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Key points

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information
  • • 
    The role that the age-dependent expression of chloride channels (ClC-1) plays on the electrical properties of muscle fibres from normal and human skeletal actin (HSA)LR mice (a model of myotonic dystrophy) was studied using a combination of electrophysiological and optical techniques.
  • • 
    Chloride currents (ICl) are significantly smaller in fibres isolated from young (2 weeks old) HSALR mice than from aged-matched control mice, but become statistically undistinguishable in adult (17 weeks old) mice. Thus, the severe ClC-1 channelopathy in young HSALR animals slowly reverses with aging.
  • • 
    The maximal chloride conductance (gCl,max) is uniformly depressed in fibres of young HSALR mice, but fibres from older animals show a wide range of gCl,max values suggestive of a mosaic expression of ClC-1 channels in FDB muscles of these animals.
  • • 
    Regardless of the age of the animals, the chloride channelopathy does not affect the normal expression of ClC-1 channels at the sarcolemma and transverse tubular system membranes.
  • • 
    The membrane resistance (Rm) is lower than expected in young HSALR animals due to an upregulation of an Rb-sensitive K conductance. In adult animals, differences in Rm are negligible between fibres of both animal strains.
  • • 
    It is proposed that, while the hyperexcitability in young HSALR mice can be accounted for by the reduction in gCl,max, a mosaic expression of ClC-1 channels and/or alterations of other conductances may be the underlying causes in adult animals.

Abstract  We combine electrophysiological and optical techniques to investigate the role that the expression of chloride channels (ClC-1) plays on the age-dependent electrical properties of mammalian muscle fibres. To this end, we comparatively evaluate the magnitude and voltage dependence of chloride currents (ICl), as well as the resting resistance, in fibres isolated from control and human skeletal actin (HSA)LR mice (a model of myotonic dystrophy) of various ages. In control mice, the maximal peak chloride current ([peak-ICl]max) increases from −583 ± 126 to −956 ± 260 μA cm−2 (mean ± SD) between 3 and 6 weeks old. Instead, in 3-week-old HSALR mice, ICl are significantly smaller (−153 ± 33 μA cm−2) than in control mice, but after a long period of ∼14 weeks they reach statistically comparable values. Thus, the severe ClC-1 channelopathy in young HSALR animals is slowly reversed with aging. Frequency histograms of the maximal chloride conductance (gCl,max) in fibres of young HSALR animals are narrow and centred in low values; alternatively, those from older animals show broad distributions, centred at larger gCl,max values, compatible with mosaic expressions of ClC-1 channels. In fibres of both animal strains, optical data confirm the age-dependent increase in gCl, and additionally suggest that ClC-1 channels are evenly distributed between the sarcolemma and transverse tubular system membranes. Although gCl is significantly depressed in fibres of young HSALR mice, the resting membrane resistance (Rm) at −90 mV is only slightly larger than in control mice due to upregulation of a Rb-sensitive resting conductance (gK,IR). In adult animals, differences in Rm are negligible between fibres of both strains, and the contributions of gCl and gK,IR are less altered in HSALR animals. We surmise that while hyperexcitability in young HSALR mice can be readily explained on the basis of reduced gCl, myotonia in adult HSALR animals may be explained on the basis of a mosaic expression of ClC-1 channels in different fibres and/or on alterations of other conductances.

Abbreviations 
9-ACA

9-anthracene-carboxilic acid

AP

action potential

ClC-1

chloride channel

C m

membrane capacitance

DM1

myotonic dystrophy type 1

DMPK

dystrophia myotonia protein kinase

EDL

extensor digitorum longus

FDB

flexor digitorum brevis

g Cl,max

chloride conductance

HSA

human skeletal actin

I Cl

chloride current

mbnl

muscleblind-like

MSA

murine skeletal actin

PCR

polymerase chain reaction

[peak-ICl]max

maximal peak chloride current

R IN

input resistance

R m

membrane resistance

τm

membrane time constant

TEA

tetraethylammonium

TTS

transverse tubular system

Introduction

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information

Myotonia is characterized by muscle hyperexcitability that leads to sustained bursts of action potentials (APs; myotonic runs) and delayed force relaxation (muscle stiffness). Myotonia in humans occurs in non-dystrophic syndromes such as the dominant (Thompsen's disease) and recessive (Becker's disease) congenital myotonias, and in autosomal dominant dystrophic syndromes, such as myotonic dystrophy type 1 (DM1), which constitutes the most prevalent adult-onset form of muscular dystrophy (1:7500 live births). Myotonia in the latter cases has been proposed to result mostly from an increase in the membrane resistance (Rm) of muscle fibres due to the defective expression of the chloride channel (ClC-1). However, in contrast to congenital myotonias in which the abnormalities of the channel arise from mutations in the gene encoding for ClC-1 (CLCN1; Koch et al. 1992; Zhang et al. 1996), in DM1 the alterations of ClC-1 expression seem to arise from expansions of CTG triplets located in the 3′ untranslated region of the dystrophia myotonica protein kinase (DMPK) gene (Brook et al. 1992). The mechanisms underlying the ultimate effects of these triplet repeats are unclear, but they seemingly involve abnormal splicing of pre-mRNA for various proteins (including ClC-1) mediated by muscleblind-like (mbnl) proteins (Charlet et al. 2002; Mankodi et al. 2002; Kanadia et al. 2003) and/or CUG-binding proteins (Charlet et al. 2002).

Animal models for DM1 include knockout mice of DMPK (Jansen et al. 1996; Reddy et al. 1996) and mbnl proteins (Kanadia et al. 2003; Hao et al. 2008), and mice engineered to express expanded CUG repeats (Mankodi et al. 2000; Seznec et al. 2001; Orengo et al. 2008). In the present study we use one of the latter, a transgenic mouse based on the human skeletal actin (HSA) gene that includes approximately 250 untranslated CUG repeats (line HSALR20b, hereafter called HSALR). These animals have been reported to be myotonic (Mankodi et al. 2000), and their myotonia claimed to be sufficiently explained by significant reductions in the ClC-1 currents (ICl). Nevertheless, to our knowledge, 70–80% of the reductions in ICl were reported only for fibres isolated from very young animals (9–20 days after birth; Lueck et al. 2007a,b). In contrast, preliminary observations from our laboratory (Yu et al. 2012) demonstrated that ICl records in fibres from adult HSALR mice were quite comparable (in amplitude, voltage dependence and kinetics) to those from their normal counterparts (FVB mice). Concurrently, we confirmed that very young animals indeed showed greatly reduced ICl. These contrasting results suggested the possibility that the severity of ICl impairment in HSALR mice was age dependent; for these reasons, we deemed it necessary to perform an exhaustive longitudinal analysis of the properties of ICl recorded in fibres from this important animal model by carefully genotyping each animal, and by contrasting the properties of ICl records with respect to those from age-matched background controls.

The electrical properties of skeletal muscle fibres are determined by ion channels located in two electrically connected membrane compartments: the sarcolemma, representing the peripheral cylindrical cable of the muscle fibre; and the transverse tubular system (TTS), a radial cable network periodically arranged so that the depolarization radially spreads towards the axis of the cylinder (Adrian et al. 1969b; Hodgkin & Nakajima, 1972b; Adrian & Bryant, 1974; Ashcroft et al. 1985; DiFranco et al. 2011, 2012; DiFranco & Vergara, 2011). We have recently demonstrated, using the potentiometric dye di-8-ANEPPS to measure voltage changes in the TTS, that in fibres from normal animals a large proportion of ICl is contributed by ClC-1 channels in the TTS membranes (DiFranco et al. 2011). Thus, we considered it important to comparatively determine whether the relative distribution of these channels is altered in fibres from HSALR animals compared with their normal counterparts, and if these alterations may be correlated with the penetrance of the chloride channelopathy at various ages.

The universal explanation that myotonia results exclusively from a chloride channelopathy rests on the assumptions that ∼85% of the resting membrane conductance is contributed by ClC-1 channels (Palade & Barchi, 1977b), and that ∼70–80% blockage (using aromatic blockers) is necessary to generate myotonia (Furman & Barchi, 1978). However, there is considerable evidence suggesting that myotonia may not exclusively result from a sarcolemma-restricted chloride channelopathy, but that non-linear properties of ClC-1 and/or other ion channels (especially in the TTS membranes) may contribute to, or even cause, the pathology (Adrian & Bryant, 1974; Aromataris & Rychkov, 2006). For example, human congenital (non-dystrophic) myotonias and DM1 have been explained on the basis of alterations of Na channels (Franke et al. 1990, 1991; Iaizzo et al. 1991; Cannon, 2006), and/or various K channels have been implicated in muscle hyperexcitability in DM1 (Behrens et al. 1994; Kimura et al. 2000; Neelands et al. 2001). In order to investigate these issues, specifically with respect to the chloride deficiency in HSALR animals, we comparatively studied the linear electrical properties of fibres from normal and mutant animals at various ages in order to carefully assess the relative contribution of gCl to the overall resting membrane conductance.

Methods

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information

Animal model

Experiments were performed using specimens of the line LR20b of the HSA mouse (HSALR) (Mankodi et al. 2000), and control specimens of the corresponding background strain (FVB). Colonies of the two strains were established at UCLA. The HSALR colony was started from founders provided by Dr C. Thornton (University of Rochester), which were re-derived at UCLA. Prior to shipment to UCLA, founders were confirmed to be homozygous specimens expressing more than 250 CTG repeats. The FVB colony was started directly from founders obtained from Jackson Laboratories. Mice were killed by deep halothane anaesthesia followed by neck dislocation. Animal handling followed the guidelines laid down by the Animal Care Committee of UCLA.

Genotyping

The genotype of every HSALR 20b mouse used for experimentation was confirmed by polymerase chain reaction (PCR) analysis of genomic DNA from tail samples taken at the time of death using protocols kindly provided by Dr C. Thornton. Briefly, 2 μl of genomic DNA (about 50 ng μl−1) was analysed in a 50 μl PCR containing 1 × PCRII buffer (PE Applied Biosystem), 2.5 mm MgCl2, 200 μm dNTP, 1.5 Units of AmpliTaq Gold DNA polymerase (PE Applied Biosystem), and 0.3 μm each of 4 or 2 oligonucleotides described below. Each DNA was analysed with two different PCRs. The first one (PCR1) detects the presence of murine skeletal actin (MSA) and the human transgene (HSA) using distinctive primers located in the 3′ non-coding region of both genes. The oligonucleotides used in this PCR were: MSA1 (5′-TCCTCAGGACGACAATCGAC-3′), MSA2 (5′-CC TAAGGAGTTCACCCAGTCTG-3′), HSA23 (5′-AAACTT ACATCTTCCCATGCTCC-3′) and HSA24 (5′-GAGA CGCCCTCTGAGAAACAG-3′). The second PCR reaction (PCR2) confirms the length of the expanded CTG repeat (approximately 250 repeats) using primers that flanked the 5′ and 3′ ends of the repeat. The oligonucleotides used in this PCR were: HSA10 (5′-TCCACCGC AAATGCTTCTAGACACAC-3′) and HSA18 (5′-GCA GGGGAGCATGGGAAGATGTAAG-3′). All reactions were done on a DNA thermal cycler (MJ-Mini Personal Thermal Cycler, Bio-Rad). In PCR1, AmpliTaq Gold DNA polymerase was activated at 95°C for 10 min, and then submitted to 33 cycles of denaturation at 94°C for 15 s, annealing at 54.5°C for 15 s and extending at 72°C for 30 s. After the 33 cycles were done, DNA synthesis was completed by incubating the reaction at 72°C for 7 min. In PCR2 AmpliTaq Gold DNA polymerase was activated at 95°C for 10 min then submitted to 21 cycles of denaturation at 95°C for 15 s, annealing at 64°C for 15 s and extending at 72°C for 2 min 22 s. After the 21 cycles were done, DNA synthesis was completed by incubating the reaction at 72°C for 7 min. Reaction products (PCR1) were analysed by electrophoresis through 1.7% agarose gels. The MSA1/MSA2 product is a 310 bp fragment, and the HSA23/HSA24 product if positive is a 249 bp fragment. For PCR2, reaction products were analysed by electrophoresis through 0.8% agarose gels. The HSA10/HSA18 product if positive is a fragment of about 1200 bp (approximately 250 repeats).

Muscle and fibre preparation

Fibres from flexor digitorum brevis (FDB) and interosseous muscles were enzymatically isolated as previously reported (DiFranco et al. 2011). Fibre selection also followed the criteria described elsewhere (DiFranco et al. 2011). The average diameter, length and surface area of the fibres were determined from images acquired using bright field illumination and a 10× objective. To this end, we implemented an algorithm in Labview (National Instruments) that first segmented the 2D images of the fibres in ∼200 cylindrical elements, and then calculated the average geometrical parameters by path and area integration (R. Serrano and J. Vergara, unpublished).

Electrophysiology

A two micro-electrode amplifier was used for electrophysiological measurements (TEV-200, Dagan Corporation, MN, USA). The preamplifiers were attached to three-axis micromanipulators mounted on the stage of an inverted microscope equipped with a standard epifluorescence attachment (Olympus IX-71, Olympus, PA, USA). The 9-anthracene-carboxilic acid (9-ACA)-sensitive ICls, transported through ClC-1 channels, were recorded under voltage-clamp conditions (holding potential −20 mV) in response to a three-pulse protocol as previously described (DiFranco et al. 2011). Namely, ICl current records were obtained by subtracting capacitive and linear leak currents (obtained in the presence of 9-ACA) from total current records acquired in the absence of the drug from fibres equilibrated with 70 mm intracellular Cl (High-Cl internal solution, see Solutions). The specific capacitance of the muscle fibres (in μF cm−2) was also measured under voltage-clamp conditions after blocking all conductances by perfusion with external tetraethylammonium (TEA)-Tyrode (see Solutions) added with 9-ACA; the values were calculated by integration of capacitive currents as previously described (DiFranco et al. 2011).

Measurements of the input resistance (RIN) were made under current-clamp conditions in fibres bathed in Tyrode (resting potential −90 mV) by injecting small current pulses (<8 nA; 300 ms duration) and measuring the steady-state values in the voltage responses (<8 mV). Detailed explanations about the theoretical background used to obtain RIN (in Ω) and underlying values of specific Rm (in Ω cm2) are given in the Results and in the Appendix.

All experiments were carried out at room temperature (20–21°C).

Optical recording of the TTS membrane potential

Membrane potential changes in the TTS were assessed with the potentiometric dye di-8-ANEPPS (DiFranco et al. 2011). Briefly, once dissociated, fibres were stained for 30 min in Tyrode solution containing 10 μg ml−1 of di-8-ANEPPS, washed thoroughly, and plated on coverslip-bottomed 3.5 cm Petri dishes. Fibres were illuminated with a disc-shaped spot of light with a diameter similar to that of the fibre. A fluorescence cube composed of 500–40//560//600LP (exciter/dichroic/emitter, nm) was used to excite di-8-ANEPPS and collect its red shifted fluorescence.

Solutions (in mm)

  • • 
    Tyrode: NaCl, 156; Mops, 10; CaCl2, 2; dextrose, 10; MgCl2, 1; KCl, 4; pH adjusted with NaOH.
  • • 
    TEA-Tyrode: HCl, 145; Mops, 10; CsOH, 10; Ca(OH)2, 2; Mg(OH)2, 1; dextrose, 5; nifedipine, 2 × 10−2; TTX, 2 × 10−4; pH adjusted with TEA-OH.
  • • 
    High-Cl internal solution: CsCl, 70; EGTA, 40; Mops, 30; ATP-Mg, 5; phosphocreatine di(tris) salt, 5; glutathione (reduced), 5.
  • • 
    K-Aspartate internal solution: aspartic acid, 70; EGTA, 40; Mops, 20; ATP-diTris, 5; phosphocreatine disodium, 5; glutathione (reduced), 5; MgCl2, 5; pH adjusted with KOH.

All solutions were adjusted to pH 7.2 and osmolality was 300 ± 5 mosmol (kg H2O)−1. Stock solutions for 9-ACA (500 mm) and nifedipine (50 mm) were prepared in DMSO. All chemicals were from Sigma (MO, USA), except for di-8-ANEPPS that was from Biotium (CA, USA).

Attenuation of TTS voltage changes

The correlation between the attenuation of TTS voltage changes, as reported by di-8-ANEPPS transients, and the magnitude of ICl were analysed in light of a radial cable model of the TTS, as previously described (DiFranco et al. 2011).

Data acquisition and statistical analysis

Voltage, current and fluorescence records were filtered at 10, 5 and 2 kHz, respectively, using 8-pole analog Bessel filters. Data points were sampled every 30 μs, using a data acquisition interface (PCI-6221, National Instruments, TX, USA) and custom software written in LabView (National Instruments).

Results

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information

Age dependence of the membrane capacitance (Cm) in fibres from control and HSALR mice

Previous work from our laboratory has shown that, in adult muscle fibres, a large fraction of ICl arises from functional ClC-1 channels in the TTS membranes (DiFranco et al. 2011). It has also been demonstrated that the total TTS membrane area, effectively contributing to the relatively large Cm of muscle fibres, depends on the diameter of the fibres (Peachey, 1965; Hodgkin & Nakajima, 1972b), and on the stage of development of the TTS that is not fully completed at birth but reaches maturity by the 4th week after birth (Franzini-Armstrong, 1991). For all these reasons, the magnitude of ICl in fibres from different mice strains at various ages is likely to be affected by the structural characteristics of the TTS. Consequently, before comparing the properties of ICl from potentially heterogeneous populations of muscle fibres, we first measured geometrical features and the specific capacitance fibres from HSALR and control mice at ages ranging from 2 to 17 weeks.

Figure 1A shows the age dependence of the average diameter of fibres. It can be seen that the diameter increases with age in a similar fashion in both mice strains, and that it approximately doubles between the ages of 2 and 17 weeks. For example, diameters are 28 ± 2 μm and 30 ± 3 μm for fibres from 2-week-old FVB and HSALR mice, and reach a maximum of 54 ± 8 μm and 52 ± 9 μm, respectively, after 17 weeks. Statistical analysis of fibre diameters from age-matched data showed no significant differences between the fibres from either strain. Besides, the average lengths of the muscle fibres from both strains were also comparable throughout the period examined (data not shown). Consequently, as expected, the average surface area of the fibres (Fig. 1B) increases similarly with age in both animal strains and, as for the diameter, no statistical difference was found for the average surface areas of age-matched fibres from control and transgenic mice. It is important to note that the similarity in the geometrical parameters reported in Fig. 1 for fibres from control and HSALR mice is in agreement with the absence of muscle wasting and developmental problems in this DM mouse model (Mankodi et al. 2000).

image

Figure 1. Age dependence of muscle fibre parameters  Variation of fibre diameter (A), surface area (B) and specific capacitance (C) with age in control (filled circles) and HSALR fibres (open circles). Data (mean ± SD) are connected with line segments. The numbers in parentheses in (A) represent the number of fibres/animals used to obtain each data point; these numbers apply to the data in the four panels. D, membrane capacitance (Cm) plotted as a function of fibre diameter for FVB (filled circles) and HSALR mice (open circles). The linear traces correspond to theoretical predictions of the fibre's capacitance taking into account the TTS contribution (radial cable model) according to eqns (B12) and (B13) in section B of the Appendix while using the parameters in Table B1 and sarcolemma resistance (RS) values of 3000, 10,000 and 20,000 Ω cm2 (dashed, continuous and dotted traces, respectively). As will be shown later in the paper (see Table 1), the capacitance values in this figure span the entire range seen experimentally.

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The above measurements, reporting similar age-dependent increases in diameters and the surface membrane areas in fibres from both mice strains, do not provide direct information about the abundance of TTS membranes in each of them. A reasonable approach to assess this in live muscle fibres is to measure the Cm as this measurable parameter not only reports the presence of the TTS, but it is also expected to increase with the fibre diameter (Peachey, 1965; Adrian et al. 1969a; Hodgkin & Nakajima, 1972b; Heiny et al. 1983; Ashcroft et al. 1985; Kim & Vergara, 1998). As shown in Fig. 1C, the average capacitance of both HSALR and FVB fibres significantly increased from values ∼3.6 μF cm−2 in very young animals (2–3 weeks; 3.7 ± 0.18 μF cm−2 and 3.5 ± 0.40 μF cm−2, for FVB and HSALR fibres, mean ± SD) to a maximum of ∼4.6 μF cm−2 in adult specimens (17 weeks; 4.4 ± 0.87 μF cm−2 and 4.8 ± 0.64 μF cm−2, for FVB and HSALR fibres, mean ± SD). Again, no significant difference was found for age-matched average capacitances between fibres from FVB and HSALR animals, suggesting that the proliferation of the TTS membranes with age may follow a comparable pattern in both mice strains. Reinforcing this idea, Fig. 1D illustrates the dependence of the specific capacitance on measured fibre diameters for the entire population of fibres from both mouse strains (FVB, filled circles; HSALR, open circles). It can be seen that there is a positive correlation between diameter and capacitance in all the fibres depicted in the scatter plot; linear regression fits to the data assuming a surface Cm of 0.9 μF cm−2 (not shown) yielded comparable (non-zero) slopes of 0.074 ± 0.0017 (R = 0.99; = 67) and 0.075 ± 0.002 (R = 0.99; = 61) μF cm−2 μm−1 for FVB and HSALR fibres. Notably, as shown in Fig. 1D, both datasets adequately conform to theoretical predictions of the fibre capacitance (green traces in Fig. 1D), taking into account the contributions from the surface and TTS membranes. The equations used to calculate the theoretical curves in Fig. 1D (dotted, dashed and continuous traces) are based on the radial cable model of the TTS (Adrian et al. 1969a; Hodgkin & Nakajima, 1972a,b) and use the specific structural parameters included in Table B1 of the Appendix. Altogether, the information contained in Fig. 1C and D, and a smaller number of similar results obtained in fibres from 6-month-old control and transgenic animals (not shown), strongly suggest that muscle fibres from control and HSALR mice display a similar developmental progression in the maturation of the TTS membranes with age.

Table B1.  Specific parameter values for passive radial cable
 SymbolValueUnit
  1. TTS, transverse tubular system.

Radius (fibre specific) a 20–30μm
Longitudinal cable resistivity R i 140Ω cm
Specific capacitance TTS wall C W 0.9μF cm−2
TTS lumen conductivity G L 10mS cm−1
TTS access resistance R a 30Ω cm2
Fraction of fibre volume occupied by the TTSρ0.0036 
Volume to surface ratio of the TTSζ1 × 10−6cm
Tortuosity factor on the TTSσ0.32 

ICl records are significantly depressed in very young HSALR mice

Because there are no published longitudinal studies on the properties of ICl in HSALR muscle fibres (including those from adult specimens), we measured them in the same populations of HSALR and FVB fibres presented in Fig. 1. Figure 2A shows ICl records obtained in response to the three-pulse protocol in a fibre from a 3-week-old FVB mouse. The family of currents displays all the canonical features of 9-ACA-sensitive ICl previously reported for fibres from adult C57BL mice under similar conditions (DiFranco et al. 2011). Namely, at the onset of the second pulse, the family of ICl records displays strong inward rectification; also, while outward currents do not decay in time, inward currents show a marked voltage-dependent deactivation that results in the observed crossover in the current records. Nonetheless, the magnitudes of ICl records in the FVB fibre shown in Fig. 2A, though smaller than those for older C57BL animals reported previously (DiFranco et al. 2011), are significantly larger than those from an aged-matched HSALR mouse, as shown in Fig. 2B. For example, the peak current of the largest ICl record (at −140 mV; Fig. 2B) is −166 μA cm−2, which is <1/3 of the −587 μA cm−2 attained in the equivalent trace for the control FVB fibre (Fig. 2A). By graphing the traces in an expanded scale (not shown), we verified that the kinetic properties of ICl traces from the HSALR fibre are not grossly different from those of the control counterpart, suggesting that the reduction in magnitude of the currents results principally from a reduction in the functional expression of ClC-1 channels. It should be noted that the diameter, surface area and capacitance of the fibres in Fig. 2A and B were quite comparable (see legend); also, the fibres had similar unspecific leak currents after blocking all ionic currents (not shown). This suggests a real difference between the magnitude of the currents from the fibres in Fig. 1A and B.

image

Figure 2. Chloride currents (ICl) from young transgenic and control fibres  Currents elicited by the three-pulse protocol in 3-week-old control (A and C) and HSALR (B and D) fibres. A and B, families of 9-ACA-sensitive currents (ICl) from a control and a HSALR, respectively. The maximal peak ICl, capacitance, length and diameter for the FVB and HSALR fibres were: −586 and −166 μA cm−2; 4.23 and 4.24 μF cm−2; 496 and 547 μm; 39 and 31 μm, respectively. C and D, the voltage dependence of peak (open squares) and steady-state values (open circles) of 9-ACA-sensitive currents for the FVB and HSALR fibres. The steady-state values of the 9-ACA-insensitive currents are plotted as open triangles. Data in C and D were obtained from nine FVB fibres (continuous) and nine HSALR fibres (three mice). Data in C and D (means ± SEM) are connected by line segments.

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Figure 2C and D shows the voltage dependence of the average peak (open squares and lines) and steady-state (open circles and lines) ICl, measured at the beginning and at the end of pulse 2, respectively, from populations of FVB (nine fibres, three mice) and HSALR fibres (nine fibres, three mice), respectively. The average residual leak currents (after blockage of all ionic conductances) for both strains are also shown (open triangles and lines). From the plotted data in Fig. 2C and D, it can be observed that ICl is significantly depressed in HSALR fibres when compared with their control counterparts. In fact, the maximal peak ICl values ([peak ICl]max, obtained in response to a hyperpolarization to −140 mV) are −153 ± 11 μA cm−2 for transgenic fibres, which are ∼74% smaller (< 0.002) than those in control fibres (−583 ± 57 μA cm−2). These results are in good agreement with the reduction in ICl previously reported (Lueck et al. 2007a) for animals of the same age. Furthermore, because the average geometrical parameters and specific capacitance of fibres from HSALR and FVB animals are not different (Fig. 1), it can be inferred that the reduction in current density in the former arises from the reduced expression of functional ClC-1 channels. Readily compatible with this finding, we observed that some fibres dissociated from HSALR muscles kept at slack length in Tyrode solution spontaneously twitched at room temperature.

Average peak ICl from HSALR adult mice does not significantly differ from that recorded in control fibres

Although the observation that peak ICl in 3-week-old HSALR mice is highly reduced concurs with previous published data (Lueck et al. 2007a), we thought it necessary to verify whether this observation was consistently observed in older transgenic animals. This is an important requirement for an animal model of DM1, as the human disease is in most cases characterized by a late onset. Thus, we comparatively measured ICl in fibres from adult HSALR and control mice of ages up to adulthood. Figure 3A shows a family of ICl records in a fibre from a 17-week-old FVB mouse; the maximum peak ICl (−716 μA cm−2) is larger than the average peak current measured from 3-week-old control mice (Fig. 2D), but similar to those previously recorded from wild-type C57BL adult fibres (DiFranco et al. 2011). The rest of the features of the currents are otherwise similar to those from young control mice. Nevertheless, in sharp contrast with the results for 3-week-old mice, we found (unexpectedly) that the maximum peak ICl in a fibre from an age-matched HSALR mouse (−588 μA cm−2; Fig. 3B) is only slightly smaller (∼20%) than that in the control fibre (Fig. 3A); also, the kinetic features of the ICl records in both cells are alike. It is important to note that their similarities are not influenced by either the diameter and/or the capacitance as those values were comparable for the fibres in Fig. 3A and B (see legend). The close resemblance in the properties of ICl records was confirmed in fibre populations from FVB and HSALR mice (Fig. 3C and D, respectively). The average values of peak ICl obtained in response to voltage pulses (open squares and lines in Fig. 3C and D) are comparable in both fibre types. For example, the values of [peak ICl]max elicited by hyperpolarizing pulses to −140 mV were −705 ± 44 μA cm−2 and −579 ± 56 μA cm−2 for the FVB (17 fibres, 4 mice) and HSALR (15 fibres, 5 mice) populations, respectively; these values are not significantly different from each other (> 0.08), although peak currents in HSALR fibres are ∼18% smaller than that in FVB fibres. Further comparison of the data in Fig. 3C and D demonstrates that the average steady-state ICl (open circles and lines) in control and HSALR fibres are also not distinguishable from each other (> 0.3).

image

Figure 3. Chloride currents (ICl) from young adult FVB and HSALR mice  Currents recorded from 17-week-old control (A and C) and HSALR (B and D) fibres in response to the three-pulse protocol. A and B, family of 9-ACA-sensitive currents from a control and a HSALR, respectively. The maximal peak ICl, capacitance, length and diameter for the FVB and HSALR fibres were: −715 and −588 μA cm−2; 4.26 and 4.17 μF cm−2; 588 and 494 μm; 53 and 49 μm, respectively. C and D, the voltage dependence of peak (open squares) and steady-state values (open circles) of 9-ACA-sensitive currents for the two populations of FVB and HSALR fibres, respectively. The steady-state values of the 9-ACA-insensitive currents are represented by the open triangles. Data in C and D were obtained from 17 FVB fibres (four mice) and 15 HSALR fibres (five mice), respectively. Data in C and D (mean ± SEM) are connected by line segments.

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Age-dependent changes of ICl in control and HSALR mice

Our studies of the properties of ICl in fibres from both mouse strains at two extreme ages (2 and 17 weeks) pose the conundrum that while myotonia has been reported at both ages (Mankodi et al. 2000), at least in the case of 17-week-old mice the pathology cannot be readily explained on the basis of the reduction in average peak ICl. Furthermore, our findings suggest an age-dependent recovery in the impairment of ICl that needs to be further investigated. To this end, we performed longitudinal studies of the properties of ICl between 2 and 17 weeks, which extends previous reports encompassing a period of only 9–20 days postnatal (Mankodi et al. 2002). Detailed electrophysiological measurements similar to those included in Figs 2 and 3 were performed in fibre populations from 2-, 4-, 6- and 9-week-old animals of both FVB and HSALR strains. Families of ICl records obtained in response to the three-pulse protocol and their corresponding IV plots are shown for 4- and 8-week-old mice as supplementary examples in Figs S1 and S2, respectively. The data in these figures illustrate that the magnitude of ICl from HSALR mice progressively increases with age until it approximately reaches values comparable to those from FVB mice. Also, as shown at the extreme ages (Figs 2 and 3), no significant differences in the kinetic properties of current records in age-matched fibres are observed (Figs S1 and S2). The complete analysis of the information provided in Figs 2 and 3, together with those in Figs S1 and S2, is summarized in Fig. 4A, where the values of [peak ICl]max in fibres from both mice strains are plotted as a function of the animal age. The values reported in Fig. 4A are the mean ± SD for FVB (filled circles and lines) and HSALR (open circles and lines) mice ranging in age from 2 to 17 weeks. It can be observed that in FVB mice, [peak ICl]max varies non-monotonically during the time period explored: it increases from −482 ± 126 μA cm−2 in 2-week-old animals to an apparent maximum of approximately −1000 μA cm−2 in animals between the ages of 6 and 14 weeks, to finally reach a plateau of approximately −700 μA cm−2 after 17 weeks. Thus, the data in Fig. 4A suggest that [peak ICl]max reflects an optimal age range (between 6 and 14 weeks) for the expression of ClC-1 channels in normal FVB animals. Interestingly, and not as expected, data from HSALR mice (open circles and lines in Fig. 4A) demonstrate that ICl increases with the animals’ age from 2 to 9 weeks, but that growth of [peak ICl]max is not as rapid as in FVB mice. Consequently, fibres from HSALR animals in this age range display values of [peak ICl]max that are significantly smaller than those from age-matched control mice. In transgenic animals, values of [peak ICl]max increase from −123 ± 58 μA cm−2 (mean ± SD) at 2 weeks to approximately −390 μA cm−2 at 9 weeks. What is surprising is that ICl continues growing in older animals, in such a way that [peak ICl]max reaches a maximum in 17-week-old HSALR mice. At this age, [peak ICl]max is approximately −580 μA cm−2, a value slightly smaller (but not significantly) than that found in age-paired FVB mice. It is also curious that in both mice strains, [peak ICl]max decreases at approximately the same rate in animals older than 17 weeks. We may summarize the above results by noting that the evolution of the expression of functional ClC-1 increases at an overall slower rate in HSALR than in control mice; during the period between 2 and 9 weeks, the rate of change of [peak ICl]max with age is ∼2.5 times faster in FVB as compared with HSALR mice. Furthermore, this slowness in the growth of ICl in HSALR animals, in combination with the finding that [peak ICl]max reaches a maximum in approximately 6-week-old FVB (control) animals, explains why the values of ICl attain similar values in specimens older than 16 weeks. In a smaller number of fibres than those reported in Fig. 4A, we have confirmed (data not shown) that the insignificant differences in [peak ICl]max between HSALR and FVB fibres are observed up until 1-year-old mice (the oldest tested). For example, fibres from 1-year-old HSALR mice (= 4) display [peak ICl]max values (−740 ± 184 μA cm−2, mean ± SD) that are comparable (to those found in the 17-week-old specimens shown in Fig. 4A).

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Figure 4. Age dependence of maximum peak chloride current ([peak ICl]max) and maximum slope chloride conductance (gCl,max)  A, average peak ICl determined at −140 mV from FVB (filled circles) and HSALR (open circles) fibres isolated from 2–17-week-old mice. The error bars represent the SD; the asterisks indicate statistical significance (< 0.05). B, the maximum slope chloride conductance was determined (as described in the text) from IV plots obtained from control (filled bars) and HSALR (hatched bars) fibres. The error bars represent the SD; the numbers indicate significance level. The number of fibres/animals used for each age and strain are the same as in Fig. 1A.

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The maximal chloride conductance (gCl,max) increases with age in transgenic animals

As an alternative approach to quantitate differences in the expression of ClC-1 channels between both mouse strains, we evaluated the slope of the linear region of peak IV plots (for hyperpolarizing pulses from −80 to −140 mV). This parameter, which assesses gCl,max (in mS cm−2) conferred by open ClC-1 channels, was calculated from all peak IV plots in Figs 2 and 3 (and also from Figs S1 and S2). Figure 4B shows the average results from 3-, 4-, 9- and 17-week-old HSALR (hatched bars) and FVB mice (filled bars). In agreement with data shown in Fig. 4A, it can be seen that gCl,max is significantly smaller in 9-week-old (or younger) HSALR mice than in their control counterparts; however, at ∼17 weeks old, gCl,max becomes indistinguishable in FVB and HSALR mice. Also, the apparent maximum of [peak ICl]max between weeks 6 and 14 shown in Fig. 4A for FBV mice is confirmed by the gCl,max data (largest at 9 weeks) as illustrated in Fig. 4B.

While the average data shown in Fig. 4 demonstrate that in HSALR animals both [peak ICl]max and gCl,max increase with age (albeit slower than in FVB mice), this information does not provide a precise insight as to the actual impairment in ClC-1 functionality in individual fibres within the population at various animal ages. To investigate this issue, we plotted frequency histograms and normalized cumulative histograms of gCl,max for 3-, 4-, 9- and 17-week-old FVB and HSALR animals (Fig. 5). Figure 5A shows that, in 3-week-old mice, the frequency distributions among fibres of both strains are centred at two very different gCl,max values: fibres from HSALR animals display a narrow distribution centred at a very small gCl,max (1.5 mS cm−2); while the FVB fibres span a wider range of gCl,max, but centred at a larger value (5.5 mS cm−2). This clearly demonstrates a substantial difference in ClC-1 functional expression between the two fibre populations. As expected, the cumulative distribution for HSALR data (open squares and dashed lines) illustrates that the entire population is constrained within small gCl,max values, and that there is little overlap between these values and those observed in FVB fibres (open circles symbols and dashed lines). In 4-week-old animals of both strains, it is observed that the cumulative distribution shifts towards larger gCl,max values (Fig. 5B). Nevertheless, as seen for 3-week-old animals, the frequency distributions are still centred at two distinct average gCl,max values, with little overlapping; namely, almost the entire population of fibres from 4-week-old HSALR animals has gCl,max values <3 mS cm−2, whereas almost all FVB fibres tested have gCl,max values >4 mS cm−2). However, a noticeable trend in 4-week-old HSALR animals is that the frequency distribution of gCl,max is broader with respect to data obtained from 3-week-old mice.

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Figure 5. Frequency histograms of maximal slope chloride conductances (gCl,max) obtained from FVB and HSALR fibres isolated from mice of various ages  The maximal slope conductance of FVB (filled bars) and HSALR (hatched bars) fibres isolated from 3-, 4-, 9- and 17-week-old mice are shown in A, B, C and D, respectively. The plots are fitted with normal distributions to the FVB and HSALR data (continuous lines). The dashed lines connect the cumulative distribution data points for FVB (open circles) and HSALR mice (open squares), normalized to the number of fibres of each strain and age group. The average maximal slope conductances for 3-, 4-, 9- and 17-week-old FVB mice were: 5.5, 6.3, 8.4 and 6.6 mS cm−2, respectively. The average maximal slope conductances for 3-, 4-, 9- and 17-week-old HSALR mice were: 1.5, 2.0, 3.7 and 5.7 mS cm−2, respectively. The number of fibres/animals used for each age and strain are the same as in Fig. 1A.

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A more substantial overlap between the gCl,max data obtained in HSALR and control fibres was seen in 9-week-old mice (Fig. 5C). At this age, the frequency distribution in HSALR animals (hatched bars, Fig. 5C) is broadened to encompass a wider range of gCl,max values, whilst the centre of the normal distributions (average) still remains lower than that for FVB animals (filled bars, Fig. 5C). This is clearly noted in the more gradual cumulative distribution for the HSALR fibre population (open squares and dashed lines in Fig. 5C). The most striking results of the frequency distribution analysis are seen in 17-week-old mice. At this age, an almost complete overlap in gCl,max values for both fibre populations becomes apparent; this results principally from a further rightward shift to larger gCl,max values in fibres from HSALR animals (hatched bars, Fig. 5D). But also, while both populations show a wide distribution in gCl,max values, the HSALR data span a broader range, some of them at particularly low gCl,max values. Thus, though both fibre populations display comparatively similar cumulative distributions (open circles and squares and line in Fig. 5D), fibres from 17-week-old HSALR mice constitute a more heterogeneous population in terms of the functional expression of ClC-1 channels than age-matched FVB fibres. We propose that these findings are quite relevant for the interpretation of the presence or absence of myotonia in adult HSALR animals, and they may hint on the limitations of this animal model for the evaluation of the chloride channelopathy in patients with DM1.

Age-dependent variations in Rm in fibres from FVB and HSALR mice

The voltage-clamp experiments described above show that there are significant differences in the functional expression of ClC-1 channels between fibres from FVB and HSALR mice at ages younger than 14 weeks old (Figs 4 and 5), but that these differences fade thereafter. A plausible prediction from these results would be that the RIN (in Ω) measured in these populations of fibres, and/or more precisely the specific Rm (in Ω cm2) calculated from current injection experiments should display age-dependence features compatible with ICl measurements. To test this hypothesis, we performed current injection experiments under conditions as close as possible to the physiological case (resting potential of −90 mV, extracellular Tyrode solution, 10 mm intracellular Cl), and measured the linear electrical properties of the fibres using a narrow range of current pulse amplitudes (±7 nA, in 0.2 nA steps). The rationale behind this approach is to induce very small changes in the membrane potential so as to limit the effects of non-linearity on the responses. Fibres from animals at two ages (4 weeks old and 17 weeks old) were used, and experiments were performed first in Tyrode with 400 nm TTX added to block Na channels, and subsequently in Tyrode with TTX, 9-ACA (400 μm, to block ICl) and Rb (5 mm to block the K inward rectifier) added in order to render the fibres electrically passive. Figure 6 shows plots from these types of experiments for four age-matched HSALR and FVB fibres in which the symbols represent average membrane potential changes (ΔV) in response to current injection pulses (ΔI); the lines are linear regressions fitted to the data points that provide an estimate of the average RIN. Figure 6A shows data obtained from young FVB fibres in the Tyrode solution (filled circles), and after rendering the fibres electrically passive (open circles). In both conditions a linear IV relationship was observed, and RIN changed from 1.24 MΩ in Tyrode to 5.2 MΩ after blocking the conductances; the change represents an ∼4.2-fold increase. Adult FVB fibres also display a linear behaviour in the same range of current injection both in Tyrode and after blocking the chloride and potassium conductances (Fig. 6B), yielding RIN values of 0.89 MΩ and ∼4 MΩ, respectively. Each of these values is significantly smaller than its respective one in fibres from young animals; in principle, this could be a result of the larger average size of fibres in adult, with respect to younger animals as illustrated in Fig. 1, but as will be shown in more detail later, additional factors must be invoked to explain the differences.

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Figure 6. Voltage–current relationship for young and old FVB and HSALR mice  AD, plots of the steady-state displacement of membrane potential (ΔVm) in response to current injection (ΔI) for FVB (A and B) and HSALR (C and D). Data for 3- and 17-week-old mice are shown in A and C, and B and D, respectively. The filled symbols represent the responses obtained in the presence of Tyrode, and the open symbols are the responses measured in the presence of 400 mm 9-ACA and 5 mm Rb. All solutions contained 400 nm TTX. The lines are linear regression of the data in the presence of Tyrode (continuous lines) or Tyrode with 9-ACA and Rb (dashed lines). The slopes for FVB fibres are: 1237 (= 9), 5153 (= 9), 982 (= 9) and 4030 (= 9) kΩ for 4 weeks/Tyrode, 4 weeks/9-ACA + Rb, 17 weeks/Tyrode and 17 weeks/9-ACA + Rb, respectively. The slopes for HSALR fibres are: 1626 (= 9), 4614 (= 9), 900 (= 9) and 3630 (= 9) kΩ for 4 weeks/Tyrode, 4 weeks/9-ACA + Rb, 17 weeks/Tyrode and 17 weeks/9-ACA + Rb, respectively. Data are mean ± SEM.

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An interesting result is that, while the RIN values obtained from current injection experiments under control conditions in young HSALR fibres (1.63 MΩ; Fig. 6C) are larger than those in age-matched FVB fibres (1.24 MΩ), the ∼25% difference does not match the ∼threefold reduction in the magnitude of ICl seen in voltage-clamp experiments (Fig. 2). If gCl was the dominant resting conductance, the drastically reduced expression of functional ClC-1 channels in fibres of young HSALR animals should have resulted in much larger values of RIN; values approximating the value of 4.6 MΩ seen under passive conditions would have been perhaps more reasonable. As expected, passive fibres from FVB and HSALR young animals reported comparable values of RIN (∼5.2 MΩ and 4.6 MΩ, respectively); this result serves as a control for the intactness of fibre types. A comparable analysis as above, but for fibres from adult HSALR animals, is shown in Fig. 6D. RIN values before and after blocking ionic conductances were 0.9 MΩ and 3.6 MΩ, respectively. It is worth noting that, by comparing the slopes of the linear fits in Fig. 6B and D, the resulting increase in RIN afforded by blocking the chloride and potassium conductances is quite similar in fibres from adult FVB (∼4.5-fold) and HSALR (∼4.1-fold).

It could be argued that the RIN values calculated from the slopes of the linear regressions with data obtained from muscle fibres of variable dimensions could be tainted by systematic errors other than those purely related to the presence or absence of ion channels that define the ohmic properties of the limiting membrane(s). In order to correct for these factors, we analysed the experimental data obtained from current injection experiments in terms of the prediction of a linear cable model for short cylindrical cells (Weidmann, 1952; Hodgkin & Nakajima, 1972b). To this end, we fitted records of the voltage changes induced by the injection of step current pulses (20 nA, 200 ms) to the solution of eqn (A2) in the Appendix, in turn modified from Hodgkin & Nakajima (1972b). The results from this analysis permitted us to calculate the value of Rm (in Ω cm2), the membrane time constant (τm, in ms) and the Cm (in μF cm−2) for individual fibres, from young and adult FVB and HSALR animals, under different experimental conditions. The average results from this analysis are shown in Table 1 and Fig. 7. As can be seen in Fig. 7A, Rm in fibres from 4-week-old FVB mice (919 ± 82 Ω cm2, filled bar) is significantly but only slightly larger (25%, < 0.05) than that for HSALR animals (1210 ± 102 Ω cm2, hatched bar) The importance of these results is that now the average values of Rm are normalized by the individual peripheral area of the muscle fibres; yet, they still do not correspond to the expectation of larger differences if Rm was dominated (as usually assumed) by gCl. Consequently, it is reasonable to suggest that, at least in these young mice, gCl cannot be the predominant resting conductance in cells under physiological conditions. As expected, Rm is greatly increased in both FVB (4463 ± 422 Ω cm2, filled bar) and HSALR (3735 ± 401 Ω cm2, hatched bar) fibres by blocking the chloride and potassium conductances; nevertheless, these values become indistinguishable from each other (> 0.2).

Table 1.  Perturbation analysis of membrane parameters of fibres from young (3–4 weeks old) and adult (>4 months old) mice in control (Tyrode) and passive (9-ACA//Rb) conditions
Fibre typeExperimental condition R IN (kΩ) R m (Ω cm2) C m (μF cm−2)τm (ms) R m* (Ω cm2)
  1. Current pulses: 20 nA. Voltage change: <6 mV (Tyrode); <15 mV (9-ACA + Rb). RIN was measured from steady-state voltage changes. Rm, Cm and τm were calculated by adjusting every experimental record to the short cable equation as outlined in Appendix A. Rm and Rm* are the specific membrane resistances referred to the peripheral area of the fibre, and to the total membrane area of the fibre (including surface and TTS membranes, as outlined in Appendix B), respectively. Rm* was calculated from eqn (B11) in Appendix B, using the parameters in Table B1 therein. Values are means ± SEM. The numbers in parentheses are the number of fibres. *Indicates statistical significance at < 0.05 between age-matched fibre populations. 9-ACA, 9-anthracene-carboxilic acid.

Young FVBTyrode1291 ± 126919 ± 824.5 ± 0.24.1 ± 0.44235 ± 511
 (n = 9)     
 9-ACA + Rb6105 ± 15594463 ± 4224.5 ± 0.419.7 ± 1.418,880 ± 3570
 (n = 3)     
Young HSALR(Tyrode)1720 ± 123*1210 ± 102*4.2 ± 0.35.1 ± 0.55967 ± 672*
 (n = 8)     
 9-ACA + Rb5127 ± 6253735 ± 4014.6 ± 0.317.8 ± 2.717,351 ± 2379
 (n = 7)     
Adult FVBTyrode870 ± 64721 ± 524.5 ± 0.23.1 ± 0.23379 ± 389
 (n = 8)     
 9-ACA + Rb4000 ± 2483654 ± 4794.9 ± 0.616.3 ± 1.118,111 ± 2901
 (n = 6)     
Adult HSALRTyrode849 ± 94783 ± 814.6 ± 0.13.6 ± 0.53045 ± 243
 (n = 9)     
 9-ACA + Rb4355 ± 8673348 ± 2665.2 ± 0.317.3 ± 1.720,885 ± 4284
 (n = 5)     
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Figure 7. Membrane resistance in fibres from young and adult FVB and HSALR mice  A, average membrane resistance from FVB (filled bars) and HSALR (hatched bars) isolated from 4-week-old mice. Data obtained in the presence of Tyrode or Tyrode added with 9-anthracene-carboxilic acid (9-ACA; 400 mm) and Rb (5 mm) are presented by filled and dashed colours, respectively. B, average membrane resistance from FVB (filled bars) and HSALR (hatched bars) isolated from 4-month-old mice. Data obtained in the presence of Tyrode or Tyrode added with 9-ACA (400 mm) and Rb (5 mm) are presented by filled and dashed bars, respectively. All data in experiments in A and B were collected in the presence of TTX (400 nm). In A and B, the error lines are the SEM.

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When the same analysis is made for adult fibres (Fig. 7B), we found that, in control conditions, Rm values of fibres from FVB (668 ± 49 Ω cm2, filled bar) and HSALR (783 ± 81 Ω cm2, hatched bar) mice are undistinguishable from each other (> 0.2). Again, this extremely important result is in disagreement with results from other laboratories showing a ∼fourfold difference in Rm in adult fibres (Mankodi et al. 2002). Furthermore, it severely questions the suggestion that in adult fibres there is a marked reduction in gCl, and this is the best explanation for their myotonia. In contrast, the results in Fig. 7B demonstrate that blocking the resting Cl and K conductances results in a significant increase in Rm, which curiously is larger in HSALR than in FVB fibres (∼4.3-fold vs. 3.5-fold, respectively).

Another result worth noting is that, by comparing the data in Fig. 7A and B, Rm values in fibres from young animals are conspicuously larger than those from the corresponding normal counterpart. In principle, this difference could be accounted for by differences in proliferation of the TTS development between these fibre populations. In order to decide on this issue, we analysed the predictions of a simple linear equivalent circuit model of the resting muscle fibre in which the contributions of both the surface and TTS membranes are taken into account (see section B in the Appendix). As shown in the Appendix, by making the specific resistance of the surface and TTS membranes the same, an assumption already contemplated by Hodgkin & Nakajima (1972a,b) for amphibian muscle fibres and amply supported by published data from our laboratory regarding ClC-1, K (KIR and KV) and NaV1.4 channels (Heiny et al. 1983; Ashcroft et al. 1985; DiFranco et al. 2011; DiFranco & Vergara, 2011; Yu et al. 2012), it becomes possible to obtain an equation (eqn (B11), Appendix) that predicts experimental values of RIN based on specific Rm values (Rm*, in Ω cm2). The calculated values of Rm*, by incorporating structural parameters of the TTS, take into account the contribution of all external membranes (sarcolemma plus TTS compartment) of each fibre, and are not limited to only the peripheral area of the cylindrical cells. For these reasons, Rm* values (last column of Table 1) provide a more accurate comparative evaluation of values of specific Rm in each population of fibres. The data in Table 1 ultimately reinforce three conclusions from previous analyses. (A) The small difference in Rm* between fibres from young HSALR mice (∼6 kΩ cm2) and those from control mice (∼4.2 kΩ cm2) is too little to be accounted for by the reduction in functional ClC-1 channels; thus, another conductance (e.g. gK,IR) must predominantly determine the relatively low value of Rm found in the fibres of mutant animals. (B) The fact that Rm* values are quite comparable in fibres from adult FVB and HSALR animals (∼3.4 and 3.1 kΩ cm2, respectively) is in agreement with the lack of difference in gCl,max, but is also compatible with the idea that another conductance may participate in defining the resting resistance in adult fibres. (C) The great similarity among Rm* values when both gCl and gK,IR are blocked (or at least largely reduced by 9-ACA and Rb in the external solution) demonstrates that the specific Rm of muscle cells under physiological conditions is indeed mostly determined by the functional expression of both ClC-1 and KIR channels. The fact that under physiological conditions Rm* is smaller in older animals than in their young counterparts further suggests that the expression of these ion channels becomes more robust with age (at least at the extreme ages tested).

ICl-dependent attenuation in optical records of TTS membrane potentials

In most of the voltage-clamp experiments, we simultaneously recorded membrane currents and potentiometric dye (di-8-ANEPPS) signals elicited by voltage pulses in order to assess for the effects of ICl on the changes in TTS membrane potential. The concept behind these measurements is that the fraction of ICl originating in the TTS membranes attenuates the changes in membrane potential in this compartment. The procedure involves recording the optical transients elicited by a family of pulses before and after blocking ICl, then subtracting the resulting traces in a one-by-one basis, and finally generating so-called ‘attenuation’ traces that specifically reflect the impact of ICl on the TTS membrane potential responses (DiFranco et al. 2011). Because we wanted to correlate age-dependent variations in gCl,max with the maximal attenuation, we focused on the responses to the largest hyperpolarization (to −140 mV) at the transition between the first and second pulse using the three-pulse protocol. Figure 8A illustrates the properties of di-8-ANEPPS transients (TTS voltage changes) recorded in a fibre from a 4-week-old HSALR mouse before (trace a) and after (trace b) blocking ICl. It can be seen that in both conditions the optical signals are quite similar to each other, as expected for the relatively small magnitude of ICl (blue trace, Fig. 8C), which is in agreement with the data in Fig. 4A. Substantially larger differences between the TTS responses recorded before and after blocking ICl are seen in fibres from 4-month-old HSALR (Fig. 8B) and FVB (Fig. 8C); these differences are well accounted for by the significantly larger ICl (traces 2 and 3, respectively) shown in Fig. 8D. The attenuation traces (in %) calculated from the data in Fig. 8AC are shown in Fig. 8E. It can be observed that, although the time course of the respective attenuation traces is comparable, their amplitude varies substantially: the smallest peak attenuation (8%) corresponds to the fibre from the 4-week-old HSALR mouse, and the largest from the 4-month-old FVB fibre (31%).

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Figure 8. Current-dependent attenuation of TTS membrane potential in young and adult FVB and HSALR fibres  AC, optical measurement of TTS membrane potential changes in response to a hyperpolarization to −140 mV. The fibres in A and B were isolated from 4- and 17-week-old HSALR mice, respectively. The data in C were obtained from a fibre isolated from a 4-month-old FVB mouse. The traces labelled a and b are the responses to the second pulse of the three-pulse protocol before and after blocking chloride current (ICl; 400 μm 9-ACA), respectively. The insets show the complete record of TTS signals in response to the three-pulse protocol. The rectangles in the insets indicate the part of the records shown in AC. D, 9-ACA-sensitive ICl currents corresponding to the optical records (trace a) in AC (before blocking ICl). E, current-dependent attenuation calculated from the data in AC. The traces labelled 1, 2 and 3 represent the data from fibres from 4-week-old HSALR (A), 17-week-old HSALR (B) and 17-week-old FVB mice (C), respectively. The error lines indicate the uncertainty in the calculation of the percentage of di-8-ANEPPS attenuation due to noise.

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The information above, illustrating a close correlation between the size of the currents and the % attenuation, not only reinforces the concept that a major proportion of ICl arises from the TTS membranes as previously reported for fibres from another (normal) mouse strain (DiFranco et al. 2011), but provides the basis for a longitudinal study of this issue. Figure 9 shows the variation of the attenuation (mean ± SD), as calculated from combined optical and electrical experiments in fibres from HSALR and FVB mice, as a function of their age from 2 to 17 weeks. Though, with higher variability, the data demonstrate that the age dependence of attenuation follows a similar course as that shown in Fig. 4A for the age dependence of the [peak ICl]max. Interestingly, the attenuation in optical records is negligible in HSALR mice at very young ages (i.e. ∼4% in 2-week-old mice) and increases progressively as the animals age (to ∼23% in 4-month-old mice). However, as for ICl (Fig. 4A), the rate of growth of the attenuation with the aging of the animals is significantly more abrupt in the control than in the mutant animals (compare filled and open symbols in Fig. 9). As a result, between 2 and 17 weeks old, the attenuation in fibres from HSALR animals is significantly smaller than that in age-matched FVB fibres. Ultimately, in 14- and 17-week-old mice, the attenuation is slightly larger (∼30%vs. 23%) in fibres from FVB than those from HSALR mice, but the difference is barely significant. Taken together, the above results from optical experiments and those shown previously for [peak ICl]max and gCl,max strongly suggest that the age-dependent increment in ICl is done at the expense of the ubiquitous expression of functional ClC-1 channels in both the surface and the TTS membranes.

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Figure 9. Age dependence of attenuation in FVB and HSALR mice  Data represent the average attenuation due to the ICl elicited by a hyperpolarization to −140 mV from control (filled circles) and HSALR (open circles) fibres isolated from 2–17-week-old mice. Data points (mean ± SD) are connected by lines segments. The numbers in parentheses indicate number of fibres; the asterisks indicate statistical significance.

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Discussion

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information

Fibre size and TTS development

The results in Fig. 1 demonstrate that the geometrical characteristics and Cm are not significantly different in muscle fibres from HSALR than those from age-matched FVB animals. In general, these results concur with previous observations that severe signs of muscle wasting are not detectable in HSALR mice (Mankodi et al. 2000). On the other hand, these data strongly suggest that, for fibres from age-matched mice, comparative differences in the magnitudes of ICl and values of Rm do not result from differences in fibres diameter, or from the relative sarcolemma/TTS membrane areas (Hodgkin & Nakajima, 1972a,b); instead, age-dependent differences between both strains must have arisen from their specific genetic differences.

Our analysis of the relationship between diameter and capacitance confirmed (for mammalian muscle fibres) that the capacitance increase can be readily predicted (Fig. 1D) by theoretical equations (section B in Appendix) previously used for amphibian fibres (Hodgkin & Nakajima, 1972a,b). This is an important result as in our case the populations of fibres used were from mice of various ages (2–6 weeks).

Age dependence of the expression of ClC-1 channels

Our data expand previous reports suggesting that ClC-1 expression is far from complete at birth. The increase in [peak ICl]max up until 6 weeks correlates well with both the maturation of TTS (Franzini-Armstrong, 1991) and the increase in capacitance illustrated in Fig. 1C, but the apparent decline after 14 weeks does not seem to have a close match in other fibre properties.

The data in Figs 2 and 4 demonstrate that the magnitude of ICl in fibres from very young (<1 month old) HSALR mice is ∼26% of that in fibres from control animals; these results confirm (and expand) previous reports from another laboratory (using the same muscle preparation) that suggest serious limitations in ICl in fibres from 9- to 22-day-old and 19-day-old HSALR mice (Lueck et al. 2007a,b). In general, results showing that both [peak-ICl]max and gCl,max increase with age differently in HSALR with respect to control animals (Figs 4 and 5) also demonstrate that the triple repeat intoxication in transgenic mutants has definite effects on the ultimate expression of functional ClC-1 channels. However, this finding is only in partial agreement with a previous report (Lueck et al. 2007a). These authors, while studying ICl in animals spanning a very narrow age range (9–22 days), reported that [peak-ICl]max increased by ∼twofold in control mice, but insignificantly in age-matched HSALR mice. In contrast, our investigations over a broader age range (up 6 months) show that the impairment in the expression of ClC-1 channels clearly ameliorates with age in mutant mice. Furthermore, the data in Figs 4 and 5 illustrate that the rate at which [peak-ICl]max and gCl,max increase with the age of the animals is significantly greater in control than in HSALR animals; this explains why Lueck and collaborators (Lueck et al. 2007a), by evaluating ICl along an insufficient age window, may have mistakenly predicted that the impairment in the expression of ClC-1 channels is sustained at all ages, a proposition in sharp contrast with our demonstration that the expression of functional ClC-1 channels progressively increases with age. Consequently, according to our data, the previous suggestion by Lueck and collaborators (Lueck et al. 2007a) that HSALR mice fail to execute the postnatal splicing transition for ClC-1 should likely be modified to indicate that the splice switching from fetal to postnatal patterns is temporarily delayed, but not prevented, in HSALR animals.

Age dependence of gCl: implications for myotonia

Our results showing that the levels of expression of functional ClC-1 channels, albeit delayed, are not permanently depressed in HSALR mice (as previously proposed) are of vital importance for the correct understanding of myotonia. Namely, our average data on [peak-ICl]max and gCl,max for very young mutant animals (up to ∼6 weeks old; Fig. 4) are readily compatible with the observation of myotonia (Mankodi et al. 2000; Lueck et al. 2007a) according to the assumption that gCl should be as low as ∼20–25% of normal to induce myotonia in normal fibres (Furman & Barchi, 1978). However, this clearly does not hold true for older animals; for example, by ∼14 weeks old, though average [peak-ICl]max was ∼20% smaller in fibres from HSALR than in those from FVB mice, the difference was not statistically significant. These average deficiencies are clearly insufficient to explain myotonia in adult HSALR mice, as claimed by other authors (Mankodi et al. 2002). In this regard, it is important to recall that while these authors correlated myotonia in HSALR mice with the (allegedly age-independent) level of transgene expression, they did report direct measurements of ICl in adult HSALR fibres. Instead, the reduction in ICl was only inferred from RIN measurements at rest (Mankodi et al. 2002). Interestingly, their report of significantly larger RIN in adult HSALR fibres, as compared with controls, is also in disagreement with our data in Fig. 6 and Table 1 (see below).

An obvious question that arises from the above discussion is: how is it possible that myotonia is observed in HSALR animals at ages in which average [peak-ICl]max and gCl,max are only slightly below normal? Two non-mutually exclusive explanations are supported by our data: (A) that conductive pathways, other than gCl, are implicated in the electrical response of the fibres during the genesis of myotonic runs; and (B) that electromyogram detection of myotonia may be biased towards the presence of highly impaired fibres in a population, while not reflecting the average impairment of gCl. Evidence in support of the first possibility is provided in Fig. 10. Namely, two fibres with comparable values of Rm, one from a control animal (Fig. 10A; R= 930 Ω cm2) and the other from an adult HSALR mouse (Fig. 10B; R= 740 Ω cm2), display very dissimilar electrical responses to identical current pulses. It can be observed that the control fibre shows the typical response for normal animals: a single AP. In contrast, the voltage response in the HSALR fibre is a train of APs, akin to a myotonic run, which is typical for this animal strain. Although the evidence is not conclusive, the data summarize our experience that, albeit the linear resting resistance and gCl may be normal in fibres from adult HSALR animals, alterations of other conductances manifest themselves in non-linear responses that lead to the existence of myotonic runs in fibres from these animals. Evidence in favour of the latter option was provided by analysing frequency distributions of gCl,max in fibres from animals at various ages (Fig. 5). For example, in very young HSALR mice (hatched bars, Fig. 5A), not only was the mean gCl,max value quite small but, most interestingly, unlike in its normal counterpart (filled bars, Fig. 5A), the distribution of gCl,max values around the mean was very narrow. This suggests that, in general, muscles from these animals may represent a rather homogenous population of impaired fibres. In contrast, values of gCl,max in fibres from adult HSALR mice (hatched bars, Fig. 5D) are distributed over a wide range that closely overlaps those from normal mice (filled bars, Fig. 5D); however, an important difference must be noted between these two datasets: the gCl,max distribution in HSALR includes low values that are not present in normal mice, i.e. this is a very heterogeneous distribution. This feature implies that, in principle, a fraction of, but not all, the fibres somehow evade the toxic effects of the triplet repeats. In conclusion, the presence of fibres with low gCl,max may explain the detection of myotonia in muscles from HSALR animals, while the average gCl,max is not statistically distinguishable from the normal value. It should be noted that the above explanation is compatible with published immunohistochemistry data showing that muscle cross-sections challenged with anti-ClC-1 antibodies show a mosaic pattern of ClC-1 expression in adult HSALR mice (Mankodi et al. 2002; Wheeler et al. 2007). 

image

Figure 10. Fibres from adult HSALR mice are more excitable than from age-matched FBV mice  The upper traces in A and B are voltage records acquired from FDB fibres of control and HSALR mice, respectively. The lower traces are the current pulses (50 nA, 300 ms). The records were obtained in Tyrode. The ages of the mice were 20 weeks and 17 weeks for A and B, respectively.

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Stability of HSALR genotype at all ages

It could be argued that the progressive increase of [peak-ICl]max and gCl,max with the age of the animals was due to a diminished expression of triple repeats in old, with respect to young, HSALR mice. As explained in Methods, we circumvented this possibility by genotyping all mice used in this study. Furthermore, tail samples were taken at the moment of death, and PCR data showed the presence of the HSA gene with 200–250 triple repeats in all samples studied, regardless of the age of the animals. Gels displayed only one recognizable band (approximately 1000–1100 bp), which is in agreement with recent reports from Dr Thornton's laboratory that the triple repeats in HSALR-20b have shortened to (CTG)220 (Wheeler et al. 2012).

Expression of ClC-1 channels in the TTS of fibres from HSALR animals

We have previously demonstrated that, in adult fibres, the majority of experimentally recorded ICl arises from channels present in the TTS membranes (DiFranco et al. 2011). Here we extended this work by performing a longitudinal analysis of the current-dependent attenuations in TTS membrane potential changes associated with the activation of ICl in fibres from both normal and HSALR mice. Several important conclusions can be drawn from our results in Fig. 9. (A) The kinetic properties and voltage dependence of di-8-ANEPPS transients (Fig. 8) provide an independent confirmation of the current-dependent effects of ClC-1 channels present in the TTS. (B) The fact that ICl-dependent attenuations were observed in di-8-ANEPPS transients recorded in fibres from both HSALR and FVB mice at all ages demonstrates that ClC-1 channels are (in all cases) expressed in the TTS; this observation argues against a possible mistargeting of ClC-1 in HSALR fibres. (C) Because the maximal peak attenuations measured in fibres from both strains increase with age and (notably) display a comparable age dependence as the corresponding [peak-ICl]max (Fig. 4A), it is likely that ClC-1 channels are similarly distributed between the TTS and the surface membranes. This conclusion, based on our previous demonstration that the maximal peak attenuation (as a percentage) is directly correlated with the [peak-ICl]max and, in quantitative model analysis of the relative distribution of channels in the TTS and sarcolemma compatible with measured attenuation values (DiFranco et al. 2011), has important implications for the understanding of myotonia as it suggests that a preferential distribution of ClC-1 channels may not be the underlying cause of the hyperexcitability.

Measurements of the linear electrical properties RIN, Rm and Rm*

An important methodological precaution in our RIN measurements (and the determination of Rm thereafter) is that they were made with very small current injections (<20 nA), eliciting small voltage perturbations (ΔV typically <6 mV), in order to critically assess the linear electrical properties of FDB fibres subject to their physiological resting potential (approximately −90 mV). In other words, the experimental conditions were designed to minimize the influence of intrinsic non-linearities of either ClC-1 and/or other channels that contribute to their resting conductance. Interestingly, our Rm values for fibres from FVB adult animals (668 ± 49 Ω cm2; Fig. 7B and Table 1) are in excellent general agreement with average values reported for a variety of mammalian skeletal muscle preparations; for example, average values of 642, 445 and 542 Ω cm2 have been reported for mouse extensor digitorum longus (EDL), rat diaphragm and rat EDL, respectively (Kiyohara & Sato, 1967; Farnbach & Barchi, 1977; Palade & Barchi, 1977a; Kerr & Sperelakis, 1983). But these linear Rm values are distinctly smaller than the value of 1040 ± 100 Ω cm2 reported for intercostal fibres from >2 month old FVB mice (Mankodi et al. 2002); though we do not fully understand the origin of this discrepancy, these authors’ observations were made using larger current injections that resulted in voltage perturbations possibly out of the linear range. Furthermore, our Rm values in fibres from adult HSALR mice are also significantly smaller than those reported by Mankodi and collaborators (783 ± 81 vs. 4080 ± 590 Ω cm2). It is important to highlight that the relatively large values of Rm obtained by us in fibres rendered electrically passive (Tyrode with 9-ACA + Rb) demonstrate that, in adult fibres under resting (physiological) conditions, Rm was mostly determined by contributions by K and Cl conductances rather than by unspecific residual conductances (from Table 1, ∼3.5- and 4.3-fold changes were found in fibres from control and HSALR animals, respectively; also see Fig. 11). Furthermore, the similarity of Rm between fibres from adult FVB and HSALR is compatible with our voltage-clamp result that values of gCl,max in these animals are not significantly different.

image

Figure 11. Conductance contributions to the resting gm in fibres from FVB and HSALR mice  The proportional contributions of gCl, gK,IR and gres to gm were calculated from Rm values obtained in fibres sequentially bathed in Tyrode, Tyrode + Rb, Tyrode + 9-ACA and Tyrode + Rb + 9-ACA. The specific experiments for these calculations are a subset of those used to calculate Rm values reported in Table 1 and Fig. 7. The percentage contributions of gCl, gK,IR and gres were calculated by algebraically solving the system of linear equations using Rm data under the four experimental conditions. A and B, the data from young and adult animals, respectively. The filled and hatched columns correspond to data from control and HSALR animals, respectively. The error bars represent the SEM. The asterisks show significance at < 0.05.

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In contrast with the observations discussed above, Rm measurements in fibres from young (4 weeks old) HSALR are significantly larger (< 0.05) than those from age-matched FVB mice (Fig. 7A and Table 1). This was a reasonable result in the light of the [peak-ICl]max and gCl,max data under voltage-clamp conditions if we accept the notion that Rm may be affected principally by ClC-1 channels (Bretag, 1987). Nevertheless, we must qualify this remark by comparing the actual Rm values in fibres from both strains. As expected, the average values of Rm in fibres rendered electrically passive are not significantly different in fibres from FVB and HSALR mice (4463 and 3735 Ω cm2, respectively; Table 1); this reinforces the idea that, other than differences in the basal conductance, the two fibre populations are almost identical. But Rm values in fibres from young HSALR animals are surprisingly small: only 32–33% larger than those of their control counterparts (Table 1), compared with the more than threefold differences in values of [peak-ICl]max and gCl,max (Fig. 4). A reasonable explanation for this important disparity is that, in fibres from these animals, conductive pathways other than gCl (e.g. the inward rectifier gK,IR conductance) play important compensatory roles in determining their relatively low linear Rm. In order to assess this option, we measured Rm in fibres treated with 9-ACA (to block gCl) and Rb (to block gK,IR) and, from these data (not shown), calculated the contributions of each conductive pathway to the total resting conductance (g= 1/Rm, in mS cm−2). Figure 11 shows that we can account for gm with contributions from gCl and gK,IR, and from an unidentified residual conductance (gres). The black columns in Fig. 11A show that, in control young mice (3–4 weeks old; = 7), the resting gm (∼1.1 mS cm−2; see Table 1) was contributed principally by gCl (∼53%), and less prominently (∼27%) by gK,IR. As expected from the significant reduction in gCl,max and [peak-ICl]max (Fig. 4), the ∼16% contribution of gCl to the resting conductance in fibres of age-matched HSALR mice (hatched columns, Fig. 11A, = 6) is also significantly smaller than in control fibres. Notably, Fig. 11A also demonstrates that the reduction in gCl is associated with an exaggerated contribution of gK,IR (∼51%) to the slightly reduced overall gm (∼0.83 mS cm−2). Thus, if we focus only on the blockable conductances, the data in Fig. 11A show that the proportion of gK,IR (η), defined as η = gK,IR/(gCl + gK,IR), is ∼34% in fibres from young control animals and ∼76% in age-matched HSALR animals. To our knowledge this is the first direct demonstration of the compensatory role gK,IR may play in fibres with significantly reduced gCl. Furthermore, we believe that this result will be critically important for the understanding (on a quantitative basis) of the underlying causes of myotonia in various animal models, and in humans. Unlike the situation in young animals, Fig. 11B shows that the contributions of gCl (and/or gK,IR) to the resting gm are not significantly different between fibres of age-matched FVB and HSALR mice. Nevertheless, albeit not significant, there is hint of the reduced contribution by gCl (compensated by gK,IR) that was observed in young HSALR mice. For example, in this case η is 42% and 65% in fibres of adult control and HSALR animals, respectively. Also, in agreement with the larger variability in gCl,max observed in frequency bar graphs (Fig. 5D), the proportional contributions of gCl and gK,IR in fibres of HSALR animals is notably larger than in control fibres. This excess variability, probably arising from a mosaic impairment of the expression of ClC-1 channels, is undoubtedly a contributing factor for the lack of statistical significance between data from adult mice of both strains.

In adult normal muscle fibres, the ∼45% contribution of gCl to the resting conductance (gm) shown in Fig. 11B may seem too low in comparison to values of up to 85% suggested in the literature (Kerr & Sperelakis, 1983; Kwiecinski et al. 1984; Rudel & Lehmann-Horn, 1985; Bretag, 1987; De Luca et al. 2003). It should be noted that, in our case, the gCl contribution is pondered in absolute terms with respect to the total resting conductance of the cell, and goes beyond relative comparisons from changes in resistances due to ion replacements. Thus, our calculations take into account the fact that there is a finite residual conductance (gres) after gCl and gK,IR are blocked. If we compute the percentage contributions taking into account only these readily blockable conductances, as done frequently in the literature, the results are 58% and 42% for gCl and gK,IR, respectively; these values are in line with published values from other laboratories for rat muscle fibres (Bretag, 1987). Nonetheless, our data for normal mouse short muscle fibres (FDB) show that, at a resting potential of −90 mV, gCl represents significantly less than 80–85% of the resting conductance as suggested previously for long fibres (Kerr & Sperelakis, 1983; De Luca et al. 2003).

Our calculations of Rm*, based on realistic theoretical assumptions about the equivalent circuit of the muscle fibres as described in the Appendix, provide important information about the ‘true’ specific resistance of the surface and TTS membranes regardless of their area contribution. As expected, for every age group and fibre type, Rm* is approximately four–fivefold larger than Rm; this closely matches the TTS/sarcolemma area ratios, as predicted from theoretical considerations (Adrian et al. 1969a; Hodgkin & Nakajima, 1972a,b). Furthermore, Rm* values for all fibres tested under passive conditions (most conductances blocked) are indistinguishable from each other. We must also highlight that the comparison of Rm* values between animal types at different ages reinforces all the conclusions reached previously while discussing Rm data; namely, fibres from adult FVB and HSALR have similar values of Rm*, but those from young HSALR specimens have slightly (but significantly) larger values of Rm* than their control counterparts.

Is the HSALR mouse a good model for DM1?

The HSALR mouse has been a helpful model to demonstrate the toxicity of CUG expansions on the splicing of pre-mRNA of the ClC-1 channel (Mankodi et al. 2000). Although several limitations of this animal as a model of DM1 have already been recognized (Gomes-Pereira et al. 2011), the transitory impairment in the expression of ClC-1 channels, as demonstrated in this paper, has been overlooked so far. In this sense, our results have important implications, not only for the interpretation of the mechanisms of myotonia in the HSALR mouse per se, but also for the use of this animal in future therapeutic genetic trials, and as a model for the chloride channelopathy in humans. Nevertheless, our results comparing the linear electrical properties of fibres from normal and HSALR fibres, while suggesting that hyperexcitability may not exclusively result from a sarcolemma-restricted chloride channelopathy but from the non-linear behaviour of ClC-1 and/or other ion channels (especially in the TTS membranes), point out complex aspects of the mechanisms of myotonia that can be optimally studied in the HSALR mouse due to the transient nature of the impairment in the functional ClC-1 expression. In other words, new avenues of research towards the quantitative understanding of the ionic basis of myotonia, which stem from this paper, still must be undertaken in fibres from this animal model.

References

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information

Appendix

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information
(A) Calculation of membrane constants of FDB muscle fibres from RIN measurements using the cable model equations for a short cylindrical cell

The values of Rm (in Ω cm2) were calculated by fitting the amplitude and kinetics of voltage records obtained in response to step current pulses to the predictions of the equation for a longitudinal short cable of radius a and length l (Hodgkin & Nakajima, 1972b). From this publication, the voltage change elicited by the injection of a current pulse of amplitude I0 injected at the centre (x = 0) of a fibre of length l (cm) is given by the general equation:

  • image((A1))

where rm is the membrane resistance per unit length (in Ω cm), ri is the internal resistivity (in Ω cm−1), cm is the membrane capacitance (in F cm−1), L = l/λ, X = x/λ and T = t/τ; λ is the space constant defined as inline image, and τ is the time constant defined as τ = rmcm. Expressing the membrane parameters per cm2 of surface membrane, we obtain:

  • image((A2))

where inline image, τ = RmCm, Ri is in Ω cm, Rm is in Ω cm2 and Cm is in F cm−2.

Instead of the three terms in the sum of eqns (A1) or (A2) proposed by Hodgkin and Nakajima to be sufficient to predict the properties of the experimental records in the case of EDL muscle fibres (in which l is ∼1.5 cm), we found that records obtained from the very short FDB fibres (in which l is ∼500 μm) required the computation of 19 terms (= −9 to + 9). Thus, the sum in eqn (A2) was calculated by adding the following terms:

  • n = −1 [RIGHTWARDS ARROW] F(−X + 2L, T) + F(−X + L, T)

  • n = 0 [RIGHTWARDS ARROW] F(X, T) + F(X + L, T)

  • n = 1 [RIGHTWARDS ARROW] F(X + 2L, T) + F(X + 3L, T)

  • n = −2 [RIGHTWARDS ARROW] F(−X + 4L, T) + F(−X + 3L, T)

  • n = 2 [RIGHTWARDS ARROW] F(X + 4L, T) + F(X + 5L, T)

  • ……………………………………………

  • n = −i [RIGHTWARDS ARROW] F(−X + 2iL, T) + F(−X + (2i – 1)L, T)

  • n = i [RIGHTWARDS ARROW] F(X + 2iL, T) + F(X + (2i + 1)L, T)

  • …………………………………………….

  • n = −9 [RIGHTWARDS ARROW] F(−X + 18L, T) + F(−X + 17L, T)

  • n = 9 [RIGHTWARDS ARROW] F(X – 18L, T) + F(X + 19L, T)

To calculate the values of Rm and Cm in Table 1, the experimental traces were fitted to eqn (A2) using the geometrical properties (radius and length) of each fibre with a least square fit routine in Berkeley Madonna (Macey and Oster).

(B) Theoretical calculation of Rm* at steady-state while taking into account the contribution from the TTS membranes

From equation 8 in Hodgkin & Nakajima (1972b), we derive that the voltage distribution at a distance x from the site of current injection (I0), centred at the midpoint (x = 0) of a short cylindrical cell of length l (as illustrated in Fig. 12A) is:

  • image((B1))
image

Figure 12. Short cable equivalent circuit  A, equivalent circuit of a cable segment. B and C, details of circuit-equivalent circuit element without (B) and with (C) access resistance Ra.

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In eqn (B1), rm is the membrane resistance per unit length (in Ω cm), ri is the internal resistivity (in Ω cm−1), L = l/λ and X = x/λ; λ is the space constant defined as: inline image. From eqn (B1), we calculate the input resistance (RIN, in Ω) as:

  • image((B2))

An equivalent expression for eqn (B2) is:

  • image((B3))

where Rm and Ri are the membrane resistance and internal resistivity, in Ω cm2 and Ω cm, respectively.

Eqn (B3) can be generalized by assuming that, instead of only surface membrane, the circuit element in the longitudinal cable of Fig. 12A is a parallel combination (Req) of sarcolemma (Rs) and the input resistance of the TTS (RT), as illustrated in Fig. 12B.

It then follows that:

  • image((B4))

From equation 14 of Adrian et al. (1969a), we infer that, for the radial cable model of the TTS, its input resistance (RT) is given by the approximation (which holds with ∼0.5% accuracy):

  • image((B5))

where GW is the wall conductance per unit area of TTS membrane (in Scm−2), GL is the lumen conductivity (in Scm−1), σ is the tortuosity factor, ρ is the fraction of volume occupied by the TTS, and ζ is the volume to surface ratio of the TTS.

We now assume, based on extensive evidence from our laboratory (Ashcroft et al. 1985; DiFranco et al. 2011; DiFranco & Vergara, 2011; Yu et al. 2012) that, in skeletal muscle fibres, GW is approximately equal to 1/RS; then,

  • image((B6))

On the other hand

  • image((B7))

Thus,

  • image((B8))

The expressions in eqns (B6) and (B7) can be readily replaced in eqn (B4) to finally calculate RIN in terms of a generalized membrane resistance per unit membrane area (RS) and other relevant structural parameters of the muscle fibre:

  • image((B9))

In order to include Ra (access resistance to the TTS) in the circuit illustrated in Fig. 12C, the expressions for Req and λ must be changed by:

  • image

Consequently, a more general equation for RIN is:

  • image((B10))

which leads (upon replacement) to the expression:

  • image((B11))

Table B1 gives the parameter values utilized in eqn (B11) to infer the specific membrane resistances (RS, in Ω cm2) associated with measured input impedances RIN*. Values used for fibres form young and adult animals, respectively.

Following the radial cable model (Adrian et al. 1969a; Hodgkin & Nakajima, 1972a) of the TTS while using the parameters in Table B1, the values of fibre capacitance were theoretically calculated as:

  • image((B12))

where CT was approximated (by neglecting Ra) by the formula (Hodgkin & Nakajima, 1972b):

  • image((B13))

In all instances, the predictions of eqns (B12) and (B13) provide excellent agreement with the experimental measurements.

Author contributions

Conception and design of the experiments: M.Di.F. and J.L.V.; collection, analysis and interpretation of data: C.Y., M.Q., M.Di.F. and J.L.V.; drafting the article and revising it critically for intellectual content: M.Di.F. and J.L.V. The experiments were performed at the Department of Physiology, David Geffen School of Medicine, University of California Los Angeles (UCLA), USA. All the authors approved the final version for publication.

Acknowledgements

The authors are greatly indebted to Dr C. Thornton (Department of Neurology, University of Rochester) for sharing breeding pairs of HSALR-20b homozygous, and for providing us a detailed description of protocols for genotyping the progeny. We also thank Dr Robert T. Dirksen (Department of Pharmacology and Physiology, University of Rochester) for helpful discussions and Mr R. Serrano (Staff Research Assistant, Department of Physiology, UCLA) for technical support. Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under Award Numbers AR047664, AR54816 and AR041802. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Supporting Information

  1. Top of page
  2. Key points
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. References
  8. Appendix
  9. Supporting Information

Supplemental Fig. S1

Supplemental Fig. S2

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