Mechanisms of Frank-Starling law of the heart and stretch activation in striated muscles may have a common molecular origin

Abstract

Vertebrate cardiac muscle generates progressively larger systolic force when the end diastolic chamber volume is increased, a property called the "Frank-Starling Law", or "length dependent activation (LDA)". In this mechanism a larger force develops when the sarcomere length (SL) increased, and the overlap between thick and thin filament decreases, indicating increased production of force per unit length of the overlap. To account for this phenomenon at the molecular level, we examined several hypotheses: as the muscle length is increased, (1) lattice spacing decreases, (2) Ca²⁺ sensitivity increases, (3) titin mediated rearrangement of myosin heads to facilitate actomyosin interaction, (4) increased SL activates cross-bridges (CBs) in the super relaxed state, (5) increased series stiffness at longer SL promotes larger elementary force/CB to account for LDA, and (6) stretch activation (SA) observed in insect muscles and LDA in vertebrate muscles may have similar mechanisms. SA is also known as delayed tension or oscillatory work, and universally observed among insect flight muscles, as well as in vertebrate skeletal and cardiac muscles. The sarcomere stiffness observed in relaxed muscles may significantly contributes to the mechanisms of LDA. In vertebrate striated muscles, the sarcomere stiffness is mainly caused by titin, a single filamentary protein spanning from Z-line to M-line and tightly associated with the myosin thick filament. In insect flight muscles, kettin connects Z-line and the thick filament to stabilize the sarcomere structure. In vertebrate cardiac muscles, titin plays a similar role, and may account for LDA and may constitute a molecular mechanism of Frank-Starling response.

Keywords: Delayed tension; Length dependent activation; Oscillatory work; Sarcomere length; Stiffness; Titin and kettin.

Fig. 1.. Model sarcomere and overlap between thick and thin filaments in cardiac muscle.

Based on Eqs. 1–3. The thin filament elongates with SL (Eq. 1). The thick filament stays approximately at the same length. The overlap decreases as SL is increased from 1.6 μm and extrapolates to 0 at SL=5 μm. Broken lines represent titin. Z=Z-line, M=M-line.

Fig. 2.. Delayed tension and oscillatory work.

(A) Delayed rise of tension (Eq. 5). Stretch occurs at ↑. β is the rate constant. (B) Oscillatory work (Eq. 6) plotted in the complex plane, where abscissa is the real axis (elastic modulus), and ordinate is the imaginary axis (viscous modulus). This plot is called Nyquist plot in muscle mechanics literature.

Fig. 3.. The time course of stretch activation.

A record of the time course of force development occurring in response to a step-length increase (at ↑, 1.5 nm/half sarcomere, which is about 0.12%) in rabbit psoas muscle fibers at 5°C during Ca²⁺ activation. Numbers 1–4 indicate the four phases of tension transients. Modified from Fig. 3 of (Davis et al., 2002), and reproduced with permission from the Biophysical Society.

Fig. 4.. Correlation between Step analysis (A) and sinusoidal analysis (B).

These are related by a linear transformation LT—LT’. (A) is the tension time course of step analysis: step increase in length by L₁ takes place at t=1 ms, and concomitant tension time course is plotted in log time axis. “1”, “2”, “3” and “4” indicates respective phases of step analysis (cf. Fig. 3). Plot of Eq. 7. (B) is a Nyquist plot of rabbit psoas (fast twitch) fibers with the elastic modulus plotted in the abscissa, and viscous modulus in the ordinate. Plot of Eq. 8. (C) represents mechanical equivalence of the fast twitch fibers. α, β, γ are apparent rate constants, and A, B, C are their respective magnitudes; H is a small constant. Ca²⁺ activation closes the switch. Y_∞=H+A−B+C, and represents stiffness extraporated to infinite frequency (∞). Modified and redrawn from Kawai and Brandt (1980).

Fig. 5.. Nyquist plots of Y(ω) of active fibers.

(A) rabbit psoas fast-twitch type IID fibers (Kawai & Brandt, 1980), (B) rabbit soleus slow-twitch fibers (Wang & Kawai, 1997), and (C) bovine ventricular cardiac muscle fibers (Lu et al., 2005); similar data in (de Tombe et al., 2010). Decade frequencies (0.13, 1, 11, 100Hz) are marked by ●. hf=high frequency end.

Fig. 6.. Simple CB models historically used.

(A) Two state model proposed by Abbott (1972). (B) Three state model proposed by Kawai & Halvorson (2007).

Fig. 7.. Nyqust plots of cross-linked fibers.

(A, C) Nyquist plots of rabbit psoas muscle fibers activated in solution of physiological ionic strength (200 mM), which contained (mM:) 6 Na₂Ca-EGTA, 5.3 Na₂Mg-ATP, 4.7 Na₄-ATP, 8 Pi, 15 phosphocreatine, 32 K propionate, 26 Na-propionate, 10 MOPS, 160 U/mL creatine kinase, pCa 4.86, and pH 7.00. Frequencies used are (clockwise) 0.25, 0.5, 1, 2, 3.1, 5, 7.5, 11, 17, 25, 35, 50, 70, 100, 135, 186, 250, 350 Hz. Decade frequencies (1, 11, 100 Hz) are shown in filled symbols. (A) is from a native fiber, (C) is from EDC cross-linked fiber. The cross-linked fibers were stretched before activation, and the stress on the fiber is shown in kPa in the corresponding plot. (B, D) Best fit of the data in (A) and (C) to Eq. 8. From (Tawada & Kawai, 1990).