https://orcid.org/0000-0002-2097-1440
Figures
Abstract
Merkel cells combine with Aβ afferents, producing slowly adapting type 1(SA1) responses to mechanical stimuli. However, how Merkel cells transduce mechanical stimuli into neural signals to Aβ afferents is still unclear. Here we develop a biophysical model of Merkel cells for mechanical transduction by incorporating main ingredients such as Ca2+ and K+ voltage-gated channels, Piezo2 channels, internal Ca2+ stores, neurotransmitters release, and cell deformation. We first validate our model with several experiments. Then we reveal that Ca2+ and K+ channels on the plasma membrane shape the depolarization of membrane potentials, further regulating the Ca2+ transients in the cells. We also show that Ca2+ channels on the plasma membrane mainly inspire the Ca2+ transients, while internal Ca2+ stores mainly maintain the Ca2+ transients. Moreover, we show that though Piezo2 channels are rapidly adapting mechanical-sensitive channels, they are sufficient to inspire sustained Ca2+ transients in Merkel cells, which further induce the release of neurotransmitters for tens of seconds. Thus our work provides a model that captures the membrane potentials and Ca2+ transients features of Merkel cells and partly explains how Merkel cells transduce the mechanical stimuli by Piezo2 channels.
Author summary
Touch is an essential way for humans to sense the physical world. It is necessary to figure out how our tactile system works. However, how Merkel cells convey mechanical stimuli into neural signals and deliver them to Aβ afferents is still poorly understood. In this work, we develop a biophysical model of Merkel cells for mechanical transduction. We show that Ca2+ and K+ channels on the plasma membrane control the membrane potentials of Merkel cells and further regulate the Ca2+ transients in the cells. Ca2+ channels on ER and MT directly contribute to the Ca2+ transients. Under indentation, the influx of Ca2+ through Piezo2 channels is sufficient to trigger the Ca2+ transients in Merkel cells and internal Ca2+ stores inherit to maintain the Ca2+ transients, which further result in a sustained release of neurotransmitters that activates the Aβ afferents. Thus our findings partly explain how Merkel cells combine with Aβ afferents to generate an SA1 response to sustained indentation by Piezo2 channels.
Citation: Mao F, Yang W (2023) How Merkel cells transduce mechanical stimuli: A biophysical model of Merkel cells. PLoS Comput Biol 19(12): e1011720. https://doi.org/10.1371/journal.pcbi.1011720
Editor: Hugues Berry, Inria, FRANCE
Received: July 2, 2023; Accepted: November 27, 2023; Published: December 20, 2023
Copyright: © 2023 Mao, Yang. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript, and Supporting information files.
Funding: This work was supported by Youth Fund of the Zhejiang Lab(K2023MG0AA02 to FM, K2023MG0AA11), the National Key Research and Development Program of China (2021YFF0600203 to WY), the Key Research Project of the Zhejiang Lab (K2022PG1BB01 to WY, 2022MG0AC04 to WY). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Tactile end organs transduce various mechanical stimuli into action potential sequences. Among them, Merkel cell-neurite complexes, which mainly produce slowly adapting type 1(SA1) responses [1–3], play an important role in the reception of corners, edges, curvatures of objects, and gentle touch [4, 5].
Merkel cell-neurite complexes generate sustained action potentials with irregular intervals when a sustained mechanical stimulus is applied to the skin [3, 6, 7]. Recent studies found that Piezo2 channels, which are expressed in Merkel cells and Aβ afferents and only generate a transient current, are necessary for the sustained firing of Aβ afferents [7–9]. However, continuous current injections are required for Aβ afferents to generate sustained action potentials [3, 10]. Recent theoretical research also thought that rapidly adapting(RA) mechanical-sensitive(MS) channels like Piezo2 cannot account for the sustained responses of Merkel cell-neurite complexes [11]. Therefore, how Merkel cells transduce the mechanical stimuli with Piezo2 channels has not been well revealed.
Recent studies found that Merkel cells express many molecules that mediate synaptic vesicle release [12–14]. Some studies further checked that Merkel cells release neurotransmitter analogs to Aβ afferents [15, 16]. Merkel cells also generate unique Ca2+ transients under mechanical stimuli [6, 17]. Ca2+ is an important signal that regulates the release of neurotransmitters [18–20]. Besides, different from other neural cells, Merkel cells do not generate the Na+-related action potentials but have the Ca2+ and K+ dominant membrane potential behaviors [17, 21–23]. Finally, Piezo2 channels transport ions into the cell under mechanical stimulus, with a preferential transport of Ca2+. Therefore, Piezo2 channels, membrane potentials, Ca2+ transients, and vesicles release together to form a line in Merkel cells to translate the mechanical stimulus. However, a detailed biophysical model of Merkel cells is still lacking. It is still unclear how these parameters participate in the mechanical transduction of Merkel cells.
To address these questions, we establish a biophysical electrophysiological model of Merkel cells. First, we validate our model with experiments of [21–24]. The membrane potentials of Merkel cells under current stimuli vary with the conductances of plasma membrane Ca2+ channels. The Ca2+ transients in Merkel cells under high K+ solutions and hypotonic shock last for tens of seconds. Then, we explore the roles of ion channels on the plasma membrane, endoplasmic reticulum(ER), and mitochondria(MT) in membrane potentials and Ca2+ transients regulations of Merkel cells. The results show that Cav1.2 channels mainly contribute to the form of the peak of membrane potentials, while Kv1.4 channels inhibit this peak. BKCa, KDR, and Cav2.1 channels mainly regulate the steady membrane potentials. Cav1.2 channels cause the increase of Ca2+ concentration at the initial time, while Cav2.1 channels, Ryanodine and IP3 receptors on the ER increase the duration of Ca2+ transients. Interestingly, the Ca2+ channels on MT also lengthen the Ca2+ transients by satisfying the peak of Ca2+ transients.
Based on the above results, we further study the mechanical transduction of Merkel cells with Piezo2 channels. The results show that Merkel cells generate a continuous neurotransmitter release under a sustained indentation, in which the duration of neurotransmitter release is positively related to indentation depth. This duration lasts for tens of seconds, corresponding to the firing time of Merkel discs under indentation [6, 7, 24]. These results can partly explain how Piezo2 channels(RA MS channels) inspire Merkel cells to have the sustained neurotransmitter excitation on Aβ afferents for their continuous firing.
Materials and methods
Kinetics of ions
Most Merkel cells are globular in shape [25], and some Merkel cells in hair follicles have an irregular shape [24]. To simplify, here we assume the Merkel cell is a sphere with a radius of r. Merkel cells contain Na+, K+, Cl−, Ca2+, and some micro-molecules A− with negative charges inside the cell. Generally, cells keep in a near electro-neutral condition [26, 27]. We denote nNa, nK, nCl, nCa, and nA as the mole numbers of Na+, K+, Cl−, Ca2+, and A− inside the cell, respectively. Then their concentrations are CNa = nNa/(V − VER − VMT), CK = nK/(V − VER − VMT), CCl = nCl/(V − VER − VMT), CCa = nCa/(V − VER − VMT), CA = nA/(V − VER − VMT), where V is the volume of Merkel cells, V = 4/3πr3, VER and VMT are Endoplasmic reticulum and Mitochondria volume. We also set CNa,out, CK,out, CCl,out, and CCa,out as Na+, K+, Cl−, and Ca2+ concentrations in environmental solutions, respectively. Ions inside the cell are regulated by ion channels embedded in the cell membrane.
K+ channels.
The molecular profiling of Merkel cells shows that they express three kinds of voltage-gated K+ channels: Kv4.2, Kv1.4, and Kv8.1 [12]. However, the study of Yamashita shows there are only two kinds of ion currents of K+ in Merkel cells, which are similar to currents of Kv4.2 and Kv1.4 [21]. Further studies elucidated that Kv8.1 channels do not generate ion currents directly but regulate other K+ channels’ activities indirectly [28]. Therefore, here we only consider Kv4.2 and Kv1.4 channels in Merkel cells.
Kv1.4 channels. Kv1.4 channels are activated rapidly with the increase of cell membrane potential. A part of the currents inactivates rapidly, while the remaining currents have a slower inactivation [21, 29]. The data for modeling Kv1.4 channels was obtained by fitting the data from [29] (Fig B in S1 Appendix),
(1)
where
is the specific membrane conductance of Kv1.4, Vm is the membrane potential, EK is the equilibrium (or Nernst) potential of K+, F is the Faraday constant. For m, hfast, and hslow [29],
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Kv4.2 channels. Kv4.2 channels are both activated and inactivated rapidly [21, 30]. The model data was obtained from [21] (Fig C in S1 Appendix),
(10)
where
is the specific membrane conductance of Kv4.2. For m, h,
(11)
(12)
(13)
(14)
(15)
(16)
In addition to the above two K+ channels, there are also Ca2+-activated K+ channels(BKCa channels) and Delayed-rectifier K channels(KDR channels) in Merkel cells [12, 21, 23]. These two kinds of channels carry the majority of K+ currents in Merkel cells [21, 23].
BKCa channels. BKCa channels are activated by membrane potential and have no obvious inactivation behavior. As the intracellular Ca2+ concentration increases, the curve of the channels’ open probability versus membrane potential has a right shift [23, 31]. Here we take a similar channel model from [32],
(17)
where
is the specific membrane conductance of BKCa,
is the Nernst potential, For n,
(18)
(19)
(20)
(21)
(22)
(23)
where
.
KDR channels present a slow activation behavior, the parameters are taken from [21] (Fig D in S1 Appendix),
(24)
where gKDR is the specific membrane conductance of KDR, EKDR is the Nernst potential, For n,
(25)
(26)
(27)
Ca2+ channels.
Ca2+ plays an important role in Merkel cells’ responses under different stimuli like mechanical stimulation, hypotonic shock, etc [12, 22, 23]. Merkel cells mainly express two kinds of voltage-gated Ca2+ channels: Cav1.2 and Cav2.1 [12].
Cav1.2 channels. Cav1.2 channels are L-type(long-lasting) channels, which exhibit a Ca2+-dependent inactivation [33, 34]. The equations were taken from [32],
(28)
where
is the specific membrane conductance of Cav1.2, ECa is the Nernst potential, for m, h, and hCa,
(29)
(30)
(31)
(32)
(33)
(34)
(35)
where KhCa = 1uM.
Cav2.1 channels. Cav2.1 channels are P/Q-type channels [33, 35], which have no obvious inactivation behavior. The equations were taken from [32],
(36)
where
is the specific membrane conductance of Cav2.1, ECa is the Nernst potential, for n,
(37)
(38)
(39)
Piezo2 channels.
Merkel cells cannot translate mechanical stimuli to neural signals without Piezo2 channels, which carry inward currents under the indentation [6, 7]. Piezo2 channels are mechanical-sensitive(MS) channels, which can also be opened by the microtubule suction of the membrane [36–38]. Therefore we assume that Piezo2 channels’ open probability is regulated by membrane tension. Given that cells have a cortex which is comprised of the cell membrane and a thin, cross-linked actin network lying beneath the membrane, we assume that Piezo2 channels open probability is regulated by the cortex stress σ [39]. Piezo2 channels exhibit a fast activation and a fast inactivation [36, 40]. Besides, Piezo2 channels have another inactivation with a much longer time scale [38]. Here we introduce C, O, In, and hslow to represent the channel closed state, open state, short-time inactivation state, and the state beyond long-time inactivation, respectively. Only channels beyond the long-time inactivation state and open state can transport ions. The data for modeling Piezo2 channels was obtained by fitting the data from [36],
(40)
where JPiezo2 is specific membrane conductance of Piezo2 channels, EPiezo2 is the Nernst potential. Under loading,
(41)
(42)
(43)
Other parameters are the same all the time.
(46)
(47)
(48)
(49)
(50)
(51)
(52)
(53)
The parameters of Piezo2 channels are listed in Table 1, and the specific descriptions of Piezo2 channels are seen in Parameters estimation in S1 Appendix. The currents through Piezo2 channels in simulation and experiments are shown in Fig 1.
The ions flow generated in Piezo2 channels under different indentation depths. triangle line: experimental results from [36], solid line: simulation results(d0 = 5.8μm, d0 = 6.7μm, d0 = 7.0μm, d0 = 7.3μm, d0 = 7.6μm, d0 = 7.9μm).
Piezo2 channels are non-selective anion channels [36, 40]. All Ca2+, K+, and Na+ could flow across Piezo2 channels. But Ca2+ has the highest priority [36, 40]. Therefore, we assumed that the currents across Piezo2 channels are Ca2+ currents.
Besides these channels above, Merkel cells have a passive electrical property. We take Na+, K+, Cl−, and Ca2+ leak channels into consideration. These leak ions flow can be written as
(54)
(55)
(56)
(57)
where gi,leak and Ei are the specific membrane conductance and the equilibrium (or Nernst) potential of i,
, R is the gas constant, T is the thermodynamic temperature, zi is the valence of ions, i = Na+, K+, Cl−, Ca2+.
Pumps, cotransporters, and exchangers.
Similar to most cells, Merkel cells also contain ion pumps, cotransporters, and exchangers to keep the ions’ balance inside the cell. Here we take Na+/K+ pumps, Na+/K+/Cl− cotransporters, K+/Cl− cotransporters, Na+/Ca2+ exchangers, and Ca2+ pumps on the plasma membrane into consideration.
Na+/K+ pumps, which transport two K+ into the cell and three Na+ out of the cell once by consuming energy, keep a high K+ concentration and a low Na+ concentration in the cell [42, 43]. The intracellular concentrations of Na+ and K+ affect the rate of Na+/K+ pumps [44, 45],
(58)
where PNaKpump is rate constant. KNa,NaK and KK,NaK are constants, KNa,NaK = 10mM, KK,NaK = 140mM [46].
Na+/K+/Cl− cotransporters, which transport one Na+, one K+, and two Cl− in the same direction once, mainly loading Cl− into the cell [47–49]. Their flow is controlled by three ions concentrations [27],
(59)
where PNKCC1 is the rate constant.
K+/Cl− cotransporters, which transport one K+ and one Cl− in the same direction once, mainly extruding Cl− from inside the cell [48]. Their flow was regulated by the Cl− and K+ concentrations across the membrane [50–52],
(60)
where PKCC2 is the rate constant.
Plasma membrane Ca2+ pumps and Na+/Ca2+ exchangers both help to eliminate Ca2+ from inside the cell [53, 54]. A general model of Ca2+ pumps was used [55],
(61)
where PCapump is the rate constant, KCapump is constant, KCapump = 0.3uM.
Na+/Ca2+ exchangers exhibit complex dynamic behavior. They are motivated by membrane potential, Ca2+ and Na+ concentrations. Under steady state, Na+/Ca2+ exchangers transport Ca2+ outside the cell. When the cell is stimulated by currents or membrane voltage, the direction of Na+/Ca2+ exchangers flow will be reversed [56, 57]. The dynamic equation of Na+/Ca2+ exchangers can be written as [57],
(62)
where PCana is the rate constant, KmNa and KmCa are constants, KmNa = 87.5mM, KmCa = 0.5uM, η = 0.1, ksat = 0.35 [57].
Internal Ca2+ dynamics
Intracellular Ca2+ sources also play an important role in Ca2+ regulation in Merkel cells. The elimination of internal Ca2+ store greatly reduces the Ca2+ transients [22, 23].
Endoplasmic reticulum and Mitochondria are the main internal Ca2+ stores. There are main three channels on the Endoplasmic reticulum (ER) membrane including Ca2+ ATPase pump, Inositol 1,4,5-trisphosphate receptor (IP3 receptor), and Ryanodine receptor. Ca2+ ATPase pumps consume energy to actively load Ca2+ into endoplasmic reticulum, and their rate increase with cytoplasmic Ca2+ concentration [58, 59]
(63)
where Ppump,ER is the rate constant, KERpump is the dissociation constant, and their values are listed in Table 2.
Ryanodine receptors and IP3 receptors involve in Ca2+-induced Ca2+ release in Merkel cells [22, 23]. The Ca2+ flux by Ryanodine receptor is defined by the equation,
(64)
where PRYR is the rate constant, Ks,RYR and Kf,RYR are constant.
IP3 receptors have three sites for the combination of Ca2+ and IP3. One site is for activated Ca2+, and one site is for inhibitory Ca2+ [60]. It means that the increase of Ca2+ concentration from a low level, the combination of Ca2+ to IP3 receptors activates the receptor, as the Ca2+ concentration increase to a very high level, the receptor will be inhibited [61]. We introduce m and h to represent the activation and inhibitory role of Ca2+ on IP3 receptor,
(65)
(66)
where τm and τh are time constants.
(67)
(68)
The remaining site is for IP3, and the increase of IP3 concentration enhances the currents of IP3 receptors [61]. Thus we assume that IP3 receptors’ open probability equals to
(69)
where Pleak and
are rate constants, Pleak represents the leak flow of Ca2+ on ER.
is the dissociation constant, CCa,ER is the concentration of Ca2+ in ER.
IP3 mobilizes Ca2+ from intracellular stores through the IP3 receptors [62], and itself also takes a dynamic regulation in a single cell [63]. Generally, the entry of Ca2+ through Ca2+ channels on the membrane cause the hydrolyzation of phosphatidylinositol 4,5-bisphosphate (PIP2), which produces IP3 [64]. Then IP3 will convert to other matters even though the Ca2+ concentration is still high [63]. Therefore, we assume the production rate of IP3 increases with the Ca2+ concentration and the conversion rate of IP3 depends on its concentration,
(70)
where
and
are the rate constants,
is the dissociation constant,
is the concentration of IP3 precursors like IP2 [64].
preIP3 will be also replenished after consumption, and keep a rather stable state [65]. So we assume that preIP3 has a production rate related to its concentration. Then the change of preIP3 will be
(71)
According to the above three Ca2+ channels, the dynamic equation of Ca2+ in ER will be
(72) CCa,ER = nCa,ER/VER.
There are Mitochondrial uniporter(MCU) and mitochondrial Na+/Ca2+ exchanger (MNCX) on the mitochondrial membrane. MCU takes up Ca2+ into Mitochondria while MNCX releases Ca2+ from mitochondria to the cytoplasm. The Mitochondrial uniporter dynamics is controlled by the cytoplasm Ca2+ concentration [32],
(73)
where PMCU is the rate constant, KMCU is the dissociation constant.
The dynamics of mitochondrial Na+/Ca2+ exchanger are controlled by mitochondrial Ca2+ concentration [32],
(74)
where PMNCX is the rate constant, KMNCX is the dissociation constant. cCa,MT is mitochondrial Ca2+ concentration, cCa,MT = nCa,MT/VMT. The dynamic equation of nCa,MT will be
(75)
where SMT is the mitochondria surface, βMT = 0.3, which represents the buffer role for Ca2+ of mitochondria membrane [32].
According to the above ion channels, the ions change inside the cell can be written as
(76)
(77)
(78)
where Sref is the reference surface area of Merkel cell.
(79)
The membrane potentials of Merkel cells are regulated by currents across total ion channels. The Na+/K+ pumps transport two K+ into the cell and three Na+ out of the cell, so there is one charge out of the cell once. The cotransporters transport a Na+, a K+, and two Cl− in the same direction once, so the total discharge is zero. The Na+/Ca2+ exchangers transduce three Na+ into the cell and one Ca2+ out of the cell once, so there is one charge out of the cell once. Then the dynamic equation of Vm is
(80)
where Cm is the specific membrane capacitance.
Volume change
The cell volume V change is dependent on the flow of water across the cell membrane [39]
(81)
where S is the cell surface area, S = 4πr2, Jwater is water flux, it is controlled by the hydrostatic pressure difference and the osmotic pressure difference across the membrane [39]
(82)
where α is a rate constant α = 10−9cm ⋅ ms−1 ⋅ Pa−1, ΔΠ is the osmotic pressure difference across the membrane, which can be described as
(83)
Cells have a cortex which is comprised of the cell membrane and a thin, cross-linked actin network lying beneath the membrane. We take the cortex as an elastic layer, the cortex stress satisfies [39]
(84)
where K is the cortex elastic modulus, K = 6000Pa, Sref represents the cell surface under no stress, σa is the active contraction stress produced by the actin network, σa = −100Pa. For a spherical cell, the relationship between the cortex stress and hydrostatic pressure satisfies [39]
(85)
where hc is the cortex thickness, hc = 0.5μm [39].
Results
Validation of the model
There are three main stimuli to study the properties of Merkel cells, which are current pulses, high K+ solutions stimuli, and hypotonic shocks [7, 21–23]. We consider these three kinds of situations below.
Current pulses.
The rectangular negative current pulses induce the membrane potential dynamics of Merkel cells(Fig 2A and 2B), and the parameters of ion channels are seen in Table 3. The solid lines are simulation results and the triangle lines are experimental results from [21]. The results show that Merkel cells have almost passive responses to negative current pulses(Fig 2B).
(A) Negetive current pulses step in 8.14pA (experimental current step in 10pA). (B) Membrane potentials change under negative current pulses. The solid lines are simulation results, and the triangles are experimental results from [21]. (C) Positive current pulses step in 8.14pA, Green line: 9 × 8.14pA, blue line: 14 × 8.14pA. (D) Membrane potentials change under positive current pulses. The solid lines are the simulation results, and the triangles are experimental results from [21]. The parameters of ion channels are seen in Table 3.
However, the membrane properties of Merkel cells under positive current pulses are rather different. As shown in Fig 2C and 2D, when the amplitude of the current pulses is small, the membrane potential dynamics of Merkel cells are still like a passive response. As the currents increase(green and wathet blue line), the membrane potentials rise rapidly to a peak, then decrease and gradually stabilize. Unlike most other sensory cells or afferents, Merkel cells do not generate action potentials [7, 21].
Some Merkel cells exhibit more complex membrane potential dynamics [24] (Fig 3A). By changing the specific membrane conductance of Ca2+ and K+ channels and rate constants of some pumps on the membrane, we can get similar results. As shown in Fig 3B, the membrane potentials of Merkel cells rapidly reach a step, then fire. Ca2+ plays an important role in this membrane potential dynamics. If the Ca2+ concentration is reduced in the external solutions, the fire of membrane potentials disappears(Fig 3C and 3D).
(A) The changes of membrane potential of experimental results from [24]. (B) Membrane potentials change under current pulses in simulation, (C) The changes of membrane potential under the condition of reduced Ca2+ concentration in external solutions from [24]. (D) Membrane potentials change under current pulses in simulation at CCa,out = 5uM. blue line: 27.14pA, red line: 54.28pA, yellow line: 67.85pA. The parameters of ion channels are seen in Table 3.
Merkel cells not only have membrane potential regulation but also show Ca2+ dynamic behaviors. The common stimuli which elicit Ca2+ in experiments are high K+ solutions and hypotonic shock.
High K+ stimulus.
High K+ solutions are made by reducing Na+ and increasing K+ concentrations in external solutions [22, 23]. The experimental results from [23] are shown in Fig 4A. Here we increase CK,out by 130mM, and reduce CNa,out by 130mM to represent the high K+ solution. The results show that the high K+ solution induces a rapid increase in Ca2+ concentration. After reaching a peak, Ca2+ concentration decreases slowly(Fig 4B). This Ca2+ transient could last for tens of seconds in Merkel cells, which is much longer than the timescale of membrane potential dynamics(Fig 2). This Ca2+ transient is regulated by both plasma membrane Ca2+ channels and internal Ca2+ channels in Merkel cells. The inhibition of ER Ca2+ stores causes a dramatic drop in fluorescence intensity of Ca2+(Fig 4C). By setting the rate constants of Ca2+ channels on ER to zero, we can simulate a similar dramatic drop of Ca2+ concentration(Fig 4D).
(A) The fluorescence intensity change of Ca2+ under high K+ solution [23]. (B) The cytoplasm concentration of Ca2+ change under high K+ solution: cK,out increases by 130nM and cNa,out reduces by 130nM in simulation. (C) The fluorescence intensity change of Ca2+ under high K+ solution by adding thapsigargin (TG), which is a specific blocker of Ca2+ pumps on ER, to deplete intracellular Ca2+ stores [23]. (D) The cytoplasm concentration of Ca2+ change under high K+ solution in simulation by setting PRYR = 0, Pleak = 0, , and Ppump,ER = 0. The parameters of ion channels are seen in Table A in S1 Appendix.
Hypotonic shock.
The hypotonic shock also results in Ca2+ transients in Merkel cells. Merkel cells were cultured in solutions that remove a part of Na+ and add the same concentration of mannitols. Then hypotonic shock was induced by removing mannitols in solutions [22, 23]. The hypotonic shock induces Ca2+ to enter the cell, and the fluorescence intensity of Ca2+ increase slowly, after reaching a peak, Ca2+ concentration goes back to the baseline(Fig 5A) [22]. In the simulation, hypotonic shock causes the opening of Piezo2 channels, Ca2+ concentration increases and reaches the peak, then gradually decreases(Fig 5B). But Ca2+ transients in the experiments of [22] increase slowly while the Ca2+ transients in the simulation have an immediate increase. An important reason is that hypotonic shock can inhibit the cytoplasmic substances’ mobility [70], which hinders the quick entry of Ca2+ into the cell and diffusion of Ca2+ in the cell. However, our model didn’t take this inhibitory role of hypotonic shock into account, which is a limitation of our model.
(A) The fluorescence intensity change of Ca2+ under hypotonic shock by removing 30mM mannitol in external solution [22]. (B) The cytoplasm concentration of Ca2+ changes under hypotonic shock by removing 30mM mannitol in external solution in simulation. The parameters of ion channels are seen in Table A in S1 Appendix.
Effects of ion channels properties on membrane potentials and Ca2+ transients
According to experiments from [21–24], Merkel cells in different locations of skin, different animals, or different experimental conditions have different expression of ions channels. For example, in experiments of yamashita [21], currents across Kv1.4 and Kv4.2 channels with inactivation property are dominated in total K+ currents. While in experiments of piskorowski [23], BKCa channels carry 50 ∼ 80% of total K+ currents. The currents only have a slight decrease with time. Therefore, it is reasonable that these channels have various conductances in different Merkel cells. The results from different experiments and our simulation results are consistent with the opinion that these ion channels and pumps in Merkel cells are the keys that regulate the dynamics of membrane potentials and Ca2+ transients. However, how these channels control the membrane potentials and Ca2+ transients is still unclear.
Membrane potentials.
First, we study how Ca2+ channels regulate the membrane potentials of Merkel cells. By changing the specific membrane conductance of Cav1.2 channels, we find that, when gCav1.2 is zero, the membrane potential rapidly increases initially, then reaches a steady state gradually. There is no sharp peak for membrane potential(Fig 6A yellow line). With the increase of gCav1.2, the membrane potential rapidly rises to its peak. After a small drop, the membrane potential gradually stabilizes(Fig 6A purple line). The peak value of membrane potentials increases with (Fig 6A).
(A) The changes of membrane potential with different , yellow line:
, purple line:
, green line:
, blue line:
. (B) The changes of membrane potential with different
, yellow line:
, purple line:
, green line:
, blue line:
. (C) The changes of membrane potential with different PCapump. yellow line: PCapump = 3 × 10−16, purple line: PCapump = 3 × 10−15, green line: PCapump = 6 × 10−15, blue line: PCapump = 3 × 10−14(mol/(cm2 ⋅ ms)).
Compared to Cav1.2 channels, Cav2.1 channels have little role in the peak form of membrane potentials. When is small, they almost do not affect the membrane potentials(Fig 6B). As
increases to 0.1, the membrane potential has a higher steady value(Fig 6B blue line).
However, the phenomenon of membrane potential fire(oscillation) does not happen whatever or
changes. Interestingly, the oscillations of membrane potentials only appear when pCapump is in the right range (Fig 6C purple and green line). When pCapump is out of the range, the membrane potentials reach a steady state (Fig 6C yellow and blue line).
Next, we study the roles of K+ channels on membrane potentials. As is zero, the membrane potential has a bigger peak(Fig 7A yellow line). With the increase of
, the peak value of membrane potentials decreases(Fig 7A). This result indicates that Kv1.4 channels inhibit the peak of membrane potentials caused by Ca2+ channels.
(A) The changes of membrane potential with different . yellow line:
, purple line:
, green line:
, blue line:
. (B) The changes of membrane potential with different
. yellow line:
, purple line:
, green line:
, blue line:
. (C) The changes of membrane potential with different gBKCa. yellow line: gBKCa = 0, purple line: gBKCa = 0.18, green line: gBKCa = 1.8, blue line: gBKCa = 18(mS/cm2). (D) The changes of membrane potential with different gKDR. yellow line: gKDR = 0, purple line: gKDR = 0.01, green line: gKDR = 0.1, blue line: gKDR = 1(mS/cm2).
As is zero or small, they have little influence on membrane potentials(Fig 7B yellow line). This also means that Kv1.4 channels mainly regulate the membrane potential peak in normal situations. As
increases to 20, Kv4.2 channels greatly reduce the resting membrane potential, further suppressing the action potential peak(Fig 7B blue line).
When gBKCa is zero, the membrane potential reaches the normal peak but continues to increase over 100mV(Fig 7C yellow line). As gBKCa increases, the membrane potentials decrease to a steady state after reaching the peak(Fig 7C). The steady value of membrane potentials decreases with the increase of gBKCa(Fig 7C).
When gKDR is zero, the membrane potentials have a little change(Fig 7D yellow line). This result also indicates that BKCa channels mainly control the steady membrane potentials. As gKDR increases, the steady membrane potentials also reduce(Fig 7D).
In experiments of [21], the inhibition of K+ channels and the enhancement of Ca2+ channels by the external solution containing Ba2+ make Merkel cells depolarize at smaller currents injection. This is consistent with our results that with the decrease of conductances of K+ channels like Kv1.4, BKCa, and KDR channels, the depolarized membrane potentials are more positive(Fig 7A, 7C and 7D). The membrane potentials also form the peak at smaller currents injection, which is consistent with the increase of and the decrease of
cause the peak of membrane potentials in simulation (Figs 6A and 7A).
Finally, we also study the influences of internal Ca2+ receptors and channels on membrane potentials. However, they almost have no function on membrane potentials(Fig 8).
(A) The changes of membrane potential with different PRYR. yellow line: PRYR = 0, purple line: PRYR = 0.08, green line: PRYR = 0.8, blue line: PRYR = 8(cm/ms). (B) The changes of membrane potential with different . yellow line:
, purple line:
, green line:
, blue line:
(cm/ms). (C) The changes of membrane potential with different PCapump,ER. yellow line: PCapump,ER = 0, purple line: PCapump,ER = 0.7 × 10−18, green line: PCapump,ER = 0.7 × 10−17, blue line: PCapump,ER = 0.7 × 10−16(mol/(cm2⋅ms)). (D) The changes of membrane potential with different PMCU(PMCU/PMNCX = 5). yellow line: PMCU = 0, purple line: PMCU = 0.5 × 10−15, green line: PMCU = 0.5 × 10−14, blue line: PMCU = 0.5 × 10−13(mol/(cm2 ⋅ ms)).
Together, these results indicate that Cav1.2 channels mainly help to form the peak of membrane potentials while Kv1.4 channels directly reduce this peak. The coupling between Cav2.1, Cav1.2 channels, and Ca2+ pumps contribute to the oscillation of membrane potentials. BKCa and KKDR channels are mainly to maintain a lower steady membrane potential.
Ca2+ transients.
First, when is zero, cytoplasmic Ca2+ concentration only increases slightly under current stimulation(Fig 9A yellow line). As
increases, cytoplasmic Ca2+ concentration has a rapid rise and fall (Fig 9A). The peak of cCa increases with
.
(A) The changes of Ca2+ concentration in the cell with different , yellow line:
, purple line:
, green line:
, blue line:
. (B) The changes of Ca2+ concentration in the cell with different
, yellow line:
, purple line:
, green line:
, blue line:
. (C) The changes of Ca2+ concentration in the cell with different PCapump. yellow line: PCapump = 0, purple line: PCapump = 0.3 × 10−15, green line: PCapump = 0.3 × 10−14, blue line: PCapump = 0.3 × 10−13(mol/(cm2 ⋅ ms)).
When is zero, they don’t affect Ca2+ transients(Fig 9B). As
increases, the Ca2+ concentration not only has a bigger peak but also keeps at a high level for a longer time(Fig 9B green line). However, if
increases to 0.002, the Ca2+ concentration rises over to 50μM(Fig 9B blue line), which less happens in normal condition. These results are consistent with the results that the inhibition of Cav1.2 or Cav2.1 reduces the Ca2+ transients in experiments of [12].
Oppositely, when PCapump is zero, the resting Ca2+ concentration is high(Fig 9C yellow line), and the Ca2+ transients elicited by the current pulse are more obvious. As PCapump increases, the resting Ca2+ concentration gets smaller, and Ca2+ transients are also weak(Fig 9C).
Next, Kv1.4 and Kv4.2 channels both have a little role in Ca2+ transients(Fig 10A and 10B).
(A) The changes of Ca2+ concentration in the cell with different . yellow line:
, purple line:
, green line:
, blue line:
. (B) The changes of Ca2+ concentration in the cell with different
. yellow line:
, purple line:
, green line:
, blue line:
. (C) The changes of Ca2+ concentration in the cell with different gBKCa. yellow line: gBKCa = 0, purple line: gBKCa = 0.18, green line: gBKCa = 1.8, blue line: gBKCa = 18(mS/cm2). (D) The changes of Ca2+ concentration in the cell with different gKDR. yellow line: gKDR = 0, purple line: gKDR = 0.01, green line: gKDR = 0.1, blue line: gKDR = 1(mS/cm2).
When gBKCa is zero, the Ca2+ concentration rapidly rises to a peak, then enters a long recovery process(Fig 10C yellow line). As gBKCa increases to 0.18, the Ca2+ cncentration reaches a bigger peak(Fig 10C purple line). But when gBKCa increase to 1.8, the peak of Ca2+ concentration decreases. If gBKCa is big enough, the Ca2+ transients are inhibited (Fig 10C green and blue line).
When KDR is zero or small, they have little role in the changes of Ca2+ concentration(Fig 10D). Only gKDR is big enough, the Ca2+ concentration has a very slight increase(Fig 10D blue line).
Finally, the internal Ca2+ stores have an obvious impact on Ca2+ transients. As PRYR is small, the Ca2+ transients are almostly unchanged(Fig 11A yellow line). When PRYR is big, the Ca2+ concentration rises to a bigger peak(Fig 11A blue line).
(A) The changes of Ca2+ concentration in the cell with different PRYR. yellow line: PRYR = 0, purple line: PRYR = 0.08, green line: PRYR = 0.8, blue line: PRYR = 8(cm/ms). (B) The changes of membrane potential with different . yellow line:
, purple line:
, green line:
, blue line:
(cm/ms). (C) The changes of Ca2+ concentration in the cell with different PCapump,ER. yellow line: PCapump,ER = 0, purple line: PCapump,ER = 0.7 × 10−18, green line: PCapump,ER = 0.7 × 10−17, blue line: PCapump,ER = 0.7 × 10−16(mol/(cm2 ⋅ ms)). (D) The changes of Ca2+ concentration in the cell with different PMCU(PMCU/PMNCX = 5). yellow line: PMCU = 0, purple line: PMCU = 0.5 × 10−15, green line: PMCU = 0.5 × 10−14, blue line: PMCU = 0.5 × 10−13(mol/(cm2 ⋅ ms)).
When is small, they also do not alter the Ca2+ transients(Fig 11B yellow and purple line). This indicates that the Ca2+ concentration increase at the beginning of the current stimulus is mostly controlled by Cav1.2 and Cav2.1. As
increases to 140, the Ca2+ transients sustain for a longer time(Fig 11B green line). If
is big enough, the Ca2+ concentration has a bigger peak(Fig 11B blue line).
The ER Ca2+ pumps have a slight role in Ca2+ transients(Fig 11C).
When PMCU is zero, the peak of Ca2+ concentration is bigger than the normal situation(Fig 11D yellow line). As PMCU increases, the peak of Ca2+ concentration decreases but the duration of Ca2+ transients increases(Fig 11D).
Together, these results indicate that Cav1.2 and Cav2.1 channels, Ryanodine and IP3 receptors could increase the Ca2+ transients, while BKCa and KDR channels reduce the Ca2+ transients. Combining the inhibition roles of BKCa and KDR on membrane potentials, it can be speculated that BKCa and KDR channels, by controlling the resting membrane potentials, further regulate the voltage-gated Ca2+ channels to influence the Ca2+ transients. Kv1.4 and Kv4.2 channels only influence membrane potentials at the initial time, which have less role in Ca2+ transients. In turn, the depolarization of membrane potentials facilitates the Ca2+ channels also regulate membrane potentials. Therefore, the membrane potentials and the Ca2+ transients in Merkel cells are coupled to each other.
How Merkel cells respond to mechanical stimulus
We have studied how ion channels on Merkel cells shape the cell membrane potentials and Ca2+ transients. However, Merkel cells are mechanical sensory cells, which could transduce tactile stimuli to SA1 afferents [6, 8, 24]. Piezo2 channels are necessary for this transduction [7, 9]. The SA1 afferents generate continuous action potentials under a static mechanical displacement. Without Merkel cells, SA1 afferents only generate action potentials at the initial moment of stimulation. The knockdown of Piezo2 channels in the Mekel cells causes similar results. A recent study held the view that Piezo2 channels in Merkel cells are not enough to help SA1 afferents generate continuous action potentials [11]. Therefore, we want to know how Piezo2 channels and other ion channels in Merkel cells participate in this process. The model is modified as follows.
Exocytosis and endocytosis.
Merkel cells transmit information to downstream afferents by releasing neurotransmitters [15, 16]. Generally, the synapse release can be divided into three parts. First, cell organelles synthesize neurotransmitters into vesicles. Many vesicles form the vesicles pools in the presynapse [71, 72]. Second, When Ca2+ ions enter the cell or cytoplasm Ca2+ concentration increases, vesicles in the pools fuse to the cell membrane(exocytosis) and release neurotransmitters [15, 16]. Finally, vesicles fused to the membrane recycle into the cell by endocytosis [73, 74]. Vesicles in the pools keep a relatively fixed number at rest, and the consumption of vesicles can be rapidly replenished. Then we assume that the vesicle synthesis rate is inversely related to the number of vesicles. The exocytosis rate increases with the cytoplasm Ca2+ concentration [20], and is positively correlated with the number of vesicles. Thus the dynamic equation of vesicles can be written as
(86)
where nve is the number of vesicles, kve and kexo are the rate constants. nve,s, nve,f, cCa,s, and cCa,f are constants.
Endocytosis is regulated by many complex signals, one of which is membrane tension [75–77]. Generally, when the membrane tension is great, more energy is required for vesicles to form from the cell membrane. Therefore, the endocytosis rate can take the form of [77, 78], where kendo is rate constant. σs,ve and σf,ve are constants. Endocytosis reduces the cell membrane, while exocytosis adds the cell membrane. Thus the reference surface Sref changes as
(87)
where rve is the average radius of vesicles. The values of parameters are seen in Table 4.
Cell compression.
The Merkel cell is a sphere before indentation, it is compressed to a cylinder of changeable radius r as shown in Fig A in S1 Appendix. It’s height H decreases with compression depth d,
(88)
where rini is the initial cell radius before compression. The other equations about the cell deformation are seen in Cell indentation in S1 Appendix.
The results show that when the Merkel cell was compressed(Fig 12A), the shape change of the cell causes the increase of cortex stress σ (Fig 12B), further activates Piezo2 channels(Fig 12C), Ca2+ flow through Piezo2 channels into the cell, which causes the depolarization of membrane potential(Fig 12D). The increase of membrane potential opens Cav2.1 and Cav1.2 channels(Fig 12E and 12F). The Ca2+ flow across Piezo2, Cav2.1, and Cav1.2 channels results in the increase of Ca2+ concentration(Fig 12G), further promoting exocytosis (Fig 12H). Then vesicles in the cell decrease (Fig 12I). Cytoplasmic Ca2+ further cause the Ca2+ release in the ER(Fig 12J).
(A) The Merkel cell was compressed at a depth d0 with a speed of 1um/ms. The dynamic change of (B) cortex stress, (C) currents generated in the Piezo2 channels, (D) membrane potential, (E) currents generated in Cav2.1 channels, (F) currents generated in Cav1.2 channels, (G) cytoplasmic concentration of Ca2+, (H) exocytosis rate, (I) number of cytoplasmic vesicles, and (J) Endoplasmic reticulum concentration of Ca2+(blue:d0 = 3μm, red:d0 = 4μm, yellow:d0 = 5μm, cyan:d0 = 6μm, green:d0 = 7μm).
Piezo2 channels inactivate rapidly under compression(Fig 12C). Without currents of Piezo2 channels, the membrane potentials repolarize(Fig 12H). It is consistent with the results of [7]. Voltage-gated Cav2.1 and Cav1.2 channels also close(Fig 12H). The Ca2+ concentration starts to decrease slowly(Fig 12G). With the increase of compression depth d0, the depolarization of membrane potential is enhanced, and the rise of Ca2+ concentration strengthens.
The above process happens in 100ms. After that, the concentration of Ca2+ continue to fall(Fig 13D), but the internal Ca2+ stores start to work. The Ca2+ in the ER enters the cell through Ryanodine and IP3 receptors, keeping a relatively high Ca2+ concentration, and continuously facilitating exocytosis to release neurotransmitters. Exocyotosis can last for tens of seconds. If we assume that neurotransmitters in every vesicle are close. Then the downstream afferents will receive continuous and stable neurotransmitter stimuli, which could generate continuous action potentials. The time of exocytosis increases with the compression depth, which is consistent with the results that the firing time of SAI Afferents increases with the indentation depth in experiments of [6, 7]. However, if Piezo2 channels were inhibited, no Ca2+ currents flow into the cell, and the membrane potential is at rest, Merkel cells will not respond to mechanical stimuli(Fig G in S1 Appendix), which is consistent with the results that the knockout of Piezo2 channel or inhibitory of Piezo2 channels by Cd2+ result in the loss of sustained action potentials in the SAI afferents [7, 24].
(A) The Merkel cell was compressed at a depth d0 with a speed of 1um/ms. The dynamic change of (B) cortex stress, (C) currents generated in the Piezo2 channels, (D) membrane potential, (E) cytoplasmic concentration of Ca2+, (F) number of cytoplasmic vesicles, (G) exocytosis rate, and (H) Endoplasmic reticulum concentration of Ca2+(blue:d0 = 3μm, red:d0 = 4μm, yellow:d0 = 5μm, cyan:d0 = 6μm, green:d0 = 7μm).
Discussion
In this article, we develop a biophysically detailed model of Merkel cells for the reception of Merkel cells. We first validate our model of Merkel cells with previous experiments. We then discuss how these ion channels control the membrane potentials and Ca2+ transients in Merkel cells. Finally, we study how Merkel cells convert the mechanical stimuli into the release of neurotransmitters with the participation of Piezo2 channels, membrane potentials, and Ca2+ transients.
The responses of Merkel cells under different stimuli
First, the membrane potentials of Merkel cells are controlled by K+ and Ca2+ channels. As shown in Fig 2, Merkel cells exhibit a nearly passive response under small current stimuli. As the injection currents increase, the membrane potential forms a peak and then has a small decrease to the steady state. How do K+ and Ca2+ contribute to this phenomenon? As the conductances of KV1.4, BKCa, and KDR decrease, the depolarized membrane potential increases, which is consistent with the results that Merkel cells are easier to depolarize with the inhibition of K+ channels [21]. Oppositely, the increase of the conductances of Ca2+ channels increases the peak of membrane potentials, which is also similar to the results that the membrane potentials form a peak with the small currents stimulus when Ca2+ channels were enhanced [21]. Ca2+ also can contribute to the oscillation of membrane potentials. As shown in Fig 3, The membrane potentials of Merkel cells initially have a rapid depolarization, then gradually enter an oscillation. By reducing the Ca2+ concentration in the external solution, this oscillation disappears [24]. In simulation, by changing the conductance of Ca2+ pumps, there is also the oscillation of membrane potentials. Though there are different Ca2+-relative membrane potentials behaviors in Merkel cells. However, it seems to have no obvious qualitative influence on the mechanical transduction of Merkel cells. The action potentials of downstream SAI afferents with two kinds of membrane potentials are still similar [7, 24]. There may be other roles for the oscillation of membrane potentials of Merkel cells, which needs further study. On the other hand, the oscillation of membrane potentials of Merkel cells is smaller than the amplitude of action potentials of neural cells. The membrane potentials are still limited on low depolarization state by K+ channels.
Secondly, a high K+ solution is a general way to stimulate Merkel cells, for the main K+ channels expressed in the cell membrane. High K+ solutions alter the Nerst potentials of K+, which causes the flow of K+ into the cell, and the membrane depolarizes. The Ca2+ channels were opened, and Ca2+ enter the cell. Ca2+ transients were inspired. This process both link with membrane Ca2+ channels and internal Ca2+ stores. The inhibition of internal Ca2+ stores greatly reduce the amplitude of Ca2+ transients(Fig 4), which is consistent with the results in [23]. The decrease of the conductances of Cav1.2 and Cav2.1 channels also reduces the Ca2+ transients(Fig 9), with is consistent with that the inhibition of Cav1.2 and Cav2.1 reduces the Ca2+ transients in experiments of [12].
Finally, the hypotonic shock also causes the Ca2+ transients(Fig 5), different from the previous two stimuli, hypotonic shock is more like a mechanical stimulus. Piezo2 channels were opened with the increase of cortex stress for the water absorption of the cell. The membrane potential increases, and Ca2+ enters the cell. It can be seen that the differences of Ca2+ transients between experiments [22] and simulation(Fig 5). The Ca2+ concentration in the simulation almost immediately increases, then gradually rises to the peak. However, in the experiments of [22, 23], the Ca2+ transients at the beginning of stimulation increase slowly, then rise and fall. One of the possible reasons is that hypotonic shock can inhibit the cytoplasmic substances’ mobility [70], thus hindering the quick entry of Ca2+ into the cell and the diffusion of Ca2+ in the cell. However, this role of hypotonic shock has not been confirmed, which is a limitation of our model.
How Merkel cells with Piezo2 channels help Aβ afferents generate sustained action potentials
According to our model, when Merkel cells are compressed, the opening of Piezo2 channels leads to the depolarization of membrane potentials and the influx of Ca2+. The increase of membrane potential further causes the influx of Ca2+ through Cav1.2 and Cav2.1. Ca2+ in the cytoplasm causes the exocytosis of neurotransmitters. Due to the rapid inactivation of Piezo2 channels, the membrane potential goes back to the resting state within hundreds of milliseconds. The Ca2+ channels are also closed. The concentration of Ca2+ in the cytoplasm decreases. But the internal Ca2+ store begins to release Ca2+ into the cell, which can last for tens of seconds. Exocytosis lasts for the same amount of time until Ca2+ transients disappear. Therefore, Piezo2 channels excite Merkel cells to produce a sustained neurotransmitter release, which further helps Aβ generate prolonged action potentials. So why does the theoretical study of [11] have such a conclusion that RA MS channels like Piezo2 channels cannot account for the sustained responses of Merkel cell-neurite complexes? Because they treat Merkel cells as ordinary nerve cells. A typical feature of these kinds of cells like afferents is that they generate Na+-related action potentials. For typical nerve cells, an action potential travels through axons and arrives at the presynapse, which depolarizes the presynaptic membrane potential. Then voltage-gated Ca2+ channels on the presynaptic membrane are opened, allowing Ca2+ to enter the cell and activate neurotransmitters release [83, 84]. But the Ca2+ transients in these nerve cells quickly return to the baseline [32, 85]. The number of vesicles released is positively correlated with the number of arriving action potentials. Therefore, the action potentials of downstream nerve cells are also positively related to the action potentials of presynapse [86–88]. If the nerve cell is compressed, the opening of Piezo2 channels will only make one or several action potentials [46]. Therefore, the misuse of neural properties in Merkel cells leads to the wrong conclusion [11].
Limitations of the model
Merkel cell-neurite complexes generate sustained action potentials with irregular intervals when a sustained mechanical stimulus is applied to the skin [3, 6, 7, 24]. This irregular interval of action potentials is also one of the important features of the SA1 response. At least in our results, the neurotransmitter release of one Merkel cell is regular. There are at least two aspects that may lead to this phenomenon. First, not only Ca2+, IP3, but also many other secondary messengers like ATP and cAMP, play important roles in exocytosis in many neurons [89–92]. These secondary messengers interact with each other, regulating the irregular exocytosis, which further contributes to the irregular intervals. Secondly, an afferent is usually linked with several Merkel cells [8, 93, 94]. It means that even if a single Merkel cell releases vesicles regularly, the combination of several or dozens of Merkel cells with small differences in channel properties may lead to irregularities in the whole action potentials. The research of [93] found that the different locations in the skin, cell size, and so on of Merkel cells may determine this irregular interval. Modeling virtual Merkel cells by different membrane capacitance, and different conductance of ion channels also helps downstream afferents generate irregular action potentials. Therefore, further studies on this irregular action potential are needed.
In this article, we didn’t consider the diffusion of Ca2+ and IP3 in the cytoplasm due to the rather small size of Merkel cells. However, the diffusion of Ca2+ may cause the Ca2+ wave within the cell. This means that the Ca2+ concentration in the cytoplasm will be nonuniform, which may lead to more complex Ca2+ behaviors. In previous studies, the Ca2+ transients in the same cell by two same stimuli can be different [22, 23].
Although the Piezo2 channels prefer Ca2+, Ca2+ in external solutions is much smaller than Na+ and K+. These two kinds of cation channels also flux through Piezo2 channels. Here we ignore ions other than Ca2+ in Piezo2 channels. It may have quantitative impacts on our results.
Generally speaking, neurotransmitters in vesicles are adequate. But for Merkel cells, the release of neurotransmitters lasts for tens of seconds, and the supplements of vesicles and neurotransmitters may need to be considered. Upon stimulation, the neurotransmitters released in the synapse and vesicles fused to the membrane will be absorbed back into the cell, and some of the neurotransmitters will also diffuse into adjacent solutions [75, 95, 96]. The time scales of reabsorption of neurotransmitters and vesicles may be out of sync. There is even a “kiss and run” approach to neurotransmitter release, where neurotransmitters are released into the synaptic cleft but the membrane of vesicles goes back to the cell immediately. Therefore, the recycling of neurotransmitters and vesicles may also influence the sustained response of Merkel cells to stimulation.
Conclusion
Although it has been identified that Merkel cells transduce tactile stimuli to SA1 afferents by Piezo2 channels, it remains unclear how Piezo2 channels with fast-inactivation properties help Merkel cells and SA1 afferents generate a slowly adapting response to mechanical stimuli. Here, we develop a biophysically detailed model for the reception of Merkel cells.
We first validate our model with several experimental results [21–24]. Merkel cells exhibit an almost passive response to negative current and small positive current pulses. As the positive current increases, the membrane potential rises to a peak value and then gradually reaches a steady state. Merkel cells also exhibit Ca2+ transients lasting tens of seconds under high K+ solutions and hypotonic shock.
We then discuss how these ion channels control the membrane potentials and Ca2+ transients in Merkel cells. Our works show that Cav1.2 channels contribute to the formation of the peak of membrane potentials, while Kv1.4 channels reduce this peak. Cav2.1, BKCa, and KDR channels mainly maintain the steady membrane potentials, Cav2.1 channels increase the steady membrane potentials, and BKCa and KDR channels reduce the steady membrane potentials. Interestingly, the oscillations of membrane potentials require the coupling of Ca2+ channels and Ca2+ pumps. Compared to these channels on the membrane, the Ryanodine and IP3 receptors on ER have little role in membrane potentials. Our works also show that Cav1.2 channels increase the peak concentrations of Ca2+, while Cav2.1 channels mainly increase the duration of high Ca2+ concentrations. Both BKCa and KDR channels suppress the Ca2+ transients. It can be speculated that these two channels inhibit the depolarization of membrane potentials, thereby inhibiting the voltage-gated Ca2+ channels on the membrane. Additionally, both Ryanodine and IP3 receptors on ER increase the Ca2+ transients.
Finally, we show that Piezo2 channels and internal Ca2+ stores are sufficient to activate continuous neurotransmitter release to downstream Aβ afferents. Surprisingly, the membrane potentials seem not necessary for Merkel cells to transduce mechanical stimuli to afferents. The depolarization of membrane potentials caused by Piezo2 channels will rapidly repolarize for the inactivation of Piezo2 channels. Oppositely, Ca2+ flows into the cell through Piezo2 channels, which activates Ryanodine and IP3 receptors on ER to keep a continuous high Ca2+ concentration. This Ca2+ transients facilitate the release of neurotransmitters, and the duration of exocytosis is corresponding to the time of Aβ afferents firing [6, 7, 24].
Thus, unlike sensory cells that generate Na+-related action potentials, Merkel cells, through stable membrane potentials and Ca2+ transients regulation, maintain a relatively stable release of neurotransmitters to mechanical stimuli.
However, knowledge about the neurotransmitter interaction between Merkel cells and Aβ afferents is still lacking [97]. In further research, we hope to establish a complete model of the Merkel cell and Aβ afferents, which may provide a better description or understanding of the sensing process of the Merkel cell-neurite complexes.
Supporting information
S1 Appendix. Description of cell indentation and additional informations about this work.
Fig A. The schematic diagram of Merkel cell under indentation. Fig B. Kv1.4 channel. Fig C. Kv4.2 channel. Fig D. KDR channel. Fig E. Piezo2 channel. Fig F. Merkel cell reaches a balanced state given an initial value at rest. Fig G. The responses of Merkel cells under compression. Fig H. The responses of the Merkel cell under three kinds of stimuli with the same parameters. Fig I. The influences of exocytosis rate on vesicle regulation. Table A. Ion channel parameters in high K+ solutions and hypotonic shock. Table B. Ion concentrations of external solutions. Table C. Initial values of variables.
https://doi.org/10.1371/journal.pcbi.1011720.s001
(PDF)
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