With accuracy down to single piconewtons (10–12 N), optical traps measure forces exerted on microscopic objects without mechanically touching them. When an object moves inside the trap, the intensity maximum of the transmitted light measured at the back focal plane (BFP) of the condenser optics is shifted proportionally. As shown in Figure 1c, a quadrant photodiode (QPD) is used to detect this shift and, via standardized calibration routines, the signal can be interpreted to determine the force that causes the movement. The detectable force range covers electrostatic interactions, molecular binding, conformational changes and dynamics, all at the single-molecule level.
Figure 1 – a) and b) The laser beam used for trapping has a 2-D Gaussian intensity distribution with an intensity gradient in the x- and y-plane (perpendicular to the beam axis). A gradient in the z-direction is established using strong focusing optics. Light that enters a particle with a higher refractive index than the surrounding medium is refracted toward the particle center, i.e., it changes direction. This change comes along with a change in momentum of the photon, which is transferred onto the particle due to physical laws of conservation. In regions with higher intensity (beam 1 in [a]), the momentum transfer which equals the force F1 in (b) is higher than in the periphery (beam 2), driving the particle toward the center of the beam focus with the highest intensity. These gradient forces establish harmonic potentials (qualitatively plotted in (a) that hold the particle in a stable position. In addition, the scattering of light at the surface pushes the particle in the direction of light propagation with the force Fscat (scattering force). Only if the gradient force exceeds the scattering force, the net force Fnet points to the beam center and trapping is possible. For small displacements, Fnet is proportional to the relative displacement of the particle against the beam center. c) This particle displacement changes the intensity distribution of the transmitted light. The shift of the intensity maximum (red circle) can be detected with a quadrant photodiode (QPD) that is placed in the back focal plane of the condenser optics. After calibration, the signal of the QPD can be converted into units of displacement (nm) and force (pN).State-of-the art optical tweezers system
Figure 2 – NanoTracker 2 integrated optical tweezers system. The optics unit in the center contains the laser and optical elements for beam deflection and alignment. The sample chamber and detection unit (left) are mounted on a research-grade inverted optical microscope used for beam focusing and imaging of the sample. The system is fully software operated for an efficient experimental workflow. Trap and sample position are monitored and controlled via the live camera image. The user interface provides full access to all relevant parameters and supports the automation of complex experimental configurations with the ExperimentPlanner scripting environment.The NanoTracker turnkey optical tweezers platform (JPK Instruments AG, Berlin, Germany) combines contemporary developments in detection, calibration, beam positioning and data handling in a safe, compact device (see Figure 2). Stable and with minimal system noise, it integrates with high-end inverted microscopes from a variety of suppliers, providing access to a range of experiments and combining precise manipulation and force detection with the most advanced optical methods.
High-speed, high-resolution detection
The BFP interferometry detection method employed in the NanoTracker offers both high resolution in force and in time. State-of-the-art electronics allow data acquisition with up to several MHz corresponding to a time resolution of less than a microsecond. This provides insight into the dynamics of molecular and cellular processes on extremely short timescales.
Multitrap configuration
Investigating complex biological and biochemical structures requires equally complex arrangements of precisely controlled optical traps. With the NanoTracker system, researchers are able to generate hundreds of moveable traps from one beam using ultrafast acousto-optical deflectors (AODs) in the so-called time-sharing or multiplexing mode. AODs can move the beam from one trapping site to the next at a rate of up to 50 kHz and thus establish stable trapping conditions at multiple locations. Especially for experiments involving cells or complicated molecular structures, this multitude of “handles” to hold and manipulate the object of interest is of great advantage.
Built-in measurement modes for common applications combine with a flexible, customizable structure that enables the design and automation of complex measurements. Supported data acquisition and analysis modes include single-molecule mechanics, rheology* and elasticity measurements as well as live cell experiments. Software-guided calibration procedures require only minimal input and time.
System flexibility
Fully integrated accessories, such as multichannel microfluidic chambers with software-controlled flow rate and temperature regulation and heatable petri dish sample holders for live-cell applications, are applied in research focusing on cell (membrane) mechanics, cell–virus interactions, single DNA mechanics, microrheology and motor protein dynamics.
Applications
Single-molecule measurements
The mechanical properties of DNA play an important role in processes like cell division, gene expression and cancer development.1 Optical tweezers allow the investigation of individual DNA molecules under well-defined conditions where the effects of temperature, DNA-binding molecules, pH and salt concentration can be investigated. An individual molecule, e.g., double-stranded DNA (dsDNA), is attached to spherical particles (beads) that serve as a handle and force sensor. A schematic representation and a typical force-elongation curve of dsDNA stretching is shown in Figure 3. By moving one of the traps, the dsDNA is elongated and stretched until it undergoes structural disintegration at a characteristic threshold force. This is referred to as an overstretching transition. The mechanical properties of DNA and thus the characteristic features of the force-elongation curve depend on the presence of DNA-interacting proteins or other molecules. With the integrated microfluidic system (multichannel laminar flow cell) the exchange of buffer solutions is fast and simple; thus the behavior under varying conditions is easily investigated.
Figure 3 – a) Measurements of single-molecule mechanics, in this case, a double-stranded DNA (dsDNA) molecule, are performed with dual-beam devices that allow the parallel manipulation and force detection with two independent traps. The molecule termini are chemically attached to two different particles. By moving one of the traps, a force is applied to the molecule. From the trap positions and the particle displacements, the end-to-end distance L of the molecule can be calculated. The measured force delivers information about the force-elongation relation of the DNA molecule. b) Typical data recorded with a lambda phage DNA molecule (contour length L0 = 16 μm) is shown. If the molecule is elongated significantly more than its contour length, it is overstretched and starts to disintegrate. The threshold for this overstretching transition is characteristic for different molecules and influenced by environmental conditions.The same approach can be used to monitor straightening of coiled DNA, single protein unfolding or unzipping of DNA in which individual base pairs of a dsDNA molecule are broken up. The ends of the molecule of interest are chemically bound to the modified surface of a polystyrene or silica bead. The optical traps are then used to apply a force load to the molecule, and the stretching process is monitored. In the case of DNA unzipping and protein unfolding, characteristic steps in the elongation curve correspond to the breaking of a base pair or the unfolding of individual domains in the protein structure.
Live cell experiments
On a cellular level, the exchange of information and material with neighboring cells or surroundings requires precise control of the communication channels in the cell membrane, which represents the interface with the environment. Local changes in the membrane’s mechanical or chemical properties are the key to specific responses and behavior under varying environmental conditions. Functionalized particles with general binding ability or specific ligand molecules on their surface are an ideal tool to probe cellular interactions. Depending on the surface modification, either the binding of specific (e.g., virus-related) molecules to the cell membrane or its local mechanical properties can be investigated. Figure 4 shows examples of such measurements.
Figure 4 – A number of experiments involving live cells can be performed with optical tweezers. a) (Left) Binding experiment in which a particle decorated with ligand molecules (e.g., antibodies) binds to the cell surface. The optical trap is used to pull the particle away from the cell until the chemical bond breaks. b) The force curve shows a bond-breaking event at a force of approx. 13 pN (red arrowhead). These measurements are used to investigate the influence of different factors like pulling speed and biochemical conditions on the force required to break a specific bond. a) (Right) Schematic representation of a so-called tether-pulling experiment. A particle is nonspecifically bound to the cell membrane. With the trap, a pulling force is applied. As soon as a certain threshold force is reached, a thin membrane tube (tether) forms that can be further elongated. c) Force-distance curve representing such an event. At a force of approx. 230 pN, the tether is formed (red asterisk). In this case, multiple tethers have been formed that rupture individually (marked with red arrowheads). Between the rupturing events, elongation of tethers occurs under constant force. From the characteristics of the force-elongation relation like the tether initiation threshold and the elongation force plateau, important insight into the mechanical properties of the cell membrane can be derived. The micrographs in (c) show different stages of the measurement. The particle-cell distance is continuously increased until the connecting tether (indicated by the red dashed line) detaches from the particle surface.In the case of specific binding (Figure 4a, left, and 4b), the force or time characteristics of intermolecular bonds on the cell surface can be captured. A bead carrying antibodies or other ligands on its surface is brought in contact with the cell. After an incubation time of a few seconds, it is pulled away from the surface, applying stress to the chemical bond. When a characteristic, load-rate-dependent threshold force is exceeded, the bond breaks and the bead detaches from the membrane.
Nonspecific binding is used to perform well-defined deformations of the phospholipid cell membrane, e.g., the formation of membrane tethers or tubes (Figure 4a, right). Here, the bead electrostatically binds to the cell membrane. The optical trap pulls the cell membrane until the force is large enough to initiate the formation of a thin tube (10–100 nm in diameter). Under constant force, the tube can be elongated (force plateaus in Figure 4c). The shape of the force-elongation curve recorded as this tube is formed and elongated from the surface of the cell shows characteristic features. These are the threshold force required for tube formation and the (lower) constant elongation force. From this data, the bending rigidity of the membrane can be calculated, which in turn enables the cell’s internal status, e.g., the transformation into malignant cancerous cells or the molecular composition of red blood cells, to be determined.2,3
Microrheology
The mechanical properties of the whole cell (not just its membrane) are closely related to its function and functional disorders. It has been shown repeatedly that the stiffness of cancerous cells is an indicator of the stage of their transformation,4,5 and malfunctions of red blood cells (RBCs, erythrocytes) are related to mechanical and morphological anomalies.6 In particular, rheological measurements of liquid-borne cells residing in the blood or lymph vessels are difficult with traditional mechanical equipment due to the extremely small scale and high sensitivity of the sample. Optical methods are able to probe the viscoelastic properties of whole cells in their native condition.
For this type of measurement, two traps are used to attach beads to diametrically opposed points of a cell (Figures 5a and b). One of the traps is periodically oscillated in a sinusoidal fashion. The response of the trapped particle (i.e., its motion following the trap position) shows a characteristic delay that depends on the frequency of oscillation as well as the ratio of the viscous and elastic contributions to the cell’s mechanical properties (Figure 5c). The NanoTracker system is equipped with beam deflection mechanisms that allow oscillating the trap several thousand times per second (kHz frequency range). Data is acquired at a broad range of oscillation frequencies. The frequencydependent response of the bead–cell system in turn delivers detailed insight into the internal structure and organization of the cell.
Figure 5 – Cell rheology measurements. In microrheology, the mechanical response of soft materials to external forces is investigated. To get a complete picture of the viscoelastic properties of the material, e.g., a cell, oscillating forces at different frequencies are applied. a) Experimental geometry of a whole-cell rheology measurement. Two particles are optically trapped and bound to opposing sides of a red blood cell (erythrocyte). One of the particles is oscillated, which results in a periodic force on the cell. b) The same situation is illustrated in a micrograph showing the cell with the attached particles. c) Due to the mechanical response of the cell to external force, the particle does not follow the trap movement immediately. Depending on the material properties of the cell and the oscillation frequency, there is a delay (phase shift) between the application of force and the deformation of the cell. The graph shows the positions of the trap and the two particles (beads) at 200-Hz oscillation. While the phase shift between the trap movement (red line) and the bead in the oscillating trap (solid black line) is small for this frequency, the delay between the oscillations of bead 2 and bead 1 is clearly visible. The dependency of the delay on the oscillation frequency contains information about the viscous and elastic contribution to the overall material properties of the cell.In general, optical tweezer-based rheological measurements can be performed on any (transparent) viscoelastic fluid or other materials. Beads are embedded in the material of interest before they are optically trapped. The behavior of the material can be investigated either under linear deformation or in the frequencydependent manner described above.
Summary
Optical tweezers have found application in biological, medical and biophysical investigations, as they have in chemical research. Major advances are being made in the understanding of cellular dynamics by quantifying intracellular forces on a single-molecule level. In addition, the mechanical properties and chemically determined force and energy landscapes that regulate single-protein folding or the coiling and looping of DNA molecules are being studied. Many interdisciplinary research groups also focus on the interaction of the ubiquitous nanoparticles found in many modern products with biological organisms. Here, as well, optical tweezers can play an important role.
References
- Bustamante, C.; Bryant, Z. et al. Nature 2003, 421, 423.
- Händel, C.; Sebastian Schmidt, B.U. et al. Cell membrane softening in human breast and cervical cancer cells. New J. Phys. 2015, 17, 083008.
- Mohandas, N.; Evans, E. Mechanical properties of the red cell membrane in relation to molecular structure and genetic defects. Ann. Rev. of Biophys. and Biomolec. Struct. 1994, 23, 787–818.
- Remmerbach, T.W.; Wottawah, F. et al. Cancer Res. 2009, 69, 1728.
- Seltmann, K.; Fritsch, A.W. et al. Proc. Natl. Acad. Sci. 2013, 110, 18,507.
- Barabino, G.A.; Platt, M.O. et al. Ann. Rev. Biomed. Eng. 2010, 12, 345.
The authors are with JPK Instruments AG, Colditzstrasse 34-36, 12099 Berlin, Germany; tel.: +49 30 726243 500; e-mail: [email protected]; www.jpk.com
*Rheology (from Greek rheo-flow) is the study of the mechanical response of soft matter and fluids under mechanical force