Reduced Electromotility of Outer Hair Cells Associated with Connexin-Related Forms of Deafness: An In silico Study of a Cochlear Network Mechanism
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- Mistrík, P. & Ashmore, J.F. JARO (2010) 11: 559. doi:10.1007/s10162-010-0226-3
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Mutations in the GJB2 gene encoding for the connexin 26 (Cx26) protein are the most common source of nonsyndromic forms of deafness. Cx26 is a building block of gap junctions (GJs) which establish electrical connectivity in distinct cochlear compartments by allowing intercellular ionic (and metabolic) exchange. Animal models of the Cx26 deficiency in the organ of Corti seem to suggest that the hearing loss and the degeneration of outer hair cells (OHCs) and inner hair cells is due to failed K+ and metabolite homeostasis. However, OHCs can develop normally in some mutants, suggesting that the hair cells death is not the universal mechanism. In search for alternatives, we have developed an in silico large scale three-dimensional model of electrical current flow in the cochlea in the small signal, linearised, regime. The effect of mutations was analysed by varying the magnitude of resistive components representing the GJ network in the organ of Corti. The simulations indeed show that reduced GJ conductivity increases the attenuation of the OHC transmembrane potential at frequencies above 5 kHz from 6.1 dB/decade in the wild-type to 14.2 dB/decade. As a consequence of increased GJ electrical filtering, the OHC transmembrane potential is reduced by up to 35 dB at frequencies >10 kHz. OHC electromotility, driven by this potential, is crucial for sound amplification, cochlear sensitivity and frequency selectivity. Therefore, we conclude that reduced OHC electromotility may represent an additional mechanism underlying deafness in the presence of Cx26 mutations and may explain lowered OHC functionality in particular reported Cx26 mutants.
Keywordscochleagap junctionouter hair cellmodellingcochlear mechanics
Deafness exists in a variety of inherited nonsyndromic forms, with more than 70 loci identified so far (Petit 2006). Mutations in a single gene, the gap junction beta 2 (GJB2) gene, account for nearly 50% of cases. The GJB2 gene encodes for the protein connexin 26 (Cx26), which together with other connexins such as Cx30, forms the gap junctions between non-sensory cells in the cochlea (for review, see Nickel and Forge 2008; Rabionet et al. 2000). The most common GJB2 mutations are single nucleotide deletions and frame shifts (such as 35delG, 167delT, and 235delC). These are well documented as leading to deafness in human populations. Missense mutations such as M34T or R75W have a dominant negative effect on hearing (Rabionet et al. 2000) and functional analysis of such mutations have identified reduced ionic conductivity of the gap junction (GJ) as the associated defect (Bicego et al. 2006; Bruzzone et al. 2003). It has also been proposed that mutations such as V84L, with reduced permeability to metabolites such as IP3 (Beltramello et al. 2005) may exert their effect by interfering with the development and maintenance of the organ of Corti.
Mutations in GJs can lead to the apoptosis of hair cells. This has been observed in an animal model with a cochlea-specific GJB2 ablation (Cohen-Salmon et al. 2002). The observation is compatible with GJs serving to buffer extracellular K+ by supporting cells, as occurs in astrocytes in the central nervous system (Kikuchi et al. 2000; Santos-Sacchi 1985). Nevertheless, cell degeneration is not inevitable, for it has been shown in an animal model expressing the human dominant-negative Cx26 mutation R75W that there may be significant anatomical deformations of the organ of Corti (Kudo et al. 2003), but that the outer hair cells (OHCs) develop normally (Minekawa et al. 2009).
Audiological examination of patients carrying GJB2 mutations exhibit reduced or missing distortion product oto-acoustic emissions (DPOAEs; Engel-Yeger et al. 2002; Engel-Yeger et al. 2003; Medica et al. 2005; Morell et al. 1998) although not in every case (Cheng et al. 2005; Santarelli et al. 2008). As reduction of the DPOAE is a sign of non-functional OHCs, such finding suggests that the underlying pathology in this case might be reduced OHC electromotility, essential for the active amplification of sound as shown by animal experiments where the ‘motor’ protein has been deleted (Liberman et al. 2002) or reduced (Cheatham et al. 2009).
We have recently developed a large-scale in silico model to describe current flow in the cochlea (Mistrik et al. 2009). Such large-scale 3D models have been developed previously to study cochlear potentials (Strelioff 1973) and in vivo cochlear stimulation (Suesserman and Spelman 1993). The model used here differs in several important aspects: (1) it is finer grained (the cochlea is divided into 300 cross-sections instead of 90 or 51 sections as previously used); (2) it uses a more accurate algorithm for the calculation of basilar membrane (BM) displacements (Mammano and Nobili 1993); and (3) the organisation of the equivalent electrical circuit reflects the advances in characterization of the molecular components of the cochlea and their electrical properties.
Such a model represents a prototype of an in silico diagnostic tool to asses the effect on system cochlear potentials of constituent molecular mutations. Previously, we used the model to analyse the role of lateral current spread through GJs in controlling extracellular field potentials and electrical filtering in the cochlear network (Mistrik and Ashmore 2009, Mistrik et al. 2009). The essential demonstration in such a model is that the extracellular fields around the OHCs can drive the cell’s electromotility largely independently of the cell’s time constant, and that these fields are modulated by current spreading through the gap junction systems in the cochlea. Such simulations show that the GJ systems are critical for keeping the anticipated frequency-dependent roll-off of the OHC transmembrane potential relatively small (6 dB/decade). For comparison, the potential of an isolated cell, outside a coupled network, would be reduced by 21 dB/decade or 6 dB/octave once above its corner frequency.
In this paper, we describe the method of implementing in the model the effects of different types of Cx mutations and the consequences for cochlear tuning and amplification. The simulations suggest that Cx26 mutations could increase the attenuation of the OHC transmembrane potential from 6 dB/decade to 14.2 dB/decade and reduce the electromotile forces by up to 35 dB at frequencies greater than 10 kHz. Such a decrease could nearly completely eliminate the 40 dB gain due to cochlear amplification associated with normal hearing. Such a mechanism might explain the impaired DPOAEs in spite of normal OHC non-linear capacitance in the R75W mutant mouse (Minekawa et al. 2009) and the absence of DPOAEs in subjects carrying the 35delG (Engel-Yeger et al. 2002) or 167delT (Morell et al. 1998) mutations.
An equivalent electrical circuit of the cochlea
The elementary circuit describing the radial current flow in a single cross-section is shown in Figure 1B. It is derived from a two-dimensional equivalent electrical model of the organ of Corti (Dallos 1984). Here, effective IHCs and OHCs are treated separately and assigned impedances ZIHC and ZOHC, respectively (Jagger and Forge 2006). The three rows of OHCs (and Deiters’ cells) were simulated as one row and the membrane parameters adjusted accordingly. The OHC is connected to a Deiters’ cell through a pathway expected to pass K+ ions during sound stimulation (Boettger et al. 2002; Johnstone et al. 1989; Santos-Sacchi 1985). The circuitry between an OHC and a supporting cell is shown in detail in Figure 1C. In contrast to previous models (Dallos 1984; Mountain and Cody 1999; O'Beirne and Patuzzi 2007; Ospeck et al. 2003), the resistors and capacitor describing the OHC baso-lateral membrane are distributed. This is to accommodate the observed spatial separation of K+ conductances (RBO) in the basal pole buried in the interface with a Deiters’ cell (node 7) and the lateral membrane with prestin (CBO) exposed to perilymph (node 11) of the space of Nuel (Boettger et al. 2002; Winter et al. 2007; Yu et al. 2006). A resistive pathway between the space of Nuel (node 11) and the perilymph (node 0) suggested by in vivo measurements of cochlear receptor potentials (Dallos et al. 1982) is facilitated in the model by current flowing through the capacitance divider CBO-CDC at the acoustic frequencies explored here. Simulations with an additional resistive element directly connecting these two nodes did not affect the gain functions calculated below and were not considered further. The additive effect of the OHC nonlinear capacitance (Spector et al. 2003) was included in the CBO value and its voltage dependence was not considered in the model as only small signals are being considered. To keep within reasonable computational times without resorting to high performance computing clusters, the complex cellular structure of stria vascularis, important for the generation of the endocochlear potential (Nin et al. 2008; Quraishi and Raphael 2008), was represented only as a single compartment and its electrical properties characterised by an effective resistor and capacitor (RSV and CSV, respectively). A battery, VSV, represents the mechanism for generating endocochlear potential, essentially at a constant value in this simulation.
The radial GJ conductance between supporting cells in the organ of Corti was implemented explicitly by the resistor RGJ connecting “uncoupled” Deiters’ (RDC and CDC) and cells lining the basilar membrane. These cells consist of Hensen’s cells, Claudius cells and Boettchers’ cells (at cochlear basal turns). The circuit connections were simplified to a single-lumped element consisting of a parallel RCC and CCC as done previously (Lagostena et al. 2001; Santos-Sacchi 1991; Santos-Sacchi and Dallos 1983). The main effect of this pathway is to allow a pathway to perilymph at high frequencies. The use of a single resistance/capacitor for theses sets of cells in each of 300 cross-sections ensured that the computational load was kept at reasonable levels although the intracellular potential of supporting cells was not defined in the circuit.
The longitudinal GJ conductance between adjacent cross-sections was implemented by three resistive connections by RGJL (see Figure 1D). The connection through the node 9 represents intercellular coupling in the organ of Corti; through the node 8, the coupling in stria vascularis and through the node 10 in the spiral limbus. An additional longitudinal coupling by the resistance RSN through the node 11 represents a low-impedance pathway at all frequencies through the extracellular space surrounding OHCs in the organ of Corti (Mountain and Cody 1999).
The acoustic stimulus was implemented by modulation of resistances RAO and RAI, which represent the MET channels in apical stereocilial membrane of the OHC and IHC respectively (Figure 1C shows the case of RAO). The MET conductances were modulated around their steady state values in proportion to the basilar membrane displacement computed by a model of BM mechanics (Mammano and Nobili 1993). This model gives realistic BM tuning, with the result that RAI and RAO were effectively modulated in 10-20% of the 300 cross-sections (see below). The critical OHC receptor potential, generated by such sound stimuli, is the voltage difference between nodes 3 and 11 (Figure 1C). This is the OHC lateral transmembrane potential which drives conformational changes in the prestin molecule.
Parameters used in simulations
IHC apical resistance
Calculated from RBI
IHC apical capacitance
(Lopez-Poveda and Eustaquio-Martin 2006)
IHC basal resistance
(Lopez-Poveda and Eustaquio-Martin 2006)
IHC basal capacitance
(Raybould et al. 2001)
IHC ionic potential
Resistance of spiral lamina
Resistance of scala tympani
OHC apical resistance
Calculated from RBO
OHC apical capacitance
Calculated from CBO
OHC basal resistance
OHC lateral resistance
Lower bound from leak resistance of OHCs
OHC lateral capacitance
(Housley and Ashmore 1992)
OHC ionic potential
Longitudinal resistance in space of Nuel
Estimate from geometry
Capacitance of Deiter’s cell
Resistance of Deiters’ cell
Resistance of gap junction
0.01 MΩ (for RGJ)
0.01 MΩ (for RGJL)
Lumped resistance of Claudius cells
Lumped capacitance of Claudius cells
Endocochlear potential in stria vascularis
Stria vascularis capacitance
(Mistrik et al. 2009)
Stria vascularis resistance
Computational model of current flow in the cochlea
Generation of OHC gain functions
The OHC transmembrane potential, ΔEOHC, indicates broader electrical tuning than its mechanical input. The broadening can be traced to longitudinal coupling between the sections. In addition, the phase of the electrical response is delayed by approximately 90° relative to the mechanical input as would be expected for a voltage generated across the capacitance of the OHC membrane (Figure 1B).
The amplitude and phase of the BM travelling waves, generated by single tones with a variety of logarithmically spaced best frequencies between 0.25 and 30 kHz, are shown in Figure 2C, D. The corresponding OHC transmembrane potentials, ΔEOHC (x, ω), are shown in Figure 2E, F. The maximal values as well as the accumulated phases at corresponding best position for each tone are indicated by an asterisk (*). Finally, ΔEOHC,max (ω), the maximum value of ΔEOHC(x, ω) at each stimulus frequency ω is shown in Figure 2G and the corresponding accumulated phase in Figure 2H. Such plots, connecting the mechanical input and electrical output, represent the gain functions (amplitude and accumulated phase) for the cochlea as a whole.
An examination of the frequency dependence of the OHC amplitude in Figure 2G reveals an attenuation of the response by 6 dB/decade with increasing frequency. For comparison, the frequency dependence of an isolated OHC is shown on the same plot, where the DC asymptote has been scaled to the same point. In this case, the external potential is 0 mV, whereas for cell coupled into a network, the external potential will depend on all the other elements in the circuit, and ΔEOHC,max will be modified accordingly. The isolated cell exhibits a roll off as 1/f, characteristic of a cell with a single RC membrane time constant with an attenuation of 21 dB/decade (or equivalently 6 dB/octave). As argued previously (Mistrik et al., 2009) the reduced attenuation of ΔEOHC,max in a cochlear network arises from the gradient in OHC conductance which increases from cochlear apex to cochlear base and the GJ coupling which allows the extracellular currents to build up non-zero extracellular potentials around the OHCs.
Cx26 mutations reducing intercellular connectivity (35delG)
The OHC gain functions from Figure 2 (the frequency dependence of the OHC transmembrane potential ΔEOHC,max) were used to assess the effect of Cx26 mutations. The changes in specific conductance of GJ were taken from the literature. For example, the residual permeability of the Cx26 mutant F83L for monovalent ions such as K+ is reported to be 72% of the wild-type (Bruzzone et al. 2003) and that of M34T 11% of the wild-type (Bicego et al. 2006). Furthermore, mutations such as 35delG, V37I, W77R, L90P, S113R, M163V, 167delT, and R184P result in a complete loss of function with residual conductivity ≤ 1% of the wild-type values (Bicego et al. 2006; Bruzzone et al. 2003). Other mutations, such as V84L, although reducing the conductivity for metabolites (Beltramello et al. 2005), were not considered here.
On the other hand, mutations such as 35delG, V37I, W77R, L90P, S113R, delE120, M163V, R184P, and 235delC with a complete loss of permeability (conductance decreasing to 0.1% of wild-type value or, equivalently, setting RGJ, RGJL = 10 MΩ) significantly reduced the ΔEOHC,max amplitude at frequencies above 1 kHz (Figure 4A). The corresponding increase in the attenuation from 6.1 to 10.7 dB/decade over the 0.25-30 kHz range (Figure 4C) can be explained by high frequency currents shunting to the ground (the perilymph) through the membrane capacitance of the supporting cells. It should be pointed out that this calculation is semiquantitive only. A larger value of RGJ is required to compensate for the supporting cell values chosen here: the precise network values are unknown experimentally. Qualitatively, at frequencies above those corresponding to the characteristic membrane time constant of the supporting cell network (here formed by RCC and CCC) most of the current gated by the transducer will pass to ground through the membrane capacitances.
A reduced ΔEOHC,max amplitude implies that the electromotile forces amplifying initial mechanical BM displacements are therefore likely to be much smaller. The simplest assumption is that the feedback forces are reduced in proportion. Nevertheless, implementing a stable feedback to the cochlear mechanics means significantly increasing the complexity of a cochlear mechanical model. For this reason, the implied reduced cochlear amplification was modelled by using a detuned rather than a sharply tuned BM displacement as the input for electrical calculations (Figure 2C, dashed lines). The BM input in this case corresponded to a quasi-passive cochlea model where the OHC feedback parameter, λ, used in Mammano-Nobili model is reduced from 1.2 to 0.05 (Mammano and Nobili 1993). The BM displacement with λ = 0.05 will be referred to below as a ‘detuned‘ input. The BM envelope still exhibited phase accumulation and frequency dependence, but the feedback was chosen to reduce the amplitude by 20 dB.
The gain functions (amplitude and accumulated phase) obtained for reduced conductances with such detuned BM input are shown in Figure 4D, E. The derived dependence of the amplitude attenuation on the GJ conductance (Figure 4F) indicated a maximal value of 12.3 dB/decade over the 0.25-30 kHz range for the mutations with 0.1% conductivity of wild-type. It should be noted that the phase accumulated at the best frequencies >300 Hz was increased (Figure 4E). Such an increase in phase accumulation arises from a parallel current injection into larger number of cross-sections as a result of a detuned mechanical input, and hence an increased filtering due the capacitance currents delaying responses in the circuit. It might be anticipated that such OHC receptor potentials would be further attenuated due to the cancelling effect of neighbouring OHC rows (Dallos and Cheatham 1976), but this would have required a finer grain model to investigate the point.
Cx26 mutations which reduce intercellular and extracellular conductivity (R75W)
It is well known that a functional epithelial cell gap junction system is essential for normal development of the inner ear as it facilitates necessary intercellular signalling (Nickel and Forge 2008). It is therefore not surprising that some GJ mutations lead to developmental malformations of the organ of Corti. For example, R75W significantly reduces the space of Nuel, the extracellular fluid-filled compartment surrounding OHCs (Kudo et al. 2003). Such defect could easily affect both the micromechanics of the cochlear partition and extracellular conductivity in the organ of Corti. In what follows, we shall explore the electrical consequences of the mutation.
When reduced electro-mechanical feedback was implemented using a detuned BM input (the case of R75W), the OHC attenuation was increased to 14.2 dB/decade over the 0.25-30 kHz range (Figure 5F). This value is larger than that obtained when only intercellular conductivity was reduced (Figure 4F, 12.3 dB/decade). Such in silico findings emphasises the importance of the low-resistance pathway through the space of Nuel in the maintenance of electromotile forces.
Cx26 and Cx30 mutations and endocochlear potential
In addition to a reduction of the gap junction conductivity in the organ of Corti, it is known that the targeted deletion of Cx26 can lead to a reduction of endocochlear potential (EP) from +80 to +40 mV, and to a reduction in endolymph potassium concentrations (Cohen-Salmon et al. 2002). It is also known that Cx30 deletions in stria vascularis can reduce EP to 0 mV (Teubner et al. 2003).
Global effects of Cx26 mutations on the OHC receptor potential
The examination of the frequency dependence of the amplitude and phase indicates a large variation in the effect of Cx26 mutations on the OHC receptor potential (Figure 7A, B). On the one hand, the responses for the M34T mutation is indistinguishable from the wild-type (the M34T result superimposes directly on top of the wild-type response). Such finding suggests that even a 11% residual GJ conductance in the in silico model of the organ of Corti is sufficient to maintain normal current flow and frequency dependence of the OHC receptor potential. Therefore, mutations such as M34T or F83L (72% residual GJ conductance) are unlikely to reduce the OHC electromotility.
On the other hand, Cx26 mutations resulting in a complete loss of function (35delG, V37I, W77R, L90P, S113R, M163V, 167delT, R184P) and residual conductivity of 0.1-1% lead to a strong increase in the attenuation at frequencies above 5 kHz. The largest effect is found for the R75W mutation where increased attenuation is apparent already for frequencies >1 kHz. This demonstrates the importance of the current flow through the space of Nuel, which is abolished by mutations resulting in a volume that does not open up during development.
The attenuation for different mutations is compared quantitatively in Figure 7C. It indicates that 35delG-like mutations double and R75W nearly triple the attenuation over the studied frequency range of 0.25-30 kHz. As the effect is largest at frequencies above 10 kHz, the effect of mutations at high frequencies is shown separately in Figure 7D. The figure compares the relative amplitude of the OHC receptor potential ΔEOHC,max at 30 kHz for wild-type and all mutants with respect to the wild-type amplitude at 250 Hz. In the case of the wild-type, the expected reduction would be 12.8 dB. On the other hand, the reduction of 26 and 35 dB was found for 35delG and R75W mutations, respectively, even before the effects of reduced electromotile feedback were included (and of 45 and 56 dB, respectively, when included). Such a reduction indicates that electrical filtering due to Cx26 mutations could, at least at frequencies ~30 kHz, nearly abolish the 40-60 dB gain provided by the OHC somatic amplification under normal physiological conditions (Ruggero and Rich 1991).
A computational laboratory for studying connexin mutations
The large-scale computational model of electrical currents used here provides an insight into the effect of circuit perturbations due to connexin mutations through their effects on ionic conductance. It offers, in addition, an opportunity to see how cells perform when coupled into a network, based on the data from single or small cell populations.
In a cochlear network circuit without any perturbations, the OHC receptor potential would be expected to show an attenuation of 6 dB/decade over the 0.25-30 kHz range. Such a low value (in a comparison to 21 dB/decade for an isolated OHC), results from the network distribution of current flow. The attenuation of 6 dB/decade is a quite conservative estimate, because the BM wave envelopes used as the input for the calculation of the frequency dependence of the potentials were all normalised to the same peak amplitude. However, there may be significant boosting of the BM amplitudes towards the cochlear base: as much as a 30 dB increase is predicted for some cochlear models (Ramamoorthy et al. 2007). This would provide a further ‘flattening’ of the OHC gain function. Thus, this minimal attenuation of the OHC transmembrane potential predicted from such cochlear models suggests that the OHC somatic electromotility can operate effectively in the whole auditory frequency range and not necessarily just in the low frequency range as originally predicted from measurements on isolated outer hair cells (Mammano and Ashmore 1996).
Effect of Cx26 mutations
The computational analysis of GJ mutation phenotypes performed here has revealed several indicative features of Cx26 mutations on current flow: (1) only a complete loss of function (0.1-1% residual GJ conductance) significantly reduces the OHC receptor potential; (2) a reduction in the OHC receptor potential requires detuning of mechanical input, presumably due to weaker electro-mechanical feedback into the system; (3) Cx26 mutations can be simulated so that some affect intercellular while others affect also extracellular connectivity; and (4) the loss of Cx26 function ( uniform reduction of GJ conductivity) associated with reduced endocochlear and electrochemical potentials can also be modelled.
The computations show how Cx26 mutations could have a significant effect on the potentials developed across the basolateral membrane of OHCs. The computed reduction was largest for the Cx26 mutations such as R75W and 35delG where the potentials ΔEOHC,max can be decreased by up to 35 dB at 30 kHz relative to wild-type. As such potentials are thought to be the driver of the OHC somatic electromotility, we suggest that these types of mutation could result in hearing loss due to reduced OHC electromotility in addition to any hair cell loss resulting from failed ionic homeostasis in the organ of Corti. Accordingly, in the R75W animal model of Cx26-related deafness, there is an absence of oto-acoustic emissions despite OHCs apparently being unaffected (Minekawa et al. 2009). A reduced input for OHC electromotility could also explain the deafness phenotype of 35delG or 167delT human carriers, who also lack DPOAEs in the absence of any other audiological defects (Engel-Yeger et al. 2002; Morell et al. 1998).
This research project was supported by European Commission FP6 Integrated Project EUROHEAR, LSHG-CT-20054-512063.