Actin concentration is also unknown, partly due

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).

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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.