updated introduction

paper/sections/new_inh_model/inhibition_model.md

@@ -14,26 +14,28 @@ Here we use a more biologically inspired model to overcome some limitations that
 (inhib-intro)=
 ### Introduction 
 
-For the vast majority of animals, sound localization is realized through two classes of hidden acoustic cues: binaural and spectral cues. In humans, binaural cues alone are sufficient to discriminate azimuth angles between -90° to +90° degrees, whereas psychoacoustic evidence has shown how spectral cues have a role in the solution of front-back ambiguities and in angle recognition along the vertical plane (i.e. elevation angles) [@Gelfand2010]. Focusing on binaural cues, the two main signals exploited by different animals in creating an acoustic spatiality are interaural time and level differences (ITDs and ILDs). Their role and their dominance over each other depend mainly on animal head size and hearing range in terms of frequencies. 
+Once immersed in the neuroanatomy literature devoted to human sound localization circuits, we realized how to fully grasp the development of ITD sensitivity in the MSO it was necessary to parallel outline the strategy by which ILDs are represented in the LSO (Lateral Superior Olive). From an evolutionary point of view, specific to the mammalian phylogenetic tree, the MSO can in fact be considered a refined version of the older LSO [@Grothe2014].
 
-It is clear at first glance how ITDs are longer for species with large head sizes, conversely, these are much shorter for smaller animals, and therefore harder to be neuronally encoded. ILDs on the other hand occur when the wavelength of the sound stimulus is shorter than the size of the animal's head, which then generates a significant attenuation at the contralateral ear. For this reason, ILDs' significance with respect to ITDs' is greater in smaller animals with a middle ear specialised for the transmission of high frequencies (thus having a high-frequency hearing range). This was the case with early mammals, which in fact only developed structures dedicated to processing ILDs.
+LSO principal cells have a bipolar dendritic tree that receives excitatory input from the ipsilateral ear and inhibitory input from the contralateral one. All mammals appear to apply one common neural strategy for processing ILDs, which consists of subtraction between these two inputs.  For instance, neurons in the right LSO will be more excited when sound arrives from the right and more inhibited when sound arrives from the left. The function that describes LSO neurons’ firing rate according to different azimuth angles is usually a sigmoid, presenting the highest values for sound coming from the hemispace ipsilateral to the nucleus, with a steep slope centred on frontal angles (i.e., close to 0°), suggesting a rate-coding strategy for identifying different ILD values with high sensitivity for frontal angles, as suggested by psychoacoustic evidence.
 
-Even today, many small mammals rely exclusively on ILDs to perform sound localization and the main neural structure involved in the processing of this cue is the Lateral Superior Olive (LSO), a nucleus placed within the superior olivary complex in the mammalian brainstem. Only afterwards the selective pressure led some mammalian species to evolve a second specialized structure, the Medial Superior Olive (MSO), for the processing of ITDs solely. This was probably due to an increase in body size that provided production of low-frequency communication calls and thus the need to implement coding of ITDs as well [@Grothe2014].
-Humans, whose hearing range is shifted towards lower frequencies with respect to many mammals, possess both a large LSO and a well-developed MSO. As a matter of fact, psychoacoustic evidence has shown how both ITDs and ILDs are used for horizontal sound localization. In particular, the MSO can be considered as a refined processing stage with respect to the LSO for the localization of low-frequency sounds, at which ILD cues are not available [@Grothe2014].
-
-Therefore, it is important to outline the coding strategy for ILDs in the LSO to fully grasp the development of ITD sensitivity in the mammalian MSO.
-LSO principal cells have a bipolar dendritic tree that receives excitatory input from the ipsilateral ear and inhibitory input from the contralateral one. All mammals appear to apply one common neural strategy for processing ILDs, which consists of subtraction between these two inputs.  For instance, neurons in the right LSO will be more excited when sound arrives from the right and more inhibited when sound arrives from the left. The function that describes LSO neurons’ firing rate according to different azimuth angles is usually a sigmoid, presenting the highest values for sound coming from the hemispace ipsilateral to the nucleus, with a steep slope centred on frontal angles (i.e., close to 0°), suggesting a rate-coding strategy for identifying different ILD values. Although the on-off nature of this subtraction strategy, for which exquisite timing of inhibitory influences appears not to be a key prerequisite, the two major inputs to the LSO are specialized for high-fidelity temporal transmission. An explanation is found in the fact that the subtraction process happening in LSO principal cells is realized in a phase-locked way with respect to the stimulus. This implies a purely suppressive coincidence mechanism happening at each period of the phase-locked inputs to the LSO (spiking occurs unless binaural coincidence is happening).
+Although the on-off nature of this subtraction strategy, for which exquisite timing of inhibitory influences appears not to be a key prerequisite, the two major inputs to the LSO are specialized for high-fidelity temporal transmission. An explanation is found in the fact that the subtraction process happening in LSO principal cells is realized in a phase-locked way with respect to the stimulus. This implies a purely suppressive coincidence mechanism happening at each period of the phase-locked inputs to the LSO (spiking occurs unless binaural coincidence is happening).
 
 The MSO, on the other hand, receives two additional inputs compared to the LSO: a contralateral excitation and an ipsilateral inhibition. As a result of experimental observations, the main hypothesis is that the combination of these four inputs has converted the suppressive coincidence mechanism present in the LSO into an excitatory coincidence one for the detection of ITDs in the MSO (spiking occurs only if binaural coincidence is happening) [@Grothe2014].
 
-Nevertheless, the most famous model that attempts to explain the functioning of the MSO, namely the Jeffress model, considers only the two excitatory inputs arriving at the MSO, assuming an array of labelled neurons providing binaural coincidence detection for specific values of ITDs, due to the presence of axonal delay lines that can create this type of sensitivity [@Jeffress1948].
-For many years, Jeffress's remained the most accepted proposal, given the discovery of axonal lines potentially similar to those theorised by Jeffress in the Nucleus Laminaris (NL) of different bird species. However, the presence of similar delay lines in the mammalian MSO, analogous to the avian NL, has never been demonstrated. 
+Through the model described in this appendix, we therefore wanted to maintain the idea that there are coincidence mechanisms in the MSO neurons as present in the Jeffress Model, already amply described in the main text. Nevertheless, we also pointed out how the neuro-anatomical strategies adopted to implement this coincidence are different from those assumed by this gold standard model, since the presence of axonal delay lines in the mammalian MSO has never been experimentally demonstrated. 
+
+We therefore evaluated the activity (measured in global spikes during one second of sound stimulation) of these four nuclei (left and right LSO and MSO), using the firing rates of our artificial LSOs as a validation platform for our network, while exploring the impact of certain parameters in the processing of ITDs in the insilico MSO.
+In order to define a firing rate activity target during this second phase of the work, we relied on the results obtained in these two past experimental works:
+
+- in`Brand2002', the analysis of _in vivo_ recordings from the MSO of the _Mongolian gerbil_ showed how all the 20 neurons tested responded maximally to sounds leading in time at the contralateral ear. Peaks in the firing rate of these neurons were found also for (artificial) ITD values higher than the highest possible ones generated by the gerbil head, which correspond to almost 120 $\mu s$ for a sound coming at 90° from the contralateral hemispace. 
+
+- in {cite:t}`Pecka2008`, the physical mechanisms underlying the shift in peaks' activity towards contralateral ITD values was explored. The results showed how the two inhibitory inputs to the MSO, which are not considered in the Jeffres model, have instead a central role in this process. By blocking the glycinergic inhibition to the MSO neurons by means of the application of its antagonist, strychnine, the authors observed the loss of the peak shift in all their response activity. Having now a symmetry in all the neuron responses, with a peak in the activity corresponding to null ITD values (i.e., 0° azimuth angle), all the information present in the MSO responses had been lost. Inhibition was thus shown to have a central role in identifying the ITD values in the MSO. Consequently, in our model we tried to block these inhibitory inputs to explore the effect that they have on the MSO activity
 
-The first steps toward a better understanding of the MSO functioning were made through the work of {cite:t}`Brand2002` in which the analysis of _in vivo_ recordings from the MSO of the _Mongolian gerbil_ showed how all the 20 neurons tested responded maximally to sounds leading in time at the contralateral ear. Peaks in the firing rate of these neurons were found also for (artificial) ITD values higher than the highest possible ones generated by the gerbil head, which correspond to almost 120 $\mu s$ for a sound coming at 90° from the contralateral hemispace. This observation led to the hypothesis that peaks in these neurons' firing rate were not coding for a specific ITD value in gerbil-relevant physiological space, suggesting instead a mapping made by the slopes in the activity curves [@McAlpine2003], in a way similar to the rate-coding strategy adopted for ILDs in the LSO (even if in LSO cells the slope is positive passing from contralateral to ipsilateral sound sources, oppositely from what happens in MSO cells response). The idea of a topographic map at the level of the MSO portrayed by different peaks in cell activity (i.e., peak-coding) risks then to be discarded in favour of a less refined rate-coding strategy, in which recognition of the ITD value generated by an input sound should occur at a higher level (e.g., at the Inferior Colliculus).
+Finally, we wanted to understand how the firing rate activity of different neurons in the MSO could be differentiated, in order to code for different ITD values and consequently different sound source azimuth angles.
 
-{cite:t}`Brand2002` and {cite:t}`Pecka2008` explored also the physical mechanisms underlying the shift in peaks' activity towards contralateral ITD values. Since the presence of axonal delay lines had been discarded, there had to be another neural mechanism capable of compensating for the external ITD value, causing a growth in the activity of MSO neurons for gradually more and more contralateral sounds. The results show how the two inhibitory inputs to the MSO, which were not considered in the Jeffres model, had instead a central role in this process. By blocking the glycinergic inhibition to the MSO neurons by means of the application of its antagonist, strychnine, it was observed the loss of the peak shift in all their response activity. Having now a symmetry in all the neuron responses, with a peak in the activity corresponding to null ITD values (i.e., 0° azimuth angle), all the information present in the MSO responses had been lost. Inhibition has thus a central role in identifying the ITD values in the MSO, whether the coding strategy adopted consists of peak-coding or rate-coding. However, even in this case, although numerous proposals have been made, it is still unclear how the two inhibitory inputs manage to cause this higher excitability of MSO neurons for contralateral sounds and thus the peak shift observed experimentally.
-Some experimental studies have reported how inhibitory inputs, especially the contralateral one, can arrive slightly in advance of the excitatory inputs from the corresponding sides, thus influencing the way ipsilateral and contralateral inputs add up in the MSO neurons and thereby generating a maximum response for contralateral ITD values [@Myoga2014;@Roberts2013]. Nevertheless, other work has characterized the hypothesis of anticipation of inhibitory inputs as implausible [@vanderHeijden2013]. For this reason, in our work, we explored the validity of another hypothesis, proposed by {cite:t}`Myoga2014`, for which the neural mechanism employed by the MSO relies on the shape of post-synaptic potentials (PSPs), both excitatory (EPSPs) and inhibitory (IPSPs). Therefore, we developed a realistic _in silico_ model of the mammalian brainstem and tested different sets of time constants that then govern the shape of these PSPs.
+Some additional experimental studies reported how inhibitory inputs, especially the contralateral one, can arrive slightly in advance of the excitatory inputs from the corresponding sides, thus influencing the way ipsilateral and contralateral inputs add up in the MSO neurons and thereby generating a range of maximum responses for contralateral ITD values [@Myoga2014;@Roberts2013]. Nevertheless, other work has characterized the hypothesis of anticipation of inhibitory inputs as implausible [@vanderHeijden2013]. 
 
+Since the absence of a clear and shared hypothesis in literature, we decided to test our own: neurons in the MSO could present different activity given to the shape of post-synaptic potentials (PSPs), both excitatory (EPSPs) and inhibitory (IPSPs). 
 
 ### Methods
 Inspired by the neurophysiological data, we implemented a complex spiking neural network in Python using the NEST Simulator framework [@spreizer_2022_6368024]. The different neuronal populations composing the brainstem circuit and their interconnections are depicted in {ref}`network_diagram`.