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Optical tweezers are tools made of light that enable contactless pushing, trapping, and manipulation of objects ranging from atoms to space light sails. Since the pioneering work by Arthur Ashkin in the 1970s, optical tweezers have evolved into sophisticated instruments and have been employed in a broad range of applications in life sciences, physics, and engineering. These include accurate force and torque measurement at the femtonewton level, microrheology of complex fluids, single micro- and nanoparticle spectroscopy, single-cell analysis, and statistical-physics experiments. This roadmap provides insights into current investigations involving optical forces and optical tweezers from their theoretical foundations to designs and setups. It also offers perspectives for applications to a wide range of research fields, from biophysics to space exploration., Comment: 181 pages, 61 figures

The biophysical properties of polymer based gels, for instance the commonly used Matrigel, crucially depend on polymer concentration. Only certain polymer concentrations will produce a gel optimal for a specific purpose, for instance for organoid development. Hence, in order to design a polymer scaffold for a specific purpose, it is important to know which properties are optimal and to control the biophysical properties of the scaffold. Using optical tweezers, we perform a biophysical characterization of the biologically relevant Matrigel while systematically varying the polymer concentration. Using the focused laser beam we trace and spectrally analyze the thermal fluctuations of an inert tracer particle. From this, the visco-elastic properties of the Matrigel is quantified in a wide frequency range through scaling analysis of the frequency power spectrum as well as by calculating the complex shear modulus. The viscoelastic properties of the Matrigel are monitored over a timespan of seven hours. At all concentrations, the Matrigel is found to be more fluid-like just after formation and to become more solid-like during time, settling to a constant state after 1-3 hours. Also, the Matrigel is found to display increasingly more solid-like properties with increasing polymer concentration. To demonstrate the biological relevance of these results, we expand pancreatic organoids in Matrigel solutions with the same polymer concentration range and demonstrate how the polymer concentration influences organoid development. In addition to providing quantitative information about how polymer gels change visco-elastic properties as a function of polymer concentration and time, these results also serve to guide the search of novel matrices relevant for organoid development or 3D cell culturing, and to ensure reproducibility of bio-relevant Matrigels.

The biomolecule is among the most important building blocks of biological systems, and a full understanding of its function forms the scaffold for describing the mechanisms of higher order structures as organelles and cells. Force is a fundamental regulatory mechanism of biomolecular interactions driving many cellular processes. The forces on a molecular scale are exactly in the range that can be manipulated and probed with single molecule force spectroscopy. The natural environment of a biomolecule is inside a living cell, hence, this is the most relevant environment for probing their function. In vivo studies are, however, challenged by the complexity of the cell. In this review, we start with presenting relevant theoretical tools for analyzing single molecule data obtained in intracellular environments followed by a description of state-of-the art visualization techniques. The most commonly used force spectroscopy techniques, namely optical tweezers, magnetic tweezers, and atomic force microscopy, are described in detail, and their strength and limitations related to in vivo experiments are discussed. Finally, recent exciting discoveries within the field of in vivo manipulation and dynamics of single molecule and organelles are reviewed.

An optical two-beam trap composed from two counter propagating laser beams is an interesting setup due to the ability of the system to trap, hold, and stretch soft biological objects like vesicles or single cells. Because of this functionality, the system was also named the optical stretcher by Jochen Guck, Josep Kaas and co-workers almost 20 years ago. In a favorable setup, the two opposing laser beams meet with equal intensities in the middle of a fluidic channel in which cells may ow past, be trapped, stretched, and allowed to move on, giving the promise of a high throughput device. Yet, single beam optical traps, aka optical tweezers, by far outnumber the existing optical stretchers in research labs throughout the world. The ability to easily construct an optical stretcher setup in a low-cost material would possibly imply more frequent use of the optical stretching technique. Here, we discuss advantages and disadvantages of choice of material and methodology for chip assembly and chip production. For high throughput investigations of stretching deformation of single cells, optical stretching is, however, out-performed by hydrodynamic deformability assays. As we will discuss, injection molded polymer chips may with advantage be applied both for optical stretching and for hydrodynamic deformability experiments.

Acoustophoresis is a widely reported and used technique for microparticle manipulation and separation. In the study described here, acustophoresis is employed to prefocus the flow (i.e., focusing occurring upstream of the analysis region) in a microfluidic chip intended for optical trapping and stretching. The whole microchip is made of silica with optical waveguides integrated by femtosecond laser writing. The acoustic force is produced by driving an external piezoelectric ceramic attached underneath the microchip at the chip resonance frequency. Thanks to an efficient excitation of acoustic waves in both water and glass, acoustophoretic focusing is observed along the channel length (>40 mm) and it is successfully demonstrated both with polystyrene beads, swollen red blood cell, and cells from mouse fibroblast cellular lines (L929). Moreover, by comparing results of cell stretching measurements, we demonstrate that acoustic waves do not alter the optical deformability of the cells and that the acoustic prefocusing results in a considerable enhancement of throughput in optical stretching experiments.

Mechanical properties, like deformability or elasticity, of cells can in some cases be indicative of the health of the organism they originate from. In this work, we explore the potential of deformability and other mechanical parameters of individual red blood cells (RBCs) from humans as a marker for the state of health of the human source, patient or donor. In particular, we have investigated the use of different experimental strategies implemented in injection molded plastic microfluidic devices. One strategy is to optically stretch the red blood cells in an optical two-beam trap, also known as an optical stretcher, in a microfluidic chip in which optical fibers have been placed during a post-processing step. Another strategy is to exert hydrodynamic shear forces on the cells by forcing the cells through a narrow constriction. The latter method has the advantage of a considerably higher throughput but does so far not allow for subsequent investigations of single “interesting” cells. The paper is a progress report with preliminary results based on the different strategies, we have pursued.

As described in the previous chapters, optical tweezers have become a tool of precision for in vitro single-molecule investigations, where the single molecule of interest most often is studied in purified form in an experimental assay with a well-controlled fluidic environment. A well-controlled fluidic environment implies that the physical properties of the liquid, most notably the viscosity, are known and the fluidic environment can, for calibrational purposes, be treated as a simple liquid.In vivo, however, optical tweezers have primarily been used as a tool of manipulation and not so often for precise quantitative force measurements, due to the unknown value of the spring constant of the optical trap formed within the cell's viscoelastic cytoplasm. Here, we describe a method for utilizing optical tweezers for quantitative in vivo force measurements. The experimental protocol and the protocol for data analysis rely on two types of experiments, passive observation of the thermal motion of a trapped object inside a living cell, followed by observations of the response of the trapped object when subject to controlled oscillations of the optical trap. One advantage of this calibration method is that the size and refractive properties of the trapped object and the viscoelastic properties of its environment need not be known. We explain the protocol and demonstrate its use with experiments of trapped granules inside live S. pombe cells.

As described in the previous chapters, optical tweezers have become a tool of precision for in vitro single-molecule investigations, where the single molecule of interest most often is studied in purified form in an experimental assay with a well-controlled fluidic environment. A well-controlled fluidic environment implies that the physical properties of the liquid, most notably the viscosity, are known and the fluidic environment can, for calibrational purposes, be treated as a simple liquid.In vivo, however, optical tweezers have primarily been used as a tool of manipulation and not so often for precise quantitative force measurements, due to the unknown value of the spring constant of the optical trap formed within the cell's viscoelastic cytoplasm. Here, we describe a method for utilizing optical tweezers for quantitative in vivo force measurements. The experimental protocol and the protocol for data analysis rely on two types of experiments, passive observation of the thermal motion of a trapped object inside a living cell, followed by observations of the response of the trapped object when subject to controlled oscillations of the optical trap. One advantage of this calibration method is that the size and refractive properties of the trapped object and the viscoelastic properties of its environment need not be known. We explain the protocol and demonstrate its use with experiments of trapped granules inside live S. pombe cells.

An optical two-beam trap, composed from two counter propagating laser beams, is an interesting setup due to the ability of the system to trap, hold, and stretch soft biological objects like vesicles or single cells. Because of this functionality, the system was also named "the optical stretcher" by Jochen Guck, Josep Kas and co-workers some 15 years ago. In a favorable setup, the two opposing laser beams meet with equal intensities in the middle of a fluidic channel in which cells may flow past, be trapped, stretched, and allowed to move on, giving the promise of a high throughput device. Yet, single beam optical traps, aka optical tweezers, by far outnumber the existing optical stretchers in research labs throughout the world. The ability to easily construct an optical stretcher setup in a low-cost material would possibly imply more frequent use of the optical stretching technique. Here, we will outline the design, the production procedures, and results obtained in a fiber-based experimental setup built within an injection molded microfluidic polymer chip. The microfluidic chip is constructed with a three layer technology in which we ensure both horizontal and vertical focusing of the cells we wish to trap, thereby preventing too many cells to flow below the line of focus of the two counter propagating laser beams that are positioned perpendicular to the direction of flow of the cells. Results will be compared to that from other designs from previous work in the group.

An attractive solution for optical trapping and stretching by means of two counterpropagating laser beams is to embed waveguides or optical fibers in a microfluidic system. The microfluidic system can be constructed in different materials, ranging from soft polymers that may easily be cast in a rapid prototyping manner, to hard polymers that could even be produced by injection moulding, or to silica in which waveguides may either be written directly, or with grooves for optical fibers. Here, we review different solutions to the system and also show results obtained in a polymer chip with DUV written waveguides and in an injection molded polymer chip with grooves for optical fibers.

At present, a major obstacle to the quantitative application of optical tweezers as a force spectrometer in living cells is the lack of a method to calibrate the tweezers. Calibration with approved methods such as the power spectrum method (Berg-Sorensen and Flyvbjerg 2004 Rev. Sci. Instrum. 75 594; Berg-Sorensen et al 2006 Rev. Sci. Instrum. 77 063106) is not possible as the viscoelastic properties of the bio-active medium are a priori unknown. Here, we present an approach that neither requires explicit assumptions about the size of the trapped particle nor about the viscoelastic properties of the medium. Instead, the interaction between the medium and the trapped particle is described in a general manner, through velocity and acceleration memory. Our method is applicable to general, at least locally homogeneous, viscoelastic media. The procedure combines active and passive approaches by the application of Onsager's regression hypothesis. It allows extraction of the trapping stiffness κ of the optical tweezers and of the response function χ(ω), which is the frequency-dependent effective inverse spring constant of the system. Finally, information about the viscoelastic properties of the medium may also be found. To test the method, we have performed simulations in which the system is driven sinusoidally. These simulations serve as an example of how to deal with real experimental data. For realistic parameters, we calibrate the trap stiffness κ with ~1% stochastic error.

An optical trapping system with two opposing laser beams, also known as the optical stretcher, are naturally constructed inside a microfluidic lab-on-chip system. We present and compare two approaches to combine a simple microfluidic system with either waveguides directly written in the microfluidic chip or with optical fibers mounted in the chip.

Optical tweezers are a versatile tool in biophysics and have matured from a tool of manipulation to a tool of precise measurements. We argue here that the data analysis with advantage can be developed to a level of sophistication that matches that of the instrument. We review methods of analysis of optical tweezers data, primarily based on the power spectra of time series of positions for trapped spherical objects. The majority of precise studies in the literature are performed on in vitro systems, whereas in the present work, an example of an in vivo system is presented for which precise power spectral analysis is both useful and necessary. The biological system is the cytoplasm of fission yeast, Schizosaccharomyces pombe in which we observe subdiffusion of lipid granules. In a search for the cause of subdiffusion, we chemically disrupt the actin network in the cytoplasm and further consider in vitro networks of filamenteous actin undergoing similar chemical disruption.

The motion of a single protein, a λ-receptor in the outer membrane of E. coli, is studied with optical tweezers. We present improved measurements and an analysis that accounts for stochastic errors, filters in the detection system, aliasing and hydrodynamic effects. We test a simple model for the protein's motion and find it in agreement with the low-frequency part of the data. We thus determine physical parameter values for the system with improved precision. The diffusion coefficient describing the motion of the λ-receptor is now obtained with 2% relative error for individual receptors, and varies between bacteria with roughly 70% root-mean-square deviation about the mean. This improved analysis also reveals that the simple model must be revised in order to agree with the high-frequency part of the power spectrum.

We characterize the frequency-dependent response of a photo detection system based on a Si-PIN photodiode and a laser with wavelength 1064 nm, a system commonly used with optical tweezers. We chopped the laser beam with chopper frequencies from 200 Hz to 14 kHz, and found an exponentially delayed response of the detection system with a characteristic delay time of ∼20 μs. The physical mechanism causing this time delay is silicon’s transparency to 1064 nm light: Photons are absorbed and create charge carriers not only in the diode’s depletion layer, where they are detected within nano-seconds, but predominantly in the n-layer, where they remain undetected till transported out by thermal diffusion. The diode’s response is dominated by this delay which can be characterized as a first-order low-pass filter with a 3dB-frequency of 8–9 kHz, depending on laser intensity. Measurements exploiting frequencies near or above this 3dB-frequency must be corrected for this unintended filter effect. We describe how to do...

Optical tweezers are the only nano-tools capable of manipulating and performing force-measurements on individual molecules and organelles within the living cell without performing destructive penetration through the cell wall and without the need for inserting a non-endogenous probe. Here, we describe how optical tweezers are used to manipulate individual molecules and perform accurate force and distance measurements within the complex cytoplasm of the living cell. Optical tweezers can grab individual molecules or organelles, if their optical contrast to the medium is large enough, as is the case, e.g., for lipid granules or chromosomes. However, often the molecule of interest is specifically attached to a handle manipulated by the optical trap. The most commonly used handles, their insertion into the cytoplasm, and the relevant micro-rheology of the cell are discussed here and we also review recent and exciting results achieved through optical force manipulation of individual molecules in vivo.

With the success of in vitro single-molecule force measurements obtained in recent years, the next step is to perform quantitative force measurements inside a living cell. Optical traps have proven excellent tools for manipulation, also in vivo, where they can be essentially non-invasive under correct wavelength and exposure conditions. It is a pre-requisite for in vivo quantitative force measurements that a precise and reliable force calibration of the tweezers is performed. There are well-established calibration protocols in purely viscous environments; however, as the cellular cytoplasm is viscoelastic, it would be incorrect to use a calibration procedure relying on a viscous environment. Here we demonstrate a method to perform a correct force calibration inside a living cell. This method (theoretically proposed in Fischer and Berg-Sorensen (2007 J. Opt. A: Pure Appl. Opt. 9 S239)) takes into account the viscoelastic properties of the cytoplasm and relies on a combination of active and passive recordings of the motion of the cytoplasmic object of interest. The calibration procedure allows us to extract absolute values for the viscoelastic moduli of the living cell cytoplasm as well as the force constant describing the optical trap, thus paving the way for quantitative force measurements inside the living cell. Here, we determine both the spring constant of the optical trap and the elastic contribution from the cytoplasm, influencing the motion of naturally occurring tracer particles. The viscoelastic moduli that we find are of the same order of magnitude as moduli found in other cell types by alternative methods.

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 (2007) ], 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.

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion., Comment: 4 pages, 4 figures, REVTeX. Supplementary Material. Physical Review Letters, at press

During the cell cycle, the organization of the cytoskeletal network undergoes dramatic changes. In order to reveal possible changes of the viscoelastic properties in the intracellular space during the cell cycle we investigated the diffusion of endogenous lipid granules within the fission yeast Schizosaccharomyces Pombe using optical tweezers. The cell cycle was divided into interphase and mitotic cell division, and the mitotic cell division was further subdivided in its stages. During all stages of the cell cycle, the granules predominantly underwent subdiffusive motion, characterized by an exponent alpha that is also linked to the viscoelastic moduli of the cytoplasm. The exponent alpha was significantly smaller during interphase than during any stage of the mitotic cell division, signifying that the cytoplasm was more elastic during interphase than during division. We found no significant differences in the subdiffusive exponents from granules measured in different stages of cell division. Also, our results for the exponent displayed no significant dependence on the position of the granule within the cell. The observation that the cytoplasm is more elastic during interphase than during mitotic cell division is consistent with the fact that elastic cytoskeletal elements such as microtubules are less abundantly present during cell division than during interphase.

The application of optical traps to manipulate or monitor intracellular processes in in vivo systems calls for precise procedures both to evaluate the characteristics of the trap and the viscoelastic properties of the intracellular medium. Here, we verify experimentally the authenticity of a calibration procedure, specifically developed for use in calibration of optical tweezers in complex, viscoelastic media (Fischer and Berg-Sorensen, J. Opt. A: Pure Appl. Opt. 9, S239 (2007)).We demonstrate the application of the procedure in i) water and in ii) entangled F-actin without cross-linkers. As the theoretical background of the procedure is essentially convenient formulations of the fluctuation-dissipation theorem, we name the procedure as the “FDT-method”. The analysis of the measurements in water may be validated directly: We can compare the results for the spring constant to results obtained with well-established methods and those for the viscoelastic properties to theoretical predictions. In the actin solution, we may similarly compare our results with results of microrheology experiments in the literature.

In a typical optical tweezers detection system, the position of a trapped object is determined from laser light impinging on a quadrant photodiode. When the laser is infrared and the photodiode is of silicon, they can act together as an unintended low-pass filter. This parasitic effect is due to the high transparency of silicon to near-infrared light. A simple model that accounts for this phenomenon (Berg-Sorensen et al., J. Appl. Phys., 93, 3167-3176 (2003)) is here solved for frequencies up to 100 kHz, and for laser wavelengths between 750 and 1064 nm. The solution is applied to experimental data in the same range, and is demonstrated to give this detection system of optical tweezers a bandwidth, accuracy, and precision that is limited only by the data acquisition board's band-width and bandpass ripples, here 96.7 kHz, resp. 0.005 dB., Comment: 12 pages, 8 figures. Submitted to Review of Scientific Instruments

In a typical position detection system for optical tweezers, laser light impinges on a quadrant photodiode, and the signal from the four quadrants of the diode is used to determine the position of a trapped object. A widely used position detection system consists of a Si-PIN photodiode and an infrared laser. In previous work we have demonstrated with two distinct experimental methods how such a system may act as an unintended low-pass filter and we modeled its physical origin mathematically. Here we demonstrate that the general solution to this model can account precisely for the "parasitic" filter's effects up to as large frequencies as we can measure, approximately 100 kHz. Thus we increase the useful bandwidth of tweezers experiments by nearly two decades. This opens for investigations of phenomena in biophysics, soft matter, and polymer science at much higher frequencies than before.

We present a procedure for a precise power spectral analysis of optical tweezers data. This procedure uses the entire frequency range of the experimental power spectrum. We apply this procedure to experimental data from a biological system, data for the motion of a microsphere attached with a biotin-streptavidin linker to a single protein, the λ-receptor of E. coli. As in [Oddershede et al, Biophys. J. 83, 3152 (2002)] and [Oddershede et al, J. Phys.: Condens. Mat. 15, S1737 (2003)], we find that the λ-receptor moves diffusively in the outer membrane, but is confined to a particular region by a harmonic potential. Here, we show that since the power spectrum is known with precision up to its Nyquist frequency of 8 kHz, one can resolve the relative motion of the λ-receptor and the microsphere attached to it. We find that the biotin-streptavidin link between them can be described as a Hookean spring. Since we can see only the microsphere, these results are based on an interpretation of the power spectrum of its motion. This interpretation is based on a model. We use the simplest model that is necessary and sufficient to interpret the power spectrum in its full range. This model fits the spectrum well and the fit yields the model's parameters with some precision. These results indicate that optical tweezers have the potential to become a tool of precision. We discuss improvements of experiments and analysis that are necessary in order to realize this potential.

The viscoelastic properties of the cytoplasm of living yeast cells were investigated by studying the motion of lipid granules naturally occurring in the cytoplasm. A large frequency range of observation was obtained by a combination of video-based and laser-based tracking methods. At time scales from 10(-4) to 10(2) s, the granules typically perform subdiffusive motion with characteristics different from previous measurements in living cells. This subdiffusive behavior is thought to be due to the presence of polymer networks and membranous structures in the cytoplasm. Consistent with this hypothesis, we observe that the motion becomes less subdiffusive upon actin disruption.

We investigate the axial position detection of a trapped microsphere in an optical trap by using a quadrant photodiode. By replacing the photodiode with a CCD camera, we obtain detailed information on the light scattered by the microsphere. The correlation of the interference pattern with the axial position displays complex behavior with regions of positive and negative interference. By analyzing the scattered light intensity as a function of the axial position of the trapped sphere, we propose a simple method to increase the sensitivity and control the linear range of axial position detection.

The first half of this chapter describes the development in mathematical models of Brownian motion after Einstein's seminal papers and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists is also an instrument of precision that requires an understanding of Brownian motion beyond Einstein's. This is illustrated with some applications, current and potential, and it is shown how addition of a controlled forced motion on the nano-scale of the tweezed object's thermal motion can improve the calibration of the instrument in general, and make it possible also in complex surroundings. The second half of the present chapter, starting with Sect. 9, describes the co-evolution of biological motility models with models of Brownian motion, including very recent results for how to derive cell-type-specific motility models from experimental cell trajectories., Comment: 18 pages, 5 figures, to appear in Proceedings of Nobel Symposium 131