Phosphate and ADP differently inhibit coordinated smooth muscle myosin groups

Abstract

Actin filaments propelled in vitro by groups of skeletal muscle myosin motors exhibit distinct phases of active sliding or arrest, whose occurrence depends on actin length (L) within a range of up to 1.0 μm. Smooth muscle myosin filaments are exponentially distributed with ≈150 nm average length in vivo--suggesting relevance of the L-dependence of myosin group kinetics. Here, we found L-dependent actin arrest and sliding in in vitro motility assays of smooth muscle myosin. We perturbed individual myosin kinetics with varying, physiological concentrations of phosphate (Pi, release associated with main power stroke) and adenosine diphosphate (ADP, release associated with minor mechanical step). Adenosine triphosphate was kept constant at physiological concentration. Increasing [Pi] lowered the fraction of time for which actin was actively sliding, reflected in reduced average sliding velocity (ν) and motile fraction (fmot, fraction of time that filaments are moving); increasing [ADP] increased the fraction of time actively sliding and reduced the velocity while sliding, reflected in reduced ν and increased fmot. We introduced specific Pi and ADP effects on individual myosin kinetics into our recently developed mathematical model of actin propulsion by myosin groups. Simulations matched our experimental observations and described the inhibition of myosin group kinetics. At low [Pi] and [ADP], actin arrest and sliding were reflected by two distinct chemical states of the myosin group. Upon [Pi] increase, the probability of the active state decreased; upon [ADP] increase, the probability of the active state increased, but the active state became increasingly similar to the arrested state.

Figure 1

Myosin group size-dependent regimes in actin sliding behavior. Short actin filaments, to which only a small number of myosins can bind simultaneously, are permanently arrested to the motility surface. Long actin filaments, to which a large number of myosins can bind simultaneously, exhibit continuous sliding at maximal velocity (ν_max). Intermediate length filaments alternate between arrest and sliding, leading to stop-and-go behavior. The small displays on top show actin (gray) with attached myosin motors (red), which in turn are attached to a rigid motility surface (black) (note that myosin number is not accurate). To see this figure in color, go online.

Figure 2

Inhibition of in vitro actin propulsion by P_i and ADP. Each graph shows the probability distribution (p(V_f2f)) of instantaneous velocities (V_f2f) within sliding filament length (L) windows for increasing [P_i] (A–F) or [ADP] (G–L). (Shading) Values of p(V_f2f), grayscale bars on the right of (F) and (L). Only filaments longer than 0.3 μm were included in the analysis. Seventy equally spaced sliding L windows were applied within a range of 0–3 μm, window width 0.5 μm. Empirical probability densities were created from individual V_f2f values using a Gaussian kernel with bandwidth 0.08 μm/s and positive support.

Figure 3

Average sliding velocity and motile fraction of intermediate length actin filaments. (A) Average sliding velocity (ν) of intermediate L actin filaments (L between 0.3 and 0.8 μm) for increasing [P_i]. (B) Motile fraction (f_mot) of intermediate L actin filaments for increasing [P_i]. (C) ν/f_mot ratio for increasing [P_i]. (D–F) Same as (A)–(C), but for increasing [ADP]. Mean ± SE, n = 10 flow-through chambers per condition, ^∗: p < 0.05.

Figure 4

Individual myosin kinetic scheme and effects of phosphate and ADP. (A) Individual myosin mechanochemical cycle. (Large circles) Long-lived chemical states; (small circle) short-lived reaction intermediate where ADP has been released and ATP is not yet bound (rigor state). (Arrows) Kinetic transitions; distances in nanometers indicate myosin step lengths for strain-dependent transitions. (B) Increasing [P_i] decreases the main power-stroke unstrained transition rate. (C) Increasing [ADP] reveals the influence of another short-lived reaction intermediate (small  solid circle), separating a strain-dependent transition and an [ADP]-inhibited transition step. (D) Increasing [ADP] also inhibits the slow, strain-independent ADP release pathway, which runs in parallel to the main ADP release pathway (dashed arrow).

Figure 5

Simulated in vitro actin propulsion. Each graph shows the V_f2f probability distributions (p(V_f2f)) for different numbers of mechanically coupled myosin binding sites (N) for increasing [P_i] (A–F) or increasing [ADP] (G–L). (Shading) Values of p(V_f2f), grayscale bars on the right of (F) and (L). The value V_f2f is pooled from 20 simulations per N, individual simulations run up to 30 s, first 24 s removed to prevent the influence of initial values. Same time resolution and density estimation parameters as for videos recorded from experiment.

Figure 6

Simulated average sliding velocity and motile fraction in intermediate length actin filaments. (A) Average sliding velocity (ν) for increasing [P_i]. (B) Motile fraction (f_mot) for increasing [P_i]. (C) ν/f_mot ratio for increasing [P_i]. (D–F) Same as (A)–(C), but for increasing [ADP]. Mean ± SE, n = 200 simulations per condition, total simulated time 30 s; to prevent influence of initial values, the first 24 s were removed.

Figure 7

Simulated myosin group kinetics with added P_i and ADP. (Arrow) For a given chemical configuration (n_pre, n_post), the emanating arrow points toward the, on average, next chemical configuration after this one (chemical transitions occur individually). (Shaded circles) Area proportional to the fraction of simulation time spent in a specific configuration. (A–C) Simulations for increasing [P_i]. (D–F) Simulations for increasing [ADP]. 150 individual simulations per condition, individual simulations run up to 30 s; first 9 s removed to prevent the influence of initial values.