Role of intraglomerular circuits in shaping temporally

Role of intraglomerular circuits in shaping temporally structured responses tonaturalistic inhalation-driven sensory input to the olfactory bulb

Ryan M. Carey,1 William Erik Sherwood,2 Michael T. Shipley,3 Alla Borisyuk,2

and Matt Wachowiak4

1Department of Biomedical Engineering, Boston University, Boston, Massachusetts; 2Department of Mathematics, Universityof Utah, Salt Lake City, Utah; 3Department of Anatomy and Neurobiology, Program in Neuroscience, University of MarylandSchool of Medicine, Baltimore, Maryland; and 4Department of Neurobiology and Anatomy and Brain Institute, University ofUtah, Salt Lake City, Utah

Submitted 23 May 2014; accepted in final form 20 February 2015

Carey RM, Sherwood WE, Shipley MT, Borisyuk A, Wa-chowiak M. Role of intraglomerular circuits in shaping temporallystructured responses to naturalistic inhalation-driven sensory input tothe olfactory bulb. J Neurophysiol 113: 3112–3129, 2015. Firstpublished February 25, 2015; doi:10.1152/jn.00394.2014.—Olfactionin mammals is a dynamic process driven by the inhalation of airthrough the nasal cavity. Inhalation determines the temporal structureof sensory neuron responses and shapes the neural dynamics under-lying central olfactory processing. Inhalation-linked bursts of activityamong olfactory bulb (OB) output neurons [mitral/tufted cells (MCs)]are temporally transformed relative to those of sensory neurons. Weinvestigated how OB circuits shape inhalation-driven dynamics inMCs using a modeling approach that was highly constrained byexperimental results. First, we constructed models of canonical OBcircuits that included mono- and disynaptic feedforward excitation,recurrent inhibition and feedforward inhibition of the MC. We thenused experimental data to drive inputs to the models and to tuneparameters; inputs were derived from sensory neuron responses dur-ing natural odorant sampling (sniffing) in awake rats, and modeloutput was compared with recordings of MC responses to odorantssampled with the same sniff waveforms. This approach allowed us toidentify OB circuit features underlying the temporal transformation ofsensory inputs into inhalation-linked patterns of MC spike output. Wefound that realistic input-output transformations can be achievedindependently by multiple circuits, including feedforward inhibitionwith slow onset and decay kinetics and parallel feedforward MCexcitation mediated by external tufted cells. We also found thatrecurrent and feedforward inhibition had differential impacts on MCfiring rates and on inhalation-linked response dynamics. These resultshighlight the importance of investigating neural circuits in a natural-istic context and provide a framework for further explorations ofsignal processing by OB networks.

neural modeling; sniffing; inhibition; temporal structure; glomerulus

IN THE MAMMALIAN OLFACTORY system, neural representations ofolfactory information are organized into temporally discrete“packets” that are tightly coupled to the respiratory cycle(Schaefer and Margrie 2007; Wachowiak 2011). Respiration-coupled activity is prominent at all levels of olfactory process-ing, including sensory neurons [olfactory receptor neurons(ORNs)], neurons of the olfactory bulb (OB) and olfactorycortical areas, and typically occurs as transient (100–200 ms)bursts of excitation and inhibition linked to particular latenciesor phases of the respiratory cycle. This stereotyped dynamic

structure may play a critical role in odor information process-ing by creating a temporal window within which odor infor-mation is encoded among neurons of the OB and integrated bydownstream neurons in olfactory cortical networks (Bathellieret al. 2008; Cury and Uchida 2010; Miura et al. 2012; Schaeferand Margrie 2007; Shusterman et al. 2011). There is alsosubstantial behavioral evidence that the precise dynamics ofactivity within this respiration-linked window shapes odorperception (Abraham et al. 2010; Smear et al. 2011; Wesson etal. 2008). Thus understanding how respiratory patterning ofolfactory activity arises is critical to understanding the neuralmechanisms underlying odor coding.

Respiration-linked packets of activity first arise amongORNs, where inhalation drives a transient burst of excitation ina subset of odorant-responsive ORNs that converge to specificOB glomeruli (Carey et al. 2009; Chaput and Chalansonnet1997; Spors et al. 2006; Wesson et al. 2008). Output from theOB via mitral/tufted cells (MCs) is also transient and linked toinhalation but is distinct from the simple excitatory bursts ofORN input, with MCs showing odorant- and cell-specificsequences of excitation and inhibition (Carey and Wachowiak2011; Cury and Uchida 2010; Shusterman et al. 2011). At thepopulation level, odorant-evoked excitatory responses of MCsshow a shorter duration and shorter rise time than do those ofORNs (Carey and Wachowiak 2011). This “temporal sharpen-ing” of respiration-linked excitation is a key feature of theinput-output transformation performed by the OB network.However, which circuit elements mediate this transformationremains unclear.

The network of connections localized to the glomerularlayer, which we refer to as the glomerular network, has beenascribed a major role in shaping MC response dynamics. Theglomerular network includes connections between ORNs,MCs, several classes of GABAergic inhibitory interneuronsand at least one type of excitatory interneuron (external tufted,or ET, cells) (Gire et al. 2012; Gire and Schoppa 2009; Hayaret al. 2004a; Shao et al. 2009; Wachowiak and Shipley 2006).Glomerular circuits hypothesized to be important in shapingrespiration-coupled MC response dynamics include feedfor-ward excitation mediated by ET cells, feedforward intraglo-merular inhibition mediated by periglomerular (PG) neurons,recurrent inhibition (RI) mediated by reciprocal connectionsbetween PG, ET and MCs, as well as interglomerular inhibi-tory connections formed by short-axon cells (Gire and Schoppa2009; Liu et al. 2013; Shao et al. 2012, 2013; Wachowiak and

Address for reprint requests and other correspondence: M. Wachowiak,Dept. of Neurobiology and Anatomy, Univ. of Utah, 33 S. Wasatch Dr., SaltLake City, UT 84112 (e-mail: [email protected]).

J Neurophysiol 113: 3112–3129, 2015.First published February 25, 2015; doi:10.1152/jn.00394.2014.

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Shipley 2006). The intrinsic properties of these neuron typesmay also play an important role in shaping temporally-struc-tured activity in the OB. For example, the intrinsic bursting ofET cells generates patterned excitation in the frequency rangeof natural sniffing behavior (Hayar et al. 2004b), and theintrinsic properties of MCs appear to facilitate temporallyprecise and well-structured output in response to phasic inputs,such as those driven by inhalation (Balu et al. 2004; Desmai-sons et al. 1999; Heyward et al. 2001; Margrie and Schaefer2003; Rubin and Cleland 2006). With a few exceptions, how-ever (Cang and Isaacson 2003; Fukunaga et al. 2012; Phillipset al. 2012; Schaefer et al. 2006), these phenomena have beenlargely described in OB slice experiments, and thus the con-tribution of synaptic and intrinsic properties of glomerularneurons to the temporal sharpening of inhalation-driven ORNinputs in vivo, and in particular during natural odor sampling,remains unclear.

Here, we used a small-network modeling approach to ex-plore how several well-described OB circuits might contributeto the temporal shaping of sensory inputs driven by inhalation.Using biophysically-based models of major OB circuit ele-ments, we asked what are the minimal circuits necessary totransform inhalation-driven packets of sensory input into tem-porally-sharpened bursts of MC output. Model simulation andevaluation were highly integrated with experimental data: weused dynamic input patterns derived from recordings of ORNpopulation responses during naturalistic odorant sampling (i.e.,sniffing), then used single-unit recordings from MC responsesevoked by the same naturalistic odorant sniffs to evaluate theaccuracy of model output (Carey and Wachowiak 2011). Thisapproach identified several features of glomerular circuits thatshape MC spiking responses with realistic inhalation-coupledtemporal structure, including slow-onset and slowly-decayinginhibition and parallel feedforward excitation via ORNs andET cells. Overall these results establish a computational frame-work for further investigation of input-output transformationsby OB networks in the context of active olfactory sensation.

MATERIALS AND METHODS

Model design. The MC model (and simulated RI) was taken fromBathellier et al. (2006); the PG cell model was modified from theHodgkin-Huxley implementation of Moehlis (2006) to include afast-inactivating transient potassium current (Puopolo and Belluzzi1998). The ET cell model was generated from a minimal single-compartment Hodgkin-Huxley-style model which includes only thoseactive currents necessary for bursting in the absence of sensory input(Sherwood et al. 2010). Each of these single cell models includesseveral ionic currents; the current balance equations for the membranevoltage of the respective cells are as follows.

1) MC:

dV ⁄ dt� � �INa�INaP�IKa�IKfast�IKs�IL� ⁄ C

2) ET:

dV ⁄ dt� � �INa�INaP�IKfast�ICaT�IH�IL� ⁄ C

3) PG:

dV ⁄ dt� � �INa�IKa�IKfast�IL� ⁄ C

where C is capacitance. Here the ionic current symbols are as follows:INa, fast transient sodium; INaP, persistent sodium; IKfast, delayedrectifier potassium; IKa, fast-inactivating transient potassium; IKs,slow-inactivating transient potassium; IH, hyperpolarization-activated

cation; and ICaT, T-type calcium current. As usual, IL � gL (V � VL),where IL is leak current, gL is leak conductance, V is membranevoltage, and VL is leak reversal potential. The kinetic equations andparameter values for each current were derived from the referencesabove and may differ among cell types.

The implementation of RI between MCs and PG or granule cells(GC) was modified from Bathellier et al. (2006), with each MC spiketriggering a slowly-decaying inhibitory synaptic conductance (gsyn)[difference of exponentials: latency time (tlatency) � 1 ms, rise time(�rise) � 1 ms, decay time (�decay) � 500 ms, synaptic reversalpotential (Vrev) � �70 mV]. Shorter RI decay values matching thoseof Bathellier et al. (�decay � 150 ms) yielded similar results. Theexcitatory synaptic connection between the ET and MC modelssimulates fast, nonadapting excitation using a model adapted from atwo-state �-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid/kainite receptor-mediated synaptic transmission model (Destexhe etal. 1994). This synaptic current takes the form Isyn � g[ET-MC]

s(VET)(VMC � Vrev), where g[ET-MC] is maximum conductance forET-MC synapse, VET is membrane voltage of the ET cell model, andVMC is membrane voltage of the MC model. Here s(VET) representsthe level of transmitter release and obeys the differential equationds/dt � �/{1.0 � exp[�(VET � V1/2)/k]}(1 � s) � � � s, where � �2.16 and � � 0.216, V1/2 is membrane voltage at half-maximalrelease, and k determines the steepness of the voltage-dependentlogistic function. The “fast” feedforward inhibitory PG-MC synapseuses the same form. The “slow” feedforward inhibition (FFI) synapseis also nonadapting and is based on a model for second-messenger-activated synaptic transmission (Destexhe et al. 1994), with kineticparameters adjusted using a parameter search and exponential curvefitting to match the desired rise and decay times (�rise of 14 ms and�decay of 140 ms, 170 ms, or 200 ms; see RESULTS).

Models were implemented in Matlab, and simulations were per-formed using the “ode15s” differential equation solver. For efficiencyof simulation, capacitance and conductance constants were rescaled,and in most cases combined. As a result, conductance values (e.g.,g[ET-MC] and gL) provided have arbitrary units and depend on thepostsynaptic neuron type; we do not attempt to provide biologically-relevant units or to make conductance values comparable acrossneuron types. Detailed descriptions of the cellular and synaptic modelcomponents can be found in the references cited above, while param-eter values and source code implementing the intraglomerular net-work models described below can be found in the ModelDB database(Hines et al. 2004) (http://senselab.med.yale.edu/modeldb/default.asp;Model no. 152111).

Modeling experimentally derived synaptic inputs. Dynamic sensoryinputs to all model circuits were derived from ORN responses re-corded from anesthetized rats using published data taken from cal-cium imaging from ORN presynaptic terminals (Carey and Wa-chowiak 2011), in which odorants were naturalistically sampled usinga “sniff playback” approach to reproduce intranasal pressure tran-sients generated (and previously recorded from) awake, head-fixedrats (Cheung et al. 2009). A total of 25 ORN input traces were used,with each trace representing the presynaptic calcium signal imagedfrom a distinct glomerulus. The 25 traces encompassed a range ofdifferent odorants and odorant concentrations, as follows: [0.2%saturated vapor ethyl butyrate (n � 4 glomeruli), 0.5% ethyl butyrate(1), 1% ethyl butyrate (6), 2% ethyl butyrate (2), 2% menthone (3);0.5% propyl acetate (2), 1.5% propyl acetate (1), 0.5% heptanal (6)].Data were compiled from 4 rats.

To convert presynaptic calcium signals into synaptic inputs for themodel, raw imaging traces from individual glomeruli were prepro-cessed to remove photobleaching effects and low-pass filtered. Traceswere then temporally deconvolved (Verhagen et al. 2007; Yaksi andFriedrich 2006) to generate an estimate of the change in actionpotential firing rate across the imaged ORN population. Next, tosimulate a population of ORNs converging onto their postsynaptictarget, the deconvolved population firing rate trace was scaled to a

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peak rate of 50 Hz (Duchamp-Viret et al. 2000) and used as the ratefunction for 500 independent inhomogeneous Poisson processes,representing 500 convergent ORN spike trains. Because short-termplasticity in the form of presynaptic inhibition and synaptic depressionis well-established at the ORN synapse (Aroniadou-Anderjaska et al.2000; Murphy et al. 2004; Wachowiak et al. 2005), we next imple-mented a depression function that attenuated the amount of spike-driven transmitter release based on the interval from the previousspike, following the paired-pulse depression model from Murphy etal. (2004), with a time constant of recovery of 675 ms and maximalattenuation of 82%. Each scaled spike train was then convolved witha simulated excitatory postsynaptic current (difference of two expo-nentials with �rise � 1 ms and �decay � 2 ms) to generate an ORNinput trace, all of which were then averaged to generate the synapticinput current from the ORN population, IORN(t). This input currentwas multiplied by an input gain factor G with arbitrary units (analo-gous to an effective gsyn for the ORN synapse) and then injected intothe model. Thus, in each model studied, the current from the ORN toeach postsynaptic target N takes the functional form Isyn � G[ORN-N]

IORN(t), where IORN(t) is independent of the state of the postsynapticneuron.

Analysis of model MC and ET output. Sniff-triggered spike timehistograms [peristimulus time histograms (PSTHs), bin size, 20 ms]were generated for each model MC, and temporal response parameters(peak firing rate, response duration, response latency) were measuredfrom a double-sigmoid curve fit to each PSTH, as described previ-ously for experimental data (Carey and Wachowiak 2011). For visualcomparison of model and experimental MC response dynamics, foreach unit instantaneous firing rate was calculated from each interspikeinterval and interpolated between spike times to generate a continuousfiring rate trace (Carey and Wachowiak 2011). These traces were thenaveraged across all model or experimental units.

For ET cell calibration, a sniff modulation index (“SMI”, see Fig.4) was calculated for inhalations at 1 Hz by generating a PSTH usingonly “burst spikes” (spikes that were within 50 ms of another spike),ignoring isolated spikes, then defining SMI as (PSTHmax � PSTHmin)/“nonsniffspikes”, where “nonsniffspikes” was the total number ofspikes evoked outside the sniff responses. This factor penalized tonicfiring, as well as bursting between sniffs. Modulation indexes werecalculated for ET cell responses to ORN input gains of 2.4 and 4.8,and these two indexes were summed to generate the final SMI plottedin Fig. 4.

In the parallel excitation model (notation: ORN-[ET]-MC; see Fig.5A), we provided excitatory input to the MC through both theORN-MC and ORN-ET-MC pathways. The ORN-MC pathway is acurrent with gain G[ORN-MC], while the ET-MC pathway is a conduc-tance with maximal synaptic conductance g[ET-MC]; these gain andmaximal conductance values are not directly comparable. Thus, foreach input pathway, we quantified its effective strength by computingthe charge per presynaptic action potential passed to the MC, averagedover our set of test stimuli. More formally, the mean charge perpresynaptic action potential transferred via the ET-MC synapse,QET-MC, was computed for each test stimulus (sniff) by integrating theET-MC synaptic current over time and dividing by the number of ETspikes. The mean charge transfer for the ORN-MC synapse, QORN-MC,for each input trace, was computed similarly by computing theintegral of current IORN(t) divided by the time interval equal to theaverage duration of an ET spike. The ratio of QET-MC to QORN-MC wasthen averaged over the whole set of test inputs. We found that�QORN-MC/QET-MC� � 3.9 � 1.7 (SD); i.e., the effective strength ofthe ORN-MC pathway is 3.9 � 1.7 times that of the ORN-ET-MCpathway. This correction factor was used to normalize the gain andconductance parameters into effective “input strength” values via eachpathway, having arbitrary units (see axes of Fig. 5, B and E). With thisnormalization, equal input strengths (points along the diagonal) cor-respond to 50/50 mean charge contribution of each pathway. In realitythese axes represent g[ET-MC] (on the horizontal axis) and G[ORN-MC]/

3.9 (on the vertical axis). This correction factor was further used todetermine the synaptic strength between the ET and PG cell in theintegrated model; because ORN inputs are 3.9 times “stronger” thanET inputs, g[ET-PG] (ET-PG conductance) was set as 3.9 � G[ORN-PG]

(ORN-PG input gain).

RESULTS

Overview of approach. Our goal was to explore the contri-bution of several known OB circuits to the temporal sharpeningof sensory inputs that is a hallmark of OB input-output trans-formations in vivo. Rather than explore all potential knowncircuits, our approach was to identify one or more minimalcircuit configurations that transformed inhalation-driven inputpatterns into bursts of MC output that matched those recordedin vivo. To this end, we implemented a series of models ofroughly increasing circuit complexity and attempted to opti-mize model performance at each iteration. Each cellular ele-ment in the model was implemented as a single-compartment,Hodgkin-Huxley model neuron using parameters taken frompreviously described models or from experimentally measuredintrinsic properties (see MATERIALS AND METHODS and text belowfor details). Each cell type was represented by a single point-source element meant to represent the population of all suchneuron types within a glomerular module. Different relativenumbers of each cell type were encapsulated in the relativesynaptic strength parameters specified in the text. We did notinclude tonic activity in any model elements, although toniclevels of excitatory and inhibitory synaptic transmission arepresent in vivo and in OB slices (Hayar et al. 2004b; Pírez andWachowiak 2008; Shao et al. 2009). Additional simplifyingassumptions specific to each circuit model are given in theirrespective sections below.

We implemented the following OB circuits: 1) a MC receiv-ing direct ORN input and no inhibition (ORN-MC); 2) theORN-MC circuit with RI mediated by PG and/or GC (ORN-MCRI); 3) the ORN-MC circuit with PG cell-mediated FFI(ORN-PG-MC); 4) a feedforward excitatory circuit mediatedby ET cells (ORN-ET-MC); 5) a feedforward excitatory circuitconsisting of the ORN-MC and ORN-ET-MC circuits in par-allel (ORN-[ET]-MC); and 6) an “integrated” model consistingof the parallel feedforward excitatory circuit (5) with theaddition of one ORN-PG and one ORN-ET-PG feedforwardinhibitory circuit. Naturalistic “sensory” inputs to the modelsconsisted of dynamic synaptic inputs that were derived fromodorant-evoked ORN presynaptic calcium signals during nat-ural sampling (i.e., “sniffing”) of odorants (Carey et al. 2009;Carey and Wachowiak 2011). Finally, model output (in theform of MC spiking patterns) was tuned by varying synapticstrength parameters (see MATERIALS AND METHODS) and evalu-ated by comparison to an experimental dataset consisting ofextracellular recordings from presumptive MCs responding toodorants sampled at 1 Hz with the same naturalistic waveformsused to activate ORN inputs (Carey and Wachowiak 2011).Thus model construction and evaluation were both con-strained by experimental data. We limited our evaluation todata from 1-Hz inhalations only to avoid confounds fromfrequency-dependent changes in circuit dynamics in thisinitial characterization.

It was neither computationally feasible nor desirable toexplore all conceivable parameter combinations for each

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model. As our goal was to compare the input-output charac-teristics of different OB circuits, we held most parameterscontrolling the intrinsic properties of the cellular componentsfixed across circuit models. The only parameters varied werethose with obvious importance for synaptic transmission andinput integration: in particular, synaptic input gain, synaptickinetics and cell excitability (gL and VL) (see MATERIALS AND

METHODS). For each model circuit, we explored a large, biolog-ically plausible region of the hyperplane defined by these freeparameters by incrementally varying each parameter and mea-suring model output in terms of the dynamics and magnitude ofinhalation-driven MC spiking (additional details below). Wethen identified the parameter values leading to model outputthat most closely matched that of experimental measurementsof response strength and dynamics. For each iteration ofincreasing circuit complexity, the parameters of the priorcircuit were typically held fixed at their optimal values, and anew set of free parameters corresponding to the added circuitconnections were explored and optimized using the sameexperimental benchmarks.

ORN-MC circuit. We first tested how a monosynaptic con-nection between ORNs and MCs transformed dynamic, sniff-driven ORN inputs. The model MC was modified slightly froma previous, single-compartment biophysical model of the MC(Bathellier et al. 2006) which includes Hodgkin-Huxley chan-nel kinetics that are well-constrained by published intrinsicparameters (see MATERIALS AND METHODS). This model approx-imates the spike clustering that MCs exhibit in response to DCcurrent injection in vitro (Fig. 1A) (Balu et al. 2004; Chen andShepherd 1997; Desmaisons et al. 1999). A synaptic currentwaveform representing the “sniff-triggered” input from a pop-ulation of homotypic ORNs converging onto a MC was derivedfrom experimental measurements of odorant-evoked ORN ac-tivity and delivered to the model MC, as described in theMATERIALS AND METHODS and below.

In vivo, sniff-triggered ORN inputs to different glomerulivary in the latency, rise-time and duration of their activation(Carey et al. 2009; Spors et al. 2006). To explore model MCresponses across this range of dynamics, we used sniff-trig-gered presynaptic calcium signals imaged from ORN inputs to25 different glomeruli in the awake rat. Figure 1B shows rawpresynaptic calcium signals and derived synaptic input currentwaveforms (IORN-MC; see MATERIALS AND METHODS) for each ofthe 25 ORN inputs, along with spike rasters of each modelMCs response for a gain of 7.5 (tested range: 0–30). Note thatthese presynaptic signals already reflect the modulation ofinput strength by presynaptic inhibition mediated by glomeru-lar circuits. In general, one sniff-triggered bout of ORN inputelicited a discrete burst of action potentials in the model MC.Across the population, MC spiking dynamics approximatedthat of the presynaptic ORN inputs, as reflected in comparisonsof individual IORN traces as well as in the comparison between“sniff-triggered” population averages of ORN and MC spikingpatterns (Fig. 1B, bottom). However, model MC responsesdiffered from the experimental dataset of presumptive MCresponses to inhalation of odorant (n � 37 units), with exper-imentally recorded MC responses showing substantiallyshorter sniff-triggered spike bursts (Fig. 1B).

We attempted to maximize the correspondence between themodel ORN-MC circuit output and experimental data by vary-ing three parameters that influence MC excitability and are not

well-constrained by prior data: the ORN input gain (G[ORN-MC])and the VL and gL of the model MC. To explore this parameterspace, we used several measures of sniff-evoked firing patternsas benchmarks to compare model output with experimentaldata: peak firing rate, total number of sniff-evoked spikes andburst duration (Fig. 1C). Across the population of 25 ORNinputs, for fixed leak parameters in the MC (gL � 0.1, VL ��65 mV), increasing the ORN input gain increased peak firingrate, number of spikes and duration of the MC spike burst;increasing input gain also decreased the latency of the responserelative to inhalation time, to a minimum of 30 ms (Fig. 1C).

To explore effects of MC excitability on response dynamics,we varied VL and gL systematically and, at each value, adjustedORN input gain to achieve a mean peak firing rate across theMC population that most closely matched that of the experi-mental dataset. Figure 1D plots the spike count (left) and burstduration (right) values at the optimal gain level at each (VL, gL)combination. Mean values from the experimental dataset foreach parameter are indicated by the color green in each subplot(12 spikes/sniff and a duration of 120 ms). For the range ofleak parameters tested (which covers a biophysically realisticrange of intrinsic excitability values), when input gain wasadjusted to match peak firing rate, both spike count andduration were significantly higher than the mean values fromthe experimental dataset. As a result, even after optimizingmodel MC parameters, the population of model MC responsesremained longer than that of experimentally recorded re-sponses (Fig. 1E).

These results suggest that, while MC intrinsic properties cangenerate some degree of temporal patterning in response tounpatterned synaptic inputs (Balu et al. 2004; Rubin andCleland 2006), the ORN-MC circuit by itself does not generateMC spiking patterns with a temporal structure matching thosemeasured in vivo in response to natural odorant sampling.Rather, MC spiking responses roughly follow that of ORNsynaptic input. Thus additional synaptic connections must beimportant to generate realistic respiration-patterned activity inMCs.

Next we added RI to the ORN-MC circuit model. In thecontext of our model, RI encompasses a variety of potentialcircuits, including inhibitory feedback from PG or GCs cou-pled through reciprocal dendrodendritic synapses (Fig. 2A)(Chen et al. 2000; Isaacson and Strowbridge 1998; Murphy etal. 2005; Schoppa and Urban 2003), as well as intraglomerularinhibition between different MCs innervating the same glom-erulus. Rather than implementing an additional cell type (i.e.,GCs) mediating RI, RI was modeled as a rapid-onset, slowly-decaying chloride conductance (�decay � 500 ms, Vrev � �70mV; see MATERIALS AND METHODS for details) triggered by eachMC spike. The slow decay of RI was chosen based on evidencethat RI between MCs and GCs, as well as inhibitory signalingfrom PG cells, involves long-lasting, asynchronous GABArelease (Chen et al. 2000; Isaacson and Strowbridge 1998;Murphy et al. 2005; Schoppa et al. 1998; Smith and Jahr 2002).The time course of RI evoked by a single sniff, with the ORNinput trace and the corresponding response in the model MC, isshown in Fig. 2B. The maximal conductance of the sniff-evoked RI input, gRI, was varied to simulate different strengthsof RI. The addition of RI strongly decreased peak firing ratesand spike counts across the MC population, although this effectsaturated as RI strength increased (Fig. 2C). Notably, however,



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Fig. 1. Response of model mitral/tufted cells (MC) to naturalistic sensory inputs. A: response of model MC to current step. MC responds with clusters of spikes,as seen in the simulated membrane voltage (Vm). Between spike clusters, the model exhibits subthreshold oscillations, which are visible in the inset. B: modelMC responses to the experimentally obtained olfactory receptor neuron (ORN) input set {ORN-MC gain (G[ORN-MC]) � 7.5}. Left: raw presynaptic calciumsignals (gray) for the 25 different glomeruli used for the input dataset (see MATERIALS AND METHODS). Center: ORN-MC synaptic input current waveforms foreach MC. Right: spike rasters of MC firing responses to each of the sniff-driven inputs. Input currents are reversed in polarity to facilitate comparison to ORNcalcium signals. Bottom: histogram of model MC spiking output (time bin � 20 ms, averaged across all inputs, dark gray), showing a close match to the ORNinput population firing rate envelope (averaged across all inputs, blue). Orange trace shows average MC response firing rates from the experimental dataset, whichconsists of much shorter sniff-triggered bursts. Histogram and traces are scaled to the same peak value. C: effects of varying ORN input gain (G[ORN-MC]) ondifferent parameters of the sniff-driven model MC spike burst. Values for leak parameters were fixed in these examples at gL (leak conductance) � 0.1 and VL

(leak reversal potential) � �65 mV. The peak firing rate, evoked spike count per sniff, and response duration all increase with ORN input gain, while latencydecreases. Error bars show means � SE of the MC response averaged across the population of 25 ORN inputs shown in B. D: effects of varying MC leakparameters on sniff-driven response dynamics. Each grid shows gL vs. VL. For each (gL, VL) point, ORN input gain is varied to achieve a mean MC peak firingrate (averaged across all 25 ORN inputs) matching that of the experimental dataset (92 spikes/s). Pseudocolor values at each point indicate the spike count (left)or burst duration (right) for that excitability value. Arrow (“exp. mean”, green pseudocolor) indicates the mean value of the experimental MC dataset. Both spikecount and duration remain larger than the experimental mean values at all tested gL and VL values. E: dynamics of experimental and model MC firing rateresponses relative to time of inhalation, averaged across all recorded (orange) or model (blue) units. gL � 0.1, VL � �65 mV, G[ORN-MC] � 7.5. Before averaging,instantaneous firing rate was calculated from each interspike interval, and a continuous trace interpolated between spike times. Shading indicates variance (SD)around mean. The model MC population responds with a longer duration and broader peak firing profile. The experimental dataset represents the sniff-triggeredresponse to the same sniff waveform recorded from 37 MCs (Carey and Wachowiak 2011).



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response durations and latencies, and thus the overall shape ofthe sniff-triggered MC response, remained essentially un-changed (Fig. 2C). Optimizing RI strength to generate the bestmatch across response descriptors of the experimental dataset,as was done for the intrinsic leak parameters of MC, led topeak spike rates and total spike counts that were smaller thanexperimental values (gRI � 0.25, G[ORN-MC] � 10; Fig. 2, Dand E). Using a faster �decay of 150 ms as originally imple-mented by Bathellier et al. (2006) yielded similar results (notshown).

ORN-PG-MC circuit. We next tested the effect of PGcell-mediated FFI on MC responses. In vitro experiments haveimplicated FFI in shaping both the excitability and temporalstructure of MC responses to ORN input (Gire and Schoppa2009; Shao et al. 2012, 2013). We implemented a model PG

cell modified from a standard spiking Hodgkin-Huxley neuron(Moehlis 2006; Puopolo and Belluzzi 1998) which receivedexcitatory ORN input and provided inhibitory input to the MC(Fig. 3A; see also MATERIALS AND METHODS). The PG-MC syn-apse was first modeled using rapid kinetics consistent with“fast” GABAA-mediated inhibition, in which each PG spikeevoked a brief (�rise of 7 ms and �decay of 14 ms) conductancetransient in the MC. Implementing the ORN-PG-MC circuitwith this synapse tended to disrupt inhalation-linked pattern-ing, primarily because FFI strongly suppressed MC spikingbefore coherent spike bursts could develop (Fig. 3B, right). Atlower FFI strengths, MC spike bursts simply followed ORNinput dynamics as in the ORN-MC circuit (Fig. 3B, left).Adjusting ORN input gain to both the PG and MC also failedto produce discrete MC spike bursts with each inhalation (not

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Fig. 2. Effect of recurrent inhibition (RI) on model MC output. A: schematic of ORN-MCRI model with RI simulating inhibitory feedback from periglomerular(PG) or granule cell (GC) neurons onto the MC after each MC spike. See text for details. B: input currents (RI, green; ORN, blue) to the model MC and MCVm in response to one inhalation of odorant. As the strength of RI [RI conductance (gRI)] is increased, MC spiking is reduced. Spikes are clipped. C: summaryof effects of RI strength (gRI) on response dynamics to sniff-driven ORN inputs at several ORN input gains (range tested: 0–30), averaged across all ORN inputsas in Fig 1 (mean � SE). Increasing RI reduces peak MC firing rates, spike counts, and response durations, but has little effect on latencies. Horizontal dashedline indicates mean experimental value, as in Fig. 1; arrow indicates optimal value for RI strength (gRI � 0.10) for best match across peak firing rate, spike countand duration for the model MC population. Latency values are also shown. D: response of ORN-MCRI model to the 25 different sniff-driven ORN inputwaveforms. Spike rasters (top) and histogram (gray, bottom) of the model MC population show reduced firing rates compared with the ORN-MC model andmoderate temporal sharpening relative to the dynamics of the ORN input, but the model MC population response remains longer than that of the experimentaldataset (orange trace). gRI � 0.10, G[ORN-MC] � 15. E: mean and variance of experimental and model MC firing rate responses relative to time of inhalation,averaged across all recorded (orange) or model (blue) units as described above.



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shown) due to the rapid onset time of FFI. Thus “fast” FFI wasnot able to produce a temporal sharpening of MC responsesrelative to ORN input bursts without also disrupting inhalation-linked patterning.

In vitro, GABAergic FFI onto MCs can exhibit slow kineticsthat may be mediated by prolonged, asynchronous release oftransmitter from PG cells (Murphy et al. 2005; Smith and Jahr2002) or by other intrinsic or network mechanisms (Cadetti andBelluzzi 2001; Liu et al. 2013; Shao et al. 2009). In a feedfor-ward circuit, such kinetics could integrate ORN inputs andproduce a delayed inhibition that could substantially alter thedynamics of the MC response. Thus we modified the kinetics

of the PG-MC synapse to produce a slower rise and decay (�rise

of 14 ms and �decay of 170 ms; see MATERIALS AND METHODS fordetails). Figure 3C shows the excitatory (ORN) and FFI inputcurrents to the model MC over the course of one inhalation.FFI accumulates more slowly over the course of the ORN inputburst. Consequently, slow FFI, unlike RI or fast FFI, modulatesthe duration of the MC spike burst, with an inverted sigmoidrelationship between the strength of the PG-MC synapse (g[PG-MC])and MC burst duration (Fig. 3D).

We tuned the ORN-PG-MC model to match experimentalMC response dynamics using the same approach as for theORN-MC circuit: G[ORN-PG] and FFI strength (g[PG-MC]) were

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varied (G[ORN-PG] range: 20–40; g[PG-MC] range: 0–3.0), and,at each of these parameter values, ORN-MC input gain wasvaried to match the mean experimental peak firing rate (92Hz), after which total spike count and burst duration of themodel MC were compared with the experimental data (Fig.3E). Model optimization led to closer matches to experimentaldata than for the ORN-MC circuit, and the ORN-PG-MCmodel with slow FFI exhibited substantial temporal sharpeningof the sniff-triggered MC spike burst relative to the dynamicsof ORN input (Fig. 3, F and G). Qualitatively similar resultswere obtained with �decay values of 140 and 200 ms (notshown). Thus the gradual development of FFI over the courseof a single inhalation significantly transformed ORN inputdynamics into MC spike bursts that matched more closelythose recorded from the intact OB in vivo.

ORN-ET-MC circuit. We next investigated the role of ETcells in shaping MC spiking dynamics. ET cells providesignificant feedforward excitatory input to MCs (De Saint Janet al. 2009; Gire et al. 2012; Hayar et al. 2004a; Najac et al.2011; Shao et al. 2012). ET cells intrinsically burst at frequen-cies in the range of inhalation frequencies in behaving rodents,can be entrained to phasic ORN input, and have been hypoth-esized to play a critical role in maintaining MC patterning byproviding direct excitation to MC, driving FFI of PG cells, orboth (Gire et al. 2012; Wachowiak and Shipley 2006). To ourknowledge, however, bursting ET cells have not yet beenincorporated into a network model of olfactory processing.

We generated an intrinsically bursting ET cell model (Fig. 4A)using a subset of active conductances known to be necessaryfor generating bursting in vitro (Hayar et al. 2004b; Liu andShipley 2008b) (see MATERIALS AND METHODS for conductancesused). The parameters of the active conductances were opti-mized to match bursting behavior in the absence of synapticinput with experimental data reported from OB slices (Liu andShipley 2008b; Sherwood et al. 2010). Additional currentsimportant in modulating intrinsic or sensory-evoked bursting(Liu and Shipley 2008a, 2008b) were not included in thismodel. Excitability of the ET cell in the presence of sniff-driven sensory inputs was then tuned by adjusting the leakparameters VL and gL to achieve maximal entrainment torepeated sniffs (at 1-Hz sniff frequency). Entrainment was

defined using a SMI (see MATERIALS AND METHODS) that washighest when ET cell bursts occurred reliably to each sniff anddid not occur between sniffs. Many VL and gL combinationsresulted in a lack of ET cell responsiveness to ORN input, evenat different input gains, while other combinations yielded poorentrainment due to weak responsiveness or near-continuousspiking (Fig. 4, A and B). We used the leak parameters VL ��85 mV and gL � 2.6 for all subsequent ET cell simulations,as they were centrally located within a large region with highSMIs. We note that this region was characterized by a lack ofbursting in the absence of sensory input, although rhythmic,spontaneous bursting is a defining feature of ET cells. Slightincreases in VL and gL did produce endogenous ET cellbursting. We nonetheless chose this region of the (VL, gL)parameter plane because ET cell behavior was more robust tochanges in the strength of ORN input. We did not attempt totune the ET cell SMI, or analyze ET cell spiking, at snifffrequencies above 1 Hz.

We incorporated the model ET cell into a simple feedfor-ward excitatory circuit (ORN-ET-MC, Fig. 4C). In this circuit,the MC receives only feedforward excitation through a fast,nonadapting synapse with a reversal potential of 0 mV(Destexhe et al. 1994). Under these conditions, the ET cellresponds to each sniff with a spike burst, and the MC alsoresponds with bursts of similar latency and duration (Fig. 4D).The strength of the ET-MC connection (g[ET-MC]) affected peakfiring rate and total spike count of the MC response but hadlittle effect on MC response duration or latency (Fig. 4E).Increasing the gain of ORN input to the ET cell led to increasesin ET (and thus MC) burst duration and spike count and modestdecreases in onset latency but had no effect on peak firing rate(Fig. 4E).

To optimize MC output dynamics of the ORN-ET-MCcircuit, the g[ET-MC] was adjusted to match mean peak MCfiring rate to the experimental dataset in response to sniff-driven ORN inputs, after which the ORN input gain G[ORN-ET]was adjusted to match the mean response durations from theexperimental dataset (as G[ORN-MC] had been for the ORN-MCmodel). After this optimization, the population dynamics of theORN-ET-MC model roughly matched that of the experimentaldataset, with spike bursts that were more transient than the

Fig. 3. Effect of feedforward inhibition (FFI) on model MC output. A: schematic of glomerular circuit incorporating FFI. ORN input is injected simultaneouslyto the MC model and a single-compartment PG cell model. The PG cell provides inhibitory synaptic input to the MC. See text for details. B: example responseof a model PG and MC to inhalation of odorant using the “fast” FFI synapse at two different FFI strengths (gPG-MC � 4.0 and 8.0). Top traces show synapticinput currents to the model MC from the PG cell (PG, green trace) and from a sample ORN population (ORN, blue). Bottom trace shows model MC Vm. At lowFFI strengths (left), MC spiking remains prolonged and roughly follows ORN input dynamics. At higher FFI strengths (right), MC spiking does not occur ina single burst and thus does not permit inhalation-linked spike patterning. ORN input gain (G[ORN-PG] and G[ORN-MC]) � 18. Spike-evoked synaptic inputtransients are clipped. C: input currents (FFI, green; ORN, blue) to the model MC and MC Vm in response to inhalation of odorant using the “slow” FFI synapsemodel at two different FFI strengths. The slower FFI current lags the ORN input current and accumulates over the course of the sniff, allowing theinhalation-linked MC spike burst to develop but shortening burst duration. ORN input gain values are different for PG and MC inputs: G[ORN-PG] � 35; G[ORN-MC] �18. D: increasing the strength of slow FFI (gPG-MC) reduces the duration of the model MC spike burst. Plots show mean � SE of the burst duration averagedacross all 25 ORN input traces for different gains of ORN input to the PG cell (G[ORN-PG]). ORN input gain to the MC was held fixed (at 18). Due to its slowonset, response latency is unaffected by FFI (not shown). E: effects of varying FFI conductance (gPG-MC) and input gain to the PG cell (G[ORN-PG]) on spike count(top) and duration (bottom) of the sniff-driven MC spike burst. ORN input gain to the MC (G[ORN-MC]) is calibrated at each tested point to generate a peak firingrate of 92 spikes/s. With the ORN-PG-MC model, spike counts matching the experimental dataset (arrow, “exp. mean”) can be achieved within a limited rangeof FFI strengths and ORN-PG input gains (indicated by green dots). Response durations remain longer than experimentally recorded values at all parametercombinations, primarily as a result of firing bursts late in the sniff phase. F: response of the ORN-PG-MC model to the 25 ORN input waveforms, showing spikerasters and population histogram (gray) for each model MC response as in Fig. 2D. The population spike histogram of each PG cell response is also shown (redtrace). FFI conductance (gPG-MC � 1.5) and gain (G[ORN-PG] � 35; G[ORN-MC] � 18) parameters were chosen to produce 92 spike/s peak MC firing rate. PG cellspiking roughly follows ORN input dynamics, while the MC spike burst is shortened and reaches a peak earlier relative to ORN inputs. Note the emergence oflate-phase spiking in some MC units with this circuit. G: population mean and variance of experimental and model MC firing rate responses relative to time ofinhalation for the ORN-PG-MC model. In contrast to the ORN-MC models in Figs. 1 and 2, the ORN-PG-MC population shows slightly shorter bursts than theexperimental dataset.



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simple ORN-MC model (Fig. 4, F and G). This model differedfrom the ORN-PG-MC circuit, however, in that MC responsedynamics in the ORN-ET-MC circuit were largely determinedby the dynamics of the ET cell’s response (Fig. 4F). Thus MCspiking occurred in a temporal window demarcated by the ETcell’s burst envelope, the start and end points of which weredetermined by the gain of the ORN-ET connection (testedrange: 1–5) and the intrinsic bursting properties of the ET cell.As a result, MC response dynamics (latency and duration)

could not be effectively modulated other than by changingORN input strength (Fig. 4E).

Parallel feedforward inputs to MCs. ORNs provide excit-atory input to both MC and ET cells, although the degree towhich MC excitation is mediated by ORN vs. ET cell inputremains unclear (Gire et al. 2012; Najac et al. 2011; Shao et al.2012). Thus we next implemented a feedforward excitatorycircuit, including the ORN-MC and ORN-ET-MC pathwaysconnected in parallel (notation: ORN-[ET]-MC; Fig. 5A) and

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explored the impact of different relative strengths of eachpathway in shaping MC output dynamics. Relative strengthwas defined as the ratio of the charge per presynaptic actionpotential passed to the MC from ORNs directly vs. from the ETcell (see MATERIALS AND METHODS for details).

We first explored how varying the strength of each pathwayaffected peak MC firing rates (Fig. 5B). Increasing the strengthof either pathway led to increases in firing rate; however, theET-MC synapse was 1.5 times as efficient in evokingchanges in peak firing rate (e.g., increasing ET-MC orORN-MC input strength from 0 to 0.4 led to firing rateincreases to 140 and 90 Hz, respectively; Fig. 5B). A targetMC peak firing rate (e.g., the experimental mean of 92spikes/s) could be generated by a wide range of ORN-to-ET-input ratios (gray line, Fig. 5B). However, different ratiosproduced different temporal patterns of MC output. Examplesof synaptic input currents to and spike output from a modelMC, as well as spike output across the model population fortwo different ratios (all producing approximately the samepeak firing rate), are shown in Fig. 5C. As the MC input ratiois shifted from 50% ORN vs. ET inputs (Fig. 5C, left) to beingdominated by ORN inputs (e.g., 90% ORN-MC, Fig. 5C,right), MC spiking dynamics shift from following the shorterET cell burst to following the slower time course of the ORNinput. In general, MC spiking more closely approximated theexperimental dataset at ratios in which the MC received similaror stronger ET cell input than ORN input (Fig. 5D).

We next tested the effect of varying input ratio on total spikecount and response duration (Fig. 5, E and F). Each of theseparameters was most strongly affected by changes in thestrength of the ORN-MC pathway. For each, a range of inputratios could generate MC responses with spike counts ordurations matching the mean of the experimental dataset (Fig.5, E and F). However, a ratio of 50% ET-MC to 50%ORN-MC (1:1 ET/ORN input strength) generated MC re-sponses in which all three metrics (peak spike rate, total spikecount and response duration) simultaneously approximatedtheir experimental means at a particular input gain (Fig. 5F).While a 1:1 ratio was optimal for this dataset, we note that evenhigher ET-MC ratios (e.g., 90% ET-MC strength) also closelyapproximated experimental MC output dynamics (not shown,but see Fig. 4G). These results predict that a parallel excitatory

network in which feedforward, ET cell-mediated input to theMC matches or dominates the direct ORN input would gener-ate MC output dynamics that approximate those recorded invivo. Furthermore, the results suggest that each pathway makesa distinct contribution to shaping MC spiking dynamics. In theORN-ET-MC pathway, intrinsic ET cell bursting propertiespredominantly determine the threshold and temporal windowfor MC activation, while the direct ORN-MC pathway mainlycontributes to peak spike rate and to modulating the duration ofthe sniff-evoked spike burst.

Integrated glomerular circuit model. Finally, having gener-ated several glomerular circuits that could mediate realistictemporal sharpening of sniff-driven ORN inputs, we incorpo-rated these circuits into an “integrated” network model andevaluated its performance in shaping MC response patterns(Fig. 6A). This model combined the ORN-[ET]-MC modelusing a 1:1 ET/ORN input strength ratio, with three pathwaysof MC inhibition: RI, “slow” FFI via a PG cell receiving directORN input (ONd-PG), and FFI via a PG cell receiving excit-atory input from the ET cell (ETd-PG) (Shao et al. 2009). ETcell-driven FFI was included because approximately two-thirdsof PG cells are directly driven by ET cells and not by ORNs(Shao et al. 2009). Parameter values for circuit connectionstrengths were conserved from the small circuit models, withthe following exceptions (Table 1). To accommodate inhibi-tion, the strengths of the excitatory connections onto the MCwere doubled from the values determined in the ORN-[ET]-MC model. ORN input gain (G[ORN-X]) was adjustedproportionally across the different input connections. Thestrengths of the two new inhibitory synaptic connections ontothe MC (e.g., ONd-PG-MC, ETd-PG-MC) were then adjustedto approximate mean peak firing rate, spike count and responseduration with the experimental dataset across all ORN inputtraces.

Sniff-driven spiking dynamics were distinct for each cellularelement in the model, resulting in distinct temporal profiles ofexcitatory and inhibitory synaptic inputs to the MC (Fig. 6B).The optimized model produced MC responses that were, acrossthe population, slightly more transient than the experimentaldataset (Fig. 6, C and D), with slightly higher peak firing ratesand slightly lower total spike counts (Fig. 6E). However, ingeneral, the integrated glomerular circuit model successfully

Fig. 4. Generating patterned MC output via feedforward excitation mediated by external tufted (ET) cells. A: spontaneous (top) and ORN-driven responses duringinhalation in a model ET cell. See text for details of ET cell model. Top trace shows spontaneous bursting of ET cell in the absence of synaptic input. Bottomtraces show rasters of ET cell spikes evoked by a sequence of inhalation-driven ORN input bursts. Each row of spikes represents a different set of ET cell leakparameters (VL, gL), indicated by square and colored circle corresponding to a location in the (VL, gL) plane shown in C. Depending on leak parameters, the ETcell may spike, burst, or fire tonically in response to inhalation-linked ORN input. B: exploration of model ET cell leak parameters to optimize inhalation-linkedmodulation of spiking. Pseudocolor points indicate the degree of modulation of spike rate by inhalation, quantified as sniff modulation index (SMI, see MATERIALS

AND METHODS) for each (VL, gL) pair in response to the ORN input trace shown in A. The ET responses at the boxed (VL, gL) points are shown in the spike rastersin B to illustrate ET behavior in several regions of the parameter space. The center of the region where the highest SMI values were observed is located neargL � 2.6, VL � �85 mV (red box, orange point). In this region, the ET model is generally silent in the absence of ORN input and generates a brief spike burstin response to each inhalation (e.g., bottom spike raster in A). These leak parameters were used for all subsequent ET cell simulations. C: schematic ofORN-ET-MC circuit model. D: example traces of ORN input, ET cell response (Vm), ET cell-driven current to the MC, and MC response (Vm). ET spiking outputshows bursting linked to the onset of sniff-driven ORN input. The MC, coupled to the ET model through an excitatory synapse, follows the ET cell burstingpattern. G[ORN-ET] � 4, g[ET-MC] � 0.3. E: effect of ET-MC synaptic strength (g[ET-MC]) on response dynamics in the ORN-ET-MC model for five ORN-ET inputgains (G[ORN-ET]). Peak firing rates increase dramatically with ET-MC synaptic strength, while spike counts increase more modestly. MC response duration andlatency are unaffected by changes in ET-MC synaptic strength, suggesting that these parameters are determined by the shape, but not the magnitude, of the ETsynaptic input. In contrast, peak firing rate is completely unaffected by the ORN-ET input gain. F: response of ORN-ET-MC model to the 25 different sniff-drivenORN input waveforms, showing spike rasters and population histogram (gray) for each model MC response, as in previous figures. The populations spikehistogram of each ET cell response is also shown (red trace). Parameters are set as in D. G: dynamics of experimental and model MC firing rate responses relativeto time of inhalation for the ORN-ET-MC model. The main discrepancies from the experimental dataset with this model are in the slightly faster onset and slightlyelevated firing rates during the decay phase of the response.



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recapitulated the temporal sharpening of ORN input dynamicsthat was a hallmark of the MC unit recordings (Fig. 6, C andD). Notably, the integrated model also produced MC responseswith a bimodal distribution of spike burst durations (Fig. 6E),recapitulating the distribution of response durations in theexperimental dataset and implying that this bimodal distribu-tion may arise from variation in the dynamics of ORN inputsto different glomeruli.

In general, however, the distribution of model MC outputresponse parameters was more narrow than that recordedexperimentally (Fig. 6E), suggesting that diverse MC responsepatterns cannot be captured solely by a fixed set of networkconnection strengths, even with the normal variation in ORNinput dynamics. One possibility is that MC response diversityarises from modest variations in the strength of circuit connec-tions within the glomerular network. An alternate possibility isthat our approach of optimizing model output using isolatedsubcircuits generated an integrated network model that wasonly locally optimized to the MC population mean. To test thisand to further validate the choice of parameters for the inte-grated network model, we varied the strengths of the fivesynaptic connections onto the MC. For each simulation in thisparameter exploration, a value for each of the five connectionstrength parameters was chosen uniformly within a range from50% to 150% of the values given in Table 1. For each set offive parameters, we calculated its distance (Euclidean distancein normalized, five-dimensional space) from the original pa-rameter set and measured peak spike rates, spike counts and

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Fig. 5. Exploring parallel excitatory input pathways in the glomerular circuit.A: schematic of ORN-[ET]-MC parallel excitation model. MC and ET cellreceive direct ORN input, and the MC also receives excitatory input from theET cell. B: peak firing rate as relative strengths of feedforward ET-MCexcitation (horizontal axis) and direct ORN-MC excitation (vertical axis) arevaried. Units for ORN-MC input strength are scaled so that equivalent valuesrepresent equivalent charge transfer to the MC compared with ET-MC inputs;see MATERIALS AND METHODS for calculation. Dashed lines indicate parameterpairs where ET-MC/ORN-MC input strength ratio is 10/90, 50/50 and 90/10.Gray line indicates parameter pairs where ORN-[ET]-MC model peak firingrate approximates the experimental mean rate of 92 spikes/s. The intersections(white circles) of the dashed lines and gray line occur at parameter pairs thatproduce peak firing rates matching the experimental mean for each inputstrength ratio. C: sniff-driven MC output from the ORN-[ET]-MC model at the“optimal” parameter values (indicated by white circles in B) at ET-MC/ORN-MC input strength ratios of 50/50 (left), and 10/90 (right). Top tracesshow input currents to the MC originating from ORNs (green) and ET cells(blue) for a representative ORN input waveform. Middle trace shows the MCVm response. At bottom are MC spike rasters for all 25 ORN input waveformsat the two input strength ratios. G[ORN-ET] is fixed at 1.5. D: comparison ofORN-[ET]-MC model and experimental relative firing rates for the 50/50 (left)and 50/50 (right) input strength ratios. Parameter values are set as in C. ModelMC firing dynamics closely match those of the experimental dataset for the50/50 input ratio, while the 10/90 ratio results in longer MC spike bursts moresimilar to the ORN-MC model output. E: effect of relative strengths of ET-MCand ORN-MC inputs on sniff-driven spike count. Dashed lines indicateparameter pairs where ET-MC/ORN-MC input strength ratio is 10/90, 50/50and 90/10, as in B. Gray line indicates parameter pairs where spike countmatches the experimental mean of 12 spikes/sniff. The intersections (magentacircles) of the dashed and gray lines occur at parameter pairs that produceexperiment-matched spike counts for the respective input strength ratios.White circles indicate parameter pairs that produce experiment-matched peakfiring rates, from B. F: effect of relative strengths of ET-MC and ORN-MCexcitation on sniff-driven MC burst duration, with dashed lines and symbolsrepresenting input ratios and matches to the experimental mean, as in E. Bluefilled circles at the intersection of the dashed and gray lines indicate parameterpairs that produce experimentally matched burst durations for each inputstrength ratio. White and magenta circles are transferred from B and E andrepresent experimentally matched parameter pairs for peak rate and spikecount, respectively. The white, magenta and blue circles on the 50/50 linecluster closest to one another (within the light gray circle), indicating thatmodel output can approximate the experimental dataset across peak firing rate,spike count, and duration measures simultaneously when the ET-MC/ORN-MC input strength ratio is 50/50. For the 90/10 ratio, duration andspike count are simultaneously optimal, but peak firing rate is too high (160spikes/s). For the 10/90 ratio, no output measures may be optimized simulta-neously.



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response durations as a function of this distance (Fig. 6F).Parameter sets closest to those originally derived from theisolated circuit models (i.e., as specified above) provided MCoutputs that most closely approximated our mean target met-

rics. Error (i.e., summed variance from experimental meansacross each MC response parameter) grew slowly as theparameter sets diverged from these original optimized values(Fig. 6F), suggesting that the minimal circuit optimization

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Fig. 6. Generating naturalistic MC response dynamics with an integrated glomerular circuit model. A: schematic of the integrated glomerular circuit model. Themodel incorporates direct ORN-MC excitation in parallel with feedforward excitation through an ET cell. Two PG cell pathways, one receiving direct ORN input(ONd-PG) and the other receiving excitatory input from the ET cell (ETd-PG), provide FFI to the MC. The MC also receives RI, simulating interactions betweenMC and GCs and/or PGs. Values at each synapse indicate the ORN input gains (G[ORN-X] used; inhibitory inputs in this figure were as follows: g[ONd-PG-MC] �g[ETd-PG-MC] � 0.5; g[RI] � 0.1). B: responses of the model circuit elements to one inhalation of odorant. i: ORN input current and spike rasters showing outputfrom the ET, ONd-PG, ETd-PG and MC components of the integrated model in response to a representative sniff-driven ORN input (same input trace as previousfigures). ii: Synaptic input currents to the model MC originating from different sources. Traces are offset from each other to facilitate comparison. C: responseof the integrated model to the 25 different sniff-driven ORN input waveforms, showing spike rasters and population histogram for each model MC response,as in previous figures, along with the population ORN input dynamics (blue). Input gains and synaptic conductances are set at parameters given in A. Note thetemporal sharpening relative to ORN input dynamics. D: dynamics of experimental and model MC firing rate responses relative to time of inhalation for theintegrated model. The dynamics of the model output closely match those of the experimental dataset. E: histograms comparing distributions of responseparameters for the model MC driven by each of the 25 ORN input traces (gray bars) and for each of 37 MT units recorded in the experimental dataset (red).The distribution of model MC outputs is narrower than that of the recorded units for each parameter, but the distributions have similar means and modes. Thedistribution of MC response durations is bimodal for both the model and experimental datasets. Bin sizes are 10 Hz (peak firing rate; i), 1 spike (spikes per sniff;ii), and 10 msec (duration; iii). F: exploration of parameter space of circuit connection strengths in the integrated model. The five synaptic input strengths to themodel MC were varied systematically by up to 50% in either direction, with “distance from center” expressed as the Euclidean distance of a parameter set fromthe initially optimized parameter values (see text for details). Plots show, from left to right: “error”, the sum squared error of the means of the model MCpopulation response metrics (peak firing rate, spike count, and response duration) relative to their respective means in the experimental dataset (i), and mean peak firingrate (ii), mean spike count (iii), and median response duration (iv) of model MC outputs. Solid circles show mean (or median) values for the population of 25 modeledMC outputs; gray bars indicate the range, defined by the 80th and 20th percentiles of values within each bin of distance-from-center values (bin size, 0.01). Note thaterror increases gradually with distance from center (i), and that each response parameter is relatively robust to modest changes in connection strengths (ii–iv).



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strategy yielded a parameter set that is near optimal for theintegrated network model, and that model responses are robustto modest parameter changes.

Varying the strength of connections within the glomerularnetwork by up to 50% also yielded variation in MC responseparameters that approximated the range of those measuredexperimentally, for example, with mean MC peak firing ratesvarying from 60 to 150 Hz. Inhalation-driven spike countsand spike burst durations did not reach values as high as thosein the experimental dataset, but nonetheless covered much ofthe range observed experimentally (Fig. 6F). This resultimplies that changes in the relative strength of connectionswithin this simplified glomerular network can account formuch of the measured diversity in inhalation-driven MCresponse dynamics.

We next used the model to explore the contributions ofparticular inhibitory circuits to shaping MC response dynam-ics. For example, GABAergic inhibition across glomerularcircuits shapes both the magnitude and temporal structure ofsensory-evoked MC responses in OB slices (Shao et al. 2012,2013); these experiments could not distinguish between RI orFFI mediated by particular glomerular circuits. We exploredthis in the model by varying the strength of FFI mediated byONd-PGs and ETd-PGs, either independently or simultane-ously (Fig. 7, A–C). We also varied the strength of RI,representing dendrodendritic inhibition between MCs and PGsor GCs, while leaving FFI parameters fixed (Fig. 7D).

Several interesting relationships emerged from these manip-ulations. For example, the strength of FFI had relatively littleimpact on peak MC firing rates but could substantially impactMC burst duration. Peak firing rate showed, at most, a 5%decrease as g[ONd-PG-MC] and g[ETd-PG-MC], either alone or intandem, were increased from zero to the maximal tested valueof 1.5 (Fig. 7, A–C). However, the direct (ONd-PG) andindirect (ETd-PG) FFI pathways each showed modest effectson response duration when the strength of each pathway wasvaried individually (Fig. 7, B and C) and showed larger effectswhen both pathways were varied together (Fig. 7A). This effectwas nonlinear for both FFI pathways (ONd-PG and ETd-PG,respectively), with FFI strength shortening burst duration sub-stantially only at higher values (Fig. 7, B and C). In contrast, RImore strongly affected peak firing rates but had little impact onburst duration: MC peak rates decreased by 25% as RIstrength was increased over the tested range (with a concom-itant decrease in total spike count), but varying RI strength

only shortened MC burst duration by, at most, 25% at thehighest values tested (Fig. 7D). Finally, ORN input gain hadlittle effect on peak MC firing rates, but a substantial effect onburst duration and, consequently, total spike count (Fig. 7).These simulations thus suggest that this “minimal” integratedOB circuit model acts robustly to temporally sharpen ORNinputs across a wide range of network synaptic strengths, andalso suggest that different inhibitory pathways within the OBcircuit make distinct contributions to the transformation ofinhalation-driven bursts into patterned MC responses.

DISCUSSION

We explored how certain previously identified OB circuitsshape inhalation-linked patterns of MC output in the context ofnaturalistic odor sampling (i.e., sniffing). We used a small-network modeling approach to reproduce key circuits in theOB network, focusing on well-described elements of the OBglomerular network, and asked how these elements, in isolationand integrated into multielement circuits, transform sniff-driven packets of sensory input into MC spiking responses.Recent experimental and theoretical studies have highlightedthe importance of the glomerular circuitry in the larger OBnetwork (De Saint Jan et al. 2009; Gire et al. 2012; Gire andSchoppa 2009; Hayar et al. 2004a; Linster and Cleland 2009;Shao et al. 2009, 2012; Wachowiak and Shipley 2006), but theexact roles that individual glomerular circuits of this networkmight play in shaping OB output in vivo remain unclear. Thecurrent study incorporates glomerular circuitry into a dynamic,biologically constrained network model and evaluates how thecircuitry transforms sensory inputs in the temporal domainrelative to sniffing.

Strategies for modeling OB network function. The networkmodel was constrained by experimental data: in addition toincorporating biophysically realistic circuit elements, sensoryinput to the model OB network was derived from recordings ofORN inputs to the OB of intact rats, and an experimentaldataset of presumptive MC recordings, evoked by the samenaturalistic sniffing patterns used to drive the ORN responses,was used as a benchmark for evaluating model output. The useof input waveforms with naturalistic dynamics differs from theconstant, pulsatile or sinusoidal inputs used in most earliernetwork models of olfactory processing (Arruda et al. 2013;Bathellier et al. 2006; Brody and Hopfield 2003; Davison et al.2003; Kunsting and Spors 2009; Linster and Cleland 2009;Margrie and Schaefer 2003; Rubin and Cleland 2006). Using

Table 1. Values for synaptic connection strengths after model optimization for the minimal circuit models tested and for the integratedglomerular network model (see text for details)

Circuit Model G[ORN-MC] gRI G[ORN-PGON]gPGON-MC G[ORN-ET] gET-MC gET-PGET

gPGET-MC

ORN-MC 7.5ORN-MC-RI 15 0.1ORN-PG-MC (slow) 18 35 1.5ORN-ET-MC 4 0.3ORN-ET-MC parallel 3.8 1.5 0.15Integrated model 7.7 0.1 35 0.25 2.5 0.3 1.37 0.25

ORN, olfactory receptor neuron; MC, mitral/tufted cell; RI, recurrent inhibition; PG, periglomerular cell; ET, external tufted cell; G[ORN-MC], ORN input gainto MC; gRI, maximum conductance for RI; G[ORN-PGON]

, ORN input gain to PGON; gPGON-MC, maximum conductance for PGON-MC synapse; gET-MC, maximumconductance for ET-MC synapse; gET-PGET

, maximum conductance for ET-PGET synapse; gPGET-MC, maximum conductance for PGET-MC synapse. In Fig. 5,“ORN-MC input strength” is a rescaled version of G[ORN-MC]. The value of 3.8 here is equivalent to an ORN-MC input strength of 0.15 (see MATERIALS AND

METHODS).



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experimentally derived inputs was important for several in-sights into OB network organization. For example, we foundthat slow FFI from PG cells to MCs was necessary to allowMC spike bursts to develop during the course of an inhalation-driven burst of sensory input. We also found that RI did littleto alter the inhalation-linked dynamics of MC firing, while FFIand feedforward excitation mediated by ET cells played animportant role in shaping these dynamics. These results arediscussed in more detail below.

A common approach to modeling neural circuit function isto construct a single, “maximal” model incorporating as muchknowledge as possible about the network; in our case such an

approach would require exploring a prohibitively large param-eter space. Instead we employed a strategy of incrementallyincreasing network complexity, tuning parameters and com-paring model output to experimental data at each step. Thebenefit of this approach was that it allowed us to explore abroader range of parameter space, to test whether particularcircuits are necessary or sufficient to generate a realistic tem-poral transformation of sniff-driven sensory inputs, and togenerate hypotheses regarding the roles of particular circuitsand, and circuit features, in generating these patterns. The setof minimal circuits tested is necessarily incomplete, but repre-sents canonical subcircuits hypothesized in earlier studies as

Ag[ONd-PG-MC] = g[ETd-PG-MC]

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Fig. 7. Contributions of inhibitory glomerular circuits to MC response patterns. A: effects of varying FFI strength (changing ONd-PG-MC and ETd-PG-MCconnection strengths simultaneously) on MC response parameters. RI strength is fixed. Results for three ORN input gains are shown. Input gain was variedproportionally across all ORN input channels, and legend shows gain relative to values in Fig. 6A. Increasing FFI via both inhibitory pathways only slightlylowers peak firing rate (left). Spike count (center) decreases substantially due to a stepwise decrease in burst duration (right). B: effects of varyingETd-PG-mediated FFI (ORN-ET-PG-MC pathway), leaving ONd-PG-MC and RI strengths fixed. There is little impact on peak firing rate and more modestimpact on spike count and duration. C: effects of varying ONd-PG-mediated FFI (ORN-PG-MC pathway), leaving ETd-PG-MC and RI strengths fixed. Effectsof varying ONd-PG FFI are similar to those of varying ETd-PG-FFI, with no impact on peak firing rate and modest impacts on spike count and duration. D:effects of varying RI, leaving FFI strengths fixed. Peak firing rate (left) and spike count (center) decrease substantially with increasing RI, while MC burstduration (right) is only slightly affected by RI strength.



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playing important roles in shaping inhalation-driven MC re-sponse patterns (Fukunaga et al. 2014; Gire and Schoppa 2009;Shao et al. 2012; Wachowiak and Shipley 2006).

Our strategy to evaluate model performance was to assesshow accurately the OB network generated output parameters,in particular, spiking dynamics, matching those recorded ex-perimentally given biologically realistic inputs. This strategydiffers from other models which have sought to identify circuitmechanisms capable of mediating particular neural computa-tions, such as concentration-invariant odor discrimination(Brody and Hopfield 2003; Cleland et al. 2007, 2012; Margrieand Schaefer 2003), contrast enhancement and pattern decor-relation (Cleland and Linster 2012; Cleland and Sethupathy2006; Imam et al. 2012; Luo et al. 2010; Wiechert et al. 2010),and representation sparsening (Assisi et al. 2007; Finelli et al.2008), among others. Our approach does not presume that anyparticular computation might be performed by a specific circuitcomponent (nor does it investigate OB computations), butrather seeks to identify how specific network componentsinfluence experimentally measured output features, in this case,inhalation-driven MC spiking patterns.

Role of OB circuits in shaping inhalation-driven responsedynamics. This approach led to several insights about criticalcircuits involved in the transformation of inhalation-drivensensory inputs into dynamic output patterns. First, our resultssuggest that multiple, relatively simple circuit configurationsare capable of approximating the temporal sharpening of sen-sory inputs that has been observed experimentally (Carey andWachowiak 2011; Shao et al. 2012). For example, in additionto the “integrated” circuit model, the ORN-PG-MC circuit withslow FFI, the ORN-ET-MC circuit and the ORN-[ET]-MCcircuit with parallel ET and ORN-mediated excitation of MCswere each capable of generating MC output patterns thatapproximated experimental data in terms of peak firing rates,spike counts and burst durations. Thus the glomerular networkmay include multiple circuits that conjointly sharpen sensoryinput. Analogous arrangements have been reported amongmotor pattern generating networks, where disparate combina-tions of intrinsic currents, synaptic mechanisms, and networkconnectivities can produce functionally identical rhythmic out-put (Prinz et al. 2004; Roffman et al. 2012). The ability ofmultiple subnetworks to generate functionally appropriate out-put dynamics may enable modulation of finer-scale features ofthe MC response, such as synchrony of spike timing or input-output dynamic range, without disrupting the basic inhalation-driven “packets” of activity that are the basis for transmittingodor information to downstream processing centers.

Second, the models suggested that that the kinetics ofinhibition are critical in shaping MC responses. The rapid onsetdynamics associated with classical, GABAA-mediated trans-mission acted to suppress MC and ET cell responses in ablanket fashion, preventing the generation of discrete inhala-tion-triggered bursts. Slower-onset and longer-lasting FFI wasinstead necessary to mediate temporal sharpening of inhala-tion-triggered MC spikes while still permitting the develop-ment of a unitary spike burst following each inhalation. Thisslow, long-lasting inhibition may be due to one or a combina-tion of several factors, including asynchronous GABA releasefrom juxtaglomerular neurons (Murphy et al. 2005; Smith andJahr 2002), N-methyl-D-aspartate receptor-dependent GABArelease from GC (Isaacson and Strowbridge 1998; Schoppa and

Urban 2003; Shao et al. 2012), polysynaptic activation ofGABA release from PG or short-axon cells (Liu et al. 2013;Shao et al. 2009), intrinsic properties of PG cells such ashyperpolarization-activated cation currents (Cadetti and Bel-luzzi 2001) or even inhibition driven by cortical feedback(Boyd et al. 2012). Regardless of mechanism, our OB networkmodel suggests a functional role for this “slow” inhibition inthe context of natural odor sampling, namely, to allow forsynaptic integration over the course of an inhalation-evokedburst of sensory input, the duration of which roughly matchesthe decay time constant of the inhibition. Notably, GABAergicglomerular circuits also mediate presynaptic inhibition of ORNinputs with similarly slow onset and decay kinetics (McGann etal. 2005; Wachowiak et al. 2005), modulating the strength ofsensory inputs without altering the temporal dynamics of eachinhalation-driven burst (Pírez and Wachowiak 2008). Giventhe possibility that multiple inhibitory pathways with distinctkinetics may be present within glomerular circuits (Shao et al.2012), it may be interesting to explore how onset and decaykinetics separately contribute to shaping MC temporal re-sponse patterns. These parameters could be explored not onlyfor the different FFI circuits, but also for RI circuits which mayvary in kinetics, depending on whether RI is mediated by PGcells or GC.

Third, we found that, in the integrated glomerular networkmodel, RI and FFI played distinct roles in shaping MC re-sponses. FFI could substantially impact MC burst duration butappeared to do so nonlinearly, with burst duration remainingrobust to FFI strength at lower values but shortening signifi-cantly at higher values. These results are consistent withexperimental evidence that FFI from PG to MCs shapes thetemporal structure of sensory-evoked responses on a time scalematching that of respiratory patterning (Shao et al. 2012). Thisresult is also interesting given that we had earlier found abimodal distribution of inhalation-driven MC spike burst du-rations (Carey et al. 2009) roughly corresponding to the rangeof durations generated by varying FFI strength in the networkmodel. In contrast, RI strength affected peak firing rates in agraded manner, but had little impact on MC burst duration.This result is consistent with hypotheses that RI between MCand GC affects MC response gain and fine-scale temporaldynamics, such as synchrony of spike timing in the gammafrequency range (Bathellier et al. 2006; David et al. 2009;Fukunaga et al. 2014; Schoppa 2006), but not respiratorypatterning.

Our modeling results support experimental evidence that theET cell plays a central role in conducting olfactory signalsthrough the glomerulus and also suggest that ET cell-mediatedexcitation of MCs, in addition to FFI, plays an important rolein shaping the dynamics of OB output (Carlson et al. 2000; DeSaint Gire et al. 2012; Jan et al. 2009; Shao et al. 2012). A keydeterminant of these dynamics is the bursting behavior of ETcells (Hayar et al. 2004b; Liu and Shipley 2008a, 2008b). Inaddition, the fact that MC response amplitudes (in terms ofpeak spike rate) were more dependent on the strength of theET-MC connection than on the ORN-MC connection suggeststhat the ET cell may serve as an effective target for centrifugalsystems that modulate OB output strength (Liu et al. 2012).

Control of MC excitation by ET cell bursting may facilitateodor coding in several ways. First, the all-or-none burst re-sponse of the ET cell to ORN inputs of sufficient amplitude



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may enhance the reliability of sensory signal transmission andfilter out small transient fluctuations in the input (Gire andSchoppa 2009; Liu and Shipley 2008b); this effect was evidentin our glomerular model. Second, the ET cell burst mayregularize the strength and duration of the signal received bythe MC. Somewhat surprisingly, in our model ET cell-medi-ated MC excitation led to temporally sharper MC responsesthan ORN-driven excitation, due to the fact that inhalation-driven ORN inputs decay relatively slowly. Temporallysharper responses are important in enabling faithful transmis-sion of inhalation-linked response patterns across the biologi-cal range of sniff frequencies (Carey et al. 2009). In general,bursting neurons can more reliably transmit temporal informa-tion than simple spiking neurons, since burst timing and thetiming of spikes within a burst are typically more precise thanthe timing of individual spikes emitted by nonbursting neurons,particularly in the presence of a noisy background (Izhikevich2002; Kepecs and Lisman 2003).

Finally, while we identified circuit configurations and con-nection strengths that best approximate the mean dynamics ofinhalation-driven activity across a population of MT cells, it isimportant to note that the responses of individual MT cells aretemporally diverse and can vary substantially around this mean(Carey and Wachowiak 2011; Cury and Uchida 2010; Smear etal. 2011). This diversity could reflect different strengths ofcircuit connections within different glomeruli or even differentindividual MT cell subtypes, for example, mitral vs. tuftedcells (Fukunaga et al. 2012). Indeed, we could generate MCresponse dynamics that varied across the range of responsedurations in our experimental dataset by varying the strength ofparticular circuit connections, such as FFI or ORN input gain.It would be interesting to further explore how diversity inglomerular circuit connectivities can account for diversity inMC response patterns using this model framework, ideallycompared with intracellular recordings of inhalation-drivenMC changes in membrane potential (Fukunaga et al. 2014).

Further explorations of OB network function using a small-network model. The small-network model developed here iden-tifies glomerular circuit elements important for generatingrealistic temporal patterns of output across a MC populationgiven realistic input patterns, but it does not (nor is it meant to)reproduce all known circuits within the OB network, or evenall known properties of individual cell types. For example, ourminimal ET cell model lacks a calcium-activated potassiumcurrent and a high-voltage-activated calcium current, both ofwhich regulate ET cell burst duration and interspike interval(Liu and Shipley 2008b). Inclusion of these currents couldallow for finer tuning of sensory-driven ET cell burst propertiesand, consequently, MC response dynamics. Neither does themodel incorporate the known diversity in intrinsic burstingfrequencies across the ET cell population, which is thought toallow for entrainment of ET cell bursting to sensory inputsdriven by a range of sniff frequencies and to tonically inhibitMCs (Hayar et al. 2004b; Wachowiak and Shipley 2006). Theimpact of these additional circuit properties could be exploredby expanding the glomerular network to include multiple ETcells with varying current densities and bursting behavior.

At the circuit level, the network model could also be ex-panded to include an emerging diversity of inhibitory circuitsin the glomerular and infraglomerular layers, such as FFImediated by short-axon cells (Liu et al. 2013; Whitesell et al.

2013), PG cell-mediated FFI of ET cells (Gire and Schoppa2009; Shao et al. 2012), GABAergic input to MCs fromrecently described parvalbumin-expressing external plexiforminterneurons (Huang et al. 2013; Kato et al. 2013; Miyamichiet al. 2013) and RI between PG and MCs (Murphy et al. 2005).Each of these circuits has the potential to contribute further toinhalation-linked temporal patterning. Distinct kinetics andconnection strengths across different inhibitory circuits mayenable a greater diversity of MC response patterns than cap-tured in our initial model. A similar framework could be usedto address the importance of interglomerular interactions viashort-axon cells in the glomerular layer or between MC/GCs.

We focused here on temporal shaping of ORN inputs by theOB network, since this transformation was highly constrainedby experimental data, but an expanded glomerular networkmodel may also be used to explore how the OB transformsrepresentations of odorant identity or concentration in thecontext of natural sampling behavior. For example, FFI via theON-PG-MC circuit has been hypothesized to sharpen MCresponse spectra by amplifying PG cell responses to weaksensory inputs (Cleland and Linster 2012; Gire and Schoppa2009). This hypothesis could be further developed by provid-ing experimentally obtained input waveforms representing theresponse of the same population of ORNs to a range ofdifferent odorants or odorant concentrations. The same frame-work should also be useful for generating predictions of howthe OB network transforms sensory inputs as a function ofchanges in odor sampling behavior, such as the bursts ofhigh-frequency sniffing that are a hallmark of exploratorybehavior (Macrides 1975; Verhagen et al. 2007; Welker 1964).

GRANTS

This work was supported by the National Institute on Deafness and OtherCommunications Disorders (Collaborative Research in Computational Neuro-science Grants DC011423 and F31 DC010312) and the National ScienceFoundation (Grants DMS-1022945 and DMS-1148230).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: R.M.C., W.E.S., A.B., and M.W. conception anddesign of research; R.M.C. and W.E.S. performed experiments; R.M.C. andW.E.S. analyzed data; R.M.C., W.E.S., M.T.S., A.B., and M.W. interpretedresults of experiments; R.M.C. and M.W. prepared figures; R.M.C., W.E.S.,and M.W. drafted manuscript; R.M.C., W.E.S., M.T.S., A.B., and M.W. editedand revised manuscript; R.M.C., W.E.S., M.T.S., A.B., and M.W. approvedfinal version of manuscript.

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