9.3.1 Stiffness Measurement of a Single Cell Based on Nanoindentation Technique

A schematic of a nanoindentation process for a single cell is shown in Figure 9.3. An atomic force microscope (AFM) cantilever with a stan-dard or modified tip is mounted on the nanomanipulator stage. The nanomanipulator is used to approach, contact, and indent the cantilever's tip on a single biological cell. Force is calculated from two parameters, that is, the cantilever's deflection angle, 8, and the cantilever's length, L, which can be obtained from the SEM images.

Figure 9.4 shows a schematic of the beam deflection. By using Macaulay's method (Stephen 2007), which is also known as the double integration method, the deflection of the beam can be represented in two relationships; that is, the length deflection, 5, and the angular deflection, 9.

Macaulay's method consists of three steps; that is, derivation of the bending moment, M(x), which acts internally at every point in the interval between x = 0 and x = L; integration of M(x) to obtain the beam slope; and second integration to get the elastic curve, v(x) . In integrating M(x), integration of two constants will emerge; that is, C₁ and C₂. In order to evaluate these constants, appropriate boundary conditions of the beam will be used to determine their values Finally, the value of x = L is substituted into each equation to find the deflection and slope at the tip of the cantilever.

Equilibrium equation for the sum of moments around point h,

∑Mh=−F(L−x)−M=0 (9.1)

Solving the moment equation for M gives

M=Fx−FL (9.2)

The moment-curvature relationship can be expressed as

EId2vdx2=M=Fx−FL (9.3)

Therefore, the general equations for the slope and deflection of the cantilever are

dvdx=−FL22EI=Φ (angular deflection in radians) (9.4)

v=−FL33EI=Δ (length deflection) (9.5)

The negative sign indicates the direction of the force. Now, we have the standard equations for the beam deflection under a condition as shown in Figure 9.4. Back to our discussion regarding the visual-based approach for force measurement of the AFM cantilever, the deflection of the AFM cantilever has to be expressed in angular deflection and not in length deflection.

By using basic mathematical manipulation from Equations (9.4) and (9.5), we arrive at the final equation of the cantilever deflection with respect to the angular deflection,

Δ=23ΦL (9.6)

where 5, 9, and L are the cantilever deflection, the angular deflection in radians, and the total length of the cantilever. The values of 9 and L are determined from analysis of the SEM images. Finally, by using Equation (9.6), modification of the Hooke's law can be written as

F=kΔ=k(23ΦL) (9.7)

Evaluation of Equation (9.7) was conducted experimentally by comparing the result of 5 obtained from a direct displacement measurement

In our experiment, we obtain 5 from the SEM image obtained from Equation (9.6). Because the base of the AFM cantilever was in fixed condition, the value of 5 can be obtained directly from the length displacement of the cantilever's tip Therefore, both parameters, 5 and 9, can be determined from the high-magnification SEM image.

9.3.2 Stiffness Measurement Using Different Indenter Tip Shapes

Figure 9.5 shows a schematic of the indenter tip-sample contact for three different indenter tips; that is, cylindrical, conical, and spherical The parameters I, h, r, 8, and R are indentation depth, sample height, radius of the cylindrical tip, and radii of the spherical tip for conical and spherical, respectively

The Hertz model is used for the indentation based on a spherical tip and the Sneddon model is used for the indentation based on the cylindrical and conical tips Therefore, the selection of the Hertz or Sneddon model depends on the shape of the indenter tip

In 1882, Hertz published a classic paper that aroused considerable interest (Hertz 1882). The load-displacement relation based on a spherical tip from Hertzian analysis is

Fspherical=43E(1−v2)R1/2I3/2 (9.8)

where v is the Poisson's ratio of the sample.

In 1965, Sneddon published a paper on indentation of linear half spaces by rigid punches of arbitrary profile (Sneddon 1965). Although he showed the load-displacement relationship of several tip shapes, only the cylindrical and conical shapes are applied in our case The load-displacement relations based on cylindrical and conical tips are

Fcylindrical=2E(1−v2)aI (9.9)

Fcone=2πtanΘE(1−v2)I2 (9.10)

The indenter is described by an arbitrary function, z = f(p) that is rotated about the z axis to produce a solid of revolution. Nevertheless, Pharr, Oliver, and Brotzen (2002) have shown that Equations (9.8)-(9.10) are also valid for a nonrevolute indenter as well such as pyramidal tip.

9.3.3 Stiffness Measurement Using Nanoprobes

We designed two approaches for determining the stiffness of a single cell as shown in Figure 9.6.

The first approach is based on the buckling phenomenon of a nanoprobe. A schematic of this approach is shown in Figure 9.6a. It is, to the best of our knowledge, a novel technique in determining the stiffness of a cell (Ahmed et al, 2008a) In this technique, the nanoprobe and the cell can be modeled as two springs in series. In order to model the nanoprobe as a spring, firstly, the nanoprobe should be able to buckle linearly, and secondly, it should have a lower or equivalent spring constant as the cell This technique prevents damage to the cell because the indentation is minimized from the buckling effect of the so-called soft nanoprobe, which avoids excessive indentation being applied to the cell.

The second approach for the measurement of cell stiffness is based on a hard nanoprobe, which relies on deformation of the cell in order to measure its stiffness. A schematic of this approach is shown in Figure 9.6b. By knowing the applied compression force and the deformation of the cell, the stiffness of the cell can be measured In order to fabricate a hard nanoprobe, strong material that is hard to bend is needed We used tungsten to construct a hard nanoprobe To prevent excessive indentation force on the cell by the hard nanoprobe, this process has to be performed by avoiding any sudden pressure that can interrupt the chemical activities of the cell; for example, a mechanotransduction effect The other preventive step is to use a lower cantilever spring constant.

The hard nanoprobe can also be used for single-cell surgery In theory, all hard nanoprobes must be able to penetrate the cell; however, in practice, for yeast cells, only some nanoprobes can penetrate the cells, whereas others are only limited to cell stiffness measurement only This is because to penetrate the cell, more compression force is needed This excessive force may exceed the force limits of the nanoprobe, causing failure.

9.4.1 Nanorobotic Manipulation System inside Electron Microscopes

The sample chambers of conventional SEMs and transmission electron microscopes (TEMs) are set under a high vacuum (HV) to reduce the distur-bance of the electron beam for observation (Fukuda, Arai, and Dong 2003).

To observe water-containing samples—for example, bio-cells—appropriate drying and dyeing treatments are needed before observations. Hence, direct observations of water-containing samples are normally quite difficult using these electron microscopes. We have presented the assembly of carbon nanotubes (CNTs) based on a nanorobotic manipulation system inside an SEM and TEM, called a hybrid nanorobotic manipulation system (Nakajima, Arai, and Fukuda 2006). An overview of the constructed hybrid nanorobotic manipulation system is shown in Figure 9.8.

Recently, we have constructed nanorobotic manipulators inside an E-SEM (Ahmad et al. 2008a, 2008b, 2010). The E-SEM can realize direct observation of water-containing samples with nanometer high resolution by a specially built secondary electron detector, which is installed close to the sample The evaporation of water is controlled by the sample temperature (~0 to ~40°C) and sample chamber pressure (10-2,600 Pa). An overview of the constructed E-SEM nanomanipulator is shown in Figure 9.9. It has been constructed with three units and 7 degrees of freedom (DOFs) in total. The temperature of sample is controlled by the cooling stage unit, as Unit3.

The unique characteristic of the E-SEM is the direct observation of the hydroscopic samples with no drying treatment. Generally, water is an important component to maintain biological cell life with chemical reactions Nanomanipulation inside the E-SEM is considered to be an effective tool for a water-containing sample with nanometer resolution

9.4.2 Observations of Biological Samples by E-SEM

Wild-type yeast cells were observed by the E-SEM The samples were cultured with YPB medium for 24 hours in a 37°C chamber. The cultured cells were dispersed in pure water. Several microliters of the solution was dropped on an aluminum cooling stage with a micropipette.

Images of the yeast cells are shown with HV and E-SEM modes as shown in Figures 9.10a and 9.10b. The HV mode is operated with the conditions of room temperature (16. 7°C) and ~2. 0 x 10^-3 Pa pressure. As shown in Figure 9.10a, almost all yeast cells show a concave and broken structure under HV mode. The E-SEM mode is operated with the conditions of 0. 0°C using a cooling stage and ~650 Pa pressure. The accreted voltage was set at 15 kV. In the E-SEM mode, when decreasing the pressure from ~700 Pa, the water, which is surrounding the cells, is gradually evaporated until showing up From Figure 9.10b, the remaining water can be seen in the intercellular spaces of yeast cells as black contrast Almost all of the yeast cells maintain their spherical shape in a water-containing condition with E-SEM operation.

To reveal the effect of observation with HV and E-SEM modes, the yeast cells were cultured again after observation The plate was divided into three regions: cultured after water dispersion, SEM observation (HV), and E-SEM observation. The number of yeast cell colonies in the E-SEM mode were greater than in HV mode. From this experiment, the living cell rate using E-SEM mode was almost the same order as that under initial conditions of water dispersion.

9.5.1 Stiffness Measurement of Single Yeast Cells Depends on Cell Sizes

The single-cell stiffness measurement is presented using an E-SEM nanoro-botic manipulation system for yeast cells (Ahmad et al 2008a, 2008b) A schematic of experimental setup is presented in Figure 9.11. The yeast cells were fixed on the temperature-controlled stage in perpendicular direction with an AFM cantilever The position of the AFM cantilever was controlled by the nanomanipulator to apply the compression force on each cell The E-SEM can provide real-time observations, that is, a cell being approached, touched, indented, and finally penetrated/burst by the AFM cantilever, can be seen clearly The penetration of a single cell by the AFM cantilever was also measured from the occurrence of the cell bursting via real-time observation.

An E-SEM photo showing the penetration of single yeast cells is shown in Figure 9.12. The penetration forces clearly show a strong relationship between cell size and strength; the latter increases with an increase in cell size as shown in Figure 9.13. The average penetration forces for 3, 4, 5, and 6 pm cell diameter ranges are 96 ± 2, 124 ± 10, 163 ± 1, and 234 ± 14 nN, respectively.

Yeast cell walls consist predominantly of glucan with (1,3)-ß and (1,6)-ß linkages and mannan covalently linked to protein (mannoprotein; Klis, Boorsma, and De Groot 2006; Lesage and Bussey 2006; Lipke and Ovalle 1998). Thus, it can be inferred that the ß-glucans composition increases when the yeast cell size increases. The average Young's modulus obtained in this work, that is, 3. 24 ± 0. 09 MPa, is reasonable compared to reported local cell stiffness values of 0. 73 MPa (Pelling et al. 2004) and 1.12 MPa (Lanero 2006), because the E values obtained in this chapter represent not only the local elastic property of the cell but the whole cell stiffness.

9.5.2 Stiffness Measurement of Single Yeast Cells Depends on Growth Phases

All cells have a unique growth phase curve during their life cycle, which is normally divided into four phases: lag, log, saturation, and death phases. In the present study we did not investigate the death phase. These phases can be easily identified from the optical density (OD) absorbance-time curve. The lag phase is located at the initial lower horizontal line where the cells adapt themselves to growth conditions and the cells mature and divide slowly. The log phase can be seen from an exponential line where the cells have started to divide and grow exponentially. The actual growth rate depends upon the growth conditions The saturation phase resembles a final upper horizontal line where the growth rate slows and ceases mainly due to lack of nutrients in the medium. During the death phase, all of the nutrients are exhausted and the cells die (Tortora, Funke, and Case 2003). It is believed that the mechanics of normal cells have different properties in each of the phases. In this section, the mechanical properties of W303 yeast cells at four different growth phases (early, mid, late log, and saturation) are discussed (Ahmad et al. 2008b).

The compression experiments were done from early log phase to saturation phase. Penetration force was analyzed for each phase as shown in Table 9.1. As expected, the force needed to penetrate a single cell increased from the early log to the saturation phase (161 ± 25, 216 ± 15, 255 ± 21, and 408 ± 41 nN), whereas the elastic properties of the cells appeared constant for all of the phases obtained; that is, 3. 28 ± 0. 17, 3. 34 ± 0. 14, 3. 24 ± 0. 11, and 3. 38 ± 0. 11 MPa.

These mechanical properties of the W303 yeast cells at different growth phases are in agreement with reported increments of average surface modulus of Saccharomyces cerevisiae cell walls as 11. 1 ± 0. 6 N/m (log phase) and 12.9 ± 0. 7 N/m (saturation phase) with no significant increase in the elastic modulus of the cell; that is, 112 ± 6 MPa (log phase) and 107 ± 6 MPa (saturation phase; Smith et al. 2000). Their values for elastic modulus are quite high is reasonable because they measured the whole elastic properties of the cell by compressing a single cell between two big flat indenters compared to local cell indentation in our case

9.6.1 Fabrication of Nanoprobes

Four kinds of nanoprobes were fabricated using a focused ion beam (FIB) process at the tip of AFM cantilevers as shown in Figure 9.14. Standard plati-num-coated tetrahedral cantilever tips with a spring constant of 2 N/m were used in the fabrication of Si, Si-Ti, and tungsten nanoprobes For the tungsten nanoprobe, a standard sharp pyramidal cantilever tip with a 0 09 N/m spring constant was used The soft Si nanoprobe was fabricated by etching (Figure 9.14a). The first type of hard nanoprobe, that is, an Si-Ti nanoprobe, was fabricated by coating the former Si nanoprobe with Ti material by sputtering (Figure 9.14b). The second type of hard nanoprobe was fabricated by first flattening the apex of the sharp pyramidal cantilever tip by using FIB etching (Figure 9.14c). Another type of tungsten hard nanoprobe was fabricated by first flattening the apex of the sharp tetrahedral cantilever tip using FIB etching, followed by tungsten deposition of a large area using FIB deposition, and finally trimmed to produce the nanoprobe structure using FIB etching (Figure 9.14d).

9.6.2 Calibration of Soft Nanoprobes

The Young's modulus and spring constant of the soft Si nanoprobe, E_needle and k_needle, were calibrated using a nanomanipulation technique. The soft nanoprobe was slowly pressed against another cantilever tip to experimentally determine the spring constant (0 110 N/m) The indentation was carried out until the nanoprobe begun to buckle Then, the buckled nanoprobe was slowly retracted until the nanoprobe returned to a straight condition as shown in Figure 9.15. The value of E_needle was determined from the Euler buckling equation as shown in Equation (9.18), where l_buckle is the length of the soft nanoprobe during the buckling condition

Esoftnanoneedle=7.68Fnℓbuckle2π2wb3 (9.18)

where F_n is the buckling force applied to the nanoprobe; E_needle is the Young's modulus of the nanoprobe; I is the second moment of area; K is the nano-probe effective length factor, whose value depends on the conditions of the end support of the nanoprobe; and I is the length of the nanoprobe. The value of the length of the soft nanoprobe was corrected with K = 0.8 for a structure that has one fixed end and the other end pinned (Timoshenko and Gere 1961). I is a property of a shape that is used to predict its resistance to buckling A soft nanoprobe that has a rectangular cross section has the value of I = (wb³)/12, where w and b are the width and height of the rectangular cross section. The values for w and b, which were obtained from an image analysis, were 165 and 170 nm, respectively.

9.6.3 Stiffness Measurement of Single Yeast Cells by Nanoprobes

The whole stiffness response of a single cell, that is, the deformation of the entire cell upon the applied load from a single point indentation, to the best of our knowledge, has not been previously reported. The difficulty in obtaining such data is due to the stiff indenter, which may penetrate or burst the cell Our soft nanoprobe can be used to prevent cell penetration by its ability to buckle during indentation The mechanism of cell deformation is stated as follows: upon indentation of the soft nanoprobe on the cell, local deformation occurs below the tip of the nanoprobe Further indentation induces the whole cell to deform in addition to the local cell deformation The ability to produce a large local point indentation could provide more information regarding the mechanical property of the organelles inside the cell. The global stiffness measurement of single cells from single point indentation was performed using an Si nanoprobe as shown in Figure 9.16. The measurement was performed using a standard indentation procedure The Si nanoprobe started to buckle after the cell deformed about 0.5 urn. From this point, the buckling rate of the Si nanoprobe increased with increased indentation depth. The values of k_cell for approximately the same physical parameters of two yeast cells, that is, 0 92 ± 0. 12 and 0.95 ± 0.36 N/m, show strongly similar mechanical properties.

The values that represent the whole cell spring constants are reasonable compared to the reported local spring constant of the S. cerevisiae yeast cell (0.06 ± 0.025 N/m). The values of whole E_cell; that is, 3.64 and 3.92 MPa, are also rational because they represent the whole cell stiffness property compared to the reported local Young's modulus of the yeast cell; that is, 0.72 ± 0.06 MPa (Pelling et al. 2004). Our method shows improved data sensitivity compared to other global stiffness measurement methods that rely on compression of a single cell between one large indenter and a substrate. Data from this method may not represent the actual global cell stiffness because extra dissipation force may be included in the measurement as reported by Smith et al. (2000) for the global cell spring constant and Young's modulus of yeast cell as 11.1 N/m and 112 MPa.