Keywords

1 Introduction

The mechanical behavior and properties of a eukaryotic cell are largely determined by the characteristics of its cytoskeleton, an elaborate network of fibrous proteins [1, 2]. More specifically, the deformability of nucleated cells is determined by the membrane, the cytoskeletal network (actin filaments, intermediate filaments, and microtubules), and its interaction with the nucleus. Incompressible viscoelastic solids with key parameters of E instantaneous and E equilibrium are proposed to model these nucleated cells. As to the deformability of red blood cells (RBCs), it is determined by the membrane skeleton network, which is modeled as cortical shell-liquid core (or liquid drop) models [3]. Abnormal cellular functions can change cytoskeletons and lead to variations in mechanical properties of cells [4, 5].

This chapter summarizes the relationships between cellular mechanical properties and various disease processes and changes in cell states, including (1) changes in stiffness of red blood cells in cytoskeletal disorders, such as malaria and sickle cell anemia [6, 7]; (2) increased cellular deformability of invasive cancer cells, compared with benign counterparts [8–10]; (3) increased stiffness of leukocytes in sepsis [11]; and (4) decreased deformability during the stem cell differentiation process [12–14].

In the following section, we discuss the well-established techniques that are being used to measure cellular mechanical properties, including atomic force microscopy (AFM) [15–24] and micropipette aspiration [25]. In addition, we describe the emerging microfluidic approaches (e.g., constriction channels, optical stretchers, hydrodynamic stretchers) for the characterization of cellular mechanical properties [26–29].

2 Cellular Mechanical Properties with Various Cell States

2.1 Red Blood Cell Disorders

Malaria is currently one of the world’s most threatening diseases, infecting about 200 million people and leading to roughly 2,000 deaths per day [30, 31]. Malaria infection is caused by a single-cell parasite of the genome of Plasmodium [32]; after parasite invasion, red blood cells undergo extensive structural and molecular changes during a 48-h intra-erythrocytic cycle, leading to decreases in cellular deformability and increases in cellular adhesiveness [4, 5, 33]. The changes in the mechanical properties of red blood cells after P. falciparum infection have been probed using micropipette aspiration [34–36], optical tweezers [33, 37, 38], and microfluidic constriction channels [39–41]. The stiffness of red blood cells with the P. falciparum infection is approximately nine times that of their healthy counterparts [33]; the stiffer infected red blood cells were found to irreversibly block the passage of normal red blood cells when they were forced to travel through microfluidic constriction channels [39].

Sickle cell anemia is a hereditary blood disorder where changes in the molecular structure of hemoglobin result in stiffer sickle or crescent-shaped red blood cells, giving rise to circulation problems and depriving tissues and organs of oxygenated blood [42–45]. Studies of cell mechanics using, for example, micropipette aspiration [46–51], have been performed to probe the changes in mechanical properties of sickle-shaped red blood cells; red blood cells from sickle cell anemia patients are stiffer and more viscous when compared with the healthy red blood cells [52, 53].

2.2 Tumor

Cancer is currently one of the leading causes of death worldwide, with roughly 14 million new cases and more than 8 million deaths in 2012 [54]. Cancer is a disease that results from rapid, unrestricted, and uncontrolled proliferation of abnormal cells, due to dysregulation of the cellular signaling pathways that control cell proliferation and apoptosis—generally caused by mutations in genes that express key proteins involved in these biochemical reactions [55, 56].

Cancer is also accompanied by specific changes in the mechanical properties of cells [8, 10, 57], which have been probed using micropipette aspiration [58–62], AFM [63–90], magnetic twisting cytometry [91], microfluidic optical stretchers [92, 93], microfluidic constriction channels [94–97], and microfluidic hydrodynamic stretchers [98]. Experimental findings have revealed that cellular stiffness decreases significantly with malignant transformation in a variety of cancers, including breast cancer, lung cancer, renal cancer, prostate cancer, oral cancer, and skin cancer (see Table 1).

Table 1 Key developments in the field of mechanical phenotypes of tumor cells
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2.3 Leukocyte Activation in Sepsis

Sepsis is a progressive, injurious, inflammatory response to overwhelming infection associated with tissue hypoperfusion and multiorgan dysfunction [99, 100]. Neutrophils are crucial components of the innate immune response during sepsis, releasing important regulatory cytokines and contributing directly to antimicrobial killing. In patients with sepsis, reprogramming of neutrophil occurs, manifested by impaired recruitment of neutrophils to sites of infection, abnormal accumulation of neutrophils to remote sites, and dysregulation of neutrophil effector responses [11, 101, 102]. Changes in neutrophil rigidity and sequestration during sepsis have also been reported, leading to neutrophil accumulation in capillary beds, particularly in the lung and liver sinusoids. The changes in the mechanical properties of neutrophils have been probed using polymeric filters [101, 103], micropipette aspiration [104–106], and microfluidic constriction channels [107–109]. The results have confirmed that leukocyte deformability decreases in patients with sepsis, and that this change negatively affects the rheological properties of whole blood.

2.4 Stem Cell Differentiation

Stem cells have unique capacities to regenerate functional tissues continually for the lifetime of an organism [110, 111]. Realization of the potential of stem cells for tissue engineering requires characterization of their unique biological, biochemical, and proteomic properties, which have yet to be fully elucidated [112]. Changes in mechanical properties of cells have been reported during stem cell differentiation [13, 14], as probed using micropipette aspiration [113–115], AFM [116–120], and microfluidic hydrodynamic stretchers [98]. Significant decreases in cellular deformability have been observed for differentiated stem cells, compared with their undifferentiated counterparts (see Table 2).

Table 2 Key developments in the field of mechanical phenotypes of stem cells
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3 Established Approaches for Quantifying Cellular Mechanical Properties

3.1 AFM

Because of increasing interest in the characterization of cellular mechanical properties, several approaches have been developed (Fig. 1) to quantify the intrinsic mechanical properties of individual cells [5, 122–124]. Among them, AFM has been proven to be a valuable tool for probing individual cellular surfaces at specific locations to measure the localized elasticity (Fig. 1a). Typically, a pyramidal or spherical probe tip attached to a flexible cantilever is pressed into the cellular surface for a set distance and then the deflection of the cantilever is measured using a laser beam, with mathematical models used to estimate the stiffness of the probed surface [15–24, 125].

Fig. 1
figure 1

Techniques enabling characterization of the mechanical properties of single cells. a AFM, where a sharp tip at the free end of a flexible cantilever generates a local deformation on the cell surface, an indicator of the cellular mechanical properties. b Micropipette aspiration, where a cell is deformed by applying suction through a micropipette placed on the surface of the cell to infer the cellular elastic responses, based on recorded geometrical changes. c A microfluidic constriction channel, where differences in hydraulic pressure squeeze cells through a channel having a small cross-sectional area, with the cell’s transit time recorded as an indicator of its mechanical properties. d A microfluidic optical stretcher, where a two-beam laser trap is formed to serially deform single suspended cells, under optically induced surface forces, to measure mechanical properties of single cells. e A microfluidic hydrodynamic stretcher, where the cell under measurement is exposed to fluid stresses and the corresponding deformations are collected as stiffness indicators

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Upon changing the external conditions, the change in elasticity of a cell membrane, quantified using AFM, is much greater than the change in the morphology of the cell, based on the following four factors [74, 88, 126, 127]. The first is the depth of indentation. For small indentation depths, histograms of the relative values of the Young’s modulus describe regions rich in the network of actin filaments; for large indentation depths, however, the modulus represents the stiffness of the whole cell, typically accompanied by a decrease in its value (see Fig. 2a, b). The second factor is the effect of the substrate used for cell attachment, potentially leading to different Young’s moduli for cells originating from the same tumor type (see Fig. 2c). The third parameter is the load rate, which can lead to significant differences in modulus after fitting with the Hertz model (see Fig. 2d). The fourth factor is linked to the position and time of the cell poking event, because the force curves, recorded at constant positions, usually manifest a narrow histogram that may not reflect the stiffness of a whole cell (see Fig. 2e, f).

Fig. 2
figure 2

Factors influencing the mechanical properties of single cells probed using AFM. a Young’s moduli determined at tip indentation depths of 100 and 400 nm (nonmalignant HCV29 bladder cell). b Young’s moduli determined as a function of tip indentation depth [human melanoma cell lines: WM239 (skin) and WM9 (lymph node metastasis)]. c Influence of surface properties on Young’s modulus, quantified using AFM (WM35-primary melanoma, and two metastatic cell lines: WM9 and A375). d Changes in Young’s modulus as a function of the tip scanning rate (nonmalignant and malignant human bladder cells). e Effect of the relative positions of cell poking on cellular Young’s modulus (melanoma 1205Lu). f Effect of repeated cell poking on the quantification of Young’s modulus (nonmalignant and malignant human bladder cells). Reproduced with permission from ref. [74]. Copyright 2012, Elsevier Ltd

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3.2 Micropipette Aspiration

Micropipette aspiration is a well-established technique that enables determination of cellular mechanical properties through aspiration of the surface of a cell into a small glass tube with the leading edge of its surface tracked (see Fig. 1b). Interpretation of the measured data, using basic continuum models, leads to values for a cell’s elastic and viscous properties. In particular, based on the equivalent model (e.g., a liquid surrounded by an elastic cortical shell), neutrophils were found to have a cortical surface tension of approximately 30 pN/μm and a viscosity on the order of 100 Pa s. On the other hand, chondrocytes and endothelial cells behave as homogeneous elastic solids with quantified elastic moduli on the order of 500 Pa [25].

Compared with AFM, micropipette aspiration deforms a cell in a more global manner, leading to more accurate characterization of cellular mechanical properties. Although precise, this technique requires skilled manual operation and proceeds with very low throughput (<1 cell/10 min) [4]. To address this issue, an automated micropipette aspiration setup was recently proposed where a micromanipulator, a motorized translation stage, and a custom-built pressure system to position a micropipette were controlled with real-time visual feedback to accurately measure cell deformations online. This system still suffers, however, from the issue of low throughput, with the mechanical properties reported from only approximately 30 cells for each cell type [128, 129].

4 Emerging Microfluidic Tools for Characterization of Cellular Mechanical Properties

Microfluidics is a science and technology related to the processing and manipulation of small volumes of fluids (from 10−9 to 10−18 l) in channels having dimensions on the scale of tens of micrometers [130–132]. The micrometer-scale dimensions of the devices match well with the size of a typical biological cell, making microfluidics an ideal platform for cell studies [133–137]. More specifically, microfluidics has been used for characterizing biochemical (e.g., gene and protein) and/or biophysical (mechanical and electrical) properties of cells at the single-cell level [138–144].

In the field of microfluidics-based characterization of cellular mechanical properties, three major approaches have been developed so far [26–29]: microfluidic constriction channels [39–41, 94–97, 145–162] (see Fig. 1d), microfluidic optical stretchers [92, 93, 163, 164] (see Fig. 1e), and microfluidic hydrodynamic stretchers [98] (see Fig. 1f). Compared with conventional techniques, these microfluidic approaches display significantly higher throughput, enabling the collection of data from large numbers of cells.

4.1 Microfluidic Constriction Channel

The microfluidic constriction channel is designed to operate by evaluating the transition process as cells pass through microchannels having cross-sectional areas smaller than the dimensions of a single cell (see Fig. 3). An attractive feature of this technique is the ability to achieve higher throughput than those of conventional approaches (e.g., micropipette aspiration) for cellular mechanical characterization (up to ca. 1 cell/s). This technique was first used to evaluate the mechanical properties of red blood cells [39–41, 145–152, 165], and then further expanded to study the deformability of white blood cells [153] and tumor cells [94–97, 154].

Fig. 3
figure 3

Experimental setup and key application results of microfluidic constriction channels used for the characterization of cellular mechanical properties. a Schematic and raw experimental images of a microfluidic constriction channel for the characterization of cellular mechanical properties, where hydraulic pressure differences squeeze cells through a channel having a small cross-sectional area, with the cell transit time recorded as an indicator of the mechanical properties. Reproduced with permission from ref. [157]. Copyright 2014, Elsevier Ltd. b Four sequences of video images recorded during four stages of malaria-infected red blood cells (early ring stage, early trophozoite, late trophozoite, schizont) passing through constriction channels. Ring-stage-infected erythrocytes retained much of the structural characteristics of normal erythrocytes and could pass through all constricted channels. Early trophozoite and late trophozoite-infected cells passed through the larger (8 and 6 μm) channels, but eventually blocked the smaller (4 and 2 μm) channels. Schizont-stage-infected erythrocytes blocked all but the 8 μm channel. The arrows indicate the direction of flow. Reproduced with permission from ref. [39]. Copyright 2003, the National Academy of Sciences of the USA. c Models of the cellular entry process into the constriction channel, enabling quantification of the cortical tensions of blood cells and tumor. Reproduced with permission from ref. [158]. Copyright 2012, Royal Society of Chemistry. d Numerical simulations of the cellular entry process into the constriction channel, using a cellular viscoelastic model, rather than a liquid droplet model, and taking cellular friction with constriction channel walls into consideration, enabling quantification of the instantaneous Young’s moduli of single cells. Reproduced with permission from ref. [157]. Copyright 2014, Elsevier Ltd

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Initially, the cellular entry time and transit velocity through the constriction channel were used as biophysical markers to evaluate the cellular mechanical properties. These parameters cannot reflect the intrinsic cellular mechanical properties because they are highly dependent on the cellular sizes. To tackle this issue, several groups have modeled the cellular entry process into the constriction channel, with the purpose of translating cell-dependent mechanical biomarkers into size-independent parameters [155–159].

Lim et al. modeled the cellular entry process into the constriction channel using numerical simulations, suggesting that the cell entry time depends strongly on the cortical stiffness [159]. Ma et al. simplified the cellular entry process and quantified the cortical tension of blood and tumor cells as the first reported use of the constriction channel design to characterize size-independent mechanical properties [158, 160]. Chen et al. used numerical simulations to model the cellular entry process into the constriction channel, employing a cellular viscoelastic model, rather than a liquid droplet model, thereby enabling the quantification of the instantaneous Young’s moduli of single cells [157]. In addition, because small constriction channels are prone to clogging, constriction channels with adjustable cross-sectional areas have also been proposed to address the clogging issue to a certain extent [161, 162].

4.2 Microfluidic Optical Stretcher

In an optical stretcher, a two-beam laser trap is used to serially deform single suspended cells, through optically induced surface forces, and, thereby, measure the mechanical properties of single cells (see Fig. 4). This technique has been integrated with microfluidic channels and operates on spherically symmetrical cells in suspension [92, 93, 163, 164]. It was first used to classify MCF-10, MCF-7, and mod-MCF-7 cells, revealing a fivefold increase in deformability for cancer cells relative to benign counterparts [92, 93].

Fig. 4
figure 4

Experimental setup of and key results from microfluidic optical stretchers used for the characterization of cellular mechanical properties. a Schematic representation of a microfluidic optical stretcher; a two-beam laser trap is used to serially deform a single suspended cell, through optically induced surface forces, to measure the mechanical properties of the cell. b The optical deformability of malignantly transformed SV-T2 fibroblasts is significantly higher than that of normal BALB/3T3 fibroblasts (ODBALB/3T3 = 8.4  ± 1.0; ODSV-T2 = 11.7 ± 1.1). c Optical deformabilities of three populations of MCF cell lines: ODMCF-10 = 10.5 ± 0.8; ODMCF-7 = 21.4 ± 1.1; ODmodMCF-7 = 30.4 ± 1.8. d Two populations of MDA-MB-231 cell lines are clearly distinguishable in the histograms of the measured optical deformability (ODMDA-MB-231 = 33.7 ± 1.4; ODmodMDA-MB-231 = 24. 4 ± 2.5). Reproduced with permission from ref. [93]. Copyright 2005, Biophysical Society

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Furthermore, the microfluidic optical stretcher has been used to quantify acute leukemia cells during differentiation therapy, revealing significant softening of neutrophils during the differentiation process [163]. In addition, the compliance of cells from cell lines and primary samples of healthy donors and cancer patients has been measured using the microfluidic optical stretcher, revealing that cancer cells were 3.5 times more compliant than cells from healthy donors [164].

The microfluidic optical stretcher does, however, have two significant limitations. First, its throughput remains at approximately 1 cell/min, and it cannot be improved significantly. This limitation is due to the trade-off between higher optical forces and increased optical power leading to significant heating of the measured cells. Second, the quantified cellular deformability is not an intrinsic biomechanical marker because it depends on the cellular size and the characterization conditions.

4.3 Microfluidic Hydrodynamic Stretcher

In a microfluidic hydrodynamic stretcher, fluid stresses are generated by elaborately designing channel geometries, which are used to deform single cells. The rigidity of RBCs has been investigated using shear flow in narrowing channels [166] and extensional flow in hyperbolic converging channels [167]. Recently, inertial focusing is used to deliver cells uniformly to a stretching extensional flow, where cells are deformed at high strain rates, while a high-speed camera records images that can be used to extract biophysical parameters (see Fig. 5) [98]. Unlike the techniques discussed above, this approach is capable of ultrahigh throughput (ca. 1000 cells/s). It has been used to quantify native populations of leukocytes and malignant cells in pleural effusions; the experimental deformability data can be used to predict disease states in patients with cancer or immune activation, with a sensitivity of 91 % and a specificity of 86 %.

Fig. 5
figure 5

Experimental setup of and key results from microfluidic hydrodynamic stretchers used for characterization of cellular mechanical properties. a Schematic representation, raw experimental images, and quantified deformability of the microfluidic hydrodynamic stretcher for characterization of cellular mechanical properties, where single cells under measurement are exposed to fluid stresses and the corresponding deformations are collected as stiffness indicators. b, c Decreased deformability has been correlated with increased stem cell pluripotency for b mouse embryonic stem cells and c human embryonic stem cells. Reproduced with permission from ref. [98]. Copyright 2012, the National Academy of Sciences of the USA

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5 Conclusion

Various proof-of-concept approaches have been developed for the characterization of the mechanical properties of single cells, enabling correlations to be made between cellular mechanical properties and cellular biophysical statuses. Nevertheless, to convince the wider cell biology and clinical communities of the merits of cellular biophysical biomarkers, much research effort remains to be exerted in the development of both equipment and applications.

For conventional approaches (e.g., AFM and micropipette aspiration) capable of collecting size-independent intrinsic biophysical markers (e.g., instantaneous and equilibrium Young’s moduli), the issue of low throughout (ca. 1 cell per 10 min) without the capability of collecting statistically significant data remains problematic. For microfluidic approaches enabling high-throughput characterization of the biomechanical properties of single cells (ca. 1000 cells/s), the collected parameters remain dependent on the cell size and experimental conditions (e.g., pressure drop, channel geometry). Thus, further technical developments remain necessary to enable characterization of the intrinsic biophysical properties of single cells in a high-throughput manner.

Furthermore, the correlations between biophysical markers and the biochemical properties of single cells should be explored further. It is possible to design experiments to characterize both cellular biophysical (e.g., Young’s modulus) and biochemical markers, including genetic and protein information, simultaneously, potentially revealing correlations between these biophysical and biochemical markers. This process should also provide a comprehensive understanding of cellular status at the single-cell level, paving the foundation for further studies of cell biology.