Mechanism of tension generation in muscle: an analysis of the forward and reverse rate constants

Abstract

Tension generation in muscle occurs during the attached phase of the ATP-powered cyclic interaction of myosin heads with thin filaments. The transient nature of tension-generating intermediates and the complexity of the mechanochemical cross-bridge cycle have impeded a quantitative description of tension generation. Recent experiments performed under special conditions yielded a sigmoidal dependence of fiber tension on temperature--a unique case that simplifies the system to a two-state transition. We have applied this two-state analysis to kinetic data obtained from biexponential laser temperature-jump tension transients. Here we present the forward and reverse rate constants for de novo tension generation derived from analysis of the kinetics of the fast laser temperature-jump phase tau(2) (equivalent of the length-jump phase 2(slow)). The slow phase tau(3) is temperature-independent indicating coupling to rather than a direct role in, de novo tension generation. Increasing temperature accelerates the forward, and slows the reverse, rate constant for the creation of the tension-generating state. Arrhenius behavior of the forward and anti-Arrhenius behavior of the reverse rate constant is a kinetic signature of multistate multipathway protein-folding reactions. We conclude that locally unfolded tertiary and/or secondary structure of the actomyosin cross-bridge mediates the power stroke.

FIGURE 1

Temperature dependence of isometric tension analyzed as a two-state transition. The continuous line represents a nonlinear least-squares fit (1) to a single-step isomerization between pre-force-generating and force-generating states. Fitted parameters to the van' t Hoff equation were ΔH^o of 116.1 ± 13.6 kJ mol⁻¹, T_m of 9.9 ± 0.6°C and maximum tension 184 ± 5 kPa and R = 0.984. The entropy change (ΔS^o) was 410.6 ± 48.1 J K⁻¹ mol⁻¹. Data were obtained from Fig. 4 a of Ranatunga (23).

FIGURE 2

Laser T-jump tension transient. A single, skinned, maximally Ca²⁺ activated, rabbit psoas fiber contracting isometrically was heated by 5°C in <1 μs to a postjump temperature of 11°C at the arrow. Nonlinear least-squares fit to the sum of three exponentials was applied to the these data (10). Resolved fits to phases, τ₁, τ₂, and τ₃, are labeled and the overall fit (the sum of their amplitudes) is drawn as a solid line through shaded raw data. Adapted from Davis and Rodgers (11).

FIGURE 3

Temperature dependencies of the amplitude of τ₂. Bell-shaped, two-state dependence of amplitudes (ΔP_o/ΔT) of τ₂ (orange) and τ₃ (green) on prejump temperature. Comparison of T_m values obtained from Gaussian fits (1°C datum excluded) to the amplitudes of τ₂ (10.6 ± 0.8°C) and τ₃ (10.0 ± 1.1°C) with the first derivative (δP_o/ δT, black) (9.9° ± 0.6°C) of the van' t Hoff fit to fiber tension (Fig. 1) indicates a common source of signal. Error bars are mean ± SE.

FIGURE 4

Temperature dependencies of the rates of τ₂ and τ₃. Arrhenius plot of the observed rate constants for phases τ₂ (orange) and τ₃ (green) versus postjump temperature. The temperature-independent rate constant of τ₃ (green) excludes this slow transition (12.6 ± 0.6 s⁻¹) from de novo tension generation (1,16). Error bars are mean ± SE. Adapted from Davis and Rodgers (11).

FIGURE 5

Arrhenius plots of the forward and reverse rate constants for tension generation. The rate of k₁ (red) increases with temperature while the rate of k₋₁ (blue) decreases (anti-Arrhenius behavior). The sum of the fits to the forward and reverse rate constants (orange) are drawn through 1/τ₂ values from Fig. 4. The forward and reverse rate constants for tension generation were calculated from the thermodynamic parameters governing the temperature dependence of fiber isometric tension (Fig. 1), and τ₂ values (Fig. 4). Rates for k₁ and k₋₁ were 168 and 30.3 s⁻¹ (20°C) and 1728 and 14.1 s⁻¹ (40°C), respectively. Activation parameters for k₁ were ΔH^‡ = 88.3 kJ mol⁻¹, ΔS^‡ = 98.9 J mol⁻¹ K⁻¹, and R = 0.993; for k₋₁ ΔH^‡ = −28.9 kJ mol⁻¹, ΔS^‡ = −315.2 J mol⁻¹ K⁻¹, and R = 0.850.