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J Appl Physiol 82: 164-171, 1997;
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Journal of Applied Physiology
Vol. 82, No. 1, pp. 164-171, January 1997
EXERCISE AND MUSCLE

Diaphragm disuse reduces Ca2+ uptake capacity of sarcoplasmic reticulum

Sandra Howell1, Wen-Zhi Zhan2, and Gary C. Sieck2

1 Departments of Biokinesiology and Physical Therapy, and Biomedical Engineering, University of Southern California, Los Angeles, California 90033; and 2 Departments of Anesthesiology and Physiology and Biophysics, Mayo Clinic, Rochester, Minnesota 55905

ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES


ABSTRACT

Howell, Sandra, Wen-Zhi Zhan, and Gary C. Sieck. Diaphragm disuse reduces Ca2+ uptake capacity of sarcoplasmic reticulum. J. Appl. Physiol. 82(1): 164-171, 1997.---Chronic phrenic tetrodotoxin (TTX) blockade and phrenic denervation (Dnv) of hamster diaphragm result in decreased maximum specific tension, prolonged contraction time, and improved fatigue resistance (W. Z. Zhan and G. C. Sieck. J. Appl. Physiol. 72: 1445-1453, 1992 [Medline] ). An underlying increased relative contribution of type I fibers to total muscle mass appears to be consistent with, but does not completely account for, changes in contractile and fatigue properties. The present study was designed to evaluate a potential role for altered cellular Ca2+ metabolism in the adaptive response of the diaphragm to chronic disuse. An analytic method based on simulation and modeling of long-term 45Ca2+ efflux data was used to estimate Ca2+ contents (nmol Ca2+/g wet wt tissue) and exchange fluxes (nmol Ca2+ · min-1 · g-1) for extracellular and intracellular compartments in the in vitro hamster hemidiaphragm after prolonged disuse. Three groups were compared: control (Con, n = 5), phrenic TTX blockade (TTX, n = 5), and phrenic denervation (Dnv, n = 5). Experimental muscles were loaded with 45Ca2+ for 1 h, and efflux data were collected for 8 h by using a flow-through tissue chamber. Compartmental analysis of efflux data estimated that the Ca2+ contents and Ca2+ exchange fluxes of the largest and slowest intracellular compartment (putative longitudinal reticulum) were reduced by ~50% in TTX and Dnv muscle groups compared with Con. In addition, the kinetic model predicted significant decreases in total intracellular Ca2+ and total diaphragm Ca2+ in TTX and Dnv muscles. We conclude that the data support the hypothesis that the capac- ity of the sarcoplasmic reticulum for Ca2+ sequestration is reduced in chronic diaphragm disuse. The impact of this effect on diaphragm contractile and fatigue properties is discussed.

calcium metabolism


INTRODUCTION

CHRONIC DISUSE is an increasingly more common condition of the human diaphragm. During mechanical ventilation (with or without neuromuscular blockade), after traumatic or pathological lesions of motor innervation, or when reflex inhibition of diaphragm activation occurs, part or all of the diaphragm stops contracting. The adaptive changes that occur in diaphragm muscle fibers in response to disuse or paralysis play an important role in ventilatory failure and failure to wean from mechanical ventilation (26).

Unlike many skeletal muscles, the diaphragm is not motionless when chronically inactive. Both mechanical ventilation and spontaneous breathing with the use of functioning inspiratory muscles expose inactive diaphragm fibers to repeated, passive movement. Experiments in denervated (Dnv) rat hemidiaphragm, in which rhythmic passive motion results from contraction of the innervated contralateral hemidiaphragm, have demonstrated an increase in cross-sectional area of type I fibers (13, 29). This effect has been attributed to enhanced protein synthesis in response to passive stretching (29). Zhan and Sieck (30) compared the effects of phrenic tetrodotoxin (TTX) blockade and phrenic Dnv on hamster hemidiaphragm and showed that both causes of paralysis induced type I fiber hypertrophy and type II fiber atrophy. These morphometric adaptations coincided with decreased maximum specific tension, prolonged twitch duration, and improved fatigue resistance. However, the differential effects on type I and II fibers did not entirely explain altered diaphragm contractile and fatigue properties after chronic disuse.

Investigations of TTX action potential blockade- and Dnv-induced paralysis of slow and fast hindlimb muscles have revealed morphometric and functional changes (7, 23-25, 30) similar to observations of hemidiaphragm paralysis. Elegant Dnv studies by Schulte et al. (23) further demonstrated specific changes in the expression of sarcoplasmic reticulum (SR) Ca2+ adenosinetriphosphatase (ATPase) that implicated slowed Ca2+ handling by the SR as a factor modifying contractile responses. Others have also reported Dnv-induced adaptive changes in SR protein that would diminish Ca2+ sequestration (16, 17). Lehotsky et al. (16) emphasized that the early response to Dnv is associated with altered cellular Ca2+ homeostasis. A high inverse correlation exists between isometric twitch duration and the rate of Ca2+ uptake by the longitudinal reticulum (8). In this regard, a reduced SR Ca2+ uptake capacity would be consistent with prolongation of twitch duration in experimental diaphragm paralysis as observed by Zhan and Sieck (30). Ca2+ metabolism has not been studied in diaphragm disuse or paralysis. The reported effects of Dnv on hindlimb muscle SR inspired us to speculate a role for altered Ca2+ metabolism in the adaptive response of diaphragm muscle to paralysis. We formulated the hypothesis that the capacity of the SR for Ca2+ sequestration is diminished after chronic diaphragm disuse induced by phrenic TTX action potential blockade and phrenic Dnv. The purpose of the present investigation was to explore the effects of disuse on compartmental Ca2+ kinetics in diaphragm from chronic models developed in hamsters by Zhan and Sieck (30). Ca2+ metabolism was studied by using methods based on physiological simulation and modeling of Ca2+ tracer data after the tracer has been introduced into isolated, living hemidiaphragm preparations. The Ca2+ metabolism model developed for the present study includes compartments and other independent constructs that allow the inclusion of known physiology. The model is used to estimate rate constants describing transfer of free ionic Ca2+ (tracer and tracee) between compartments. Rate constants are then incorporated to define quantitative measures of steady-state masses and exchange fluxes of tracee.


METHODS

Preparation of Experimental Animals

General procedures. Mature, 10- to 12-wk-old male hamsters were obtained from a single source. Animals were separated into three groups: sham-operated controls (Con; n = 5), phrenic TTX blockade (TTX; n = 5), and phrenic denervation (Dnv; n = 5). For survival surgeries, hamsters were anesthetized by injection of ketamine (60 mg/kg im) and xylazine (9 mg/kg im). All surgical procedures were performed with aseptic techniques. After surgery, wounds were treated topically with 0.2% nitrofurazone solution, and animals were injected with ampicillin (0.1 g/kg body wt im) for 2 days. The recovery period of animals from surgery was monitored. Body weights were measured throughout the experimental period.

TTX blockade of phrenic nerve action potential propagation. The main trunk of the right phrenic nerve was dissected in the neck. Superfusion of the nerve with TTX or saline solution was accomplished by using a miniosmotic pump-nerve cuff system. A Silastic cuff (2.0 mm OD, 1.5 mm ID, 2 mm long) was placed loosely around the phrenic nerve and then sutured to the surrounding musculature. A polyethylene cannula connected the nerve cuff to a miniosmotic pump (Alzet model 2002, Alza) through which the TTX or saline solutions (pH 7.2) were superfused onto the nerve. This miniosmotic pump (3 cm long, 0.7 cm diameter, weighing 1.1 g, and containing 225 µl fluid volume) was implanted subcutaneously on the dorsum of the animal, and the connecting tube was tunneled to the nerve cuff. In the TTX group, prolonged blockade of axonal action potential conduction was achieved by superfusing the right phrenic nerve with a TTX solution (0.0125% TTX dissolved in saline) delivered at a constant rate of 0.5 µl/h. In the Con animals, saline solution was superfused onto the right phrenic nerve. With the use of the miniosmotic pump-nerve cuff, the TTX or saline solutions were applied continuously for 2 wk. At the time of the terminal experiment, right hemidiaphragm paralysis was confirmed by documenting the absence of spontaneous and evoked electromyographic (EMG) responses. Before the excision of the right hemidiaphragm from anesthetized animals, pairs of fine-wire electrodes (32-gauge stranded stainless steel wires, bared at the tip for ~1 mm) were implanted in the sternal, ventral, and dorsal costal regions of the hemidiaphragm. The EMG signal was amplified, band-pass filtered between 20 and 5 kHz (Service Associates analog processor), and displayed on a storage oscilloscope (Gould, model 1425).

In separate acute studies on eight animals, the efficacy of the TTX concentration and perfusion rate was verified by stimulating (single 0.2-ms duration rectangular pulses at supramaximal intensity; Grass stimulator, model S88) the right phrenic nerve proximal to the nerve cuff and recording evoked distal neurographic responses before and after application of the TTX solution through the nerve cuff. In all cases, TTX abolished the evoked response. The neurographic responses were recorded by use of bipolar silver wire electrodes placed on the nerve, with the signals amplified and filtered with the use of a differential amplifier (model 2124; Data). In all chronic animals, the efficacy of the TTX-induced nerve block was demonstrated by asymmetric movement of the abdominal wall during ventilation, suggesting hemidiaphragm paralysis. In addition, there was an invariable absence of inspiratory-related EMG activity.

Dnv of the phrenic nerve. The right phrenic nerve was transected in the lower neck, and a 3- to 4-mm length of nerve was removed to prevent possible reinnervation of the diaphragm. Nerve transection at this location left ~30-mm length of nerve connected to the diaphragm within the thoracic cavity.

Measurement of arterial blood gases. To assess the impact of unilateral hemidiaphragm paralysis on ventilatory control, arterial blood gases were measured in a separate study on five Con and five Dnv animals. Con and Dnv hamsters were anesthetized, and the left common carotid artery was cannulated with a catheter (PE 10) filled with heparinized saline. After a strain-relief loop was placed in the catheter, the catheter was tunneled subcutaneously and externalized at the dorsum of each animal. Animals were allowed to recover from surgery for a minimum of 24 h before arterial blood samples (65 µl) were drawn for analysis of PO2, PCO2, and pH at 37°C with a blood-gas analyzer (model IL 1304, Instrumentation Laboratory System).

Long-term 45Ca2+ Efflux Experiments

Ca2+ tracer measurements. Hamsters were anesthetized with pentobarbital sodium via intraperitoneal injection. After EMG recordings, the right hemidiaphragm, with the ribs and central tendon attached, was rapidly excised and placed in a dissection dish containing a bicarbonate-buffered Ringer solution maintained at 27°C and oxygenated with 95% O2-5% CO2. The Ringer solution was composed of (in mM) 117 NaCl, 3.5 KCl, 1.2 KH2PO4, 1.2 MgSO4, 24 NaHCO3, 1.2 CaCl2, 10 glucose, and 6 mg/l tubocurarine. The muscle preparation was sustained by the same oxygenated, physiological solution throughout the experiment.

Eight-hour 45Ca2+ efflux protocols were adopted to obtain tracer data from the hamster diaphragm. Long-term experiments are necessary to resolve slowly exchanging intracellular Ca2+ compartments as well as extracellular compartments with rapid turnover kinetics (15, 20). Freshly excised hemidiaphragms from Con, TTX, and Dnv animals were placed in a dissecting dish, the ribs were removed, and a wire stimulating electrode was implanted for assessing tissue viability at the end of the experiment. Each muscle was then moved to a glass chamber (100-ml volume) containing oxygenated Ringer solution (containing 1.2 mM 40Ca2+) at 27°C for a 1-h preexperiment equilibration period to achieve a steady state. The experiment was initiated by transferring the muscle to a plastic vial (7-ml volume) for 1-h loading of 45Ca2+. The loading solution contained 4 ml Ringer and ~5 × 10-7 disintegrations/min (dpm)/ml 45Ca2+ with a half-life of 164 days. The loading chamber was located in a water bath maintained at 27°C and bubbled with 95% O2-5% CO2. The exact loading solution activity was determined for each experiment at the end of the loading period. After the load, the muscle was rinsed and mounted at its estimated optimal length [(Lo) gauged as 1.4 × resting length] in an efflux chamber (7-ml volume) that was perfused with a 45Ca2+-free Ringer solution at a constant flow rate of 7 ml/min. The superfusate was delivered at 27°C and continuously mixed with a fine gas bubble (95% O2-5% CO2) as it washed around the diaphragm strip. One milliliter/min of the effluent flowing from the efflux chamber was diverted to a fraction collector; the exact flow diversion and the total perfusate flow were recorded for each experiment. Fractions were collected in 2-min intervals over the 8-h efflux period. Effluent samples collected in 7-ml polyethylene minivials were prepared with 3 ml of liquid scintillation cocktail for counting in a scintillation counter (Beckman LS). At the termination of the washout period, each muscle was electrically stimulated with a single supramaximal impulse and a 1-s tetanic train of impulses at 50 Hz. Muscles that did not produce a healthy twitch response and a marked tetanic contraction at 50-Hz stimulation were not included in the study. The muscle was then removed from the efflux chamber, blotted, and weighed. The efflux data, expressed in disintegrations per minute per milligram, were normalized for activity of the 45Ca2+-loading solution and the wet weight of the muscle.

Analysis and modeling of kinetic data. Kinetic analysis was carried out with the use of the simulation, analysis, and modeling (SAAM) and interactive CONSAM computer program (4, 9) for general analysis of Ca2+ tracer data. This is a long-recognized method for obtaining estimates of organ and cellular Ca2+ metabolism that are not directly ascertainable from the data (19, 21, 22). Model development in the present study was based on earlier studies by Phair and Hai (20), focusing on resolution of intracellular Ca2+ metabolism in smooth muscle, and on studies of Ca2+ kinetics in rat diaphragm by Howell et al. (15).

45Ca2+ efflux data from hamster diaphragm were analyzed, using the seven-compartment model represented in Fig. 1. Models represent hypotheses to be tested for compatibility with the tracer data. Figure 1 is the minimal hypothesis or simplest model that is mathematically consistent and physiologically realistic with respect to the data. To begin setting up the model, exponential equations were initially fitted to tracer data from single experiments to characterize the complexity of the curve (5). A minimum of four exponentials was necessary to achieve an adequate fit of the data, suggesting a model of at least four compartments with independent rates of turnover (2). However, a four-compartment model was insufficient to account for the kinetic data and the in vitro physiological system as well. Therefore, the fundamental model was systematically expanded. The stipulation of seven compartments was based on the four terms in the sum of exponentials (Ca3, Ca4, Ca6, Ca7), on two known physiological entities (Ca2, Ca5), and on the methodology (Ca1). The intercompartmental arrows represent rate constants and are designated as L(into,from), or L(i, j), which indicates the fraction of Ca2+ (tracer and tracee) in compartment j that moves to compartment i per unit of time. Most rate constants were directly calculated from the efflux data. However, some rate constants were unresolvable by data fitting, so it was necessary to assign fixed values by using published estimates or to calculate values by using data from our own pilot studies. The rate constants that were fixed in the model include 1) L(1,2), movement of Ca2+ into the perfusate from the extracellular fluid (ECF), 2) L(5,2) and L(2,5), bidirectional exchange of Ca2+ across the plasma membrane between the cytosol and the ECF, and 3) L(6,5), movement of Ca2+ into the terminal cisternae from the cytosol. All other rate constants were considered free and adjustable with respect to data fitting.
Fig. 1. Schematic drawing of model used to simultaneously fit the 45Ca2+ efflux data. Ca1, efflux chamber; Ca2, extracellular fluid (ECF); Ca3, peripheral sarcolemma Ca2+-binding site; Ca4, putative t tubular membrane Ca2+; MEM, sarcolemma; Ca5, cytosolic free and rapidly exchanging Ca2+; Ca6, putative terminal cisternae Ca2+ compartment; Ca7, putative longitudinal sarcoplasmic reticulum Ca2+ compartment.
[View Larger Version of this Image (14K GIF file)]

Hypotheses testing. Data fitting was carried out with the use of SAAM/CONSAM. Differential equations representing models to be tested were solved for each datum, using the exponential method (5). Solutions were assessed periodically for congruity with classical Runge-Kutta and Gear numerical integrators. Initial estimates of the rate constants, L(i, j), were adjusted by an iterative process until a least-squares fit of the data was obtained (1). Once a successful hypothesis was established, final estimates of the rate constants and their coefficients of variation were estimated. This constituted the information extracted from the experimental data. Statistical uncertainties associated with the final parameter estimates were calculated by multiplying the inverse normal equation matrix by the best estimate of the variance of the data.

All steady-state solutions for Ca2+ contents and fluxes were calculated by using the matrix equation U + LM = 0. This equation refers to unlabeled Ca2+. U is the vector of compartmental input rates of tracee. 40Ca2+ is not produced or initiated in any cellular compartment. It enters the physiological system only from the perfusate (Ca1). Because there are seven compartments, there are seven elements of the U vector. Six elements are equal to zero because they are not a source of 40Ca2+ into the system. The nonzero element of the U vector is Ca1. L is the n × n matrix of rate constants with diagonal elements, L(i,i), defined as the negative sum of all the rate constants leaving the ith compartment. M is the vector of compartmental concentrations of tracee. Zero (0) refers to a null matrix. The equation assumes only steady state and conservation of mass and enables interpretation of tracer kinetic data [L(i, j)] into steady-state 40Ca2+ concentrations and fluxes (1).

Statistical Analysis

Mean values for estimated compartmental Ca2+ contents and exchange fluxes from hemidiaphragms after 2 wk of paralysis, either by phrenic TTX blockade or phrenic Dnv, were compared with Con by one-way analysis of variance with Student's t-test for post hoc analysis. The accepted level of significance was P < 0.05. Results are expressed as mean values ± SE.


RESULTS

Effects of Disuse on Diaphragm Ca2+ Metabolism

Paralysis of the right hemidiaphragm in TTX and Dnv hamsters was confirmed by the absence of spontaneous and evoked EMG responses measured in anesthetized animals before the 45Ca2+ efflux experiment. An average weight gain of 7.0 g was measured over the 2-wk experimental period in Con, TTX, and Dnv animals, with no significant difference among groups. Animals with right hemidiaphragm paralysis also displayed normal arterial blood-gas levels. Animal weight and blood-gas data were reported previously (30).

Figure 2, A and B, compares mean 45Ca2+ efflux data from Con vs. TTX and Con vs. Dnv diaphragms, respectively. The effects of phrenic TTX blockade and phrenic Dnv on diaphragm Ca2+-tracer kinetics appear similar, whereas the late, slow portion of the efflux curves dropped below the tail of the Con curve. Analysis of individual efflux data sets was carried out by iterative adjustment of rate constants. The fractional standard deviation (FSD) of the rate constants obtained from an individual fit indicated the confidence interval for the measured rate constants. The average FSD was 0.21 ± 0.04 (SE).



Fig. 2. A: effects of disuse on hemidiaphragm 45Ca2+ efflux data. Mean curve from control muscles (square , n = 5) is compared with mean curve from tetrodotoxin (TTX) blockade of the phrenic nerve (black-down-triangle , n = 5). B: effects of paralysis on hemidiaphragm 45Ca2+ efflux data. Mean curve from control muscles (square , n = 5) is compared with mean curve from phrenic denervation (Dnv; black-down-triangle , n = 5). DPM, disintegrations per min. Error bars are not shown because individual curves were essentially superimposable in each experimental condition.
[View Larger Versions of these Images (11 + 11K GIF file)]

Kinetic analysis of efflux data from Con animals revealed that Ca3 and Ca4 are fast compartments and dominate the efflux curve for ~0-100 min. Conversely, Ca6 and Ca7 demonstrated markedly slower kinetics such that these compartments did not completely turn over in 8 h. Previous Ca2+ tracer studies in smooth and skeletal muscle have convincingly shown that the fast compartments are extracellular, whereas slow compartments are intracellular (15, 20).

Different models representing alternative hypotheses were tested for congruity with the Dnv- and TTX-induced decline in the late portion of the efflux curve. Parameter estimation is very sensitive, and there is not a great deal of freedom with the fitting of alternative models, because the efflux curve at any one point is dominated by one compartment. Calculation of the relative sensitivity of the data for adjustable parameters, by using the partial derivatives of simulated values, revealed that the early, fast portion of the curve was strongly influenced by rate constants for Ca3 and Ca4, whereas the late, slow part of the curve was sensitive to rate constants for Ca6 and Ca7. Plasma membrane permeability to Ca2+ also had to be considered because of its influence on cytosolic Ca2+ concentration ([Ca2+]i) and thus on Ca2+ exchange between the cytosol and intracellular compartments. We tested the effects of reducing Ca2+ influx across the plasma membrane on Ca6 and Ca7 and found it was not possible to simultaneously fit all portions of the efflux curve with this strategy. We then examined the premises that flux of Ca2+ into the terminal cisternae [L(5,6)] was decreased and/or leaking of Ca2+ out of the terminal cisternae [L(6,5)] was increased by Dnv and TTX paralysis. These, too, were not successful hypotheses. Fitting of the data was ultimately achieved by reducing the rate constant representing movement of Ca2+ into C7 [L(7,5)] by ~50%. Knowledge of the rate constants combined with the known concentration of 40Ca2+ in the medium permitted calculation of Ca2+ contents for every compartment as well as steady-state exchange fluxes along intercompartmental pathways. Figure 3, A and B, shows the estimated Ca2+ contents for extracellular and intracellular compartments, respectively, for Con, TTX, and Dnv hemidiaphragms. The Ca2+ contents of extracellular Ca3 and Ca4 and intracellular Ca6 were not altered in TTX and Dnv muscles. However, the Ca2+ content of Ca7 was reduced by 40% in the TTX-treated muscles and by 50% in Dnv-treated muscles. Table 1 reveals the calculated steady-state exchange fluxes between compartments. In both groups, the fluxes related to Ca7 were decreased by ~50%. Moreover, the model predicted significant decreases in total [Ca2+]i and total tissue Ca2+ (Table 1).



Fig. 3. A: effects of phrenic TTX blockade and phrenic Dnv on the content of diaphragm Ca2+ compartments. Mean data from extracellular compartments Ca3 and Ca4 are compared for control (solid bars), phrenic TTX blockade (hatched bars), and phrenic Dnv (open bars). B: mean data for intracellular compartments Ca6 and Ca7 are compared for control, phrenic TTX blockade, and phrenic Dnv. Bars as in A; error bars correspond with 1 SE. * Significantly different from control; P <=  0.05.
[View Larger Versions of these Images (17 + 23K GIF file)]

Table 1. Ca2+ contents and intercompartmental Ca2+ fluxes in diaphragm under conditions of control, phrenic tetrodotoxin blockade, and phrenic denervation


Parameter Control TTX Dnv

Total tissue Ca2+, mmol/g wet wt 7,510 ± 496  5,598 ± 350* 5,627 ± 179*
Total [Ca2+]i, nmol/g wet wt 5,423 ± 397  3,339 ± 452* 3,392 ± 223*
R(5,2)  38dagger  38dagger  38dagger
R(3,2) 3,501 ± 400  3,432 ± 980  3,706 ± 120 
R(4,2) 27 ± 4  31 ± 7  17 ± 5 
R(6,5) 227dagger 227dagger 227dagger
R(7,5) 30 ± 2  16 ± 3* 14 ± 2*
R(6,7) 4 ± 6  2.2 ± 1.4  1.7 ± 1

Values are means ± SE. TTX, tetrodotoxin; Dnv, denervation. Total intracellular Ca2+ concentration ([Ca2+]i) includes a small contribution from cytosol (Ca5). R(i,j), steady-state flux of Ca2+ into the ith compartment from the  jth compartment. Because there is a steady-state, R(i,j) = R(j,i). Steady-state fluxes are defined as R(5,2), transmembrane flux of Ca2+ into cytosol from the extracellular fluid (ECF); R(3,2), flux of Ca2+ to peripheral sarcolemmal-bound sites from ECF; R(4,2), flux of Ca2+ to t tubular membrane-bound sites from ECF; R(6,5), flux of Ca2+ into terminal cisternae from cytosol; R(7,5), flux of Ca2+ into longitudinal reticulum from cytosol; and R(6,7), flux of Ca2+ into terminal cisternae from longitudinal reticulum. * Significantly different from control, P < 0.05; dagger No SE is shown for R(5,2) and R(6,5) because a ratio of rate constants for these compartments was estimated and constrained by available information. Intercompartmental rate constants, L(i,j ), extracted from tracer data are not shown but may be estimated from Ca2+ contents shown in Fig. 3 and fluxes delineated in the table, using the equation L(i,j ) = R(i,j )/M(j).


DISCUSSION

Critique of Experimental Procedures

The hamster diaphragm is appropriate for long-term in vitro studies because it is uniformly thin, thus increasing the likelihood that oxygen diffuses to the core of the muscle. The fact that the experimental muscles in this study were resting and in a steady state presupposes that energy consumption was low. Intuitively, this suggests that the resting in vitro diaphragm would have good viability. Indeed, every muscle in the study generated marked twitch and tetanic contractions at the end of each experiment. We know from pilot studies that muscles were in a steady state at the beginning of the 45Ca2+ load. This was achieved during the preceding 1-h equilibration period (in Ringer solution with 1.2 mM 40Ca2+). Experiments testing the effects of 2-h (n = 3) and 3-h (n = 3) equilibration periods before loading of 45Ca2+ revealed that the efflux data were not different from 1 h. If a steady state did not exist at 1 h, the efflux patterns after 2- and 3-h equilibrations would have been different. This indicates strong stability of in vitro diaphragm Ca2+ metabolism as a function of time.

It is important to note that a 1-h loading period for 45Ca2+ is insufficient time to achieve isotopic equilibrium, particularly in the intracellular compartments with very slow exchange rates. However, the kinetic model accounts for 45Ca2+ uptake as well as efflux, so the extent to which each compartment attains isotopic equilibrium during the load is incorporated into the analysis. In pilot experiments, diaphragms (n = 3) were loaded for >1 h, and predictably the slowly equilibrating compartments took up more 45Ca2+, so that there was elevation of the last 6 h of the efflux curve. A relatively high specific activity loading solution was used in this study to improve the resolution of smaller compartments. This does not influence the results, because the data are normalized for this factor. It does, however, improve the resolution of smaller compartments.

Critique of the Kinetic Analysis

Independent constructs in the model. Physiological measurements and numeric values that are important for model development, but cannot be determined from the kinetic data, must be acquired from external sources and incorporated as independent constructs in the model. In the present study, one source of supplemental information was the experimental protocol that contained values for 40Ca2+ concentration in the perfusate (1.2 mM) and turnover rate of the efflux chamber (7 ml/min). The research literature provided measurements of skeletal muscle cytosolic volume (0.26 ml/g; Ref. 10) and [Ca2+]i (50 nM; Ref. 28). Results from previous preliminary experiments in rodent diaphragm (sucrose washout studies and atomic absorption spectrometry) also provided measures of ECF volume (0.32 ml/g) and total tissue Ca2+ content (5,000 nmol/g), respectively (R. S. Fitzgerald and S. Howell, unpublished observations). In addition, the rate constants that could not be resolved by data fitting were systematically assigned fixed values in the model. The rate constant for movement of Ca2+ into the perfusate from the cytosol, L(1,2), was calculated and fixed at a rate that would maintain the ECF volume at approximately the known value of 0.32 ml/gm. Determination of L(1,2) also incorporated the fact that L(1,2) had to be fast so that more remote compartments would not appear well mixed and unresolvable and so there would be no backflux of 45Ca2+ as it was washed out of the muscle. The inability to resolve transmembrane exchange of Ca2+, L(5,2) and L(2,5), suggested that the plasma membrane was not rate limiting for organellar Ca2+ efflux. Consequently, these rate constants were fixed at values compatible with published measurements of plasma membrane Ca2+ permeability (20) and also congruous with maintenance of the cytosolic volume and [Ca2+]i at the known values of 0.26 ml/g and 50 nM, respectively. Movement of Ca2+ into the terminal cisternae from the cytosol, L(6,5), was fixed at an approximated value, whereas the leakage of Ca2+ out of the terminal cisternae, L(5,6), remained free. Iterative adjustment of the rate constant L(5,6) was then carried out to fit the data related to Ca6. The use of fixed parameters to constrain the model is beneficial because it increases the sensitivity of the model to estimate values for the remaining unknown parameters.

Theoretical considerations. It is indisputable that tracer kinetic data reflect only the tracer, and that extrapolation of tracer results to the tracee requires certain assumptions. Whether the identification of physiological parameters is valid depends, in part, on the extent to which the assumptions are validated. Five assumptions were delineated for this study. 1) Ca2+ enters or leaves the system through Ca2. This assumption is not only physiologically appropriate but is consistent with the kinetic analysis when proposed models with a second entrance or exit could not be fitted to the data. 2) The binding of Ca2+ to calciproteins in the cytosol does not affect long-term 45Ca2+ efflux data. Calmodulin, the major intracellular receptor for free Ca2+ has four metal-binding sites. During the resting state, when [Ca2+]i is low, only Mg2+ ions compete with K+ ions for occupation of calmodulin metal-binding sites. All Ca2+-containing species represent <1.5% of the total (6). Because the 45Ca2+ efflux experiments were conducted in resting diaphragm, we concluded that the assumption is valid. 3) The tracer is quantitatively small and does not alter discrete behavior of the tracee. It is true that the quantity of 45Ca2+ used in each efflux experiment is very small. Moreover, it has been demonstrated that the tracer takes up kinetics in a manner uniquely dependent on the tracee status (19, 22). In this respect, the assumption is legitimate. 4) The system cannot distinguish the tracer from the tracee, but a distinction is possible experimentally. The first part of this assumption is valid in view of the conclusion that the status of the tracee governs the behavior of the tracer (19, 22). The second part is also valid with regard to scintillation counting technology in which only the radioisotope (tracer) is detected and measured in a given sample, whereas the nonradioactive material (tracee) is not recognized experimentally. 5) Properties of the tracer (e.g., half-life) do not preclude isolation of biological processes. The stability of 45Ca2+ (half-life = 164 days) ensures that detection of traceable biological processes would not be overlooked in the 8-h efflux experimental protocols utilized here.

Physiological Identity of Diaphragm Ca2+ Compartments

Intracellular compartments. The physiological identities of the two intracellular compartments were approximated by previous long-term 45Ca2+ kinetic studies in rat diaphragm with the use of pharmacological probes (15). Isoproterenol (10-5 M) or caffeine (20 mM) were added to all phases of the efflux experiment to continuously induce Ca2+ release from the SR (11, 27), thereby decreasing or preventing uptake of 45Ca2+ by that organelle. Isoproterenol and caffeine both significantly reduced the Ca2+ content of the two slow compartments (Ca6 and Ca7), albeit the response to caffeine was far more dramatic. These findings suggest that Ca6 and Ca7 represent two parts of the SR that have independent rates of turnover. The effects of caffeine on 45Ca2+ efflux studies have also been tested in hamster diaphragm, and the data yielded a similar conclusion (S. Howell, unpublished observations).

Meissner (18) was the first to identify heavy and light fractions of the SR as the junctional terminal cisternae and nonjunctional longitudinal reticulum, respectively. Although the longitudinal reticulum has been shown to sequester maximal amounts of Ca2+, it has been suggested that the Ca2+ ATPase pump of the terminal cisternae actually turns over more rapidly (18). However, net Ca2+ uptake by the terminal cisternae is restricted because heavy SR is very leaky to Ca2+ compared with virtually no leak from light SR. Thus the Ca2+ exchange flux for the terminal cisternae is faster than the longitudinal reticulum. Data analysis in the present study was consistent with more rapid rate constants and estimated exchange fluxes in relation to Ca6 compared with Ca7. This suggests that Ca6 is terminal cisternae and Ca7 is longitudinal reticulum. Recent findings from Ca2+ metabolism studies in fatigued hamster diaphragm strongly support this premise (14).

Extracellular compartments. Long-term 45Ca2+ efflux studies in rat diaphragm continuously exposed to caffeine lead to a significant redistribution of Ca2+ from intracellular to extracellular compartments (15). Results of Ca2+ tracer experiments in frog sartorius suggested that caffeine initiates translocation of Ca2+ from a slowly exchanging pool (time constant = 800 min) to a fast compartment with a turnover rate of <60 min, which the authors speculated represented transfer of Ca2+ from the terminal cisternae to the t tubules (3). With the use of electron-probe analysis in frog muscle, other studies revealed that fatiguing stimulation leads to accumulation and shifting of Ca2+ from the terminal cisternae to the t tubules (12). Kinetic analysis of 45Ca2+ efflux data from fatigued hamster diaphragm revealed a significant increase in the Ca2+ contents of intracellular Ca6 (identified as terminal cisternae) and, as yet, unidentified extracellular Ca4 (14). In light of the data described above, the author speculated that the slower extracellular compartment, Ca4, represents remote t tubular membrane Ca2+. Accordingly, the most rapidly exchanging extracellular compartment, Ca3, was argued to be peripheral sarcolemma-bound Ca2+.

Interpretation of Diaphragm Paralysis Efflux Data

Zhan and Sieck (30) reported that the distribution of fibers in control hamster diaphragm is 25% type I and 75% type II, and furthermore, that paralysis induced by phrenic TTX blockade and phrenic Dnv did not change the fiber type composition. Nonetheless, hypertrophy of type I and atrophy of type II fibers increased the relative contribution of type I fibers to total muscle mass by ~10% and decreased the contribution of type II fibers by ~10% in both experimental conditions. These alterations in cross-sectional area did not satisfactorily explain corresponding physiological studies describing changes in muscle function.

In the present study, the kinetic data contained measurements collected simultaneously from type I and type II fibers. Thus, parameter estimates reflected the averaged information from all fibers with type II fibers being dominant. Fitting of the kinetic model to efflux data from both TTX and Dnv muscles was accomplished by markedly reducing the rate constant for Ca2+ movement into the longitudinal reticulum. Subsequently, the model predicted a decrease in Ca2+ content and Ca2+ turnover by the longitudinal reticulum. The longitudinal reticulum is known to be the most important domain for Ca2+ uptake in skeletal muscle SR (18). Schulte et al. (23) showed that Dnv decreases protein expression of the slow Ca2+ pump isoform in slow muscle and fast Ca2+ pump isoform in fast muscle. He also studied contractile properties and found that Dnv leads to increased twitch relaxation time and decreased fusion frequency. These findings suggest a correlation between decreased expression of SR Ca2+ ATPase and slowing of twitch relaxation. Results of the present study strongly support this speculation and provide further interpretation of the prolonged twitch duration after phrenic TTX blockade and phrenic Dnv reported by Zhan and Sieck (30).

Despite the finding that oxidative enzyme activity was shown to be reduced after phrenic TTX blockade- and phrenic Dnv-induced hemidiaphragm paralysis (31), fatigue resistance was improved (30). Under many conditions, a positive correlation does exist between muscle oxidative capacity and fatigability. However, it is also not unusual for this relationship to be uncoupled under certain circumstances. In conditions in which the initial isometric force is significantly reduced by atrophy, fatiguing stimulation commonly does not produce decrements in force that are proportional to control. In this circumstance, the mathematically derived index of fatigue would indicate that fatigue resistance is improved. However, this is not representative of the intrinsic fatigue-resistant properties of the muscle, but instead, is an indicator of a predominant effect on large, fatigable fast-twitch fibers with sparing of smaller fatigue-resistant fibers. The slowed rate of Ca2+ uptake by longitudinal reticulum may have contributed to the misleading finding that diaphragm paralysis increases fatigue resistance (30). During slowed Ca2+ uptake, elevated [Ca2+]i prolongs relaxation, thus enhancing fusion. Increased fusion of tetanic contractions during fatiguing stimulation would mask the decrement in force that heralds the development of fatigue.

We conclude that phrenic TTX blockade- and phrenic Dnv-induced hemidiaphragm paralysis results in a net slowing of Ca2+ uptake by the longitudinal reticulum of the SR. This reduces the Ca2+ content of that compartment and total tissue Ca2+ as well. The dramatic effect of hemidiaphragm paralysis on SR Ca2+ uptake and storage kinetics helps explain unique alterations in contractile and fatigue properties after diaphragm paralysis.


ACKNOWLEDGEMENTS

The authors thank Dr. R. D. Phair, BioInformatics Services, for advice and insights with respect to development and implementation of the kinetic model.


FOOTNOTES

   This investigation was supported by the Parker B. Francis Foundation, the Whitaker Foundation, the American Lung Association, and National Heart, Lung, and Blood Institute Grants HL-34817 and HL-37680.

Address for reprint requests: S. Howell, Dept. of Biokinesiology and Physical Therapy, 1540 East Alcazar St., CHP 155, Los Angeles, CA 90033.

Received 6 March 1995; accepted in final form 27 August 1996.


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