Biomechanical analysis of structural deformation in living cells
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Most tissues are subject to some form of physiological mechanical loading which results in deformation of the cells triggering intracellular mechanotransduction pathways. This response to loading is generally essential for the health of the tissue, although more pronounced deformation may result in cell and tissue damage. In order to determine the biological response of cells to loading it is necessary to understand how cells and intracellular structures deform. This paper reviews the various loading systems that have been adopted for studying cell deformation both in situ within tissue explants and in isolated cell culture systems. In particular it describes loading systems which facilitate visualisation and subsequent quantification of cell deformation. The review also describes the associated microscopy and image analysis techniques. The review focuses on deformation of chondrocytes with additional information on a variety of other cell types including neurons, red blood cells, epithelial cells and skin and muscle cells.
KeywordsCell deformation Mechanotransduction Mechanics Confocal Biomechanics
1 Cell deformation
All tissues in mammalian organisms are composed of an assembly of cells, most of which are situated in structures subjected to a degree of mechanical loading. The mechanical stimuli are transferred to the cells, typically through any associated extracellular matrix (ECM) resulting in deformation to the living cells. This physiological or pathological loading may alter cellular behaviour in a process termed mechanotransduction. For example, applied forces and associated cell deformation induce a variety of cellular processes including growth, differentiation, adaptation and cellular breakdown. Knowledge of the deformation or strain, experienced by the cells within a tissue, can aid in the understanding of these mechanotransduction processes which are vitally important in many aspects of tissue health, damage and disease. Common examples include mechanosensory mechanisms in bone , cartilage maintenance and homoeostasis as affected by both static and dynamic compression [41, 66] and the formation of atherosclerotic plaques in vascular tissues [15, 51]. In addition, in vitro mechanical conditioning strategies for cell-seeded scaffolds, have been proposed as an essential feature for ensuring the long term functionality of tissue engineered implants, such as those for ligament  and cartilage [37, 54, 79]. This requires the development of suitable bioreactors, incorporating mechanical loading modules for use in a controlled biological environment. Accordingly, the manner in which tissues and cells respond to different mechanical environments has attracted a wide interest. Many studies have investigated the influence of mechanical loading on different aspects of cell function and the associated mechanotransduction signalling pathways in a diverse range of cell types. However, one significant criticism of many of these studies is that the researchers have little or no idea of the biomechanical stimuli at a cellular level such as the degree of cell deformation. Without this fundamental knowledge it is difficult to fully elucidate the underlying mechanostransduction signalling mechanisms and pathways. This review therefore examines the analysis of cell deformation and the techniques that may be employed for a variety of cell types exposed to different biomechanical stimuli. In addition this review examines techniques that may be used to calculate cellular mechanical properties by combining measurements of cell deformation with precise measurements of applied force or pressure.
2 Mechanical loading systems for the study of cell deformation
For several decades, there has been interest in visualising and measuring the deformation of living cells. Measurements generally involve deformation of the cell surface, at least in part, by a known force, stress or applied strain. There are numerous techniques to impart some form of deformation on living cells whilst simultaneously enabling direct microscopic visualisation and/or measurement of cell deformation. There have been many studies describing specialist loading rigs and bioreactor systems designed to apply in vitro mechanical stimuli to cells in order to study their metabolic or injury responses (for review see ).
Typically, the deformation of most cells in vivo occurs through the gross mechanical loading of the whole tissue. This tissue deformation is transferred to the cells, either directly, via the extracellular matrix, as in muscle, or indirectly as in bone where loading induced fluid flow causes shear deformation at the cell surface. However, for blood cells, physiological deformation occurs during flow through narrow capillaries . Similarly endothelial cells forming the lining of blood vessels experience deformation through a combination of fluid shear and circumferential mechanical stretch of the tissue . In addition, changes in extracellular osmotic pressures may trigger cell deformation in the form of volumetric changes [13, 21, 34]. Clearly, a range of different loading parameters and in vitro cell based model systems are therefore required to investigate physiological deformation in different cell types.
2.1 Cell deformation in tissue explants
Whatever the tissue type and loading modality, it is clear that the heterogeneous nature of most biological tissues frequently results in heterogeneous levels of local deformation, such that the local tissue strains differ greatly from the applied gross strain. This can be illustrated by analysing the local strains within viable fascicles dissected from tendon explants and subjected to tensile strain in a microscope-mounted loading rig similar to that shown in Fig. 1 . Using the nuclei of the tendon cells as displacement markers, the local strains along the collagen fibres were found to be consistently smaller, never exceeding 1.2% even at a gross applied strain of 8%.
Where gross mechanical loading induces local tissue deformation, this may be transferred to the cells via the extracellular matrix which interfaces with the cell through cell surface receptors and integrins. In the case of intact cartilage explants, gross compressive strain is transferred to the chondrocytes, resulting in cell deformation with an associated reduction in cell volume [25, 27]. This loss of cell volume in situ may result directly from mechanical deformation squeezing fluid from the cell. Alternatively, fluid loss from the compressed extracellular matrix may produce an increase in pericellular osmolarity and hence an osmotic deformation of the cells. Similar cell deformation via mechanical and physicochemical processes may also occur in other tissues.
2.2 Deformation of isolated cells seeded in 3D scaffolds
For many cell types, appropriate in vitro model systems involve culturing the living cells within a 3D scaffold. Accordingly, studies have examined the deformation of the various cell types subjected to mechanical stimuli within 3D scaffold systems. In addition, the increasing interest in tissue engineering techniques has led to the development of cell-seeded scaffolds systems for repair of diseased or damaged tissues including cartilage, bone, ligament, liver and nerve. In order to optimise the design of mechanical conditioning bioreactors used for tissue engineering, it is important to understand the mechanical stimuli perceived by isolated cells in 3D scaffolds. Thus it is necessary to determine the degree of cell deformation and how this varies in space and time. For low modulus scaffolds, such as the widely used hydrogels, agarose and alginate, compressive strain can be applied using relatively simple microscope-mounted loading rigs such as that shown in Fig. 1. These enable simultaneous visualisation of cells at different levels of applied gross compression. Equivalent systems can also be used to apply tensile strain to cell seeded scaffolds, although, in this case, the ends of the specimen need to be securely gripped.
It is important to appreciate that the nature of cell deformation in 3D scaffolds can differ from that experience in the native tissue. This may be the result of difference in the scaffold mechanical or physicochemical properties, differences in cell attachment or the effects of newly elaborated extracellular matrix. For example, compression of freshly isolated chondrocytes in agarose, as shown in Fig. 1, occurs with significant lateral expansion and conservation of cell volume  in contrast to the behaviour in cartilage explants [25, 27]. Furthermore, the matrix synthesised by isolated cells can form a pericellular shell which is stiffer than the surrounding agarose and thus prevents cell deformation during gross compression . Furthermore the viscoelastic properties of the scaffold relative to the cell can lead to temporal changes in cell deformation during either static or cyclic compression [43, 45].
Analysis of cell deformation in 3D scaffolds has also been utilised as a means of quantifying cell mechanical properties. An example of this indirect method involves compressing isolated chondrocytes in 2% (w/v) alginate gel (GMB low viscosity, Kelco, UK) using the microscope mounted loading rig shown in Fig. 1. By monitoring the reduction in cell deformation over a 60 min period of static compression and relating this to the viscoelastic stress relaxation in the gel, measured using a 2.5 N load cell, it was possible to estimate the cell compressive modulus (E = stress/strain) at a value of approximately 3 kPa [2, 3, 45]. However, this approach does not take into account the long term viscoelastic behaviour of the cell as demonstrated in previous studies [45, 77].
2.3 Deformation of cells using substrate tension
2.4 Deformation of cells subjected to fluid shear forces
2.5 Cell deformation using atomic force microscopy
Atomic force microscopy (AFM) systems, which were developed from a simple cell poking approach, are now available in both laboratory-based and commercial systems (e.g. Veeco Instruments). They have been employed in a range of applications, primarily in the broad area of nanotechnology and micromechanics. Their use in cell deformation, involves the indentation of the cell surface with a small probe, whose movement is controlled at constant velocity [64, 68]. The tip, with a radius of curvature of less than 20 nm, is typically pyramidial in shape, 0.6 μm in height and 4 μm in diagonal length of base. The tip is carefully moved towards the surface of an individual cells, imaged through a conventional light microscope. It can interact with various locations on the cell surface with the force indirectly recorded under indentation control of the tip. Hence structural properties, in the form of the force-deformation relationship, can be obtained. However, it should be recognised that interpretation of the results from AFM deformation is complicated by the tapered shape of its probe tip and its small size relative to the depth of indentation. Therefore to determine material properties, such as the cell modulus from this experimental approach, finite element models have been proposed . However, this mode of deformation has little physiological relevance to most cell types.
2.6 Cell deformation using micropipette aspiration
2.7 Specialised systems for deformation of single isolated cells
There exist several different techniques for stimulating individual isolated cells through the direct application of mechanical deformation, frequently via a micropipette. However, these so called cell “poking” or “puffing” techniques are non-quantitative, of low repeatability and can not be used to elucidate the influence of different biomechanical loading parameters, such as strain magnitude, rate, frequency and duration. Accordingly, other single cell loading systems have been proposed for examining the role of cytoskeletal actin and the nucleus on the time-dependent compressive behaviour of single muscle cells up to ultimate bursting [60, 61]. In addition, a tensile loading system has also been described, incorporating two micropipettes to grip either side a single fibroblast . One micropipette is fixed to a load cell and the other is attached to a linear actuator providing controlled tensile or compressive strains to the cell. Both tension and compression yield force-deformation curves, which thereby enable measurement of the mechanical and anisotropic properties of the cell.
3 Intracellular deformation
Whilst the measurement of cell deformation is essential for analysing gross cell mechanics and potential mechanotransduction mechanisms, an understanding of intracellular deformation provides additional, important information in both these areas. In particular, it can provide clearer understanding of both the structures which provide cells with their viscoelastic time dependent mechanical properties and the intracellular signalling pathways through which cell deformation is translated into an alteration in cell activity. For example mechanical loading of cartilage induces cell deformation with associated distortion of cellular organelles including the rough endoplasmic reticulum , mitochondria , nucleus  and the primary cilium , all of which may have a role in mechanotransduction.
Whilst cell shape may be relatively stable over time, the intracellular environment exhibits significant temporal dynamics. This may occur at both the molecular level, such as the continuous turnover of cytoskeletal proteins, and at the structural level with continuous movement and remodelling. Thus any measurement of intracellular deformation, which occurs over a finite time span, must take into account the inherent temporal dynamics of the system. This is best achieved by limiting the time between unstrained and strained images and comparing measurements of displacement and apparent deformation with those that occurs in unstrained cells over the same time period.
The situation is further complicated by the fact that mechanical stimuli can induce both a direct mechanical deformation on the cell and its intracellular structures as well as an indirect remodelling effect. For example, fluid shear as experience by epithelial cells, creates an initial cell deformation which, in turn, triggers substantial morphological changes, cell reorientation and cytoskeletal remodelling . Care must therefore be taken to distinguish between the direct and indirect effects of mechanical stimuli. This can be partially achieved by considering the time scales over which any cellular or intracellular deformation occurs, with more instantaneous effects most likely to be associated with a direct mechanical deformation. However, this is complicated by the fact that any deformation is likely to be time-dependent due to the viscoelastic properties of the cell [2, 28, 39, 69, 80].
Of all the intracellular structures, mechanical deformation of the nucleus has been most commonly examined. Previous studies, using a variety of cell types, indicate that gross compression is transferred from the cell membrane through the cytoplasm to the nucleus . This results in nucleus deformation which may be involved in mechanotransduction through changes in gene expression and nuclear transport . Studies using pipette aspiration to estimate the mechanical properties of the nucleus report that it is approximately 10 times stiffer than the surrounding cytoplasm . Thus, the levels of nucleus deformation are typically less than that of the cell [26, 45, 50]. However, changes in the mechanical properties of the nucleus, for example during differentiation or disease, may result in changes in nucleus deformation and associated alterations in mechanotransduction. In addition, the relative stiffness of the nucleus means that where cell deformation is sufficient to induce nuclear distortion, the nucleus is likely to provide a significant contribution to the gross mechanical stiffness of the cell. Nucleus morphology and deformation are typically heterogeneous and nonuniform, even in situations where the cell morphology and deformation may be considered uniform, such as compression of chondrocytes in 3D constructs . This needs to be considered when quantifying nucleus deformation ideally performed using live cell imaging. Cytoskeletal integrity is important for strain transfer to the nucleus [19, 38] and thus changes in cytoskeletal organisation may also result in alterations in nucleus deformation [45, 50].
4 Visualisation of cellular and intracellular deformation
4.1 Live cell fluorescence microscopy
The inherent variability in the size, shape and orientation of living cells means that accurate measurement of changes in these parameters is best performed when the same cell can be visualised in both the unstrained and strained state. This therefore precludes the use of techniques such as scanning electron microscopy (SEM) or transmission electron microscopy (TEM) which, although providing high resolution images, require cells to be fixed before imaging. Therefore, in order to quantify the nature and magnitude of cell deformation during physiological mechanical stimuli, studies have adopted various forms of live cell light microscopy. These include techniques such as brightfield, phase contrast or differential interference contrast microscopy as well as epi-fluorescensce and confocal laser scanning microscopy. Of these, the fluorescence-based techniques not only provide clear images of the cell, but are also useful for investigating the deformation of intracellular structures and organelles which can be fluorescently tagged.
The use of fluorescence or confocal microscopy is typically performed using viable fluorescent whole cell stains, such as Calcein AM or Cell Tracker Green (Molecular Probes) . An alternative approach is to saturate the extracellular environment with a low molecular weight fluorescent molecule such as FITC, which is excluded from viable cells. This thereby creates an inverse image of the cell as demonstrated for chondrocytes within intact articular cartilage . Which ever technique is adopted, it is necessary to clearly define the boundary of the cell for precise measurement of cell dimensions and deformation. For fluorescence-based imaging this may be achieved using a high pass digital filter with an intensity threshold set at either a fixed value or a percentage of the maximum intensity [22, 27].
For the study of intracellular deformations, the optical sectioning capability of confocal laser scanning microscopy enables clear, blur-free imaging of intracellular structures. The scope of this technology has been greatly enhanced by the every increasing range of fluorescent compounds for labelling intracellular structures and organelles in living cells (see Molecular Probes: http://probes.invitrogen.com/). Thus viable fluorescent markers are now available for organelles including the nucleus, mitochondria and endoplasmic reticulum. Whilst most of these compounds are cell permeable, for labelling of other structures, such as the cytoskeletal protein networks, it is possible to use microinjection of fluorescent analogues (for review see ). Alternatively the development of transfection techniques involving fluorescent tags, such as green fluorescent protein (GFP), provides a powerful tool for visualising intracellular structural dynamics and deformation within living cells (Fig. 6).
4.2 Image resolution
Thus for a typical x63/1.4NA objective lens and an excitation of 488 nm, the limit of axial resolution is approximately 0.21 μm. Clearly this is sufficient to measure changes in the shape or size of cells on the micrometer scale (Fig. 3), but insufficient to directly visualise sub-micron level deformation such as localised distortion of the cell membrane. However, the development of fluorescence resonance energy transfer (FRET) techniques or specialised probes such as Laurdan  may provide exciting new approaches for measuring deformation and strain beyond the limit of optical resolution.
4.3 Confocal microscopy for quantification of 3D cell deformation
An interesting alternative approach for quantifying cell volume changes can be performed by measuring the average fluorescent intensity within cells labelled with the fluorescent stain 5-chloromethylfluorescein diacetate (CMFDA, Molecular Probes) . Changes in cell volume associated with the transport of water across the cell membrane, produce changes in the concentration of the fluorescent stain and hence the intensity of the fluorescent images.
4.4 Digital image correlation for analysis of intracellular deformation
5 Implications of cell deformation in health and disease
5.1 Nerve tissue
Neurons in the peripheral nervous system (PNS) have axons that lie mainly outside the vertebral column and hence are subject to a continual dynamic mechanical environment . The axonal endings of these neurons lie in the skin, muscle and viscera and are subjected to a complex array of compressive, tensile and shear strains. Indeed, some PNS neurons act as specialised mechanoreceptors whose function is to detect these mechanical stimuli through a specialised mechanotransduction pathway involving localised cell deformation. In addition, the axonal shafts of peripheral neurons may experience considerable tensile deformation during physiological joint articulation. For example, gross tensile strains of up to 18% have been measured in human median nerve bed , although it is unclear the extent to which this is accommodated by localised sliding of the nerve. Undoubtedly however, the tensile cell deformation of neurons during joint movement is exacerbated by the formation of fibrous adhesions in the nerve root. These can arise due to brachial plexus injury, carpal tunnel syndrome, traumatic crush injuries or following surgery.
Cell deformation can have profound effects on neurons which, depending on the neuronal type and the nature of the loading, can range from induction of neuronal signalling , promotion of neurite outgrowth  or cell death . While considerable progress has been made in elucidating cellular mechanisms of transduction for light, sound, odour and taste, the role of cell deformation in neuronal mechanotransduction and the associated signalling pathways are as yet unclear.
Muscle tissue is particularly susceptible to prolonged tissue compression leading to the development of pressure ulcers. It is well established that skeletal muscle degeneration starts at the cellular level and is characterised by nuclear pyknosis and an early disintegration of the contractile proteins in the cells, followed by inflammatory reactions and tissue necrosis. Although it is clear that both the magnitude and duration of compression affect cellular breakdown, the underlying mechanisms whereby tissue compression results in cell damage are poorly understood. Theories on impaired perfusion and transport of nutrients and metabolic waste products across the cell membrane can only partly explain the onset of tissue damage and have, to date, not been fully verified [20, 46, 78]. It has been hypothesised that sustained deformation of the muscle cells in the tissue plays an additional role in this process. Cell deformation triggers a variety of effects which may be involved in early cell damage, such as local membrane stresses which may lead to buckling and bursting of the membrane, volume changes, and modifications of cytoskeletal organisation affecting its integrity . In addition, changes in the mechanical and chemical environment of the cell may induce further damage. A contribution of cell deformation to mechanotransduction, which influences cell damage and adaptation, might be expected in the presence of compressive strains.
It is evident that physiological mechanical loading is important in the development, health and homeostasis for a wide range of biological tissues. However the associated mechanotransduction pathways, through which the cells detect and respond to their mechanical environment, are as yet, unclear. In addition, the response of cells to mechanical injury is often poorly understood despite the fact that it is critical to the development of strategies to prevent the occurrence of damage or to elicit tissue remodelling. Moreover, the translation of gross mechanical loading of a tissue into cell deformation will determine the ultimate response of the tissue to mechanical loading. Fundamental to these issues is an understanding of how cells deform in response to mechanical loading and the study of cellular biomechanics. Additionally, in order to understand the associated cellular mechanotransduction pathways it is necessary to understand the deformation of specific cellular structures, such as the nucleus and the primary cilium. The emergence of new technology, such as confocal microscopy, GFP transfection, and computational image analysis, provides a powerful toolkit for visualising and quantifying cellular and sub-cellular deformation. Such a multidisciplinary approach can clarify the mysteries of cellular mechanotransduction and mechanical injury and the underlying importance of cell deformation in mechanobiology.