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Latin American applied research

versión impresa ISSN 0327-0793versión On-line ISSN 1851-8796

Lat. Am. appl. res. vol.43 no.4 Bahía Blanca oct./dic. 2013

 

Dynamic manipulation of spherical yeast cells based on atomic force microscopy

M.H. Korayem, M. Geramizadeh and M. Taheri

Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran. E-mail: hkorayem@iust.ac.ir

Abstract— Nowadays the importance of biological cells in life activities is not hidden to anyone. There is an increasing need to understand the biological processes and since the experiments which consider a group of cells to be analyzed can only give average biological results, research on single cell could be really beneficial. So single cell analysis has become an interesting topic in recent years. In such an analysis, one of the most important steps could be the ability to transport the single cell to exact locations. In this paper, the process of manipulation of spherical yeast cells based on atomic force microscopy (AFM) has been investigated. The dynamic governing equations have been considered and a simulation based on them gave the results of the analysis. In order to verify the obtaining results, a comparison has been made with an experimental work of another group. The simulation results show that the critical sliding force in manipulation process of yeast cell is 5.648 micro N and in the experiment this force was 6.661 micro N. So it seems that there is a negligible difference between these two amounts and the results of the simulation are correct. The biological liquid is ethanol in all the parts, but a comparison has been made between three liquids (ethanol, methanol and blood) in order to investigate the effect of environment on the results. The results show that the viscosity of the environmental liquid has more effect rather than its surface tension. The comparison between three important contact theories (JKR, DMT and Hertz) shows that there is a small difference between the critical times and forces of them. Also the contact depth and contact radius of the three models are compared to each other and they also confirmed the small differences between these three models.

Keywords—Yeast Cells; Atomic Force Microscopy; Manipulation Process

I. INTRODUCTION

Yeast cells are eukaryotic single-celled microorganisms classified in the fungi. Yeast species inhabit diverse habitats, including skin, marine water, leaves, and flowers. The economic benefits of yeast have been known for centuries. As the cell cycle of yeast cell is very close to that of humans, it has been largely used as a system to study the genes and gene products of human organisms. For instance, yeast cells have been used as a model cell of human to study human disease, such as cancer, Parkinson's disease and so on. As yeast cells form unwanted drug- resistant biofilms by adhering to medical devices, some works have been done to understand their underlying mechanisms and develop better methods to prevent the biofilms. A novel method for measuring an adhesion force of single yeast cell was proposed by Shen et al. (2011) based on a nanorobotic manipulation system in side an environmental scanning electron microscope (ESEM). The adhesion force between an AFM cantilever and a tungsten probe (substrate) was evaluated at various humidity conditions. Shen et al. (2011) also performed in-situ single cell manipulation with force measurement inside the Environment-SEM. They fabricated the mechanical end effector from a commercial AFM cantilever and used it in the nanorobotic manipulation system in order to control the position of the particle. They achieved the movements of releasing, sliding and rolling of single cell on a substrate by controlling the humidity condition inside E-SEM. The influence of humidity to the single cell manipulation inside E-SEM was also discussed. In this case, the humidity around the cell is about 98%, so a water-contained bio-sample can maintain their nature condition. AFM allows the study of the mechanical properties of biological structures in on the micro and nanoscales. By means of AFM techniques, we can have a versatile platform for imaging and manipulating living cells to single-molecule resolution. It enables us to answer important questions in master areas of cell biology, such as cell adhesion and signaling, embryonic and tissue development, cell division and shape, and microbial pathogenesis. Recently, many AFM experiments have been done on force displacement curves using AFM with reviews showing lots of contributions. A typical cell detachment experiment was carried out by Bowen et al. (1998) who showed that a yeast cell adhering to mica could be detached in the experiments. Most force experiments on single cells have focused on the elastic and plastic deformations of the particles. For example, a typical experiment on yeast cells was carried out by Ren et al. (2008) in which the cells were imaged in an environmental scanning electron microscope and remained alive for 5 min, during which they could be compressed to understand their mechanical behavior. The cells were not fully elastic and showed substantial time dependent deformation. However a computer model of the using light in the form of an optical trap to manipulate microscopic objects without physical contact is a new method in this area. In biology, an optical trap provides a new and novel tool for the manipulation of microorganisms and cells. Taguchi et al. (1997) worked on rotational manipulation of a yeast cell using two optical fibers. The experimental results showed that a yeast cell was rotated and trapped near the focal point of the trapping fiber and also, the control of counterclockwise and clockwise rotation of a yeast cell was easily realized by controlling the output power from each trapping fiber. These experimental results verified that the proposed method using two optical fibers was useful for the manipulation of a microorganism and a biological cell. An optical trapping system for manipulation of yeast cells was built and discussed by Hu et al. (2005). Yeast cells can be trapped and manipulated by moving the sample chamber or the tapered fiber probe in three dimensions. Twenty-one yeast cells have been manipulated to create a pattern of two letters "TH". Next, the optical-trapping-force curves as a function of the offset were measured and discussed by reference to static and dynamic methods at various laser powers. In another experiment, the electric fields from the sequentially energized micropost electrodes moved yeast cells and polystyrene beads using positive and negative dielectrophoresis. A two dimensional addressable array of microelectrodes for DEP manipulation offers the possibility of programmable, real time control over the location of cells and particles in a microfluidic system. Manipulation process of nanoparticles by AFM has been studied by many researches till now. Sitti and Hashimoto (2000) considered the surface forces by using the Johnson-Kendall-Robert theory (JKR), and proposed a new model for the tele-operated nanoparticle pushing process. Korayem and Zakeri (2009) investigated the manipulation models and developed a model for the sensitivity analysis of particle pushing in critical conditions. Obtaining a characterizing model also has been studied in various researches. Motaghi et al. (2010) considered the liquid environment condition on a nano scale. Some of the newly discovered effects such as the viscous drag force on both sides of the cantilever and the relevant local surface tension of cantilever at the air/liquid interface were added to the dynamic model of manipulation in air. These forces, which are applied on the cantilever, were extracted and the new dynamic model was obtained for the manipulation of the submerged nanoparticles in liquid environment. The advantage in an atomic force microscope system is that the force can be measured with the exact amounts and an input device with force feedback will allow the operator to detect the position of nano and micro objects and at the same time push them around, and also to feel the action and even see the results in 3-D with virtual reality equipment.

II. THEORY

Dynamic equations are developed based on the free body diagram of pushing system, including AFM cantilever and probe, nano-particle and substrate. The total force (FT) and its angle (ψ) are finally calculated using these formulas. In this formula, FY and FZ are vertical and horizontal forces of the probe tip and θ is the torsion angle of cantilever.

Finally pushing force and angle of applying probe force are calculated using the following equations. In this formula, FY and FZ, are bending forces of cantilever. FY and FZ are vertical and horizontal forces of the probe tip and θis the torsion angle of cantilever. Fd is the drag force and Fel, Fsq, Fhyd are electrostatic force, squeeze film force and hydration force respectively.

(1)
(2)
(3)

In order to start the sliding and rolling movements, the total force should overcome the sliding and rolling friction forces (Korayem et al., 2011).

In this part the using method for calculating the manipulation force in the experiment done by Shen et al. (2011) is described. A scheme of the single cell manipulation experiment was shown in Fig. 1. The end effector was assembled on the nanorobotic system to apply the manipulation force. Yeast cells were deposited on the tungsten probe, which was fixed on the cooling stage inside E-SEM. Under the driving of the nanorobotic system, the end effector will move towards the single cell. The real time observation of yeast cell pushing and releasing can be realized from the E-SEM image directly. Meanwhile, the deformation of end effector beam can be measured from the images. With which, the manipulation force can be calculated. Finally, the relationship between manipulation force and cell movement can be achieved. The value of manipulation force F during the manipulation can be calculated by the Hooke's law:


Fig. 1. Schematic drawing of the single cell manipulation using end effector after deformation

(5)

where k is the spring constant which is 2 N/m in this experiment. δ is the displacement of the cantilever, for the AFM cantilever, that can be obtained by

(6)

where θ and L are the displacement angle in radian and the length of the cantilever respectively. Values of θ and L can be got from direct measurements of ESEM images. Finally the manipulation force can be calculated by the following equation:

(6)

III. SIMULATION ASSUMPTIONS

The AFM geometric constants and mechanical properties are shown in Table 1. These are the standard values which are usually used for simulating the AFM work process.L, t and W are length, thickness and width of the cantilever and H is the probe height. Also Rt is the tip radius. E and G are Young and Shear modulus and v is Poisson's coefficient.


Table 1.AFM geometric constants and mechanical properties

The used properties of yeast cell are also shown on Table 1. ω is work of adhesion. K is the reduced elasticity modulus between two contacted materials which is calculated by using the following formula.

(7)

Assuming a substrate velocity of 100 nm/s the initial conditions are obtained by simplifying the equations at t=0.

IV.RESULTS AND DISCUSSION

In this part, different diagrams of simulation process are shown. Figure 2 demonstrates the critical conditions of motion for yeast cell of 2 micro meter radius during the pushing process. The medium is considered to be "Ethanol". The critical sliding force is larger than the critical rolling force. In other words, for a particle in this size, the total force will overcome to the sliding resistance later than rolling resistance and rolling motion happens first. In order to verify the obtained results, the experimental work of another group has been used. In the present work the critical sliding force of manipulation of a yeast cell in the simulation results is 5.648 μN and the experimental work shows it to be about 6.666 μN. So it can be seen that there is a negligible difference between these two amounts and the simulation results are close to reality. This small difference can be because of the assumptions that we have made such as ignoring the smaller forces and differences between the environments in which the process has been happened. In the present work, the biological liquid in this part has been assumed to be ethanol, while in the experimental work it is only mentioned that it happens in an environment with 98% humidity. So it could be any liquid and the small differences are predictable


Fig. 2.Critical conditions of motion for yeast cell

In the next part, different liquids are considered as the environment. Three biological liquids (ethanol, methanol and blood) have been used and their used properties in the simulation are shown in Table 2. The comparison has been done between the three conditions in the Figs. 3 and 4. It can be seen that viscosity has a greater effect on the results than tension surface, thus it is the effective parameter in this case.


Table 2. Properties of the used liquids


Fig. 3. Rolling resistance force for 3 different liquid environment


Fig. 4. Sliding resistance force for 3 different liquid environment


Fig. 5. Contact radius changes between tip and particle


Fig. 6. Contact depth changes between tip and particle

In order to investigate the effect of contact theory which is used in the process on the critical time and force, the simulation has been done for three major contact models: Hertz, JKR and DMT. The results are shown in Fig. 7 and Table 3 shows the comparison between them. It can be seen that there is a negligible difference between the critical times and forces of these theories. So each of them can be used for this simulation.


Fig. 7. Critical A.sliding and B.rolling force and time JKR, Hertz and DMT theory


Table 3: Critical rolling and sliding time and force for Hertz, JKR and DMT theories

Figures 5 and 6 show the increase of Contact depth and Contact radius between tip and particle, during the static phase of the process for the three theories which are a proof that there is no sliding between the tip and the particle. They also show that there is a small difference between these theories.

V. CONCLUSION

In this paper, nano manipulation of the yeast cell has been investigated in fluid environmental conditions. The manipulation process is simulated for nanoparticles of 2 micro meter radius in ethanol and for a cantilever that is half-submerged in liquid. The critical sliding force which is obtained in this simulation is close enough to the experimental amount, so the results of the simulation are correct. As the radius of the particle is 2 micro meter, rolling happens before sliding. So critical force and time are related to rolling are smaller than the ones for sliding. The investigation of different liquids shows that viscosity has a greater effect than surface tension. In other word the effective parameter is viscosity and as the viscosity of the liquid environment increases, the critical sliding and rolling forces will have a bigger amount. The comparison between three contact models (Hertz, JKR and DMT) shows that there is not a significant difference between using them and they all show almost the same results. So using each of them to simulate this process is correct. Increasing the depth and contact radius during the process shows that there is no sliding between probe and particles so manipulation can be done successfully. It can be seen also that there is a small difference between the depth and contact radius for three contact theories, so it is another proof for close results of these theories.

Finally, it should be mentioned that for an accurate nanoparticle manipulation in liquid media, more studies are needed, considering various intermolecular forces that are involved in different situations. Future works in this area could be the simulation of manipulation process for other biological cells using AFM. Other biological cells with different shapes will have a different situation and the simulation should consider the exact shape of the particle. As in this work only spherical shaped particles have been considered, another work in this area could be simulation of manipulation process of other biological cells with different shapes such as cylindrical or any other shape.

REFERENCES
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Received: July 19, 2012
Accepted: December 3, 2012
Recommended by Subject Editor: María Lújan Ferreira

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