Implementation of the direct force measurement method in optical tweezers

Abstract

Mechanics is the branch of physics that studies movement and force, and plays an evident role in life. The swimming dynamics of bacteria in search of nutrients, organelle transport by molecular motors or sensing different kinds of stimuli by neurons, are some of the processes that need to be explained in terms of mechanics. At a human scale, distance and force can be measured with a ruler and a calibrated spring. However, assessing these magnitudes may become an important challenge at a micron scale. Among several techniques, optical tweezers stand out as a non-invasive tool that is capable of using light to grab micron-sized particles and measuring position and force with nanometer (10(-9) and femto-Newton (10(-15) accuracy. Small specimens, such as a bacterium or a cell membrane, can be trapped and effectively manipulated with a focused laser beam. Light momentum exchanged with the trapped sample can be used for eventually measuring the otherwise inaccessible forces that govern biological processes. Optical tweezers have enabled, after trapping cell vesicles in vivo, to measure the pulling force exerted by molecular motors, such as kinesin. Flagellar propulsion forces and energy generation have been investigated by optically trapping the head of a bacterium. Cell membranes have been deformed with optical tweezers and the underlying tension determined. However, the exact forces exerted by optical tweezers are difficult to measure beyond the in vitro approach. In order to calibrate the optical traps, the trapped samples often need to be spherical or present some degree of symmetry, it is important to bear information on the experimental parameters, and one needs high control of several variables that determine the trapping dynamics, such as medium homogeneity and temperature. A cutting-edge method, developed in the Optical Trapping Lab – BiOPT, from the Universitat de Barcelona, targets the light-momentum change as a direct reading of the force exerted by an optical trap. This frees experiments from the necessity of calibrating the optical traps, and makes possible to perform accurate force measurement experiments in vivo and involving irregular samples. In my PhD thesis, the direct force detection method for optical tweezers has been implemented and tested in some of such situations. I first give a technical description of the set-up used for the experiments. The use of a spatial light modulator (SLM) for holographic optical tweezers (HOTs), a piezo-electric platform to induce drag forces, and the trapping laser emission characteristics, are explained in detail. The light-momentum set-up is tested against certain situations deviating from the ideal performance and some steps for optimization of several effects are analyzed. Backscattering light loss is quantified through experiments and numerical simulations and finally assessed to account for an average ±5% uncertainty in force measurements. Then, the method is used to measure forces on irregular samples. First, arbitrary systems composed of microspheres of different kinds are collectively treated as irregular samples, in which the global momentum exchanged with the trapping beam coincides with the total Stokes-drag force. Second, pairs of optical tweezers are used to stably trap cylinders of sizes from 2 milimicras to 50 milimicras and measure forces in accordance with slender-body hydrodynamic theory. Another aspect of the thesis deals with the temperature change induced by water absorption of IR light, which is one of the major concerns within the optical trapping community. As main reasons, accurate knowledge of local temperature is needed for understanding thermally-driven processes, as well as eventual damage to live specimens. Here we use direct force measurements to detect changes in viscosity that are due to laser heating, and compare the results with heat transport simulations to discuss the main conclusions on this effect. The last goal of my thesis has been the implementation of the method inside tissue. The laser beam is affected by the scattering structures present in vivo, such as refractive index mismatches throughout different cells, nuclei, cell membranes or vesicles. As a primary result, despite the trapping beam is captured beyond 95%, I quantified this effect to result in an increase in the standard deviation of force measurements around ±20%. The approach has consisted in comparing the trapping force profiles of spherical probes in vitro (water) and in vivo (zebrafish embryos). To conclude, I here demonstrate that the direct force measurement method can be applied in an increasing number of experiments for which trap calibration becomes intricate or even impossible. Quantitative measurements become feasible in samples with unknown properties, the more important examples being arbitrary, non-spherical samples and the interior of an embryonic tissue.

Les pinces òptiques són una eina que permet la manipulació d'objectes de mida micromètrica mitjançant llum làser. En no ser necessari el contacte mecànic directe sobre una mostra, els dóna la característica de ser una eina no invasiva, fet que obre moltes aplicacions en nombrosos camps de la biologia, com ara en estudis de mecànica cel·lular en teixits. A més a més, una pinça o trampa òptica pot emprar-se per tal de realitzar mesures quantitatives, com ara posicions i forces amb precisió de nanòmetres (10-9) i femto- Newtons (10-15). D'aquesta manera, magnituds que altrament foren inaccessibles, com ara la força en un contacte cel·lular, poden obtenir-se i engegar així una nova dimensió en la recerca en biomecànica. El mètode de mesura directa de forces analitza els canvis en el moment lineal dels fotons que conformen el feix per tal de mesurar forces òptiques. Aquest mètode permet de mesurar forces sense dependre d’un alt control experimental, cosa que fa possible la mesura de forces, per exemple, en objectes irregulars. Per contra, això és gràcies a un disseny experimental capaç de capturar tota la llum que crea la pinça òptica i de mesurar-ne els canvis de moment. En la meva tesi doctoral, demostrem l’aplicabilitat del mètode en situacions en què la força no es pot obtenir de manera indirecta a partir de tècniques de calibració. En primer lloc, analitzem les millores tècniques que fan del mètode de detecció de moment una eina robusta per tal de realitzar mesures de força en un ampli ventall de situacions experimentals. Seguidament, emprem pinces òptiques controlades hologràficament per tal d’atrapar objectes irregulars, com ara sistemes de múltiples esferes i micro-cilindres, i mostrem la capacitat de mesurar l’intercanvi de moment entre el feix i les partícules que dóna lloc a les forces òptiques. Un altre aspecte àmpliament analitzat gràcies a aquesta tècnica de mesura és l’escalfament que origina una pinça òptica sobre el medi que envolta la partícula atrapada. Finalment, ens endinsem en la biologia de teixits per esbrinar com la dispersió a través d’aquests afecta el moment del feix i, per tant, les mesures. Les meves conclusions demostren l’aplicabilitat del mètode de mesura en situacions en què la calibració in situ pot esdevenir-se molt complicada o, fins i tot, impossible. Podem considerar que, per tant, el camp d’aplicació de les pinces òptiques anirà creixent i trobarà nous experiments en què s’elucidaran alguns dels interrogants més importants de la biologia.