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Biologically Inspired Robotics
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.
9.3.3.1 Measurement of Single-Cell Stiffness Using a Soft Nanoprobe
The spring constant of the cell, k cell, can be calculated from the relationship of
two springs in series as described in Equation (9.11).
⎛ Δ total − Δ cell ⎞
k = k
cell
needle ⎝ ⎜
⎠ ⎟
(9.11)
Δ cell
where k needle is the spring constant of the soft nanoprobe, Δ total is the total
displacement of the nanoprobe and the cell, and Δ cell is the deformation of
the cell.
The Hertz and Sneddon models, which are based on the shape of the tips,
that is, conical, spherical, and cylindrical, were used to estimate the Young’s
modulus of the cells. The equations are derived from the classic Hertz
mechanics model for linear elastic material (Pharr, Oliver, and Brotzen 2002).
Parameters E, v, α, R, a, and δ are the Young’s modulus; the Poisson’s ratio (v
= 0.5 for soft biological materials; Lanero et al. 2006) of the elastic half space
(cell’s surface); the half opening angle of a conical tip; the radius of curvature
of a spherical tip; the radius of a cylindrical tip; and the displacement of the
cantilever, respectively. Values for α, R, and a were obtained from E-SEM
images, and determination of the value of δ is obtained from Equation (9.6),
respectively.
The following Equations (9.12)–(9.14) are used to estimate the stiffness of
the cell from an indentation by an indenter, which has a body of revolution.
Biologically Inspired Robotics
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.
9.3.3.1 Measurement of Single-Cell Stiffness Using a Soft Nanoprobe
The spring constant of the cell, k cell, can be calculated from the relationship of
two springs in series as described in Equation (9.11).
⎛ Δ total − Δ cell ⎞
k = k
cell
needle ⎝ ⎜
⎠ ⎟
(9.11)
Δ cell
where k needle is the spring constant of the soft nanoprobe, Δ total is the total
displacement of the nanoprobe and the cell, and Δ cell is the deformation of
the cell.
The Hertz and Sneddon models, which are based on the shape of the tips,
that is, conical, spherical, and cylindrical, were used to estimate the Young’s
modulus of the cells. The equations are derived from the classic Hertz
mechanics model for linear elastic material (Pharr, Oliver, and Brotzen 2002).
Parameters E, v, α, R, a, and δ are the Young’s modulus; the Poisson’s ratio (v
= 0.5 for soft biological materials; Lanero et al. 2006) of the elastic half space
(cell’s surface); the half opening angle of a conical tip; the radius of curvature
of a spherical tip; the radius of a cylindrical tip; and the displacement of the
cantilever, respectively. Values for α, R, and a were obtained from E-SEM
images, and determination of the value of δ is obtained from Equation (9.6),
respectively.
The following Equations (9.12)–(9.14) are used to estimate the stiffness of
the cell from an indentation by an indenter, which has a body of revolution.