1. Introduction

The mechanisms responsible for cells reshaping and cells motility are subjects of active research. Although the molecular functions of organelles are fairly well understood, there is still no general consensus regarding the details of the mechanism that governs the overall cell behavior and determines their migration from one site to the other. Recently, it has been suggested that cells movement and reshaping may be determined by stochastic processes such as Brownian motion [1] or inner cell mechanical arrangements [2]. These reports explain the cell motility by the stochastic generation and dissolving of actin filaments.

Actin filaments (F-actin) exert forces by elongating towards the membrane of the cell. This elongation is determined by the attachment of globular actin (G-actin) monomers to the F-actin’s end that is touching the membrane. The choice of G-actin attachment at one end or another is controlled by the F-actin polarity and by the critical concentrations at which G-actin monomers can attach or detach from the F-actin ends [3]. When the plus end of an F-actin filament is the one touching the membrane and the concentration of G-actin is above the critical value, the filament will elongate towards the membrane initiating the protrusion. Under normal conditions, the displacement of G-actin is stochastic in nature and is governed by Brownian like movement [1]. When external forces act on either the G-actin monomers or on the F-actin filaments, their movement and, consequently, the cell growth and displacement can be affected. This process can be controlled by applying certain external optical fields.

The idea of mechanical action of light on matter has its origin in the corpuscular theory of light. Most of the practical applications rely on optical forces applied to particles having a refractive medium different from that of the surroundings. The applied force is in general dissipative as it points along the direction of propagation and results in acceleration [4]. However, if the particle is subjected to an optical field with a significant intensity gradient, a conservative force develops which acts along the gradient of intensity. When the conservative component dominates, small particles can be trapped and controlled within the confined volume of an intense laser beam [5]. Conservative forces also develop as a result of manipulating the wavefront or the polarization of light beams [6,7].

Interestingly, apart from forces, optical fields can also exert torques and therefore can rotate small particulates [8,9]. The existence of optical torques can be traced to source of mechanical action of light: the exchange of momentum between radiation and matter.

Beside different areas of colloidal physics, light induced forces and torques have been used in a number of biological applications [10]. Cells plating [11], floating cells and chloroplast manipulation [12-14], and cell growth guiding [15-18] are just few relevant examples. What is common to all these applications is that trapping and manipulating cells requires fairly large optical intensities. Furthermore, because of the highly localized nature of the optical trapping field, these techniques commonly operate on single cells or on particular parts of a cell. Influencing the behavior of an entire collectivity of cells is a more complex problem that has not been approached yet. Here we will show for the first time that optical torques exerted by electromagnetic fields can direct cells motility and can control the alignment of large cell clusters. As we will demonstrate in the following, the large scale guiding is accomplished using only the polarization-induced torques, in the absence of any other optical forces. The cells motility is practically controlled by manipulating the stochastic motion of the G-actin monomers and F-actin filaments which, in turn, influences the directional movement of an entire cell or even the alignment and displacement of entire cluster of cells. Moreover, the manipulation of large clusters of cells is accomplished at much lower irradiance levels than required for optical trapping, which opens the door for many yet to be explored applications.

The paper is structured as follows. First, we discuss the mechanism for gradual alignment of small rod-like particles subjected to both Brownian motion and polarization-induced optical torques. This model will be further used to explain the optical manipulation of actin filament networks. Experimental results will then be presented demonstrating both the effect of light polarization on cytoskeleton and the dynamic cells guiding using optical torques. Finally, we will make some concluding remarks suggesting further applications.

2. Rod-like particles subject to optical torques

In the presence of an external directional field, F-actin and G-actin can be treated as dielectric rods subject to both Brownian motion and torques. We will show that this representation can explain our main experimental observations, namely the cells’ tendency to modify their motility characteristics as a result of actin filaments alignment and growth in response to the applied optical field. The major elements of the model are (i) the random movement of actin filaments due to thermal forces in normal conditions and (ii) the influence of a weak optical field through induced torques.

2.1 Brownian motion of rod-like particles subject to external torques.

The G-actin monomers and the actin filaments can be regarded as rods of different dimensions. The G-actin monomers, although never measured directly, were found to be 5.5nm in length and 3.5nm in diameter using indirect measurements [19]. The actin filaments on the other hand can be seen as bundle of filaments as long as 10µm and with a diameter of 1µm. These particles are all subject to Brownian motion due to thermal forces as well as to external forces and torques. The associated Langevin equation is

where x and θ are the location and orientation of the particle, respectively. In Eq. (1), $\tilde{\xi }$ (t) and $\tilde{\xi }$_θ(t) are the random processes describing the Brownian translation and rotation, Γ is the mobility tensor while Γ_θ is the rotational mobility coefficient. F and T denote the external forces and torques. Assuming that the inertial effects are negligible, i.e. ∂ ² x/∂t ²=∂ ²θ/∂t ²=0, Eq. (1) can be rewritten as,

where ξ(t)=Γ(t)$\tilde{\xi }$(t) and ξ_θ(t)=Γ_θ(t)$\tilde{\xi }$_θ(t). For simplicity, one can further consider that the random processes are Gaussian distributed with zero mean (the maximum probability to find the particle will be in its original position) and have the variance

where k_B is the Boltzmann’s constant, T is the temperature, and D is the diffusion coefficient. The angle brackets denote an ensemble average. For rod like particles, the diffusion coefficients are different for each degree of freedom. We are interested in a two-dimensional geometry where the diffusion coefficients corresponding to the free movement of the particle are [20]:

Here D_a and D_b denote the translational diffusion coefficients along the short and the long axis of the rod-like particle while D_θ represents the rotational diffusion coefficient. In Eq. (4), η s is the viscosity, L and Φ are the length and diameter of the particle and r=L/Φ. As can be seen, the rotational diffusion coefficient is strongly dependent on the particle length meaning that, for longer particles, the time in which the diffusion becomes anisotropic is longer.

2.2 Optical torques.

A crucial step in the understanding the mechanical effects of light was Beth’s work on the angular momentum of polarized light. In his famous experiment it was demonstrated that macroscopic, anisotropic objects can rotate as a result of the torque exerted by a beam of circularly polarized light [9]. Since then, the subject fascinated many people and has been the focus of sustained research. Notable developments include the manipulation of phase and polarization distributions across the illuminating beam in order to rotate particles that are optically anisotropic [8]. It has also been realized that the rotation of a small particle doesn’t necessarily require an intrinsically anisotropic optical material as long as the shape is asymmetric. Recent reports have shown that linearly polarized light can exert torques on small microparticles as long as they have aspheric shapes [12-14, 21-24]. This can be easily explained by considering the particles as dipoles excited by the radiation’s electric field. The secondary emission from these dipoles (scattering) doesn’t necessarily need to be polarized along the direction of excitation. Hence, this modification of the direction of the electric field direction determines a torque on the particle. For anisotropic particles, this torque can be written as

where P=χ E is the polarizability vector of the dipole [24]. In Eq. (5), E is the incident electric field, I₀=cε ₀|E|² is the beam’s intensity, χ_o and χ_e are the ordinary and the extraordinary susceptibilities, A is the particle cross section perpendicular to the beam propagation axis, Δt is the measurement integration time, ε ₀, c are the vacuum permittivity and light velocity, and θ is the angle between P and E. As can be seen from Eq. (5), the torque is maximal for an angle of 45° between the scattered and the exiting electric fields and it is minimal when they are either collinear or orthogonal. However, the orthogonal direction is a non-stable equilibrium as for smaller and larger angles the torque has opposite signs.

Let us consider now the two-dimensional problem of rod-like actin filaments and rod-like actin monomers. For simplicity we will consider a plane wave illumination that is horizontally polarized (the electric field is in plane and aligned along the x axis). When using in the Langevin equation the expression for the torque in Eq. (5), one obtains

where θ ₀ is the initial alignment angle, α=τ₀Γ_θ, τ ₀=I ₀(χ_o-χ_e)·A·Δt, and ζ(t) is a random process with a 0 average and a variance of 2D_θΔt.

 

Fig. 1. (a-c) Results of numerical simulations illustrating the orientation of 1×10µm rods before and after 2 and, respectively, 4.5 seconds after the irradiation with light polarized along the indicated direction. (d-f) The temporal evolution of the angular orientation of the same rods; the rods in (e) and (f) were subjected to five and, respectively, ten times more intense radiation then those in (d). (g-i) The temporal evolution of the angular orientation of rods of different sizes: (g) 0.2×2 µm, (h) 0.5×5 µm, and (i) 1×10 µm.

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We used this model to further illustrate the behavior of rod-like Brownian particles that are subjected to optical torques of different strength. As summarized in Fig. 1, the rods become progressively aligned after an external optical torque is applied. One can see that initially, when no torque is applied, the distribution of rods’ orientation is arbitrary. After applying an optical torque for 2 seconds, an increasing number of rods become aligned along the direction of polarization. Finally, after 4.5 seconds of irradiation, the majority of the rods are rather well aligned. Of course, the time scale of this process also depends on the level of irradiation.

In Fig. 1(d)-1(f) we depict the evolution of the distribution of orientation angles for a large number of rods exposed to different levels of light intensity. As can be seen, when increasing the intensity, the distribution function becomes narrower faster indicating an efficient alignment of the ensemble of rods. As shown in the preceding analysis, the magnitude of the torque depends not only on the irradiance level but also on the size of the dielectric body. This is illustrated in Fig. 1(g)-1(i) where similar distributions of rods’ orientation is calculated for ensembles of rods having the same aspect ratio but different lengths. It is clear that, in similar environmental conditions, larger rods tend to align faster for the same level of irradiation. This analysis forms the basis for explaining the experimental observations presented in the following.

3. Experimental results

The setup used to investigate the effect of optical torque on cells motility is depicted in Fig. 2. A linearly polarized doubled YAG laser beam (Intelite, model GSF32-200P, λ=532nm, and beam intensity of P=6mW), is transmitted through a polarization state generator (a half wave plate) followed by a long working distance objective lens (x50 epiplan objective from Zeiss) to illuminate an incubation chamber that contains the cells attached to a substrate. The cells are also illuminated with unpolarized white light (power density of about 30mW/mm ²) and imaged in transmission through the same objective lens onto a charge coupled device (CCD). The laser beam is filtered out using a band pass filter. The irradiation process was continued for several hours while the direction of polarization was modified every half hour. During the entire period, the cells manifested the tendency to align along the direction of polarization.

 

Fig. 2. The experimental setup comprises a laser beam passing a polarization state generator (PSG) and illuminating a cell culture through a microscope objective (MO). The cells are placed inside an incubation chamber (IC) and are imaged using an unpolarized light source and a charged coupled device (CCD).

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The results reported here were obtained using SH-Sy5 neuroblastoma cells. The cells were plated at a density of 5 X10⁶ per 75cm² in tissue culture treated flask (Corning). The cell culture medium was Dulbecco’s modified Eagle’s medium with F-12 (DMEM/F12, Invitrogen), supplemented with 10% heat inactivated fetal bovine serum (Atlanta Biologics). An incubation chamber was used to maintain a humidified atmosphere of 5% CO2 and 37°C. SH-Sy5 cells were passed twice a week by trypsin/EDTA (Invitrogen) treatment.

 

Fig. 3. (a) Fluorescence image of fixed SH-SY5 cells that were not subjected to illumination. (b) Image of fixed SH-Sy5 cells after being illuminated with light linearly polarized at 45 as indicated. (c, d) Fourier transform distributions of the corresponding cell images in (a) and (b).

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In order to demonstrate the alignment of cell filaments along the direction of polarization we used a fluorescence method in which cells, cultured and irradiated with polarized light, were fixed using ethanol and filaments were stained using phalloidin attached to a green fluorescing dye (Alexa Fluor @ 488, Invitrogen). The SH-Sy5y cells were first fixed with ethanol, then washed with Phosphate-buffered saline, pH 7.4 (PBS). The fixed cells were stained with the dye solution composed of 5µl of phalloidin (Alexa Fluor @ 488, Molecular Probes) and 200µl of PBS followed by 20 minutes of room temperature incubation. The last stage was to wash the cover slips with PBS. The entire procedure including the incubation was conducted in the dark.

Figure 3(b) depicts the fluorescent image of cells that were irradiated with polarized light along the direction indicated. For comparison, we also show a typical fluorescence image of cells that were not irradiated with polarized light (Fig. 3(a)). The alignment of the actin filaments is obvious. Furthermore, a quantitative evaluation of filaments orientation can be performed based on the Fourier analysis of the microscope images. One expects that 2D Fourier transform of an image of aligned cells or structured shapes will manifest more anisotropic features than the ones corresponding to randomly oriented cells. This is evident in Fig. 3(c) and 3(d) where we present the Fourier transform of the corresponding images in 3(a) and 3(b). A simple inspection of the Fourier transform images reveals the significant difference between the two examples. It is obvious that in the case of polarized illumination the Fourier transform is highly asymmetric as opposed to the situation where unpolarized illumination was used. Moreover, the asymmetry is oriented perpendicularly to the direction of polarization as a result of the filament orientation according to the results of our numerical simulations.

 

Fig. 4. (a) The time evolution of an ensemble of SH-Sy5 cells exposed to unpolarized light. (Media 1) (b) and (c) Two different examples of the time evolution of SH-Sy5 cells exposed to light linearly polarized along the direction indicated by the arrows. In time, an evident structure formation develops along the direction of polarization as explained in the text (Media 2 and Media 3).

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As suggested by our simulations, the tendency of actin filaments to align along the direction of polarization can cause cells reshaping and directional movement. Even though a detailed description of such a complex dynamic process would require more complex considerations, the major elements can be clearly accounted for. As a consequence of irradiation with polarized light we have been able to observe, in real time, directional movement and alignment of cells. Some of the results are illustrated in Fig. 4. Remarkably, in time, the cells have an evident tendency to orient and move along the direction of polarization of the electric field as opposed to cells exposed to unpolarized light.

It is also worth noting that entire ensembles of cells gradually align along the direction of polarization indicated by the arrows. Further and perhaps more impressive evidence is included in the supplementary movies Media 2 and Media 3 where one can observe how the directional cell movement is clearly guided by the symmetry break due to the direction of light polarization. The cells tend to move along this direction as explained before while in the absence of polarization no distinctive orientation can be observed throughout the entire examination period as illustrated in Fig. 4(a) and also in Media 1. Note also that, apart from the degree of polarization, the irradiance levels are very similar for the observations illustrated in Fig. 4 and the additional movies.

The cell alignment is also apparent in Fig. 5 where we present the Fourier transform along with the images of cells irradiated with light polarized horizontally and at 45° as indicated. A simple inspection of the Fourier transforms reveals the significant difference between the two examples. It is evident in both situations that the Fourier transforms are asymmetric and, as mentioned in the preceding discussion, the asymmetries are oriented perpendicularly to the direction of polarization. To emphasize these differences even more, we show in Figs 5(e) and 5(f) two different orthogonal cross sections of the Fourier transform images. In the intermediate spatial frequency regions where the shape information resides, the different spectral content along the two orthogonal directions proves once again the anisotropy of the Fourier transforms.

 

Fig. 5. (a), (b) ensembles of cells illuminated with light linearly polarized horizontally and at 45° as indicated. (c), (d) Low spatial frequency region of the corresponding two-dimensional Fourier transforms of the images in (a) and (b). (e), (f) Cross sections of the two Fourier transforms along the directions indicated in (c) and (d).

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We would like to emphasize that in order to secure the cells viability, all motility experiments presented here were performed at low levels of light intensity (less than 40mW/mm ²). The vitality of the cells was evident on images taken every 30 minutes and it was also assessed by observing population growth after reincubating the cells. The absence of photo-toxicity as a result of long time exposure to polarized light was also established by subjecting the cells to similar low-levels irradiation in the absence of any directional polarization. No effect on cells viability could be detected as seen in movies recorded over extended periods of time (several hours).

4. Conclusions

We have demonstrated novel means for directing and controlling cells motility. The new mechanism for guiding cells motility exploits the optical torque exerted on the actin filaments that are part of the cytoskeleton which, in turn, is responsible for the cell movement and cell reshaping. We have also presented a physical model explaining this phenomenon by assuming that the G-actin monomers and the F-actin filaments act as anisotropic dipoles characterized by a certain orientation of their polarizability vectors. Consequently, when a polarized field is applied, the optical torque exerted on the filaments biases their Brownian motion which eventually leads to directional movement and reshaping of the cells. The experimental observations are well described by a simple model considering rod-like actin filament that are simultaneously subjected to Brownian motion and a directional external field. The use of radiation forces for manipulation has become a routine practice in biology but, to our best knowledge, the present results constitute the first demonstration of optical torques exerted by linearly polarized light in the absence of any other external optical forces.

We would like to emphasize that the results presented here were achieved with quite low intensity illumination such that the cells’ viability was secured. The non-invasiveness of our procedure was clearly confirmed by the images taken for several hours at 30 minutes intervals. The experiments also included non-polarized illumination with similar intensity levels which also demonstrate the absence of photo-toxicity. In addition, the cells viability was also examined by observing population growth after reincubating the exposed cells.

Finally, apart from cells directional motility, we have also experimentally demonstrated the tendency of large groups of cells to preferentially align when exposed to linearly polarization radiation. Cells’ collective behavior has been addressed in recent publications [25, 26] and it was essentially attributed to intercellular communication. Nevertheless, establishing the influence of external optical signaling on these processes requires further investigations.