Calibration of trapping force and response function of optical tweezers in viscoelastic media

Abstract

At present, a major obstacle to the quantitative application of optical tweezers as a force spectrometer in living cells is the lack of a method to calibrate the tweezers. Calibration with approved methods such as the power spectrum method (Berg-Sorensen and Flyvbjerg 2004 Rev. Sci. Instrum. 75 594; Berg-Sorensen et al 2006 Rev. Sci. Instrum. 77 063106) is not possible as the viscoelastic properties of the bio-active medium are a priori unknown. Here, we present an approach that neither requires explicit assumptions about the size of the trapped particle nor about the viscoelastic properties of the medium. Instead, the interaction between the medium and the trapped particle is described in a general manner, through velocity and acceleration memory. Our method is applicable to general, at least locally homogeneous, viscoelastic media. The procedure combines active and passive approaches by the application of Onsager's regression hypothesis. It allows extraction of the trapping stiffness κ of the optical tweezers and of the response function χ(ω), which is the frequency-dependent effective inverse spring constant of the system. Finally, information about the viscoelastic properties of the medium may also be found. To test the method, we have performed simulations in which the system is driven sinusoidally. These simulations serve as an example of how to deal with real experimental data. For realistic parameters, we calibrate the trap stiffness κ with ~1% stochastic error.