The generation of cortical novelty responses through inhibitory plasticity

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    Evaluation Summary:

    This paper presents the results of a model for cortical plasticity and resulting increase in neuronal responses to unexpected stimuli. This is an elegant study that provides a number of interesting, experimentally testable, hypotheses and develops a prediction for a mechanism for novelty response generation. However, a number of concerns were raised about the model, including how it relates to certain experimental data, that should be addressed.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

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Abstract

Animals depend on fast and reliable detection of novel stimuli in their environment. Neurons in multiple sensory areas respond more strongly to novel in comparison to familiar stimuli. Yet, it remains unclear which circuit, cellular, and synaptic mechanisms underlie those responses. Here, we show that spike-timing-dependent plasticity of inhibitory-to-excitatory synapses generates novelty responses in a recurrent spiking network model. Inhibitory plasticity increases the inhibition onto excitatory neurons tuned to familiar stimuli, while inhibition for novel stimuli remains low, leading to a network novelty response. The generation of novelty responses does not depend on the periodicity but rather on the distribution of presented stimuli. By including tuning of inhibitory neurons, the network further captures stimulus-specific adaptation. Finally, we suggest that disinhibition can control the amplification of novelty responses. Therefore, inhibitory plasticity provides a flexible, biologically plausible mechanism to detect the novelty of bottom-up stimuli, enabling us to make experimentally testable predictions.

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  1. Author Response:

    Reviewer #2:

    This study by Schulz et al flushes out in fine detail an interesting consequences of inhibitory synaptic plasticity in plastic neuronal networks, showing that its ability to balance precisely only previously experienced stimuli makes this type pf plasticity an excellent candidate mechanism to allow novelty detection. Strong transient responses will be evoked only by those stimuli which have not previously activated (and thus trained) the stimulus specific set of inhibitory stimuli. An open question remains with regard to the time scales and speed of learning at these inhibitory sites, something that will be answerable by the experimental audience of this paper (but could be investigated in a bit more detail in the model as well).

    We thank the reviewer for their constructive feedback. We have addressed the comments below, and included new substantial information to our manuscript. This includes a new Supplementary Figure (Figure 4-Figure Supplement 2) in which we analyze how the novelty response and the adapted responses depend on the inhibitory learning rate and a detailed discussion about experimental and theoretical studies related to inhibitory plasticity.

    Reviewer #3:

    This computational paper addresses the mechanisms of sensory adaptation and novelty detection in the auditory cortex. A spiking RNN model of 5000 (4000 excitatory/1000 inhibitory) units is developed and adapted to sequences of inputs (ABC…) followed by a novel stimulus N. As with experiments the model captures the adaptation to the repeated stimuli, as well as a strong response to a novel stimulus. In contrast to many models of sensory adaptation that rely on short-term synaptic plasticity, here adaptation arises from STDP at the Inh->Ex connection. Specifically, during ABCABC … the inhibitory connection onto active Ex units is enhanced through associative plasticity mechanisms, but not onto the inactive Ex units, thus the adaptation does not apply to the novel stimuli. While the approach seems fairly novel it is also speculative and seems to run contrary to the existing experimental data.

    We thank the reviewer for their feedback. In our view, through the process of answering the comments below, we have improved our manuscript substantially. To answer the reviewer’s comments, we added new figures to the manuscript (Figure 5) and (Figure 6-Figure Supplement 1 and Figure 1-Figure Supplement 1,5) and added new text in the Discussion (see ‘Timescales of plasticity mechanisms’, and ‘Robustness of the model’). In the following, we give detailed answers to each of the comments.

    1. The reason many models of adaptation focus on short-term synaptic plasticity (STP) as opposed to STDP is that the later generally is not thought to operate on the adaptation time scale of seconds. Specifically, STDP is generally considered to be a form of long-term associative plasticity, and thus to rely on mechanisms such as the insertion of new receptors-a processes that is unlikely to operate on a time scale of a second or so. Adaptation is robustly observed at 400 ms (e.g., Natan et al 2017), a time scale that is generally considered to be incompatible with STDP. E.g. in the D'Amour paper the authors cite, STDP is induced over a 5 minute pairing protocol, and can still increase over the course of 5-10 minutes post pairing (e.g., Fig 1H). I'm not aware of any evidence suggesting that iSTDP could be induced and expressed on the subsecond to a few seconds time scales. So this seems to be a fundamental issue that needs to addressed or at least discussed.

    Related to the point above the model also contains subtractive normalization implemented with a time step of 20 ms. Again if this normalization is critical to the model this assumption would pose a serious challenge to the model because there is little or no experimental data suggesting that normalization can operate at that time scale.

    In our new Figure 1-Figure Supplement 5 we find that the timescale of the subtractive normal- ization mechanism does not influence the generation of novelty responses in our model. Adaptation occurs over multiple timescales from hundreds of milliseconds to tens of seconds or even days [Ulanovsky et al., 2004, Lundstrom et al., 2010, Homann et al., 2017, Latimer et al., 2019, Haak et al., 2014, Ramaswami, 2014]. Our work shows that inhibitory plasticity can readily lead to adaptation on multiple timescales without the need for any additional assumptions. Although during the induction of inhibitory STDP it takes several minutes to sev- eral tens of minutes to achieve a stable baseline of inhibitory synaptic strength [D’amour and Froemke, 2015, Field et al., 2020], inhibitory postsynaptic currents increase significantly immediately after the induction of plasticity (see e.g. [D’amour and Froemke, 2015, Field et al., 2020]). Therefore, inhibitory synaptic strength seems to already change during the plasticity induction protocol. Hence, we propose that inhibitory STDP is a suitable, though clearly not the only, candidate to explain the generation of novelty responses and adaptive phenomena occurring over multiple timescales.

    Justification:

    The points raised by the reviewer are extremely valuable in critically evaluating the model. We first address the issue of the timescale of normalization.

    The generation of adapted and novelty responses in our model does not rely on the fast subtractive normal- ization mechanism, since the normalization only affects the excitatory and not the inhibitory weights; and it is the change in inhibitory synaptic weights through iSTDP that is the key mechanism to explain adapted and novelty responses. In Figure 1-Figure Supplement 5 we now show that even for a normalization time step of 50 seconds, adaptation to repeated stimuli and a novelty response occur. Therefore, we can conclude that the fast normalization mechanism is not a necessary ingredient in our model. We added a discussion at line 542 and in the Methods at line 749. Even if no normalization is applied throughout the entire stimulation paradigm, our findings do not change.

    We note that while normalization is common practice in circuit models, there is a discrepancy between the fast timescales of normalization mechanisms used in computational models to stabilize network dynamics and the much slower timescales measured experimentally ([Fox and Stryker, 2017, Turrigiano, 2017, Keck et al., 2017], among others). This discrepancy has been termed the ‘temporal paradox’ [Zenke and Gerstner, 2017, Zenke et al., 2017].

    Many computational models which implement normalization mechanisms justify them by the experimentally observed synaptic scaling despite the discrepancy between timescales (see e.g. Figure 1 in [Zenke et al., 2017]), which we now acknowledge at line 543. In related work, we propose a different biologically plausible candidate for fast homeostatic stabilization – heterosynaptic plasticity – which operates on similar timescales as homosy- naptic plasticity mechanisms [Field et al., 2020]. Incorporating this mechanism in addition to, or instead of, the fast normalization in recurrent networks is very interesting but beyond the scope of this work.

    Next, we address the issue of the timescale of iSTDP. We studied long-term iSTDP as a candidate mech- anism for the generation of adapted and novel responses for multiple reasons: (1) to explain adaptation over multiple timescales which range from hundreds of milliseconds to tens of seconds [Ulanovsky et al., 2004, Lundstrom et al., 2010, Homann et al., 2017, Latimer et al., 2019], and even multiple days in the case of habitu- ation [Haak et al., 2014, Ramaswami, 2014]. Rather than including STP mechanisms that operate over all those different timescales, we demonstrate that iSTDP is a straightforward mechanism to bridge different timescales without the need of multiple mechanisms or fine-tuning of parameters (Figure 4). (2) We were inspired by the growing experimental literature suggesting an important role of inhibition and inhibitory plasticity in adaptive phenomena (see Discussion subsection “Inhibitory plasticity as an adaptive mechanism”). (3) In computational models, iSTDP is usually studied in the context of balancing excitation [Sprekeler, 2017]. In our study, we present functional consequences of inhibitory plasticity.

    Although inhibitory plasticity is indeed induced over several minutes in pairing experiments [Field et al., 2020, D’amour and Froemke, 2015], inhibitory postsynaptic currents are already increased directly after plasticity in- duction – though it takes additionally several minutes to reach a stable new baseline (e.g. Figure 2A,B in [Field et al., 2020]). For example, the mean increase of inhibitory synaptic strength right after plasticity in- duction in [Field et al., 2020] is approximately 30-50%, while a new stable baseline at about 80-100% increase is reached after approximately 20 minutes (Figure 2A in [Field et al., 2020]; similar results in Figure 1H,I in [D’amour and Froemke, 2015]). This suggests that significant changes of inhibitory synaptic strength in iSTDP experiments already occur while the plasticity induction protocol is still ongoing. How fast these plasticity mech- anisms act in an in vivo setting during stimulation with naturalistic stimuli is to our knowledge not known. In general, the question of the true timescale of iSTDP is still an open problem [Sprekeler, 2017].

    We also point out that the inhibitory synaptic weight changes induced via iSTDP are rather small in our model, i.e. Figure 4C shows that the mean inhibitory synaptic weights onto the adapted excitatory population increase approximately 15-20%. Therefore, we propose that relatively small inhibitory weight changes are suffi- cient for the occurrence of a novelty response and these weight changes might already be happening during the paring protocol in experiments, as we argue above.

    Although we agree with the reviewer that short-term plasticity mechanisms are an important aspect to understand adaptation phenomena (especially on short timescales), we would not a priori exclude iSTDP only based on the argument of timescales. To get a full understanding of adaptive phenomena on all timescales, more detailed experimental and theoretical studies are needed to investigate the role of short versus long-term plasticity of excitatory and inhibitory synapses and how these mechanisms interact in a recurrent circuit.

    Modifications:

    In the new Figure 1-Figure Supplement 5 we study the effect of the timescale of subtractive normalization on the occurrence of a novelty response. In Figure 4-Figure Supplement 2 we quantify the response amplitude and the decay time constant of the novelty response as a function of the learning rate of inhibitory plasticity (see also our response to comment 1 of reviewer 2). Indeed, we find that fast inhibitory plasticity is needed to detect a novelty response. We discuss the mismatch between timescales of homeostatic plasticity in theoretical and experimental studies in lines 543 and 739. Additionally, we added new text in the Discussion subsections ‘Timescales of plasticity mechanism’ (line 509) and ‘Robustness of the model’ (line 533) where we discuss the timescale of inhibitory plasticity and subtractive normalization.

    A further issue relates to the temporal structure of adaptation. The authors show that adaption is independent of the sequence of the stimuli (ABCABC vs BACCBA) (it would be best to refer to this as sequential structure not temporal structure, which would often include the duration of stimuli and interval between stimuli). It is well established that the longer the interstimulus interval the less the adaptation. The model may or may not capture this effect depending on the assumptions regarding the spontaneous activity during the ISI as a result of the non-associative (pre-only) iLTD. However, given that STDP generally grows after induction it seems like the model is not likely to capture the standard observation that adapation should be less if the stimuli are presented with an ISI of 800 ms versus 400 ms. In figure 5, for example what happens if stimuli are presented for 20 seconds consecutively versus for 10 second then a silence of 2 seconds before another 10 second stimulation? No mention of the time course of spontaneous recovery from adaptation is made.

    Recovery from adaptation depends on the background activity level in the network during the inter- stimulus interval (Figure 5 and Figure 6-Figure Supplement 1). Specifically, low background activity between stimulus presentations slows the recovery from adaptation (Figure 6-Figure Supplement 1). However, increasing background activity between stimulus presentations can capture the decreased adaptation as the inter-stimulus interval increases (we show this in our new Figure 5).

    Justification:

    We agree with the reviewer that the term ‘temporal structure’ is misleading, and therefore exchanged it with the term ‘sequence structure’ in our manuscript (see for e.g. line 228).

    As the reviewer aptly predicted, the recovery of the response from adaptation indeed depends on the level of background activity between two stimulus presentations. In our model, the direction of inhibitory weight change (iLTD or iLTP) depends on the firing rate of the postsynaptic excitatory cells (see [Vogels et al., 2011]). Postsynaptic firing rates above a ‘target firing rate’ will on average lead to iLTP, while postsynaptic firing rates above the target firing rate will lead to iLTD. In turn, the average magnitude of inhibitory weight change depends on the firing rate of the presynaptic inhibitory neurons (see [Vogels et al., 2011]). Therefore, if the background activity between two stimulus presentation in our model is very low, recovery from adaptation only happens on a very slow timescale. To show this, we performed simulations similar to Figure 6 where a stimulus (A) was presented again after a pause of either 9 seconds (Figure 6-Figure Supplement 1A) or after 225 seconds (Figure 6-Figure Supplement 1B). Whereas the response to the stimulus was still adapted after 9 seconds, it fully recovers after more than 200 seconds. As expected, the stimulus-specific inhibitory weights decreased very slowly after stimulus presentation (Figure 6-Figure Supplement 1A, B; bottom). This slow decrease of inhibitory weights follows from the fact that the network is silent if no stimulus is being presented. We now discuss this result in line 357.

    However, if the background activity in the inter-stimulus interval is higher (either because of a higher back- ground firing rate or because of evoked activity from other sources, for example other stimuli), the adapted stimulus can recover faster. To address how such elevated background activity can affect adaptation to a specific stimulus, we performed additional simulations (Figure 5), in which we used the experimental paradigm from Figure 1A. Similar to Figure 2C, we changed the number of stimuli in the sequence, which leads to different inter-repetition intervals (the interval until the same stimulus is presented again) of a repeated sequence stimu- lus. For example, if two repeated stimuli (A, B) are presented, the inter-repetition interval for each stimulus is 300 ms apart because each stimulus is presented for 300 ms. If four repeated stimuli are presented (A, B, C, D), the inter-repetition interval for each stimulus is 900 ms. Importantly, this means that in the time between the presentation of the same stimulus, the network is not silent (as in Figure 6-Figure Supplement 1), but active because other stimuli in the sequence are presented. We defined the adaptation level as the difference of the onset population rate, measured at the onset of the stimulation, and the baseline rate, measured shortly before the presentation of a novel stimulus. We found that an increase in the inter-repetition interval reduced the adaptation level of the excitatory population (Figure 5A, D) due to a decrease of inhibitory synaptic strength onto stimulus-specific assemblies (Figure 5B, E). Therefore, we conclude that our model can capture the reduced adaptation for longer inter-repetition intervals when background activity in the inter-repetition interval is elevated, in this case because of the presentation of other stimuli.

    Modifications:

    We replaced the term ‘temporal structure’ with the term ‘sequence structure’ in our manuscript (Results section “Stimulus periodicity in the sequence is not required for the generation of a novelty response”, line 211). We also included a new main figure to demonstrate the effect of varying the inter-repetition interval in the presence of evoked network activity from other stimuli (Figure 5), discussed in the new section ‘The adapted response depends on the interval between stimulus presentations‘” on line 306. Furthermore, we added Figure 6-Figure Supplement 1 to the manuscript and we discuss our findings in line 357 and line 469.

    1. It also does not seem like the model will capture recently reported effects such as the observation that optogenetic inactivation of inhibitory neurons during pulse n can actually increase adaptation to tone n+1 (Seay et al, 2020), indeed I believe the current model would make the opposite prediction

    Our model cannot capture the n+1 experiment in [Seay et al., 2020] because inactivation of inhibition will always increase the response to stimulus n (as in our disinhibitory experiment in Figure 7), hence decreasing adaptation.

    Justification:

    [Seay et al., 2020] measured several different types of short-term plasticity in the auditory cortex at synapses involving two different types of inhibitory interneurons: strong feedforward short-term depression onto PV interneurons and from PV to pyramidal neurons, as well as strong feedforward short-term facilitation onto SST interneurons and very weak short-term facilitation from SST to pyramidal neurons. We believe that including different interneuron types, as well as short-term dynamics of the respective synapses, might be nec- essary to explain this phenomenon. Indeed, using the experimentally observed short-term plasticity in a model, [Seay et al., 2020] showed that inactivation of PV interneurons can decrease the response, hence increase adap- tation, to the next (n+1) tone. Since our model includes a single type of inhibitory interneuron and implements long-term inhibitory plasticity rather than short-term plasticity, we are not surprised that our model cannot capture the increased adaptation in the very specific n+1 experiment. As we acknowledge in the manuscript, our proposed mechanism is not the only candidate to explain the generation of novelty responses and adaptive phenomena in the brain, and likely interacts with other types of plasticity and cell type dynamics.

    Modifications:

    We agree with the reviewer that the findings of [Seay et al., 2020] need to be discussed in context of our manuscript (see also our response to comment 9 of reviewer 1). Therefore, we added the reference and discuss it at line 499.

    1. In its current state I don't think (I may be mistaken) the model accounts for a related and very general property of auditory cortex: lateral inhibition (e.g., Brosch and Schreiner, 1997; Phillips, Schreiner, Hasenstaub, 2017).

    The term ‘lateral inhibition’ seems to have a somewhat different meaning in visual versus audi- tory cortex. In the visual cortex it is often considered as a spatial form of inhibition, while in the auditory cortex it also includes a temporal aspect. Since our model was mostly inspired by data in the visual cortex [Homann et al., 2017], we will answer the question in the context of the visual cortex, but also speculate about the auditory cortex.

    Justification:

    In the visual cortex, lateral inhibition is often defined in a ‘spatial’ manner whereby activated pyramidal neurons reduce the activity of their neighbors. Specifically, SOM-mediated spatial lateral inhibition contributes to surround suppression in visual cortex [Adesnik et al., 2012]. Our model already implements a form of spatial lateral inhibition. Based on experimental data (see e.g. [Harris and Mrsic-Flogel, 2013] for a review), we modeled inhibitory neurons as more broadly tuned than excitatory neurons, such that a single inhibitory neuron is more likely to be driven by multiple external stimuli (probability 15%) than a single exci- tatory neuron (probability 5%). During stimulus presentation, as inhibitory plasticity adjusts the strength of inhibitory-to-excitatory synapses, an inhibitory neuron with a given stimulus selectivity will likely strengthen synapses to multiple excitatory neurons selective to different stimuli – hence implementing spatial lateral inhi- bition.

    In the auditory cortex, lateral inhibition is often referred to as ‘forward suppression’ (or ‘forward masking’) [Brosch and Schreiner, 1997, Phillips et al., 2017]. Here, a preceding ‘masker stimulus’ influences the response of a probe stimulus. This influence depends on several factors, including the time difference between the masker and the probe stimulus, as well as the frequency of the pure tone masker stimulus [Brosch and Schreiner, 1997]. The time differences measured in these experiments are usually too short to be captured by the inhibitory plasticity mechanism proposed in our model. Similar as our answer to comment 3, we suspect that capturing feedforward suppression requires short-term plasticity plasticity (for e.g. [Phillips et al., 2017]).

    Modifications:

    We now included additional text in the Methods to address the issue of spatial lateral inhibi- tion, see line 796 and we now mention the phenomenon of forward masking in line 504.

  2. Evaluation Summary:

    This paper presents the results of a model for cortical plasticity and resulting increase in neuronal responses to unexpected stimuli. This is an elegant study that provides a number of interesting, experimentally testable, hypotheses and develops a prediction for a mechanism for novelty response generation. However, a number of concerns were raised about the model, including how it relates to certain experimental data, that should be addressed.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

  3. Reviewer #1 (Public Review):

    This is an interesting and well-written paper which presents the results of a model for cortical plasticity and resulting increase in neuronal responses to unexpected stimuli. Overall, this is an elegant study that provides a number of interesting, experimentally testable, hypotheses and develops a prediction for a mechanism for novelty response generation. The results are clearly presented, and provide for an insightful contribution in linking circuit models with function.

    Below, we comment on the relation between the model findings and published experimental results.
    The authors use the term "novelty" response, it is unclear to me whether this is a true novelty response because a number of stimulus parameters differs from those identified in the literature. The network is not sensitive to temporal structure, which suggests that it does not completely replicate certain aspects of neuronal adaptation in cortex. MEG studies in humans and electrophysiology in rats suggest that cortex should exhibit a differential response to different sequences of stimuli drawn from the same distribution. This model may be adjusted to produce temporal dependencies.

    In Homann 2017, the stimuli were scenes comprised of many Gabor patches. It would be interesting to consider how a broader pattern of stimulation would affect the results.

    One of the primary findings of Natan et al., 2015 was the differential effect of optogenetic disinhibition of SOM vs PV interneurons on the SSA response. It is possible that the differential learning rules for PVs and SOMs could produce variations in the novelty responses.

    An emerging theme from this paper and from other models such as Yarden and Nelken, 2017 and Park and Geffen, 2020, may be that the tonotopic organization of similarly tuned neurons helps facilitate adaptation. Tuned assemblies were a key feature of the models in these papers. Here, the tonotopic organization arises from the STDP rule here, with plasticity supporting tonotopic organization.

  4. Reviewer #2 (Public Review):

    This study by Schulz et al flushes out in fine detail an interesting consequences of inhibitory synaptic plasticity in plastic neuronal networks, showing that its ability to balance precisely only previously experienced stimuli makes this type pf plasticity an excellent candidate mechanism to allow novelty detection. Strong transient responses will be evoked only by those stimuli which have not previously activated (and thus trained) the stimulus specific set of inhibitory stimuli. An open question remains with regard to the time scales and speed of learning at these inhibitory sites, something that will be answerable by the experimental audience of this paper (but could be investigated in a bit more detail in the model as well).

  5. Reviewer #3 (Public Review):

    This computational paper addresses the mechanisms of sensory adaptation and novelty detection in the auditory cortex. A spiking RNN model of 5000 (4000 excitatory/1000 inhibitory) units is developed and adapted to sequences of inputs (ABC...) followed by a novel stimulus N. As with experiments the model captures the adaptation to the repeated stimuli, as well as a strong response to a novel stimulus. In contrast to many models of sensory adaptation that rely on short-term synaptic plasticity, here adaptation arises from STDP at the Inh->Ex connection. Specifically, during ABCABC ... the inhibitory connection onto active Ex units is enhanced through associative plasticity mechanisms, but not onto the inactive Ex units, thus the adaptation does not apply to the novel stimuli. While the approach seems fairly novel it is also speculative and seems to run contrary to the existing experimental data.

    1. The reason many models of adaptation focus on short-term synaptic plasticity (STP) as opposed to STDP is that the later generally is not thought to operate on the adaptation time scale of seconds. Specifically, STDP is generally considered to be a form of long-term associative plasticity, and thus to rely on mechanisms such as the insertion of new receptors-a processes that is unlikely to operate on a time scale of a second or so. Adaptation is robustly observed at 400 ms (e.g., Natan et al 2017), a time scale that is generally considered to be incompatible with STDP. E.g. in the D'Amour paper the authors cite, STDP is induced over a 5 minute pairing protocol, and can still increase over the course of 5-10 minutes post pairing (e.g., Fig 1H). I'm not aware of any evidence suggesting that iSTDP could be induced and expressed on the subsecond to a few seconds time scales. So this seems to be a fundamental issue that needs to addressed or at least discussed.

    Related to the point above the model also contains subtractive normalization implemented with a time step of 20 ms. Again if this normalization is critical to the model this assumption would pose a serious challenge to the model because there is little or no experimental data suggesting that normalization can operate at that time scale.

    1. A further issue relates to the temporal structure of adaptation. The authors show that adaption is independent of the sequence of the stimuli (ABCABC vs BACCBA) (it would be best to refer to this as sequential structure not temporal structure, which would often include the duration of stimuli and interval between stimuli). It is well established that the longer the interstimulus interval the less the adaptation. The model may or may not capture this effect depending on the assumptions regarding the spontaneous activity during the ISI as a result of the non-associative (pre-only) iLTD. However, given that STDP generally grows after induction it seems like the model is not likely to capture the standard observation that adapation should be less if the stimuli are presented with an ISI of 800 ms versus 400 ms. In figure 5, for example what happens if stimuli are presented for 20 seconds consecutively versus for 10 second then a silence of 2 seconds before another 10 second stimulation? No mention of the time course of spontaneous recovery from adaptation is made.

    2. It also does not seem like the model will capture recently reported effects such as the observation that optogenetic inactivation of inhibitory neurons during pulse n can actually increase adaptation to tone n+1 (Seay et al, 2020), indeed I believe the current model would make the opposite prediction

    3. In its current state I don't think (I may be mistaken) the model accounts for a related and very general property of auditory cortex: lateral inhibition (e.g., Brosch and Schreiner, 1997; Phillips, Schreiner, Hasenstaub, 2017).