Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model

1994 ◽  
Vol 267 (2) ◽  
pp. H779-H795 ◽  
Author(s):  
A. Landesberg ◽  
S. Sideman
Keyword(s):  
Cardiac Muscle ◽  
Calcium Binding ◽  
Mechanical Activity ◽  
Free Calcium ◽  
Shortening Velocity ◽  
Cross Bridge ◽  
Mechanical Constraints ◽  
Force Velocity ◽  
Cross Bridges ◽  
Reported Data

This study describes the regulation of mechanical activity in the intact cardiac muscle, the effects of the free calcium transients and the mechanical constraints, and emphasizes the central role of the troponin complex in regulating muscle activity. A “loose coupling” between calcium binding to troponin and cross-bridge cycling is stipulated, allowing the existence of cross bridges in the strong conformation without having bound calcium on the neighboring troponin. The model includes two feedback mechanisms: 1) a positive feedback, or cooperativity, in which the cycling cross bridges affect the affinity of troponin for calcium, and 2) a negative mechanical feedback, where the filament-sliding velocity affects cross-bridge cycling. The model simulates the reported experimental force-length and force-velocity relationships at different levels of activation. The dependence of the shortening velocity on calcium concentration, sarcomere length, internal load, and rate of cross-bridge cycling is described analytically in agreement with reported data. Furthermore, the model provides an analytic solution for Hill's equation of the force-velocity relationship and for the phenomena of unloaded shortening velocity and force deficit. The model-calculated changes in free calcium in various mechanical conditions are in good agreement with the available experimental results.

Coupling calcium binding to troponin C and cross-bridge cycling in skinned cardiac cells

1994 ◽  
Vol 266 (3) ◽  
pp. H1260-H1271 ◽  
Author(s):  
A. Landesberg ◽  
S. Sideman
Keyword(s):  
Cardiac Muscle ◽  
Calcium Binding ◽  
Troponin C ◽  
Cardiac Cells ◽  
Loose Coupling ◽  
Cross Bridge ◽  
Length Relationship ◽  
Troponin Complex ◽  
Cross Bridges

This study examines the coupling of calcium binding to troponin with the force developed by the cross bridges in the skinned cardiac muscle. It emphasizes the key role of the troponin complex in regulating cross-bridge cycling and defines four distinct states of the troponin complex in the single-overlap region. These include a "loose-coupling" state, wherein cross bridges can exist in the strong conformation without having calcium bound to the neighbor troponin C. Published simultaneous measurements of the force and the bound calcium are used to calculate the apparent calcium binding coefficients. The force-length relationships at different free calcium concentrations are used to evaluate the cooperative mechanism. The dependence of the affinity of troponin for calcium on the number of force-generating cross bridges is the dominant cooperative mechanism. The proposed loose-coupling model, with a positive feedback of force on calcium binding, describes the role of calcium in force regulation and the force-length relationship in skinned cardiac muscle. The ability to simulate the rate of force development is demonstrated.

scholarly journals Influence of partial activation on force-velocity properties of frog skinned muscle fibers in millimolar magnesium ion.

1986 ◽  
Vol 87 (4) ◽  
pp. 607-631 ◽  
Author(s):  
R A Podolin ◽  
L E Ford
Keyword(s):  
Muscle Fibers ◽  
Ion Concentration ◽  
Segment Length ◽  
Magnesium Ion ◽  
Free Calcium ◽  
Shortening Velocity ◽  
Cross Bridge ◽  
Partial Activation ◽  
Significant Difference ◽  
Force Velocity

Segments of briefly glycerinated muscle fibers from Rana pipiens were activated rapidly by a brief exposure to 2.5 mM free calcium followed by a solution containing calcium buffered with EGTA to produce the desired level of force. Steps to isotonic loads were made using a servomotor, usually 3-5 s after the onset of activation. The relative isotonic forces (P/P0) and velocities from contractions obtained under similar circumstances were grouped together and fitted with hyperbolic functions. Under the condition of 6 mM MgCl2 and 5 mM ATP, there was no significant difference in the relative force-velocity relations obtained at full activation compared with those obtained at partial activation when developed force was approximately 40% of its full value. Control experiments showed that a variety of factors did not alter either the relative force-velocity relations or the finding that partial activation did not change these properties. The factors investigated included the decline in force that occurs with each successive contraction of skinned fibers, the segment length (over a range of 1-3 mm), the sarcomere length (over a range of 1.9-2.2 microns), the magnesium ion concentration (26 microM and 1.4 mM were tested), the ATP concentration, the presence of free calcium, and the age of the preparation (up to 30 h). Attempts to repeat earlier experiments by others showing a dependence of shortening velocity on activation were unsuccessful because the low ionic strength used in those experiments caused the fibers to break after a few contractions. The main conclusion, that the shortening velocity is independent of the level of activation, is consistent with the hypothesis that the cross-bridges act independently and that activating calcium acts only as an all-or-none switch for individual cross-bridge attachment sites, and does not otherwise influence the kinetics of cross-bridge movement.

Oxytocin-mediated recruitment of slowly cycling cross bridges and isometric force in rat myometrium

1996 ◽  
Vol 270 (2) ◽  
pp. E203-E208
Author(s):  
A. L. Ruzycky ◽  
B. T. Ameredes
Keyword(s):  
Isometric Force ◽  
Additional Stress ◽  
Shortening Velocity ◽  
Cycling Rate ◽  
Quick Release ◽  
Cross Bridge ◽  
Cross Bridges ◽  
Unit Stress ◽  
Release Method ◽  
The Relationship

The relationship between cross-bridge cycling rate and isometric stress was investigated in rat myometrium. Stress production by myometrial strips was measured under resting, K+ depolarization, and oxytocin-stimulated conditions. Cross-bridge cycling rates were determined from measurements of maximal unloaded shortening velocity, using the quick-release method. Force redevelopment after the quick release was used as an index of cross-bridge attachment. With maximal K+ stimulation, stress increased with increased cross-bridge cycling (+76%; P < 0.05) and attached cross bridges (+112%; P < 0.05). Addition of oxytocin during K+ stimulation further increased stress (+30%; P < 0.05). With this force component, the cross-bridge cycling rate decreased (-60%; P < 0.05) similar to that under resting conditions. Attached cross-bridges did not increase with this additional stress. The results suggest two distinct mechanisms mediating myometrial contractions. One requires elevated intracellular calcium and rapidly cycling cross bridges. The other mechanism may be independent of calcium and appears to be mediated by slowly cycling cross bridges, supporting greater unit stress.

Heat production of rat anococcygeus muscle during isometric contraction

1988 ◽  
Vol 255 (4) ◽  
pp. C536-C542 ◽  
Author(s):  
J. S. Walker ◽  
I. R. Wendt ◽  
C. L. Gibbs
Keyword(s):  
Energy Expenditure ◽  
Heat Production ◽  
Progressive Increase ◽  
Isometric Contractions ◽  
Shortening Velocity ◽  
Anococcygeus Muscle ◽  
Cross Bridge ◽  
Time Integral ◽  
Rat Anococcygeus Muscle ◽  
Cross Bridges

Heat production, unloaded shortening velocity (Vus), and load-bearing capacity (LBC) were studied in the isolated rat anococcygeus muscle during isometric contractions at 27 degrees C. The relation between the total suprabasal heat produced and the stress-time integral for isometric contractions of various durations was curvilinear, demonstrating a decreasing slope as contractile duration increased. The rate of heat production at 600 s was approximately 68% of the peak value of 6.55 mW/g that occurred at 10 s. At the same time, force rose from a mean of 92 mN/mm2 at 10 s to a value of 140 mN/mm2 at 600 s. This produced a nearly threefold increase in the economy of force maintenance. The decline in the rate of heat production was accompanied by a decline in Vus from 0.56 Lo/s at 10 s to 0.28 Lo/s at 600 s, where Lo is the length for optimal force development. This suggests the fall in the rate of heat production was caused, at least in part, by a slowing of cross-bridge kinetics. The ratio of LBC to developed tension at 10 s was not significantly different from the ratio at 600 s, suggesting that the increase in tension was due to an increased number of attached cross bridges. The decline in heat production, therefore, appears contradictory, since an increased number of attached cross bridges would predict an increased rate of energy expenditure. The observations can be reconciled if either 1) the increase in force is caused by a progressive increase in the attachment time of a constant number of cross bridges that cycle at a lower frequency or 2) the decline in energy expenditure caused by the slowing of cross-bridge cycling is sufficient to mask the increase caused by the recruitment of additional cross bridges.

Regulation of shortening velocity by cross-bridge phosphorylation in smooth muscle

1988 ◽  
Vol 255 (1) ◽  
pp. C86-C94 ◽  
Author(s):  
C. M. Hai ◽  
R. A. Murphy
Keyword(s):  
Smooth Muscle ◽  
Shortening Velocity ◽  
Internal Load ◽  
Cross Bridge ◽  
Bridge Model ◽  
The Family ◽  
Cross Bridges ◽  
Latch State ◽  
The Relationship ◽  
State Stress

We have proposed a model that incorporates a dephosphorylated "latch bridge" to explain the mechanics and energetics of smooth muscle. Cross-bridge phosphorylation is proposed as a prerequisite for cross-bridge attachment and rapid cycling. Features of the model are 1) myosin light chain kinase and phosphatase can act on both free and attached cross bridges, 2) dephosphorylation of an attached phosphorylated cross bridge produces a noncycling "latch bridge," and 3) latch bridges have a slow detachment rate. This model quantitatively predicts the latch state: stress maintenance with reduced phosphorylation, cross-bridge cycling rates, and ATP consumption. In this study, we adapted A. F. Huxley's formulation of crossbridge cycling (A. F. Huxley, Progr. Biophys. Mol. Biol. 7: 255-318, 1957) to the latch-bridge model to predict the relationship between isotonic shortening velocity and phosphorylation. The model successfully predicted the linear dependence of maximum shortening velocity at zero external load (V0) on phosphorylation, as well as the family of stress-velocity curves determined at different times during a contraction when phosphorylation values varied. The model implies that it is unnecessary to invoke an internal load or multiple regulatory mechanisms to explain regulation of V0 in smooth muscle.

Regulation of energy consumption in cardiac muscle: analysis of isometric contractions

1999 ◽  
Vol 276 (3) ◽  
pp. H998-H1011 ◽  
Author(s):  
Amir Landesberg ◽  
Samuel Sideman
Keyword(s):  
Energy Consumption ◽  
Cardiac Muscle ◽  
Feedback Mechanism ◽  
Isometric Contractions ◽  
Cross Bridge ◽  
Time Integral ◽  
Length Relationship ◽  
Cross Bridges ◽  
Force Time ◽  
Force Time Integral

The well-known linear relationship between oxygen consumption and force-length area or the force-time integral is analyzed here for isometric contractions. The analysis, which is based on a biochemical model that couples calcium kinetics with cross-bridge cycling, indicates that the change in the number of force-generating cross bridges with the change in the sarcomere length depends on the force generated by the cross bridges. This positive-feedback phenomenon is consistent with our reported cooperativity mechanism, whereby the affinity of the troponin for calcium and, hence, cross-bridge recruitment depends on the number of force-generating cross bridges. Moreover, it is demonstrated that a model that does not include a feedback mechanism cannot describe the dependence of energy consumption on the loading conditions. The cooperativity mechanism, which has been shown to determine the force-length relationship and the related Frank-Starling law, is shown here to provide the basis for the regulation of energy consumption in the cardiac muscle.

scholarly journals Stiffness-distortion sarcomere model for muscle simulation

1999 ◽  
Vol 87 (5) ◽  
pp. 1861-1876 ◽  
Author(s):  
Maria V. Razumova ◽  
Anna E. Bukatina ◽  
Kenneth B. Campbell
Keyword(s):  
Differential Equations ◽  
Kinetic Scheme ◽  
Simple Method ◽  
Thin Filaments ◽  
Cross Bridge ◽  
Model Predictions ◽  
Force Velocity ◽  
Cross Bridges ◽  
Shearing Motion ◽  
State Kinetic

A relatively simple method is presented for incorporating cross-bridge mechanisms into a muscle model. The method is based on representing force in a half sarcomere as the product of the stiffness of all parallel cross bridges and their average distortion. Differential equations for sarcomeric stiffness are derived from a three-state kinetic scheme for the cross-bridge cycle. Differential equations for average distortion are derived from a distortional balance that accounts for distortion entering and leaving due to cross-bridge cycling and for distortion imposed by shearing motion between thick and thin filaments. The distortion equations are unique and enable sarcomere mechanodynamics to be described by only a few ordinary differential equations. Model predictions of small-amplitude step and sinusoidal responses agreed well with previously described experimental results and allowed unique interpretations to be made of various response components. Similarly good results were obtained for model reproductions of force-velocity and large-amplitude step and ramp responses. The model allowed reasonable predictions of contractile behavior by taking into account what is understood to be basic muscle contractile mechanisms.

scholarly journals Are Force Enhancement after Stretch and Muscle Fatigue Due to Effects of Elevated Inorganic Phosphate and Low Calcium on Cross Bridge Kinetics?

Medicina ◽  
2020 ◽  
Vol 56 (5) ◽  
pp. 249
Author(s):  
Hans Degens ◽  
David A. Jones
Keyword(s):  
Muscle Fatigue ◽  
Isometric Force ◽  
Force Enhancement ◽  
Shortening Velocity ◽  
Cross Bridge ◽  
Fatigued Muscle ◽  
Butanedione Monoxime ◽  
Combined Action ◽  
Cross Bridges ◽  
Muscle Contractile

Background and Objectives: Muscle fatigue is characterised by (1) loss of force, (2) decreased maximal shortening velocity and (3) a greater resistance to stretch that could be due to reduced intracellular Ca2+ and increased Pi, which alter cross bridge kinetics. Materials and Methods: To investigate this, we used (1) 2,3-butanedione monoxime (BDM), believed to increase the proportion of attached but non-force-generating cross bridges; (2) Pi that increases the proportion of attached cross bridges, but with Pi still attached; and (3) reduced activating Ca2+. We used permeabilised rat soleus fibres, activated with pCa 4.5 at 15 °C. Results: The addition of 1 mM BDM or 15 mM Pi, or the lowering of the Ca2+ to pCa 5.5, all reduced the isometric force by around 50%. Stiffness decreased in proportion to isometric force when the fibres were activated at pCa 5.5, but was well maintained in the presence of Pi and BDM. Force enhancement after a stretch increased with the length of stretch and Pi, suggesting a role for titin. Maximum shortening velocity was reduced by about 50% in the presence of BDM and pCa 5.5, but was slightly increased by Pi. Neither decreasing Ca2+ nor increasing Pi alone mimicked the effects of fatigue on muscle contractile characteristics entirely. Only BDM elicited a decrease of force and slowing with maintained stiffness, similar to the situation in fatigued muscle. Conclusions: This suggests that in fatigue, there is an accumulation of attached but low-force cross bridges that cannot be the result of the combined action of reduced Ca2+ or increased Pi alone, but is probably due to a combination of factors that change during fatigue.

scholarly journals Stretch of active muscle during the declining phase of the calcium transient produces biphasic changes in calcium binding to the activating sites.

1990 ◽  
Vol 96 (5) ◽  
pp. 1013-1035 ◽  
Author(s):  
A M Gordon ◽  
E B Ridgway
Keyword(s):  
Calcium Binding ◽  
Time Course ◽  
Control Level ◽  
Calcium Transient ◽  
Length Change ◽  
Positive Phase ◽  
Active Force ◽  
Cross Bridge ◽  
Calcium Affinity ◽  
Cross Bridges

In voltage-clamped barnacle single muscle fibers, muscle shortening during the declining phase of the calcium transient increases myoplasmic calcium. This extra calcium is probably released from the activating sites by a change in affinity when cross-bridges break (Gordon, A. M., and E. B. Ridgway, 1987. J. Gen. Physiol. 90:321-340). Stretching the muscle at similar times causes a more complex response, a rapid increase in intracellular calcium followed by a transient decrease. The amplitudes of both phases increase with the rate and amplitude of stretch. The rapid increase, however, appears only when the muscle is stretched more than approximately 0.4%. This is above the length change that produces the breakpoint in the force record during a ramp stretch. This positive phase in response to large stretches is similar to that seen on equivalent shortening at the same point in the contraction. For stretches at different times during the calcium transient, the peak amplitude of the positive phase has a time course that is delayed relative to the calcium transient, while the peak decrease during the negative phase has an earlier time course that is more similar to the calcium transient. The amplitudes of both phases increase with increasing strength of stimulation and consequent force. When the initial muscle the active force. A large decrease in length (which drops the active force to zero) decreases the extra calcium seen on a subsequent restretch. After such a shortening step, the extra calcium on stretch recovers (50 ms half time) toward the control level with the same time course as the redeveloped force. Conversely, stretching an active fiber decreases the extra calcium on a subsequent shortening step that is imposed shortly afterward. Enhanced calcium binding due to increased length alone cannot explain our data. We hypothesize that the calcium affinity of the activating sites increases with cross-bridge attachment and further with cross-bridge strain. This accounts for the biphasic response to stretch as follows: cross-bridges detached by stretch first decrease calcium affinity, then upon reattachment increase calcium affinity due to the strained configuration brought on by the stretch. The experiments suggest that cross-bridge attachment and strain can modify calcium binding to the activating sites in intact muscle.

scholarly journals Series-to-parallel transition in the filament lattice of airway smooth muscle

2000 ◽  
Vol 89 (3) ◽  
pp. 869-876 ◽  
Author(s):  
Chun Y. Seow ◽  
Victor R. Pratusevich ◽  
Lincoln E. Ford
Keyword(s):  
Smooth Muscle ◽  
Airway Smooth Muscle ◽  
Muscle Length ◽  
Thick Filament ◽  
Cycling Rate ◽  
Cross Bridge ◽  
Parallel Change ◽  
Force Velocity ◽  
Cross Bridges ◽  
Trachealis Muscle

Force-velocity curves measured at different times during tetani of sheep trachealis muscle were analyzed to assess whether velocity slowing could be explained by thick-filament lengthening. Such lengthening increases force by placing more cross bridges in parallel on longer filaments and decreases velocity by reducing the number of filaments spanning muscle length. From 2 s after the onset of stimulation, when force had achieved 42% of it final value, to 28 s, when force had been at its tetanic plateau for ∼15 s, velocity decreases were exactly matched by force increases when force was adjusted for changes in activation, as assessed from the maximum power value in the force-velocity curves. A twofold change in velocity could be quantitatively explained by a series-to-parallel change in the filament lattice without any need to postulate a change in cross-bridge cycling rate.

Sign in / Sign up

Export Citation Format

Share Document