oneM2M

Using the isometric force clamp described in methods, we were able to

subject myo1bb to a variety of loads resisting the motion of the power stroke. As

shown in panel B of figure 3.5, we observed dramatic increases in attachment

duration under loads of up to 4 pN in the presence of 50 µM ATP. A scatter plot of

data collected from 12 different myosins is shown in figure 3.6, where the actin

attachment lifetime is seen to increase in response to increasing force up to ~1.5 pN,

after which the lifetimes appeared to be force-independent. We assumed a model

for the rate of actomyo1b detachment that includes force-dependent and force-

independent pathways:

where kg is a force-dependent rate constant and ki is a force-independent rate

constant for actomyo1b dissociation. The force dependence of the detachment rate

104 Equation 10 i kT d F g i k e k k k F k = + = + ∗ − det 0 0 det( )

where kg0 is the rate of kg in the absence of force, ddet is the distance parameter (the

distance to the transition state of the force dependent step, or the distance over

which the force acts), F is force, k is the Boltzmann constant, and T is the

temperature. Because the attachment durations at each force are expected to be

exponentially distributed, we used bootstrap monte carlo simulations to generate

data for maximum likelihood estimations (MLEs) which were used to determine the

values and confidence limits of the parameters that describe the distribution of

attachment lifetimes.

From the MLEs, the best-fit value of kg0 = 1.6 s-1 (+0.5/-0.35 s-1) is

105

methods (1.8 s-1) (Lewis et al. 2006) which is expected to limit detachment from the

actin filament in the absence of force. The distance parameter, ddet = 12 nm (+1.6/-

3.0 nm), is extraordinarily large and distinguishes myo1b as an extremely strain-

sensitive molecular motor. The force independent rate of detachment ki,

representing the rate of detachment at forces > 1.5 pN, was found to be 0.021 s-1

(+0.007/-0.004 s-1). The errors of the fit parameters represent the 97% confidence

limits of 250 bootstrap Monte Carlo simulations of our data, calculated as described

107

To determine the predicted duty ratio as a function of force, we measured the

steady-state ATPase and transient rate of phosphate release from actomyo1b. The

actin dependence of both the ATPase rate and Pi release rate from actomyo1b is

shown in figure 3.7 (panel A). The solid line is a fit of the steady-state ATPase

rates to the Michaelis-Menten equation, yielding Vmax = 0.38 + 0.14 s-1 and KM =

310 + 160 µM. The overlayed graphs show that the steady state rate ATPase of

myo1b is dominated by rate-limiting phosphate release from actomyo1b.

A plot of the detachment rate as a function of force is shown in panel B of

figure 3.7. The blue dots represent the inverse averages of 20 consecutive points

(by force), where the black line is the fit of the model above to the raw data. The

inset shows the predicted duty ratio as a function of force, according to the equation:

Equation 11 duty ratio(F) = ) ( det F k k k att att +

where kdet(F) is our measured rate of detachment at force F (figure 3.7B), and katt is

the rate of entry into the strong binding states estimated by the rate of Pi release at

saturating actin concentration (figure 3.7A). Myo1b, therefore, transitions from a

low duty ratio motor to a high duty ratio motor when working against loads greater

108

3.1.4 ADP release is the predominant strain-sensitive transition in the myo1b biochemical cycle

The two biochemical steps that could be modified to increase the lifetime of

the strongly bound state in the myo1b ATPase cycle are inhibition of ADP release

from the AM·ADP state or inhibition of ATP binding to the rigor complex. To

distinguish between these two potential biochemical steps, we investigated the

effect of force on the lifetimes of the working stroke substeps. Interactions acquired

in the presence of 50 µM ATP with the isometric force clamp (see methods)

engaged were binned by force immediately prior to detachment into groups

corresponding to all events between 0 to 0.125, 0.125 to 0.25, 0.250 to 0.50, 0.500

to 0.750, 0.75 to 1.0, 1.0 to 2.0, and 2.0 – 4.0 pN. We ensemble averaged the force

binned events according to the end points of the interactions and observed transient

increases in force in the ~500ms immediately preceding detachment (figure 3.8).

Single exponential fits of the ensemble averaged ends yielded rates that decreased

with increasing force, and the force dependence of the rates was fit to the equation

Equation 12 kT dend F end end F k e k • − = 0 ) (

where kend0 is the rate of the time course in the absence of force and dend is the

distance parameter of the substep.

The best fit rate of kend0 (22 + 2.5 s-1) is in agreement with the rate of ATP

binding at 50 µM ATP as determined by the fit to the end-time averages of data

110

Taken together these data suggest that the transient increases in force describe the

lifetime of the same transition (ATP binding and detachment) as the unloaded data.

The rate of kend decreases with force, however the best fit value for dend (2.5 + 0.83 s- 1_{) is much smaller than d}

det. Therefore the predominant force sensitive transition

most likely responsible for the large value for ddet is not restriction of ATP binding

to the AM(rigor) state, but rather inhibition of ADP release. Additionally, we

observed decreases in force immediately prior to the rapid increases in force

immediately prior to detachment in expanded ensemble averages (figure 3.9).

These decreases in force may represent fluctuations due to mechanical vibrations of

the stage prior to detachment, a potential artifact corrected for in later experiments

(see discussion).