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.

Length-dependent activation in intact ferret hearts: study of steady-state Ca(2+)-stress-strain interrelations

1996 ◽  
Vol 270 (6) ◽  
pp. H1940-H1950 ◽  
Author(s):  
R. Stennett ◽  
K. Ogino ◽  
J. P. Morgan ◽  
D. Burkhoff
Keyword(s):  
Steady State ◽  
Heart Function ◽  
Hill Coefficient ◽  
Physical Factors ◽  
Stress Strain ◽  
Ventricular Structure ◽  
Intact Muscle ◽  
Rapid Stimulation ◽  
Whole Heart ◽  
State Stress

We examined the steady-state stress-strain relationships and the steady-state stress-intracellular calcium concentration ([Ca2+]i) relationship in intact ferret hearts and compared these to previously published analogous relationships in skinned and intact muscle. Langendorff-perfused ferret hearts were treated with ryanodine and tetanized by rapid stimulation to create steady-state conditions. [Ca2+]i was measured concurrently by macroinjected aequorin. Over a range of volumes corresponding to strains between 1.0 and 0.75, steady-state stress decreased by 33% when saturating levels of perfusate calcium were used, indicating the degree to which physical factors contribute to the Frank-Starling relationship. The steady-state stress-[Ca2+]i relationship was sigmoidal with a mean Hill coefficient (nH) of 4.91 +/- 0.29 at a strain of 1.0, and the [Ca2+]i required for half-maximal activation (K1/2) was 0.41 +/- 0.03 microM. K1/2 increased and nH decreased with decreasing strains. These results are similar to those observed in intact muscle but differ quantitatively from results obtained in isolated, skinned preparations. Based on these results, we suggest that whole heart function can be related to average sarcomere function without the need for complex models of ventricular structure.

Intracellular Ca2+ transients in the cat papillary muscle

1982 ◽  
Vol 60 (4) ◽  
pp. 524-528 ◽  
Author(s):  
J. P. Morgan ◽  
J. R. Blinks
Keyword(s):  
Papillary Muscle ◽  
Papillary Muscles ◽  
Contractile Apparatus ◽  
Tension Development ◽  
Cat Papillary Muscle ◽  
Intracellular Ca ◽  
Bioluminescent Protein

Intracellular Ca2+ transients in cat papillary muscles were detected with the calcium-sensitive bioluminescent protein aequorin and correlated with tension development. The effects of a variety of inotropic interventions are interpreted in terms of their probable effects on Ca2+ entry, Ca2+ release, Ca2+ sequestration, and the Ca2+ -sensitivity of the contractile apparatus. In contrast to results reported in dog Purkyně strands, the aequorin signals in cat papillary muscles appear to be dominated by release of Ca2+ from intracellular stores.

scholarly journals Cat Heart Muscle in Vitro

1965 ◽  
Vol 48 (5) ◽  
pp. 949-956 ◽  
Author(s):  
Ernest Page
Keyword(s):  
Steady State ◽  
Heart Muscle ◽  
Arrhenius Plot ◽  
Papillary Muscles ◽  
Wide Range ◽  
Heart Muscle Cells ◽  
Mammalian Heart Muscle ◽  
Apparent Activation Energies ◽  
Cat Heart

In quiescent cat papillary muscles JK, the rate of exchange of cellular K with K42 in the steady state, has been measured in the presence and absence of NaCl over a wide range of temperatures. JK was found to be independent of the presence of external NaCl under the steady state conditions investigated. The Arrhenius plot for K exchange was linear over a range of temperatures from 2.5 to 37.5°C in the absence of NaCl, and from 17.5 to 37.5°C in the presence of NaCl. The corresponding apparent activation energies were, respectively, 10,200 and 8,800 calories/mole. JK in the absence of NaCl was not affected by 10-5 M ouabain. These results are consistent with a passive distribution for the K of heart muscle cells. The observations suggest that a carrier-mediated forced exchange of K for Na does not occur during the steady state in mammalian heart muscle.

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 Single adult rabbit and rat cardiac myocytes retain the Ca2+- and species-dependent systolic and diastolic contractile properties of intact muscle.

1986 ◽  
Vol 88 (5) ◽  
pp. 589-613 ◽  
Author(s):  
M C Capogrossi ◽  
A A Kort ◽  
H A Spurgeon ◽  
E G Lakatta
Keyword(s):  
Steady State ◽  
Scattered Light ◽  
Low Frequency ◽  
Adult Rabbit ◽  
Papillary Muscles ◽  
Adult Rats ◽  
Intact Muscle ◽  
Rat Myocytes ◽  
Diastolic Properties ◽  
Frequency Of Stimulation

The systolic and diastolic properties of single myocytes and intact papillary muscles isolated from hearts of adult rats and rabbits were examined at 37 degrees C over a range of stimulation frequencies and bathing [Ca2+]o (Cao). In both rabbit myocytes and intact muscles bathed in 1 mM Cao, increasing the frequency of stimulation from 6 to 120 min-1 resulted in a positive staircase of twitch performance. During stimulation at 2 min-1, twitch performance also increased with increases in Cao up to 20 mM. In the absence of stimulation, both rabbit myocytes and muscles were completely quiescent in less than 15 mM Cao. Further increases in Cao caused the appearance of spontaneous asynchronous contractile waves in myocytes and in intact muscles caused scattered light intensity fluctuations (SLIF), which were previously demonstrated to be caused by Ca2+-dependent spontaneous contractile waves. In contrast to rabbit preparations, intact rat papillary muscles exhibited SLIF in 1.0 mM Cao. Two populations of rat myocytes were observed in 1 mM Cao: approximately 85% of unstimulated cells exhibited low-frequency (3-4 min-1) spontaneous contractile waves, whereas 15%, during a 1-min observation period, were quiescent. In a given Cao, the contractile wave frequency in myocytes and SLIF in intact muscles were constant for long periods of time. In both intact rat muscles and myocytes with spontaneous waves, in 1 mM Cao, increasing the frequency of stimulation from 6 to 120 min-1 resulted, on the average, in a 65% reduction in steady state twitch amplitude. Of the rat myocytes that did not manifest waves, some had a positive, some had a flat, and some had a negative staircase; the average steady state twitch amplitude of these cells during stimulation at 120 min-1 was 30% greater than that at 6 min-1. In contrast to rabbit preparations, twitch performance during stimulation at 2 min-1 saturated at 1.5 mM Cao in both intact rat muscles and in the myocytes with spontaneous waves. We conclude that the widely divergent, Ca2+-dependent systolic and diastolic properties of intact rat and rabbit cardiac muscle are retained with a high degree of fidelity in the majority of viable single myocytes isolated from the myocardium of these species, and that these myocytes are thus a valid model for studies of Ca2+-dependent excitation-contraction mechanisms in the heart.

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 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.

On the Measurement of Cooperativity and the Physico-Chemical Meaning of the Hill Coefficient

2019 ◽  
Vol 20 (9) ◽  
pp. 861-872 ◽  
Author(s):  
Andrea Bellelli ◽  
Emanuele Caglioti
Keyword(s):  
Ligand Binding ◽  
Hormone Receptors ◽  
Fundamental Property ◽  
Statistical Correlation ◽  
Hill Coefficient ◽  
Biological Macromolecules ◽  
Physico Chemical ◽  
Physiological Relevance ◽  
Minimum Estimate ◽  
The Hill

Cooperative ligand binding is a fundamental property of many biological macromolecules, notably transport proteins, hormone receptors, and enzymes. Positive homotropic cooperativity, the form of cooperativity that has greatest physiological relevance, causes the ligand affinity to increase as ligation proceeds, thus increasing the steepness of the ligand-binding isotherm. The measurement of the extent of cooperativity has proven difficult, and the most commonly employed marker of cooperativity, the Hill coefficient, originates from a structural hypothesis that has long been disproved. However, a wealth of relevant biochemical data has been interpreted using the Hill coefficient and is being used in studies on evolution and comparative physiology. Even a cursory analysis of the pertinent literature shows that several authors tried to derive more sound biochemical information from the Hill coefficient, often unaware of each other. As a result, a perplexing array of equations interpreting the Hill coefficient is available in the literature, each responding to specific simplifications or assumptions. In this work, we summarize and try to order these attempts, and demonstrate that the Hill coefficient (i) provides a minimum estimate of the free energy of interaction, the other parameter used to measure cooperativity, and (ii) bears a robust statistical correlation to the population of incompletely saturated ligation intermediates. Our aim is to critically evaluate the different analyses that have been advanced to provide a physical meaning to the Hill coefficient, and possibly to select the most reliable ones to be used in comparative studies that may make use of the extensive but elusive information available in the literature.

Effect of adrenomedullin on the production of endothelin-1 and on its vasoconstrictor action in resistance arteries: evidence for a receptor-specific functional interaction in patients with heart failure

2001 ◽  
Vol 101 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Chris HILLIER ◽  
Mark C. PETRIE ◽  
Michael P. LOVE ◽  
Fiona JOHNSTON ◽  
Margaret R. MACLEAN ◽  
...  
Keyword(s):  
Heart Failure ◽  
Hill Coefficient ◽  
Receptor Interaction ◽  
Resistance Arteries ◽  
Functional Interaction ◽  
High Potassium ◽  
Endothelin 1 ◽  
Patients With Heart Failure ◽  
Small Resistance ◽  
The Hill

Endothelin-1 (ET-1) and adrenomedullin (ADM) are both produced in the arterial wall, but have opposing biological actions. Evidence from experimental animals suggests a functional interaction between ET-1 and ADM. We have tested this in humans. Small resistance arteries were obtained from gluteal biopsies taken from patients with chronic heart failure (CHF) due to coronary heart disease (CHD), or with CHD and preserved ventricular function. The contractile responses to big ET-1 and to ET-1 in both sets of vessels were studied in the absence (control) and presence of ADM at 20 pmol/l (low ADM) or 200 pmol/l (high ADM), using wire myography. ADM did not affect the conversion of big ET-1 into ET-1 in vessels from patients with either CHD or CHF. Low ADM did not alter the contractile response to ET-1 in vessels from patients with CHF. Low ADM was not tested in vessels from patients with CHD, but high ADM did not affect this response in arteries from these patients. High ADM did, however, significantly reduce the vasoconstrictor effect of ET-1 in vessels from patients with CHF. The maximum response, as a percentage of the response to high potassium, was 199% (S.E.M. 25%) in the control experiments (n = 14), 205% (27%) in the low-ADM (n = 7) studies and 150% (17%) in the high-ADM (n = 6) experiments (P < 0.001). Furthermore, the Hill coefficient increased from 0.57±0.05 in the absence of ADM to 1.16±0.15 in the high-ADM experiments, indicating that ADM at 200 pmol/l specifically antagonized one receptor type in vessels from patients with CHF. We conclude that there is a one-site receptor interaction between ADM and ET-1 that is specific for vessels from patients with CHF. This functional interaction between ADM and ET-1 in resistance arteries may be of pathophysiological importance in CHF.

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