Proprietà meccaniche e biofisiche di singole cellule

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Mechanical and biophysical properties of single cells

by

Thomas Lanzicher

THESIS

Presented to the Graduate School of Nanotechnology, at the University of Trieste

in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy in Nanotechnology

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Acknowledgements

“Acknowledgement is the only way to keep love alive”

Barry Long

I would like to thank all those who helped me in drafting the thesis with suggestions, criticisms and observations: to them my gratitude goes, even though I have responsibility for every error contained in this thesis. Being here to write thanks today is a great victory! I would like to thank, therefore, all those who have allowed and favored the achievement of this goal. It is not easy to quote and thank, in a few lines, all the people who contributed to the birth and development of this work: those with a constant collaboration, those with moral or material support, those with advice and suggestions or just with words of encouragement. I hope not to forget anyone, but if you, my dear reader, you do not find your name in the next lines. . . tell me and I thank you in person for the mere fact that you have interest in reading.

First of all would like to express my deep-felt gratitude to my advisor, Dr. Orfeo Sbaizero of the Material Engineer Department at the University of Trieste for his advice, encouragement, enduring patience and constant support. Thanks to my colleagues Daniele Borin, Ilaria Pecorari, Laura Squarcia and Valentina Martinelli, you supported me greatly and were always willing to help me.

I would particularly like to thank Dr. Henk Granzier for offering me to be part of his group, welcoming me to carry out this research in his lab and introducing me to biological techniques. He was never ceasing in his belief in me (though I was often doubting in my own abilities), always providing clear explanations when I was (hopelessly) lost, constantly driving me with energy.

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past and present members of the Henk’s Granzier Laboratory for all their helpful discussion and encouragement and more than everyone Kyoko Nakajima, for helping me in a foreign land, and making me feel a little closer to home.

I am thankful to our collaborators Dr. Luisa Mestroni and Dr. Matthew Taylor from University of Colorado. Their enthusiasms for research and constant encouragement have inspired me to overcome every challenge that I encountered during my research. Their insightful directions to achieve our goal have always been helpful and led me to find the right path. With a special mention to Jena Jacobs and Brisa Pena. It was fantastic to have the opportunity to work part of my research in your facilities and share time with you. What a cracking place to work!

A big thank you to all the dear friends who, in different ways, through words, gestures, messages and laughs have encouraged me! Thank you Alberto, Alessandro, Anja, Anna, Enrico, Giacomo, Matteo, Stefano, Piero. You are always so helpful and encouraging.

I would like to acknowledge the financial support of the Fondation Leducq for the three year scholarship, the SarcoSi program and “Associazione Amici del Cuore” to the financial integrations during the periods spent abroad in the U.S.A.. Many thanks to my teachers and professors from elementary, junior and high school to university, who encouraged me to continuously learn and provided me with the foundations for my academic career.

I also wish to thank the members of my revision thesis committee, Dr. Ali J. Marian of University of Texas and Dr. William McKenna of the University College London. Their suggestions, comments and additional guidance were invaluable to the completion of this work.

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Abstract

A living biological cell is a highly complex, multi-functional system whose mechanical cues have been recognized to be fundamental in its overall regulation. Despite the recent ad-vances undergone by nanotechnologies, many doubts still surround how cell behavior is influenced by specific gene mutations and their encoding of part of their structural prop-erties. Using traditional molecular techniques such as immunofluorescence staining, com-bined with atomic force microscopy, through systematic examination, it has been possible to demonstrate the important structural role of the nuclear lamina. Moreover, such proce-dures allowed for the determination of how mutations in a gene encoding part of it have consequences in the deformability and change in shape of cardiac cells. In recent years me-chanical properties have been used to identify diseased states such as cancer. Other groups have used both simple models and isolated nuclei in an attempt to characterize their nu-clear properties. Thus, in this study, we examine the nucleus of intact cells. In response to lamin modification, the shape of the nucleus results both complex and unable to be pre-cisely characterized by isotropic mechanical properties. However, as demonstrated through our findings, the characterization of the cell’s biomechanical properties is absolutely cru-cial in the field of biological physics. Are been assested properties like elasticity, adhesion caratheristic of the membrane, viscoelastic behaviour with single cell force spectroscopy and stress relaxation test. The data suggests that all the researched mutations generate distinctive structural changes in cardiomyocytes, and cardiac fibroblasts. Furthermore, with single molecule force spectroscopy has been characterize the elastic part of the huge protein titin and its interactions with a protein member of the MARP gene family. For the first time the N2A Unique Sequence of the titin has been characterized, furthermore, how the CARP protein interacts with it increasing the persistence length and the forces necessary to unfold the Ig domains.

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Riassunto

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Nomenclature

ADP Adenosine Diphosphate AFM Atomic Force Microscopy

ARVC Arrhythmogenic Right Ventricular Cardiomyopathy

ATP Adenosine Triphosphate AW Adhesion Work

CAM Cell-Adhesion Molecule

CARP Cardiac Ankyrin-Repeat Protein DCM Dilated Cardiomyopathy

E Young’s Modulus ECM ExtraCellular Matrix

EDMD Emery-Dreifuss Muscular Dystro-phy

FBs Cardiac FibroBlasts GTP Guanosynthyphosphate HF Heart Failure

IFs Intermediate Filaments INM Inner Nuclear Membrane Lc Contour Length

Lp Persitence Length

LINC LInker of the Nucleoskeleton and Cytoskeleton

MAPK Mitogen Activated Protein Kinase MARP Muscle Ankyrin-Repeat Protein MFs Actin Microfilaments

MTs Microtubules

NET Nuclear Envelope Transmembrane NRVMs Neonatal Rat Ventricular Myocytes ONM Outer Nuclear Membrane

SCD Sudden Cardiac Death

SCFS Single-Cell Force Spectroscopy SEC-MALL Size Exclusion Chromatography

with Multi Angle Laser Light scat-tering

SFM Force Scanning Microscopy SLS Standard Linear Solid SMA Spinal Muscular Atrophy

SMFS Single-Molecule Force Spectroscopy SPM Scanning Probe Microscopy

SR Stress Relaxation

STM Scanning Tunneling Microscope TIRF Total-Internal-Reflection

Fluores-cence

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List of Tables

2.1 Comparison of elastic moduli for single cells in culture . . . 6

3.1 Theoretical values of the correction factor βn for a free rectangular and a V-shaped cantilever . . . 50

5.1 Statistical data of circularity of cardiomyocytes nuclei . . . 77

5.2 Statistical data of area of cardiomyocytes nuclei, expressed in µm2 _{. . . . .} ₇₈

5.3 Statistical data of height of cardiomyocytes cells, expressed in µm . . . 79

5.4 Statistical data of Young’s modulus of cardiomyocytes, expressed in kPa . 81 5.5 Statistical data of adhesion work of cardiomyocytes, expressed in fJ . . . . 83

5.6 Statistical data of plasticity index of cardiomyocytes . . . 84

5.7 Statistical data of Young’s modulus of cardiomyocytes with LMNA muta-tions treated with 0.1 µM p38 MAPK inhibitor A797, expressed in kPa . . 87

5.8 Statistical data of adhesion work of cardiomyocytes with LMNA mutations treated with 0.1 µM p38 MAPK inhibitor A797, expressed in fJ . . . 88

5.9 Statistical data of Plasticity Index of cardiomyocytes with LMNA mutations treated with 0.1 µM p38 MAPK inhibitor A797 . . . 89

5.10 Statistical data of E0 of cardiomyocytes with LMNA mutations, expressed in kPa . . . 91

5.11 Statistical data of E1 of cardiomyocytes with LMNA mutations, expressed in kPa . . . 92

5.12 Statistical data of τ of cardiomyocytes with LMNA mutations, expressed in seconds . . . 93

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List of Figures

2.1 Single-cell measurement techniques. . . 9

2.2 Deflection signal measured on cardiomyocytes . . . 10

2.3 Schematic of the force-based single-molecule techniques . . . 16

2.4 An overview of the mechanical models for living cell . . . 17

2.5 Cross-section of a cell that shows the main cellular structures of the cy-toskeleton . . . 22

2.6 A) Lattice structure of actin filaments. B) Dense meshwork of actin filaments 24 2.7 A) Lattice structure of microtubule. B) Dense meshwork of microtubules filaments . . . 25

2.8 A) Lattice structure of intermediate filaments. B) Dense meshwork of keratin filaments . . . 26

2.9 Nuclear envelope structure . . . 28

2.10 Nuclear lamins: localization at the nuclear periphery and within the nucle-oplasm. . . 30

2.11 Structure of nuclear lamins. . . 31

2.12 Exon-intron structure of human titin gene . . . 35

2.13 Domain structure of extensible I-band region of cardiac isoforms, N2B and N2BA in cardiac muscle, and N2A in skeletal muscles . . . 37

3.1 Representation of the measuring principle of the AFM. . . 42

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3.3 Force potential diagram showing the operational regions of each of the

imag-ing modes. . . 45

3.4 Schematic representation of an atomic force microscope (AFM) . . . 48

3.5 Illustration of AFM tips used in this work . . . 49

3.6 Scheme of the first three symmetric modes for a rectangular cantilever . . . 50

3.7 Example of a force-indentation curve performed on a live cardiomyocyte nucleus in a liquid environment . . . 52

3.8 Three different strategies to measure adhesion force using AFM. . . 54

3.9 Zener model. One elastic and one viscoelastic Maxwell element arranged in parallel . . . 55

3.10 Typical single-molecule force spectroscopy force vs extension . . . 58

3.11 Chain conformation depends on persistence length . . . 60

4.1 Schematic representation of constructs used for SMFS . . . 67

4.2 AFM images of a cardiomyocyte . . . 68

4.3 Schematic of the AFM force experiment with a spherical probe applied to the nucleus of a cell . . . 70

4.4 Different relaxation profiles on cardiomyocytes NT, using four different forces of load . . . 72

4.5 Three different AFM equipments used in this thesis . . . 73

5.1 Circularity histograms of cardiomyocytes with LMNA mutations . . . 76

5.2 Area histograms of cardiomyocytes nuclei with LMNA mutations . . . 77

5.3 Height histograms of cardiomyocytes cells with LMNA mutations . . . 78

5.4 Examples of alterations in nuclear morphology . . . 80

5.5 Actin relative fluorescence intensity for mutant cells compared to NT and WT 80 5.6 Young’s modulus of cardiomyocytes plotted with Tukey Box Plot . . . 81

5.7 Adhesion work of cardiomyocytes plotted with Tukey Box Plot . . . 82

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5.9 Young’s modulus of cardiomyocytes treated with p38 MAPK inibithor at

different concentrations, plotted with Tukey Box Plot. . . 85

5.10 Young’s modulus of cardiomyocytes with LMNA mutations, before and after 0.1 µM p38 MAPK inhibitor A797, plotted with Tukey Box Plot . . . 86

5.11 Adhesion work of cardiomyocytes with LMNA mutations, before and after 0.1 µM p38 MAPK inhibitor A797, plotted with Tukey Box Plot . . . 87

5.12 Plasticity index of cardiomyocytes with LMNA mutations, before and after 0.1 µM p38 MAPK inhibitor A797, plotted with Tukey Box Plot . . . 88

5.13 Profiles of a typical Stress Relaxation test for two of the conditions analyzed in this work . . . 90

5.14 E0 of cardiomyocytes with LMNA mutations, plotted with Tukey Box Plot 91 5.15 E1 of cardiomyocytes with LMNA mutations, plotted with Tukey Box Plot 92 5.16 τ of cardiomyocytes with LMNA mutations, plotted with Tukey Box Plot . 93 5.17 η of cardiomyocytes with LMNA mutations, plotted with Tukey Box Plot . 94 5.18 Average curve of fitting from Equation 4.5, plotted for each cardiomyocytes condition . . . 95

5.19 Storage module G' profile versus the angular frequency ω . . . 96

5.20 Loss module G'' profile versus the angular frequency ω . . . 96

5.21 Loss tangent profile versus the angular frequency ω . . . 97

5.22 Young’s modulus of cardiac fibroblasts plotted with Tukey Box Plot . . . . 99

5.23 Adhesion work of cardiac fibroblasts plotted with Tukey Box Plot . . . 100

5.24 A force-extension curve of the N2Aus constructs . . . 102

5.25 Increase of contour length in the three N2Aus constructs . . . 102

5.26 Persistence length distribution of N2Aus in absence and in the presence of CARP . . . 104

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7.1 LMNA expression in NRVM infected with AdV-LMNA WT , AdV-LMNA and non-treated uninfected (NT) control . . . 149 7.2 Cellular localization of human WT-LMNA and mutants (E161K,D192G,

N195K) . . . 150 7.3 Representative images of fluorescently stained actin cytoskeleton of mutant

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Chapter 1 Introduction

“If we can reduce the cost and improve the quality of medical technology through advances in nanotechnology, we can more widely address the medical conditions that are prevalent and reduce the level of human suffering”

Ralph Merkle

1.1 Themes and motivation

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dynamic living materials have not only opened a new horizon in scientific research but also generated a significant societal impact.

This thesis will use AFM for two main reasons. On the one hand, it will enable us to characterize the biomechanical properties of cardiac cells together with the description of the titin’s N2A isoform. On the other, the discoveries wrought by it could allow biologists to carry out more systematic and detailed examinations while also lead to a deeper under-standing of cell behavior. This study is motivated by the ways in which particular genetic mutations in nuclear lamina affect the biomechanical properties of cells. At the same time, we aimed to characterise an elastic isoform of the titin together with its interaction with a protein member of the MARP gene family, by conducting single-molecule experiments.

The structure and mechanical integrity of the cell can have profound effects on an ex-tremely various number of processes, namely growth, differentiation, migration, apoptosis, and gene expression. A thorough understanding of the regulation of mechanical and cel-lular functions by external and internal mechanical stimuli requires the study of celcel-lular and subcellular mechanical properties. The basic principles of cellular mechanical property testing include the application of a controllable force which not only deforms the cell but also the assembly of cellular deformation resulting in appropriate mathematical models. Mechanical properties are obtained through the relationship between the geometry of the AFM tip, the applied force, and the displacement/indentation of the sample.

1.2 Objectives

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study are:

To assess the biomechanical properties of cardiac cells (cardiomyocytes and fibrob-lasts), such as elasticity, adhesion properties and plastic behaviour.

To characterize the viscoelasticity of cardiomyocytes using stress relaxation tests. Try to rescue cardiomyocytes with a specific drug, testing if the biomechanical

prop-erties are restored.

To use the AFM to describe the biomechanical properties of the giant protein titin’s N2A region

To measure the changes introduced in the titin by the interaction between the N2A el-ement and a protein member of the MARP gene family: the cardiac-specific CARP/Ankrd1.

1.3 Thesis organization

After expounding the motivation and objective of this work in Chapter One, Chapter Two summarizes the existing knowledge of cellular and nuclear mechanics while also reviewing the existing techniques for measuring the mechanical properties of cells and molecules, with a specific focus on both lamin and titin.

The Chapter Three analyses the AFM technique together with the mathematical models used to interpret AFM data.

Chapter Four shows the materials and methods used in this thesis.

Chapter Five presents the results acquired on the mechanical properties of both cardiomy-ocytes and cardiac fibroblasts and those obtained with the rescue of cardiomycardiomy-ocytes. Ad-ditionally, the results achieved for the elasticity of titin assessed with AFM spectroscopies will also be mentioned.

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Chapter 2 Background

So many books, so little time.

Frank Zappa

2.1 Why study mechanics in biological systems?

Researchers have recently established the link between cellular function and structure. The structure of a cell contributes to its overall elasticity and is the product of more than one organization level. In particular, the elasticity of a cell (stiffness is the opposite of the elasticity) allows the latter to restore its shape after a quick deformation by external pressure.

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calculated rigidity depending on the measurement’s time scale. Most calculations are based on model fitting that assumes a homogeneous, isotropic cell material.

Cell type Elastic modulus (kPa) Method

Rat aortic smooth muscle 1.5 − 11 Elongation between plates

Endothelial 1.5 − 5.6 AFM

Aortic endothelial: normal/cholesterol depleted 0.32/0.54 Microaspiration Endothelial 0.5 cytoplasm 5 nucleus Uniaxial compression

Inner hair cell 0.3 AFM

Outer hair cell 2 − 3.7 AFM

Cardiac myocytes 35 − 42 AFM

Fibroblast 0.6 − 1.6 AFM

Fibroblast 1 − 10 (differential stretch modulus) Uniaxial stretching/compression Bovine articular chondrocytes 1.1 − 8 Creep cytoindentation apparatus

Chondrocytes, Endothelial 0.5 Microaspiration

Neutrophils passive/activated 0.38/0.8 AFM

C2C12 myoblasts 2 Cell loading device (global compression) Alveolar epithelial 0.1 − 0.2 Magnetic twisting cytometry

Epithelial normal/cancerous 10 − 13/0.4 − 1.4 AFM

Osteoblast 1 − 2 AFM

Fibroblasts normal/transformed 0.22/0.19; 0.42 − 0.48/1.0 Optical stretcher

Melanoma 0.3 − 2.0 frequency dependent Magnetic twisting rheometry

Kidney epithelial Cell cortex/Cell interior 0.16/0.04 Magnetic twisting rheometry Tracer diffusion 3T3 fibroblast before/after shear flow 0.015/0.06 Tracer diffusion

C2-7 myogenic 0.66 Uniaxial stretching rheometer

Table 2.1: Comparison of elastic moduli for single cells in culture [Janmey and McCulloch, 2007]

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an extended period of time, two moduli can be identified: the instantaneous modules at the initial resistance to deformation and the relaxation modules identified as the rigidity of the cell once the load reaches the equilibrium [Darling et al., 2008]. Instantaneous and relaxation cellular moduli can be used as biomarkers to characterize and distinguish between different types of cells [Liu et al., 2016, Liu et al., 2012], However this thesis focuses on the elastic responses to mechanical deformation of the cardiomyocytes and fibroblasts, and relaxation modules for just the cardiomyocytes.

Mechanical deformation of in vivo cells can result from a variety of stresses, it can take the form of pure liquid in the lumen of the arteries and veins or a weight in the bones. The cell also experiences in vivo internal pressures that have been shown to act through the cytoskeleton and affect the cell’s mechanical properties. These, in turn, can also change their behavior [Chan and Ulfendahl, 1997]. The elasticity of a living cell is the product of the components of the cytoskeleton and organelles of it. The three main components of the cytoskeleton are: the actin filaments, microtubules, and intermediate filaments. The most important contribution to cellular elasticity is due to the actin network [Haga et al., 2000]. Actin filaments within the cells are made up of polymerized chains of actin monomer. The actin polymerization process is extremely dynamic and contributes to a variety of cellular processes including motility [Cardamone et al., 2011]. On the other hand, there is less evidence on the effect on the cell’s elasticity of the other two components of the cytoskeleton, with no evidence being found on the microtubules and limited influence of the intermediate filaments, has been shown in one work [Wang and Stamenovic, 2000]

The mechanical behavior of the nucleus also contributes to the cellular elasticity. Several studies reported that it is between three and ten times more rigid than the surrounding cytoplasm while also being almost twice as viscous [Guilak et al., 2000, Caille et al., 2002]. From a mechanical point of view, the nucleus can be divided into two parts: the inner nucleus, which consists of chromatin and nucleoli and the outer nuclear envelope of lamins and membrane.

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mN/m2 _{[Dahl, 2004]. In addition, it has been shown that cell nucleus deformation not} only varies in response to shear flow, compression, and stretching, but that this different deformation also alters the DNA packaging within the nucleus itself [Maniotis et al., 1997], changing in this way genes transcription and therefore the overall cell behavior [Shattil and Ginsberg, 1997].

Even though assessing cell elasticity is a complex procedure, researchers have been able to use elasticity data as a distinguishing factor when investigating cancerous cell lines [Faria et al., 2008], the ageing process [Lieber et al., 2004], or wound healing [Wagh et al., 2008]. Furthermore, cell elasticity data are becoming more and more useful when it comes to explaining complex phenomena such as mechanotransduction [Charras and Horton, 2002, Zahn et al., 2011], cell migration [M¨uller et al., 2009] and cell division [Houchmandzadeh and Dimitrov, 2000].

2.2 Methods for measuring single-cell biomechanics

To study biomechanics on a single-cell level, the techniques currently being used can be classified into two main categories that include the local deformation of a cell area by a probe or the mechanical stimulation of the entire cell. The first category includes atomic force microscopy techniques and torsional cytometry by magnetic twisting cytometry. Aspiration by micropipettes, optical tweezers, and microplate deformation fall into the second category. These techniques are used primarily to determine the mechanical properties of the cellular structure. Whereas the forces scale applied ranges from 10 pN to 1 N and the length scales may vary from micrometers to picometers.

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Figure 2.1: Single-cell measurement techniques. A) Atomic Force Microscopy B) Magnetic twisting cytometry C) Cytoindentation D) Laser/optical tweezers E) Microplate stretcher F) Microfabricated post array detector G) Micropipette aspiration H) Shear flow I) Sub-strate stretcher

2.2.1 Atomic Force Microscopy

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(1) Topographic AFM measurements need a tip associated with a microfabricated can-tilever that is scanned through the surface of a sample into a series of horizontal sweeps. A laser beam from a solid state diode is reflected from the back of the cantilever and picked up by photodiodes. Disorders due to surface topography lead to changes in the deflection of the cantilever and thus to a change in the reflection path of the laser beam detected by the photodiodes.

(2) The amount of force detected by the cantilever when the tip approaches, contacts, and indents the cell surface is measured by a force curve. The slope of each force curve rep-resents the elasticity of the sample. The AFM can measure cell deformation in one specif point or across the entire cell surface by recording a set of 2D force curves in a force-volume mode.

(3) In addition to high resolution imaging of biological structures and elasticity measure-ments, AFM has been extensively used in the assessment of the vicoelastic properties of biological materials when a load is applied for a certain amount of time [Moreno-Flores et al., 2010a, Moreno-Flores et al., 2010b, Darling et al., 2006, Darling et al., 2007]. As will be explained in Chapter Four, this thesis uses AFM single-cell force spectroscopy to characterize the biomechanical properties of the cardiac cells, and a AFM single-molecule spectroscopy to characterize the mechanical properties of the elastic isomer of the titin, N2A.

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2.2.2 Optical Tweezers

Optical tweezers were described in 1969 by an experiment conducted by Arthur Ashkin [Ashkin, 1970]. Although at that time the technique had already been widely used in other fields such as physics [Galajda and Ormos, 2002], it had repeatedly been proven to be extremely valuable in the mechanical characterization of cells, cytoskeleton, and viscoelasticity [Icard-Arcizet et al., 2008]. The term optical tweezers derives from the fact that a sphere of dielectric material with a high refractive index is trapped through a typically infrared laser beam. When photons pass through a high refractive index dielectric object they are subjected to a momentary change that results in forces exerted on the same object that pushes it toward the focal point of the laser beam. The forces being exerted are as great as 300 pN and as weak as 0.1 pN. Focusing this intense light through a microscope objective lens and directing it onto small particles (usually ranging from less than 1 µm to ∼ 10 µm) can literally trap them in a ‘well’ of photons. The balance of scattering and gradient forces keeps the bead stable. Trapping is made possible because of the change in momentum experienced by the photons as they are refracted by a transparent dielectric object - a bead in this example. This results in an equal but opposite momentum force which acts upon the bead; it is this force that can be divided in to ‘scattering’ and ‘gradient’ components. While the former act in the direction of light propagation, the latter act to push the bead toward the laser’s focus point.

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of the particle in the trap can be tracked with video tracking, quadrant photodiodes, or by a position-sensitive detector [Kuo, 2001]. Today, optical tweezers can be used to subject biological systems, cells, and biological motors, to precisely calibrated forces and measure the local viscoelasticity as well as the force generated by the systems themselves [Moffitt et al., 2008]). Furthermore, optical traps have been used to assess membrane elasticity, cell motility, cell spreading, adhesion forces, and cytoskeleton mechanics [Schinkinger et al., 2004, Lim et al., 2006]. While some groups have used just one bead, it is more common to see two beads being used to stretch cells [Mills et al., 2004].

2.2.3 Magnetic Bead Microrheometry

The magnetic bead microrheometry also known as magnetic tweezers, is often mentioned alongside the optical tweezers since both involve the accurate beads manipulation to apply forces to the biological system of interest. Similar to the optical tweezers, the beads used in magnetic bead microrheometry are usually coated with proteins such as fibronectin and/or in some case functionalized with ligands to specific cell surface receptors. The general idea for the magnetic tweezers is that a magnetic pole is brought into close proximity with the cell. The magnetic field is non-uniform and as a result, a magnetic force acts on the magnetic particle. The direction and magnitude of this force depends on the scalar product of the magnetic dipole moment of the magnetic particle and the gradient of the magnetic field. The beads used in this technique are typically around 5 µm in diameter and need to be of ferromagnetic materials.

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In order to calibrate the force acting on the magnetic bead and thus reliably measure local viscoelasticity, the speed of displacement of the bead in a solution of known viscosity was measured optically in real time. Young’s modulus could be extracted by applying Stoke’s law to the relationship between magnetic field and the speed of movement, through the viscous solution yields force curves, and using amongst others Hertz’s model [Bausch et al., 1998]. When the magnetic field was applied to the cell they were not directly affected. However, the pull on the cell’s surface caused the probe bead’s bound to be displaced as well. Mapping both the direction and distance of the probe beads in relation to the magnetic bead gave a map of the strain field sensed by the cell. This method has been used on umbilical vein endothelial cells and resulted in data suggesting an anisotropic structuring of the actin cytoskeleton [Feneberg et al., 2004]. It has been also used to study mechanotransduction by applying loads onto focal adhesion sites in cells [Matthews et al., 2004, Matthews, 2006]. The magnetic tweezers are unique since they afford passive, infinite bandwidth, force clamping over large displacements. Furthermore, it has also been used to study nucleic acid enzymes, particularly DNA topoisomerases [Charvin et al., 2005, Strick et al., 2000, Gore et al., 2006].

2.2.4 Micropipette aspiration

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lumen and the movement of the edge can be tracked manually with a cursor imposed on the video screen. A plot of the deformation undergone by the cell membrane against the negative hydrostatic pressure is then taken. This ‘pressure-deformation’ graph essentially gives values of the elasticity of the cell membrane. The technique has been successfully used on living cells in order to study their mechanical behaviour and, as will all methods of characterizing cell mechanics, is subject to a variety of mathematical interpretations of the gathered data [Hochmuth, 2000]. A wide range of cell types have been described with this technique: neutrophils [Derganc et al., 2000], erythrocytes [Artmann et al., 1997] and outer hair cells [Sit et al., 1997].

2.2.5 Microfluidics

Microfluidics can measure cell deformation by forcing cells through small channels. In general, a microfluidic system is first built by fabricating a master mold on a silicon wafer and then pouring a polymer on top of the master mold. For a review of this technique see [Beebe et al., 2002]. The polymer being used must have several properties useful for biological studies including permeability to gases, optical transparency, reproducibility, and nanometer-level fidelity to the original mold. For these reasons the most frequently used polymer is polydimethylsiloxane (PDMS).

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2.3 Methods for measuring single-molecule

biomechanics

There is a wide variety of single-molecule techniques that are available. These methods are separated into two different features: force and fluorescence detection, respectively. These two groups are separated based upon the different time resolutions, span of observations, and different spatial resolutions. In Section 2.2 we have already discussed the specific techniques of the force-based detection methods, i.e. atomic force microscopy, optical tweezers, tethered particle motion and magnetic tweezers. On the other hand, fluorescence imaging includes confocal microscopy and total-internal-reflection fluorescence (TIRF).

This part will solely focus on force-based techniques, techniques described and illus-trated with examples highlighting current capabilities and limitations in a review published on Nature [Neuman and Nagy, 2008]. What all these methods have in common that one end of the molecule being studied is attached to a substrate surface while the free end is attached to either an optically trapped bead, a magnetic bead, or an AFM tip, through which force is applied (see Figure 2.3).

2.3.1 Atomic Force Microscope (Single-Molecule)

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Figure 2.3: Schematic of the force-based single-molecule techniques, (a) AFM, (b) magnetic tweezers, and (c) optical tweezers, showing the folded structure of interest is sandwiched between two long dsDNA handles for mechanical manipulation

2.3.2 Magnetic Tweezers

The Magnetic tweezers setup described in Section 2.2.3 can simultaneously apply both force and rotation to a tethered biomolecule. Used in the study of DNA structural properties and protein-DNA transactions [Manosas et al., 2010], magnetic tweezers work in the constant force mode, since the force is an important control parameter for the interaction of interest. Magnetic tweezers is usually used for studying the structural properties of DNA and protein-DNA transactions [Manosas et al., 2010].

2.3.3 Optical Tweezers

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is pulled out of the aforementioned trap.

2.4 Mechanical models for living cells

In this part, we will examine some mechanical models that have been developed to charac-terize mechanical responses of living cells when subjected to either short or long time scale. For more detailed information refer to reviews such as [Lim et al., 2006, Chen, 2014].

Figure 2.4: An overview of the mechanical models for living cells from [Lim et al., 2006]

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over short time scales with a finite shear modulus whereas it acts as a viscous liquid over longer time scales [Fletcher and Geissler, 2009]. In intermediate regimes the ratio between the elastic and the viscous part governs the cell’s mechanical response. At different hier-archical levels, individual microstructural elements of the cytoskeleton are perturbed by application of force and consequently deformed at microscopic scales to accommodate the resulting macroscopic deformations. Furthermore, processes such as continuous turnover of cytoskeletal fibers, association/dissociation of cross-linkers and activity of molecular mo-tors prove that the cell is an active biological material [Fletcher and Geissler, 2009] that exhibits rheological behaviours by coupling active and passive biochemical and mechanical processes. Indeed, time-dependent measurements of cellular properties reveal a spectrum of relaxation times strongly influenced by the size, stability, geometry, and flexibility of filaments cross-linkers, active motions, and changes in filament structure due to turnover [Lim et al., 2006].

Continuous mechanical models developed for living cells can be divided into two major categories: viscoelastic and biphasic models. The former can in turn be summarized in the three following typologies:

Cortical shell-liquid core (or liquid drop) model; Solid models;

Fractional derivative models

The shell - liquid core cortical models were initially developed to take account of the rheological results obtained by aspiration of neutrophils with micropipettes. This category includes the following four models:

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The compound liquid drop model sees the eukaryotic cell as a structure composed of three distinct layers:

– the outer layer, made up of both the plasma membrane and the ectoplasm with a thickness of about 0.1 µm under a constant tension state;

– the central layer of the fluid like endoplasm, which represents the softest part of the cell;

– the innermost layer, constituted by the nucleus and the surrounding cytoskele-ton, even under constant tension.

This model is more refined than the previous one based on the fact that the core is more viscous and stiffer than the surrounding cytoplasm. This helps to explain some of the experimentally observed phenomena that cannot be considered in the homogeneous model [Hochmuth et al., 1993, Dong et al., 1991].

The shear thinning liquid drop model analyzes the dependence of the apparent cy-toplasmic viscosity from the velocity gradient in the presence of large deformations. This model standardize the cellular cortex as a layer under constant tension, More-over, it also emphasizes how the cytoplasm does not behave like a Newtonian fluid but as a fluid whose viscosity follows a certain law of power function of the defor-mation velocity. In particular, an increase in speed gradient leads to a decrease in viscosity. This trend is also verified by rheological studies conducted on polymeric solutions. Thus, this pattern is consistent with the cell structure rich in polymer structures constituting the cytoskeleton [Tsai et al., 1993];

Maxwell’s liquid drop model takes into account the first and initial deformations and explains the early rapid elastic input of the cell during aspiration into the mi-cropipette. Moreover, according to this model the cell is made up of a a preformed cortex containing a fluid with viscoelastic behavior [Dong et al., 1988].

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the external cortical layer is not considered. The experimental bases for solid models reside in the ability to reach a balance after applying a certain amount of load. For example, endothelial cells and chondrocytes flow into the pipette only when the suction pressure exceeds a critical value. The solid model can be divided into two categories:

the incompressible elastic solid model; the viscoelastic solid model.

The first one is a simplified model that does not consider the time factor. While it is inadequate to describe cellular mechanics, the incompressible elastic solid model is used as a starting point for the viscoelastic solution. The model is represented by two parallel springs, one of which is in series with a damper. Although it was originally proposed to model the behavior of leukocytes, subsequent studies have shown that the latter can be best described using the liquid drop model. However, other types of cells such as endothelial cells, osteoblasts, and chondrocytes have shown a behavior that can be described with the solid model, which is used as a starting point for the viscoelastic solution [Schmid-Sch¨onbein et al., 1981].

The viscoelastic solid model is represented by two parallel springs, one of which is in series with a damper. The aforementioned models can generally be derived with the use of transitional load conditions. However, since cells are frequently subjected to dynamic forces in their physiological environment, it is interesting to evaluate their behavior even under these conditions. The dynamic module exhibits at low frequency (< 10Hz) exponential behavior, However, with a viscous Newtonian component the dynamic module becomes important at high frequencies [Fabry et al., 2003, Alcaraz et al., 2003]. This behavior cannot be explained with spring-damper models (eg the Newton model, Maxwell, and linear solid models) since these would overstate the frequency dependence [Pritz, 1996]. In order to model the rheological behavior for the adherent cells, an exponential structural damping equation was proposed [Fabry et al., 2003].

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cyto-plasm is divided into a fluid and a solid phase consisting of polymer structures. Therefore, because it is appropriate to treat the two phases separately a two-phase model has been developed. This model has been widely used to study the mechanics of musculoskeletal cells, especially single chondrocytes and their interactions with the extracellular cartilage matrix. While the solid phase is treated as a linear elastic material, the fluid phase is in turn treated as a non-viscous liquid. The biphasic properties of bone and cartilage cells have been applied to characterize the dynamic environment of the extracellular matrix where chondrocytes are located [Humphrey, 2001].

To conclude, the choice of different models can influence the interpretation of exper-imental data and lead to different mechanical properties. Also, different techniques and experimental parameters resulting from the cell’s structural heterogeneity can influence the choice of models and thus the experiment’s outcome. It is also necessary to make a distinc-tion between experimental tests performed with the applicadistinc-tion of small deformadistinc-tions to the cells and tests performed with the subjection if the latter to larger deformations. For example, by subjecting white blood cells to large deformations, the cytoskeletal cross-linked structure breaks down, resulting in the possible assumption of the cytoplasm of character-istics usually connected to polymeric solution for which the Newtonian droplet model or the ‘thin-cut’ ‘thin-drop model’ of cut are generally adequate. On the other hand, smaller deformations may leave the cytoskeleton as cross-link and show viscoelastic behavior. In this particular case the Maxwell model and the solid models are more appropriate.

2.5 Mechanical structures in cells

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rearrange both the organization and contractile activity of the cytoskeleton and redistribute the intracellular stress [Chen et al., 2004].

Figure 2.5: Cross-section of a cell that shows the main cellular structures of the cytoskeleton

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each other sideways.

Actin filaments are helical polymers 5 − 10 nm in diameter, with a rigidity defined by a persistence length of ∼ 17 µm [Gittes et al., 1993]. They constitute a significant portion (5−20%) of all eukaryotic cell proteins. The highest presence of actin occurs in muscle tissue cells (about 20% of total protein), where it is essential for the contraction process. Actin is a monomer that binds a nucleotide (ATP or ADP, an adenosine triphosphate is one of the reagents necessary for the synthesis of the RNA, is hydrolyzed to the adenosine diphosphate trough an exothermic process and can be converted to ATP by various processes). Although actin-based filaments can be found almost everywhere in the cell, they often concentrate in the thick area just below the cell membrane. Here, they can stiffen the liquid contents of the cytoplasm, forming the cellular cortex, often giving to the cell plasma membrane their characteristic shape.

The structural unit of actin microfilaments is actin-G, a globular protein that is assem-bled to form protofilaments. Two parallel protofilaments wind up in a straight propeller forming the actin-F filament of the diameter of about 7 nm and a length up to 100 µm (Figure 2.6-A). Actin filaments interacting with particular proteins can also be arranged in parallel bundles or in bundles that are interlaced in bi- or tridimensional networks. The typical morphology of an F-actin cytoskeleton is presented in Figure 2.6-B.

The F-actin cytoskeleton is a key determinant of the cell’s shape and mechanical be-haviour. Advances in quantitative approaches, imaging technology, molecular biology, and biochemistry have enabled rapid progress, both in the control over F-actin cytoskeletal networks in living cells, and in the ability to reconstitute F-actin networks in vitro.

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A) B)

Figure 2.6: A) Lattice structure of actin filaments. B) Dense meshwork of actin filaments

gels, it has been observed that both the stiffness and the mechanical behavior of the actin cytoskeleton are crucially dependent on the type and concentration of actin cross-linking proteins such as filamin and α-actinin [Tseng et al., 2002].

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A) B)

Figure 2.7: A) Lattice structure of microtubule. B) Dense meshwork of microtubules filaments

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A) B)

Figure 2.8: A) Lattice structure of intermediate filaments. B) Dense meshwork of keratin filaments

IFs protein family are encoded by at least 70 genes [Herrmann et al., 2009]. Intermediate filaments have a complex hierarchical structure. The basic building blocks of the filament are two protein chains intertwined as a helix. Pairs of helices lie side-by-side to form a linear protofilament some 2 − 3 nm in width. The intermediate filament itself is a bundle of eight protofilaments in a roughly cylindrical shape about 10 nm in diameter [Parry et al., 2007]. Many intermediate-filament monomers have masses in the 40 − 70 kDa range and lengths of the order 50 nm, such that the mass per unit length of a four-strand protofilament is about 4.5 kDa/nm, and that of a 32-strand filament is about 35 kDa/nm, with some variations (Figure 2.8-A).

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2.6 Nuclear mechanics

The nucleus is the largest organelle within the cell. It houses the nuclear genome and provides a functional environment for the information that will maintain and reproduce not only the cell but also the whole organism. The nuclear envelope which bounds the nucleus to the cytoplasm is composed of the outer nuclear membrane (ONM), the inner nuclear membrane (INM), and the nuclear lamina on the nucleoplasmic side.

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Figure 2.9: Scheme of the interacting proteins at the nuclear envelope. The inner and outer membrane are connected at nuclear pore complexes. The cytoskeleton is anchored to the nucleus via the LINC complexes, composed by nesprins and sun proteins, while on the intranuclear side, the heterochromatin enters in contact at some points with the nuclear lamina.

2.7 Nuclear lamina

The nuclear lamina is a network with extensive regions of four-fold connectivity [Aebi et al., 1986, McKeon et al., 1986]. The lamina consists of interpolated (cytoskeletal) filaments of protein polymers with a molecular weight of 60 − 75 kDa and are assembled into a 10 − 20 nm thick meshwork. The intermediate filaments of the lamina are 10.5 ± 1.5 nm in diameter and are typically separated by about 50 nm in the network [Hoger et al., 1991]. The thickness varies depending on the type of cell, and may also depending on the physiological and pathological state [Ghadially, 1988].

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cells do not express lamins [Dittmer and Misteli, 2011] and do not migrate, they have rigid cell walls that physically protect their genomes.

Lamins are broadly classified in types A and B lamins. In vertebrates, alternative splic-ing of the LMNA gene yields two isoforms A and C. The most internal lamins, those facsplic-ing the nucleoplasm, are the A-type lamin (coded with the LMNA gene) and are expressed mainly in differentiated cells. There are three types of lamins B (B1, B2 or B3), based on the gene that produces them. B-type lamins are usually ubiquitously expressed, whereas A-type lamins are expressed in developmentally regulated temporal patterns.

Lamin A and C are identical for the first 566 amino acids. However lamin C lacks 98 amino acids at the carboxyl terminus that are present in pre-lamin A (before post translational processing) and contains a unique six amino acid carboxyl terminus. The lack of amino acids is the result of the alternative splicing of the gene product to mammalian cells [Pollard et al., 2007]. Other two minor isoforms of LMNA are the isoform C2 and the A∆10. In contrast to cytoplasmic IF proteins, which are very dynamic, nuclear lamins are relatively stable once integrated into the nuclear lamina [Broers et al., 1999].

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heterochro-Figure 2.10: Nuclear lamins: localization at the nuclear periphery and within the nucle-oplasm. Immunofluorescence staining of lamin A/C (red) and lamin B1 (green) in U2OS human osteosarcoma cell and MEF cell nuclei, respectively. From [Dittmer and Misteli, 2011]

matin [Solovei et al., 2013].

2.7.1 Characteristic structural features of lamins

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Figure 2.11: Structure of nuclear lamins [Dechat et al., 2008]. A) Schematic drawing of a pre-lamin polypeptide chain. The central α-helical rod domain (red), the nuclear local-ization signal or NLS (gray), the Ig-fold (blue; its simplified structure indicating the nine β-sheets is depicted), and the C-terminal CAAX box (green) are shown. B) Post-translational processing of pre-lamin A, B1, and B2. These steps lead to mature lamin B1 and B2

Lamins dimerize using their α-helical rod domain, which contains the characteristic coiled-coil heptad repeat pattern. Higher-order polymerization of lamins involves head-to-tail parallel association between two or more lamin dimers, resulting in a lamin polymer.

2.7.2 Pathological conditions associated to lamins

Lamins’ mutations cause a variety of diseases collectively termed laminopathies. So far nearly 400 different disease-causing mutations in A-type lamins have been identified, un-derscoring their significance to cell and tissue biology and human physiology.

Laminopathies can be generally grouped in different subcategories. The more detailed classification is based on the organs or system affected by diseases, as already reported by Liu and Zhou [Liu and Zhou, 2008]. The first human disease to be caused by LMNA mutations and identified by positional cloning was the autosomal dominant Emery-Dreifuss muscular dystrophy [Bonne et al., 1999].

Several pathologies related to mutations in LMNA are (On-line Mendelian Inheritance in Man entry numbers are given in parentheses):

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and Recessive (#604929), autosomal dominant limb-girdle muscular dystrophy 1B (#159001), dilated cardiomyopathy 1A (#115200));

Lipodystrophy Syndromes (Dunningan type familial partial lipodystrophy, called FPLD (#151660), Lipoatrophy with Diabetes, Hepatic Steatosis, Hypertrophic Car-diomyopathy and Leukomelanodermic Papules (#608056), Recessive Mandibuloacral Dysplasia (#248370)[Mandibuloacral dysplasia also has features of accelerated ag-ing])

Peripheral Neuropathy (Charcot Marie tooth disease type 2B1, called CMT2B1 (#605588)); Accelerated Aging Disorders (Hutchinson Gilford progeria syndrome, called HGPS

(#176670), Werner Syndrome (#277700 for Werner syndrome), Restrictive Dermopa-thy Lethal (#275210))

The mutations that usually cause pathologies in adipose tissues are generally located close to the C-terminus and usually, the closer the mutation is to this terminus, the more severe the progeriod syndrome is [Liu and Zhou, 2008]. Instead mutations that lead to pathologies in striated muscles and peripheral nerves are generally located closer to the N-terminus. Mutations causing laminopathies include recessive as well as dominant alleles with rare de novo mutations creating dominant alleles that do not allow their carriers to reproduce before death. It is worth emphasizing that all the aforementioned pathologies are not mutually exclusive since both phenotypes and features can in fact overlap.

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et al., 2016, Forleo et al., 2015, Quarta et al., 2012, Valtuille et al., 2013]. Over the years, the attempts to connect LMNA mutations with both common and rare diseases have largely increased in number. Besides the already mentioned case of ARVC, a linkage between a lamin A/C gene mutation and spinal muscular atrophy (SMA) in the autosomal dominant form has been demonstrated [Rudnik-Sch¨oneborn et al., 2007, Iwahara et al., 2015].

Since all the aforementioned pathologies involve mutations in the lamin A/C gene, they are considered as primary laminopathies. It is worth mentioning the existence of another class of diseases, namely the secondary laminopathies, which involve genes that encode for proteins and molecules interacting with lamins (e.g., emerin, ZMPSTE24).

Moreover, further evidences hav ehighlighted the link between lamin and other diseases. In particular, lamins have been studied in relation to cancer and several studies have shown that in cancers the lamin levels of many organs change when compared to normal tissue. Deregulated lamin expression has been observed in various cancers. Loss of lamin A/C expression has been reported in colon cancer [Wu et al., 2009], small cell lung cancer [Broers et al., 1993], leukemias and lymphomas [Stadelmann et al., 1990, Agrelo et al., 2005], ovarian cancer [Capo-chichi et al., 2011], and breast cancer [Capo-Chichi et al., 2011, Wazir et al., 2013]. On the other hand, overexpression of lamin A/C has been reported in ovarian cancers [Hudson et al., 2007], colorectal cancer [Willis et al., 2008], prostate cancer [Kong et al., 2012], and skin cancer [Tilli et al., 2003, Venables et al., 2001].

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cardiomy-opathy phenotype has never been investigated.

As it has been reported in several families in the literature, the E161K mutation may represent an important mutation hotspot [Perrot et al., 2009, S´ebillon et al., 2003].

The D192G mutation has only been described in one family with a severe phenotype. The initial report, along with follow-up studies, have noted severe ultrastructural disruption of nuclear envelope architecture [Lanzicher et al., 2015b, Lanzicher et al., 2015a].

Mutation N195K was selected for this study because it was the among one of the first reported LMNA mutations linked to dilated cardiomyopathy in a seminal paper by Fatkin [Fatkin et al., 1999].

Recent data shows that cytokine cascades induced by p38 MAPK pathway activation are implicated in several cardiovascular diseases [Kerkela and Force, 2006]. In addition, p38 MAPK may be involved in many aspects of cardiac pathology, independent from the well-described inflammatory cytokine and chemokine pathway interactions, including gene reg-ulation, interstitial remodeling, and endothelial dysfunction [Behr et al., 2003, Petrich and Wang, 2004]. The effect of the p38 inhibition are several. Not only it decreased cardiomy-ocyte apoptosis and improved cardiac function after myocardial ischemia and reperfusion [Ma et al., 1999], but it was also shown to reduce hypertrophy and left ventricular dys-function in cardiomyopathic hamsters [Kyoi et al., 2006]. Finally, p38 activation produces negative inotropic and restrictive diastolic effects thus confirming the role of this pathway in the development of both ventricular diastolic and systolic remodeling [Liao et al., 2001]. Hyperactivation of p38α was detected in heart tissue in humans with dilated cardiomyopa-thy caused by LMNA mutation [Muchir et al., 2012] as well as in two well-known mouse models of LMNA-related DCM.

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Figure 2.12: Exon-intron structure of human titin gene

2.8 Titin

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anchorage supplied by myosin binding protein-C [Kampourakis et al., 2014]. The extensible behaviour of titin is derived from the I-band region, which serves to restore muscles to their resting length, prevent damage that may arise from over-stretch, and maintain sarcomere homogeneity and stability by centering myosin [Labeit et al., 2003]. Titin’s extensible region is composed of immunoglobulin (Ig)-like domains, the PEVK segment [rich in amino-acids proline (P), glutamate (E), valine (V) and lysine (K)], and the N2B [Granzier and Labeit, 2004]. The proximal and distal Ig segments are mechanically and spatially different enough to require a separate classification [Li et al., 2002]. Differential splicing of the titin gene results in muscle-specific isoforms of varying lengths [Linke et al., 2002], which translates into unique elastic behaviours in different muscles [Freiburg et al., 2000]. The heart of small mammals such as mice and rats expresses predominantly N2B titin, whereas larger mammals, including humans, co-express N2B and N2BA titins [Yamasaki et al., 2001]. N2BA titin molecules contain a much longer PEVK segment than N2B titin, an additional tandem Ig segment, and the N2A element. In addition to isoform variation,the force production of titin is further complexed through dynamic adjustments to short term events such as calcium flux [Labeit et al., 2003] or phosphorylation [Anderson et al., 2010, Granzier and Labeit, 2006].

At the extreme COOH- terminus of titin, the domains M7-M10 bind to A- and B-type lamins [Zastrow et al., 2006]. This interaction likely involves nuclear forms of titin found in non-muscle cells [Machado and Andrew, 2000], which could contribute via their lamin-binding properties to nuclear organization during interphase. In C. elegans embryos, titin co-localizes with lamins at the nuclear envelope, and because this localization required lamins, it suggests that the nuclear titin is anchored or organized by lamin filaments. Titin is also slightly enriched at the nuclear envelope in human cells [Zastrow et al., 2006].

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Mutations in titin cause both ARVC [Taylor et al., 2011] and dilated cardiomyopathy [Gerull et al., 2002]. Interestingly enough, these kinds of cardiomyopathy are also a clinical phenotype in many lamin-linked syndromes [Capell and Collins, 2006].

While titin’s chemical composition and structure are well understood, its mechanical and elastic properties and the specific way in which those properties contribute to muscle function are less comprehended, therefore making them the central focus of this particular study.

Figure 2.13: Domain structure of extensible I-band region of cardiac isoforms, N2B and N2BA in cardiac muscle, and N2A in skeletal muscles. Number of Ig domains (red) inter-spersed between N2B and N2A elements varies

2.8.1 Titin phosphorylation and CARP interaction

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by protein kinases, and, possibly, oxidative stress through disulfide bond formation. Due to the huge size of titin, there are numerous predicted phosphosites or areas where titin can be phosphorylated. However, only a few of them have been confirmed to change the biomechanical properties of this protein. More than 70 serine/threonine/tyrosine phospho-sites in total were confirmed in titin using a phosphoproteomics approach [Hamdani et al., 2013], with 17 others suggested to be phosphorylated by Ca2+_{/calmodulin-dependent} pro-tein kinase-II (CaMKII). Although many phosphosites are located in the Ig domain folds, these have proven difficult to expose without unfolding the domain. This is also true for the proximal and middle Ig domains of titin, which preferentially unfold under physiological conditions [Rivas-Pardo et al., 2016]. By in vivo quantitative phosphoproteomics, I-band titin phosphosites were also detected in three Ig domains and in a linker sequence between two such domains, located in the proximal and middle Ig segments and the N2A element, respectively [Hamdani et al., 2013].

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The recombinant N2A region of titin has been shown to be phosphorylated by PKG in back-phosphorylation assays, but the precise phosphorylation sites were not located. Contrary to N2Bus, PKG phosphorylation did not appear to alter the mechanical properties of the N2Aus in single-molecule AFM force-extension measurements [Kr¨uger et al., 2009]. In conclusion, changes in titin phosphorylation not only change myofibril stiffness but also alter the capacity of the cardiomyocytes to correctly sense the afterload and stop the hypertrophic signaling triggered by the increase in right ventricle wall stress [Rain et al., 2016].

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Chapter 3 Atomic force Microscopy (AFM) and

mathematical models for assessing

cell and molecules properties

The science of today is the technology of tomorrow.

Edward Teller

3.1 AFM operational principle

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de-Figure 3.1: Representation of the measuring principle of the AFM. A laser is reflected on the back of the tip and is detected on a four-quadrant photodiode. Feedback is made by the software to adjust the height of the tip

flection. This was the result of the Force Scanning Microscopy (SFM), otherwise called Atomic Force Microscopy (AFM) [Binnig et al., 1986].

Force scanning microscopy measures the interactions between the sensor and the surface, such as electrostatic, van der Waals, capillary, or magnetic forces. What the biologists were most excited about was the possibility of generating high resolution images of fixed and living cells [Braet et al., 1998, Le Grimellec et al., 1998].

The cantilever present in the AFM, which uses a force sensing mechanism, presents a sharpened tip positioned at its end which is scanned across the sample in a similar way to the STM. Due to interaction forces, the cantilever is deflected according to the sample’s topography. These deflections are recorded using a laser spot reflected off the back of the cantilever onto the center of a quadrant photodetector. The voltage required to change the height of the piezo stack to keep the laser spot inside the edges is utilized to develop a picture of the surface (Figure 3.1).

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A) B)

Figure 3.2: Effect of tip diameter on the lateral resolution of an AFM. In A), the tip is not able to image the bottom of round objects, whereas in (B), the tip is not able to image the bottom and lateral surface between the objects. The dotted line represents the image produced by the AFM.

the AFM does not operate in a similar fashion to traditional microscopes. The resolution of an AFM is not limited by the wavelength of light but instead by the geometry of the probe tip and the forces acting between the AFM itself and the sample surface. The resolution of an AFM image has a lot to do with the geometry of the cantilever tip. Generally the sharper the tip the higher the resolution achievable as it will be able to resolve smaller and smaller topographical variations in the sample as it is raster scanned across (Figure 3.2).

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Figure 3.3: Force potential diagram showing the operational regions of each of the imaging modes.

3.2 Operation modes

Imaging with AFM can be divided in to two main subtypes. Those in which the static deflection of the cantilever is measured, and those which measure changes in the cantilever’s oscillation. The AFM’s scan range of the AFM (100 x 100 µm max) is large enough to encompass the majority of a cell body. Consequently, it can be used to gain an overview of the whole cell before deciding upon the locations for further investigation.

3.2.1 Contact mode

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cell they are sufficient to ‘feel’ the underlying tensile structures of the cell as the plasma membrane is folded around due to the force of the tip. Contact mode cantilevers are often made of silicon nitride, thus making them extremely flexible and soft enough to image live cells. Although this mode stabilizes the vertical force exhibited by the cantilever over the sample, it also creates high lateral forces which are capable of displacing or even tearing delicate biological samples such as cells and biopolymers.

3.2.2 Non-contact mode

In non-contact mode the tip of the cantilever does not touch the surface of the sample. The cantilever is oscillated at a frequency close to or equal to the resonance frequency in which the oscillation amplitude is typically of few nanometers (< 10 nm).

Van der Waals forces (which are stronger to sample surface (1 nm to 10 nm) from the surface, or any other long-range interaction force that the tip feels), act to reduce the cantilever resonance frequency. Because the feedback system is affected by this decrease, it adjusts to maintain a steady oscillation and regulates the average distance between tip and sample. Measuring the point-to-point distance allows the scanning software to construct a topographic image of the sample’s surface. In case of rigid samples, the contact and non-contact modes differ only in the quality of the image obtained. To achieve optimal image resolution and minimum ‘wear’ on the tip it is essential that of non-contact imaging is carried out in air.

3.2.3 Tapping mode

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the sample surface is not damaged. Tapping mode also prolongs the lifetime of the tip as blunting can be reduced and the tip is gentler to loosely adhered or fragile samples, a typical tip-sample force of is around 2 nN every ‘tap’ [Putman et al., 1994]. Due to the nature of the technique, tapping cantilevers must be significantly stiffer than those used in contact mode so as to allow such high frequency oscillations with the power to overcome the sample adhesive fluid. Like contact mode, tapping mode takes place in the repulsive contact region of the force potential curve (Figure 3.3). Therefore, although lateral forces acting upon the sample are greatly reduced, the sample is still subject to compression forces which can impact upon the specimen’s behaviour.

3.3 Principal elements of an Atomic Force Microscope

The main structural parts of an AFM are (see Figure 3.4):

a probe, consisting of a lever (cantilever) with a tip mounted at its end; a vertical probe detection system;

a translation system that allows the sample to be moved below the probe (sample scanning) or vice versa (tip scanning);

a computer through which the operator can interface to start most procedures.

3.3.1 Cantilever and tip

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Figure 3.4: Schematic representation of an atomic force microscope (AFM)

cantilevers may support tips of various lengths. A possible classification divides the tips into three categories:

normal tip, consisting of a pyramid of about 3 µm in height and with a radius of curvature of 30 nm;

supertip, longer and slender than the previous one. It is produced by electronic bombardment of a normal tip and subsequent deposition of carbonaceous material; ultralever, even thinner and longer (100 µm) tip that can reach a 10 nm bend radius. The pyramidal tip in the cantilever is used to analyze individual molecules where the iteration is limited to the tip end, and with curvature radius generally of about 10 nm. Con-versely, when a less invasive contact with the sample area is needed, a spherical geometry is a better choice.

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Figure 3.5: On the left a triangular cantilever with a sharp tip for SMFS experiments and on the right a spherical tip used for SCFS and SR test.

single molecule spectroscopy experiments.

Assessment of the cantilever spring constant

The cantilever spring constant k can be calculated from the total cantilever deflection (∆z ) due to thermal fluctuations [Hutter and Bechhoefer, 1993]. If the cantilever is modeled as a harmonic oscillator in thermodynamic equilibrium, the mean-square displacement of the cantilever tip from its neutral position is described by [Stark et al., 2001]

< ∆z2 >= kBT kc

(3.1) with kB being the Boltzmann constant and T the temperature. Due to the cantilever’s geometry several vibration modes are possible (Figure 3.6), to obtain the mean square deflection of one mode < ∆z2 _{> (often the first), a correction factor β}

n must be used < ∆z_n2 >= kBT

kc

βn (3.2)

Proprietà meccaniche e biofisiche di singole cellule

Acknowledgements

Abstract

Riassunto

Nomenclature

Table of Contents

List of Tables

List of Figures

Chapter 1

Introduction

1.1

Themes and motivation

1.2

Objectives

1.3

Thesis organization

Chapter 2

Background

2.1

Why study mechanics in biological systems?

2.2

Methods for measuring single-cell biomechanics

2.2.1

Atomic Force Microscopy

2.2.2

Optical Tweezers

2.2.3

Magnetic Bead Microrheometry

2.2.4

Micropipette aspiration

2.2.5

Microfluidics

2.3

Methods for measuring single-molecule

biomechanics

2.3.1

Atomic Force Microscope (Single-Molecule)

2.3.2

Magnetic Tweezers

2.3.3

Optical Tweezers

2.4

Mechanical models for living cells

2.5

Mechanical structures in cells

2.6

Nuclear mechanics

2.7

Nuclear lamina

2.7.1

Characteristic structural features of lamins

2.7.2

Pathological conditions associated to lamins

2.8

Titin

2.8.1

Titin phosphorylation and CARP interaction

Chapter 3

Atomic force Microscopy (AFM) and

mathematical models for assessing

cell and molecules properties

3.1

AFM operational principle

3.2

Operation modes

3.2.1

Contact mode

3.2.2

Non-contact mode

3.2.3

Tapping mode

3.3

Principal elements of an Atomic Force Microscope

3.3.1

Cantilever and tip