The electrochemical transmission in I-Band segments of the mitochondrial reticulum

Abstract

Within the mitochondrial reticulum of skeletal muscle, the I-Band segments (IBS) traverse the cell and form a contiguous matrix with the mitochondrial segments at the periphery (PS) of the cell. A tight electrical coupling via the matrix between the PS and IBS has been demonstrated. In addition, oxidative phosphorylation complexes that generate the proton motive force (PMF) are preferentially located in the PS, while Complex V, which utilizes the PMF, is primarily located along the IBS. This has led to the hypothesis that PS can support the production of ATP in the IBS by maintaining the potential energy available to produce ATP deep in the muscle cell via conduction of the PMF down the IBS. However, the mechanism of transmitting the PMF down the IBS is poorly understood. This theoretical study was undertaken to establish the physical limits governing IBS conduction as well as potential mechanisms for balancing the protons entering the matrix along the IBS with the ejection of protons in the PS. The IBS was modeled as a 300 nm diameter, water-filled tube, with an insulated circumferential wall. Two mechanisms were considered to drive ion transport along the IBS: the electrical potential and/or concentration gradients between the PS to the end of the IBS. The magnitude of the flux was estimated from the maximum ATP production rate for skeletal muscle. The major transport ions in consideration were H⁺, Na⁺ and K⁺ using diffusion coefficients from the literature. The simulations were run using COMSOL Multi-physics simulator. These simulations suggest conduction along the IBS via H⁺ alone is unlikely requiring un-physiological gradients, while Na⁺ or K⁺ could carry the current with minor gradients in concentration or electrical potential along the IBS. The majority of conduction down the IBS is likely dependent on these abundant ions; however, this presents a question as to how H⁺ is recycled from the matrix of the IBS to the PS for active extrusion. We propose that the abundant cation-proton antiporter in skeletal muscle mitochondria operates in opposite directions in the IBS and PS to permit local recycling of H⁺ at each site driven by cooperative gradients in H⁺ and Na⁺/K⁺ which favor H⁺ entry in the PS and H⁺ efflux in the IBS.

Graphical Abstract

Introduction

Recently, the presence of an electrically coupled mitochondrial reticulum (MR) was structurally delineated in three dimensional electonmicrographs and super resolution optical imaging studies as well as demonstrated to be electrically coupled in living murine skeletal muscle cells [1]. Skulachev et al. previously had suggested that a connected reticulum of mitochondria exists in myocytes that could facilitate potential energy distribution [2]. Glancy et al. [1] demonstrated a tight electrical coupling between the central and peripheral regions of the muscle cell using an exogenously applied, optically gated mitochondrial uncoupler (MitoPhotoDNP) [3]. The conduction of electrical energy throughout the coupled regions of the MR has been proposed to be a major pathway for the distribution of potential energy throughout the muscle cell to support oxidative phosphorylation. Consistent with this notion, Complex IV, which contributes to generating the proton motive force (PMF) across the inner membrane, was found preferentially located in the cell periphery while Complex V, which utilizes the PMF, was preferentially located in the central regions [1]. These data suggest that the peripheral mitochondrial segments (PS) primarily generate the PMF which then is conducted into the interior regions of the cell for ATP synthesis by Complex V. An obvious candidate for the conduction pathway from the periphery to the interior of the cell is the I-band mitochondrial reticulum segments (IBS). These IBS run perpendicular to the long axis of the muscle cell [1] as seen in the large field of view projection of a stimulated emission depletion (STED) image of a tetramethyl rhodamine (TMRM) labeled, isolated living murine soleus fiber in Figure 1.

Figure 1.

False colored 3D projection image of TMRM labeled murine soleus fiber. Image is from an stack of images using the methodology presented in Glancy et al [1] where the intensity thresholding was used to improve contrast on the TMRM emission. Note the ordered and repeating mitochondrial reticulum connecting the periphery of the muscle fiber to the cell interior. I-Band mitochondrial segments (IBS) pass along the I-Band regions of the muscle fiber. Peripheral mitochondrial segments (PS) are located around the periphery of the cell with the nuclei.

The conduction pathway from the PVS to the IBS is presented schematically in Figure 2. However, it is unclear what are the ions responsible for the electrical conduction down the IBS system and how the protons are recycled between the regions of PMF generation and PMF utilization. The purpose of this work was to model the ionic transport in the IBS to generate a hypothesis on how the myocyte interior and periphery are electrically coupled and the required cycling of H⁺ across the inner membrane is accomplished.

Figure 2.

Model illustrating hypothetical conduction of the PMF down IBS extensions (not to scale). Top left: FIB-SEM micrograph based reconstruction of IBS and PS units. The PS, located in the periphery of the myocyte, is responsible for PMF generation while the IBS utilize the PMF for ATP synthesis.

Methods

The finite element method (FEM) was used to model the transport of ions within the mitochondrial I-band segments (IBS) via COMSOL Multiphysics 5.2 (COMSOL Inc., Burlington, MA). The model IBS (mIBS) consisted of a simple tube of length L (L = 5 or 10 μm), and diameter d (d = 300 nm). Since the permeability of the outer membrane is poorly defined under in vivo conditions [4], we assumed that the major barrier for ion transport is the inner membrane permitting the simplification of the model without considering the poorly characterized outer membrane and intermembrane space compartment. This simplification has little impact on the conductance down the IBS, the major concern of this analysis, but potentially could impact the driving forces for ion transport in this model. The PS were observed to have a mean diameter of approximately 900 nm [1]. These diameters were consistent with those measured from reconstructions of focused ion beam electron microscopy (FIB-SEM) micrographs of the IBS and PS [1]. The lengths of the IBS structures were more difficult to assess since most extended beyond the FIB-SEM field of view of 4 to 5 microns in most blocks. Thus, we have directly observed IBS of minimal length of 5 microns. In living cell STED images with field of views that cover the entire width of the TMRM labeled cells (20 to 30 μm), numerous IBS were on the order of 8 to 10 μm (Figure 1). The inner membrane of the mIBS was assumed to have an infinite resistance. This simplification was made due to the relatively low permeability of the inner mitochondrial membrane to ions. The mitochondrial matrix was modeled as water which likely over estimates the ion diffusion rates in a matrix with ^~50% protein content [5, 6]. The diffusion coefficients of the ions used in the model are shown in Table 1. Modelling the matrix as water also ignored the presence of pH buffers in the matrix solution. This simplification was made because steady state ion transport was studied, where transient effect of a static buffer on pH can be ignored. Indeed, a significant fixed proton buffer pool, likely present in the protein rich matrix, would reduce the effective proton diffusion coefficient [7]. Facilitated diffusion of protons in the matrix was also ignored as the major buffer species in the matrix are fixed or large proteins with poor diffusion characteristics. The only known highly mobile buffer with an appropriate pK_a is phosphate, however, its concentration is much too low to make a significant contribution to proton flux consistent with observations in model systems [7, 8]. This latter assumption was tested for its validity as explained later in the Results section. Proton diffusion along the inner mitochondrial membranes was not considered since the enhancement of the proton diffusion coefficients at the membrane/water interface is controversial [8]. While some have previously reported an enhancement of the diffusion coefficient by a factor of 20 [9], measured diffusion coefficients for H⁺ along lipid bilayers are smaller than the proton diffusion coefficient in bulk water due to the fixed buffer effects of membrane proteins [7, 8]. Based on these theoretical and direct observations we believe that using the free water diffusion coefficient is likely an overestimate of the effect proton diffusion coefficient in the protein rich matrix. As shown in our calculations below, even enhancing the proton diffusion constant by 20-fold would not alter our major conclusions regarding proton movements within the IBS.

Table 1.

Cytosolic concentrations [23] and diffusion coefficients [24].

Cation	Cytosolic Concentration (mM)	Diffusion Coefficient in Water at 25°C (10−5 cm2/sec)
H+	10−4	9.31
K+	139	1.96
Na+	12	1.33

Note that the diffusion coefficients at 25°C were used as coefficient values could not be determined at 37°C.

In the skeletal muscle mitochondrial reticulum, the ratio of Complex IV, that generates PMF, to Complex V, that utilizes PMF for ATP production, is three-fold higher in the PS than in the IBS. This observation suggested that the PS is more capable of being a source for PMF than the IBS which is better suited for ATP production near the muscle cell ATPase activity. Other than this gross localization, the precise distribution of these Complexes along these segments is still unknown; we reasoned that generating this extreme case would be the most illustrative of the physics involved in this process. Thus, we simulated having no PMF production in the IBS, only consumption via Complex V at the end of the structure. To simulate the preferential distribution of PMF producing complexes in the PS and PMF utilizing complexes in the IBS, the inward H⁺ flux, associated with PMF utilization, was assumed to occur only at cell interior end of the mIBS, while ion efflux, associated with PMF generation, was assumed to occur only at the PS end of the mIBS.

The ion flux through the mIBS was determined from estimates of the V̇_O2max per unit inner membrane (7.29 μmol•min⁻¹•m⁻²) [10]. Given that approximately 20 protons are pumped out of the inner membrane per molecule of O₂, and that the inner membrane area of a IBS and PS could be approximated as a tube of diameter d, and length L connected to a sphere of 900 nm diameter, the ion flux (all ions have valence =1) through the IBS can be estimated at V̇_H+ ≈ 2.9•10⁻¹⁷mol/s (when L = 10 μm). This ion flux represents the maximum current requirements of the system. Thus , we have set up a “worst case scenario” examining the maximum flux requirements with the sinks (Complex V) and sources (Complex IV) of PMF completely separated with the IBS between them (Figure 2).

Two mechanisms driving ion transport in the IBS were considered: diffusion and electric migration. Electric migration was considered in the case that a potential difference may occur along the length of an IBS to facilitate ion transport toward the PS. The transport of only a single ion species was modeled in each case.

The 2D-axisymmetric FEM model was discretized into quadrilateral elements using a 2D-mapping technique with uniform mesh density. As mentioned above, the circumferential boundary of the mIBS was assumed to be perfectly insulating, and therefore was modeled to have zero normal current flux. At the boundary at the PS end of the mIBS, the flux across the boundary was set to V̇_H+. The concentration of Na⁺ and K⁺ in the matrix is controversial, especially in intact cells, running from nearly equivalent to the cytosolic concentrations to values approaching two-fold greater [11, 12]. For the purposes of this simulation, we assumed the transported ion species concentration at the PS boundary was set to its cytosolic value, as listed in Table 1. Additionally, in cases where transport in the presence of an electric gradient was modeled, a prescribed voltage difference was applied between the ends of mIBS. From this system, the concentration distribution (c) necessary to meet the flux requirement at the PS end of the mIBS was calculated solving Equation 1.

$$\nabla \cdot (-D_i\nabla c_i-z_i{u}_{m,i}F{c}_i\nabla V)=0$$ (1)

Where D_i is the species diffusion coefficient, c_i is the species concentration, z_i is the species valence, F is the Faraday constant, V is the electric potential, and u_m,i is the species ionic mobility $(u_{m,i}=\frac{D_i}{RT})$, where R is the universal gas constant and T is the temperature (assumed to be 300K).

In general, the data from the simulations are reported as the steady state concentration profile of the transported species, (in pH or mM) along the mIBS as a function of distance from the PS. Again, the PS concentration boundary conditions and diffusion coefficients for transported species studied are presented in Table 1.

Results

In the case of proton transport driven by a concentration gradient, the simulations revealed that to attain adequate flux of H⁺ along the IBS, an un-physiological concentration gradient from the IBS to the PS on the order of 3-4 pH units was required depending on mIBS length (Figure 3). A possible additional driving force for the ion transport from IBS to PS could be an electrical potential difference between the PS as the “source” and the IBS as the sink. The polarity of this gradient based on the distribution of Complexes would be more negative in the PS with the electrogenic ejection of H⁺ while the IBS would be more positive with the influx of H⁺ via Complex V (see Figure 2). As illustrated in Figure 3, even enhancing the transport driving H⁺ between the IBS to PS with a 10 mV or even an unrealistic 50 mV potential gradient still requires several pH units to meet flux requirements. Thus, the geometry, current density and the concentration of H⁺ make it highly unlikely that the protons alone account for the electrical coupling through the IBS. Based on these calculations, additional mechanisms need to be explored to explain the conduction of current and H⁺ recycling in the IBS and PS during maximum rates of oxidative phosphorylation.

Figure 3.

Concentration profiles of H+ along the mIBS to meet flux requirements aided by electric fields of various strengths. Note that large pH gradients (3-4 units) are necessary to meet flux requirements at maximum respiration.

The facilitated diffusion of H⁺ via phosphate buffer was evaluated. Phosphate was selected due to is appropriate pK_a (7.21), its high mobility (diffusion coefficient ≈ 1×10⁻⁵ cm²/sec [7]), and estimated 1 mM concentration based on cytosolic measures [13] and equilibration across the inner membrane [14]. For phosphate to facilitate proton diffusion, a pH gradient from the PS to IBS must be present to generate a gradient in the protonated forms of phosphate. Assuming the diffusion coefficient of phosphate has the same value for protonated and deprotonated forms, a 1.2 mM gradient of the protonated form is required to meet flux requirements in a 5 μm IBS. The gradient in protonated phosphate is generated by a pH gradient. If we assume a large 0.5 pH gradient from the PS to the end of the IBS, it would require a total free phosphate concentration of ^~7mM. This concentration requirement seems unrealistic for the estimation of matrix free phosphate content outlined above. Therefore, while mobile buffers may contribute to proton conduction, this contribution is likely very modest. This is especially true given that the effect of numerous fixed buffers in the matrix would compete with the mobile buffer ability to enhance the effective diffusion coefficient [7].

It was reasoned that more abundant ions such as K⁺ and Na⁺ are responsible for the conduction of current along the IBS. To evaluate this possibility, we examined both K⁺ and Na⁺ as the transported species within the IBS. Running the same parameters as for the H⁺ simulation, we found that K⁺ and Na⁺ would only require minor gradients, on the order of 1 to 3 mM to support the transport requirements even without an electrical potential difference from the IBS to PS (see Figure 4). The simulations suggest that Na⁺ and K⁺ could easily transmit the current requirements of this system with a minor concentration gradient. Interestingly, we found that adding a potential difference from the PS to the IBS was extremely effective in increasing the flux due to the high concentration of these ions. The potential difference between the PS and IBS that provided the required flux with no concentration gradient was found to be 0.4 mV for K⁺ and 6.5 mV for Na⁺ for at 10 μm IBS. Thus, even a very small electrical potential difference between the PS and IBS would facilitate an appropriate Na⁺ or K⁺ current down the IBS.

Figure 4.

Concentration profiles of Na+ and K+ in mIBS to meet flux requirements without the assistance of an electric field. Note that relatively small concentration gradients are necessary to meet flux requirements at maximum respiration.

The simulations suggest that Na⁺ and K⁺ could easily transmit the current requirements of this system with very modest concentration gradients. However, this presents the question as to how the protons recycle between the ejection sites at the PS and the influx in the IBS. In addition, as this is a steady state system, the current carrying ions also have to be recycled to prevent buildup and depletion in the different segments. The latter concern is not a trivial since these currents associated with these small structures can quickly lead to significant concentrations of ions. For example: we can take the quantitative data from Schwerzmann et al [10] who determined the maximum oxygen consumption per unit mitochondrial volume to be ^~260 μM×min⁻¹ ×cm⁻³ using 20 H⁺ ejected per O₂ and we assume all of the protons flux is exchanged with a Na⁺ this makes the potential rate of change in matrix [Na⁺] without a efflux mechanism a staggering 80 mM/sec. Cation-H⁺ antiporter activity is present in muscle mitochondria [11, 12, 15]. We propose that these transporters can provide a mechanism to locally recycle protons at the IBS and PS membranes while permitting Na⁺ or K⁺ to transmit the current along the IBS. This scheme is presented in Figure 5. In the PS, H⁺ ions are pumped out of the matrix slightly alkalizing the matrix. This would favor cation-H⁺ exchange in the direction of moving cation out and H⁺ in to replace the ejected H⁺. The opposite would be occurring in the IBS where H⁺ are entering the matrix, via Complex V and ATP production, slightly acidifying the matrix. This would favor cation H⁺ exchange in the direction of ejecting H⁺ that had entered via Complex V. The overall effect of these reactions is a recycling of H⁺ in the PS and IBS generating small H⁺-Na⁺-K⁺ ion concentration gradients running between the IBS and PS within the matrix. As noted in our simulations, a relatively small potential difference between PS and IBS or gradient in Na⁺/ K⁺ could support the ion transport required for the distribution of PMF along the IBS. Thus, this hypothesis suggests that the current running from the PS to IBS is supported by a Na⁺-K⁺ flux and that the H⁺ required for PMF generation and utilization for ATP production are provided by a local recycling of H⁺ via the cation- H⁺ antiporter.

Figure 5.

Alternative model for ion conduction along the IBS. Abundant matrix cations transport charges along the IBS while protons are recycled locally in the IBS and PS via cation/proton antiporters.

Discussion

The distribution of PMF across a mitochondrion has not been an area of interest since the common perception of the mitochondria is a rather uniform ^~1 micron structure where diffusion distances are very small. However, with the demonstration of a MR that extends over large regions of the cell (Figure 1) together with the partial segregation of the elements of oxidative phosphorylation that generate and utilize the PMF [1], the ability to distribute the PMF and protons throughout the MR becomes important to understanding the function of this complex organelle.

Herein, we examined different models for distributing the PMF as well as protons throughout the MR via the IBS in skeletal muscle. The IBS geometry together with the current density requirements for supporting oxidative phosphorylation make it unlikely that proton conductance alone can support the current flow or recycling of protons between the IBS and PS with physiological pH values (Figure 3). This was primarily due to the low concentration of protons (^~0.1 μM) at physiological pH. Mobile buffers and surface migration enhancing proton diffusion rates were considered unlikely. The abundance of Na⁺ and K⁺ make these ions much more likely to carry the current and simulations support this notion by demonstrating that only small gradients of Na⁺ or K⁺ are required to support the current density prescribed, even without an electrical potential difference between the PS and IBS. However, this presents a problem as to how the protons being ejected at the PS are recycled with the protons entering the matrix at the IBS (see Figure 2). We suggest that this is accomplished via electroneutral cation-proton exchange operating in opposite directions in the IBS and PS (see Figure 5). Thus, in this model, termed cation dependent local proton recycling (CDLPR), the current required to distribute the PMF is carried by the high concentration ions in the matrix, Na⁺ and K⁺, while the protons are locally recycled in the mitochondrial segments by the cation-proton antiporters. It is interesting to note that even the early work by Mitchell [16] suggested that these cation-proton or anion-hydroxyl antiporters dissipate the pH gradient in favor of a membrane potential consistent with this hypothesis.

As noted earlier, several approximations were made when modeling IBS ion transport. The current model represents the worst case scenario: metabolic rate was set at physiologic maximum, the IBS membrane was considered to be a perfect insulator, and the location of PMF generating sites and PMF utilizing sites were segregated to opposite ends of the mIBS. In reality, the inner membrane would have some leak, and the distribution of Complex V and ETC components is less discrete. Clearly our assumptions for this simulation illustrate the upper limits for ion transport in the IBS-PS system. Additionally, multiple cations and anions would be dissolved in the matrix, while the model ignored the migration of multiple cationic and anionic species for simplicity.

Several gaps in knowledge need to be filled to fully evaluate the CDLPR hypothesis. The identities of the mitochondrial cation exchangers (KHE and NHE) have not yet been clearly determined [17-20]. For the CDLPR model to work, the flux capacity of the cation-proton antiporter systems needs to approach the proton fluxes generated by oxidative phosphorylation with rather small cooperating gradients of cations and protons across the inner membrane. Regrettably, the kinetics of any of the mitochondrial cation proton antiporters with regard to the magnitude of the flux supported by the cation or proton gradients are poorly defined. Likely this data is not readily available since most of the focus on these antiporters has been on mitochondria volume regulation [11, 21, 22]. The distribution of the PMF, cation concentrations and pH within the MR matrix and intermembrane space needs to be established at high workloads when the currents are significant to evaluate the fundamental driving forces for ion movements.

What direct experiments could be conducted in cells to test the LPR hypothesis? Since the system is most stressed approaching maximum rates of ATP production, operating near the maximum ATP turnover rate would be a desirable experimental condition along with the direct observation of the composition of the matrix space in a microscope. The system best suited for this might be a permeabilized skeletal muscle where the metabolic rate could be driven by the direct addition of ADP under conditions where contraction is blocked to prevent motion for microscopic observations. Numerous probes are available to monitor matrix pH, membrane potential and ion composition even using super resolution approaches such as STED [1]. Regrettably, no specific inhibitors of the mitochondrial cation-proton exchangers are available and the regional differences in the Na+-K+ and proton gradients under normal conditions maybe too low (10%) to detect with conventional tools based on our models. Thus, total ion substitution could be used in this permeabilized preparation to test the role of different cations and antiporters in the distribution of PMF across the reticulum. We look forward to experimental work evaluating the CDLPR hypothesis in the future.

In summary, simulations of the ion transport in the IBS of the skeletal muscle mitochondrial reticulum reveal that H⁺ transport along the IBS is not adequate to equilibrate the PMF nor provide the required H⁺ recycling between the IBS and PS. Based on these simulations, we propose that the distribution of the PMF within the reticulum is through the movement of Na⁺ and/or K⁺ while the recycling of H⁺ occurs locally at the IBS and PS via electroneutral cation-H⁺ antiporters operating in opposite directions at these two sites.

Highlights.

• - Muscle cell mitochondrial reticulum (MR) distributes the proton motive force (PMF)

• - The MR I-Band segments (IBS) are major distribution pathways for PMF

• - Simulations reveal H+ diffusion in IBS is inadequate to support maximum respiration

• - Na+ and/or K+ diffusion in IBS can distribute PMF at maximum respiration

• - We propose local H+ recycling via cation-H+ antiporters for PMF production and use