A computational model of the underlying mechanisms of 1 temporal coding in the auditory cortex 2

In primary auditory cortex, slowly repeated acoustic events are represented temporally by phase-locked 11 activity of single neurons. Single-unit studies in awake marmosets (Callithrix jacchus) have shown that a sub12 population of these neurons also monotonically increase or decrease their average discharge rate during stimulus 13 presentation for higher repetition rates. Building on a computational single-neuron model that generates phase14 locked responses with stimulus evoked excitation followed by strong inhibition, we find that stimulus-evoked 15 short-term depression is sufficient to produce synchronized monotonic positive and negative responses to slowly 16 repeated stimuli. By exploring model robustness and comparing it to other models for adaptation to such stimuli, 17 we conclude that short-term depression best explains our observations in single-unit recordings in awake 18 marmosets. Using this model, we emulated how single neurons could encode and decode multiple aspects of an 19 acoustic stimuli with the monotonic positive and negative encoding of a given stimulus feature. Together, our 20 results show that a simple biophysical mechanism in single neurons can allow a more complex encoding and 21 decoding of acoustic stimuli. 22


Introduction 24
Our ability to discriminate complex sounds such as music [1,2], speech [3,4], and conspecific 25 vocalizations [5], relies on the auditory system's analysis of an acoustic signal's spectral and temporal structures.

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For sequences of brief sounds, the timing of each acoustic event is explicitly encoded by the stimulus-locked 27 activity of neurons throughout the ascending auditory pathway. In primary auditory cortex (A1), neurons can 28 temporally lock to individual acoustic events up to around 40-50 Hz [6-10], matching the upper limit of acoustic 29 flutter (the percept of a sequence of discretely occurring events). While repetition rates within the perceptual range 30 of acoustic flutter are represented by A1 neurons with phase-locked activity, some of these neurons can also 31 simultaneously vary their firing rate by monotonically increasing (Sync+) or decreasing (Sync-) firing rate over 32 the range of repetition rates that span the range of flutter perception [11]. Temporal coding provides a faithful, 33 unambiguous representation of the timing of acoustic events. However it must be analysed across time to 34 determine the repetition rate of the stimulus. Rate coding, on the other hand, provides a more "processed" and 35 instantaneous readout of repetition rate. Although rate coding is more ubiquitous in brain regions downstream 36 from auditory cortex, one potential issue is that rate coding is used to represent multiple acoustic features in 37 auditory cortex. For example, in a typical auditory cortical neuron, an increase in firing rate could represent a 38 change in frequency, sound level [12], and/or sound location [13] In order for rate coding to be useful to 39 downstream brain regions, neural circuits must be able to demultiplex concurrently encoded acoustic features.

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In multiple brain regions, rate coding takes the form of positive and negative monotonic tuning. This form of 41 opponent coding (positive/negative sloped rate relationship with a stimulus parameter) has been postulated to 114 (Fig.2d). Together, these observations suggest that adaptation to repeated stimuli was stronger for Sync-neurons  modified E-I model, we independently varied these two parameters for both excitatory and inhibitory inputs. We 133 observed that by varying these two parameters, we were able to produce Sync+ (Spearman correlation coefficient 134 ρ > 0.8, P < 0.05) and negative (ρ < -0.8, P < 0.05) responses ( Fig.3b-

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. CC-BY-NC-ND 4.0 International license certified by peer review) is the author/funder. It is made available under a The copyright holder for this preprint (which was not this version posted June 6, 2019. . https://doi.org/10.1101/661751 doi: bioRxiv preprint    192 not seem to be affected by changes in these parameters (Fig.7a). In Sync-neurons however, the monotonicity 193 index was reduced to 0 for IE ratios under 1.0 (Fig.7b). In addition, for stronger excitatory input amplitudes the

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Monotonicity is negative only when inhibition is stronger than excitation (IE ratio larger than 1) (B.). Vector 206 strength is maintained for E strength above 2nS and is minimally affected by IE ratio in both scenarios (C, D.).

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Different mechanisms for adaptation to repeated acoustic pulses. So far in this study we explored short-term 209 depression as a possible underlying mechanism for Sync+ and Sync-neurons observed in A1. Next, we explored 210 other possible mechanisms that may allow neurons to adapt to acoustic pulse trains and compared their effects to 211 that of our short-term depression model. One such mechanism is short-term facilitation (STF); the adaptation 212 of neural activity during stimulus presentation for higher repetition rates could arise from facilitation of inhibition, 213 as opposed to depression of adaptation. We thus modelled short-term facilitation using the same parameters as 214 short-term depression. However, instead of decreasing the probability of release (and therefore the conductance 215 input amplitude), this probability was increased at each acoustic input until it was recovered back to its initial

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Another possible mechanism for adaptation to stimulus statistics is spike-frequency adaptation (SFA).

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Although the time scale for SFA is generally much shorter than that of short-term depression [18. 19], the two 242 effects could be complimentary. In order to separate SFA from our observations, we studied Inter-Spike Intervals    (Fig.11b, c). We speculated that these two parameters could be "demultiplexed" by 320 simply adding or subtracting Sync+ and Sync-responses from each other. Subtracting Sync-responses from 321 Sync+ responses, generated a firing rate that was insensitive to changes in stimulus amplitude, providing a robust 322 monotonic change in firing rate to repetition rate (Fig.11d, e). Using the opposite approach and summing Sync+ 323 and Sync-responses created an invariant response to repetition rate while preserving the monotonic tuning to 324 stimulus amplitude (Fig.11f, g).

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We quantified this further by comparing the mutual information (MI) between firing rate and each 337 stimulus feature with our simulations. We observed that subtracting Sync-responses from Sync+ responses 338 resulted in the most MI regarding stimulus repetition rate (Fig.12a), while having the least MI for stimulus 339 amplitude, compared to other combinations (Fig.12b). This demonstrates that the difference in firing rates between 340 Sync+ and Sync-neurons preserves the rate code for stimulus repetition rate while ignoring stimulus amplitude.

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Furthermore, MI for stimulus repetition rate was significantly higher when subtracting Sync-responses from 342 Sync+ responses than only using Sync+ neurons, suggesting that this "demultiplexing" procedure can even lead 343 to an enhancement of the rate code. If instead we summed the Sync+ and Sync-responses, we observed the 344 opposite result-MI increased for stimulus amplitude and decreased for stimulus repetition rate. Thus the 345 summation of firing rates between Sync+ and Sync-neurons preserves the rate code for stimulus amplitude while 346 ignoring stimulus repetition rate. Altogether, these results indicate that more than one acoustic feature can be 347 multiplexed together, by concurrently encoding each feature using a monotonically tuned rate code. However, it 348 is critical to have both positive and negative monotonic tuning to at least one acoustic feature for this to work.

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Demultiplexing this information downstream only requires summing or subtracting firing rates between different 350 groups of neurons, which is both mechanistically simple and biologically plausible.

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In the auditory pathway, we observe a loss of temporal fidelity to repetitive stimuli as we move along         the rate response was also considered significant (average discharge rate 2 s.d. above the mean spontaneous rate 514 and an average of more than 1 spike per stimulus), then the neuron was considered Sync. If the rate response was 515 significant but the neuron did not pass the synchrony criteria, it was considered nSync. In our dataset 125/210 516 neurons were classified as Sync.

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Classification of neurons, Monotonicity. The monotonicity of the discharge rate for a given repetition rate was 518 determined by calculating the Spearman correlation coefficient ( ) for stimuli spanning from 8 to 48Hz. If 519 coefficient was larger than 0.8 and statistically significant (p-value < 0.05) the neuron was considered positive 520 monotonic. If the coefficient was smaller than -0.8 and statistically significant, the neuron was considered negative

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The authors thank Catherine Perrodin and James Cooke for comments and suggestions related to this manuscript.