Estimation of flexural rigidity of proteinaceous filaments like microtubules and Actin.

Now the inverse Fourier transform of equation 1 gives the amplitude of the modes,

Which are estimated by the following approximate relation:

(32.9)

where

(32.10)

The experimental estimation of the amplitude of the different modes are however not free of error, in fact errors creep in due to poor resolution of the microscope and the video recording system. As a result the measured position of a point deviates from its actual position by a random distance . This error, which varies from filament to filament depending on the image quality adds directly to the true variance of the amplitude of each mode and thus to the estimate of the flexural rigidity EI. For small amplitude fluctuations, the measurement error  that contributes to  remains independent of  itself. Then we can estimate it with