Modelling firing regularity in the ventral cochlear nucleus: Mechanisms, and effects of stimulus level and synaptopathy
Graphical abstract
Introduction
The auditory system makes use of acoustic information on a wide range of temporal scales, from the microsecond scale of interaural time differences, up to the second or more scale of adaptation to stimulus statistics (Joris et al., 2004, McDermott and Simoncelli, 2011, McDermott et al., 2013). An important stage of temporal processing in the auditory system is the cochlear nucleus (e.g. Rhode and Greenberg, 1992). Many neurons in this nucleus receive spikes directly from auditory nerve fibres (in addition to other structures), and these spikes retain stimulus-induced precise timing. Given this, the cochlear nucleus is expected to be an important neural structure for the initial extraction of temporal features to be used by the rest of the auditory system. Indeed, many cell types in this area show interesting temporal responses to stimuli, such as cells that respond only or primarily to the onset of a stimulus. All signals pass through the cochlear nucleus, so understanding how temporal structure is transmitted or processed by neurons in this nucleus is key to understanding processing in the whole auditory system.
A striking example of temporal structure in the spike trains of cochlear nucleus neurons is found in the chopper cell of the ventral cochlear nucleus, which initially responds to a pure tone stimulus with a highly regular spike train. Chopper cells have been suggested to be important in the coding of temporal envelope cues (e.g. Lorenzi et al., 1995, Carney et al., 2015; for a review see Joris et al., 2004), which is widely agreed to be essential for understanding speech (Shannon et al., 1995, Friesen et al., 2001). In some chopper cells, the initial regular firing is sustained over the whole duration of the tone, in which case the cell is classified as a sustained chopper. In other cases, this regularity is reduced after a few tens of milliseconds, in which case they are classified as transient choppers. This distinction is illustrated in Fig. 1. A number of hypotheses have been put forward to explain this difference, including the effect of adaptation, the low-pass effect of dendritic filtering, the number of innervating fibres, and the degree of inhibition (Molnar and Pfeiffer, 1968, Blackburn and Sachs, 1989, Banks and Sachs, 1991, Hewitt et al., 1992, Hewitt and Meddis, 1993).
So far, no consensus has been reached to explain the mechanisms underlying the difference between transient and sustained choppers. This is partly due to a lack of knowledge of key properties of these cells. Choppers are generally thought to be stellate cells, although the direct evidence for this is based on a relatively small number of cells for which anatomical and electrophysiological data have been collected (e.g. five sustained chopper cells in Smith and Rhode, 1989). As an example of the problem, consider the number of auditory nerve fibres synapsing onto chopper cells. Most models assume a relatively large number (e.g. 60 in Hewitt and Meddis, 1993), but experimental data on the number of inputs to stellate cells has a very wide range. Ferragamo et al. (1998) suggest a minimum as low as 5 auditory nerve fibre inputs, while Young and Sachs (2008) suggest at least 10–20, and note that the methods used in both papers may only be finding the strongest synapses, so that both may be substantial underestimates. Further complicating matters, recent physiological evidence suggests that there may not be clearly defined classes, but rather a continuum of cell types (Typlt et al., 2012, Rothman and Manis, 2003a, Rothman and Manis, 2003b).
Most models of chopper cells make rather specific assumptions about these parameters (Banks and Sachs, 1991, Guerin et al., 2006, Hewitt et al., 1992, Hewitt and Meddis, 1993, Rothman and Manis, 2003a, Rothman and Manis, 2003b, Wang and Sachs, 1995, Wiegrebe and Meddis, 2004). Different assumptions for different models make it difficult to compare them and determine what are the essential features of the models that contribute to their behaviour. This study presents a reduced mathematical model that reproduces the full range of observed response patterns on the basis of a small set of parameters, that can then be related systematically to observed or hypothesized anatomical and physiological mechanisms. The low number of parameters allows us to see which of these mechanisms have a common effect on the model variables and therefore response patterns. It also allows us to perform a thorough search of the parameter space to assess the robustness of the model (how much the behaviour depends on fine tuning of parameters), and to identify which variables – and therefore mechanisms – are critical to reproduce the observed patterns. For a further discussion of the advantages of this approach to modelling, see O'Leary et al. (2015).
In recent years, many researchers have investigated the idea of a “hidden hearing loss” (e.g. Kujawa and Liberman, 2009, Schaette and McAlpine, 2011; for reviews see Plack et al., 2014, Plack et al., 2016, Oxenham, 2016, Liberman et al., 2016) in which neural output from the cochlea is reduced due to synaptopathy, but absolute (audiometric) thresholds may be normal or near-normal (so that the deficit is not detected in a standard clinical test). Kujawa and Liberman (2009) found that after an acoustic overexposure in which absolute thresholds only shifted temporarily, there was permanent damage to the cochlea. In particular, synapses were lost within 24 h and auditory nerve fibres over several months. Schaette and McAlpine (2011) proposed (as a hypothesis to explain tinnitus) that the brain may compensate for this loss of input fibres with a homeostatic mechanism that increases gain centrally, boosting the synaptic strength of the remaining auditory nerve fibres in order to restore the original firing rates of neurons in the cochlear nucleus. In this study, we investigate the consequences of this hypothesis on the temporal response properties of cochlear nucleus neurons. We focus on temporal properties for two reasons. Firstly, by construction, cochlear nucleus neural firing rates will be left unchanged according to this hypothesis. Secondly, the cochlear nucleus is known to have an important role in the initial processing and transmission of temporal information to the rest of the auditory system.
The code for this paper is available online at https://github.com/neural-reckoning/vcn_regularity. It is also possible to interactively explore the figures in this paper online without having to install the software locally, including changing all parameters.
Section snippets
Chopper cells
Sound entering the auditory system is initially transduced in the cochlea leading to the firing of spikes in auditory nerve (AN) fibres. These auditory nerve fibres project excitatory connections to the cochlear nucleus (CN) which is divided into two areas, dorsal and ventral (DCN and VCN). Neurons in the CN receive both excitatory and inhibitory inputs (Campagnola and Manis, 2014). “Chopper” cells are located in the VCN, and are characterised by their initial very regular response to a tone at
Model behaviour
We start by giving some intuition for the behaviour of the model developed in section 2 and defined by equation (2) before presenting the results in detail. Recall that this is a model only of the ongoing and not the initial part of the response of a chopper cell to a pure tone stimulus. The model states that the membrane potential v fluctuates as an Ornstein-Uhlenbeck process (similar to a Brownian motion) around a mean value μ, with a time scale τ, and a spatial scale σ (so that the majority
Discussion
We can summarise the results above as follows: in a reduced mathematical model of the ongoing response of chopper cells, we can robustly reproduce sustained and transient chopper cell behaviour through a variety of mechanisms. This supports the idea that there may not be a single factor or mechanism governing chopping behaviour. However, in all cases we find that removing auditory nerve fibre inputs to the cell – for example as a result of noise-induced hearing loss (Kujawa and Liberman, 2009)
Acknowledgements
D.G., A.d.C., and C.L. were supported by two grants from ANR (HEARFIN and HEART projects). This work was also supported by ANR-11-0001-02 PSL* and ANR-10-LABX-0087.
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