Built to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury
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Built to Last: Functional and structural mechanisms in the moth
olfactory network mitigate effects of neural injury
Charles B. Delahunt · Pedro D. Maia · J. Nathan Kutz
arXiv:1808.01279v3 [q-bio.NC] 11 Sep 2020
Abstract jury. More generally, robustness to injury is a vital design
principle to consider when analyzing neural systems.
Most organisms suffer neuronal damage throughout their
Keywords neuronal injury · injury mitigation · focal axonal
lives, which can impair performance of core behaviors. Their
swellings (FAS) · moth olfactory network
neural circuits need to maintain function despite injury, which
in particular requires preserving key system outputs. In this
work, we explore whether and how certain structural and
Author Summary
functional neuronal network motifs act as injury mitigation
mechanisms. Specifically, we examine how (i) Hebbian learn- Neuronal injuries and degeneration are commonplace across
ing, (ii) high levels of noise, and (iii) parallel inhibitory and species and organisms, compromising cognitive function and
excitatory connections contribute to the robustness of the neurosensory integration. Despite abrupt or gradual neuron
olfactory system in the Manduca sexta moth. We simulate impairment, neuronal circuits and networks must maintain
injuries on a detailed computational model of the moth ol- functionality of key outputs in order to provide robust per-
factory network calibrated to in vivo data. The injuries are formance. A common type of impairment found at the cellu-
modeled on focal axonal swellings, a ubiquitous form of lar level in traumatic brain injuries and in a number of lead-
axonal pathology observed in traumatic brain injuries and ing neurological diseases is known as Focal Axonal Swelling
other brain disorders. Axonal swellings effectively compro- (FAS). Similarly to demyelination, FAS typically distorts,
mise spike train propagation along the axon, reducing the confuses or blocks the information encoded in spike trains.
effective neural firing rate delivered to downstream neurons. We simulate FAS-inspired injuries on a detailed computa-
All three of the network motifs examined significantly mit- tional model of the olfactory circuitry of the Manduca sexta
igate the effects of injury on readout neurons, either by re- moth to examine the injury mitigation effects of various com-
ducing injury’s impact on readout neuron responses or by mon neural motifs such as high noise levels and Hebbian
restoring these responses to pre-injury levels. These motifs plasticity. Our results indicate that these motifs may serve
may thus be partially explained by their value as adaptive as adaptive mechanisms for mitigating the effects of neu-
mechanisms to minimize the functional effects of neural in- ronal injury. For example, the Hebbian learning mechanism
strongly mitigates effects of injury on system function by
Charles B. Delahunt protecting vital downstream neurons from effects of upstream
(a) Dept of Applied Mathematics, (b) Computational Neuroscience injury.
Center; University of Washington, Seattle, WA, USA.
E-mail: delahunt@uw.edu
Pedro D. Maia
Department of mathematics, University of Texas at Arlington, Texas, 1 Introduction
USA.
E-mail: pedro.maia@uta.edu Injuries are inevitable for most organisms, yet maintaining
J. Nathan Kutz a satisfactory level of functionality can be decisive for their
Dept of Applied Mathematics, University of Washington, Seattle, WA, survival. The progressive wear of a honeybees wings, for
USA. E-mail: kutz@uw.edu example, challenges the insect to sustain its load lift or face
2 Charles B. Delahunt et al.
Table 1 List of acronyms used throughout this article. to major forms of neuronal injury. They posit phenomeno-
logical input/output rules to transform healthy neuronal spike
AL Antennal Lobe PN Projection Neuron train responses into injured ones, with filters that can be ei-
EN Extrinsic (Readout) Neuron QN Inhibitory Projection Neuron
FAS Focal Axonal Swelling RN Receptor Neuron ther discrete-time (for spike trains) or continuous-time (for
FR Firing Rate SNR Signal-to-Noise Ratio
MB Mushroom Body SSNR Signal-to-Spontaneous Noise Ratio
firing rates) signal processors. These filters were derived mod-
MON Moth Olfactory Network eling the effects of demyelination and Focal Axonal Swellings
(FAS), which are present in a broad array of neurological
disorders [42, 30, 28, 27].
Fig.1C exemplifies how a FAS-like injury distorts the
less nourishing foraging trips [18, 39]. Functional robustness propagation of spike trains along the axon, effectively block-
is desirable for neural systems as well. While computer de- ing or filtering signals encoded to downstream neurons. In
vices operate in a regime of near-zero tolerance for phys- this work, we are agnostic concerning the exact biological
ical damage, the middle-aged human brain undergoes sig- underpinnings and pathological mechanisms that may affect
nificant neuronal losses on a daily basis [37]. Robustness to an injured/aging moth. Instead, we simply posit that its neu-
injury is often overlooked when analyzing the purpose and rons might be exposed to detrimental effects that can affect
function of neural structures while the transmission of max- their signaling capabilities. In this sense, and as explained in
imum information, high signal-to-noise ratio, and low en- Maia et al. [32], FAS-based filters provide a more nuanced
ergy consumption are often primarily considered [11]. Ana- way to model neuronal malfunction than purely binary abla-
lyzing neural information processing in the context of these tion which treats a neuron and/or its connections as either
principles is certainly important, but arguably incomplete. fully functional or 100% impaired. Recent computational
The goal of this work is to examine whether certain neural studies that consider the effects of FAS-like injury in neu-
mechanisms and architectural structures can be understood ral networks are providing new insight to decision-making
as adaptive, built-in systems for robustness to brain injury deficits [31], learning impairments [25, 41], memory deteri-
from trauma, aging, and/or other disorders. That is, we ex- oration [45], and motor-function decline [22].
amine how biological neural systems are “built to last”. In While FAS models effects at the level of spike trains, it
particular, we explore how certain neural architectures can also has a meaningful representation in Firing Rate models
protect the system’s key downstream outputs (the “deliver- such as MothNet. In particular, unlike ablation, FAS causes
ables” of the system) from the effects of damage to upstream reduced but still non-zero FRs. In addition, the low-pass fil-
regions. tering effect of FAS, which impacts closely-bunched clus-
The olfactory system of the Manduca sexta moth, though ters of spikes more than sparse spikes, in analogous manner
simple, shares many neural structures and mechanisms with impacts high FRs more strongly than low FRs. Thus FAS,
higher organisms [9, 21]. These include (i) Hebbian plastic- applied in a FR model, results in neuron FRs being reduced
ity, (ii) reward-triggered stimulation of neural outputs via but not ablated, with high FR neurons affected more strongly
neuromodulators, (iii) high noise levels, and (iv) inhibitory than low FR neurons. For a fixed amount of total damage,
feed-forward channels running parallel to excitatory chan- FAS results in relatively many partially-damaged neurons,
nels. It is thus an ideal model organism to investigate the while ablation results in relatively few destroyed neurons.
injury mitigation effects of these elements. MothNet is a In our simulations, we varied the parameters of each net-
computational model of this olfactory network which incor- work feature-under-test, applied FAS-type injuries to dif-
porates known biophysical parameters and which was cal- ferent subnetworks of the system (simulating the outcome
ibrated to in vivo firing rate data recorded during learning of a traumatic brain injury or concussion) and assessed the
tasks [8]. See Figure 1 for a system schematic. net effects on EN outputs. In particular, we examined two
The moth olfactory network (MON) also contains well- aspects of FR behavior for a single representative EN: (i)
defined Readout Neurons (ENs, for Extrinsic Neurons), which changes in raw FR, and (ii) the ability of the EN to discrim-
are downstream outputs that deliver key actionable encod- inate between a trained and untrained odor.
ings to the rest of its body [3, 17]. From a functional view- Our experiments led to four main findings concerning
point, internal damage is unimportant as long as the key out- injury-mitigation structures in the moth olfactory system:
puts (readouts) of the system are preserved. Thus, to exam-
ine injury mitigation effects we ran in silico simulations of 1. The learning mechanism, based on the combination of
neural injury on the MothNet model, and measured how the octopamine stimulation and Hebbian growth, can restore
firing rates (FRs) of readout ENs were affected by injuries both the magnitude and discriminative ability of down-
and by injury-mitigation mechanisms. stream readout neurons after upstream neurons are in-
Maia et al. [32] recently introduced a computational model jured.
for the cellular level effects that may distort firing rates due
Built to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury 3
Fig. 1 Overview of the Moth Olfactory Network (MON) and axonal injury mechanisms. A, B: The MON is organized as a feedforward
cascade of four distinct subnetworks and a reward mechanism [33,23]. Receptor Neurons (RNs) in the Antennae detect relevant odors in the
environment and transmit specific signals to the Antennal Lobe (AL) [46,34], which acts as a pre-amp, providing gain control and sharpening odor
codes [2]. The AL neurons project odor codes forward to the Mushroom Body (MB) [4] by means of noisy [10] excitatory Projection Neurons
(PNs), and to a smaller number of parallel inhibitory neurons (here called QNs). The Kenyon Cells in the MB fire sparsely (due to global inhibition
from the Lateral Horn), and encode odor signatures as memories [36,20]. Finally, Extrinsic Neurons (ENs) are viewed as readout units that
interpret the MB codes, delivering actionable output to the rest of the body [3,17]. In response to reward (sugar at the proboscis), a large neuron
releases octopamine in the AL and MB. In the AL, this neuromodulator induces stronger responses in AL neurons (stimulation), though intra-AL
connections are not plastic. Synaptic connections into and out of the MB (AL→MB and MB→ENs) are plastic [5,34] given octopamine, though
octopamine does not stimulate KCs in the MothNet model (biological data is lacking). Learning fails in the absence of octopamine [14,15]. For
accurate anatomy, see e.g. [26]. C: Focal Axonal Swellings (FAS) are ubiquitous across all severities of traumatic brain injuries and present in
other leading brain disorders. They can cause some or all neural spikes in the train to die off in transit, reducing the overall firing rate arriving at
the downstream target neuron. Adding FAS-like effects to the MON are the basis of our damage/injury protocols. Panel C is adapted from [31].
See the Materials and Methods section for details.
2. The presence of inhibitory neurons parallel to excitatory ciently strong FRs, but precisely these FRs are impaired by
neurons connecting the subnetworks can mitigate the ef- injury. Our experiments indicate that octopamine-induced
fects of injury through a “canceling out” effect. stimulation of the injured upstream neurons is crucial to
post-injury plasticity, because it boosts the FRs of upstream,
3. A broad noise envelope on neural firing rates (FRs) en- injured neurons back to levels that enable non-trivial Heb-
ables the strongest downstream neural responses to con- bian updates. Without such stimulation, the FRs of the in-
tinue to exceed action-triggering thresholds, despite up- jured neurons, as well as the FRs induced by the injured
stream injury. neurons in the downstream neurons, are too low to induce
gains in synaptic strength via a Hebbian mechanism [8].
4. Simple ablation injuries in upstream region produce dis-
tinct downstream effects from those of more biologically
plausible types of injury. That is, ablation may be a poor Our computational approach allowed us to quantify the
proxy for naturalistic injury in some neural systems. mitigating effect of a neural structure-under-test as a func-
tion of injury level, injury location, and structure parameters.
We recognize that, as in any computational model, specific
Concerning item 1 (learning as an injury mitigation mech- quantitative outcomes necessarily depend on the particular
anism), we note that while it is intuitive that Hebbian plas- parameters and assumptions of the MothNet model. How-
ticity might help repair an injured network, it is not clear that ever, MothNet’s architecture is tethered to known biophysi-
Hebbian updates alone can repair damage. Hebbian “fire to- cal findings, and its parameter values are calibrated to bio-
gether, wire together” updates are proportional to the FRs of physical findings and in vivo FR data [8]. We believe this ap-
both the incoming and the receiving neurons. Hebbian plas- proach enables our experimental results to refer back mean-
ticicity thus requires that the upstream neurons have suffi- ingfully to the biological structure.4 Charles B. Delahunt et al.
2 Results
µtrain − µcontrol
Throughout this work, we target two distinct regions with Fd = (1)
our injury protocols: (i) the Antennae and (ii) the channel 0.5(σtrain + σcontrol )
between the Antennal Lobe (AL) and the Mushroom Body where µ, σ are the mean and std. dev. of EN responses to
(MB). Their specific locations are shown in Fig.2. trained and control odors. In these simulations, prior to in-
(i) The antennae comprise the outermost region of the jury one odor was trained so the system could discriminate
olfactory system and are arguably the most exposed to ex- the trained odor vs. control odor (Fd ≈ 5). We either used
ternal environmental shocks. Damage in this location should two randomly-generated odor profiles with broad, overlap-
affect primarily the Receptor Neuron (RN) subpopulation ping projections onto the AL; or {odor + noise} vs. noise,
(∼30,000). We note that hundreds of RNs responsive to a with mean noise magnitude set between 0.2 and 1.0 times
given odor are spread throughout the antennae, ensuring that the odor magnitude (in MothNet, odor magnitude is con-
localized damage to an antenna does not disproportionately trolled by a scalar which multiplies unit-length odor vectors
reduce the response to a particular odor. before they are inputted to the RNs).
(ii) The AL→MB channel is an internal region and is
(i) EN magnitude: As expected, injury reduced raw EN
one of the core centers for signal transfer in the network.
response magnitude, and training restored some of this loss.
Damage in this location should affect both excitatory projec-
The MON was much more robust to RN (antennae) dam-
tion neurons (PNs) and inhibitory projection neurons (QNs)
age than to PN damage. Complete restoration was achieved
that link the AL to the MB.
(on average) for injury levels below 25% for RN damage
The Moth Olfactory Network (MON) contains some plas-
and below 8% for PN damage. At these injury values, in-
tic synaptic connections, and it can learn [8]: In response to
jury reduced EN odor responses to approximately 70% of
reward (sugar at the proboscis), a large neuron sprays oc-
the naive baseline, and training restored them to baseline.
topamine over the AL and MB. This strengthens the plas-
See the plots in Fig.4(A, B). We note that at low injury lev-
tic synaptic connection in the AL→MB and MB→Readout
els, the system was able to boost EN output by about 140%
channels in a Hebbian-like way, enabling readout neurons
to 150%, a value constrained by the model’s saturation pa-
(extrinsic neurons, ENs) to deliver actionable encodings to
rameter for the synaptic connection weights. At high levels
the rest of the body. Typical EN responses before injury, af-
of injury to PNs, however, the learning mechanism’s ability
ter injury, and after subsequent training, are shown in Fig.3.
to recover EN performance decreased (see green curves in
Fig.4).
2.1 Plasticity-induced recovery from injury (ii) Discrimination: Injury had less effect on discrimi-
native ability than on magnitude, since injury affected both
The goal of this set of experiments was to examine how far trained odor and control EN responses. Given two odors,
the Hebbian learning mechanism can compensate for neu- injury reduced discrimination, while retraining readily re-
ral injury. In the first experiment, RNs in the Antennae→AL stored all losses (Fisher discriminant plots in Fig.4(C, D).
channel were injured (Fig.2A). In the second experiment, Between {odor + noise} vs. noise, injury had no effect on
PNs in the AL→MB channel were targeted (Fig.2B). AL discriminative ability at any noise level, likely because the
noise was set to naturalistic levels (calibrated per in vivo sparsely-firing MB is an effective noise filter [8]. Post-injury
data [8]) and FAS-like injury levels ranged from 0% to 60%. training served to further increase discrimination between
The MON was subsequently retrained with 5 odor puffs, {odor + noise} and noise (results not shown).
close to sufficient to max out the allowable synaptic weights.
The average EN readout response was recorded, as a key
measure of the actionable output of the system. A typical 2.2 Inhibitory neurons and protective canceling out effect
timecourse is shown in Fig.3. In each experiment, over 30
(n = 34 - 38, mean = 36) MothNet instances were generated Each glomerulus in the AL has ≈ 5 excitatory PNs that feed
from template (i.e. a specification of network parameters forward to the MB. The moth also has a smaller number
used to randomly generate MothNet instances) and tested of inhibitory neurons (here called QNs) that also feed for-
at each injury level. We examined two properties of the EN ward to the MB, analogous to and in parallel with the PNs.
readout: We note that these feed-forward QNs are one of three in-
(i) Magnitude, a basic property relevant to triggering be- hibitory networks in the AL-MB. The other two, viz. lateral
havioral response to an odor. Examining effects on EN mag- inhibitory neurons within the AL [47] and global sparsity-
nitude required no pre-training of the network prior to injury. inducing inhibition onto the MB from the Lateral Horn [1]
(ii) Discriminative ability between two odors (one trained (or global self-inhibition by the MB as in drosophila [24]),
and one control), measured as the Fisher linear discriminant have different functions and are assumed to be non-plastic.Built to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury 5
Fig. 2 Location of injuries in experiments. Damage to Antennae affects the Receptor Neurons (RNs) (red stars) and reduce the overall input
to the Antennal Lobe (AL). Damage to the AL→MB channel (orange stars) will weaken the signals passed by both excitatory projection neurons
(PNs) and inhibitory projection neurons (QNs).
Our experiments target the QNs, which innervate only a sub- regarding the Signal-to-Noise Ratio,
set of MB neurons, and are presumed in MothNet to be plas-
tic like PNs. SNR = µ(F)/σ (F), (2)
The goal of this set of experiments was to test whether where µ and σ correspond to the mean and standard de-
the existence of QNs parallel to PNs might mitigate the ef- viation, and F = { fi , i = 1...n} is the set of discrete EN
fect of injuries applied to this region (orange stars in Fig.2). responses (peak FR) to a series of odor puffs. Naive SNR
We varied the QN:PN ratio (0, 2, 4, 5, and 7 QNs/glomerulus, values (i.e. pre-injury, pre-training) were similar for all QN
compared to 5 PNs/glomerulus) while injuring the AL→MB counts (Fig.5D). While post-injury SNR always dropped pro-
channel. Each parameter pair (e.g. “4 QNs, 50% FAS in- portionally to the severity of the injury, high QN counts sub-
jury”) had at least 30 moth instances (31 to 40, mean = stantially reduced these losses to SNR, suggesting that raw
35). We found out that higher numbers of QNs correlated EN firing rates were better preserved (Fig.5E).
strongly with reduced effects on EN output magnitudes from However, high QNs counts also carried a downside. They
upstream injury, but had no clear effect on discriminative had a much lower EN Signal-to-Spontaneous Noise Ratio,
ability. Results reported here are for effects on EN magni-
tude. SSNR = µ(F)/µ(Sp), (3)
Moths with high QN counts had stronger post-injury EN
where F is defined as above and Sp is the spontaneous EN
odor responses, and post-injury training sessions allowed
firing rate. The SSNR measures the clarity of the signal with
them to fully recover from much higher levels of injury than
respect to background noise, and their values for different
moths with few or no QNs (≈ 8% injury for QNs = 0, ≈
QN counts are shown in Fig.5F. Many templates with high
15% injury when QNs = 4, and ≈ 30% injury when QNs
QN counts were rejected due to untenably high naive spon-
= 7). High QN counts had another, unexpected advantage
taneous noise.
P-values corresponding to Fig.5 (A, B) are given in Ta-
bles 9 and 10 in the Appendix. They indicate that the injury-
mitigating effect of high QN ratios was meaningful (we avoid
the term “significant” in association with P-values, follow-
ing the arguments in [44]).
Our results demonstrate that the presence of parallel in-
hibitory neurons help protect the signal from injury (at the
cost of decreased SSNR). We hypothesize that QNs achieve
this by a canceling out mechanism: When inhibitory QNs
are injured, the overall transmitted signal increases, offset-
ting the decreases caused by injury to excitatory PNs.
Fig. 3 Typical EN timecourse. Readouts from the EN in a typical ex-
periment, in which injury attenuated the EN odor response, and train-
ing partly restored it. x-axis is time. y-axis gives magnitude of EN re- 2.3 AL noise preserves the highest EN responses
sponse (dimensionless units), with pre-injury response to the odor ≈
1 (absent odor, EN response ≈ 0). Events (with times in parentheses) The AL is a noisy network. We ask whether this neural noise
are: Naive response (20-55); injury (red dot at 60); injured response
has injury-mitigation benefits. We suppose that vital odor-
(100-150); 5 puffs training (170-190), with the very strong (cropped)
responses due to octopamine; post-training response (240-280). related behavior is triggered when a discrete EN response
f exceeds some threshold, and that due to AL noise these6 Charles B. Delahunt et al.
responses f to a particular odor (+ concentration) vary as This corresponds to fi boosted by fortuitous noise effects
if drawn from a distribution. The moth gets n exposures and thus most likely to exceed the triggering threshold.
to a given odor plume, and thus has n discrete responses The AL noise level is controlled by a single parameter
F = { fi , i = 1...n}. Then to induce the behavior, a triggering in MothNet. We adjusted neural noise in the AL to differ-
response (i.e. fi > threshold) is needed for only some, not ent multiplicative factors of the “natural” AL noise level
all, fi . (i.e. the level matching our in vivo data). Factors were 0,
In this case, it suffices for the system to protect only the 0.33, 0.67, 1.0, and 1.33, where 1.0 is the natural level. Var-
strongest (top-scoring) EN responses from injury-induced ious severities of FAS-like injury were applied to RNs in the
attenuation in order to maintain its behavioral response. The Antennae→AL channel (Fig.2A). Over 30 (31 to 62, mean
goal of this experiment was to examine whether higher AL = 40) moth instances were generated from template for each
noise levels might preferentially protect the top-scoring EN
responses from injury-induced attenuation. Noting that F
parametrizes a Gaussian
N (µ(F), σ (F)) = N (mean(F), std dev(F)) (4)
we define this top-scoring tranche as those responses at the
top end of the distribution: { fi ∈ F | fi > µ(F) + σ (F)}.
Fig. 4 Learning as injury compensation mechanism. Red/orange:
Post-injury EN odor response, normalized by naive, healthy odor re-
sponse. Blue: Post-training EN response, normalized by naive, healthy
odor response. Green: Relative increase from post-injury response due Fig. 5 Effects of parallel inhibitory channels. A: Post-injury EN
to training. µ ± σ . A: Injury to RNs: Trained EN responses (blue) fully odor responses normalized by naive healthy odor responses, vs injury
regained their pre-injury levels (black line) from injured levels (red) level. Each curve corresponds to a number of QNs per 5 PNs, from 0
if injury was on average ≤ 25%. The ability of training to recover to 7. Higher QN:PN ratios resulted in much lower impact on EN re-
lost ground was fairly steady vs injury level (green). B: Injury to PNs sponses for a given level of injury. B: Post-training EN odor responses
was more traumatic: Post-injury EN response (orange) was lower, and normalized by naive healthy odor responses, vs injury level. Each curve
trained responses (blue) fully regained pre-injury levels if injury was corresponds to a number of QNs per 5 PNs, from 0 to 7. Higher QN:PN
on average ≤ 8%. Also, the ability of training to recover lost ground ratios resulted in stronger recovery. C: Ratio of post-training to post-
decreased as injury level increased (green). Each datapoint shows the injury EN odor responses vs injury level. Recovery rate dropped off at
mean and std dev, over n = 31 to 62 (mean = 40) moth instances. A injury levels ≥ 20% for #QN = 0, but higher numbers of QNs reduced
moth’s EN response was defined as its mean response to 15 odor expo- this drop-off, i.e. ensured better recovery. D: Box-whisker plots (show-
sures. C, D: Changes in Fisher discriminant between pre-trained odor ing 25 and 75%iles as a blue box and median as a red line) of the ratio
and control odor, due to injury and subsequent additional training (val- of naive healthy EN odor responses to spontaneous EN noise (SSNR).
ues are normalized to the initial Fisher discriminant). Injury reduced This measure of signal clarity was much lower in moths with high QN
the ability to discriminate (red/orange curves), while post-injury train- counts. E: Raw Signal-to-Noise Ratio (SNR) of naive healthy EN re-
ing fully restored it to above baseline (blue curves). For 0% injury, sponses was fairly uniform across #QNs. F: Post-injury SNR normal-
slight deviations from 1 are due to variations in responses to two groups ized by pre-injury SNR. High QN counts gave strong protection against
of odor puffs, pre- and post-injury. C: Injury to RNs. D: Injury to PNs. injury-induced degradation of SNR.Built to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury 7
{AL noise, injury level} datapoint. To measure attenuation ing AL noise, since both trained odor and control were at-
in top-scoring responses, we defined the Top-End Preserva- tenuated (results not shown).
tion P as:
µ(Fj ) + σ (Fj )
P(Fj ) = , (5)
µ(Fh ) + σ (Fh )
where Fh is the set of pre-injury (healthy) responses to re-
peat applications of some stimulus, and Fj is the set of dis-
crete responses to the same stimulus post-injury at level j.
P(Fj ) measures how much an injury affects the top-scoring
responses (represented by µ(F) + σ (F)) when it shrinks
the entire response distribution from N (µ(Fh ), σ (Fh )) to
N (µ(Fj ), σ (Fj )). P(F, j) ranges between 1 and 0, where 1
implies no injury-induced attenuation, and 0 implies total at-
tenuation. P(Fj )) is plotted in Figs.6 (A, B) and 7, for both
post-injury P and post-injury-plus-training P.
Higher AL noise increased the top-end preservation P of
EN responses caused by a given level of injury (Fig.6A). It
also increased the post-training recovery possible: For ex-
ample, full recovery occurred for injury ≤ 20% when AL
noise = 0, vs ≤ 28% when AL noise was greater than natu-
ral level (Fig.6B).
However, high AL noise levels had a significant down-
side, namely, lower SNR (signal to noise ratio) and SSNR
(signal to spontaneous noise ratio) values, as seen in Fig.6
Fig. 6 Effects of AL noise: Given RN injury, AL noise protects down-
(C-E). This suggests that the moth must make a trade-off stream neurons from loss (A, B), but exacts a cost in terms of signal-
between robustness to injury and signal quality. to-spontaneous noise ratio (SSNR, C and D) and signal-to-noise ratio
In addition, we found that this protection did not apply to (SNR, E). A: Post-injury EN responses of the top 15% tranche (i.e. the
all EN responses: Top-scoring EN responses received more strongest odor responses), normalized by their pre-injury response, vs
injury level. Higher AL noise reduced attenuation due to injury, at any
injury-mitigation benefit from higher AL noise levels than level of injury. Each curve corresponds to a level of AL noise, from
µ(F )
did average EN responses, i.e. P(F) > µ(F j ) . That is, the 0 to 1.33 where 1 = “natural” level. Pre-injury response = black line.
h
extra robustness to injury conferred by higher noise levels (For 0% injury, slight deviations from 1 are due to variation in response
to two groups of odor puffs, pre- and post-injury.) B: Post-injury EN
was greater for top-scoring responses than for average re- responses of the top 15% tranche, normalized by their pre-injury re-
sponses. This meshes with the notion that the system needs sponse, vs injury level. Higher AL noise allowed training to give full
not protect all responses, just the ones most likely to exceed recovery of these top EN responses from larger injuries, ≈28% injury
triggering threshold. Fig.7 shows this difference in protec- given maximum noise vs ≈20% injury given no AL noise. C: Naive
healthy ratio of EN SSNR was much lower at high AL noise levels.
tive effect, top-scoring vs average. D: Post-injury SSNR, normalized by pre-injury ratios, vs injury level.
P-values are given in the Appendix as follows: P-values Injury lowered SSNR far more in moths with high AL noise. E: Naive
corresponding to Figs.6 (A, B) are given in Tables 3 and healthy SNR by AL noise level. SNR was much lower in moths with
high AL noise.
5. P-values corresponding to Fig.7 (C, D) are given in Ta-
bles 4 and 4. P-values comparing injury-mitigating effects
on top-scoring vs average responses, (i.e. Fig.7, A vs C and
B vs D) are given in Tables 7 and 8. They indicate that (i)
the increased protective effect due to increased AL noise
was meaningful on the top-scoring responses; (ii) the pro- 2.4 Ablation is a poor proxy to biological injury
tective effect was noticeably lower for average responses;
and (iii) the protective effect was meaningfully greater for Neuronal pathologies are often modeled in a binary way, i.e.
top-scoring than for average responses. by treating a neuron and/or its connections as either fully
Results given here are for experiments that tracked in- functional or fully impaired, and ablation injuries are widely
jury’s effects on magnitude of EN response. Injury’s effects studied in theoretical and experimental settings. But recent
on odor discrimination were only slightly affected by vary- FAS studies show that most injured neurons maintain some8 Charles B. Delahunt et al.
residual firing rate activity. On large, homogeneous popu- nel (red stars in Fig.2) and the PN channel (orange stars in
lations of neurons where outputs are pooled, such as the Fig.2). All parameters were generated from a MothNet tem-
30,000 RNs in the moth AL-MB, one can expect an approx- plate, with AL noise at natural levels and number of QNs = 0
imate equivalence in ablation and FAS modulo a conversion (QNs = 2 gave similar results). Half the moths were injured
factor. This is because the effect of injuring or ablating any by ablation and half were injured by FAS, with injury levels
single RN is relatively small, and the overall effects of injury from 0 to 60%, in order to compare the relative empirical ef-
to the population can be approximated by average injury ra- fects on EN outputs. In each experiment, over 30 (31 to 40,
tios. In this case, we estimate that ablation alone is roughly mean = 35) moth instances were generated for each injury
1.75× more harmful than FAS-like injury, i.e. ablating n% {type, level, location} datapoint.
of neurons in a population causes the same relative drop in The qualitative effects of ablation and FAS were simi-
total summed FRs as FAS injury to ≈ 1.75n% of the neuron lar, at each injury site. However, the relative quantitative ef-
population. For calculations, see section 5.3.3). fects of the two injury types varied greatly depending on the
However, where neuron numbers are smaller and neu- site of injury. For RN channel damage, ablation effects were
ral outputs are not pooled, so that individual neurons have roughly in line with that predicted by theory for large ho-
relatively unique effects on the system, it is not clear that mogeneous populations, i.e. 1.75× FAS damage. This match
ablation effects can be reliably mapped to effects of more between theoretical and experimental ablation effects is seen
biologically-plausible FAS-like injuries. Injury to PNs more in Fig.8 A. The match makes sense given the assumptions on
closely resembles this case, since there are only 60 glomeruli number and distribution of RNs stated above.
in the moth AL, each handling unique information. In contrast, ablation injury to the PN channel was much
In ablation studies, injury levels are typically measured less harmful relative to FAS-like injury than predicted by
as percentage of neurons ablated. To assess whether ablation theory. For example, 10% ablation would theoretically in-
is a good proxy for naturalistic FAS injury, we ran experi- duce the same EN loss as 17.5% FAS injury and 20% ab-
ments to test whether the impacts on EN response magni- lation would correspond to 35% FAS injury. However, in
tude of ablation injury vs. FAS-like injury had a consistent our experiments 10% ablation corresponded to only ∼12%
1.75× relationship at these two locations, i.e. the RN chan- FAS injury (a ratio of 1.2), and 20% ablation corresponded
to only ∼25% (a ratio of 1.25). This effect is seen in Fig.8
B by following horizontal lines, which correspond to equiv-
alent EN loss, and comparing the percentage injury levels
of (from right to left) experiment FAS, experiment abla-
tion, and theoretical ablation. The experimental ablation lev-
els required to induce a fixed EN loss were much closer to
the FAS levels than theory predicted (ratio ∼1.25 instead of
1.75).
We remark that this measured discrepancy between theo-
retical and actual effects is not at the site of injury, but at the
downstream (readout) neurons, i.e. after the impact of the
upstream injury has been nonlinearly modulated by moving
through the cascaded system.
This variability in the ratio of ablation injury to equiv-
alent FAS injury, dependent on which neurons are injured,
suggests that ablation may be an unreliable proxy for natu-
ralistic neuronal damage in some contexts.
Fig. 7 Protective effects of AL noise on strongest vs average EN
responses Given RN injury, increased AL noise had a greater protec-
tive effect on the top 15% tranche of EN odor responses than on more 3 Discussion
average odor responses, both post-injury and post-training. Each curve
corresponds to a noise level. A wider spread of curves indicates greater
injury mitigation from higher noise. A, B: Top 15% of EN responses, Our simulations indicate that the neural mechanisms and
normalized to their pre-injury responses, post-injury (red, grey) and motifs we tested have clear injury-mitigation properties. In
post-training (blue, grey). The spread of curves indicates the relative this section we suggest mechanisms by which these struc-
benefit of higher noise. (These are the same subplots as in Fig.6 A, B.)
tures might protect readout neuronal activity from upstream
C, D: All responses, normalized by their pre-injury responses, post-
injury (red, grey) and post-training (blue, grey). Average EN responses injury. We note that from a functional point of view, overall
had less injury mitigation benefit from high noise than top-scoring EN resilience of a cascaded system depends partly on whether
responses. upstream regions can avoid damage, but mainly on whetherBuilt to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury 9
downstream units can still transmit key readout signals to 3.1 Hebbian plasticity-induced recovery from injury
the rest of the body despite upstream damage. Cascaded net-
works are ubiquitous among biological neural systems, so Learning in the moth olfactory network occurs via a combi-
the principles discussed in the moth’s olfactory network may nation of octopamine stimulation and Hebbian growth. Oc-
be applicable to other settings. We also discuss the discrep- topamine stimulation temporarily boosts neural firing rates
ancy between axonal swelling injuries vs ablation injuries. during reinforcement by sugar reward, while Hebbian up-
Finally, we argue that robustness to injury is a key principle dates strengthen the synaptic weight wab , between two neu-
of biological neural design. rons a and b, proportionally to the product of their firing
rates:
∆ wab ∝ fa (t) fb (t). (6)
Injuries to the upstream regions of a network result in spike
deletions and weaker encodings arriving at downstream neu-
rons. If the damaged region cannot activate downstream neu-
rons with the existing synaptic connection strengths, there is
a functional loss of information. However, the combination
of octopamine stimulation and a Hebbian update mechanism
can evidently mitigate or reverse this effect. We note that
the original injured neurons are not themselves repaired, as
plasticity only boosts downstream synaptic connections.
We note that the Hebbian mechanism alone is not suffi-
cient to repair damage, because updates to synaptic strengths
require sufficiently strong FRs in both the incoming and the
receiving neurons. If injury reduces the FRs of upstream
neurons, and these reduced inputs lead to lower FRs in down-
stream neurons, Hebbian updates are significantly degraded.
Thus, octopamine-induced stimulation of the injured upstream
neurons is crucial to post-injury plasticity, because it tem-
porarily boosts the FRs of injured upstream neurons back to
levels that enable the Hebbian mechanism to strengthen the
relevant connections.
We propose that degraded firing rates in downstream neu-
rons are restored via the following mechanism (see schematic
in Fig.9A):
1. Octopamine temporarily increases the firing rates of in-
jured upstream neurons.
2. The transient boosted encodings are sufficient to trig-
ger firing in the downstream neurons with the existing
synaptic connection strengths.
Fig. 8 Level of Ablation and FAS injury needed to induce a given 3. Since neurons on both sides of the plastic connections
EN loss: The relationship of ablation and FAS injury effects varied
with injury location, implying that ablation is an unreliable proxy for are firing, Hebbian growth strengthens their connections.
FAS injury. In both plots: dots and crosses are experimental results for 4. Firing rates from the injured upstream region return to
FAS and ablation respectively. Solid and dashed curves are fits to ex- their reduced rate once octopamine is withdrawn. How-
perimental results for FAS and ablation respectively. The dotted curve ever, due to the stronger synaptic connections, these en-
is the theoretical result for ablation, given the FAS experimental re-
sults and a 1.75× ratio (see Section 5.3.3). A: When RNs were in- codings are now sufficient to trigger the downstream neu-
jured, ablation induced loss to EN response consistent with theory (1 rons. This restores the transmission of key information
unit Ablation ≈1.75 units FAS injury). Curves do not meet at origin to the rest of the body.
because they are fits to data points. B: When PNs were injured, abla-
tion induced a much smaller loss than theory (1 unit Ablation ≈1.25 Because the {octopamine stimulation + Hebbian updates}
units FAS injury). This can be seen by looking at horizontal lines (i.e. learning mechanism is automated, i.e. hard-wired as a re-
fixed EN loss), and comparing injury levels that induce this loss for ward mechanism for adaptive stimuli such as sugar, it acts
(from right to left) experimental FAS injury, experimental ablation, and
as a passive injury mitigation system (absent injury, it serves
theoretically-expected ablation. A large gap exists between experimen-
tal and theoretical ablation levels required to induce a given EN loss. to boost network responses to adaptive stimuli). Since learn-
ing is activated repeatedly throughout life (by any rewarding10 Charles B. Delahunt et al.
stimulus), it can be expected to act post-injury as an auto- functional constraints. We note that learning and plasticity
matic repair mechanism. Alternately, learning can be viewed are not pre-requisites for this mechanism.
as a built-in tuning mechanism that in event of injury serves
to restore network responses towards their pre-injury states.
We hesitate to call this learning mechanism homeostatic, 3.3 Upstream noise protects downstream behavior
even though in the context of injury it automatically moves
the system towards a prior state, because the restoration is Suppose that the behavioral response is preserved after in-
one-way. Learning will not revert responses that have been jury if at least a subset of stimuli elicit downstream responses
previously strengthened (by learning itself). Rather, it is an that exceed action-triggering thresholds. In this case, a large
automated mechanism for tuning a network towards stronger noise envelope on upstream neurons may help protect the
responses to adaptive stimuli, which in the event of injury network’s functionality.
has a homeostatic effect. Assume the firing rate of an upstream neuron FR re-
sponds to stimuli following a Gaussian distribution N(µ, σ ),
and that it needs to exceed a threshold T to activate down-
3.2 Inhibitory neurons and protective canceling out effect stream neurons. If the neural damage reduces this FR in av-
erage by δ , a large noise envelope (large σ ) will ensure that
The moth olfactory network has both excitatory projection some post-injury responses still exceed threshold, i.e. that
neurons and inhibitory projection neurons that feed-forward µ − δ + σ ≥ T . This idea is sketched in Fig.9C for two FRs
from the antennal lobe to the mushroom body. We propose a characterized by N(µ, σ1 ) and N(µ, σ2 ) with σ1 > σ2 .
mechanism to explain how this can protect downstream neu- Our experiments indicate that AL noise does enable the
rons from the effects of upstream damage, assuming down- highest EN responses to exceed threshold after injury, even
stream dynamics depend on the summed input from upstream as the average EN response drops. However, the injury mit-
neurons: igating benefit of increased upstream noise comes at a cost
to other system functionalities, e.g. it reduces signal-to-noise
ratio. Noise levels in biological networks (such as in the an-
(w · u) = w+ · u+ − w− · u− , where (7)
tennal lobe) may represent an evolved/optimized trade-off
between injury mitigation effects and negative side-effects
w+ = connection weights from excitatory neurons
such as reduced SNR. We note that the sparsity of the MB
u+ = FRs from upstream excitatory neurons acts as a powerful noise filter [8]. Plasticity is not a pre-
w− = connection weights from inhibitory neurons requisite to this mechanism.
u− = FRs from upstream inhibitory neurons.
When FAS-like injury is applied to the PN+QN pipeline in 3.4 Ablation is a poor proxy to biological injury
our neural architecture (mimicking the outcome of a phys-
ical shock), the net effect on the summed signal reaching Neuronal injuries are often modeled in a binary way, i.e. by
downstream target neurons varies according to the propor- treating a neuron and/or its connections as either fully func-
tion of QNs to PNs (u− : u+ , assuming uniform weights tional or fully impaired. Our results indicate, however, that
w). When all feed-forward signals are excitatory (i.e., u− in some situations ablations are a poor proxy for more nat-
= 0), injury will always reduce the summed input reaching uralistic FAS-types of injuries regarding effects measured
a downstream neuron. If QNs exist, however, and both PNs downstream from the injury site.
and QNs share the same exposure to injury, then the overall When the neuron population to be injured is large, and
reduction to the summed input will be mitigated on average, has pooled outputs to the next layers (in our model, the an-
since any injury to QNs will increase the summed input, off- tennae/RNs), ablation maps to FAS injury in a predictable
setting decreases due to PN injury. A schematic of this “can- manner due to averaging effects over the population (see
celling out” mechanism is shown in Fig.9 B. section 5.3.3). However, when the neuron population is small
The injury resistance provided by high QN counts comes (in our model, the PNs) the effects of ablation vs FAS are not
at a cost to other functionalities, e.g. higher spontaneous EN predictable. Ablation of PNs had much lower impact than
noise relative to odor response. Presumably, biological net- large-population theory would predict
works have QN counts which optimally balance the benefits Our key finding is that ablation effects are inconsistent
of injury mitigation on one hand versus the need for high relative to FAS-like effects, depending on the location and
signal-noise-ratio, as well as other concerns such as the en- characteristics of the injured neurons. This calls into ques-
ergy cost to the organism. If the QN counts are low (e.g. tion the value of ablation as a proxy for naturalistic neu-
QN:PN ≤ 20%, as in the moth), this injury mitigation ben- ral injuries. We suggest that in systems with large numbers
efit is likely less important relative to other architectural or of somewhat interchangeable units (e.g. the 30,000 RNs)Built to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury 11
Fig. 9 Injury mitigation hypotheses: In a cascaded network, various architectures can mitigate the effects of injury to upstream neurons by
protecting or restoring functionality of downstream units. A: Learning itself can compensate for injury: Octopamine temporarily stimulates the
damaged neuron, allowing Hebbian growth to strengthen downstream synaptic connections.Though the injured neuron’s signal is not restored,
the downstream neurons receive an amplified input, cancelling out the injury. B: Parallel inhibitory channels can reduce the effect of generalized
injury by spreading damage among excitatory and inhibitory signals, so that losses cancel out in terms of inputs to downstream neurons. C: Wide
noise envelopes on upstream neuron outputs can protect the strongest stimulus responses from injury-induced attenuation δ , to the degree that their
std dev σ > δ . This allows the injured neuron’s strongest responses to still exceed their activation threshold (green line) for downstream neurons,
protecting downstream functionality. D: Two simple examples of non-linearities that can result in qualititative change in the relative effects of
ablation and FAS-like injury: In an AND gate, ablation can have a worse effect than FAS downstream, depending on the gate’s input threshold T .
In an OR gate, ablation can be harmless, while FAS can have a worse effect downstream, depending on T .
ablation is a suitable way to model injury; while in sys- 4 Conclusion
tems with smaller numbers of specialized neural units (e.g.
the AL with 60 glomeruli) ablation is a poor injury model. We investigated the moth olfactory network with the goal of
This unsuitability is sharpened when the actionable effects understanding how its basic architectural components serve
of injury are measured downstream from the regions injured, to make sensory processing robust to injury. Since most or-
because there is a complex interplay between the injuries ganisms are exposed to neuronal damage throughout their
and network nonlinearities, making the outcome somewhat lives, it is important to understand how such neuronal cir-
unpredictable. Simple examples of possible effects of non- cuits are structured to maintain functionality despite impair-
linearities (AND and OR gates) that might cause ablation vs. ments. In this work, we showed explicitly how certain struc-
FAS-like injury models to diverge are shown in Fig.9 D. tural and functional network motifs act as injury mitiga-
tion mechanisms. Specifically, we examined how (i) Heb-
bian learning, (ii) high levels of noise, and (iii) presence
3.5 Limitations of both inhibitory and excitatory connections, can support
overall robustness to injury in the olfactory system in the
Our computational model assumed only one readout neu- Manduca sexta moth.
ron and one broadly-activating odor. A more realistic assess- Our findings indicate that, in addition to accurate sen-
ment of injury and mitigation might involve several readout sory processing, biological neural networks such as those
neurons to allow for disparate effects on various readouts, found in the moth olfactory system hold robustness to in-
and might use more narrowly-activating odors. We do not jury as a central design principle. Our findings also sug-
know if the PN+QN channel is a realistic target for injury. gest an additional hypothesis: Plasticity coupled with neuro-
We chose it in order to investigate deficits caused by injury modulatory stimulation, now central to learning, may have
to innermost hubs. Our study certainly did not exhaust all originally evolved as a repair mechanism for neural systems
potentially interesting combinations of structures-under-test to offset injury and maintain function, and was only later
and injuries. ported to the task of developing responses to new informa-12 Charles B. Delahunt et al.
tion (exaptation). If this is the case, then the gift of learning RN responds to exactly one, and that all RNs responsive to a
is due originally to the exigencies of brain damage. certain target innervate the same glomerulus in the AL. Thus
Our results also show that these architectures can in fact atomic odors and AL glomeruli are assumed to correspond
cause worse performance by some other performance met- 1-to-1.
rics, e.g. SNR. Thus, trying to explain these architectures
from the point-of-view of, for example, information theory Antennal Lobe (AL):
risks running against the fact that they are actually subopti- The AL acts as a pre-amp, converting the weak electrical
mal according to that particular lens. A more comprehensive signals into an output signal strong enough to tolerate noise
and nuanced framing of the neural signal processing task, and allow further processing. It also modulates the odor’s
positing multiple design goals including injury mitigation, encoding via intra-AL lateral inhibition. The AL structure
can enable better understanding of neurosensory processing. contains approximately 60 neural units (glomeruli) which
That is, a neural architecture can be understood only if its in- process odors and send excitatory signals (via projection
jury mitigation function, and the trade-offs between this and neurons PNs, ≈ 5 per glomerulus) and inhibitory signals
other desired functions, are considered. Indeed, it is possible (via QNs) downstream to the mushroom body. In the version
that some neural structures and mechanisms, including the of MothNet used here, QNs have dendrites in one glomeru-
ability to learn, are best understood as evolutionary solutions lus, rather than in several (as in the actual MON), and were
to the challenge of maintaining function despite injury. parametrized as inhibitory analogs to PNs, with the same
connection distributions and FR behavior as PNs. This en-
abled us to vary the ratio of QNs to PNs from 0 to 1.4 ac-
5 Materials and Methods cording to experiment.
In this section, we first detail the computational model Moth-
Mushroom Body (MB):
Net used in all experiments. We then describe focal axonal
The MB is a high-dimensional (≈ 4000 neurons), sparsely-
swelling (FAS), a characteristic form of neuronal injury uti-
firing structure that encodes odor signatures and memories,
lized as a model of damage, and how it was applied to the
and contains plastic synaptic connections. Odor responses
network. Lastly, we provide details about the experimental
feed-forward from the AL to the MB via PNs (excitatory)
setups involved in our key findings.
and (in moths) QNs (inhibitory). MB neurons feed-forward
to the Readout Neurons.
5.1 MothNet architecture Sparsity in the insect MB is enforced by global inhibi-
tion either from the Lateral Horn (moth) or from the MB
We use close variants of the model of the moth olfactory itself ([1], drosophila [24], locust [35, 13]). In MothNet, MB
network (MothNet) developed in [8], modifying the archi- sparsity is enforced by injecting a time-varying inhibitive
tecture features as needed for each experiment. We provide input term into all MB neurons, such that only the most
only selected details about the architecture here. For a fuller strongly-excited neurons fire and the percentage of MB neu-
description, please see [8] and its associated codebase, as rons with positive FRs is fixed (at e.g. 5 to 15%). This in-
well as the Matlab codebase for MothNet and injury simula- hibitive term models input from the Lateral Horn, which is
tions available at [7]. thus implicitly, not explicitly, modeled by global inhibition
MothNet uses firing rate dynamics for neural firing rates of the MB.
[6], evolved as stochastic differential equations [19], and
Hebbian plasticity for synaptic weight updates [16]. A ta- Readout Neurons (ENs):
ble of governing equations and parameters are given below. Odor codes in the Mushroom Body (MB) feed-forward to
For the experiments in this work, the relevant architectural Readout Neurons (Extrinsic Neurons, ENs), which are as-
structures of the MON were: sumed to act as decision-making neurons. Strong EN re-
sponses trigger actionable messages (such as “fly upwind”).
Antennae: When assessing effects of injury, we focus on the ENs, since
Network structures in which chemical receptors detect odor these represent the final, actionable output of the system.
and send signals to the Antennal Lobe via receptor neurons MothNet posits one EN, whose output firing rate serves to
(RNs). There are approximately 30k RNs (assumed here to measure the functional effects of upstream injury.
be ≈ 500 per glomerulus) that MothNet combines into one
averaged RN per glomerulus. All injury protocols applied to Octopamine effects:
RNs accounted for this many-to-one abstraction (for details, Octopamine is crucial to learning in the MON. In MothNet,
see Section 5.3.2. While RNs can respond to several atomic effects of octopamine instantiate in three ways: (1) It stim-
odors, MothNet makes the simplifying assumption that each ulates AL neurons (RNs, LNs, PNs), making them moreBuilt to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury 13
responsive to excitatory inputs and less responsive to in- 3. For experiments examining effects of learning and of
hibitory inputs (see Eqns in Section 5.6); (2) It activates AL noise, we set the number of QNs per glomerulus to
plasticity in AL→MB and MB→EN synaptic connections zero. Setting the number of QNs equal to 2 (equivalently,
(in MothNet this simply means that plasticity in these re- QN:PN ratio = 0.4) gave similar results. These QN val-
gions is “turned on” when octopamine is non-zero; (3) It re- ues remain close to that of realistic models.
duces the sparsity parameter of the KCs in the MB, to model
that it makes KCs less responsive to Lateral Horn inhibition. The extremes of the parameter regimes described above de-
Our experiments indicated that items 1 and 2 are necessary viated significantly from calibrated models, and sometimes
for learning (as in [14, 15]), while item 3 is optional [8]. created moths with untenably noisy, dysfunctional EN re-
sponses to odor. Thus, we discarded moths with naive EN
odor response-to-spontaneous FR (SSNR) outside an enve-
lope defined by µ(F)
µ(s) < 12. These comprised about 12% of
5.2 Moth template parameters moths generated, with the percentage depending on the var-
ied parameters: Templates with high numbers of QNs and/or
In each experiment, over 30 moth instances (per data point) very high AL noise had more rejected moths; templates with
were randomly generated from the MothNet template defin- few QNs and normal/low AL noise had few rejected moths.
ing the architecture, which included biologically-plausible Extra moths were generated as needed to match numbers
choices for numbers of neurons, synaptic connection weights, across all experiments, so that each {parameter-under-test,
how odor is projected onto the glomeruli of the AL, as well injury level} pair (e.g. “4 QNs, 50% FAS injury”) had ≥ 30
as learning rates and SDE time and noise constants. To gen- moth instances.
erate connection matrices, non-zero connections were ran-
domly assigned according to architectural constraints and
template parameters, then non-zero connection weights were 5.3 FAS-like injury
then drawn from gaussian distributions with parameters de-
pendent on types of neuron. For full details of how MothNet Focal Axonal Swellings (FAS) is a neural injury associated
instances are generated from templates, please see [8]. The with traumatic brain injury (TBI), typically caused by phys-
templates were realistic in the senses of having (i) PN fir- ical shock. Examples in current events include blast injuries
ing rate behavior matching in vivo data from live moths and from recent wars, as well as impact injuries in contact sports.
(ii) architecture parameters that match what is known from FAS presents as swollen neural axons (the signal delivery
the literature [8]. Some templates were moved to the bound- pipelines) with dramatic diameter changes, causing signals
aries of, or out of, a known realistic regime by varying key from the upstream source to be diminished or lost entirely
parameters-under-test when required by the experiment. before reaching downstream target neurons [29]. This degra-
dation can be expressed as reduced FRs from upstream neu-
1. The number of QNs per glomerulus varied from 0 to 7, rons, characterized in a computational model by [31], which
in order to test the injury-mitigating effect of inhibitory found that signals traveling down an injured axon are atten-
QNs in parallel with PNs in the feed-forward AL →MB uated to greater or lesser degree according to the amount of
channel. PNs were fixed at 5 per glomerulus, as in moths. swelling and the firing rate of the signal. While ablation is
In moths, each QN has dendrites in several glomeruli. In a ready and oft-used means to model neural injury, it im-
our experiments, each MothNet QN has dendrites in ex- poses a binary all-or-nothing effect which is not present in
actly one glomerulus (like PNs), to make QN:PN ratios FAS injuries. In these experiments we model neural injury
meaningful. Moths may have QN:PN ratio ≈ 0.2 (i.e. according to [31], hereafter FAS type or FAS.
relatively few QNs), insofar as a ratio can be estimated
(actual values are not known). We note that more QNs 5.3.1 FAS in the FR model context
means that more individual MB neurons receive extra
inhibition. The global inhibition mechanism modulated While FAS models effects at the level of spike trains, it also
by the Lateral Horn is distinct, and is not affected by QN has a meaningful representation in Firing Rate models such
numbers. as MothNet. In particular, unlike ablation, FAS causes re-
duced but still non-zero FRs. In addition, the low-pass filter-
2. The level of Gaussian noise affecting all AL neurons ing effect of FAS, which impacts closely-bunched clusters
varied from 0 to 1.33, where 1.0 represents natural lev- of spikes more than sparse spikes, in analogous manner im-
els (i.e. fitted to in vivo data). The purpose of this noise pacts high FRs more strongly than low FRs. Thus FAS, ap-
range was to test for any injury-mitigating values for the plied in a FR model, results in neuron FRs being reduced but
AL structure. not ablated, with high-FR neurons affected more strongly
than low-FR neurons. For a fixed amount of total damage,You can also read
