Excitation–contraction coupling model to estimate the recirculating fraction of activator calcium in intact cardiac muscle

1990 ◽  
Vol 68 (8) ◽  
pp. 1041-1048 ◽  
Author(s):  
Ferdinand Urthaler ◽  
Alfred A. Walker ◽  
Russell C. Reeves ◽  
Lloyd L. Hefner
Keyword(s):  
Steady State ◽  
Coupling Model ◽  
Hill Coefficient ◽  
Slow Inward Current ◽  
Excitation Contraction Coupling ◽  
Contraction Coupling ◽  
Extracellular Compartment ◽  
Sigmoidal Curve ◽  
State Force ◽  
The Hill

Potentiated contractions were evoked with a rapid pace pause maneuver in 14 length-clamped ferret papillary muscles paced 12 times/min at 25 °C. At 1.25 mM [Ca2+]o the average steady-state force was 2.94 ± 1.08 g/mm2 and the potentiated contraction averaged 10.96 ± 1.61 g/mm2. At 5.0 mM [Ca2+]o the steady-state force increased to 6.18 ± 1.23 g/mm2 and the potentiated contraction averaged 12.08 ± 1.15 g/mm2. Under the conditions of these experiments the potentiated contraction obtained at 5.0 mM [Ca2+]o is equal to the maximum twitch tension (Fmax) these muscles can generate. We have previously shown that Fmax is an equivalent of maximal calcium activated force. Since there is a beat to beat nearly exponential decay of the evoked potentiation, the fraction (= fraction x) of the potentiation that is not dissipated with each beat is nearly constant. Using an excitation–contraction coupling model we have previously found that x reflects a measure of the recirculating fraction of activator calcium. Because the tension–calcium relationship is better characterized by a sigmoidal curve, we have now incorporated the Hill equation in the model. To account for the inverse relationship between [Ca2+]i and the magnitude of the slow inward current, a term for negative feedback (h) was also included. We have determined the quantity (x – h) because x and h could not be determined separately. The quantity (x – h) was denoted as x′. The average values of x′ at 1.25 and 5.0 mM [Ca2+]o were significantly different (p < 0.0001), approximately 20% at the lower [Ca2+]o and about 50% at the higher [Ca2+]o. An attempt to estimate both x′ and the Hill coefficient N simultaneously has shown that the determination of N must be considered inaccurate, but even larger variations of N have little influence on x′. Thus, in intact ferret ventricular muscle, the model predicts that at 1.25 mM [Ca2+]o only about 20% of the activator calcium recirculates, while some 80% comes across the sarcolemma from the extracellular compartment. The model also predicts that the recirculating fraction doubles when [Ca2+]o is elevated to 5 mM.Key words: length-clamped papillary muscle, maximum twitch tension, excitation–contraction coupling model, recirculating fraction of activator calcium, transsarcolemmal fraction of activator calcium.

scholarly journals The relationship between contractile force and intracellular [Ca2+] in intact rat cardiac trabeculae.

1995 ◽  
Vol 105 (1) ◽  
pp. 1-19 ◽  
Author(s):  
P H Backx ◽  
W D Gao ◽  
M D Azan-Backx ◽  
E Marban
Keyword(s):  
Steady State ◽  
Cyclopiazonic Acid ◽  
Hill Coefficient ◽  
Atpase Inhibitor ◽  
Relaxation Phase ◽  
Contractile System ◽  
To Come ◽  
State Force ◽  
Relationship Of ◽  
The Relationship

The control of force by [Ca2+] was investigated in rat cardiac trabeculae loaded with fura-2 salt. At sarcomere lengths of 2.1-2.3 microns, the steady state force-[Ca2+]i relationship during tetanization in the presence of ryanodine was half maximally activated at a [Ca2+]i of 0.65 +/- 0.19 microM with a Hill coefficient of 5.2 +/- 1.2 (mean +/- SD, n = 9), and the maximal stress produced at saturating [Ca2+]i equalled 121 +/- 35 mN/mm2 (n = 9). The dependence of steady state force on [Ca2+]i was identical in muscles tetanized in the presence of the Ca(2+)-ATPase inhibitor cyclopiazonic acid (CPA). The force-[Ca2+]i relationship during the relaxation of twitches in the presence of CPA coincided exactly to that measured at steady state during tetani, suggesting that CPA slows the decay rate of [Ca2+]i sufficiently to allow the force to come into a steady state with the [Ca2+]i. In contrast, the relationship of force to [Ca2+]i during the relaxation phase of control twitches was shifted leftward relative to the steady state relationship, establishing that relaxation is limited by the contractile system itself, not by Ca2+ removal from the cytosol. Under control conditions the force-[Ca2+]i relationship, quantified at the time of peak twitch force (i.e., dF/dt = 0), coincided fairly well with steady state measurements in some trabeculae (i.e., three of seven). However, the force-[Ca2+]i relationship at peak force did not correspond to the steady state measurements after the application of 5 mM 2,3-butanedione monoxime (BDM) (to accelerate cross-bridge kinetics) or 100 microM CPA (to slow the relaxation of the [Ca2+]i transient). Therefore, we conclude that the relationship of force to [Ca2+]i during physiological twitch contractions cannot be used to predict the steady state relationship.

scholarly journals Modification of sarcoplasmic reticulum (SR) Ca2+ release by FK506 induces defective excitation-contraction coupling only when SR Ca2+ recycling is disturbed

2005 ◽  
Vol 83 (4) ◽  
pp. 357-366 ◽  
Author(s):  
Shu Yoshihara ◽  
Hiroshi Satoh ◽  
Masao Saotome ◽  
Hideki Katoh ◽  
Hajime Terada ◽  
...  
Keyword(s):  
Steady State ◽  
Sarcoplasmic Reticulum ◽  
Normal Condition ◽  
Binding Protein ◽  
Excitation Contraction Coupling ◽  
Contraction Coupling ◽  
Cell Shortening ◽  
Fk506 Binding Protein ◽  
Ec Coupling ◽  
Protein Dissociation

This study examined whether the effects of FK506-binding protein dissociation from sarcoplasmic reticulum (SR) Ca2+ release channels on excitation-contraction (EC) coupling changed when SR Ca2+ reuptake and (or) the trans-sarcolemmal Ca2+ extrusion were altered. The steady-state twitch Ca2+ transient (CaT), cell shortening, post-rest caffeine-induced CaT, and Ca2+ sparks were measured in rat ventricular myocytes using laser-scanning confocal microscopy. In the normal condition, 50 µmol FK506/L significantly increased steady-state CaT, cell shortening, and post-rest caffeine-induced CaT. When the cells were solely perfused with thapsigargin, FK506 did not reduce any of the states, but when low [Ca2+]0 (0.1 mmol/L) was perfused additionally, FK506 reduced CaT and cell shortening, and accelerated the reduction of post-rest caffeine-induced CaT. FK506 significantly increased Ca2+ spark frequency in the normal condition, whereas it mainly prolonged duration of individual Ca2+ sparks under the combination of thapsigargin and low [Ca2+]0 perfusion. Modification of SR Ca2+ release by FK506 impaired EC coupling only when released Ca2+ could not be taken back into the SR and was readily extruded to the extracellular space. Our findings could partly explain the controversy regarding the contribution of FK506-binding protein dissociation to defective EC coupling.Key words: FK506, ryanodine receptor, sarcoplasmic reticulum Ca2+-ATPase, Na+/Ca2+ exchange, excitation-contraction coupling

Possible mechanisms underlying differences in force production between normal and cardiomyopathic hamster atria

1991 ◽  
Vol 261 (5) ◽  
pp. H1603-H1608
Author(s):  
J. Bobet ◽  
S. E. Howlett ◽  
T. Gordon
Keyword(s):  
Steady State ◽  
Force Production ◽  
Recent Model ◽  
Bay K 8644 ◽  
Rest Interval ◽  
Contraction Coupling ◽  
Rate Of Recovery ◽  
Cardiac Excitation ◽  
State Force ◽  
J 51

The rate of recovery of force after a long rest interval is lower than normal in left atria from 80- to 85-day-old cardiomyopathic (CM) golden Syrian hamsters. To determine whether this difference was due to a reduced amount of Ca2+ available for release with each beat, we manipulated the amount of Ca2+ entering excised atria using the Ca2+ agonist BAY K 8644 and the antagonist nifedipine. We also simulated altered Ca2+ influx in a recent model of cardiac excitation-contraction coupling (V. J. A. Schouten, J. K. Van Deen, P. de Tombe, and A. A. Verveen Biophys. J. 51: 13-26, 1987) by varying the parameter representing Ca2+ influx and observing the effect on the force it predicted. Steady-state force of normal and CM atria was recorded in response to 1-Hz stimulation and recovery of steady-state force was monitored after a 600-s rest interval. Ca2+ fluxes were manipulated by raising external Ca2+ or by the presence and absence of drug. The recovery of force after a 600-s rest interval was digitized and fitted with an exponential function, and the time constant and steady-state force to which the muscle recovered after the pause were compared. Inclusion of the Ca2+ agonist BAY K 8644 (0.25 or 2.0 microM) made the response of CM atria similar to that of normal, while inclusion of the Ca2+ antagonist nifedipine (0.8 microM) made the response of normal atria similar to that of the CM. Similarly, decreasing the simulated Ca2+ influx in the model produced all of the differences observed between normal and CM muscle.(ABSTRACT TRUNCATED AT 250 WORDS)

Frog ventricle: participation of SR in excitation-contraction coupling

1989 ◽  
Vol 256 (5) ◽  
pp. H1432-H1439
Author(s):  
M. E. Anderson ◽  
I. J. Fox ◽  
C. R. Swayze ◽  
S. K. Donaldson
Keyword(s):  
Steady State ◽  
Sarcoplasmic Reticulum ◽  
Inhibitory Effects ◽  
Excitation Contraction Coupling ◽  
Contraction Coupling ◽  
Resting Tension ◽  
Mammalian Myocardium ◽  
Frog Myocardium ◽  
Frog Ventricle ◽  
Important Site

Activation of the first beat (B1) following a 60-s pause is diminished in isometrically contracting frog ventricular strips, in contrast to the augmentation documented for sarcoplasmic reticulum (SR)-dependent mammalian myocardium. However, treatment of frog ventricular strips with ouabain, an indirect inhibitor of the sarcolemmal Na+-Ca2+ exchanger, selectively enhanced postpause beats suggesting that in the absence of ouabain significant extrusion of cellular Ca2+ occurred during the pause. Because resting tension did not increase during the pause in ouabain-treated strips, the nonextruded Ca2+ must have been sequestered into a compartment such as SR. Steady-state beats were not affected by ouabain; its actions appeared to be separate from its known positive inotropism. Caffeine, a direct SR stimulus, initially enhanced B1 and subsequently decreased activation of all beats, which was consistent with initial augmentation of SR Ca2+ release and subsequent depletion of SR Ca2+ stores. Ouabain both potentiated the stimulatory effects and blocked the inhibitory effects of caffeine, suggesting that ouabain increased Ca2+ stores in the same intracellular Ca2+ pool as that acted on by caffeine, the SR. Ryanodine, an inhibitor of SR in mammalian myocardium, did not affect activation of frog myocardium. SR may be an important site for activator Ca2+ cycling in frog myocardium under control conditions as well as after long diastolic intervals in the presence of ouabain.

scholarly journals Voltage Dependence of the Apparent Affinity for External Na+ of the Backward-Running Sodium Pump

2001 ◽  
Vol 117 (4) ◽  
pp. 315-328 ◽  
Author(s):  
Paul De Weer ◽  
David C. Gadsby ◽  
R.F. Rakowski
Keyword(s):  
Steady State ◽  
Sodium Pump ◽  
Channel Model ◽  
Pump Current ◽  
Hill Coefficient ◽  
Access Channel ◽  
Electrogenic Sodium Pump ◽  
The Difference ◽  
Loligo Pealei ◽  
The Hill

The steady-state voltage and [Na+]o dependence of the electrogenic sodium pump was investigated in voltage-clamped internally dialyzed giant axons of the squid, Loligo pealei, under conditions that promote the backward-running mode (K+-free seawater; ATP- and Na+-free internal solution containing ADP and orthophosphate). The ratio of pump-mediated 42K+ efflux to reverse pump current, Ipump (both defined by sensitivity to dihydrodigitoxigenin, H2DTG), scaled by Faraday's constant, was −1.5 ± 0.4 (n = 5; expected ratio for 2 K+/3 Na+ stoichiometry is −2.0). Steady-state reverse pump current-voltage (Ipump-V) relationships were obtained either from the shifts in holding current after repeated exposures of an axon clamped at various Vm to H2DTG or from the difference between membrane I-V relationships obtained by imposing Vm staircases in the presence or absence of H2DTG. With the second method, we also investigated the influence of [Na+]o (up to 800 mM, for which hypertonic solutions were used) on the steady-state reverse Ipump-V relationship. The reverse Ipump-V relationship is sigmoid, Ipump saturating at large negative Vm, and each doubling of [Na+]o causes a fixed (29 mV) rightward parallel shift along the voltage axis of this Boltzmann partition function (apparent valence z = 0.80). These characteristics mirror those of steady-state 22Na+ efflux during electroneutral Na+/Na+ exchange, and follow without additional postulates from the same simple high field access channel model (Gadsby, D.C., R.F. Rakowski, and P. De Weer, 1993. Science. 260:100–103). This model predicts valence z = nλ, where n (1.33 ± 0.05) is the Hill coefficient of Na binding, and λ (0.61 ± 0.03) is the fraction of the membrane electric field traversed by Na ions reaching their binding site. More elaborate alternative models can accommodate all the steady-state features of the reverse pumping and electroneutral Na+/Na+ exchange modes only with additional assumptions that render them less likely.

scholarly journals Relationship between force and intracellular [Ca2+] in tetanized mammalian heart muscle.

1986 ◽  
Vol 87 (2) ◽  
pp. 223-242 ◽  
Author(s):  
D T Yue ◽  
E Marban ◽  
W G Wier
Keyword(s):  
Steady State ◽  
Hill Coefficient ◽  
Papillary Muscles ◽  
Tension Development ◽  
Intact Muscle ◽  
Bioluminescent Protein ◽  
Mammalian Heart Muscle ◽  
The Hill ◽  
Steady Force ◽  
Intact Heart

To determine features of the steady state [Ca2+]-tension relationship in intact heart, we measured steady force and intracellular [Ca2+] ([Ca2+]i) in tetanized ferret papillary muscles. [Ca2+]i was estimated from the luminescence emitted by muscles that had been microinjected with aequorin, a Ca2+-sensitive, bioluminescent protein. We found that by raising extracellular [Ca2+] and/or by exposing muscles to the Ca2+ channel agonist Bay K 8644, tension development could be varied from rest to an apparently saturating level, at which increases in [Ca2+]i produced no further rise in force. 95% of maximal Ca2+-activated force was reached at a [Ca2+]i of 0.85 +/- 0.06 microM (mean +/- SEM; n = 7), which suggests that the sensitivity of the myofilaments to [Ca2+]i is far greater than anticipated from studies of skinned heart preparations (or from previous studies using Ca2+-sensitive microelectrodes in intact heart). Our finding that maximal force was reached by approximately 1 microM also allowed us to calculate that the steady state [Ca2+]i-tension relationship, as it might be observed in intact muscle, should be steep (Hill coefficient of greater than 4), which is consistent with the Hill coefficient estimated from the entire [Ca2+]i-tension relationship derived from families of variably activated tetani (6.08 +/- 0.68; n = 7). Finally, with regard to whether steady state measurements can be applied directly toward understanding physiological contractions, we found that the relation between steady force and [Ca2+]i obtained during tetani was steeper than that between peak force and peak [Ca2+]i observed during physiological twitches.

scholarly journals Inactivation of excitation-contraction coupling in rat extensor digitorum longus and soleus muscles.

1988 ◽  
Vol 91 (5) ◽  
pp. 737-757 ◽  
Author(s):  
M Chua ◽  
A F Dulhunty
Keyword(s):  
Steady State ◽  
Membrane Potential ◽  
Voltage Clamp ◽  
Extensor Digitorum Longus ◽  
Threshold Concentration ◽  
Extensor Digitorum ◽  
Excitation Contraction Coupling ◽  
Contraction Coupling ◽  
Steady State Inactivation ◽  
Spontaneous Relaxation

K contractures and two-microelectrode voltage-clamp techniques were used to measure inactivation of excitation-contraction coupling in small bundles of fibers from rat extensor digitorum longus (e.d.l.) and soleus muscles at 21 degrees C. The rate of spontaneous relaxation was faster in e.d.l. fibers: the time for 120 mM K contractures to decay to 50% of maximum tension was 9.8 +/- 0.5 s (mean +/- SEM) in e.d.l. and 16.8 +/- 1.7 s in soleus. The rate of decay depended on membrane potential: in e.d.l., the 50% decay time was 14.3 +/- 0.7 s for contractures in 80 mM K (Vm = 25 mV) and 4.9 +/- 0.4 s in 160 mM K (Vm = -3 mV). In contrast to activation, which occurred with less depolarization in soleus fibers, steady state inactivation required more depolarization: after 3 min at -40 mV in 40 mM K, the 200 mM K contracture amplitude in e.d.l. fell to 28 +/- 10% (n = 5) of control, but remained at 85 +/- 2% (n = 6) of control in soleus. These different inactivation properties in e.d.l. and soleus fibers were not influenced by the fact that the 200 mM K solution used to test for steady state inactivation produced contractures that were maximal in soleus fibers but submaximal in e.d.l.: a relatively similar depression was recorded in maximal (200 mM K) and submaximal (60 and 80 mM K) contracture tension. A steady state "pedestal" of tension was observed with maintained depolarization after K contracture relaxation and was larger in soleus than in e.d.l. fibers. The pedestal tension was attributed to the overlap between the activation and inactivation curves for tension vs. membrane potential, which was greater in soleus than in e.d.l. fibers. The K contracture results were confirmed with the two-microelectrode voltage clamp: the contraction threshold increased to more positive potentials at holding potentials of -50 mV in e.d.l. or -40 mV in soleus. At holding potentials of -30 mV in e.d.l. or 0 mV in soleus, contraction could not be evoked by 15-ms pulses to +20 mV. Both K contracture and voltage-clamp experiments revealed that activation in soleus fibers occurred with a smaller transient depolarization and was maintained with greater steady state depolarization than in e.d.l. fibers. The K contracture and voltage-clamp results are described by a model in which contraction depends on the formation of a threshold concentration of activator from a voltage-sensitive molecule that can exist in the precursor, activator, or inactive states.

scholarly journals Activation of calcium-dependent chloride channels in rat parotid acinar cells.

1996 ◽  
Vol 108 (1) ◽  
pp. 35-47 ◽  
Author(s):  
J Arreola ◽  
J E Melvin ◽  
T Begenisich
Keyword(s):  
Steady State ◽  
Voltage Dependence ◽  
Acinar Cells ◽  
Hill Coefficient ◽  
Patch Clamp Technique ◽  
Channel Activation ◽  
Parotid Acinar Cells ◽  
Steady State Current ◽  
Rat Parotid ◽  
The Hill

The Ca2+ and voltage dependence of Ca(2+)-activated Cl- currents in rat parotid acinar cells was examined with the whole-cell patch clamp technique. Acinar cells were dialyzed with buffered free Ca2+ concentrations ([Ca2+]i) from &lt; 1 nM to 5 microM. Increasing [Ca2+]i induced an increase in Cl- current at all membrane potentials. In cells dialyzed with [Ca2+]i &gt; 25 nM, depolarizing test pulses activated a Cl- current that was composed of an instantaneous and a slow monoexponential component. The steady-state current-voltage relationship showed outward rectification at low [Ca2+]i but became more linear as the [Ca2+]i increased because of a shift in Cl- channel activation toward more negative voltages. The Ca2+ dependence of steady-state channel activation at various membrane voltages was fit by the Hill equation. The apparent Kd and Hill coefficient obtained from this analysis were both functions of membrane potential. The Kd decreased from 417 to 63 nM between -106 and +94 mV, whereas the Hill coefficient was always &gt; 1 and increased to values as large as 2.5 at large positive potentials. We found that a relatively simple mechanistic model can account for the channel steady-state and kinetic behavior. In this model, channel activation involves two identical, independent, sequential Ca2+ binding steps before a final Ca(2+)-independent transition to the conducting conformation. Channel activation proceeds sequentially through three closed states before reaching the open state. The Ca2+ binding steps of this model have a voltage dependence similar to that of the Kd from the Hill analysis. The simplest interpretation of our findings is that these channels are directly activated by Ca2+ ions that bind to sites approximately 13% into the membrane electric field from the cytoplasmic surface.

scholarly journals The Voltage Dependence of a Cloned Mammalian Renal Type II Na+/Pi Cotransporter (NaPi-2)

1998 ◽  
Vol 112 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Ian Forster ◽  
Nati Hernando ◽  
Jürg Biber ◽  
Heini Murer
Keyword(s):  
Steady State ◽  
Voltage Dependence ◽  
Hill Coefficient ◽  
Affinity Constant ◽  
Potential Range ◽  
Dependent Manner ◽  
Type Ii ◽  
Boltzmann Function ◽  
The Hill ◽  
Variable Substrate

The voltage dependence of the rat renal type II Na+/Pi cotransporter (NaPi-2) was investigated by expressing NaPi-2 in Xenopus laevis oocytes and applying the two-electrode voltage clamp. In the steady state, superfusion with inorganic phosphate (Pi) induced inward currents (Ip) in the presence of 96 mM Na+ over the potential range −140 ≤ V ≤ +40 mV. With Pi as the variable substrate, the apparent affinity constant (KmPi) was strongly dependent on Na+, increasing sixfold for a twofold reduction in external Na+. KmPi increased with depolarizing voltage and was more sensitive to voltage at reduced Na+. The Hill coefficient was close to unity and the predicted maximum Ip (Ipmax) was 40% smaller at 50 mM Na+. With Na+ as the variable substrate, KmNa was weakly dependent on both Pi and voltage, the Hill coefficient was close to 3 and Ipmax was independent of Pi at −50 mV. The competitive inhibitor phosphonoformic acid suppressed the steady state holding current in a Na+-dependent manner, indicating the existence of uncoupled Na+ slippage. Voltage steps induced pre–steady state relaxations typical for Na+-coupled cotransporters. NaPi-2-dependent relaxations were quantitated by a single, voltage-dependent exponential. At 96 mM Na+, a Boltzmann function was fit to the steady state charge distribution (Q-V) to give a midpoint voltage (V0.5) in the range −20 to −50 mV and an apparent valency of ∼0.5 e−. V0.5 became more negative as Na+ was reduced. Pi suppressed relaxations in a dose-dependent manner, but had little effect on their voltage dependence. Reducing external pH shifted V0.5 to depolarizing potentials and suppressed relaxations in the absence of Na+, suggesting that protons interact with the unloaded carrier. These findings were incorporated into an ordered kinetic model whereby Na+ is the first and last substrate to bind, and the observed voltage dependence arises from the unloaded carrier and first Na+ binding step.

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