1. Introduction

Optical forces and their mechanical effect upon colloidal systems are well documented and understood [1], and the very same light fields can exert mechanical forces upon cellular systems. In 1991 it was observed that mammalian cells (Swiss 3T3) could respond to light by extending pseudopodia and migrate towards a focused laser [2]; however, the mechanism which underlies this phenomenon is still poorly understood. Such research is of fundamental importance within the field of neurobiology as developing an understanding of the migration and behavior of neuronal growth cones in response to light may lead to novel treatment regimes for the regeneration of damaged neurons.

The dynamics of axon growth involve a complicated myriad of chemical induced signalling pathways [3], which suggests that the underlying mechanisms of laser induced guidance could also be similarly complex and multifaceted. However, all guidance is reported to involve the actin cytoskeleton [4,5,6]. In 2002, this phenomenon was observed in neuronal cell-lines (NG-108, PC12), where infra-red laser light in the form of a Gaussian spot was shown to influence the development of growth cones [4]. This experiment made use of a focused Ti:Sapphire beam (800 nm) of relatively low power (<100 mW) and attributed the guidance of the neurites to the optical tweezing of actin monomers to provide nucleation sites for the actin polymerisation which drives cellular growth [4].

Another proposed mechanism for laser induced guidance is that the focused light is causing a localised heating effect due to absorption. However, in 2006 a study on optically guided neuron growth compared the efficiency of guiding by two different wavelengths of laser light (780 and 1064 nm) and directly measured for the first time the degree of localised heating caused by absorption [5]. The experiment used the same neuronal cell-line (NG-108) at a constant temperature (37 °C) to compare the effects of the different wavelengths. It was shown that there was no significant temperature increase due to wavelengths of 780 and 1064 nm and that there was no clear dependence on guided growth efficiency with the different wavelengths [5]. This therefore indicated that a localised heating is unlikely to be the dominant mechanism in optically guided neuronal growth for cells growing at 37 °C.

A further experiment in 2005 suggested an alternative mechanism related to optical forces. Using a different neuronal cell line (N1E-115) and experimental conditions than other studies, the authors indicated that an asymmetrical line trap (1064 nm) could enhance the rate of neuronal growth [6]. This ability was attributed to the effect of the asymmetry in the trap to ‘slingshot’ G-actin monomers along the major axis of the line towards the leading edge of the axon. However, this hypothesis was not fully explored as no experiments were performed to examine if an asymmetrical line trap, oriented in a configuration to move actin monomers away from the leading edge, could retard the rate of neuronal growth. In the same study, symmetric line traps were not seen to induce neuronal guidance. The experiment was further impaired by being conducted upon a relatively small number of cells at non-optimal biological conditions (25 °C).

Overall the detailed study of a line trap has significance as one might envisage the use of such structured optical light fields for initiating more complex growth trajectories in neuronal cells. Therefore in this study we investigated in depth the effect of an asymmetrical line trap on neuronal growth cone guidance. Specifically, we tested whether an asymmetrical line trap in the reverse configuration can retard neuronal growth by biasing the flow of actin monomers away from the leading edge of the growth cone. Our studies were performed for large numbers of cells (n>30) maintained at 37 °C. We show that an asymmetrical line trap in the reverse configuration does not retard neuronal growth. In fact, this configuration resulted in similar levels of guided growth efficiency when compared with the forward bias configuration. This suggests that actin flow is not being affected by the presence of the laser since it is vital to cellular growth.

During the course of the investigation we observed that on occasion the filopodia (thin spike-like protrusions which can form from the growth cone, along which the cells tend to grow [3]) extending from the growth cone aligned themselves with the major axis of the line trap, which led the extending growth cone to subsequently align and grow along the line trap. Filopodia alignment has been postulated as a mediator for laser guided neuron growth [7], and our observations add strength to the importance of this as a mechanism. This suggests that for these filopodia there is a significant force upon them which we attribute to the laser light producing an optical gradient force. To help explain this, we developed a theoretical model describing the optical torques, and subsequent alignment with the optical field, experienced by filopodia.

2. Experimental setup

The experimental setup for this neuronal growth study is shown in Fig. 1. A 1 W 1064 nm Nd:YAG laser (Photonics Innovation Centre) was expanded to ~7 mm in diameter and sent into a Nikon 60× Oil (NA=1.4) phase contrast objective in a Nikon TE-2000 inverted microscope. To produce the asymmetric line profile, the beam was focused through a cylindrical lens and then truncated by a beam block at the focus resulting in an asymmetric beam (Fig. 1, 2) of dimensions 1 µm×45 µm and of total power 35–70 mW at the sample plane. Notably, we deliberately focused our line through the center of the objective to avoid effects resulting from the intense radiation pressure of focusing the center of the beam through the edge of the objective’s back aperture (this effectively makes the objective itself the beam block, a setup used previously [6]). The symmetric line trap used as a control for the experiments was created by using a second beam block at the other side of the line to keep the same dimensions as the asymmetric line. The sample plane was imaged through the final dichroic mirror before the objective, onto a CCD camera.

Experiments were performed upon the NG108 cell line. Briefly, the cells were cultured in Dulbecco’s Modified Eagle Medium (DMEM) (Sigma) containing 10% fetal calf serum (FCS) (Globepharm), 20 units/ml of penicillin and 20 µg/ml of streptomycin (Sigma) in a humidified atmosphere of 37 °C and 5% CO₂. 12 hours prior to experimentation, the cells were plated at a low seeding density onto a modified Carrel flask [8] adapted with a type 2 coverslip and containing a surface coating of 5 µg/cm² of laminin (Sigma). 4 hours before the start of an experiment, the medium was changed to DMEM containing 1% FCS; this is done to promote the differentiation of the cells into a growth cone presenting state. Immediately before experimentation the Carrel flask containing the cells was hermetically sealed in an atmosphere of 5% CO₂ and placed on a temperature stabilised stage at 37±0.5 °C. Cells could survive in this setup for days without signs of stress though experiments rarely lasted longer than 10 hours.

 

Fig. 1. The optical setup. A 1064 nm laser was focused at the sample plane after having its profile altered to be an asymmetric line. The cylindrical lens squeezes the beam in one dimension and the beam block truncates the profile to provide the asymmetry. It is important to note that the line formed by the cylindrical lens at the focus extends perpendicular to the plane of the diagram and so the beam block is raised slightly out of the plane so as not to block the whole beam. The profile of the laser is shown in the dotted circles before and after the cylindrical lens and beam block and it should be noted that since the line trap formed is perpendicular to the plane of the diagram, the asymmetrical profile displayed in the dotted circle is, so that it can be seen, not in the same orientation as the line trap. [Media 1]

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Fig. 2. Profile of beam taken with beam profiler. Left, oblique view of how the intensity profile of the asymmetric beam varies over space. Right, top down view of beam profile showing contour lines linking areas of same intensity.

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The asymmetric laser profile was used in one of two configurations that we designated ‘forward’ and ‘reverse’ bias (see Fig. 3). Forward bias is the orientation of the beam so that the growth cone would be expected to extend forward along the major axis of the line as per the theory from [6], and reverse bias is the opposite of this (expected to retard growth). The major axis was always orientated along the direction of desired growth (not the initial direction the growth cone is moving in, but an angle of ≥30° from this direction) and the edge of the growth cone was always illuminated by the part of line with the steepest optical gradient. The laser was then adjusted as the neuron grew to maintain this configuration.

Cells chosen for experimentation were monitored for at least 10 minutes before irradiation to determine whether they were actively growing. Cells that were found to have no actively growing cones were not experimented upon. Guided growth did not last indefinitely and after an average time of approximately 20–30 minutes of laser application, successful cells started to stall and retract. Cells that had actively growing cones that did not respond (or retracted) within 10 minutes under the influence of the laser were counted as unsuccessful in any given experimental run.

 

Fig. 3. A typical growth cone is shown above with an arrow added to represent an asymmetric line trap in the forward (right image) or reverse (left image) bias configuration. The dash in the arrow represents the most intense region of the beam. Actin would be expected to move along the arrow due to the ‘slingshot’ effect reported in [4]. On the left the laser is configured to induce an optical bias on the edge of the growth cone to grow along x (reverse bias) and on the right the laser is configured to produce the bias to grow along -x (forward bias). Scale bar is 10 µm.

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3. Results and discussion

3.1 Laser guided neuron growth in asymmetric and symmetric line traps

Table 1. Results of studies using line trap (Averages are ±SEM)

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This experiment was designed to explore in detail the optical bias generated by the asymmetric line trap. If such a trap can enhance growth by biasing the flow of actin, as was previously suggested [6], then one would expect to observe a retardation of growth if the bias of the trap is reversed to drive actin away from the leading edge. However, this was not the case and in experiments designed to retard growth, we established that guidance actually increases with the same efficiency as a forward bias configuration of the beam (Table 1, Fig. 4). The growth cones were observed to change direction from their initial trajectory to line up with the major axis of the beam regardless of the orientation of the asymmetry. A symmetric beam (no bias in either direction) used as a control also has the same efficiency as both asymmetric configurations. The efficiency (the number of successfully guided cells to number of cells experimented on) for using a line trap appears to be less than previous reports for standard Gaussian beams [4,5]. Growth rates were calculated by measuring the distance a growth cone grew in a known time. These are not instantaneous growth rates but average rates taken between the time the laser was applied and when the cell stopped growing and the laser was removed. Averages of these growth rates (as well as the full range) were calculated for each beam configuration and are displayed in Table 1.

 

Fig. 4. Time lapsed sequence showing examples of neuronal growth in forward (left) and reverse bias (configurations). Frames flow from top to bottom; each frame is five minutes apart with time stamp in minutes in lower right corner. The field of view changes as the sample stage is moved to keep the beam on the growing cell. To compensate for this changing field of view a manually drawn outline is added to successive frames to represents where the edge of the growth cone was in the previous frame. Each neuron grows up until about frame 6 at which time they begin to stall and retract. Scale bar is 10 µm.

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3.2 Observation of filopodia alignment in asymmetric and symmetric line traps

The growth of the neuron can be mediated by filopodia which are composed of bundles of parallel actin filaments. These actin filaments are cross-linked by actin-binding proteins and surrounded by the cell membrane [3]. On six different experimental occasions the filopodia from an extending growth cone were clearly seen to align themselves with the major axis of the line trap as they grew outwards (Fig. 5). This was independent of the asymmetrical bias orientation. We attribute this to the optical forces attracting the filopodia. Since filopodia are important in determining which direction a growth cone will grow [3] we propose this aligning as an important mechanism for optically guided neuron growth. This therefore supports previous suggestions that the filopodia are influenced by laser light [7].

 

Fig. 5. (439 KB) Movie of the alignment of filopodia on leading edge of a growth cone during exposure to a symmetric line trap. This particular example is representative of six observations of similar behavior, regardless of line trap bias. Speed is approximately 100 times and the scalebar is 10 µm. The representive frames in the still image are 15 seconds apart.

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3.3 Modeling optical torques acting on filopodia

Modeling the complex biological, chemical and mechanical interactions taking place during filopodia growth is a challenging task. Here, we concentrated on the torque exerted by the focused laser beam on these filopodia and the direction towards which they turn under laser illumination. This study complements the Ehrlicher et. al [4] theoretical approach where the optical force on the individual G-actin monomers was calculated by considering the gradient forces acting on an r_act=3 nm sphere with an index of refraction of n_act=1.59.

Here, we determine the optical forces on a Rayleigh range sized particle using the time average total force acting on a dipolar sphere [9]

where the brackets stand for the time average, the star for the complex conjugate and where we implied summation over repeating indices. Further, we considered the electric field E given by an elliptically shaped Gaussian beam (ω_0x=500 nm, ω_0y=22.5 µm) linearly polarized along the x-axis. The polarizability, α ₀, is corrected for the radiative reaction term [10] giving the polarizability, α, in Eq. (1)

where k ₀=2π/λ is the vacuum wave-vector and $n_{H_{2}O}$ the index of refraction of water. The optical force acting on each G-actin sphere is summed over the whole actin filament structure. This filament consists of a helical structure of actin dimers (Fig. 6) with a 74 nm pitch containing 14 dimers [11,12,13]. A filopodium is made up of a bundle of approximately 20–30 actin filaments up to 2 µm in length. Here, we considered 25 filaments, 10 nm apart, in a 5×5 square lattice. The entire filopodium considered has approximately 19,000 monomers. Finally, we determine the optical torque on the filopodium by summing all the individual torques calculated with respect to one end of the filopodium.

After building the model of a single filopodium, we then modeled multiple filopodia as being free to turn around one of their ends, i.e. like a rod with a pivot point representing the end of the filopodium linked to the cell body. The optical forces and torques were calculated for several positions and orientations of the filopodium with respect to the laser beam. Fig. 7 shows these optical torque acting on a bundle of 25 filaments with its pivot offset with respect to the center of the Gaussian beam, and with respect to the center of a symmetric line trap. We observe that the torque varies with the angle of the filopodium; attractive equilibrium angular positions are reached when the optical torque changes from positive to negative as the angle of the filopodium increases. In the case of a circular Gaussian beam, there exists only one equilibirum angle (Fig 7a), whereas for the line trap there are two (Fig. 7b).

 

Fig. 6. Schematic representation of one period of the actin filament consisting of 28 actin monomers. The monomers pair up into dimers which then twist helically with a full twist occurring every 14 dimers which is approximately 74 nm in length [10,12,13].

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Fig. 7. Optical torques acting upon a bundle of 25 filaments as a function of its orientation with respect to the major axis of the line trap. Fig. 7a represents the torque as a function of angle for a Gaussian beam of dimensions 7 µm×7 µm and Fig. 7b is for a line trap of dimensions 1 µm×45 µm. Both lasers have a total power of 75 mW.

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Fig. 8. Graphical representation of filopodia equilibrium orientations in optical traps. Fig. 8a represents filopodia of 2 µm length being fixed at one end in the Gaussian beam. A grayscale intensity profile of the beam is shown behind the filopodia. Fig. 8b shows the same filopodia in the line trap. The dashed line links the points of maximum intensity between the two profiles.

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In Fig. 8 we can see the filopodium as short lines with the spot at the end representing the fixed pivot point. This shows that the equilibrium position occurs in the Gaussian beam when the filopodium is pointing towards the center of the beam. In the line trap there are two equilibrium positions as seen in Fig. 7. The filopodia in Fig. 8 were all given initially a horizontal position (pointing left with respect to the fixed end) and then orientated into the equilibrium position in the presence of the beam. Notably, regardless of the position of the maximum intensity of the line trap, the filopodia align with the major axis of the beam profile (Fig. 8). The filopodia do not pivot round and point towards the most intense part of the beam profile and so they fall into the other attractive equilibrium position. This is consistent with our experimental observations and supports the view that the optical gradient alone along the line trap is not sufficient to influence growth, as suggested previously [6]. Also in Fig. 8, the filopodia cross over the maximum intensity of the line trap beam. This can be explained when considering the optical forces acting on the different sections of the filopodium (Fig. 9). The equilibrium position is reached when the net total torque is zero and the filopodium must cross over the center of the major axis for the individual optical torques to balance.

 

Fig. 9. The optical forces (arrows) acting on the different sections of a single filopodium in a line trap.

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4. Conclusions

In [6] the authors reported the enhanced effects of a forward bias asymmetric line trap for neuronal growth. Using a more controlled environment, our observations do not support their conclusions. While optical gradient forces are an important factor in the influence of the line trap on axonal guidance, asymmetry along the line is inconsequential to the manipulation of neuronal growth.

In this work we have also observed what has been suggested previously in the literature [7], that filopodia alignment can occur as a precursor to direct growth. To expand on the idea that filopodia alignment may mediate directed growth, we modeled the optical torque on the filopodia using the Rayleigh forces acting on a bundle of actin filaments. The individual actin monomers, bound together within the F-actin structure, are treated as dielectric spheres [4]. Our model shows that filopodia will indeed feel a small optical torque, on the order of a couple of pN·nm, which would reorientate freely pivotable filopodia. This reorientation occurs regardless of the beam shape. There is no significant difference between an asymmetric line trap of either orientation or a symmetric line trap, in the ability to promote guidance. Taken together, this suggests that optical torques may be a further mechanism to be considered when dealing with this interesting phenomenon.