, inhibitory postsynaptic potential. From Shepherd (1974). B: experimental recording of different extracellular wave responses at the same site to the same odor stimulation. In a urethane-anesthetized rat, continuous odor stimulation with a moderate concentration of amyl acetate began at time 0. The initial response consisted of fast gamma waves around 50 Hz, shifting to slower beta waves around 20 Hz. From Neville and Haberly (2003).

This application of the model was slower to develop. Oscillations were known to be prominent in the olfactory bulb by the classical work of Edgar Adrian (1942), but closer study did not begin until Walter Freeman (1975) began to invoke the dendro-dendritic interactions for generating the fast oscillations he recorded in the olfactory cortex and olfactory bulb. This led to identification of two main field potential waves at different frequencies—gamma (40–100 Hz) and beta (15–30 Hz)—which remarkably can flip from one to the other at the same recording site and cell (Fig. 6B). Many studies have tested and supported this idea (Fourcaud-Trocmé et al. 2014; Lagier et al. 2007), but they have also raised the question: how can the same synaptic circuit generate oscillations at two different frequencies?

Current source density analysis indicates that the gamma oscillations arise in the deep external plexiform layer (Neville and Haberly 2003), consistent with the original model; further study has even revealed two levels of gamma, and contributions by the glomerular layer. The larger amplitude waves likely reflect the summed currents around the parallel granule cell dipoles, as earlier noted. Gamma waves may depend in addition on intrinsic membrane resonance, while beta oscillations are more dependent on the piriform cortex through the synaptic feedback contacts on the granule cells.

The ability of the dendrodendritic synaptic microcircuit to generate the two oscillatory frequencies has been demonstrated in a computational model by Osinski and Kay (2016) in which the critical factor is the excitability of the granule cell. As illustrated in Fig. 7A, the granule cell is the node where sensory input, piriform cortex feedback, and centrifugal modulatory fibers converge, to set the excitability of the granule cell. As shown in Fig. 7B, during initial odor exploration, low granule cell excitability occurs and fast gamma oscillations are prominent, which may enhance odor detection and discrimination. As odor exploration continues, granule cell excitability increases, voltage dependent Ca²⁺ influx increases, and the mitral-granule interaction shifts to slower beta oscillation, reflecting stronger inhibition from the granule cells. Behaviorally this is associated with increased sniffing of highly volatile odors and with learning of odor discrimination associated with reward (reviewed in Kay 2014). The beta oscillations at this stage are believed to be involved in binding together activity across regions, not only between the olfactory bulb and cortex, but including motor systems generating olfactory guided behavior.

Fig. 7.

A: the model of Osinski and Kay (2016) which accounts for the transition from gamma to beta frequencies. The excitability of the granule cell is key; it is controlled by sensory input, cortical inputs, and central neuromodulatory systems (see Fukunaga et al. 2014). GC, granule cell; GLO, glomerulus; MC, mitral cell; ORN, olfactory receptor neuron. B: transition from gamma to beta by simulated inhibitory local field potential (ILFP) (black left y-scale) in response to changing granule cell membrane potential (Vrest,GC) (red right y-scale) from −74 to −60 mV over 1 s with varying speeds (slowest at top, fastest at bottom). In the bottom row, the dotted vertical lines indicate the duration of the excitability transition for that plot, which is roughly 80 ms. Note the similarity of the gamma (left) and beta (right) wave frequencies, of the model and the transitions in the middle and bottom traces, to the experimentally recorded potentials in Fig. 6B. From Osinski and Kay (2016).

UPDATING THE MODEL

Based on the studies that have been reviewed here, Figs. 8 and 9 attempt a summary of an updated version of the original mitral-granule cell dendrodendritic model. The same core framework of mitral and granule cells interconnected by reciprocal dendrodendritic synapses is present.

Fig. 8.

Updated dendrodendritic microcircuits contained within a glomerular unit. B, Blanes (deep short- axon) cell; c, centrifugal axon; ET, external tufted cell; Gm, mitral connected granule cell; Gt, tufted cell connected granule cell; M, mitral cell; PGe, periglomerular cell (input from ET cell); PGo, periglomerular cell (input from ORN); sSA, superficial short-axon cell; T, middle tufted cell. Excitatory actions shown by red cells and terminals; inhibitory by blue cells and terminals. All cells except the M and T cells turn over during life. Note the multiple layers for lateral inhibitory and related processing actions. The complex patterns of glomerular synapses are under active investigation. The diagram is from Shepherd et al. (2018), which represents a synthesis of studies by multiple authors, including Wachowiak and Shipley (2006), Cleland and Sethupathy (2006), Linster and Cleland (2009), Migliore et al. (2010), Nagayama et al. (2014), Cavarretta et al. (2016), and Burton and Urban (2015).

Fig. 9.

Diagram of updated dendrodendritic model for generating widespread lateral inhibition and gamma oscillatory activity in the olfactory bub (Migliore and Shepherd 2008). Mitral cells 1–3 form glomerular processing units with their granule cells (GC1–GC3) and at the glomerular level, superficial short axon cells (sSA) and external tufted cells (ET) (simplified from Fig. 8). Histograms indicate the number of action potentials elicited in a given mitral (M) cell by each odor input without (top histograms) or in the presence of granule cells in the network (bottom histograms). The effect of lateral inhibition in suppressing M2 output in response to flanking odor molecules is schematically represented by the black bars; this is similar to the report of contrast enhancement by Yokoi et al. (1995) (cf. Fig. 3B). Weak odor stimulation was modeled with 60% of the strong odor concentration. Note that because mitral cell action potentials can backpropagate along lateral dendrites, they can target glomerular units at arbitrary spatial positions. The dendrodendritic synaptic interconnections are similar to those indicated in Fig. 8. For simplicity, each GC is represented with a single branch. Adapted from Shepherd et al. (2018).

The model is extended to include, first: in a given glomerulus, odor stimulation activates a set of neuron types connected directly or indirectly to that glomerulus, forming what is called a “glomerular unit” (Fig. 8). At its core is the original model of dendrodendritic synapses between mitral and granule cells, plus dendrodendritic synapses between mitral tuft dendrite and periglomerular cell dendrites. The proposed inhibitory action of the original model also applies to the glomerular layer.

Second, odors activate multiple glomerular units which are potentially widely distributed, forming odor maps (Xu et al. 2003).

Third, active primary dendrites enhance the excitability of the mitral/tufted cells in response to the olfactory input.

Fourth, the long lateral mitral dendrites stretch across potentially many glomerular units to activate the lateral inhibition of mitral cells through granule cells, as in the original model, while axons of periglomerular and external tufted cells connect to surrounding glomeruli to form a rich network of excitatory and inhibitory actions (Liu et al. 2016; Nagayama et al. 2014; Shao et al. 2019; Tavakoli et al. 2018).

The current framework for relating the functions at the glomerular and granule cell levels is that lateral inhibition at the glomerular level is acting on sensory information still mostly in the sensory domain, as reflected in inputs from a specific olfactory receptor to a specific glomerulus, whereas lateral inhibition at the granule cell level is mediated by mitral cell lateral dendrites, which extend across many different glomerular units to activate granule cell inhibition of many mitral cells in more complex combinations before output through the mitral cell axon. It is tempting to speculate that these are first critical steps in reducing the hyperdimensionality of the odor molecular stimuli as the basis for olfactory perception.

Fifth, the active properties of the lateral dendrites enable lateral inhibition around a given mitral cell to be imposed on other mitral cells through activation of granule cells at arbitrary distances, to create nontopographical functional maps (Xiong and Chen 2002) (Fig. 9).

Sixth, the widely distributed inhibition at both levels gives rise to oscillatory gating of the correspondingly widely distributed mitral cells activated from their odor activated glomeruli. This response begins with gamma frequency oscillations, which evolve into beta frequency oscillations, binding together the activated population of mitral cells to give rise to a temporally and spatially coherent output to the olfactory cortex. Simulations have shown that distributing activated dendrodendritic synapses in clusters related to glomerular units enhances the strength of their oscillatory activity (McTavish et al. 2012).

Finally, this coherent output, analogous to the output from V1, activates the olfactory cortex (including the anterior olfactory nucleus, olfactory tubercle, and piriform cortex), which processes the complex “odor images” from the olfactory bulb in analogy with the higher visual association area for processing faces. These higher order cortical regions feed back onto the granule cell to modulate their own input by fine-tuning the excitability of the dendrodendritic microcircuit. For orientation to the organization of olfactory cortices and their functional roles, see Wilson and Barkai (2018) and Mori and Sakano (2011).

This leaves many properties of the dendrodendritic interactions as challenges for the future. For example, what are the precise roles of the different oscillation frequencies in information processing within the olfactory system and beyond (Lagier et al. 2007; Li and Cleland 2017)? What is the role of feedback dendrodendritic inhibition in contrast with lateral inhibition? What are the relative roles of lateral inhibition at the glomerular and granule cell levels and how do they complement each other?

An important upgrade of the original model is to add the remarkable ability of the granule cell (and periglomerular cell) in the rodent to turn over during adult life. This was first reported (Altman 1969) at about the same time as the original model, and was rediscovered in the 1990s (Luskin 1993), along with the similar turnover of cells in the dentate gyrus. This is an exciting area of research for its critical insights into mechanisms of neurogenesis, odor processing, and plasticity (Hardy and Saghatelyan 2017). The dendrodendritic synapses play a central role in this process.

As we have noted, lateral inhibition by granule cells causes decorrelation of mitral cell responses. This has been demonstrated to mediate pattern separation (Sahay et al. 2011) and allows even very similar odors to be discriminated perceptually. A simplified computational model of the dendrodendritic circuit (Chow et al. 2012) has simulated this process. It has further been found that granule cell survival depends on repeated odor stimulation. Less stimulated granule cells gradually weaken and die and are replaced by new granule cells that are continually produced from the subventricular zone and migrate via the rostral migratory stream to replace less active cells that are eliminated by apoptosis.

These new granule cells have a higher excitability and are more responsive to odors: they function as novelty detectors. Their dendrodendritic synapses make feedback connections on themselves and lateral connections onto coactive mitral cells, during which the synapses are balanced between the strengths of their feedback and lateral inhibition (Saghatelyan et al. 2005); decorrelation is enhanced by stronger lateral inhibition and decreased by stronger self inhibition. In effect, the ongoing cell turnover produces a constant supply of sensitive granule cells that enable a “critical period” of plasticity that lasts through adulthood. Precise placement of dendrodendritic synapses along mitral lateral dendrites may be critical for temporal coding (Bartel et al. 2015). The newly incorporated dendrodendritic inhibition also brings with it enhancement of ongoing oscillatory gating to bind together the whole system.

Current work thus provides a strong basis for future studies incorporating these and other properties into increasingly refined Rall-type models with time dependent properties. These will allow new insights into the dynamic molecular and cellular mechanisms of neurogenesis and plasticity at the synaptic (Carleton et al. 2003), spine (Sailor et al. 2016) and microcircuit levels (Chow et al. 2012), and show how they create behavior at the level of perception and learning (Forest et al. 2020; Moreno et al. 2009; Sahay et al. 2011).

In summary, the computational models of the mitral and granule cell, despite the limited computational capacity of the early computers, provided a useful starting point for extending the Rall compartmental modeling approach to brain neurons. With the high power of modern computers and their use within experimental laboratories, neuron and microcircuit models are now routine in interpreting experimental data. Published models for many brain neurons and microcircuits are available on public databases (see https://senselab.med.yale.edu/ModelDB/).

The olfactory bulb study shows that unexpected counterintuitive results do not depend on the amount of computer power alone, but rather on starting with a model that can distinguish between competing hypotheses and give insights into real functional properties. This exemplifies the enduring strength of the Rall approach, bonding together experiment and theory in a unified, recurrently enhancing, interaction to produce new insights into the neural basis of brain function.

Finally, the granule cell had been a mystery since its discovery by Golgi and Cajal. Since it lacks an axon, was it even a neuron? Electrophysiological data built into a computational model together with EM evidence solved the problem, showing that, as in the retina, a cell can function as a neural processing system without an axon, and even sometimes without an impulse; the necessary property is synaptic interactions, down to the local level of an individual spine. Despite such apparently modest abilities, the granule cell has progressed from a classical enigma to playing a central role in olfactory processing through its dendrodendritic interactions with the mitral (and tufted) cells and its function in central and cortical systems. The specific mechanisms by which the model can combine self and lateral inhibition, and gamma and beta oscillations, to play central roles in olfactory processing during ongoing neurogenesis should continue to be a challenge in the future, giving further insights into sensory mechanisms and cortical function.

GRANTS

Our work has been supported by the SenseLab R01 DC 009977-10 to GMS, R01-DC016851 to CAG, and EU Horizon 2020 Framework Programme for Research and Innovation under the Specific Grant Agreement 785907 (Human Brain Project SGA2) to MM.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

G.M.S., M.L.H., M.M., W.R.C., and C.A.G. conceived and designed research; G.M.S., M.L.H., M.M., W.R.C., and C.A.G. performed experiments; G.M.S., M.L.H., M.M., W.R.C., and C.A.G. analyzed data; G.M.S., M.L.H., M.M., W.R.C., and C.A.G. interpreted results of experiments; G.M.S., M.M., W.R.C., and C.A.G. prepared figures; G.M.S. and C.A.G. drafted manuscript; G.M.S., M.L.H., M.M., W.R.C., and C.A.G. edited and revised manuscript; G.M.S., M.L.H., M.M., W.R.C., and C.A.G. approved final version of manuscript.