Optical and mechanical analysis on a biological cell in optical tweezers

La réponse mécanique d’une cellule à une force externe permet d’inférer sa structure et fonction. Les pinces optiques s’avèrent une approche particulièrement attrayante pour la manipulation et caractérisation biophysique sophistiquée des cellules de façon non invasive. Cette thèse explore l’utilisation de trois types de pinces optiques couramment utilisées : 1) statiques (static), 2) à exposition partagée (time-sharing) et 3) oscillantes (oscillating). L’utilisation d’un code basé sur la méthode des éléments finis en trois dimensions (3DFEM) nous permet de modéliser ces trois types de piégeage optique afin d’extraire les propriétés mécaniques cellulaires à partir des expériences. La combinaison des pinces optiques avec la mécanique des cellules requiert des compétences interdisciplinaires. Une revue des approches expérimentales sur le piégeage optique et les tests unicellulaires est présentée. Les bases théoriques liant l’interaction entre la force radiative optique et la réponse mécanique de la cellule aussi. Pour la première fois, une simulation adaptée (3DFEM) incluant la diffusion lumineuse et la distribution du stress radiatif permet de prédire la déformation d’une cellule biconcave –analogue aux globules rouges—dans un piège statique double (static dual-trap). À l’équilibre, on observe que la déformation finale est donnée par l’espacement entre les deux faisceaux lasers: la cellule peut être étirée ou même comprimée. L’exposition partagée (time-sharing) est la technique qui permet de maintenir plusieurs sites de piégeage simultanément à partir du même faisceau laser. Notre analyse quantitative montre que, même oscillantes, la force optique et la déformation sont omniprésentes dans la cellule : la déformation viscoélastique et la dissipation de l’énergie sont analysées. Une autre cellule-type, la tige cubique, est étudiée : cela nous permet d’élucider de nouvelles propriétés sur la symétrie de la réponse mécanique. Enfin, l’analyse de la déformation résolue en temps dans un piége statique ou à exposition partagée montre que la déformation dépend simultanément de la viscoélasticité, la force externe et sa forme tridimensionnelle. La technique à force oscillante (oscillating tweezers) montre toutefois un décalage temporel, entre la force et la déformation, indépendant de la forme 3D; cette approche donnerait directement accès au tenseur viscoélastique complexe de la cellule.

Cell force measurements in 3D microfabricated environments based on compliant cantilevers.

We report the fabrication, functionalization and testing of microdevices for cell culture and cell traction force measurements in three-dimensions (3D). The devices are composed of bent cantilevers patterned with cell-adhesive spots not lying on the same plane, and thus suspending cells in 3D. The cantilevers are soft enough to undergo micrometric deflections when cells pull on them, allowing cell forces to be measured by means of optical microscopy. Since individual cantilevers are mechanically independent of each other, cell traction forces are determined directly from cantilever deflections. This proves the potential of these new devices as a tool for the quantification of cell mechanics in a system with well-defined 3D geometry and mechanical properties.

Numerical simulation of micro-scale morphological changes of plant food materials during drying - a meshfree approach

This thesis developed a high preforming alternative numerical technique to investigate microscale morphological changes of plant food materials during drying. The technique is based on a novel meshfree method, and is more capable of modeling large deformations of multiphase problem domains, when compared with conventional grid-based numerical modeling techniques. The developed cellular model can effectively replicate dried tissue morphological changes such as shrinkage and cell wall wrinkling, as influenced by moisture reduction and turgor loss.

Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates

Besides the elastic stiffness, the relaxation behavior of single living cells is also of interest of various researchers when studying cell mechanics. It is hypothesized that the relaxation response of the cells is governed by both intrinsic viscoelasticity of the solid phase and fluid-solid interactions mechanisms. There are a number of mechanical models have been developed to investigate the relaxation behavior of single cells. However, there is lack of model enable to accurately capture both of the mechanisms. Therefore, in this study, the porohyperelastic (PHE) model, which is an extension of the consolidation theory, combined with inverse Finite Element Analysis (FEA) technique was used at the first time to investigate the relaxation response of living chondrocytes. This model was also utilized to study the dependence of relaxation behavior of the cells on strain-rates. The stress-relaxation experiments under the various strain-rates were conducted with the Atomic Force Microscopy (AFM). The results have demonstrated that the PHE model could effectively capture the stress-relaxation behavior of the living chondrocytes, especially at intermediate to high strain-rates. Although this model gave some errors at lower strain-rates, its performance was acceptable. Therefore, the PHE model is properly a promising model for single cell mechanics studies. Moreover, it has been found that the hydraulic permeability of living chondrocytes reduced with decreasing of strain-rates. It might be due to the intracellular fluid volume fraction and the fluid pore pressure gradients of chondrocytes were higher when higher strain-rates applied.

细胞黏附的力学建模及其力敏感性的机理研究

细胞黏附在机体的生理和病理过程中起着重要的作用。作为细胞内、外信息交流和传递的通道，细胞黏附斑具有独特的力敏感性。实验表明，在力的作用下，黏附斑不仅可以生长、成熟和破坏，而且还能感知外部环境的力学性质，如基底硬度、硬度梯度和形貌等等。细胞黏附如何响应不同的力学刺激，物理机理是什么，如何定量描述这些物理机理？这些问题是细胞生物学和细胞力学中的重要问题。本论文通过在分子和亚细胞尺度上的力学建模研究了黏附斑的力敏感性机理，主要包括以下几方面的内容： (1) 发展了一个非线性的撕裂模型，研究了细胞黏附的稳定性和边缘依赖性。通过引入黏附分子键的非线性本构关系，并考虑黏附分子键的多种分布形式，我们发现黏附分子键的非线性效应对维持细胞黏附的稳定性起着至关重要的作用。黏附分子键的非线性力学性质使黏附分子键可以同时承载，降低了细胞对黏附分子键分布的依赖性，大大提高了细胞的黏附强度。本文的预测结果与实验结果一致。 (2) 建立了细胞黏附的细观力学模型，研究了在力作用下黏附斑生长和失稳的分子机理。在细观力学模型中，引入了“整联蛋白的聚集”和“整联蛋白-配体的反应”两个分子作用机理，并用两个化学反应来描述。通过基于Monte Carlo思想的Gillespie算法模拟了细胞黏附在不同载荷下的响应。我们发现黏附斑只能在一定范围的张力下生长，在这个范围内整联蛋白的聚集机制占主导。而当张力大于某个临界值时，黏附斑将失稳并导致破坏，这时整联蛋白-配体分子键的解离机制占主导。因此，黏附斑对作用力的不同响应，是不同分子作用机制在力作用下相互消长的结果。同时我们还建立了一个唯象的热力学模型中，验证了我们的细观力学模型。 (3) 基于细胞黏附的细观力学模型，研究了周期性载荷下细胞的重排和转向机理。在细观力学模型中，通过黏附块(adhesion plaque)，将整联蛋白-配体分子键和细胞骨架联系起来。基于Monte Calro模拟，我们发现存在一个载荷临界值，当外载大于临界值时，细胞将进行重排。细胞重排的原因是在周期性载荷下黏附斑的失稳。通过引入整联蛋白-配体成键的化学反应动力学和应力纤维的粘弹性性质，解释了细胞黏附稳定性的频率依赖性。本文预测的细胞转向临界载荷和重排方向，与实验结果一致。

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to investigate the effects of ageing on biophysical stimuli generated within a cell. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina, and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of Atomic Force Microscopy (AFM) indentation was performed and results showed a force/indentation simulation with the range of experimental results.

Ageing was simulated by both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age). Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain compared to young cells, but the difference, surprisingly, is very small and would not be measurable experimentally. Ageing is predicted to have more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models whose force/displacement behaviour is within experimentally observed ranges. the models suggest only small, though possibly physiologically-significant, differences in internal biophysical stimuli between normal and aged cells.

Biomechanical effects of environmental and engineered particles on human airway smooth muscle cells

The past decade has seen significant increases in combustion-generated ambient particles, which contain a nanosized fraction (less than 100 nm), and even greater increases have occurred in engineered nanoparticles (NPs) propelled by the booming nanotechnology industry. Although inhalation of these particulates has become a public health concern, human health effects and mechanisms of action for NPs are not well understood. Focusing on the human airway smooth muscle cell, here we show that the cellular mechanical function is altered by particulate exposure in a manner that is dependent upon particle material, size and dose. We used Alamar Blue assay to measure cell viability and optical magnetic twisting cytometry to measure cell stiffness and agonist-induced contractility. The eight particle species fell into four categories, based on their respective effect on cell viability and on mechanical function. Cell viability was impaired and cell contractility was decreased by (i) zinc oxide (40-100 nm and less than 44 mu m) and copper(II) oxide (less than 50 nm); cell contractility was decreased by (ii) fluorescent polystyrene spheres (40 nm), increased by (iii) welding fumes and unchanged by (iv) diesel exhaust particles, titanium dioxide (25 nm) and copper(II) oxide (less than 5 mu m), although in none of these cases was cell viability impaired. Treatment with hydrogen peroxide up to 500 mu M did not alter viability or cell mechanics, suggesting that the particle effects are unlikely to be mediated by particle-generated reactive oxygen species. Our results highlight the susceptibility of cellular mechanical function to particulate exposures and suggest that direct exposure of the airway smooth muscle cells to particulates may initiate or aggravate respiratory diseases.

Mapping the cytoskeletal prestress

Park CY, Tambe D, Alencar AM, Trepat X, Zhou EH, Millet E, Butler JP, Fredberg JJ. Mapping the cytoskeletal prestress. Am J Physiol Cell Physiol 298: C1245-C1252, 2010. First published February 17, 2010; doi: 10.1152/ajpcell.00417.2009.-Cell mechanical properties on a whole cell basis have been widely studied, whereas local intracellular variations have been less well characterized and are poorly understood. To fill this gap, here we provide detailed intracellular maps of regional cytoskeleton (CSK) stiffness, loss tangent, and rate of structural rearrangements, as well as their relationships to the underlying regional F-actin density and the local cytoskeletal prestress. In the human airway smooth muscle cell, we used micropatterning to minimize geometric variation. We measured the local cell stiffness and loss tangent with optical magnetic twisting cytometry and the local rate of CSK remodeling with spontaneous displacements of a CSK-bound bead. We also measured traction distributions with traction microscopy and cell geometry with atomic force microscopy. On the basis of these experimental observations, we used finite element methods to map for the first time the regional distribution of intracellular prestress. Compared with the cell center or edges, cell corners were systematically stiffer and more fluidlike and supported higher traction forces, and at the same time had slower remodeling dynamics. Local remodeling dynamics had a close inverse relationship with local cell stiffness. The principal finding, however, is that systematic regional variations of CSK stiffness correlated only poorly with regional F-actin density but strongly and linearly with the regional prestress. Taken together, these findings in the intact cell comprise the most comprehensive characterization to date of regional variations of cytoskeletal mechanical properties and their determinants.

Quantification of cellular action fibers alignment from confocal microscopic images.

The cellular rheology has recently undergone a rapid development with particular attention to the cytoskeleton mechanical properties and its main components - actin filaments, intermediate filaments, microtubules and crosslinked proteins. However it is not clear what are the cellular structural changes that directly affect the cell mechanical properties. Thus, in this work, we aimed to quantify the structural rearrangement of these fibers that may emerge in changes in the cell mechanics. We created an image analysis platform to study smooth muscle cells from different arteries: aorta, mammary, renal, carotid and coronary and processed respectively 31, 29, 31, 30 and 35 cell image obtained by confocal microscopy. The platform was developed in Matlab (MathWorks) and it uses the Sobel operator to determine the actin fiber image orientation of the cell, labeled with phalloidin. The Sobel operator is used as a filter capable of calculating the pixel brightness gradient, point to point, in the image. The operator uses vertical and horizontal convolution kernels to calculate the magnitude and the angle of the pixel intensity gradient. The image analysis followed the sequence: (1) opens a given cells image set to be processed; (2) sets a fix threshold to eliminate noise, based on Otsu's method; (3) detect the fiber edges in the image using the Sobel operator; and (4) quantify the actin fiber orientation. Our first result is the probability distribution II(Δθ) to find a given fiber angle deviation (Δθ) from the main cell fiber orientation θ0. The II(Δθ) follows an exponential decay II(Δθ) = Aexp(-αΔθ) regarding to its θ0. We defined and determined a misalignment index α of the fibers of each artery kind: coronary αCo = (1.72 ‘+ or =’ 0.36)rad POT -1; renal αRe = (1.43 + or - 0.64)rad POT -1; aorta αAo = (1.42 + or - 0.43)rad POT -1; mammary αMa = (1.12 + or - 0.50)rad POT -1; and carotid αCa = (1.01 + or - 0.39)rad POT -1. The α of coronary and carotid are statistically different (p < 0.05) among all analyzed cells. We discussed our results correlating the misalignment index data with the experimental cell mechanical properties obtained by using Optical Magnetic Twisting Cytometry with the same group of cells.

Biomechanical effects of environmental and engineered particles on human airway smooth muscle cells

The past decade has seen significant increases in combustion-generated ambient particles, which contain a nanosized fraction (less than 100 nm), and even greater increases have occurred in engineered nanoparticles (NPs) propelled by the booming nanotechnology industry. Although inhalation of these particulates has become a public health concern, human health effects and mechanisms of action for NPs are not well understood. Focusing on the human airway smooth muscle cell, here we show that the cellular mechanical function is altered by particulate exposure in a manner that is dependent upon particle material, size and dose. We used Alamar Blue assay to measure cell viability and optical magnetic twisting cytometry to measure cell stiffness and agonist-induced contractility. The eight particle species fell into four categories, based on their respective effect on cell viability and on mechanical function. Cell viability was impaired and cell contractility was decreased by (i) zinc oxide (40-100 nm and less than 44 microm) and copper(II) oxide (less than 50 nm); cell contractility was decreased by (ii) fluorescent polystyrene spheres (40 nm), increased by (iii) welding fumes and unchanged by (iv) diesel exhaust particles, titanium dioxide (25 nm) and copper(II) oxide (less than 5 microm), although in none of these cases was cell viability impaired. Treatment with hydrogen peroxide up to 500 microM did not alter viability or cell mechanics, suggesting that the particle effects are unlikely to be mediated by particle-generated reactive oxygen species. Our results highlight the susceptibility of cellular mechanical function to particulate exposures and suggest that direct exposure of the airway smooth muscle cells to particulates may initiate or aggravate respiratory diseases.

Micro-fabrication of bio-MEMS based force sensor to measure the force response of living cells

Understanding how a living cell behaves has become a very important topic in today’s research field. Hence, different sensors and testing devices have been designed to test the mechanical properties of these living cells. This thesis presents a method of micro-fabricating a bio-MEMS based force sensor which is used to measure the force response of living cells. Initially, the basic concepts of MEMS have been discussed and the different micro-fabrication techniques used to manufacture various MEMS devices have been described. There have been many MEMS based devices manufactured and employed for testing many nano-materials and bio-materials. Each of the MEMS based devices described in this thesis use a novel concept of testing the specimens. The different specimens tested are nano-tubes, nano-wires, thin film membranes and biological living cells. Hence, these different devices used for material testing and cell mechanics have been explained. The micro-fabrication techniques used to fabricate this force sensor has been described and the experiments preformed to successfully characterize each step in the fabrication have been explained. The fabrication of this force sensor is based on the facilities available at Michigan Technological University. There are some interesting and uncommon concepts in MEMS which have been observed during this fabrication. These concepts in MEMS which have been observed are shown in multiple SEM images.

Mechanical behavior in living cells consistent with the tensegrity model

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.

Quantum Mechanics Studies of Fuel Cell Catalysts and Proton Conducting Ceramics with Validation by Experiment

We carried out quantum mechanics (QM) studies aimed at improving the performance of hydrogen fuel cells. This led to predictions of improved materials, some of which were subsequently validated with experiments by our collaborators.

In part I, the challenge was to find a replacement for the Pt cathode that would lead to improved performance for the Oxygen Reduction Reaction (ORR) while remaining stable under operational conditions and decreasing cost. Our design strategy was to find an alloy with composition Pt3M that would lead to surface segregation such that the top layer would be pure Pt, with the second and subsequent layers richer in M. Under operating conditions we expect the surface to have significant O and/or OH chemisorbed on the surface, and hence we searched for M that would remain segregated under these conditions. Using QM we examined surface segregation for 28 Pt₃M alloys, where M is a transition metal. We found that only Pt₃Os and Pt₃Ir showed significant surface segregation when O and OH are chemisorbed on the catalyst surfaces. This result indicates that Pt₃Os and Pt3Ir favor formation of a Pt-skin surface layer structure that would resist the acidic electrolyte corrosion during fuel cell operation environments. We chose to focus on Os because the phase diagram for Pt-Ir indicated that Pt-Ir could not form a homogeneous alloy at lower temperature. To determine the performance for ORR, we used QM to examine all intermediates, reaction pathways, and reaction barriers involved in the processes for which protons from the anode reactions react with O₂ to form H₂O. These QM calculations used our Poisson-Boltzmann implicit solvation model include the effects of the solvent (water with dielectric constant 78 with pH 7 at 298K). We found that the rate determination step (RDS) was the O_ad hydration reaction (O_ad + H₂O_ad -> OH_ad + OH_ad) in both cases, but that the barrier for pure Pt of 0.50 eV is reduced to 0.48 eV for Pt₃Os, which at 80 degrees C would increase the rate by 218%. We collaborated with the Pu-Wei Wu’s group to carry out experiments, where we found that the dealloying process-treated Pt2Os catalyst showed two-fold higher activity at 25 degrees C than pure Pt and that the alloy had 272% improved stability, validating our theoretical predictions.

We also carried out similar QM studies followed by experimental validation for the Os/Pt core-shell catalyst fabricated by the underpotential deposition (UPD) method. The QM results indicated that the RDS for ORR is a compromise between the OOH formation step (0.37 eV for Pt, 0.23 eV for Pt_2ML/Os core-shell) and H₂O formation steps (0.32 eV for Pt, 0.22 eV for Pt_2ML/Os core-shell). We found that Pt_2ML/Os has the highest activity (compared to pure Pt and to the Pt₃Os alloy) because the 0.37 eV barrier decreases to 0.23 eV. To understand what aspects of the core shell structure lead to this improved performance, we considered the effect on ORR of compressing the alloy slab to the dimensions of pure Pt. However this had little effect, with the same RDS barrier 0.37 eV. This shows that the ligand effect (the electronic structure modification resulting from the Os substrate) plays a more important role than the strain effect, and is responsible for the improved activity of the core- shell catalyst. Experimental materials characterization proves the core-shell feature of our catalyst. The electrochemical experiment for Pt_2ML/Os/C showed 3.5 to 5 times better ORR activity at 0.9V (vs. NHE) in 0.1M HClO₄ solution at 25 degrees C as compared to those of commercially available Pt/C. The excellent correlation between experimental half potential and the OH binding energies and RDS barriers validate the feasibility of predicting catalyst activity using QM calculation and a simple Langmuir–Hinshelwood model.

In part II, we used QM calculations to study methane stream reforming on a Ni-alloy catalyst surfaces for solid oxide fuel cell (SOFC) application. SOFC has wide fuel adaptability but the coking and sulfur poisoning will reduce its stability. Experimental results suggested that the Ni4Fe alloy improves both its activity and stability compared to pure Ni. To understand the atomistic origin of this, we carried out QM calculations on surface segregation and found that the most stable configuration for Ni₄Fe has a Fe atom distribution of (0%, 50%, 25%, 25%, 0%) starting at the bottom layer. We calculated that the binding of C atoms on the Ni4Fe surface is 142.9 Kcal/mol, which is about 10 Kcal/mol weaker compared to the pure Ni surface. This weaker C binding energy is expected to make coke formation less favorable, explaining why Ni₄Fe has better coking resistance. This result confirms the experimental observation. The reaction energy barriers for CHx decomposition and C binding on various alloy surface, Ni₄X (X=Fe, Co, Mn, and Mo), showed Ni₄Fe, Ni₄Co, and Fe₄Mn all have better coking resistance than pure Ni, but that only Ni₄Fe and Fe₄Mn have (slightly) improved activity compared to pure Ni.

In part III, we used QM to examine the proton transport in doped perovskite-ceramics. Here we used a 2x2x2 supercell of perovskite with composition Ba₈X₇M₁(OH)₁O₂₃ where X=Ce or Zr and M=Y, Gd, or Dy. Thus in each case a 4⁺ X is replace by a 3⁺ M plus a proton on one O. Here we predicted the barriers for proton diffusion allowing both includes intra-octahedron and inter-octahedra proton transfer. Without any restriction, we only observed the inter-octahedra proton transfer with similar energy barrier as previous computational work but 0.2 eV higher than experimental result for Y doped zirconate. For one restriction in our calculations is that the O_donor-O_acceptor atoms were kept at fixed distances, we found that the barrier difference between cerates/zirconates with various dopants are only 0.02~0.03 eV. To fully address performance one would need to examine proton transfer at grain boundaries, which will require larger scale ReaxFF reactive dynamics for systems with millions of atoms. The QM calculations used here will be used to train the ReaxFF force field.