**3.1 The regulation of the cell chain**

**Figure 1** schematically shows the formation and regulation process of an *E. coli* cell chain. After *E. coli* cells trapped one by one, a cell chain consisted of six *E. colis* was organized at the probe tip. By adjusting FP 2 to approach *E. coli* 5, the cell is rotated and orientated toward the axial direction of FP 2. Then, *E. coli* 5 is removed from the chain with the cell contact sequence changed. By shifting FP 2 along the +*x* direction, *E. coli* 5 is put between the *E. coli* 3 and 4 (**Figure 1c**). After turning off the laser in FP 2, *E. coli* 5 is gradually rotated and orientated along the axial

#### **Figure 1.**

*Schematic of the regulation process and experimental setup. (a) A cell chain is organized at the tip of FP 1. (b) By manipulating FP 2, E. coli 5 is rotated and then removed from the cell chain. (c) E. coli 5 is added back at a new position into the chain. (d) After turning off the laser in FP 2, E. coli 5 is orientated along the axial direction of FP 1. (e) Schematic of the experiment setup [38].*

direction of FP 1 (**Figure 1d**), changing the cell contact sequence again. **Figure 1e** schematically shows the experimental setup. After sheathed with a glass capillary, FPs 1 and 2 were fixed on microstages 1 and 2, respectively. The probe tips were immersed in the *E. coli* solution, while their ends were connected to the lasers 1 and 2, respectively. The wavelength of both lasers is set at 980 nm due to the low absorption for the biological cells [36]. Such a wavelength induces little optical damage to bacteria and mammalian cells [37]. The *E. coil* solution was dropped on a glass slide with an injector. The slide was mounted on an *x*–*y* manual translation stage (resolution: 50 nm) to achieve fine positioning and mechanical stability. An optical microscope incorporated with a charged coupled device (CCD) was used for the real time monitoring, image capturing, and video recording.

To demonstrate the operation mechanism, a dynamic regulation of the cell chain was experimentally conducted. After the laser beam injected into FP 1 (*P*1 = 30 mW) at *t* = 0 s, a cell chain was organized at the probe tip, which was consisted of 10 *E. colis*. Then, FP 2 was adjusted to approach the downside tip of *E. coli* 3 (indicated by the yellow dot) in the cell chain (**Figure 2a**). After turning on the laser in FP 2 (*P*2 = 50 mW), the downside tip of *E. coli* 3 was trapped by FP 2 (**Figure 2b**). With a shift of 1.9 μm along the −*x* direction, the downside tip was shifted along the −*x* direction, while the upside tip (indicated by the red dot) remained stationary (**Figure 2c**). After that, *E. coil* 3 was rotated clockwise and gradually orientated along the axial direction of FP 2 (**Figure 2d**). Then, it was removed from the cell chain and shifted along the −*x* direction. After that, FP 2

#### **Figure 2.**

*Optical microscopic images of adjusting the cell contact sequence. (a) FP 2 was adjusted to approach E. coli 3. (b–d) E. coli 3 was rotated and then trapped by FP 2. (e and f) E. coli 3 was shifted with FP 2 along the +y and +x direction. (g–i) The E. coli 3 was added back into the cell chain. The two tips of E. coil 3 were indicated by yellow and red dots [38].*

**15**

**Figure 3.**

*on the E. coli 3 as a function of X [38].*

*Optical Fiber Probe-Based Manipulation of Cells DOI: http://dx.doi.org/10.5772/intechopen.81423*

tion point *i*. *FEM* can be expressed as:

changed to 1-2-4-3-5-6-7-8-9-10 (**Figure 2h** and **i**).

was shifted along the +*y* direction with a distance of ~1 μm (**Figure 2e**), followed by a shift of 9 μm along the +*x* direction (**Figure 2f**). Then, *E. coli* 3 was added back into the chain between *E. coils* 4 and 5 (**Figure 2g**). After the laser off in FP 2, *E. coli* 3 was reorientated along the axial direction of FP 1, and the contact sequence was

To quantitatively interpret the above experiment, the optical torques (*T*) on the

*T* = ∫*r<sup>i</sup>* × *dFEM* (1)

where *ri* is the position vector pointing from the central point of *E. coli* to the interaction point, *d***F***EM* is the electromagnetic force element exerted on the interac-

*FEM* = ∮*S*(〈*TM*〉 ⋅ *n*)d*S* (2)

where *dS* is the surface element surrounding the cell, *n* is the surface normal vector, and 〈*TM*〉 is the time-independent Maxwell stress tensor. The optical torque along the +*z* direction is defined as positive, under which the cell will be rotated counterclockwise. As shown in **Figure 3**, the torques are positive and negative in the regions I (−50° < *θ* < 0°) and II (0° < *θ* < 50°). Thus, *E. coli* 3 will be rotated counterclockwise and clockwise, as indicated by the red and blue arrows, respectively. Finally, *E. coli* 3 will be oriented along the axis direction of FP 2, that is, at

*Calculated optical torque and force during the regulation progress. (a) Calculated optical torque exerted on the 10 E. colis as a function of θ (FP 1: 30 mW and FP 2: 50 mW). The inset shows the energy density distribution at θ = 0°. (b) Calculated optical torque exerted on the 10 E. colis as a function of θ (FP 1: 30 mW and FP 2: 0 mW). The inset shows the energy density distribution at θ = 130°. (c) Calculated optical force Fx and torque* 

*E. colis* were calculated in the regulation process, which is defined as:

*Optical Fiber Probe-Based Manipulation of Cells DOI: http://dx.doi.org/10.5772/intechopen.81423*

*Fiber Optics - From Fundamentals to Industrial Applications*

real time monitoring, image capturing, and video recording.

direction of FP 1 (**Figure 1d**), changing the cell contact sequence again. **Figure 1e** schematically shows the experimental setup. After sheathed with a glass capillary, FPs 1 and 2 were fixed on microstages 1 and 2, respectively. The probe tips were immersed in the *E. coli* solution, while their ends were connected to the lasers 1 and 2, respectively. The wavelength of both lasers is set at 980 nm due to the low absorption for the biological cells [36]. Such a wavelength induces little optical damage to bacteria and mammalian cells [37]. The *E. coil* solution was dropped on a glass slide with an injector. The slide was mounted on an *x*–*y* manual translation stage (resolution: 50 nm) to achieve fine positioning and mechanical stability. An optical microscope incorporated with a charged coupled device (CCD) was used for the

To demonstrate the operation mechanism, a dynamic regulation of the cell chain was experimentally conducted. After the laser beam injected into FP 1 (*P*1 = 30 mW) at *t* = 0 s, a cell chain was organized at the probe tip, which was consisted of 10 *E. colis*. Then, FP 2 was adjusted to approach the downside tip of *E. coli* 3 (indicated by the yellow dot) in the cell chain (**Figure 2a**). After turning on the laser in FP 2 (*P*2 = 50 mW), the downside tip of *E. coli* 3 was trapped by FP 2 (**Figure 2b**). With a shift of 1.9 μm along the −*x* direction, the downside tip was shifted along the −*x* direction, while the upside tip (indicated by the red dot) remained stationary (**Figure 2c**). After that, *E. coil* 3 was rotated clockwise and gradually orientated along the axial direction of FP 2 (**Figure 2d**). Then, it was removed from the cell chain and shifted along the −*x* direction. After that, FP 2

*Optical microscopic images of adjusting the cell contact sequence. (a) FP 2 was adjusted to approach E. coli 3. (b–d) E. coli 3 was rotated and then trapped by FP 2. (e and f) E. coli 3 was shifted with FP 2 along the +y and +x direction. (g–i) The E. coli 3 was added back into the cell chain. The two tips of E. coil 3 were indicated by* 

**14**

**Figure 2.**

*yellow and red dots [38].*

was shifted along the +*y* direction with a distance of ~1 μm (**Figure 2e**), followed by a shift of 9 μm along the +*x* direction (**Figure 2f**). Then, *E. coli* 3 was added back into the chain between *E. coils* 4 and 5 (**Figure 2g**). After the laser off in FP 2, *E. coli* 3 was reorientated along the axial direction of FP 1, and the contact sequence was changed to 1-2-4-3-5-6-7-8-9-10 (**Figure 2h** and **i**).

To quantitatively interpret the above experiment, the optical torques (*T*) on the *E. colis* were calculated in the regulation process, which is defined as:

$$\mathbf{T}' = \int \mathbf{r}\_i \times d\mathbf{F}\_{EM} \tag{1}$$

where *ri* is the position vector pointing from the central point of *E. coli* to the interaction point, *d***F***EM* is the electromagnetic force element exerted on the interaction point *i*. *FEM* can be expressed as:

$$\mathbf{F}\_{EM} = \oint\_{\mathcal{S}} \{ \langle \mathbf{T}\_M \rangle \cdot \mathbf{n} \} \mathrm{d}\mathbf{S} \tag{2}$$

where *dS* is the surface element surrounding the cell, *n* is the surface normal vector, and 〈*TM*〉 is the time-independent Maxwell stress tensor. The optical torque along the +*z* direction is defined as positive, under which the cell will be rotated counterclockwise. As shown in **Figure 3**, the torques are positive and negative in the regions I (−50° < *θ* < 0°) and II (0° < *θ* < 50°). Thus, *E. coli* 3 will be rotated counterclockwise and clockwise, as indicated by the red and blue arrows, respectively. Finally, *E. coli* 3 will be oriented along the axis direction of FP 2, that is, at

#### **Figure 3.**

*Calculated optical torque and force during the regulation progress. (a) Calculated optical torque exerted on the 10 E. colis as a function of θ (FP 1: 30 mW and FP 2: 50 mW). The inset shows the energy density distribution at θ = 0°. (b) Calculated optical torque exerted on the 10 E. colis as a function of θ (FP 1: 30 mW and FP 2: 0 mW). The inset shows the energy density distribution at θ = 130°. (c) Calculated optical force Fx and torque on the E. coli 3 as a function of X [38].*

*θ* = 0°. **Figure 3b** shows the torques exerted on *E. colis* after turning off the laser in FP 2. The torques were positive and negative in the region I (80° < *θ* < 130°) and II (130° < *θ* < 180°), respectively. At *θ* = 130°, the torque exerted on *E. coli* 3 was zero so that *E. coli* 3 will be stably trapped and oriented along the axial direction of FP 1. Moreover, during the shift process of FP 2, the optical force and torque exerted on *E. coli* 3 were calculated as shown in **Figure 3c**. During the shift process, the optical force was negative while the torque remained to be zero, indicating *E. coli* 3 will be stably trapped and shifted with FP 2.

Further, the numerical simulations show that the method can be used for the regulation of cell chains consisted of cells with different sizes and shapes (e.g., spherical). After the FPs incorporated into lap-on-chip platforms, the presented regulation method is expected to enable a new opportunity for the investigation of cell growth, intercellular singling pathway, and pathogenic processes.
