Hystereses in the force-length relation and regulation of cross-bridge recruitment in tetanized rat trabeculae

Dynamics of parathyroid hormone secretion in health and secondary hyperparathyroidism

This review examines the dynamics of parathyroid hormone secretion in health and in various causes of secondary hyperparathyroidism. Although most studies of parathyroid hormone and calcium have focused on the modification of parathyroid hormone secretion by serum calcium, the relationship between parathyroid hormone and serum calcium is bifunctional because parathyroid hormone also modifies serum calcium. In normal animals and humans, factors such as phosphorus and vitamin D modify the basal parathyroid hormone level and the maximal parathyroid hormone response to hypocalcemia. Certain medications, such as lithium and estrogen, in normal individuals and sustained changes in the serum calcium concentration in hemodialysis patients change the set point of calcium, which reflects the serum calcium concentration at which parathyroid hormone secretion responds. Hypocalcemia increases the basal/maximal parathyroid hormone ratio, a measure of the relative degree of parathyroid hormone stimulation. The phenomenon of hysteresis, defined as a different parathyroid hormone value for the same serum calcium concentration during the induction of and recovery from hypo- and hypercalcemia, is discussed because it provides important insights into factors that affect parathyroid hormone secretion. In three causes of secondary hyperparathyroidism--chronic kidney disease, vitamin D deficiency, and aging--factors that affect the dynamics of parathyroid hormone secretion are evaluated in detail. During recovery from vitamin D deficiency, the maximal parathyroid hormone remains elevated while the basal parathyroid hormone value rapidly becomes normal because of a shift in the set point of calcium. Much remains to be learned about the dynamics of parathyroid hormone secretion in health and secondary hyperparathyroidism.

The mechanoelectric feedback: a novel "calcium clamp" method, using tetanic contraction, for testing the role of the intracellular free calcium

Mechanical perturbations affect the membrane action potential, a phenomenon denoted as the mechanoelectric feedback (MEF), and may elicit cardiac arrhythmias. Two plausible mechanisms were suggested to explain this phenomenon: (i) stretch-activated channels (SACs) within the cell membrane and (ii) modulation of the action potential by the intracellular Ca(2+) (the Calcium hypothesis). The intracellular Ca(2+) varies mainly due to the effects of the mechanical perturbations on the affinity of troponin for calcium. The present study concentrates on the unique experimental methods that allow differentiating between the effects of SAC and Ca(2+) on the action potential. This is achieved by controlling the sarcomere lengths (SLs) independently of the intracellular Ca(2+) concentration, in the intact fiber. A dedicated experimental setup allowed simultaneous measurements of the membrane potential and the mechanical performance (Force and SL). The action potential was measured by voltage-sensitive dye (Di-4-ANEPPS). The SL was measured by laser diffraction technique and was controlled by a fast servomotor. The intracellular Ca(2+) was controlled (calcium clamp) by imposing stable tetanic contractions at various extracellular calcium concentrations ([Ca(2+)](0)s). Tetanus was obtained by 8 Hz stimulation in the presence of cyclopiazonic acid (CPA) (30 muM). Isolated trabeculae from a rat's right ventricle were studied at different SLs and [Ca(2+)](0)s. The experimental data strongly support the calcium hypothesis. Although the action potential duration (APD) decreases at longer SL, the [Ca(2+)](0) has a significantly larger effect on the APD. The APD decreases as the [Ca(2+)](0) increases. Understanding the underlying mechanism opens new research avenues for the development of therapeutic modalities for cardiac arrhythmias.

Regulation of energy liberation during steady sarcomere shortening

Energy liberation rate ( Ė) during steady muscle shortening is a monotonic increasing or biphasic function of the shortening velocity ( V). The study examines three plausible hypotheses for explaining the biphasic Ė-V relationship (EVR): 1) the cross-bridge (XB) turnover rate from non-force-generating (weak) to force-generating (strong) conformation decreases as V increases; 2) XB kinetics is determined by the number of strong XBs (XB -XB cooperativity); and 3) the affinity of troponin for calcium is modulated by the number of strong XBs (XB -Ca cooperativity). The relative role of the various energy-regulating mechanisms is not well defined. The hypotheses were tested by coupling calcium kinetics with XB cycling. All three hypotheses yield identical steady-state characteristics: 1) hyperbolic force-velocity relationship; 2) quasi-linear stiffness-force relationship; and 3) biphasic EVR, where Ė declines at high V due to decrease in the number of cycling XBs or in the weak-to-strong transition rate. The hypotheses differ in the ability to describe the existence of both monotonic and biphasic EVRs and in the effect of intracellular free calcium concentration ([Ca2+]i) on the EVR peak. Monotonic and biphasic EVRs with a shift in EVR peak to higher velocity at higher [Ca2+]iare obtained only by XB -Ca cooperativity. XB -XB cooperativity provides only biphasic EVRs. A direct effect of V on XB kinetics predicts that EVR peak is obtained at the same velocity independently of [Ca2+]i. The study predicts that measuring the dependence of the EVR on [Ca2+]iallows us to test the hypotheses and to identify the dominant energy-regulating mechanism. The established XB -XB and XB -Ca mechanisms provide alternative explanations to the various reported EVRs.

Analysis of hystereses in force length and force calcium relations

Analysis of the hystereses in the force-length relationship at constant Ca(2+) concentration and in the force-calcium relationship at constant sarcomere length (SL) provides insight into the mechanisms that control cross-bridge (XB) recruitment. The hystereses are related here to two mechanisms that regulate the number of strong XBs: the cooperativity, whereby the number of strong XBs determines calcium affinity, and the mechanical feedback, whereby the shortening velocity determines the duration for which the XBs are in the strong state. The study simulates the phenomena and defines the role of these feedbacks. The model that couples calcium kinetics with XB cycling was built on Simulink software (Matlab). Counterclockwise (CCW) hysteresis, wherein the force response lags behind the SL oscillations, at a constant calcium level, is obtained in the force-length plane when neglecting the mechanical feedback and accounting only for the cooperativity mechanism. Conversely, the force response precedes the SL oscillations, yielding a clockwise (CW) hysteresis when only the mechanical feedback is allowed to exist. In agreement with experimental observations, either CW or CCW hysteresis is obtained when both feedbacks coexist: CCW hystereses are obtained at low frequencies (<3 Hz), and the direction is reversed to CW at higher frequencies (>3 Hz). The cooperativity dominates at low frequencies and allows the muscle to adapt XB recruitment to slow changes in the loading conditions. The changeover frequency from CCW to CW hysteresis defines the velocity limit above which the muscle absorbs rather than generates energy. The hysteresis in the force-calcium relation is conveniently explained by the same cooperativity mechanism. We propose that a single cooperativity mechanism that depends on the number of strong XBs can explain the hystereses in the force-length as well as in the force-calcium relationships.

The Adaptive Intracellular Control of Cardiac Muscle Function

This study explores the mechanisms dominating the regulation of the biochemical energy consumption and the mechanical output of the actin-myosin motor units, the crossbridges (Xbs), in the cardiac sarcomere. Our analytical model, which couples Xbs cycling dynamics with the kinetics of the free Ca(2+) binding to troponin-C (Tn-C), includes two feedback mechanisms: (1) a cooperativity mechanism, whereby the amount of force generating Xbs determines the affinity of calcium binding to the regulatory protein and the force-length relationship (FLR); and (2) a mechanical (negative) feedback, whereby the filament shortening velocity affects the rate of Xb turnover from the force- to the nonforce-generating state, allows the analytical solution for the muscle force-velocity relationship (FVR), and the linear relation between energy consumption and the generated mechanical energy. Our experimental and analytical studies of the force response to large-amplitude sarcomere length (SL) oscillations at various frequencies and constant [Ca(2+)] in the isolated tetanized rat trabeculae reveal that the generated force depends on the history of contraction and establishes the validity of these two feedbacks. The cooperativity mechanism generates counterclockwise (CCW) hystereses, where the muscle generates external work; while at higher frequencies the mechanical feedback produces clockwise (CW) hystereses, where the muscle behaves as a damper. The cooperativity provides the adaptive control of the cardiac response to short-term changes in the load by modulating Xb recruitment. The cardiac efficiency, defined as the ratio of the generated mechanical energy (i.e., external work and pseudo-potential energy) to the sarcomere energy consumption, is determined by the mechanical feedback, reflecting an inherent property of the single Xb. The efficiency is thus independent of the number of strong Xbs and is constant and load independent.