Actin filaments (F-actin) are polymers of globular free

monomers (G-actin). Actin polymerisation generates mechanical force from the difference

in chemical potential between a free G-actin and that same actin subunit

embedded in the filament (Footer, Kerssemakers, Theriot, & Dogterom, 2007). When a biological load is

close to a polymerising actin filament, the filament is thought to generate

pushing forces via a ratcheting mechanism. Filament growth is predicted to slow

and eventually stall as the applied force on the end of the filament approaches

the value determined by

where kB is Boltzmann’s constant, T is the

absolute temperature, ? is the elongation distance for addition of a single

subunit (2.7 nm for actin), C is the concentration of monomers in solution, and

Ccrit is the critical concentration for polymerization (equivalent

to koff/kon for elongation at a single filament end).

The total actin concentration in cells is typically is ~100

?M, of which 10-100 ?M is G-actin (Podolski & Steck, 1990). However, it is unknown what

percentage of this G-actin pool is available for polymerisation. The critical

concentration is also unknown, partly due to the involvement of actin-binding

proteins. Using the most generous assumptions that 100 % of the G-actin in a

cell is bound to ATP and able to polymerise, and that the effective in vivo

critical concentration is the same as the critical concentration for pure

ATP-actin in standard polymerisation buffer at the end of a filament (0.12 ?M)(Pollard, 1986), the maximum theoretical

force that could be generated in a cell by elongation of a single filament is ~

9pN.

Work is defined as

Thus, the maximum work that could be done is

(4) Optical trapping.

My Stokes drag calibration gives trap stiffness = 0.05 pN nm-1. What

will be the RMS deviation of position of a 0.5 ?m bead in this trap?

The root-mean-square (RMS) deviation is given by

where is the Boltzmann constant, T is the absolute

temperature, and is the trap stiffness. Assuming a

standard temperature of 298.15 K, the RMS deviation will be 9 nm. The bead size

is not required for this calculation since it has already been used in the

Stokes drag calibration.

(5) Calculate the

free energy (energy available to to do work) released by the hydrolysis of 1

mole of ATP:

The free energy released by the hydrolysis of 1 mole of ATP

is

where is the standard Gibbs free energy of formation

of ADP and from 1 mole of ATP, is the Boltzmann constant, and T is the

absolute temperature. The Gibbs free energy change is dependent on the

concentrations of ATP, ADP and .

Under ‘standard’

conditions, where ATP, ADP and are all at 1 M, the Gibbs free energy of ATP

hydrolysis ranges from -28 to -34 kJmol-1, depending on the

concentration of Mg2+, which aids in ATP stabilisation (Rosing

& Slater, 1972). Physiological conditions are far from

this standard, and vary greatly between organisms. Using a of -37.6 kJmol-1 (“How

much energy is released in ATP hydrolysis?,” n.d.), and conditions in human

resting muscle (where ATP,ADP, and are 8 mM, 9 ,

and 4mM respectively), the free energy released by the hydrolysis of 1 mole of

ATP is -68 kJmol-1.