The Effects of Mechanical Preload on Transmural Differences in Mechano-Calcium-Electric Feedback in Single Cardiomyocytes: Experiments and Mathematical Models

Abstract

Transmural differences in ventricular myocardium are maintained by electromechanical coupling and mechano-calcium/mechano-electric feedback. In the present study, we experimentally investigated the influence of preload on the force characteristics of subendocardial (Endo) and subepicardial (Epi) single ventricular cardiomyocytes stretched by up to 20% from slack sarcomere length (SL) and analyzed the results with the help of mathematical modeling. Mathematical models of Endo and Epi cells, which accounted for regional heterogeneity in ionic currents, Ca²⁺ handling, and myofilament contractile mechanisms, showed that a greater slope of the active tension-length relationship observed experimentally in Endo cardiomyocytes could be explained by greater length-dependent Ca²⁺ activation in Endo cells compared with Epi ones. The models also predicted that greater length dependence of Ca²⁺ activation in Endo cells compared to Epi ones underlies, via mechano-calcium-electric feedback, the reduction in the transmural gradient in action potential duration (APD) at a higher preload. However, the models were unable to reproduce the experimental data on a decrease of the transmural gradient in the time to peak contraction between Endo and Epi cells at longer end-diastolic SL. We hypothesize that preload-dependent changes in viscosity should be involved alongside the Frank-Starling effects to regulate the transmural gradient in length-dependent changes in the time course of contraction of Endo and Epi cardiomyocytes. Our experimental data and their analysis based on mathematical modeling give reason to believe that mechano-calcium-electric feedback plays a critical role in the modulation of electrophysiological and contractile properties of myocytes across the ventricular wall.

Keywords: electromechanical coupling; length-dependent activation; mechanical preload; mechano-calcium-electric feedback; single cardiomyocytes; transmural differences.

FIGURE 1

Schematic links between mechanisms of electromechanical coupling and mechano-calcium-electric feedback in the mathematical Endo and Epi models. Solid lines show direct links between the mechanisms of excitation–contraction coupling and dashed lines show feedback links. Cooperative mechanisms of Ca²⁺ activation of myofilaments [Xb–CaTnC, CaTnC–CaTnC, and regulatory unit (RU) end-to-end cooperativity] are described in the text.

FIGURE 2

Representative recordings of auxotonic tension in experiments (top panel) and mathematical model simulations of tension, cytosolic Ca²⁺ concentration ([Ca²⁺]_i) and action potential (V) during the cardiac cycle (bottom panel) of Endo and Epi isolated cardiomyocytes at varying preload (cell stretch 5 and 10% relative to the initial end-diastolic length).

FIGURE 3

Transmural gradient in the parameters of mouse cardiomyocyte contraction at slack end-diastolic sarcomere length (EDSL) in experiments [Endo: n = 8 (N = 3), Epi: n = 9 (N = 5)] and mathematical models. (A) Tension amplitude (F₀), (B) Time to peak contraction (T_max), (C) Time to 50% relaxation (TR₅₀). *p < 0.05 Endo vs. Epi, Student’s unpaired t test. N = number of animals, n = number of cells.

FIGURE 4

Length-dependent changes in passive, total, and active (total minus passive) tension of single mouse ventricular Endo and Epi cardiomyocytes in experiments [Endo: n = 8 (N = 3), Epi: n = 9 (N = 5)] and mathematical models. (A) End-diastolic force–length relation curves (EDFLR) from experimental (exp) data set and model simulations. (B) EDFLR slopes as the stiffness index in experiments and mathematical models. (C) End-systolic force–length relation curves (ESFLR) from experimental (exp) data set and model simulations. (D) ESFLR slopes and FSG index (the ratio of ESFLR and EDFLR slopes) in experiments and mathematical models. (E) Active force–length relation curves (F_activeLR) from experimental (exp) data set and model simulations. (F) F_activeLR slopes in experiments and mathematical models. p < 0.05 Endo vs. Epi, Student’s unpaired t test. N = number of animals, n = number of cells. ED, end-diastolic; ES, end-systolic.

FIGURE 5

Length-dependent changes in the time to peak contraction (T_max) and time to 50% relaxation (TR₅₀) of single mouse ventricular Endo and Epi cardiomyocytes in experiments [Endo: n = 8 (N = 3), Epi: n = 9 (N = 5)] and mathematical models. (A) T_max–length relation curves (T_maxLR) from experimental (exp) data set and model simulations. (B) T_maxLR slopes in experiments and mathematical models. (C) No correlation was found between TR₅₀ and changes in the end-diastolic cell length in experiments. *p < 0.05 Endo vs. Epi, Student’s unpaired t test. N = number of animals, n = number of cells. ED, end-diastolic.

FIGURE 6

Model predictions of length-dependent changes in the amplitude of Ca²⁺ transient (CaT Ampl), time from peak to 50% and 90% Ca²⁺ decay (CaT₅₀, CaT₉₀), and action potential duration at 90% repolarization (APD₉₀) in Endo and Epi cells. (A) CaAmplLR, CaT₅₀LR, Ca₉₀LR, and APD₉₀LR—Ca²⁺ transient amplitude–length relation, CaT₅₀–length relation, CaT₉₀–length relation, and APD₉₀–relation curves, respectively. (B) The slopes of CaAmplLR, CaT₅₀LR, CaT₉₀LR, and APD₉₀LR. ED, end-diastolic.