MEMBRANE ELECTROMECHANICS AT HAIR-CELL SYNAPSES

Transcription

1 MEMBRANE ELECTROMECHANICS AT HAIR-CELL SYNAPSES W. E. BROWNELL AND B. FARRELL Department of Otolaryngology, Baylor College of Medicine, Houston, TX 77030, USA R. M. RAPHAEL Department of Bioengineering, Rice University Houston, TX 77005, USA Both outer hair cell electromotility and neurotransmission at the inner hair cell synapse are rapid mechanical events that are synchronized to the hair-cell receptor potential. We analyze whether the forces and potentials resulting from membrane flexoelectricity could affect synaptic vesicle fusion. The results suggest that the coupling of membrane curvature with membrane potential is of sufficient magnitude to influence neurotransmitter release. 1 Introduction Phase-locking. Neurotransmitter release is an electromechanical event. Changes in membrane potential regulate the mechanics of vesicle fusion with the presynaptic membrane. Vesicles at auditory hair-cell afferent synapses collect around ribbon structures opposite a single afferent terminal ending. These synapses are characterized by the tonic release of neurotransmitter. Membrane depolarization increases, and hyperpolarization decreases, the rate of neurotransmitter release and neural discharge. The release of transmitter from a single vesicle is sufficient to trigger an action potential in the postsynaptic nerve fiber [3]. The time interval between presynaptic release and action potentials in the nerve fiber follows a Poisson distribution. When low-frequency sinusoidal acoustic stimuli are presented a periodicity emerges from the random discharge; action potentials tend to occur at a preferred phase angle (θ) and are suppressed about θ ± π. This neuronal synchronization or phase-locking is present at very low sound intensities, and improves with intensity until a limit is reached at mid to high intensities. As frequency is increased, synchronization remains high until a species-specific limit is reached, above which it rolls off. Vertebrate auditory neurons can phase-lock at frequencies approaching 10 khz [6], a frequency limit an order of magnitude greater than might be achieved by most molecular motors and cell signaling cascades. The ability of the hair-cell synapse to precisely dictate post-synaptic action-potential initiation during the period of a stimulus sinusoid represents unparalleled temporal control of presynaptic mechanics, namely vesicle fusion and neurotransmitter release. We speculate that a flexoelectric effect accompanies exocytotic fusion. Our calculations show that electromechanical coupling during Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 169

2 fusion pore formation produces forces and voltages that could in principle modulate neurotransmission. The flexoelectric effect. Synaptic vesicle exocytosis involves the fusion of a highly curved vesicle membrane with the relatively planar presynaptic membrane. The degree of curvature and temporal precision of phase-locking suggest a mechanism similar to one we proposed for electromotility of outer hair cells (OHCs) [9]. It incorporates the piezoelectric-like coupling of electrical potential and membrane curvature known as flexoelectricity [8]. Flexoelectric theory predicts that membranes bend in response to an applied electric field. The magnitude of the bending moment is directly proportional to the applied field and the magnitude of the flexoelectric coefficient. The flexoelectric coefficient is proportional to membrane polarization, which is a function of the charge and properties of the phospholipid and integral membrane proteins that make up the membrane. Because large curvature changes occur during vesicle fusion, even a small potential difference across the membranes may influence membrane mechanics or conversely the change in curvature could influence potential gradients. Linear forms for the direct (mechanoelectric transduction) and converse (electromechanical transduction) flexoelectric effects are applied to the fusion event. When the radius of curvature (R) is much greater than the thickness of membrane (d), R>>d, linear expressions are valid, but when this is not true, additional non-linear terms may contribute. Although the composition of cellular membranes is asymmetric, we present a static analysis based on the tractable theory developed for symmetric bilayer membranes. 2 Model and Results 2.1 The magnitude of the direct flexoelectric effect during the formation of the exocytotic fusion pore that forms from two flat membranes It is readily shown that for a flat symmetric bilayer the polarization per unit area will be zero, when the same bilayer is curved the induced polarization is no longer zero but is a linear function of the mean curvature [8]. Similarly, when two identical flat membranes fuse to form a rotationally symmetric fusion pore (Fig. 1) the curvature-induced polarization is described by P = i ( c c )f (1) s s m + p Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 170

3 where P s is the area density of flexoelectric polarization, c m and c p are the meridian and parallel curvatures of the pore, f is the flexoelectric coefficient and i s is a unit vector normal to the membrane surface and positive into the pore. The shape of the z (nm) cytosol z y vesicle x extracellular cytosol 0 30 x (nm) Figure 1. Geometry of a fusion pore. The pore is formed by fusion of the vesicle membrane with the plasma membrane. It is represented as a meridian surface through its axis of rotation (x = 0). Upper inset shows a parallel circle, a section of the pore orthogonal to the axis of rotation. The lines show the neutral surface of the fused pore membrane. In this example the aqueous channel has a radius of 0.5 nm at the pore waist (z = 0), c b is nm -1 and the length of the pore is ~ 18 nm. The ionic composition of the cytosol and pore fluids are identical in our analysis. fusion pore formed at the moment of fusion is unknown, but experimental evidence from secretory cells suggests that it is hourglass shaped. In this case, the membrane is not homogenously curved (i.e., it does not exhibit spherical or cylindrical curvature) and P s is a local property that depends upon the geometric curvature at a point. We adopt the approach of Markin and Albanesi [7] and do not assume the pore's shape, but calculate P s assuming the total bilayer curvature of the neutral surface (that plane within the membrane where the stress is zero), c b, is constant, i.e. c b = c m + c p. For weakly curved structures (i.e., c b is at least 50d, where d is the thickness of the bilayer at 4 nm) the flexoelectric potential difference, induced across an (inhomogenously) curved membrane can be estimated with the Helmholtz equation, which when combined with (1) is U f fc b /εε 0 ; where ε 0 is the dielectric permittivity of free space and ε is the average dielectric constant of the medium. Because the flexoelectric coefficent is the sum of dipolar and charge effects it is useful to write U f as: U f C D c b f f + (2) ε 0 εw ε L where ε W and ε L and are the dielectric constants of water in the double layer region and within the lipid membrane, and f C and f D are the flexoelectric coefficients of the charge and dipolar contributions. The charge term dominates for both strongly and weakly charged lipids. For negatively charged lipids both contributions have different signs and tend to reduce each other. In addition, the flexoelectric coeffcient also depends upon the mechanical coupling of both monolayers within the bilayer. If each monolayer is bent around its own neutral surface, f is at least a Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 171

4 factor of two less than that observed if the bilayer is bent around the neutral surface of the bilayer. Because the monolayers are bent around their own neutral axis during the fusion process, we calculate the induced voltage with values of f at f D /2. The coupling has a smaller influence on the charge component and we do not consider it. Outlined in Table 1 are the induced voltages calculated with first or second term of Eq. (2) where we assume ε L and ε w are 2 and 80, respectively. We calculate a maximum induced voltage of about -4 mv for a pore lined by uncharged lipids to 18 mv for a pore lined by charged lipids (Table 1). This polarization is induced across each membrane, and for this symmetrical case the polarization should set up P s P s U f (x 10 3, µv) C b (nm -1 ) cytosol fused membrane U f pore fluid 4 5 Figure 2. Direct flexoelectric effect resulting from fusion. Top left: schematic of polarization across fused membrane at the moment the aqueous channel forms. Bottom left: solid lines show electrical potential profile across the two flat bilayers before fusion and dashed lines show the profile upon fusion pore formation; Uf is the bending induced potential. The plot on the right shows that the flexoelectric potential is a decreasing function of the average bilayer curvature, c b, f D = 1.5 x J. a repulsive force between apposing membranes helping to stabilize the pore. The polarization will be offset by ions that will flow inwards and outwards through the pore, with a time course dependent upon the geometry of the pore. The bending energy to form the pore (Fig. 1) from two flat bilayers is 50 kt calculated as outlined by Markin and Albanesi [7], assuming 1 x J for the bending stiffness, where the spontaneous curvature of symmetric bilayers is zero when they are bathed in the same medium. Calculating the induced voltage during fusion for geometry closer to the synaptic vesicle-membrane event (i.e. the hair-cell synapse) requires developing flexoelectric theory beyond the linear region (cf. Eq. 1), because of the high Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 172

5 curvatures (0.05 nm -1 ). Charge movement is governed by Maxwell relaxation time and the slower diffusive relaxation process R 2 /D (R: radius of vesicle and D: diffusion coefficient in the region beyond the double layer). For a D of 6 x 10-6 cm 2 /s and R ~ 20 nm this corresponds to ~0.6 µs, so that the polarization may be involved in stabilizing the pore during the first few µs of the fusion event. Table 1. U f. calculated for bilayer curvature of nm -1 and reported values [8] of flexoelectric coefficients for four standard membrane lipids. Diphytanoylphosphatidylcholine (synthetic) 0.15 M KCl phosphatidyl serine (bovine brain, 0.1 M KCl) phosphatidyl choline (egg yolk,0.1 M Na Cl) phosphatidyl ethanolamine (E. coli 50 m M K Cl) f D + f C (x10-18, C) charge/lipid head group(%) U f (mv) Calculated with 2 nd term of equation 3 with f D /2; calculated with 1 st term 2.2 Converse flexoelectric effects leading to force production Once fusion pores form they fluctuate around a mean size after which they either expand irreversibly or close. The effect that an applied field has upon formation, fluctuation and expansion of the fusion pore has not been analyzed (see references within [7]). We briefly consider it here in light of the converse flexoelectric effect. When a field (E) is applied across a newly formed pore the electric component of the energy (H E ) may be described as E ( fc b ) A p H E (3) where A p is the pore area. For a potential of 30 mv and f of 3 x C across a pore of area 6500 nm 2 and curvature nm -1 the energy will be about kt, with the sign dependent upon the direction of the field and f. If the flexoelectric coeffcient is larger (2 x C), 4 kt will be generated for a potential difference of 1 mv. Whether an applied field will influence the dynamics of the fusion process will depend upon the direction of the field in relation to the size and direction of f. When added to the mechanical energy derived from bending, the electromechanical effect should influence pore dynamics, at least when the charge contribution (f C ) is present. Because the size and direction of the field may either increase or decrease tension (depending upon the direction of the field, properties of the membrane and participating ions) we suggest that it will also influence pore dynamics through its Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 173

6 effect on membrane tension. As described previously, phase-locking requires a modulation of the fusion process within a single cycle of the stimulus sinusoid and flexoelectric forces and fields could increase the probability of pore opening at θ, or, when the field reverses, pore closure at θ ± π. 3 Discussion Several events occur between acoustically evoked basilar-membrane vibrations and auditory-nerve firings. Displacement of mechanosensitive hair bundles leads to cation influx and receptor potentials which modulate voltage-gated calcium channels and the release of neurotransmitter. The magnitude of inner hair cell receptor potentials varies with stimulus intensity [2] yet the timing of neural discharge is intensity invariant for both clicks [5] and best frequency tones. In both mammals [1] and frogs [4], the preferred phase angle is invariant with sound intensity at best frequency. Temporal invariance in the presence of receptor potentials of increasing magnitude argues for a feedback mechanism resembling that of the cochlear amplifier on basilar-membrane vibrations. OHC mechanical feedback preserves the temporal fine structure of basilar-membrane vibrations throughout a broad range of intensities [11]. Temporal shifts of basilar-membrane vibration zero-crossings and local peaks and troughs would occur in the absence of mechanical feedback and these shifts are not observed experimentally [10]. We suggest that hair-cell afferent synaptic transmission involves flexoelectric mechanisms similar to those responsible for OHC electromotility [9]. Phase-locking is found in all vertebrates auditory systems. A corollary of our hypothesis is that OHC electromotility evolved from a membrane-based motor mechanism, this synaptic amplifier, associated with the presynaptic membranes at hair-cell afferent synapses. There are essential differences between the two because the frequency limit for electromotile force production is at least an order of magnitude greater than the frequency limit for phase-locking. While our results establish that the magnitudes of the forces and fields resulting from membrane flexoelectricity are sufficient to modulate neurotransmitter release, further work is required to experimentally verify our proposal and to extend our findings beyond simple membranes to the more complex membranes of living cells. The manner by which electromechanical coupling in synaptic membranes can explain the precise temporal control responsible for phase-locking will require still further analysis. Just as cochlear amplifier models are based on the intrinsic tuning of the basilar membrane, it may be necessary to consider either mechanical or electrical tuning at the synapse. Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 174

7 Acknowledgments We thank Drs. Eatock, Johnson, Oghalai, Petrov, Sachs, Saggau, Snyder, and Spector for useful discussions and critical review of a previous version of the manuscript. Supported by research grant DC00354 from NIDCD. References 1. Anderson, D.J., Rose, J.E., Hind, J.E., Brugge, J.F., Temporal position of discharges in single auditory nerve fibers within the cycle of a sine-wave stimulus: frequency and intensity effects. J. Acoust. Soc. Am. 49, Dallos, P., Response characteristics of mammalian cochlear hair cells. J. Neurosci. 5, Glowatzki, E., Fuchs, P.A., Transmitter release at the hair cell ribbon synapse. Nat. Neurosci. 5, Hillery, C.M., Narins, P.M., Neurophysiological evidence for a traveling wave in the amphibian inner ear. Science 225, Kiang, N.Y.S., Watanabe, T., Thomas, E.C., Clark, L.F., Discharge Patterns of Single Fibers in the Cat's Auditory Nerve. MIT, Cambridge, MA. 6. Köppl, C., Phase locking to high frequencies in the auditory nerve and cochlear nucleus magnocellularis of the barn owl, Tyto alba. J. Neurosci. 17, Markin, V.S., Albanesi, J.P., Membrane fusion: stalk model revisited. Biophys. J. 82, Petrov, A.G., The Lyotropic State of Matter: Molecular Physics and Living Matter Physics. Gordon and Breach Science Publishers, Amsterdam. 9. Raphael, R.M., Popel, A.S., Brownell, W.E., A membrane bending model of outer hair cell electromotility. Biophys. J. 78, Recio, A., Rhode, W.S., Basilar membrane responses to broadband stimuli. J. Acoust. Soc. Am. 108, Shera, C.A., Intensity-invariance of fine time structure in basilarmembrane click responses: implications for cochlear mechanics. J. Acoust. Soc. Am. 110, Comments and Discussion J. Howard: Does the flexoelectric effect shed light on the function of the synaptic ribbon or synaptic body? Answer: The role of the synaptic body at hair-cell synapses is not immediately apparent from a flexoelectric analysis. It could play a role if its dielectric constant Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 175

8 were significantly different than cytoplasm because voltage-dependent membrane tension and bending induced changes in membrane polarization are dependent on the immediate electrical environment. The presence of similar structures at the synapses of retinal photoreceptors and bipolar cells suggests the synaptic body is not involved. Visual transduction is slower than acoustic transduction and synchronizing neurotransmitter release to the membrane potential is not as demanding for the processing of visual information. Direct and converse flexoelectric effects may still be playing a role even if the visual system does not require the speed of membrane-based electromechanical coupling. Neurotransmitter release from hair cells and visual-system synapses is characterized by a steady baseline release of neurotransmitter, presumably in response to calcium entry associated with the silent and dark currents respectively. It has been suggested that the presynaptic body is involved in maintaining a readily releasable pool of vesicles. D. Oliver: To change the timing of the exocytosis process substantially, you need to change the kinetics of the rate-limiting steps. However, it has been shown for synapses and for the IHC synapse in particular (Beutner et al., Neuron 29, , 2001) that the rates of exocytosis are steeply dependent on Ca 2+, indicating that the Ca 2+ -dependent steps are rate-limiting. Thus, even if the dynamics of fusion pore formation are modulated by membrane potential, this should not show up in the speed of exocytosis? Answer: Calcium is required for vesicle fusion and your argument would be correct if pore formation was the result of a sequence of chemical reactions. The temporal precision of the event requires we entertain the possibility of mechanisms acting in parallel. One scenario is that calcium sets the level of neurotransmitter release. The time interval between this calcium-mediated vesicle release follows a Poisson distribution. The voltage-dependent membrane tension effect rides on top of this random process and either advances or retards pore formation depending on the direction of the electric field. Early and more recent models of calcium concentration at the synapse (Kidd and Weiss, Hear. Res. 49, , 1990; Sumner et al., J. Acoust. Soc. Am. 111, , 2002) propose a cascade of low-pass filters that can reproduce a delay (or latency) and the frequency-limit of phase-locking. These models do not account for the intensity invariance of the phase angle at the hair-cell s best frequency. Beutner et al. (Neuron 29, , 2001) invoke a concentration threshold for vesicle fusion and this value should be reached at increasingly shorter times as intensity is increased. The pore formation requires feedback similar to that of the outer hair cell on basilar-membrane mechanics. We are proposing that strong electromechanical coupling may account for both mechanisms. Brownell-BIOCOCHLEA.doc 1/31/ :08 AM 176