Active-passive calibration of optical tweezers in viscoelastic media

Abstract

In order to use optical tweezers as a force measuring tool inside a viscoelastic medium such as the cytoplasm of a living cell, it is crucial to perform an exact force calibration within the complex medium. This is a nontrivial task, as many of the physical characteristics of the medium and probe, e.g., viscosity, elasticity, shape, and density, are often unknown. Here, we suggest how to calibrate single beam optical tweezers in a complex viscoelastic environment. At the same time, we determine viscoelastic characteristics such as friction retardation spectrum and elastic moduli of the medium. We apply and test a method suggested ͓M. Fischer and K. Berg-Sørensen, J. Opt. A, Pure Appl. Opt. 9, S239 ͑2007͔͒, a method which combines passive and active measurements. The method is demonstrated in a simple viscous medium, water, and in a solution of entangled F-actin without cross-linkers.

Force measurements with optical tweezers inside living cells

“…However, whether this method could still be accurately used inside a cell is unclear as the trapping beam will have go through a packed cytoplasm, which contains plenty of additional scattering structures, and cross the lipid membrane before it can be captured and analyzed. Following this rationale, we validated the light momentum method by comparing the value of the constant α determined from first principles (equation 2) with calibration experiments carried out in the cytoplasm by the active-passive method 8,9 , in two different cell types: plant and mammalian cells.…”

“…The active-passive calibration method (also known as the fluctuation-dissipation theorem method) was specifically developed in order to measure the stiffness of an optical trap κ, the positional calibration factor β, and additional information about the rheological properties of a viscoelastic medium 8,9 . The method considers a generalized Langevin equation that incorporates viscoelastic friction γ 1 and hydrodynamic memory γ 2 :…”

“…Some attempts to measure forces in cells have relied on extrapolations of a prior calibration done on purified vesicles, in a buffer that reproduced the index of refraction of the cytoplasm 4 . Methods better grounded in theory, specifically targeted to calibrate optical traps in a viscoelastic medium such as the cytoplasm are few 8,9 and only recently have started to be implemented and validated.…”

Multidepth, multiparticle tracking for active microrheology using a smart camera

“…3 Active methods are also important in instrument calibration: when working with viscoelastic media of unknown properties, such as the cytoplasm of a living cell, only by a combination of active and passive measurements can in situ force calibration of optical tweezers be performed. 4,5 Active calibration and viscosity measurements can also be used for purely viscous media, and optical trap calibration to a precision of 3% has been reported using an active phase-shift-based method. 6 To use active microrheology it is typically necessary to perform synchronized measurements of an external driving motion and the response of an optically trapped probe particle, in order to compare the two.…”

“…1,2 In the case where a piezoelectric stage is used, the driving motion measurement is derived from feedback signals of the sample stage. 5 The separate driving and bead position measurements are then captured for computer processing via a data acquisition card, or compared in realtime using a lock-in amplifier. 6,7 These techniques to measure the driving motion present a number of challenges.…”