A Mechanical Model to Interpret Cell-Scale Indentation Experiments on Plant Tissues in Terms of Cell Wall Elasticity and Turgor Pressure

International audienceMorphogenesis in plants is directly linked to the mechanical elements of growing tissues, namely cell wall and inner cell pressure. Studies of these structural elements are now often performed using indentation methods such as atomic force microscopy. In these methods, a probe applies a force to the tissue surface at a subcellular scale and its displacement is monitored, yielding force-displacement curves that reflect tissue mechanics. However, the interpretation of these curves is challenging as they may depend not only on the cell probed, but also on neighboring cells, or even on the whole tissue. Here, we build a realistic three-dimensional model of the indentation of a flower bud using SOFA (Simulation Open Framework Architecture), in order to provide a framework for the analysis of force-displacement curves obtained experimentally. We find that the shape of indentation curves mostly depends on the ratio between cell pressure and wall modulus. Hysteresis in force-displacement curves can be accounted for by a viscoelastic behavior of the cell wall. We consider differences in elastic modulus between cell layers and we show that, according to the location of indentation and to the size of the probe, force-displacement curves are sensitive with different weights to the mechanical components of the two most external cell layers. Our results confirm most of the interpretations of previous experiments and provide a guide to future experimental work

Measuring the mechanical properties of plant cells by combining micro-indentation with osmotic treatments

A combination of osmotic treatments, micro-indentation with cellular force microscopy, and inverse finite-element modelling gives an estimate for both turgor pressure and cell wall elasticity in plant cell

Polarized cortical tension drives zebrafish epiboly movements

The principles underlying the biomechanics of morphogenesis are largely unknown. Epiboly is an essential embryonic event in which three tissues coordinate to direct the expansion of the blastoderm. How and where forces are generated during epiboly, and how these are globally coupled remains elusive. Here we developed a method, hydrodynamic regression (HR), to infer 3D pressure fields, mechanical power, and cortical surface tension profiles. HR is based on velocity measurements retrieved from 2D+T microscopy and their hydrodynamic modeling. We applied HR to identify biomechanically active structures and changes in cortex local tension during epiboly in zebrafish. Based on our results, we propose a novel physical description for epiboly, where tissue movements are directed by a polarized gradient of cortical tension. We found that this gradient relies on local contractile forces at the cortex, differences in elastic properties between cortex components and the passive transmission of forces within the yolk cell. All in all, our work identifies a novel way to physically regulate concerted cellular movements that might be instrumental for the mechanical control of many morphogenetic processes.Peer ReviewedPostprint (author's final draft

Loops versus lines and the compression stiffening of cells

Both animal and plant tissue exhibit a nonlinear rheological phenomenon known as compression stiffening, or an increase in moduli with increasing uniaxial compressive strain. Does such a phenomenon exist in single cells, which are the building blocks of tissues? One expects an individual cell to compression soften since the semiflexible biopolymer-based cytoskeletal network maintains the mechanical integrity of the cell and in vitro semiflexible biopolymer networks typically compression soften. To the contrary, we find that mouse embryonic fibroblasts (mEFs) compression stiffen under uniaxial compression via atomic force microscopy (AFM) studies. To understand this finding, we uncover several potential mechanisms for compression stiffening. First, we study a single semiflexible polymer loop modeling the actomyosin cortex enclosing a viscous medium modeled as an incompressible fluid. Second, we study a two-dimensional semiflexible polymer/fiber network interspersed with area-conserving loops, which are a proxy for vesicles and fluid-based organelles. Third, we study two-dimensional fiber networks with angular-constraining crosslinks, i.e. semiflexible loops on the mesh scale. In the latter two cases, the loops act as geometric constraints on the fiber network to help stiffen it via increased angular interactions. We find that the single semiflexible polymer loop model agrees well with our AFM experiments until approximately 35% compressive strain. We also find for the fiber network with area-conserving loops model that the stress-strain curves are sensitive to the packing fraction and size distribution of the area-conserving loops, thereby creating a mechanical fingerprint across different cell types. Finally, we make comparisons between this model and experiments on fibrin networks interlaced with beads as well as discuss the tissue-scale implications of cellular compression stiffening.Comment: 19 pages, 17 figure

COMPUTATIONAL APPROACHES TO UNDERSTAND PHENOTYPIC STRUCTURE AND CONSTITUTIVE MECHANICS RELATIONSHIPS OF SINGLE CELLS

The goal of this work is to better understand the relationship between the structure and function of biological cells by simulating their nonlinear mechanical behavior under static and dynamic loading using image structure-based finite element modeling (FEM). Vascular smooth muscle cells (VSMCs) are chosen for this study due to the strong correlation of the geometric arrangement of their structural components on their mechanical behavior and the implications of that behavior on diseases such as atherosclerosis. VSMCs are modeled here using a linear elastic material model together with truss elements, which simulate the cytoskeletal fiber network that provides the cells with much of their internal structural support. Geometric characterization of single VSMCs of two physiologically relevant phenotypes in 2D cell culture is achieved using confocal microscopy in conjunction with novel image processing techniques. These computer vision techniques use image segmentation, 2D frequency analysis, and linear programming approaches to create representative 3D model structures consisting of the cell nucleus, cytoplasm, and actin stress fiber network of each cell. These structures are then imported into MSC Patran for structural analysis with Marc. Mechanical characterization is achieved using atomic force microscopy (AFM) indentation. Material properties for each VSMC model are input based on values individually obtained through experimentation, and the results of each model are compared against those experimental values. This study is believed to be a significant step towards the viability of finite element models in the field of cellular mechanics because the geometries of the cells in the model are based on confocal microscopy images of actual cells and thus, the results of the model can be compared against experimental data for those same cells

Predictions of Indentation Stiffness of Musculoskeletal Regions Using Ultrasound

Tissue indentation response is an important metric for understanding how different musculoskeletal regions respond to loading and is a function of the tissue’s form. Modem imaging techniques provide information about the internal structures of human tissue. Ultrasound remains one of the most common imaging techniques performed, given its portability and low costs. Prior work and data collection on 100 patients involved the collection of ultrasound images at eight different locations across the musculoskeletal extremities. Given the tissue structure information that the medical imaging provided, it was hypothesized that the mechanical properties of the tissue could be predicted from this data. This work aimed to incorporate various forms of patient data into different machine learning models for the prediction of tissue indentation response. These surrogate models would be capable of prediction of tissue compliance once input features are provided, potentially making them relevant in the clinical domain. Eight different surrogate models were developed, with four statistics models built and four deep learning models built to assess which method and which input factors were most suitable for accurately predicting indentation mechanics. The first four models were informed by tissue thicknesses and indentation region. The statistics surrogate models consist of two pure statistical models, while the other two models were based on a physics-based interpretation of two springs in series. The statistical models showed reasonable capability of predicting tissue surface stiffness, with the mean absolute percent difference ranging from 25.4% to 29.7% across the four models. The deep learning approach was divided between two separate forms of deep learning. The first model was fed only demographic features, while a second model of demographics and manually extracted tissue thicknesses. These models also showed reasonable capability of predicting tissue indentation stiffness, with a mean absolute percent difference of 25.5% and 26.3%, respectively. A final modeling approach involved using convolutional neural networks, which utilized the raw ultrasound images. One model was only given the ultrasound image and gave a mean absolute percent difference of 31.5%. A final model consisted of the raw image, image metadata, and demographics and returned a mean absolute percent difference of 25.9%

Nanoindentation of hydrated materials and tissues

Nanoindentation techniques have recently been adapted for the study of hydrated materials, including biological materials and hydrogels. There are unique challenges associated with handling and testing hydrated samples. For hydrated materials, a poroelastic or poroviscoelastic analysis, which explicitly treats the fluid flow through the porous material, is used to extract material properties from experimental data. Some key results from recent works using nanoindentation to evaluate hydrated materials are reviewed in the context of these challenges. Finally, as these studies represent relatively recent developments in the nanoindentation field, an outlook for the future is presented, in which it is clear that a consensus is emerging for quantitative evaluation of hydrated materials via a modified nanoindentation approach.This is the accepted manuscript. The final version is available at http://www.sciencedirect.com/science/article/pii/S1359028615000236

Application and Development of Mechanoresponsive Polymer Structures

Mechanoresponsive Systeme antworten auf mechanische Reize mit einer Eigenschaftsänderung. Diese Dissertation umfasst die Arbeiten mit zwei mechanoresponsiven Systemen, die optisch auf mechanische Reize antworten. Sie basieren auf polymeren Strukturen, einer Polymerbürste und einem Hydrogelnetzwerk. Ihr optischer Antwortmechanismus ermöglicht die Beobachtung wirkender Kräfte als ein Ansatz zur in situ-Kraftmessung. Im ersten Teil wird ein existierendes, mechanoresponsives System zur Anwendung gebracht, das auf einer mit Fluoreszenzfarbstoff markierten Polyelektrolytbürste basiert. Die Ladungen des Polyelektrolyts können die Fluoreszenz des Farbstoffs unterdrücken, sodass lokale Kompression und Zugspannung über die Fluoreszenzintensität unterschieden werden können. Die mechanoresponsive Polymerbürste wurde als mechanosensitive Oberflächenbeschichtung angewandt, um Unterschiede in der Kontaktspannungsverteilung von Gecko-inspirierten adhäsiven Mikrostempelstrukturen aufzuklären. Die erarbeiteten Ergebnisse und daraus abgeleiteten Ablösemechanismen der Mikrostempeltypen deckten sich qualitativ mit Vorhersagen aus theoretischen Ansätzen. Aufgrund geometrischer Einschränkungen einer planaren Oberflächenbeschichtung zielt der zweite Teil darauf ab, dieses mechanoresponsive Prinzip in ein dreidimensionales Netzwerk zu überführen und ein mechanoresponsives Hydrogelnetzwerk als Plattform zur Kraftmessung zu entwickeln. Konzeptionell besitzt ein homogenes Netzwerk vorhersagbare mechanische Eigenschaften, sodass lokale optische Antworten auf mechanische Kräfte ermöglichen könnten, die wirkenden Kräfte zu lokalisieren und quantifizieren. Basierend auf einer Gestaltung nach der Flory-Rehner-Theorie wurden Präkursoren mit vordefinierter Größe und Architektur für die Hydrogelherstellung eingesetzt, um auf ein homogenes Netzwerk abzuzielen. Zu diesem Zweck wurde das Mischungsvolumen durch Tropfenmikrofluidik reduziert. Für den optischen Antwortmechanismus wurden die Hydrogelnetzwerk-Präkursoren mit zwei verschiedenen Fluorophoren markiert, die sich durch abstandsabhängige Emission über Förster-Resonanzenergietransfer auszeichnen. Die Funktionalität des optischen Antwortmechanismus wurde auf globaler Ebene durch Kollabieren und kontrolliertes Quellen des Netzwerks, dann auf lokalisierter Ebene durch definierte mechanische Belastung mit Rasterkraftmikroskopie gezeigt. Durch ihre Anpassbarkeit könnte die Hydrogelplattform zukünftig verschiedenste Anwendungen im Bereich intrisischer Kraftmessung weicher Materie bedienen.Mechanoresponsive systems respond to mechanical triggers by changes in a certain property. This thesis covers the work conducted with two mechanoresponsive systems that respond optically to mechanical triggers. These two systems are based on polymer structures, a polymer brush and a hydrogel network. Thus, the optical response mechanism allows observing acting forces as an approach to force sensing in situ. In the first part, an existing mechanoresponsive system based on a polyelectrolyte brush labeled with a fluorescent dye is engaged in application. The charges of the polyelectrolyte are able to quench the fluorescence of the dye so that local compression or tension can be distinguished from the local fluorescence intensity. The mechanoresponsive polymer brush was applied as mechanosensitive surface coating to elucidate differences in the contact stress distributions of gecko-inspired adhesive micropillar structures. The determined results and the derived detachment mechanisms of the micropillar types were in qualitative accordance with predictions from theoretical approaches. Overcoming the geometrical limitations of a planar surface coating, the second part aims at translating the mechanoresponse principle to a three-dimensional network and developing a mechanoresponsive hydrogel as a platform for force sensing. Conceptually, a homogeneous network allows to predict mechanical properties so that localized optical mechanoresponses could enable locating and quantifying acting forces. Based on network design principles from the Flory-Rehner theory, precursors with predefined size and architecture were utilized in hydrogel preparation, aiming for a homogeneous network. Further in this regard, the mixing volume was reduced by employing droplet microfluidics. As optical response mechanism, the hydrogel network precursors were labeled with two kinds of fluorophore, featuring distance-dependent emission from Förster Resonance Energy Transfer. The functionality of the optical response mechanism was demonstrated on global level by collapsing and controlled swelling of the network, and on a localized level by defined mechanical stress, applied with Atomic Force Microscopy. Owing to its adjustability, the hydrogel platform might be employed in various applications that require intrinsic force sensing of soft matter in future

Atomic force microscopy-based mechanobiology

Mechanobiology emerges at the crossroads of medicine, biology, biophysics and engineering and describes how the responses of proteins, cells, tissues and organs to mechanical cues contribute to development, differentiation, physiology and disease. The grand challenge in mechanobiology is to quantify how biological systems sense, transduce, respond and apply mechanical signals. Over the past three decades, atomic force microscopy (AFM) has emerged as a key platform enabling the simultaneous morphological and mechanical characterization of living biological systems. In this Review, we survey the basic principles, advantages and limitations of the most common AFM modalities used to map the dynamic mechanical properties of complex biological samples to their morphology. We discuss how mechanical properties can be directly linked to function, which has remained a poorly addressed issue. We outline the potential of combining AFM with complementary techniques, including optical microscopy and spectroscopy of mechanosensitive fluorescent constructs, super-resolution microscopy, the patch clamp technique and the use of microstructured and fluidic devices to characterize the 3D distribution of mechanical responses within biological systems and to track their morphology and functional state.Peer ReviewedPostprint (published version

Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells.

Although it is a central question in biology, how cell shape controls intracellular dynamics largely remains an open question. Here, we show that the shape of Arabidopsis pavement cells creates a stress pattern that controls microtubule orientation, which then guides cell wall reinforcement. Live-imaging, combined with modeling of cell mechanics, shows that microtubules align along the maximal tensile stress direction within the cells, and atomic force microscopy demonstrates that this leads to reinforcement of the cell wall parallel to the microtubules. This feedback loop is regulated: cell-shape derived stresses could be overridden by imposed tissue level stresses, showing how competition between subcellular and supracellular cues control microtubule behavior. Furthermore, at the microtubule level, we identified an amplification mechanism in which mechanical stress promotes the microtubule response to stress by increasing severing activity. These multiscale feedbacks likely contribute to the robustness of microtubule behavior in plant epidermis. DOI: http://dx.doi.org/10.7554/eLife.01967.001