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

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 [Ca 2+ ] o the average steady-state force was 2.94 ± 1.08 g/mm 2 and the potentiated contraction averaged 10.96 ± 1.61 g/mm 2 . At 5.0 mM [Ca 2+ ] o the steady-state force increased to 6.18 ± 1.23 g/mm 2 and the potentiated contraction averaged 12.08 ± 1.15 g/mm 2 . Under the conditions of these experiments the potentiated contraction obtained at 5.0 mM [Ca 2+ ] o is equal to the maximum twitch tension (F max ) these muscles can generate. We have previously shown that F max 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 [Ca 2+ ] 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 [Ca 2+ ] o were significantly different (p < 0.0001), approximately 20% at the lower [Ca 2+ ] o and about 50% at the higher [Ca 2+ ] 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 [Ca 2+ ] 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 [Ca 2+ ] o is elevated to 5 mM.