Insights From Computational Modeling Into the Contribution of Mechano-Calcium Feedback on the Cardiac End-Systolic Force-Length Relationship

Megan E Guidry; David P Nickerson; Edmund J Crampin; Martyn P Nash; Denis S Loiselle; Kenneth Tran

doi:10.3389/fphys.2020.00587

Insights From Computational Modeling Into the Contribution of Mechano-Calcium Feedback on the Cardiac End-Systolic Force-Length Relationship

Front Physiol. 2020 May 29:11:587. doi: 10.3389/fphys.2020.00587. eCollection 2020.

Authors

Megan E Guidry¹, David P Nickerson¹, Edmund J Crampin^{2

3}, Martyn P Nash^{1

4}, Denis S Loiselle^{1

5}, Kenneth Tran¹

Affiliations

¹ Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand.
² Systems Biology Laboratory, School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, Australia.
³ ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, School of Chemical and Biomedical Engineering, The University of Melbourne, Melbourne, VIC, Australia.
⁴ Department of Engineering Science, The University of Auckland, Auckland, New Zealand.
⁵ Department of Physiology, The University of Auckland, Auckland, New Zealand.

Abstract

In experimental studies on cardiac tissue, the end-systolic force-length relation (ESFLR) has been shown to depend on the mode of contraction: isometric or isotonic. The isometric ESFLR is derived from isometric contractions spanning a range of muscle lengths while the isotonic ESFLR is derived from shortening contractions across a range of afterloads. The ESFLR of isotonic contractions consistently lies below its isometric counterpart. Despite the passing of over a hundred years since the first insight by Otto Frank, the mechanism(s) underlying this protocol-dependent difference in the ESFLR remain incompletely explained. Here, we investigate the role of mechano-calcium feedback in accounting for the difference between these two ESFLRs. Previous studies have compared the dynamics of isotonic contractions to those of a single isometric contraction at a length that produces maximum force, without considering isometric contractions at shorter muscle lengths. We used a mathematical model of cardiac excitation-contraction to simulate isometric and force-length work-loop contractions (the latter being the 1D equivalent of the whole-heart pressure-volume loop), and compared Ca²⁺ transients produced under equivalent force conditions. We found that the duration of the simulated Ca²⁺ transient increases with decreasing sarcomere length for isometric contractions, and increases with decreasing afterload for work-loop contractions. At any given force, the Ca²⁺ transient for an isometric contraction is wider than that during a work-loop contraction. By driving simulated work-loops with wider Ca²⁺ transients generated from isometric contractions, we show that the duration of muscle shortening was prolonged, thereby shifting the work-loop ESFLR toward the isometric ESFLR. These observations are explained by an increase in the rate of binding of Ca²⁺ to troponin-C with increasing force. However, the leftward shift of the work-loop ESFLR does not superimpose on the isometric ESFLR, leading us to conclude that while mechano-calcium feedback does indeed contribute to the difference between the two ESFLRs, it does not completely account for it.

Keywords: calcium-troponin binding affinity; cardiac calcium transient; cardiac excitation-contraction model; end-systolic force-length relations; mechano-calcium feedback; thin filament activation.