Flexural Rigidity Measurements of Biopolymers Using Gliding Assays

Summary

A method to measure the persistence length or flexural rigidity of biopolymers is described. The method uses a kinesin-driven microtubule gliding assay to experimentally determine the persistence length of individual microtubules and is adaptable to actin-based gliding assays.

Abstract

Microtubules are cytoskeletal polymers which play a role in cell division, cell mechanics, and intracellular transport. Each of these functions requires microtubules that are stiff and straight enough to span a significant fraction of the cell diameter. As a result, the microtubule persistence length, a measure of stiffness, has been actively studied for the past two decades¹. Nonetheless, open questions remain: short microtubules are 10-50 times less stiff than long microtubules^2-4, and even long microtubules have measured persistence lengths which vary by an order of magnitude^5-9.

Here, we present a method to measure microtubule persistence length. The method is based on a kinesin-driven microtubule gliding assay¹⁰. By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores attached to the microtubule, the gliding trajectories of single microtubules are tracked with nanometer-level precision. The persistence length of the trajectories is the same as the persistence length of the microtubule under the conditions used¹¹. An automated tracking routine is used to create microtubule trajectories from fluorophores attached to individual microtubules, and the persistence length of this trajectory is calculated using routines written in IDL.

This technique is rapidly implementable, and capable of measuring the persistence length of 100 microtubules in one day of experimentation. The method can be extended to measure persistence length under a variety of conditions, including persistence length as a function of length along microtubules. Moreover, the analysis routines used can be extended to myosin-based acting gliding assays, to measure the persistence length of actin filaments as well.

Introduction

The cytoskeleton, a network of biopolymers found in most eukaryotic cells, plays a role in cellular organization, intracellular transport, and cell mechanics. The mechanical characteristics of the biopolymers of the cytoskeleton (primarily actin and microtubules) play a significant role in determining the mechanical characteristics of the cell as a whole¹². Since whole cell mechanics can characterize healthy and diseased cells^13,14 and is involved in cellular motility¹⁵, the mechanical properties of the underlying cytoskeletal components have been an active area of study for the past two decades¹.

The flexibility (or stiffness) of biopolymers is characterized by the persistence length, the length of polymer which bends by approximately one radian under thermal fluctuations at ambient temperature. A number of techniques have been developed to measure persistence length¹⁶, for example active techniques which involve bending the polymer using hydrodynamic flow, optical traps, or electric fields^4,17,18 , and passive techniques which measure the fluctuations of free polymers in solution^5,6 . The active measurements, however, require specialized setups to implement known forces on the micrometer scale, and the free-fluctuation measurements can be challenging due to diffusion out of the plane of focus of the microscope used.

In this article, we describe a complementary, passive, technique to measure the persistence length of microtubules, a cytoskeletal polymer. The technique involves gliding assays, which ensure that the polymer always remains in the focal plane¹⁹. Moreover, it involves tracking single fluorophores attached permanently to the polymer of interest, so that specific locations along the polymer are well characterized.

A cartoon of the method is shown in Figure 1. Kinesin moves specifically toward the + end of microtubules, so the microtubules in a gliding assay are propelled unidirectionally. The leading end of the microtubule, beyond the last kinesin attached, is free to fluctuate under the thermal forces of the surrounding solution. As the microtubule is propelled forward, the end fluctuates until binding to a new kinesin molecule further along the glass slide freezes in a given fluctuation. Because kinesin attaches microtubules very strongly, the microtubule is constrained to follow the path of the leading end. Therefore, the statistical fluctuations frozen into the microtubule trajectory are the same as the statistical fluctuations of the free end of microtubules¹¹, and can therefore be used to calculate the persistence length according to²⁰

where l_p is the persistence length of the microtubule, θ_s is the angle between tangents to the trajectory separated by a contour length s, and <> denotes an average over all pairs of positions separated by a contour length s.

The gliding assay itself uses kinesin biotinylated at the coiled-coil²¹ specifically bound to the glass slide via a streptavidin-biotin linkage. This attachment ensures that the motor domains are free to bind to and propel microtubules. In order to follow microtubule trajectories, microtubules are sparsely labeled with organic fluorophores^22,23 – the labels must be sparse enough that single fluorophores are resolvable using single molecule fluorescence microscopy. Single fluorophores are tracked using image analysis routines written in IDL. The trajectories of each fluorophore bound to a given microtubule are combined into a composite microtubule trajectory automatically²⁴. The tangent angles θ to each point along a trajectory are calculated; from these tangent angles the <cosθ_s> value is calculated for each contour length s. Finally, these data are fit to Eq. 1 in order to extract a persistence length for a given microtubule, or for many microtubules in the same gliding assay.

The method is robust enough to work with microtubules prepared in a wide variety of conditions (with different stabilizing agents or other small molecules bound to the microtubule, with bound microtubule associated proteins (MAPs), or with a variety of viscous solutions). In our lab, the technique has been used to characterize the persistence length of microtubules as a function of length along the microtubules and microtubules with different stabilizing agents. The main restriction is that the microtubules must still support kinesin motility. Since kinesin is a robust motor enzyme, this is a fairly loose restriction. By replacing microtubules with actin and kinesin with a myosin family enzyme, the persistence length of actin can be measured using the same technique.

Protocol

1. Microtubule Gliding Assay Stock Solutions Prepare ahead of gliding assay. Polymerize 0.5 mg microtubules sparsely labeled with bright organic fluorophore 22. The target label concentration is 1 fluorophore per micrometer of microtubule, or a labeling density of approximately 1 fluorophore per 1,500 tubulin dimers. Store at room temperature, light protected with aluminum, foil for up to two weeks. Purify biotin-kinesin21 at approximatel…

Representative Results

A snapshot from a gliding assay is shown in Figure 2. A good microtubule density is 1-10 microtubules per field of view; substantially more will result in mistracking as microtubules cross each other. A plot of the 11 microtubule trajectories from the gliding assay in Figure 2 is shown in Figure 3. Typical trajectories are 10 to 30 μm long; some trajectories have gaps where one microtubule crosses another. These trajectories may be discarded from analysis….

Discussion

Persistence length measurements are a good characterization of the mechanical properties of individual biopolymers. In this article, we have described a method of measuring the persistence length of microtubules. As noted in the introduction, this method is readily extended to examining microtubule mechanical properties in a variety of conditions simply by varying the reagents, temperature, or viscosity in the final step of the gliding assay, 3.9, or by polymerizing microtubules, step 1.1, under different condition…

Materials

			Reagents
imidazole	Sigma-Aldrich	I2399
potassium chloride	Sigma-Aldrich	P9541
magnesium chloride	Sigma-Aldrich	M8266
EGTA	Sigma-Aldrich	E3889
BSA	Calbiochem	126615
biotinylated BSA	Thermo Scientific	29130
α-casein	Sigma-Aldrich	C6780
streptavidin	Thermo Scientific	21125
dithiothreitol	Sigma-Aldrich	D0632
paclitaxel	LC Laboratories	P-9600
glucose oxidase	Sigma-Aldrich	G2133
catalase	Sigma-Aldrich	C100
glucose	Sigma-Aldrich	G8270
ATP	Sigma-Aldrich	A2383
2-mercaptoethanol	Sigma-Aldrich	M3148	Toxic. Buy small amount.
24X60 mm No. 1 1/2 cover glass	VWR	48393-252
22X22 mm No. 1 cover glass	Gold Seal	3306
High Vacuum Grease	Dow-Corning	NA
			Equipment
TIRF microscope	many	NA	The TIRF microscope used in this method was home-made.
IDL (software)	Exelis	NA	Could substitute MATLAB, ImageJ, or other image analysis software.