Reduced electromotility of outer hair cells associated with connexin-related forms of deafness: an in silico study of a cochlear network mechanism

Abstract

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.

FIG. 1

The three-dimensional model of current flow in the cochlea. A Schematic representation of radial current flow between different cochlear compartments in a single cross-section with stria vascularis (StV), inner/outer hair cells (IHC/OHC), Deiters’ (DC), Hensen (HC), Claudius (CC) cells and Reissner’s membrane (RM). B An equivalent electrical circuit of a cochlear cross-section, Z_IHC and Z_OHC, the effective IHC and OHC impedances, respectively. The circuit implants the detailed current flow around the OHC seen in (C). R_DC and C_DC, effective resistor and capacitor of Deiters’ cells membrane; R_HC and C_CC for Claudius cells; V_SV, R_SV and C_SV, the effective battery, resistance and capacitance of stria vascularis; R_SL and R_LS, resistors of spiral limbus; R_GJ, radial GJ connection between Deiters’and Claudius cells. Nodes 8, 9 and 10 are coupled between adjacent cross-sections and represent longitudinal intercellular GJ connections in StV, organ of Corti and spiral limbus. Nodes 11 in adjacent sections are connected by the resistor R_SN representing the space of Nuel (extracellular space surrounding OHCs). C Electrical coupling between an outer hair cell and a supporting cell (the OHC impedance in detail). R_AO, C_AO resistance and capacitance of the OHC apical membrane (R_AO is modulated by sound input); R_BO, C_BO resistance and capacitance of OHC basolateral membrane; V_OHC the OHC electrochemical battery, EP endocochlear potential. The IHC impedance is treated similarly, but R_BI and C_BI, the resistor and capacitor representing IHC basolateral membrane, are in parallel. Nodes 3 and 5 of IHC correspond to 2 and 4 of OHC (Mistrik et al. 2009). See Table 1 for values. D View of the circuit along the tonotopic axis at the level of OHCs and showing longitudinal current flow extracellularly through the space of Nuel (node 11 and R_SN) and intercellularly through organ of Corti (node 9, R_GJL).

FIG. 2

The generation of cochlear gain functions for the OHC transmembrane potential, ΔE_OHC,max. A and B An overlay of normalised BM travelling wave (broken line) and ΔE_OHC tonotopic pattern (solid line) produced by a 1 kHz tone (A amplitude, B phase). ΔE_OHC(x) is the OHC receptor potential between nodes 3 and 11 at the BM position x (0 < x < 1), relative to the stapes. C and D An overlay of eight BM travelling waves corresponding to frequencies of 0.25, 0.5, 1, 2, 4, 8, 16 and 32 kHz (C amplitude, D phase). For comparison, the travelling waves evoked in the tuned (solid line) and detuned (broken line) cochlea are both plotted. The amplitude of the detuned BM travelling wave is 20 dB smaller than in the tuned case. E and F An overlay of eight tonotopic patterns of ΔE_OHC generated using the tuned BM travelling waves from panels C and D. For each tone, the maximal amplitude (E) as well as the phase accumulated in the corresponding best position (F) are both indicated (asterisk). G The frequency dependence of the maximum OHC transmembrane potential, ΔE_OHC,max, for each tone (asterisk) derived from E. The case of an isolated OHC is also shown (broken line), where the external potential would be 0 mV. H The frequency dependence of the phase accumulated at the best position. The responses in this and subsequent figures correspond to low level acoustic stimuli (20-40 dB SPL), permitting computations to be made from a linearised model (Eq. 2).

FIG. 3

OHC gain function and the effect of the apex base gradient in the OHC membrane conductance. A The frequency dependence of ΔE_{OHC, max} for different apex-base gradients (–, fivefold increase between base and apex conductance; -.-, 20-fold; ---, 50-fold; …, 100-fold). B The dependence of the ΔE_{OHC, max} attenuation in the 0.25-30 kHz range on the tonotopic conductance gradient. The slope is computed from the results in A. C The frequency dependence of the phase accumulated at the best BM position for different apex base gradients.

FIG. 4

The effect of 30delG-like mutations on the OHC gain functions. A and B The frequency dependence of the amplitude and accumulated phase of ΔE_{OHC, max} for different residual GJ conductance (100%, –; 10%, -.-; 1%, --, 0.1% …). The GJ conductance was decreased by increasing the value of R_GJ and R_GJL. This represents the situation of 30delG-like mutations reducing intercellular conductivity between supporting cells in the organ of Corti. Tuned BM travelling waves ware used as the input for the calculation of ΔE_OHC. C The dependence of the attenuation of amplitude in the 0.25-30 kHz frequency range on the GJ conductivity. D and E Like A and B but with detuned BM travelling wave as input (and as a result the amplitude is 20 dB smaller than in Figure 2C). F The dependence of the attenuation on the GJ conductivity (a detuned BM was used as input).

FIG. 5

The effect of R75W-like mutations on the OHC gain functions. The same as in Figure 4 but in addition to R_GJ and R_GJL, R_SN was also increased in these simulations to mimic reduced extracellular conductivity through the space of Nuel (0.1%).

FIG. 6

The effect of reducing endocochlear potential. Non-functional connexins are associated with a decrease of the endocochlear potential battery (V_SV) and of K⁺ electrochemical potentials (V_OHC and V_IHC for OHC and IHC, respectively), see Table 1. In the case of Cx26^−/−,V_SV was reduced from 80 to 40 mV and both V_OHC and V_IHC from −100 to −70 mV to maintain stable intracellular resting potentials. Similarly, in the case of Cx30^−/−, V_SV was reduced to 0 mV and V_OHC and V_IHC to −55 mV. The frequency dependence of the OHC receptor potential with A tuned and B detuned mechanical input in the presence (wt) or absence of any of the two connexins. C The amplitude reduction due to a deletion of Cx26 or Cx30. Whether the BM was sharply tuned or detuned had no effect.

FIG. 7

Connexin mutations can reduce the OHC receptor potential. A and B The frequency dependence of the amplitude (A) and accumulated phase (B) for different Cx26 mutations. The curve for M43T was obtained with a tuned BM input and 10% residual GJ conductivity (R_GJ = R_GJL = 1 MΩ); delG with a detuned BM input, 0.1% residual GJ conductivity (R_GJ = R_GJL = 100 MΩ) and reduced circuit batteries as in Figure 6; R75W with a detuned BM input, 0.1% conductance (R_GJ = R_GJL = 100 MΩ), reduced extracellular conductivity in space of Nuel (R_SN = 50 MΩ) and reduced circuit batteries as in Figure 6. C The amplitude attenuation for the OHC transmembrane receptor potential ΔE_{OHC, max} at the 0.25-30 kHz range for different Cx26 mutations. The attenuation was calculated from the data in panel A. D The difference (shift) between the ΔE_{OHC, max} amplitude generated by a 30 kHz tone and a wt reference (250 Hz) for different Cx26 mutants. GJ the contribution purely due to electrical filtering through the cochlear network; BM + GJ the case with detuned mechanical input.