Calibration of optical traps by dual trapping of one bead

In situ calibration of position detection in an optical trap for active microrheology in viscous materials

In optical trapping, accurate determination of forces requires calibration of the position sensitivity relating displacements to the detector readout via the V-nm conversion factor (β). Inaccuracies in measured trap stiffness (k) and dependent calculations of forces and material properties occur if β is assumed to be constant in optically heterogeneous materials such as tissue, necessitating calibration at each probe. For solid-like samples in which probes are securely positioned, calibration can be achieved by moving the sample with a nanopositioning stage and stepping the probe through the detection beam. However, this method may be applied to samples only under select circumstances. Here, we introduce a simple method to find β in any material by steering the detection laser beam while the probe is trapped. We demonstrate the approach in the yolk of living Danio rerio (zebrafish) embryos and measure the viscoelastic properties over an order of magnitude of stress-strain amplitude.

Measurement of Elastic Modulus of Collagen Type I Single Fiber

Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle/fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.