Dynamics of Sensory Integration of Olfactory and Mechanical Stimuli Within the Response Patterns of Moth Antennal Lobe Neurons

Odors emanating from a biologically relevant source are rapidly embedded within a windy, turbuluent medium that folds and spins filaments into fragmented strands of varying sizes. Environmental odor plumes therefore exhibit complex spatiotemporal dynamics, and rarely yield an easily discernible concentration gradient marking an unambiguous trail to an odor source. Thus, sensory integration of chemical input, encoding odor identity or concentration, and mechanosensory input, encoding wind speed, is a critical task that animals face in resolving the complex dynamics of odor plumes and tracking an odor source. In insects, who employ olfactory navigation as their primary means of foraging for food and finding mates, the antennal lobe (AL) is the first brain structure that processes sensory odor information. Although the importance of chemosensory and mechanosensory integration is widely recognized, the AL itself has traditionally been viewed purely from the perspective of odor encoding, with little attention given to its role as a bimodal integrator. In this work, we seek to explore the AL as a model for studying sensory integration - it boasts well-understood architecture, well-studied olfactory responses, and easily measurable cells. Using a moth model, we present experimental data that clearly demonstrates that AL neurons respond, in dynamically distinct ways, to both chemosensory and mechanosensory input; mechanosensory responses are transient and temporally precise, while olfactory responses are long-lasting but lack temporal precision. We further develop a computational model of the AL, show that our model captures odor response dynamics reported in the literature, and examine the dynamics of our model with the inclusion of mechanosensory input; we then use our model to pinpoint dynamical mechanisms underlying the bimodal AL responses revealed in our experimental work. Finally, we propose a novel hypothesis about the role of mechanosensory input in sculpting AL dynamics and the implications for biological odor tracking.


Background
Integration of chemosensory input (encoding odor identity and concentration) and mechanosensory input (encoding wind velocity) is critical for olfactory navigation and the ability of insects to home in on and locate an odor source (Mamiya and Dickinson, 2015). One particularly crucial task for an insect is the ability to track an odor source mid-flight. This ability is critical for finding food, but poses a monumental challenge: turbulent wind eddies produce complex patterns of odor strands of different sizes and concentrations intermixed with clear media, obfuscating the odor source and rarely yielding an easily discernible 'concentration gradient' to follow (Vickers, 2000;Carde and M.. Willis, 2008;Murlis and Jones, 1981). To successfully track an odor, an insect must simultaneously classify odor identity and rapidly resolve the spatio-temporal dynamics of the odor plume, all while maintaining balance and bearing during flight.
Evidence strongly suggests that the ability of insects to track odors mid-flight relies on the integration of mechanical with chemical input, and, accordingly, chemosensory and mechanosensory bimodality is indeed widespread within the central nervous system of insects. In terms of sensory organs, while Johnston's organ and Böhm's bristles on the antenna are well known to detect wind velocity and guide flight maneuvers (Patella and Wilson, 2018;Jarman, 2002;Sane et al., 2007), there are also less studied bimodal sensilla (Jarman, 2002;Sane et al., 2007). For example, a subtype of trichoid sensilla on the antenna of the male hawkmoth (Lee and Strausfeld, 1990) and sensilla chaetica on the honeybee antenna (Whitehead and Larsen, 1976) exhibit chemo-and mechano-sensory bimodality. A wide range of animals have been shown to be adept at intelligently sampling environmental odor plumes to home in on an odor source (Ando and Kanzaki, 2015;Pasternak, Bartumeus, and Grasso, 2009;Pyk, 2006;Vergassola, Villermaux, and Shraiman, 2007); moths, in particular, employ a strategy in which they surge upwind upon encountering odor strands and cast across wind when losing contact with odors (Vickers and T. Baker, 1994). This suggests that chemosensory and mechanosensory input may augment and corroborate each other, consistent with the close link between odor plume structure and air turbulence; the apparent convergence on this strategy across many species reveals the importance of sensory integration in tracking odor sources.
The antennal lobe (AL) is the first brain area to substantially process odor information arriving from olfactory receptor neurons (ORNs) in the sensory periphery. While the AL has been traditionally thought to function exclusively within the domain of odor (and CO 2 ) detection, there exist some data in moths and tadpoles suggesting that AL neurons (in moths) or olfactory bulb neurons (in tadpoles) are actually bimodal (Han, Hansson, and Anton, 2005;Brinkmann and Schild, 2016); recently, a couple of studies in mice have shown that olfactory bulb glomeruli are responsive to mechanosensory input (in the absence of odor) arising from air speed and pressure (Iwata, Kiyonari, and Imai, 2017;K. Baker et al., 2019). Unfortunately, such data have been collected only rarely and sparsely and have received little attention, and the AL has hence been investigated only from the perspective of odor encoding. The AL has therefore not yet been rigorously established as a model system for the study of sensory integration, despite the fact that sensory integration is an important aspect of odor tracking. The AL, however, is an otherwise ideal system for the study of bimodality -specifically, AL architecture is well understood, AL odor response dynamics are well-studied, and AL neurons are easy to measure individually and in aggregate.
Additionally, the anatomy and physiology of the AL is analogous to that of the olfactory bulb in vertebrates (Hildebrand and Shepherd, 1997), and hence may provide insight into chemo-and mechano-sensory integration in a broad range of species.
Experimental studies suggest that the moth AL is indeed acting as a bimodal integrator.
Some preliminary data shows that projection neurons (PNs) within the AL respond to both olfactory and mechanosensory signals, and that these two sources of input may influence AL dynamics in starkly disparate ways. These data indicate that strong mechanosensory input enhances the amplitude and temporal precision of AL odor responses (causing a sharp, transient burst in AL activity at odor onset), as well as possibly contributing to the correlational structure of responses across AL neurons.
To examine the dynamics underlying experimental observations, we construct a realistic, large-scale biophysical model of the moth AL consisting of projection neurons (PNs) and local neurons (LNs) organized into glomeruli; using physiologically reasonable model components and parameters, we simulate both olfactory and mechanosensory input to the model. We first probe the responses of our model network to odor input alone, and we not only show that our model exhibits the triphasic odor responses observed experimentally in moth PNs (Christensen and Hildebrand, 1987b;Waldrop, Christensen, and Hildebrand, 1987;Christensen and Hildebrand, 1988;Christensen and Hildebrand, 1990;Christensen, Waldrop, Harrow, et al., 1993), but we also dissect model dynamics to provide plausible mechanistic explanations for how such response patterns arise. We then explore model responses to mechanosensory input alone, and show that the transient, temporally precise nature of responses to mechanosensory signals arises as a consequence of pervasive slow inhibition activated via excitation of the global LN network. Finally, we show that model dynamics are capable of capturing empirically observed response patterns to olfactory and mechanosensory input in combination, and we examine the implications of bimodality for odor discrimination and tracking.

The Olfactory Pathway
The olfactory pathways is substantially studied, and thus is relatively well understood. This section will outline what is known about how olfactory stimuli are processed, and what the physiology of the involved brain regions, particularly the AL, looks like.

Olfactory Transduction Pathway
Olfactory transduction begins in the antennae, sensory organs which respond to the presence of chemical stimuli comprising distinct odors. The antennae contain thousands of ORNs, which each express one of approximately 60 different odorant receptors. With only 60 unique odorant receptors, odor discrimination relies on a highly combinatorial process; each scent perceived by the antennae stimulates a subset of the odorant receptors, and thus a subset of the ORNs. By varying which subset of olfactory receptors are stimulated, the antennae are able to respond uniquely to approximately 2 60 distinct odors. ORN axons bundle together to form the antennal nerve, and relay information to the first brain structure, the AL (Cazamine and Hildebrand, 1979).
The AL is composed of approximately 60 distinct bundles of neurons called glomeruli.
Each glomerulus contains approximately 6 GABAergic, inhibitory LNs, and 10-15 excitatory, output PNs, leading to a total of around 360 LNs and 840 PNs within the entire AL (Homberg, Christensen, and Hildebrand, 1989;Kingan and Hildebrand, 1985;Hoskins et al., 1986;Hildebrand, Hall, and Osmond, 1979;Matsumoto and Hildebrand, 1981;Christensen and Hildebrand, 1987a;Homberg, Montague, and Hildebrand, 1988). Each glomerular subunit responds most strongly to one of the 60 types of ORNs, similarly to how each type of ORN has only a single odor receptor. This means that odor identity is relatively well preserved, as specific glomeruli will respond most strongly to specific odors. The dendritic trees of PNs are typically confined to a single glomerulus, although few PN trees span across multiple glomeruli and thus integrate input from multiple olfactory receptor types (Kanzaki et al., 1989). LNs serve to bridge the gap between glomerular units, as they create a diffuse inhibitory network which is able to connect multiple glomerular subunits (Reisenman et al., 2004;Lei, Christensen, and Hildebrand, 2004). The axons of PNs only exit the AL and provide input to the next brain region, the mushroom body.
The mushroom body is the first brain region believed to be responsible for odor association and memory. It is composed of thousands of Kenyon Cells (KCs), which greatly outnumber the number of input PNs. KCs have relatively high depolarization thresholds, and thus exhibit nearly no background firing. Furthermore, these neurons exhibit extreme odor selectivity, and minimal overlapping odor representations. Odor-evoked responses, while highly selective, are extremely limited, consisting of only a few spikes. Any particular odor will excite approximately 10-20% of KCs, and typically does so within the first 500 ms of odor stimulus onset (Ito et al., 2008). This entire olfactory pathways is summarized in the schematic diagram illustrated in figure 1.1. The antennae contains ORNs which each express a single odorant receptor. These ORNs send signal to the AL, shown in the middle, which is comprised of subunits called glomeruli. Each glomerulus contains GABAergic, inhibitory LNs and excitatory, output PNs. PNs send signal to the mushroom body, shown on the right, which is the first brain region responsible for odor association and memory. The mushroom body is composed of Kenyon Cells, which have highly selective, odor-evoked responses.

The Antennal Lobe
Of particular focus in this research is modeling the AL, as it is the first brain region to process olfactory stimuli. To create a realistic simulation, the experimental dynamics observed within the AL must be reasonably replicated. The response patterns of PNs in particular are well studied, and will serve as a benchmark for the simulations.
PN response to olfactory stimulation is triphasic, as shown in figure 1.2. The first phase, the I 1 or initial hyperpolarization (IHP), is characterized by suppression of PN firing for approximately 50 ms. This phase is mechanistically well understood, and is believed to be the result of GABA A based inhibition from the LNs within the network. Application of bicuculline, a GABA A antagonist, removes the IHP phase, and thus supports the belief that fast inhibition from LNs is responsible for this phase (Waldrop, Christensen, and Hildebrand, 1987;Christensen and Hildebrand, 1988;Christensen, Waldrop, Harrow, et al., 1993;Christensen, Waldrop, and Hildebrand, 1998).
The following phase is phase II, characterized by sudden depolarization of PNs and rapid firing for the remainder of the odor stimulus. PN behavior varies widely from PN to PN within this phase, with some PNs firing more homogeneously and others firing with more burst-like patterns. Experimentally, this spectrum of behaviors is not well understood.
The final phase, I 2 or after hyperpolarization (AHP), is characterized by suppression of PN firing for approximately one second following the termination of olfactory stimulation (Christensen and Hildebrand, 1987b;Waldrop, Christensen, and Hildebrand, 1987;Christensen and Hildebrand, 1988;Christensen and Hildebrand, 1990;Christensen, Waldrop, Harrow, et al., 1993). Unlike the IHP, this phase is not well understood mechanistically.
This complex dynamical response of PNs to olfactory stimuli serves as a target behavior that our model will hopefully recreate. Once our model does recreate this behavior, predictions can be made as to what mechanistic components give rise to these specific behaviors that at this point are not experimentally understood. 2 PN response to olfactory stimulus, represented by the black bar, is triphasic. The first phase, I 1 or IHP, is characterized by hyperpolarization of PN voltage, and thus suppression of firing. Phase II occurs afterwards for the remainder of the olfactory stimulus, during which PNs depolarize and fire rapidly. The firing behavior of PNs during this phase varies, where some fire more homogeneously and others fire with more burst-like behavior. Finally, following olfactory stimulus termination, I 2 or AHP is characterized by a long lasting hyperpolarization of PNs for 1 second. PN voltage trace was taken from Heinbockel et al. (Heinbockel, Christensen, and Hildebrand, 1999)

Experimental Data
Experimental data was collected from our collaborator Dr. Hong Lei at Arizona State University. In the sphinx moth Manduca sexta, the cell bodies of uniglomerular AL PNs are located within the medial cluster, a convenient target for identifying PNs (figure 1.3A); dye injection into glomerular neuropil often results in partial staining at the soma. Data from such PN recordings, in response to scented and non-scented air puffs at various air flow speeds, are shown in figure 1.3. We recorded from a total of 10 PNs, most of which showed a clear increase in spike rate in response to non-scented air puffs. One representative example is shown in figure 1.3. This PN displayed clear responses to mechanical stimulation alone (figure 1.3D), with a stronger response to air puffs infused with pheromone (which provides both chemical and mechanical stimulation) (figure 1.3E). Furthermore, within our recorded PN population, increasing the puffing speed of non-scented air puffs from 0.5 liter/min (low speed) to 1 liter/min (high speed) increased the intensity of the response of the PN population, as shown in figure 1.3B,D,F. Published work in a noctuid moth (Spodoptera littoralis) has reported similar phenomena (Han, Hansson, and Anton, 2005;Froese, Szyszka, and Menzel, 2014).
We further parse the dependence of the PN response on air speed from the data displayed in figure 1.3. The sample PN did not respond to non-scented air puffs at low speed (figure 1.3B), but displayed a clear, long-lasting response to pheromone-infused air puffs at low speed (figure 1.3C); the correlation coefficient of these two response patterns (based on peristimulus time histograms) is rather low (r=-0.19). However, at high air-puffing speed, the PN exhibited a rather robust bursting response to non-scented puffs (figure 1.3D), but showed a clear and substantial increase in response intensity to pheromone-infused air puffs at the same speed (figure 1.3E); interestingly, these two response patterns are remarkably similar (r=0.67).
Thus, the data indicate that PNs respond robustly to strong mechanosensory input (i.e., high wind speed), even in the absence of an olfactory signal. Moreover, mechanical and chemical input appear to trigger distinct response patterns in PNs -strong mechanosensory input alone elicits a transient, temporally precise burst of spikes lasting a few hundred ms, while olfactory input alone (at low wind speed, mechanical input is reduced) yields a sustained spiking response lacking temporal precision. When the two modalities are combined (i.e., odor delivered at high wind speed), both of the corresponding response patterns appear to merge and contribute to PN dynamics -PN responses exhibit a large, transient, temporally precise burst of spikes followed by a lower-intensity sustained spiking response.
Finally, it is tantalizing that there is a high correlation between a PN's response pattern to strong mechanosensory input alone and its response pattern to strong mechanosensory input plus olfactory input; this suggests that, in natural environments, strong mechanosensory input may serve to mold and shape the dynamic, correlational structure of PN responses (see Discussion for further elaboration upon this latter observation). 3 Mechanosensory input shapes PN response patterns. A) Confocal microscopic images show a single PN cell body (arrow) located in the medial cluster, labeled with Lucifer yellow fluorescent dye. The square in A1 is magnified in A2. MC: medial cluster of cell bodies; LC: lateral cluster of cell bodies; G: glomerulus; D: dorsal; V: ventral; L: lateral; M: medial. B-E) Response of a representative PN to consecutive non-scented air puffs or pheromone-infused air puffs. While responses to pheromone-infused air puffs are stronger, non-scented air puffs induce robust responses as well. The peristimulus histograms were based on responses to 5 puffs of non-scented air (B1) and pheromone blend (C1) at low air speed, and responses to the same stimuli but at high air speed (D1, E1). Examples of the raw intracellular spike traces show response to single stimulus puff under each air speed-stimulus scenario (B2, C2, D2, E2). Note that a non-scented air puff at high speed evoked a response pattern similar to that evoked by pheromone at high puffing speed. The correlation coefficient between D1 and E1 is 0.69 whereas the correlation coefficient between B1 and C1 is only 0.19. F) Response to non-scented air puffs is markedly stronger in high air speed than in the low air speed. Scatter plot (F1) shows the averaged firing rate during responses to air puffs in 10 different PNs; the plot is mostly biased towards the high air speed. Mean PN response (averaged over PNs) to a non-scented air puff at low or high puffing speed (F2, n=10), however, was not statistically significant (Sign test, p=0.15).

Chapter Two
Developing the Model

Model Summary
In order to examine the mechanisms underlying AL responses to olfactory or mechanosensory input, as well as the juxtaposition of the two, we construct a realistic, large-scale, spikingnetwork model of the moth AL; the model consists of six glomeruli, with 10 PNs and 6 LNs per glomerulus (Homberg, Christensen, and Hildebrand, 1989;Kingan and Hildebrand, 1985;Hoskins et al., 1986;Hildebrand, Hall, and Osmond, 1979;Matsumoto and Hildebrand, 1981;Christensen and Hildebrand, 1987a;Homberg, Montague, and Hildebrand, 1988). Individual PNs and LNs are governed by integrate-and-fire spiking dynamics, with random but fixed network connectivity -LNs synapse onto other LNs within the same glomerulus and onto PNs both within and across glomeruli, while PNs synapse only onto PNs and LNs within the same glomerulus (Reisenman et al., 2004;Lei, Christensen, and Hildebrand, 2004). LNs are GABAergic and inhibit other neurons through fast GABA A receptors, and LNs also deliver a slow inhibitory current to PNs, acting over ∼500-1000 ms time scales, via slower metabotropic GABA receptors. PNs within the model are cholinergic and act synaptically through fast nicotinic acetylcholine receptors; PNs are also equipped with an intrinsic calcium-dependent potassium (SK) current that activates following several PN spikes and serves to curtail further spiking (Mercer and Hildebrand, 2002b;Mercer and Hildebrand, 2002a). Figure 2.1 Schematic of model AL network. Each column represents a glomerulus; squares represent PNs (10 per glomerulus) and circles represent LNs (6 per glomerulus). Arrow heads indicate excitation, while bar heads indicate inhibition. Within a glomerulus, all cell types form synapses with each other (with cell typespecific connection probabilities), while glomerular cross-talk is mediated only via LN→PN synapses. An odor is simulated via delivery of excitatory stimulus current to all cells within a subset of three glomeruli (solid incoming arrows), while strong mechanosensory input is simulated via delivery of excitatory stimulus current to all cells within all glomeruli (dashed incoming arrows).
We simulate both chemosensory and mechanosensory input to the model, both in isolation and in conjunction. In accordance with the well-established combinatorial odor code employed by olfactory receptor neurons (ORNs) (Joerges et al., 1997;Vickers, Christensen, and Hildebrand, 1998;Malnic et al., 1999;Ache and Young, 2005;Wang et al., 2003;Ng et al., 2002), an odor (in the absence of significant mechanosensory input) is simulated by delivering an excitatory stimulus current to all cells within a subset of model glomeruli (half of model glomeruli are designated to receive stimulus current); different odors are simulated by varying the composition of the glomerular subset receiving stimulus current. Mechanosensory input is modeled by sending stimulus current to all cells within the entire AL network, in accordance with our data indicating that PN responses to mechanosensory input are widespread and, seemingly, non-specific. Stimuli, whether olfactory or mechanosensory, are delivered in the form of a 1 second current pulse.
We employ two paradigms to simulate both modalities in conjunction (i.e., an odor delivered within the context of strong mechanosensory input due to high wind speed): (i) Additive Paradigm -the stimulus current due to mechanosensory input and odor input are simply added together to construct the high wind speed odor stimulus; (ii) Normalized Paradigm -the stimulus current due to mechanosensory input and odor input are both halved in amplitude then added together. Paradigm (i) may be more akin to physiological reality, since PN responses from our data (figure 1.3) are suggestive of the possibility that the mechanosensory response and the odor response of a PN augment each other to obtain the response to an olfactory signal delivered at high wind speed. Paradigm (ii) allows analysis of network dynamics when net excitation to the AL is kept approximately constant in the three cases of odor input alone, mechanosensory input alone, and odor+mechanosensory input, permitting a more distilled comparison of the dynamical effects of the two modalities in isolation and in conjunction. Figure 2.1 shows a schematic of the model network.

Model Details
We construct a spiking model of the AL network that strives to attain enough architectural complexity to achieve the complex dynamics of the AL while maintaining enough simplicity to allow for investigation of core mechanistic components. Below, we elaborate the components and connectivity of our model.

The Neuron Model
The model is composed of two subclasses of neurons: excitatory, cholinergic PNs and inhibitory, GABAergic LNs. The membrane potential of the j th PN (V j P N (t)) or the j th LN (V j LN (t)) are modeled using integrate-and-fire dynamics by the following set of ODEs, which include both intrinsic and synaptic currents: PN j in the model is equipped with an intrinsic slow potassium current (SK), and receives stimulus-induced input (from external background, odor, and mechanosensory sources), fast excitatory input from other PNs, fast inhibitory input from LNs, and slow inhibitory input from LNs. LN j in the model receives stimulus-induced input (from external background, odor, and mechanosensory sources), fast excitatory input from PNs, fast inhibitory input from other LNs, and slow inhibitory input from other LNs. In these equations, V L = 0, V exc = V stim = 14 3 , and V SK = V inh = − 2 3 (expressed in nondimensional units) represent reversal potentials associated with leakage, excitation, and inhibition respectively. The leakage timescale is given by τ V = 20ms. Upon any neuron reaching a threshold voltage of V thres = 1, a spike is recorded and its voltage subsequently reset to V L = 0 (and held at V L = 0 for a refractory period of τ ref = 2ms). The neuron model is based on a reduced dimensional integrate-and-fire model previously developed in the literature (Tao et al., 2004;Lei, Yu, et al., 2016).
The term g j exc (t) represents the membrane conductance of neuron j to excitatory synaptic input from PNs, and is modeled as follows: In this equation, S represents the set of all spike times of all PNs presynaptic to neuron j. The parameter S P N is the coupling strength of a network PN to neuron j; S P N = .01 if neuron j is a PN, while S P N = .006 if neuron j is an LN. The function α exc (t|s) has instantaneous rise time and exponential decay time, with time constant τ exc = 2ms (whether neuron j is an LN or a PN).
The other synaptic conductances, g j inh (t) and g j slow (t), as well as the stimulus conductance, g j stim (t), are modeled similarly:.
For the g j inh (t) and g j slow (t) equations, S represents the set of all spike times of all LNs presynaptic to neuron j. For the g j stim (t) equation, S represents the set of all spike times of the external input delivered to neuron j; these stimulus-induced spike times arise from simulation of background input, odor input, and mechanosensory input as Poisson processes of incoming spike events (see Stimulus Modeling section below for details). If neuron j is a PN, the coupling strengths are given by S inh = 0.0169, S slow = .0338, and S stim = .004, while if neuron j is an LN, the coupling strengths are given by S inh = 0.015, S slow = .04, and S stim = .0031. The fast inhibition and stimulus timescales are comparable to excitation, with τ inh = τ stim = 2ms, while the slow inhibition time scale is dramatically slower, with τ slow = 750ms (whether neuron j is a PN or an LN).
Finally, the SK current is an intrinsic slow potassium current, displayed by only PNs, that activates upon spiking and serves to curb further spiking activity. Rather than an instantaneous jump, the rise time of the SK current is modeled as sigmoidal; this noninstantaneous rise time allows PNs to potentially emit multiple spikes prior to suppression of firing activity by the SK current. The SK current for PN j is modeled as follows: S represents the set of all firing times of PN j. The strength S SK of the SK current is a randomly determined, but fixed, parameter, and hence varies from PN to PN; the value of S SK for PN j is drawn from a normal distribution with mean µ = .5 and standard deviation σ = .2. While rare, it is possible for S SK to be negative with this distribution, so any negative value for S SK is manually set to 0. The parameter τ SK = 250ms, and the rise of the SK current is modeled as sigmoidal with a half-rise time of τ rise = 25ms.
In the above, H(t) is the standard Heaviside Step Function:

Network Architecture
Our AL model consists of 6 glomeruli, with each glomerulus consisting of 10 PNs and 6 LNs; connectivity within glomeruli is dense in comparison with relatively sparse connectiv-

Stimulus Modeling
Rather than explicitly modeling the behavior of ORNs or the cells responsible for mechanosensory sensory inputs, input to each cell within the network is modeled as a Poisson process of incoming spikes. An incoming spike to neuron j within the network is modeled as an instantaneous jump in g j stim (t) of size .004 if neuron j is a PN, or .0031 if neuron j is an LN, followed by exponential decay with time constant τ = 2ms (whether neuron j is a PN or an LN). Each cell has three potential sources of input; all cells receive a background rate of λ back = 3.6 spikes/ms, while odor input (simulating the presence of a single odor) is delivered at a maximum rate of λ max odor = 3.6 spikes/ms and mechanosensory input is delivered at a maximum rate of λ max mech = 1.8 spikes/ms. The total rate of incoming spikes for the j th cell is therefore given by: where O j (t) and M j (t) are functions that range between 0 and 1 and serve to model the temporal dynamics of odor and mechanosensory input pulses, respectively.
To simulate background AL activity, we set λ j odor = 0 and λ j mech = 0 for all j. To simulate a single odor (without simulation of mechanosensory input) presented at time t on and removed at time t of f , we send odor-induced input to all cells within 3 out of 6 model glomeruli (with the glomerular subset signifying odor identity); we therefore set λ j odor = 0 if cell j belongs to an unstimulated glomerulus and λ j odor = λ max odor if cell j belongs to a stimulated glomerulus, and set λ j mech = 0 for all j. To simulate a pulse of mechanosensory input (without an accompanying olfactory stimulus) from time t on to time t of f , we set λ j odor = 0 and λ j mech = λ max mech for all j. Hence, within the model, olfactory input stimulates a focal glomerular subset, while mechanosensory input represents a global signal delivered to the entirety of the AL.
In addition to simulating olfactory and mechanosensory input in isolation, we also simulate the two in combination. To simulate a stimulus pulse (from time t on to time t of f ) consisting of a single odor accompanied by a mechanosensory signal, we employ two distinct paradigms -the additive sensory integration and the normalized sensory integration paradigms. In the additive sensory integration paradigm, we set λ j odor = 0 if cell j belongs to a glomerulus not responsive to the odor and λ j odor = λ max odor if cell j belongs to a glomerulus activated by the odor, and set λ j mech = λ max mech for all j. In the normalized sensory integration paradigm, we set λ j odor = 0 if cell j belongs to a glomerulus not responsive to the odor and λ j odor = 1 2 λ max odor if cell j belongs to a glomerulus activated by the odor, and set λ j mech = 1 2 λ max mech for all j. Hence, the additive paradigm simply 'adds' together the isolated olfactory and mechanosensory signals, while the normalized paradigm scales the two signals in order to maintain a similar overall level of excitation sent to the AL network in comparison to the cases of olfactory input or mechanosensory input in isolation.
Finally, to simulate two odors simultaneously (as in figure 3.6), we simply 'add' the inputs resulting from the two odors in isolation. In other words, we set λ j odor = 0 if cell j belongs to a glomerulus stimulated by neither odor, λ j odor = λ max odor if cell j belongs to a glomerulus stimulated by only 1 of the 2 odors, and λ j odor = 2λ max odor if cell j belongs to a glomerulus stimulated by both odors.
The function O j (t) represents the temporal dynamics of the olfactory component of a stimulus pulse beginning at time t on and ending at time t of f (with t of f − t on = 1000ms -i.e., stimulus pulses are modeled as having a 1 sec duration). The function O j (t) = 0 for t < t on ; at time t on , O j (t) increases from 0 to 1 with a prescribed rise time, while for t > t of f , O j (t) decreases from 1 to 0 with a prescribed decay time. If neuron j is a PN, rise is sigmoidal with a half-rise time of τ rise = 35ms, while decay is exponential with τ decay = 384ms: If neuron j is a LN, rise is instantaneous, while decay is exponential with τ decay = 384ms: Similarly, the function M j (t) represents the temporal dynamics of the mechanosensory component of a stimulus pulse beginning at time t on and ending at time t of f (t of f − t on = 1000ms). The function M j (t) = 0 for t < t on ; at time t on , M j (t) increases from 0 to 1 with a prescribed rise time, while for t > t of f , M j (t) decreases from 1 to 0 with a prescribed decay time. If neuron j is a PN, rise is instantaneous and decay is exponential with τ decay = 384ms: If neuron j is a LN, τ rise = 300ms and τ decay = 384ms: We included a significantly longer rise time for mechanosensory input to LNs, relative to that for PNs, in order to ensure that global LN inhibition at the inception of a stimulus pulse (mediated by fast inhibitory synapses) is not overwhelmingly powerfully enough to prevent PN spiking altogether, and that substantial suppression of PN spiking must await the lengthy activation time of slow inhibitory synapses. This assumption, however, is not necessarily required to obtain physiologically reasonable dynamics -for example, weakening fast inhibitory synapses from LNs to PNs or strengthening slow inhibition while reducing the density of LN→PN synapses can yield similar dynamical effects without such a disparity in rise times. Since the dynamics of mechanosensory input to AL cells has not yet been studied within the experimental literature, we (somewhat arbitrarily, due to ignorance of the actual physiological mechanism at play) chose to include this mechanism of a disparity in rise times to ensure robust PN spiking at stimulus onset. However, we note that including a disparity in rise times does not affect the basic dynamical behavior of the model, other than delaying suppression of PN spiking at stimulus onset.

Model Dynamics with Olfactory Input in Isolation
We begin by probing model responses to olfactory input alone (i.e., without simulating mechanosensory input), modeled as strong, focal stimulus current delivered to a subset of AL glomeruli (glomeruli 1,2, and 3). We verify that model responses to olfactory input alone recapitulate the salient features of experimentally observed moth AL odor dynamics, and we further dissect the dynamical mechanisms underlying model behavior. Experimentally, during prolonged odor presentation PNs within activated glomeruli tend to exhibit a characteristic triphasic response; the first phase (I 1 ) occurs at odor onset and consists of a brief membrane potential hyperpolarization that lasts ∼50 ms, after which rapid depolarization accompanied by spiking ensues for the duration of the stimulus (phase II), while odor offset triggers the third phase (I 2 , also called the AHP phase) of hyperpolarization followed by a slow decay back to background over ∼1 sec (Christensen and Hildebrand, 1987b;Waldrop, Christensen, and Hildebrand, 1987;Christensen and Hildebrand, 1988;Christensen and Hildebrand, 1990;Christensen, Waldrop, Harrow, et al., 1993).  induced by the stimulus (Reisenman et al., 2004;Lei, Christensen, and Hildebrand, 2004).
Figure 3.1A further shows that PNs within activated glomeruli exhibit the characteristic triphasic odor response observed experimentally. Phase I (the I 1 phase) occurs due to the stimulus current inducing LNs to reach threshold prior to PNs; hence, odor onset yields an initial burst of synchronized LN spikes within activated glomeruli, leading to compounded fast inhibition from LNs briefly hyperpolarizing and silencing glomerular PNs. Following the initial burst of LN spikes, LN activity desynchronizes and diminishes slightly (due to LN→LN fast synaptic inhibition), allowing PN depolarization to commence and phase II PN spiking to ensue. This is consistent with experimental evidence showing that direct GABA application mimics an I 1 -type response in PNs and that the GABA antagonist bicuculline eliminates the I 1 phase of odor-evoked PN activity (Waldrop, Christensen, and Hildebrand, 1987;Christensen and Hildebrand, 1988;Christensen, Waldrop, Harrow, et al., 1993;Christensen, Waldrop, and Hildebrand, 1998); indeed, blockade of fast GABAergic synapses within our model eliminates the phase I hyperpolarization of PNs following odor onset (figure 3.3A). As SK strength increases, firing behavior shifts from being continuous to bursting.
(C) The standard deviation of interspike interval during odor stimulation was used to quantify the burstiness of a PN. A small standard deviation represents relatively homogeneous firing, while a larger standard deviation represents fluctuations between short interspike intervals within a burst and long interspike intervals between bursts. The scatter plot shows SK strength and standard deviation in interspike interval for each PN during odor presentation (only PNs within active glomeruli are included). A positive correlation of r=0.57 reveals that SK currents indeed play a role in the emergence of heterogeneous bursting behavior.
However, while experiments indicate that the I 1 response seems driven by GABA A receptors, the mechanisms underlying the phase II response and the AHP (or I 2 ) phase are empirically less well-understood. During the phase II response, PN spike patterns can vary broadly across PNs; within active glomeruli, some PNs fire spikes in sporadic or irregular bursts, while others fire more continuously at moderate (∼50 Hz) firing rates, with a range of response patterns intermediate between the extremes of bursting and continuous firing.
Moreover, the phase II dynamics exhibited by a PN shows no spatial dependency -in fact, a significant amount of intraglomerular variability has been observed during stimulation (Christensen, Pawlowski, et al., 2000).  fixed at a high value for all PNs (right), suggesting that a lack of SK currents tends to yield continuously firing PNs, while potent SK currents tend to produce burst-like PN behavior. This is further corroborated by measuring the phase II behavior of a single, fixed PN as the strength of its SK current is varied -figure 3.2B shows that the phase II response pattern of a PN undergoes a clear, progressive, and gradual transition from continuous firing behavior to sporadic bursting behavior as SK strength is increased. Indeed, within the normal network (with randomly drawn SK strengths), there is a substantial correlation between the degree of burst-like behavior and SK current strength across PNs (figure 3.2C).

Figure 3.3 (A)
Raster plot of the model AL during odor presentation with no mechanosensory input (left) and membrane potential, SK current, incoming synaptic excitation, slow inhibition, and fast inhibition for a sample PN (right); plots shown are in the case that fast inhibition is removed from the network. Note that removing fast inhibition diminishes the phase I hyperpolarization (I 1 ) of PNs upon odor onset. (B) Similar plots as in (A), but with slow inhibition rather than fast inhibition removed from the network. Note that removing slow inhibition eliminates the prolonged AHP phase (I 2 ) of PNs following odor offset. Black bar represents odor stimulus.
Within our model, the AHP (or I 2 ) phase of lengthy hyperpolarization following prolonged odor presentation emerges as a dynamical consequence of slow inhibition from LNs to PNs.
During phase II spiking in the midst of prolonged odor presentation, the slow inhibitory current activates and exerts a damping effect on PN spiking, but the potent odor-induced current impinging upon stimulated glomeruli is still able to elicit substantial PN spiking responses. Upon odor offset, however, the odor-induced current rapidly dissipates, while slow inhibition from LNs to PNs decays over a longer 1-2 second time scale, allowing the gradually dwindling slow inhibitory current to suppress PN activity for ∼1 second following odor offset. Indeed, severing slow inhibitory synapses within the model virtually eliminates the AHP phase of PN odor dynamics, and PNs return to background activity levels immediately following odor offset (figure 3.3B).

Model Dynamics with Mechanosensory Input
We now examine the behavior of our model with the inclusion of strong mechanosensory input, simulated as a one second current pulse delivered to all glomeruli, though weakened in comparison to an odor-induced current pulse to a stimulated glomerulus (an odor alone, as in the previous section, is simulated as a stronger one second current pulse delivered to only three glomeruli). Thus, we construct four stimulus scenarios: (i) odor only, with no mechanosensory input, which simulates odor delivered at low wind speed; (ii) mechanosensory input only, which simulates a nonscented, high speed air puff; (iii) additive paradigm of high wind speed odor delivery, simulated by simple summation of the current pulses in the odor-only and mechanosensory-only scenarios; (iv) normalized paradigm of high wind speed odor delivery, simulated by halving then summing the current pulses in the odor-only and mechanosensory-only scenarios. The additive paradigm is likely more representative of the physiological reality of moth AL dynamics in response to high wind speed odor presentation (the moth data in figure 1.3 suggest that PN responses to high wind speed odor stimuli are approximately given by the sum of the response to mechanosensory input alone and odor input alone). However, the normalized paradigm maintains similar net excitation to the AL as in the odor-only and mechanosensory-only scenarios, allowing direct comparison of scenarios (i), (ii), and (iv); this permits distillation of the dynamical effects of odor input and mechanosensory input alone, and the two in conjunction, without the potential confound posed by variation in the net integrated excitation impinging upon the AL.

Odor Discrimination Dynamics within the Model
Experimental studies show that simultaneous presentation of multiple odors can actually have a damping effect on responses within the moth AL, often resulting in less intense network-wide PN activation than in the case of single-odor presentation (Lei and Vickers, 2008;Silbering and Galizia, 2007;Yamagata et al., 2009). Our model exhibits behavior consistent with these empirical observations -simultaneous presentation of two odors that activate sufficiently disparate sets of glomeruli triggers network-wide inhibition that is stronger than the enhancement in excitatory ORN input to the network resulting from simulating two odors (rather than a single odor), producing a net suppressive effect on model dynamics (figure 3.6A). This is due to the diffuse, glomeruli-spanning LN network (Reisenman et al., 2004;Lei, Christensen, and Hildebrand, 2004); simultaneous presentation of two odors, provided the odors activate minimally overlapping glomerular subsets, activates a broad swath of this LN network (in comparison to a single odor), resulting in a substantial increase in the barrage of globally pervasive slow (and fast) inhibitory inputs impinging upon PNs across glomeruli that more than offsets the greater stimulus-induced excitation.
We further assess the ability of PN activity within our model to classify different odors.
Since a single odor within our model is represented by the identity of the three (out of six) glomeruli that receive odor-induced stimulus current, this implies that our model is capable of simulating a suite of 20 distinct odorants. We employ a simple linear classification scheme to test the ability of PN activity within the model to discriminate among the panel of twenty odorants -each odorant is represented by a template, given by the trial-averaged vector of PN firing rates in response to presentation of the odor (100 trials per odor), and each trial is designated as 'correctly classified' by the network if the distance between the vector of PN firing rates corresponding to that trial to the various odor templates is minimized for the correct odor template (see Appendix A for details). Interestingly, however, figure 3.6B (left) indicates that while the odor-only scenario yields more accurate odor classification during the initial few hundred ms of the odor response, the additive sensory integration scenario actually yields slightly higher classification rates during the subsequent few hundred ms of the odor response (with the two scenarios yielding comparable performance after ∼500 ms). The reason for this can be ascertained by compar-ing spike rasters of odor-stimulated glomeruli in the two scenarios (figure 3.4A versus figure   3.4C); note that, in glomeruli receiving olfactory input, the initial burst of PN spikes at odor onset in the additive sensory integration case outlasts the initial burst in the odor-only case by a few hundred ms, which presumably enhances the separation between distinct odor templates in the 60 dimensional PN phase space for the additive sensory integration scenario in comparison to the odor-only scenario (beginning a few hundred ms after odor onset and ending ∼500 ms after odor onset). Thus, odor discrimination is better in the additive sensory integration case versus the odor-only case during this brief temporal window.
This feature of odor classification dynamics is an emergent consequence of the slow inhibitory current from LNs to PNs. In the odor-only scenario, odor-stimulated glomeruli receive less net ORN input than in the additive sensory integration scenario, since in the latter scenario odor-stimulated glomeruli receive the odor-induced signal (as in the former scenario)

Discussion
In this work, we present experimental evidence showing that PNs within the moth AL respond not only to ambient olfactory stimuli, but also to mechanosensory signals arising from high-speed air flow across the antennae, firmly establishing the AL as a structure that integrates input from multiple sensory modalities (rather than simply responding to olfactory input

Biological Implications and Hypotheses
The Odor Discrimination Regime: A relatively small level of mechanosensory input (e.g., when the insect has landed on the surface of or is hovering near a food source) may place the AL within an odor-discrimination dynamic regime (since, without strong, rapidly fluctuating mechanosensory input, tracking odor pulses is less meaningful while fine odor discrimination, enhanced by lost-lasting odor inputs, may be a more profitable endeavor). When air speed is low, the minimal mechanosensory input may fail to induce large, correlated subthreshold voltage fluctuations across PNs, and accompanying odors may then yield uncorrelated and lower intensity spiking responses across PNs within responsive glomeruli. Additionally, PN responses may be longer-lasting, sacrificing temporal precision for duration. Thus, AL activity is globally unorganized, and is instead dominated by 'patchy' local dynamics unfolding over prolonged time scales, placing the network within a regime devoted to parsing the multitude of environmental odors (rather than tracking rapidly fluctuating odor pulses).
This picture of the biological role of the AL is suggestive, and we therefore propose three overarching, testable hypotheses about the effects of mechanosensory input on AL dynamics: (1) Strong mechanosensory input correlates activity across PNs and glomeruli and results in greater global coherence and synchrony; (2) Strong mechanosensory input enhances the temporal precision and pulse-tracking ability of PN responses; (3) Strong mechanosensory input diminishes the ability of AL activity to discriminate among similar odors (as suggested by figure 3.6).
Thus, within the insect, strong mechanosensory input may serve as a 'switch' that alternates the AL between odor tracking and odor discrimination dynamic regimes. In the absence of strong mechanosensory input, there is little environmental information to guide tracking of an odor source, and hence the AL may employ locally disconnected, 'patchy', long-lasting dynamics to devote its resources to fine odor discrimination. In the presence of strong mechanosensory input, however, the AL may 'switch' to a more globally coherent regime with temporally precise responses; this allows AL activity to faithfully follow the spatiotemporal dynamics of environmental odor pulses and track an odor source, while sacrificing the ability of network dynamics to finely discriminate among similar odors.

Sources of Mechanosensory Input to the AL
While our data clearly indicate that AL neurons respond to mechanosensory input in the form of air speed and pressure, this observation leads to a natural query: what are the potential mechanisms by which both mechanosensory and chemosensory information to glomeruli within the AL are conveyed? Olfactory input to the AL is well-known to arise from antennal ORNs, yet the source of mechanosensory input is less certain. However, there are two apparent possibilities that exist. The first may be similar to a mechanism found in vertebrate ORNs. In one study (Grosmaitre et al., 2007), mouse ORNs were shown to respond to both olfactory and mechanical stimuli, and inhibiting adenylyl cyclase completely blocked both types of responses, suggesting that cyclic adenosine monophosphate (cAMP) is involved as a second messenger. Furthermore, knocking out CNG channels eliminated mechanosensitivity. The authors speculated that either some odorant receptors are sensitive to mechanical pressure or a mechanosensor in the membrane might cross-link to the cAMP cascade. In Manduca sexta, CNG channels are believed to be similar to those in vertebrates and are directly activated by cAMP and another second messenger, cGMP (Krannich and Stengl, 2008). The similarities in signal cascade pathways between moth and mouse ORNs may be indicative of physiological similarities as well. The second possibility may be related to the physical proximity of specialized mechanosensitive neurons and ORNs. The somata of bipolar ORNs reside below the base of the sensilum in close physical proximity to one another (Keil, 1989); the axons of mechanosensory neurons (such as those from the Johnston's organ) travel in the same nerve bundle as the axons of ORNs towards the brain (Keil, 1989;Sane et al., 2007), providing opportunities for ephaptic interactions between axons (Jefferys, 1995;Anastassiou et al., 2011;Hillier and Vickers, 2011). The ephaptic effects may be further augmented by the fact that invertebrate neurons lack compact myelin sheaths (Zalc, 2016).

Future Directions
Our future work will involve further testing, through combined experimental and computational work, of the hypotheses described above. We will examine the effects of strong mechanosensory input on the correlational structure of PN responses across glomeruli, assessing its effects on global coherence and synchrony within the AL. We will also assess the effects of high air-speed stimuli on the odor discrimination ability of AL activity in order to further refine and probe the mechanisms underlying the modeling results presented in this paper (figure 3.6).
In particular, we will investigate the ability of PN activity (individually and in aggregate) to track transient odor pulses. Odor stimuli tend to present in nature as a series of discontinuous filaments that occur with higher spatial frequency and in increasing concentration as the odor source is approached. Thus, as a moth travels towards an odor source, it encounters brief pulses of odor that tend to occur at a more rapid rate as the odor source becomes less distant (Murlis, Elkinton, and Carde, 1992). Additionally, behavioral experiments in which male moths were tested using the female pheromone blend have indicated that intermittent stimuli are more effective at prompting the male moths to exhibit source-seeking behavior than continuous odor plumes (T. Baker, M. Willis, et al., 1985;T. Baker, Hansson, et al., 1988;T. Baker, 1989;Kramer, 1992;Kaissling and Kramer, 1990). Collectively, these results suggest that the ability of PNs to track stimuli delivered in a pulsatile fashion may be more behaviorally relevant than measuring static responses.
Indeed, experiments show that a series of short (several hundred ms) odor pulses evokes a sequence of corresponding spike trains in activated PNs; each individual pulse produces an I 1 hyperpolarization followed by phase II depolarization and a burst of spikes, with pulse offset eliciting abrupt truncation of spiking activity. The prolonged AHP phase, however, does not manifest until the end of the final pulse in the stimulus train (Christensen, Waldrop, and Hildebrand, 1998;Lei, Christensen, and Hildebrand, 2002). Intracellular recordings from AL neurons using 50 ms odor pulses show that moth PNs act as low-pass filters of pulse rate (each cell tracks odor pulses with bursts of spikes up to a certain cutoff frequency that varies across PNs). Remarkably, PNs have been found that are capable of tracking up to ten odor pulses per second, while pulse rates exceeding a cell's cutoff frequency elicit responses consisting of tonic firing. Furthermore, the cutoff frequency for pulse tracking is directly related to the amplitude of the I 1 hyperpolarization -PNs that display large I 1 membrane potential deflections are capable of locking to higher pulse rates (Christensen and Hildebrand, 1997;Heinbockel, Christensen, and Hildebrand, 1999). The transiency of experimentally observed PN responses to odor pulses tantalizingly mirrors the effects of strong mechanosensory input on AL dynamics explored in this paper. Experimentally assessing the effects of strong mechanosensory input on features of PN pulse-tracking ability, while concurrently employing computational modeling to dissect and clarify the underlying dynamical mechanisms, will provide a valuable avenue for investigating the nature, function, and purpose of sensory integration within the AL.

Appendix A Simulation, Stability, and Data Analysis
Means and standard deviations are taken over 100 trials. Normalized firing rates (as in figure 3.5) are determined by dividing the firing rate during a period of interest (in our case, the last 500ms of an odor pulse) by the firing rate during 1 second of background activity (both averaged over 100 trials). Thus, a normalized firing rate greater than 1 represents enhanced spiking activity (over background) while a normalized firing rate less than 1 represents reduced spiking activity (relative to background).
Odor discrimination rates within the model (as in figure 3.6) are determined using a linear classification scheme. To calculate the time-dependent ability of the network to discriminate among n stimuli, we split the total simulation time into nonoverlapping 10ms time bins; for stimulus i ∈ [1, n] and time bin k, we construct a template for stimulus i in time bin k as the 60-dimensional vector of PN firing rates within time bin k averaged over 100 trials of stimulus i presentation. This yields a total of 100n odor trials and n odor templates for time bin k. For an individual stimulus trial (for, say, stimulus l ∈ [1, n]), we designate the trial as 'correctly classified' within time bin k if the Euclidean distance between the 60-dimensional vector of PN firing rates for that trial and each of the n odor templates is smallest for the template for odor l; otherwise, we designate the trial as 'incorrectly classified'. The classification rate of the network in time bin k is then determined as the number of 'correctly classified' odor trials within time bin k divided by 100n.
Numerical simulations were carried out using the Euler Method with a time step of ∆t = 0.1ms. Stability was verified by observing qualitatively similar behavior with a timestep an order of magnitude smaller, as seen in figure A.1.

Model code was written in C++ with data analysis and plotting carried out in Matlab.
Model code is available in Appendix C.

Appendix B Varying Pulse Length and Frequency
This section contains information on the most recent investigation of variable pulse length and pulse frequency. I did not feel this section is complete enough to include in the regular results section, but there is some interesting preliminary data that will be discussed here.

B.1 Pulse Length
Experimental studies show that PNs are able to encode the length of olfactory stimulus through the length of their own phase II firing period (Christensen, Waldrop, and Hildebrand, 1998;Lei, Christensen, and Hildebrand, 2002). To see if our model reproduces this behavior, we created simulations with variable olfactory pulse lengths. To determine the start of the PN response to olfactory stimulus, we simply recorded the first spike following the IHP.
The cutoff for the firing response was assigned when the interspike interval was greater than three times the interspike interval of the first 5 spikes following the IHP. Choosing such a high cutoff for the interspike interval serves not only to create a conservative guess on the length of the PN response, but also serves to account for the fact that firing rate is  complex dynamics of short odor plumes and pulses, rather than single, long-lasting odors.

B.2 Pulse Frequency
In addition to encoding pulse length, we are interested in determining the PNs's ability to follow pulses at a fixed frequency. As stated previously, insects are required to resolve the complex dynamics of pulses of stimulus rather a single, long-lasting stimulus. Because the frequency of these pulses contains information such as the distance from the odor source, accurately following pulse frequency is a requirement of the AL. To model this, we simulate short 50 ms pulses at varying frequencies. At this time we lack a methodology for quantifying a frequency cutoff, though a qualitative picture of model dynamics can be observed in figure   B.3.
As can be seen in B.3A, when presented with odor pulses at a low enough frequency nearly all PNs within the model are able to track pulses precisely. However, as pulse frequency increases fewer PNs are able to precisely track frequency and instead display a response very similar to a single, long-lasting stimulus. However, when presented with only mechanosensory stimulus, as shown in figure B.3B, PNs tend to be able to track pulses at a much higher frequency than in the odor only paradigm. This is likely due to the pervasive slow inhibition throughout the model which allows for suppression of firing between the stimulus pulses. Similar to how this pervasive inhibition leads to the transient response of PNs under prolonged stimulus, this inhibition likely enhances the observed pulse frequency tracking.
Interestingly, when combining both olfactory and mechanosensory stimuli, as seen in figure   B.3C, it appears that PNs in glomeruli that are not stimulated by the odor actually pulse track better than those in stimulated glomeruli. This leads to the natural hypothesis that there is a division of labor within the AL; PNs within stimulated glomeruli are primarily responsible for encoding pulse length and odor identity, while those in nonstimulated glomeruli are responsible for tracking the pulse frequency. Further modeling and analysis will solidify With odor alone (A), most PNs are able to track pulse frequency at low rates but elicit responses similar to single, long-lasting stimuli when the rate is too high. In mechanosensory only (B), PNs tend to track better than odor alone, likely due to the pervasive slow inhibition in the neural network. When adding odor and mechanosensory (C), it appears that nonstimulated glomeruli track frequency very well, while stimulated glomeruli do not. these predictions, and will hopefully serve to elucidate some of the mechanisms behind the complex dynamical behavior observed during pulse tracking.

Appendix C The Model Code
In an effort to be organized, the model code is divided into various files by function. Upon compiling the code, these files are linked together to create the cohesive program. The entire code was written in C++. 130 v e c t o r <s t r i n g > Odor_String = { " . / 0 prob " , " . / 1 prob " , " . / 2 prob " , " . / 3 prob " , "