Direct force measurements of subcellular mechanics in confinement using optical tweezers

During the development of a multicellular organism, a single fertilized cell divides and gives rise to multiple tissues with diverse functions. Tissue morphogenesis goes in hand with molecular and structural changes at the single cell level that result in variations of subcellular mechanical properties. As a consequence, even within the same cell, different organelles and compartments resist differently to mechanical stresses; and mechanotransduction pathways can actively regulate their mechanical properties. The ability of a cell to adapt to the microenvironment of the tissue niche thus is in part due to the ability to sense and respond to mechanical stresses. We recently proposed a new mechanosensation paradigm in which nuclear deformation and positioning enables a cell to gauge the physical 3D environment and endows the cell with a sense of proprioception to decode changes in cell shape. In this article, we describe a new method to measure the forces and material properties that shape the cell nucleus inside living cells, exemplified on adherent cells and mechanically confined cells. The measurements can be performed non-invasively with optical traps inside cells, and the forces are directly accessible through calibration-free detection of light momentum. This allows measuring the mechanics of the nucleus independently from cell surface deformations and allowing dissection of exteroceptive and interoceptive mechanotransduction pathways. Importantly, the trapping experiment can be combined with optical microscopy to investigate the cellular response and subcellular dynamics using fluorescence imaging of the cytoskeleton, calcium ions, or nuclear morphology. The presented method is straightforward to apply, compatible with commercial solutions for force measurements, and can easily be extended to investigate the mechanics of other subcellular compartments, e.g., mitochondria, stress-fibers, and endosomes.MK acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through the Plan Nacional (PGC2018-097882-A-I00), FEDER (EQC2018-005048-P), Severo Ochoa program for Centres of Excellence in R&D (CEX2019-000910-S; RYC-2016-21062), from Fundació Privada Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya through the CERCA and Research program (2017 SGR 1012), in addition to funding through ERC (MechanoSystems) and HFSP (CDA00023/2018). V.R. acknowledges support from the Spanish Ministry of Science and Innovation to the EMBL partnership, the Centro de Excelencia Severo Ochoa, MINECO's Plan Nacional (BFU2017-86296-P, PID2020-117011GB-I00) and Generalitat de Catalunya (CERCA). V.V. acknowledges support from the ICFOstepstone PhD Programme funded by the European Union's Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant agreement 665884Peer ReviewedPostprint (published version

Análisis de la fuerza transversal en las aproximaciones de Rayleigh y Mie para un rayo de captura TEM00 y TEM*01

Optical tweezers use a highly-focused laser beam to capture and manipulate micro- and nanometric objects. These have been demonstrated to be a promising devices for state-of-the-art research in several fields, such as microbiology and biophysics. The prediction of the optical forces that are present in this phenomenon is a current problem in continuous evolution. Additionally, the recent use of vortex beams with exotic properties as the orbital angular momentum, with advantages as the rotational manipulation of the captured microparticles and reduction of the optical damage in biological samples (Opticution), makes the problem even more complex.  Mathematical expressions in the Rayleigh and Mie regimes for the radiation force on a dielectric sphere captured by TEM00 and TEM*01 mode beams are presented. Theoretical results are then compared with experimental measurements obtained with a direct force measurement device based on light-momentum detection.Las pinzas ópticas utilizan un rayo láser altamente enfocado para capturar y manipular objetos micro y nanométricos. Se ha demostrado que son un dispositivo prometedor para la investigación de vanguardia en varios campos, como la microbiología y la biofísica. La predicción de las fuerzas ópticas presentes en este fenómeno es un problema actual en continua evolución. Además, el reciente uso de haces de vórtice con propiedades exóticas como el momento angular orbital, con ventajas como la manipulación rotacional de las micropartículas capturadas y la reducción del daño óptico en las muestras biológicas (Opticution), hace que el problema sea aún más complejo. Se presentan expresiones matemáticas en los regímenes de Rayleigh y Mie para la fuerza de radiación sobre una esfera dieléctrica capturada por los haces de los modos TEM00 y TEM*01. A continuación se comparan los resultados teóricos con las mediciones experimentales obtenidas con un dispositivo de medición directa de la fuerza basado en la detección del momento de la luz

Axonal plasticity in response to active forces generated through magnetic nano-pulling

Mechanical force is crucial in guiding axon outgrowth before and after synapse formation. This process is referred to as "stretch growth." However, how neurons transduce mechanical input into signaling pathways remains poorly understood. Another open question is how stretch growth is coupled in time with the intercalated addition of new mass along the entire axon. Here, we demonstrate that active mechanical force generated by magnetic nano-pulling induces remodeling of the axonal cytoskeleton. Specifically, the increase in the axonal density of microtubules induced by nano-pulling leads to an accumulation of organelles and signaling vesicles, which, in turn, promotes local translation by increasing the probability of assembly of the "translation factories." Modulation of axonal transport and local translation sustains enhanced axon outgrowth and synapse maturation

Implementation of the direct force measurement method in optical tweezers

[eng] 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.[cat] 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

Precisió del direccionament de feixos en pinces òptiques hologràfiques

[ANGLÈS] The use of spatial light modulators (SLMs) to achieve dynamic control of optical tweezers is observed to provide subnanometer precision in single trap positioning. However, some features concerning the digitalized structure of SLMs cause a loss of precision in certain kinds of experiments. In this work, positioning accuracy of holographic optical tweezers (HOTs) is profoundly analysed in these cases, and a correction methodology is proposed in order to improve trap positioning.[CASTELLÀ] El uso de moduladores espaciales de luz con tal de llevar a cabo el control de pinzas ópticas proporciona precisión subnanométrica en el posicionamiento de trampas individuales. No obstante, ciertos aspectos relacionados con la estructura digital de estos dispositivos son la causa de una disminución de la precisión en algunas situaciones experimentales. En este trabajo estudiaremos en profundidad el posicionamiento de pinzas ópticas holográficas i propondremos una metodología para la mejora de su precisión.[CATALÀ] L'ús de moduladors espacials de llum per tal de dur a terme el control de pinces òptiques ens proporciona precisió subnanomètrica en el posicionament de trampes individuals. Tanmateix, certs aspectes relacionats amb l'estructura digital d'aquests dispositius són la causa d'una disminució de la precisió en algunes situacions experimentals. En aquest treball estudiarem en profunditat el posicionament de pinces òptiques hologràfiques i proposarem una metodologia per a la millora de la seva precisió

Implementation of the direct force measurement method in optical tweezers

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

Precisió del direccionament de feixos en pinces òptiques hologràfiques

[ANGLÈS] The use of spatial light modulators (SLMs) to achieve dynamic control of optical tweezers is observed to provide subnanometer precision in single trap positioning. However, some features concerning the digitalized structure of SLMs cause a loss of precision in certain kinds of experiments. In this work, positioning accuracy of holographic optical tweezers (HOTs) is profoundly analysed in these cases, and a correction methodology is proposed in order to improve trap positioning.[CASTELLÀ] El uso de moduladores espaciales de luz con tal de llevar a cabo el control de pinzas ópticas proporciona precisión subnanométrica en el posicionamiento de trampas individuales. No obstante, ciertos aspectos relacionados con la estructura digital de estos dispositivos son la causa de una disminución de la precisión en algunas situaciones experimentales. En este trabajo estudiaremos en profundidad el posicionamiento de pinzas ópticas holográficas i propondremos una metodología para la mejora de su precisión.[CATALÀ] L'ús de moduladors espacials de llum per tal de dur a terme el control de pinces òptiques ens proporciona precisió subnanomètrica en el posicionament de trampes individuals. Tanmateix, certs aspectes relacionats amb l'estructura digital d'aquests dispositius són la causa d'una disminució de la precisió en algunes situacions experimentals. En aquest treball estudiarem en profunditat el posicionament de pinces òptiques hologràfiques i proposarem una metodologia per a la millora de la seva precisió

Precisió del direccionament de feixos en pinces òptiques hologràfiques

[ANGLÈS] The use of spatial light modulators (SLMs) to achieve dynamic control of optical tweezers is observed to provide subnanometer precision in single trap positioning. However, some features concerning the digitalized structure of SLMs cause a loss of precision in certain kinds of experiments. In this work, positioning accuracy of holographic optical tweezers (HOTs) is profoundly analysed in these cases, and a correction methodology is proposed in order to improve trap positioning.[CASTELLÀ] El uso de moduladores espaciales de luz con tal de llevar a cabo el control de pinzas ópticas proporciona precisión subnanométrica en el posicionamiento de trampas individuales. No obstante, ciertos aspectos relacionados con la estructura digital de estos dispositivos son la causa de una disminución de la precisión en algunas situaciones experimentales. En este trabajo estudiaremos en profundidad el posicionamiento de pinzas ópticas holográficas i propondremos una metodología para la mejora de su precisión.[CATALÀ] L'ús de moduladors espacials de llum per tal de dur a terme el control de pinces òptiques ens proporciona precisió subnanomètrica en el posicionament de trampes individuals. Tanmateix, certs aspectes relacionats amb l'estructura digital d'aquests dispositius són la causa d'una disminució de la precisió en algunes situacions experimentals. En aquest treball estudiarem en profunditat el posicionament de pinces òptiques hologràfiques i proposarem una metodologia per a la millora de la seva precisió

Positioning Accuracy in Holographic Optical Traps

Spatial light modulators (SLMs) have been widely used to achieve dynamic control of optical traps. Often, holographic optical tweezers have been presumed to provide nanometer or sub-nanometer positioning accuracy. It is known that some features concerning the digitalized structure of SLMs cause a loss in steering efficiency of the optical trap, but their effect on trap positioning accuracy has been scarcely analyzed. On the one hand, the SLM look-up-table, which we found to depend on laser power, produces positioning deviations when the trap is moved at the micron scale. On the other hand, phase quantization, which makes linear phase gratings become phase staircase profiles, leads to unexpected local errors in the steering angle. We have tracked optically trapped microspheres with sub-nanometer accuracy to study the effects on trap positioning, which can be as high as 2 nm in certain cases. We have also implemented a correction strategy that enabled the reduction of errors down to 0.3 nm