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Laser Tweezers and Applications in Biology
MAURICIO CAMARGO T
Prof. Seth Fraden
Phys 39a: Advanced Physics Laboratory
October, 2006
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Laser Tweezers and Applications in Biology
Historical Background
In the late nineteenth century, James C. Maxwell was the first to show
theoretically that light could exert optical force. This type of force, commonly referred as
radiation pressure, had been observed centuries before in astrological phenomena. An
example of these observations was the fact that comet tails always point away from the
sun, implying that there exists some kind of radiation force from the sun.
Due to the weakness of this radiation force, Maxwell’s proposal could not be
confirmed until the mid-twentieth century, after lasers appeared. Arthur Ashkin was the
first to exert forces on small dielectric spheres (μm size) by focusing laser light into
narrow beams, being able to levitate and push these micron-size spheres. Later in the
1980s, using a microscope objective, Ashkin showed that a stable thee-dimensional trap
for dielectric objects could be achieved. Further studies in the field have gone into
optimizing these types of optical traps by studying the geometry of the trap, changing the
frequency and power of the laser (Williams).
Optical traps, also called laser tweezers, have had a major impact in the field of
biology, essentially because they constitute an excellent tool for manipulating and
trapping microscopic objects, thus, enhancing the study of living things in this micronscale world.
Theoretical Background
1) Radiation Pressure and Trapping Qualitative View
The term radiation pressure refers to the forces exerted by photons due to their
scattering, absorption, emission, or re-radiation. These forces may manifest themselves in
different ways, of which the scattering force in the most common. The scattering
radiation pressure is the force consequential to the momentum change experienced by
scattered photons from any given object. This force is proportional to the number of
photons hitting the object per unit time per unit area (the intensity of the light) and acts in
the direction of propagation of the photons. Another manifestation of radiation pressure,
which is essential for laser tweezers, is the gradient force. This force is proportional to
the intensity gradient of a given light distribution and acts in the direction where the
maximum intensity rests (Moses). Other forms of radiation pressure exist, but emphasis
will be given to the two forces mentioned above; optical traps rely mainly on these two.
When light passes through a transparent, dielectric object, both scattering and
gradient forces act on the particle. For objects much bigger than the wavelength of the
light (radius >> λ), a ray-optics picture explains very well the trapping event. Rays of
light carry momentum and are refracted when passing through a dielectric sphere with a
higher refractive index than the medium. The change in momentum experienced by the
light passing through is accompanied by an equal and opposite change in momentum by
the sphere. The rate of change of momentum (dP/dt = F) produces that trapping force.
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In the first picture, from left to right, a net force is experienced by the sphere in
the direction of the focal point, as expected. In the second picture, a parallel beam of light
with a gradient of intensity, gives rise to reaction forces in the bead that tend to pull it
rightwards towards the more intense light (the brighter ray transmits more force than the
dimmer one). In the third picture, which is essentially the same situation as in the first
picture, two sets of rays are drawn. Those rays close to the vertical axis produce
momentum kicks due to refraction that are almost equal and opposite, contributing little
to the trapping force desired. These same rays, however, contribute much to the scattering
force, due to great reflection of the ray. On the other hand, rays further away from the
axis have little reflection and produce momentum changes with a resultant backward
component. This third picture suggests that laser tweezers owe their trapping ability to
those laser rays that come into the dielectric sphere with a high angle of incidence (from
the vertical axis). One can conclude that the stability of the three-dimensional trap,
obtained when the gradient force surpasses the scattering force, occurs only with the
steepest light gradients. Such steep configurations are produced by microscope objective
lenses with high numerical aperture (NA). This fact will become important when
discussing the design of optical traps for laboratories (Ashkin).
For objects much smaller that the wavelength of light (r << λ), also called the
Rayleigh regime, the ray-optics view is not quite accurate. The focus point is no longer
seen as a point but as a diffraction-limited pattern with size close to the wavelength.
Nonetheless, the particles behave as point dipole scatters, and the trapping occurs in a
similar fashion: the magnitude of the trapping force is proportional to the field gradient
(Ulanowski).
2) Trapping Theory:
The force exerted in optical traps is expressed in the following way (Ashkin):

F = QnP / c
(1)
Where P is the laser power measured at the particle being trapped, n is the index
of refraction of the medium, c is the speed of light, and Q is a dimensionless constant that
indicates the fraction of power that actually exerts force. Given that most experiments
take place in aqueous mediums, the factor n cannot be changed in order to increase the
trapping force. The power, P, of the laser itself can be manipulated and increased, but one
has to take into account the fact that high laser power creates optical damage. The
dimensionless constant, Q, however, can be exploited in order to increase the optical
trapping force. As one will discuss later, Q depends on the geometry of the trapped
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particle, and on other details of laboratory setup (microscope specifications, laser
characteristics, etc).
Rayleigh Regime (r << λ):
In this regime, the scattering force (FS) and the gradient force (FG) can be written
in the following way:

FS = n S σ / c
(2)
Where
σ = 8/3π(kr)4 r2 [(m2-1)/(m2+2)]2 (the scattering cross section of the sphere)
S (Poynting vector)
m = nsphere / n (relative index)
k = 2πn / λ (wave number)
r (radius)

FG = α/2
E2 (3)
Where
α = n2r3 [ (m2-1)/(m2+2) ] (polarizability of the particle)
Stable trapping must have a gradient force bigger than the scattering force. By
increasing numerical aperture (NA) of the microscope objective, the focus point
decreases and the gradient strength increases. Therefore, the dependence of F on Q can be
exploited by increasing the NA.
Ray-Optics Regime (r >> λ):
A known set of rays enters the
back of a microscope objective and is
focused to a point. The rays reflect and
refract at the surface of a sphere and a
net force is exerted. The overall force
experienced by the sphere is the vector
sum of all the forces resulting from the
collection of rays in the beam.
F = (nP/c) {1+Rcos(2θ)–[T2(sin(2θ-2ε)+Rcos(2θ))] / [1+R2+2Rcos(2ε)]} k
+ (nP/c) {Rsin(2θ)–[T2(sin(2θ-2ε)+Rsin(2θ))] / [1+R2+2Rcos(2ε)]} i
Where k and i are the scattering and gradient forces, respectively, θ is the angle of
incidence, ε is the angle of refraction, R and T are the Fresnel reflection and refraction
coefficients (Ashkin).
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As stated before, the stability of the trap is determined by the degree in which the
gradient force overcomes the scattering force. The ray-optics theory correctly predicts
that a stronger trap is achieved when overfilling with the laser the back aperture of the
microscope objective. Just as in the Rayleigh regime, a high NA also increases the force
in the trap, although only until a certain extent. One can immediately assert that laser
distributions that have more intensity at bigger angles of incidence than at smaller angles
should work more effectively. From this prediction, the laser mode chosen for laboratory
setups plays an important role in optical traps, as well as frequency considerations as one
will see later in the text.
In order to maximize the dimensionless constant Q, scientists working on the
theory of tweezers have predicted optimal values for the variables affecting the trapping
force. Such values are, for instance, numerical aperture NA=1.3, index of refraction of
particle n=1.69, which give rise to Qmax of 0.14 for beads of 0.1μm size (Block).
One can estimate the forces that can be exerted just with the predictions above.
F = QnP/c  F/P = Qn/c = (0.14)*(1.33) / (3*108) = 6*10-10 N/W
F/P = 0.6 pN / mW
Considering that lasers available in the market are usually in the order of tens of
miliwatts, then an estimate of the forces that can be exerted on the particles are of about
tens of piconewtons.
Theoretical predictions in this area have always turned out to be overestimates by
a factor of about 4 (Block). The discrepancy between theory and measurement may be
due to the roughness of the bead surfaces, which can increase the scattering force.
Radiometric forces may play some role as well.
Electromagnetic Theory:
Another way to predict the forces that can be exerted with laser tweezers is
through the electromagnetic approach.
For particles much bigger than the wavelength of light, one can view the spheres
under the influence of a focused laser beam, as an analog to a dielectric material between
a parallel plate capacitor under the influence of the electric field due to the separation of
charges. The bead experiences a net force in the direction of the intensity peak just as the
dielectric material is pulled in between the capacitor.
From the picture: k is the dielectric constant of the material, E and V the electric
field and the voltage across the capacitor respectively, L and W the length and width of
the capacitor, d the separation of the plates, and x the length of the dielectric material
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already inside the capacitor while it is being pulled in. The following relations are useful
for the force estimate:

U = ½ CV2 (C=capacitance, V=voltage, U=electric potential energy)

Q = CV

C = kε0A/d (ε0 =permitivity of vacuum, A=LW area of capacitor plate)
(Q=charge)
(4)
(5)
(6)
From the above equations, one can write an expression for the capacitance as:
Q/V = C = ε0[(L-x)W]/d + kε0(xW)/d
The first part of the expression is the capacitance of the section without the
dielectric material in between, and the second part the section with the dielectric material.
Replacing this expression into equation (4):
U = ½ V2 ε0W(L – x + kx)/d
By definition, the force experienced by the dielectric material is the rate at which
the electric potential energy, U, changes with respect to the distance traveled, x.

F = -dU/dx = -½ V2 ε0W(k - 1)/d
(7)
For a typical bead under the influence of a focused laser beam, the size of both W
and d is about 1 micron, and the dielectric constant of the material is k=2, which leaves:
F (magnitude) = ½ V2ε0
One can relate the voltage across the capacitor to the electric field, and the electric
field can be related to the intensity of light.

I = ½ n2ε0E2c (n=index of refraction, c=speed of light, E=electric field)
(8)
Given that the intensity of the light is equal to the power of the laser used (about
1mW) divided by the area at which is it shone (the size of the bead), one gets that:
I = 1mW/ 1μm2 = 109 W/m2 , substituting in equation (8), the electric field is:
E = [(109 W/m2 )/ (ε0c) ]1/2 = 6*105 V/m, therefore, the voltage is approximately:
V = (6*105 V/m)(1*10-6m) = 0.6 V
Substituting the voltage in eq.(7), one gets a force of about 1.6 piconewtons per
milliwatt of laser power. This value closely agrees with the ray-optics estimate.
3) Lasers and Beads:
Choosing the right frequency for the trapping laser and correct dielectric material
for the micron-size sphere is essential to achieve the desired forces and experimental
results. For both biological specimens and for dielectric materials like silica and
polystyrene, light in the visible range causes photodecomposition and heating. An
interesting effect of visible light in the above dielectric materials, both semiconductors, is
photoconductivity. The material’s conductivity increases sharply when photons in the
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visible range are absorbed, and this effect reduces the gradient force (less light is
transmitted) and boosts light scattering. One can explain this phenomenon using the
concept of energy bands. The energy gap, EG, between the valence band and the
conduction band in a semiconductor is usually in the order of 2eV (Moses). To overcome
the energy gap, an electron absorbs a photon and then jumps up to the conduction band
(=hc/EG). Photons carrying the minimum energy for this jump happen to have
wavelengths usually in the 1m order. This means that photons in the visible light part of
the spectrum can excite electrons into the conduction band, and boost the conductivity.
In the opposite case, light in the infrared part of the spectrum causes vibration and
stretching of water molecules and common chromophores like Hb and HbO2. The
wavelength at which maximum transmission (minimum absorption) appears happens to
be around 1050nm (Block). Nonetheless, scientists in the field have found that long-term
exposure to this wavelength range produces photodynamic damage to cells, probably due
to the optical pumping of singlet molecular oxygen.
Lasers in the near infrared range described above are easily found in the market;
their power, which is a major factor that increases trapping force, can be found in the
range of 0.2W to about 4W.
From the above frequency range, one can find the width of the diffraction pattern
peak, which determines the area at which the laser is shone. This determines whether our
electromagnetic estimate for the intensity is correct. Taking typical values for the
diameter of the microscope objective lens, d=10mm, distance from lens to trap, L=5mm,
and wavelength, λ=1000nm, one finds that the width, W, of the intensity peak is:

W
~ (λ/d)L = (1000nm/10mm)(5mm) = 0.5μm. (9) (Agrees with E-M estimate)
Although some biological macromolecules can be caught with laser tweezers,
most are not refractile enough to be trapped with sufficient force. Therefore the dielectric
material used for beads play an important role in optical trapping. As mentioned before,
the best index of refraction predicted theoretically is n=1.69, which makes polystyrene
(n=1.59) a better trapping material than silica (1.47). Indexes of refraction above n=1.69
result in a disproportionate increase in the scattering force (Ashkin).
The chemistry used at the bead surfaces is also important for attaching
biological material. Silica beads are quite useful because red blood cells bind
permanently to it. Also, bead manufacturers offer particles with a variety of chemistries,
including both polystyrene and silica beads coated with amine, bromomethyl, carboxyl,
chloromethyl, droxyl, hydroxyl, and sulfate groups that make possible protein binding.
Work is currently done to decrease the microroughness of beads, make their roundness
precise (or perhaps developing other geometries), and increase the chemistry variety, in
order to improve trapping force and feasibility of their use in the biological field.
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Materials and Laboratory Setup:
For our experiment, we use a conventional light microscope. With an oil
immersion objective lens with high numerical aperture (NA=1.25), and 100x
magnification, the red light laser is focused (visible light lasers are less expensive than
near infrared light lasers, and are easier to manipulate). The index of refraction of the
medium is 1.56. 2μm size dielectric beads (dielectric constant = 1.3) are used in the
experiments, and the medium is made of 1 part of water, and 4 parts of heavy water
(density fluid = 1.084 g/ml and viscosity fluid = 1.201 mPa*s at room temperature). In
order to maximize the trapping force, the back pupil of the objective is slightly overfilled;
this assures that the laser is focused tightly. The trap is moved by steering the laser beam
using a galvo mirror controlled by a joystick. The following single beam optical trap
setup is similar to the one used:
The lenses are separated by twice their focal length to form an intermediate image
plane. In our simple case, 450 dichroic mirrors guide the laser to the objective.
Movements in the galvo mirror generate, for small displacements, a corresponding
movement in the trap. The galvo mirror, controlled by a joystick, is also connected to a
signal generator which can make the mirror oscillate at a specific frequency. The dichroic
mirrors have defect-free surfaces with high reflectance and high damage threshold in
order to transmit as much laser power as possible.
The trap is imaged on a webcam, which can then be process through video
acquisition software and Matlab.
Force and Displacement Measurements:
Trapping theory is still undeveloped for it to predict exactly the forces involved in
catching dielectric beads. Therefore, direct measurement of forces constitutes an
important portion of the use of laser tweezers.
Once a dielectric bead is trapped in a laser beam, it behaves as a spring: the force
exerted on it is proportional to the distance it travels away from the center of the trap.
One assumes that the stiffness of the trap remains constant. The maximum distance that it
can move away from equilibrium point determines the force of escape of the bead, which
in turn is the maximum force that can be exerted on the bead by the beam.
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By symmetry, one can observe there is a different spring constant for the z-axis
(the vertical axis in the left side picture) than for the x and y-axis. In order to find the
spring constants of the trap, and calibrate the setup so that an observed distance precisely
corresponds to a particular force, one must first consider the following information.
The Reynolds number in this system is considerably small:

Re = (vLρ)/η = 10-5
(10)
Where v=average velocity (20μm/s), L=length of the object (1μm), ρ= density of
the medium (1g/cm3), and η=viscosity (10-2 g/cm*sec). In this case, where Re<<1, the
movement of the particles is friction-dominated and inertia is negligible. Therefore, by
applying a fluid with a known velocity, and using Stoke’s Law, one can find the applied
force. The distance the bead moves can be measured and, relating this to the applied
force, the spring constant can be found. Stoke’s law, for spherical objects is the
following: (Γ= drag coefficient)
F = Γv = (6πηr)v
(11)
A common calibration procedure consists of leaving the bead and chamber
stationary and applying a flow with increasing velocity until the bead just escapes. In our
approach, we will trap the bead and make it oscillate with specific amplitude, and observe
the frequency at which the bead escapes the trap. With the amplitude and frequency, we
can calculate the escape velocity, and therefore, the maximum force of the trap. The
equation of motion of the bead is, for one dimension:

F = mx” = -Γx’ - kx
(12)
As mentioned earlier, for low Reynolds number, Re<<1, then our system is
friction dominated, and the mx’’ term is negligible. Therefore, the maximum force that
the trap can exert is simply F = (6πηr)v (13)
The equation of motion described above, does not take into consideration the role
Brownian motion plays in this system. There is an extra term to the equation of motion
that is proportional to kBT, and is responsible for the random “jiggling” of the bead in the
trap. Taking into account this detail, we can make use of Brownian motion in order to
calibrate the trapping force. Considering that the bead has ½kBT of kinetic energy for
each degree of freedom, this can be equated to the potential energy of the spring-model
system to find the spring constant. In our case, we only measure the x and y
displacements.

½kr2= kBT  k= kBT/(x2+y2) = kBT/(xrms2 + yrms2) (14)
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This equation assumes that the spring constant is the same for both x and y
directions. Although the trap seems perfectly symmetrical, we might find that this may
not be the case in our system, and that kx and ky can be different.
To measure the displacements of the beads we use video microscopy. Although
the resolution is not perfect and the actual shape of the object cannot be determined
exactly, we measure displacements between the center of mass of different images.
Although we do not measure the z displacement of the bead, this can be done by
analyzing the diffraction pattern changes shown when moving vertically (Gelles).
Data and Analysis:
Static Measurements:
We processed the videos taken from several traps, and found the average
displacements from the center of mass in order to find the x-y plane spring constant. The
intensity of the laser was varied, in order to find a linear relationship predicted by theory
of laser power vs. spring constant. The power meter was calibrated so that a 1mW step in
the laser would measure a 0.1 step on the meter screen. The distance to unit scale ratio
was measured to be 19.25 units/μm. The following plots were obtained from the static
measurements:
1) Laser Power = 3.3mW
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2) Laser Power = 5.5mW
12
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2) Laser Power = 12mW
14
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From the x-y scatter plots, the covariance matrix was calculated in order to
determine how noncircular/elliptical and rotated the distribution of points is.
x2
xy
xy
y2
If the (xy) value in this matrix is significantly higher than the (x 2) and (y2) values,
then the distribution is elliptical or unaligned, and the (xy) values should be used for the
variance of x and y. In all of our traps, the distributions were not significantly elliptical,
and the x and y variance were used for calculating the spring constant of the trap. The
following is the covariance matrix for one of our trials, that of the 12mW laser:
0.4562
-0.0755
-0.0755
0.4005
The table below summarizes the x and y variances of the different traps, as well as
the corresponding spring constants:
Power
(mW)
3.3
5.5
12.0
Var(x)
2.1474
1.6786
0.4562
Var(x) (m2)
5.7949E-15
4.5300E-15
1.2311E-15
Var(y)
1.2363
0.2864
0.4005
Var(y) (m2)
KBT
3.3363E-15
7.7275E-16
1.0808E-15
4.1154E-21
4.1154E-21
4.1154E-21
k=
2kBT/(var(x) +
var(y)) (N/m)
9.0138E-07
1.5522E-06
3.5602E-06
k (pN/μm)
0.9014
1.5522
3.5602
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Spring Constant vs. Laser Power
Spring Constant (pN/um)
4.0000
3.5000
y = 0.2929x
R2 = 0.9975
3.0000
2.5000
2.0000
1.5000
1.0000
0.5000
0.0000
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Power (mW)
Escape Force Measurements:
For this experiment, the trap was manipulated so that it oscillated at a given
amplitude and frequency. The frequency was slowly increased, keeping the amplitude
constant, until the bead escaped the trap. The frequency at which the trap escaped was
recorded. This experiment was repeated at different laser powers in order to find a linear
relation between power and maximum trapping force. The following graphs correspond
to one of our trials, and following them is a table summarizing the results for all trials:
1) Sample Trial, Power = 1.9mW:
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Given, the screen scale to distance ratio found, the amplitude of oscillation (from
graphs), and the escape frequency, we can find the maximum force of the traps as a
function of power:
Laser Power
(mW)
1.9
3.0
5.5
11.0
Unit/um ratio
η (mN*s*m-2)
η (pN*s*μm-2)
r (μm)
Amplitude
(screen
units)
92.18
90.01
87.64
94.06
19.25
1.201
0.001201
1
Amplitude
(μm)
4.79
4.68
4.55
4.89
Escape
Frequency
(Hz)
0.80
1.85
3.50
6.00
Velocity= 2A*f
(μm/s)
7.66
17.30
31.87
58.63
Force =
6πrηv (pN)
0.173
0.392
0.721
1.327
Force (pN)
Laser power vs. Maximum Force
1.600
1.400
1.200
1.000
0.800
0.600
0.400
0.200
0.000
y = 0.1225x
2
R = 0.9911
0.0
2.0
4.0
6.0
Power (mW)
8.0
10.0
12.0
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Discussion:
After analyzing both sets of data above, we can immediately see experimentally
that the trap does behave very similarly to a spring model. Furthermore, we can observe
the linear relation between laser power and force that is predicted by trapping theory. The
spring model, however, is not precisely correct for an optical trap. This happens simply
because the potential well of the trap is not infinite, and the bead escapes the trap at a
finite distance from it. A more accurate model would be a piecewise function with part
being a parabola, and the other two parts being a constant potential after a specific
distance from the minimum of the parabola. Also, an upside-down Gaussian would work
better than an infinite potential.
On one hand, the static force measurements gave us a linear relation of power vs.
spring constant. However, we can see discrepancies between the k y and kx spring
constants. By just looking at the variances of x and y, we can see that k y is larger than kx.
This implies that either the laser front was not circular (maybe elliptical or even
asymmetrical), and therefore the trap should give these results, or that our data
distribution was rotated. From the correlation matrix we cannot assert with certainty that
the distribution was not rotated. Nonetheless, the data obtained did give us some useful
results, the most important of which was the relation of spring constant vs power:
approximately 0.293pN/μm per mW of power.
From the maximum force measurements, we observed that our trap gives
approximately 0.123 pN per mW of power. This value is considerably smaller than our
rough theoretical estimate in the introduction section, indicating that the trap could be
more efficient than it was in the experiment. The next step would be to quantify how
efficient the trap is, in terms of the geometrical, dimensionless Q factor of the trap. From
trapping theory we know that:
F = QnP/c
Where P is the laser power measured at the particle being trapped, n is the index
of refraction of the medium, c is the speed of light, and Q is a dimensionless constant that
indicates the fraction of power that actually exerts force. Having n=1.56, and F/P = 0.123
pN/mW, we obtain a Q factor of approximately 0.024. This value is roughly ten times
smaller than that of an optimal trap. Therefore, we should have had plenty of power loss
in our setup for this trap to be so inefficient. Part of the power loss is due to absorbance
by the mirrors, aberration by the lenses, geometrical roughness of the beads, and
imprecise alignment of the setup. Apart from the issues mentioned above that can be
corrected (until some extent), another way to improve the trap’s efficiency would be to
partially cover the center of the back pupil of the objective, so that the light that is
focused is only coming from large angles relative to the vertical. In this way we would
reduce the scattering forces and the gradient forces would become relatively higher.
Sources of Errors:
The data obtained in this experiment is not completely reliable. There are several
important factors that could make us obtain flawed data.
For instance, the laser power meter measurements were considerably unreliable.
We measured the power of the laser by reflecting it and directing it to the meter using a
cover glass. Depending on the exact position of the laser beam with respect to the area of
the meter, the reading could be very different. A slight movement of the laser from the
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center of the meter reduced the reading to less than one half the original values.
Furthermore, by just turning off the lights of the laboratory, the reading changed by a
small fraction as well. All this implies that our data could be based on wrong readings of
intensity. However, considering that the most valuable results of this experiment were
relative values (i.e. slopes of graphs) and not absolute values, this particular source of
error does not hurt our conclusions.
On the other hand, our maximum force measurements were indeed affected by
one of our assumptions. We assumed that the amplitude of oscillation did not change as
we varied the frequency, and we used the maximum displacement in our data sets as the
measure of amplitude. During the experiment, we observed that the amplitude of
oscillation decreased as the frequency increased. This observation can be explained by
either of the following particularities of the experiment: One is that the oscillation of the
laser did maintain the same amplitude, but the bead’s amplitude could not move as
quickly as the laser due to the drag force of the medium. In other words, by the time the
laser got to its amplitude and reversed its direction, the bead had not reached the laser’s
amplitude yet. A second possibility is that the signal generator used a triangle wave to
direct the oscillation, and therefore, as the frequency increased, the peak of the triangle
wave smoothened out. Both of these situations imply that the amplitude decreased as the
frequency increased.
Finally, our procedure for preparing our trapping samples was not consistent, and
could have been a source of error. Different samples had different amounts of fluid, and
the “tightness” with which we sealed the sample against the cover glass varied
considerably. This tightness variability could have allowed some of our sample beads to
move more freely than others, having as a result corrupted data.
Experiment Conclusions:
Although not exactly accurate, the experiment itself and the results obtained did
give us an insight of how optical traps work. Our results supported the theoretical
predictions of a linear relation between laser power and trapping force closely agreed
with theoretical predictions. In short, this simple experimental setup allowed us to
observe the ease with which we can use optical traps, and to think about the potential
applications laser tweezers can have in other fields.
Biological Applications:
Laser tweezers have had multiple applications in biology. The main area in which
they are applied seems to be that in which forces and elastic properties are studied. At the
University of California at Berkeley, optical traps have been used to study the physical
behavior of helical proteins, like DNA, and observe that, when stretched out, they behave
similar to a spring. Ashkin used laser tweezers to stretch cell membranes and study their
elasticity. Other scientists have used traps, in combination with ultraviolet lasers to cut
biological material and carry out microsurgery. Also, effort has been put in determining
the swimming force of different unicellular species, like E.coli and sperm cells. The
discovery of molecular rotary motors were possible because of the ability of laser
tweezers to trap these motors and see the circular patterns they created when put against a
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viscous screen. A great deal has been understood of the cell division process by using
laser tweezers to manipulate chromosomes. Current research is focused, for instance,
towards the study of motor enzymes like DNA polymerases, RNA polymerases, and
DNA helicases, which move along these strands; the forces these motors exert are
valuable information for understanding the decoding processes. Many other examples of
optical traps applications can be mentioned, but the list is endless.
All of the experiments above have been done in environments that mimic the real
living conditions of the specimens being dealt with. However, the need for experiments
in vivo using laser tweezers has become another main area of research. An interesting
example of these kinds of study is the research Michael Welte’s laboratory is doing at
Brandeis, with collaboration of Steven Gross’ lab at the University of California, Irvine.
These labs use laser tweezers to stop individual moving lipid vesicles and measure the
forces the motor proteins moving them can exert.
Molecular motors like kinesin and dyneins move within the cell from the center to
the peripherals, or vice-versa. They carry several types of cargo, some of which are lipid
vesicles. Their motion can be followed by video microscopy. These motor proteins walk
along microtubule polymer tracks and exert force while dragging the cargo. Gross and
Welte’s labs use laser tweezers to stop moving vesicles and quantify the forces exerted in
their locomotion.
These lipid vesicles happen to be slightly more refractile than water. Their index
of refraction is, on average, about 1.4, making them less trappable than silica beads, but
still refractile enough. Their homogeneity is not quite as good as that of silica or
polystyrene beads; the lipid droplets are not perfect spheres and have considerable
roughness at their surfaces, allowing much more photon scattering (thus decreasing the
trapping force) than regular beads. Even more so, the vesicles are not transparent, which
makes them even more reflective. The vesicles have periods of time in which they clear
up, but they are intermittent. The transmittance of lipids is similar to that of water at the
near infrared part of the spectrum. Because water is at a minimum absorbance point at the
near IR light range, then the lipid droplets should also transmit most of the light at this
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light range that is shone at them. The absorption coefficient for silica and polystyrene is
considerably low, and that of water at the near infrared is around 0.1 cm-1.
All of these characteristics lead to a decrease in the effectiveness of optical traps
for lipid vesicles. The forces exerted on the beads, given by F=QnP/c, are drastically
reduced relative to other beads.
For lipid droplets of about 1micron in diameter, a good estimate would be that
the dimensionless constant, Q, drops by a factor of 10. Ashkin found values of Qmax for
different types of beads, and measured some to be as high as 0.14 for polystyrene beads,
and as low as 0.005 for opaque macromolecules with index of refraction only slightly
above that of water. Therefore, assuming Qdroplets = 0.01 would be a close approximation.
This implies that in order to achieve forces similar to those exerted with silica or
polystyrene beads, ten times more power should be used.
F/P = Qn/c = (0.01)(1.33)/(3*108 m/s) = 4.4*10-11 N/W = 0.044 pN/mW
Although lipid droplets require an incidence power of about 100mW in order
for manipulation to be possible, this is not a big limitation. As mentioned before, lasers in
the market can be found from a couple of hundred milliwatts, to about 4 Watts in power.
However, close attention should be put on the medium-term optical damages that may
appear with the exposure of high power lasers.
Final Remarks:
Laser tweezers will continue to impact biological research in the years to come.
The developments of new trapping geometries, as well as the arrival of low-cost lasers,
will make of optical traps even more powerful tools that they are today. It remains to the
ingeniousness and dedication of today’s scientists to find new ways of applying laser
tweezers while expanding the horizons of biological and biophysical knowledge.
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Bibliography
1) AFZAL, Robert S., and TREACY, Brian. Optical Tweezers using a Diode
Laser.
2) ASHKIN, A. Forces of a Single-Beam Gradient Laser Trap on a Dielectric
Sphere in the Ray Optics Regime.
3) BERG, Howard. Random Walks in Biology.
4) BLOCK, Steven M. Biological Applications of Optical Forces.
5) http://www.bio.brandeis.edu/faculty01/gelles.html (Gelles’ Lab)
6) http://www.bio.brandeis.edu/faculty01/welte.html (Welte’s Lab)
7) http://www.biophysics.org/education
8) www.physicsweb.org
9) MAHAMMAD LUTFUL, Arefin. Optical Tweezers.
10) MOSES, et al. Modern Physics.
11) ULANOWSKI, Zbigniew. Optical Tweezers – Principles and Applications.
12) WILLIAMS, Mark C. Optical Tweezers: Measuring Piconewton Forces.