**2.3. Optical cell stretcher**

The optical stretcher is a non-destructive tool that can be used to quantify cell deformation. The optical stretcher was first developed by Guck et al. [23] based on the principle that a dielectric object, when placed between two opposed and non-focused laser beams, experiences a net force. The cell is suspended or "optically trapped" and is stable only if the total force is zero. Additive surface forces are capable of stretching an object, such as a cell, along the beam axes [11]. Both the exerted force and corresponding time-dependent deformations can be quantified. An optical stretcher allows the measurement of cell mechanics without physical contact, but the intense laser exposure tends to heat cells [24]. Recently, however, it has been demonstrated that heating does not affect cell cytoskeletal structure, proliferation, motility, or viability [25]. Another potential limitation is the complexity of the force profiles, which require extensive theoretical modeling. Nonetheless, the optical stretcher has proven to be an effective way of measuring the contribution of cytoskeletal filaments to cell viscoelasticity since single suspended cells are probed as welldefined viscoelastic objects [25].

## **2.4. Optical tweezers**

128 Viscoelasticity – From Theory to Biological Applications

**2.2. Microplate rheometry** 

measure viscoelasticity.

**2.3. Optical cell stretcher** 

micropipette. The measurement of suction pressure, location of the cell and movement of its edge in the micropipette can be used to calculate the viscous and elastic parameters [7].

There are several draw-backs associated with this method since quantitative measurement of cell stiffness relies heavily on theoretical models [6]. The most recent application of

Over the past decade there has been much progress in the study of rheological behaviour for single cells, including the development of several models which explain the mechanical properties of cytoskeletal networks. A microplate rheometer, invented by Thoumine and Ott in 1997 [8], consists of two parallel microplates that support cell adhesion and spreading. The plates can be made flexible and in some cases are coated with an adhesive material. A whole cell is stretched or compressed between the two plates while the flexible microplate is used as a nN-scale force sensor. Integration with an inverted microscope allows cells that are being manipulated to be directly observed. Several adaptations to the instrumentation allow measurement of creep function, area of expansion modulus, contraction forces of single cells, adhesive interactions and stress-strain responses. The latter can be used to

The force applied to the cell is directly proportional to the relative stiffness of the microplate, hence measurement of cell deformation offers valuable information on cell mechanical properties. Measureable forces range between 1 nN – 1 μN, and several manipulation modes are possible, including compression, traction, aspiration and adhesive rupture. Following their invention, microplate rheometers have been improved by a number of scientists. The behaviour of cells in response to compression, traction, aspiration or adhesion, for which elastic, viscous and contractile regimes can be distinguished based on time scale, can be used to calculate the viscoelastic modulus of living cells. The instrument has been modified for probing single layers of cells at once using the novel cell monolayer rheology (CMR) technique, making possible harmonic oscillation experiments and step

The optical stretcher is a non-destructive tool that can be used to quantify cell deformation. The optical stretcher was first developed by Guck et al. [23] based on the principle that a dielectric object, when placed between two opposed and non-focused laser beams, experiences a net force. The cell is suspended or "optically trapped" and is stable only if the total force is zero. Additive surface forces are capable of stretching an object, such as a cell, along the beam axes [11]. Both the exerted force and corresponding time-dependent deformations can be quantified. An optical stretcher allows the measurement of cell mechanics without physical contact, but the intense laser exposure tends to heat cells [24]. Recently, however, it has been demonstrated that heating does not affect cell cytoskeletal

shear or step stress experiments which reveal different viscoelastic regimes [9].

micropipette aspiration is to capture and hold cells for manipulation [7].

Optical tweezers can be used to capture tiny dielectric particles with a highly focused laser beam [17]. The movement of dielectric particles can be controlled with two main optical forces. The scattering force acts along the direction of beam propagation, while the electric field induces a dipole in the dielectric particles, producing an electric field gradient that pulls particles towards the focus. When the gradient force dominates, the dielectric particles can be confined in a stable three-dimensional optical trap. The trap is then moved to manipulate the bead, so the applied force and resultant particle displacement are interpreted in terms of mechanical response [26]. To obtain viscoelastic information, an oscillatory force is applied to the dielectric bead by oscillating the laser position with a movable external mirror. The resultant amplitude of the bead motion and the phase shift are interpreted in terms of viscoelastic response. The experimental data from optical tweezers can only be used to study the viscoelastic responses at low force in the linear regime [18]. Local heating and phototoxicity ("opticution" as coined by Block) can result from the intense laser powers required to trap biological samples.

## **2.5. Magnetic probes**

Another way to explore the viscoelasticity of cells involves manipulation of their movement through an externally applied magnetic field. The earliest application of this technique was pioneered by Freundlich and other researchers [12,27], in which magnetic particles were embedded in the material of interest (*e.g.* cells). The viscoelasticity can then be probed using magnetic tweezers or magnetic twisting. The ability to functionalize magnetic colloidal beads allows for their specific localization within the cell [28, 29].

The magnetic tweezer technique involves the manipulation of a super paramagnetic bead with an applied magnetic field generated by four pairs of soft ferromagnetic cores, each wound with a separate field coil arranged at special angles [30]. The movement of the bead is monitored by its induced magnetic dipole as it interacts with the field gradient of the strong magnet to which it is exposed. The corresponding displacement of the magnetic bead is used to measure cell properties. The movement of magnetic beads can also be controlled, albeit only in one direction, by a strong magnetic field gradient arising from electromagnets generated by axis-symmetrically arranged magnetic coils on a sharp iron tip [31]. Multiple pairs of electromagnetic tips are required for more complex movements of the magnetic bead, which for these experiments are smaller than the size of

the cell, and thus are limited to probing the viscoelastic response of a microenvironment rather than the whole cell.

Viscoelasticity in Biological Systems: A Special Focus on Microbes 131

 ൌ ൈ (1)

**Figure 2.** A schematic representation of the atomic force microscope. Printed with permission

sample is deformed depends on its viscoelastic properties.

Cantilever deflection can be converted to force using Hook's law:

where k is the cantilever spring constant, and d is cantilever deflection.

AFM offers the further advantage of being able to correlate sample topography with mechanical properties across the sample surface using indentation forces as small as 10 pN. With force spectroscopy (single point) or force mapping (multiple points), the tip approaches the sample, indents the sample and then retracts at each point, generating a force versus distance curve at a specific point on the cell surface (Figure 3). Cantilever deflection as a function of distance of the tip from the cell surface is initially represented by photodiode voltage as function of piezo displacement. This voltage is then converted to cantilever deflection and finally a force or indentation distance. The extent to which the

Force spectroscopy and mapping are used to quantify the mechanical behavior of the cell with the help of theoretical models. The indentation of the biological sample can be determined by subtracting the difference between cantilever deflection on hard surfaces and

(Springer, USA).

Twisting magnetometry [32] and the more recently developed magnetic twisting cytometry [33] can also be used to measure the movement of magnetic beads, which usually consist of colloidal metal or polycrystalline iron oxide. The cell is deformed under a twisting magnetic field that is applied perpendicularly to the initial magnetic field once it has been turned off [34]. The change in the magnetic field direction causes reorientation of the magnetic bead towards the twisting field, and once both are turned off, the rate of magnetic bead rotation and the amount of recoil are measured to interpret local viscoelasticity.
