Two-Photon Microscopy for Biomedical Studies Yassel Acosta University of Texas at El Paso, Yassel.Acosta@Gmail.Com

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Open Access Theses & Dissertations

2014-01-01 Two-Photon Microscopy For Biomedical Studies Yassel Acosta University of Texas at El Paso, [email protected]

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This is brought to you for free and open access by DigitalCommons@UTEP. It has been accepted for inclusion in Open Access Theses & Dissertations by an authorized administrator of DigitalCommons@UTEP. For more information, please contact [email protected]. TWO-PHOTON MICROSCOPY FOR BIOMEDICAL STUDIES

YASSEL ACOSTA Department of Physics

APPROVED:

Chunqiang Li, Ph.D., Chair

Vivian Incera, Ph.D.

Kyung-An Han, Ph.D.

Bess Sirmon-Taylor, Ph.D. Interim Dean of the Graduate School

by Yassel Acosta 2014

TWO PHOTON MICROSCOPY FOR BIOMEDICAL STUDIES

YASSEL ACOSTA, B.S. Electronic Engineering

THESIS

Presented to the Faculty of the Graduate School of The University of Texas at El Paso in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

Department of Physics

THE UNIVERSITY OF TEXAS AT EL PASO August 2014

Table of Contents

Table of Contents ...... iv

List of Tables ...... vi

List of Figures ...... vii

Chapter 1: Two-Photon Microscopy ...... 1 1.1 Theory of Two-Photon Absorption ...... 1 1.2 Two-Photon Fluorescence Intensity ...... 8 1.3 Axial Resolution in Two-Photon Microscopy ...... 9 1.4 Scattering and Absorption...... 11 1.5 Two-Photon Laser-Scanning Fluorescence Microscope ...... 13

Chapter 2: Fluorescence Resonance Energy Transfer ...... 22

2.1 The Rate of Energy Transfer ...... 22 2.2 The efficiency of Energy Transfer ...... 24 2.3 Semi-classical Derivation of FRET ...... 25 2.4 Orientation Factor ...... 31 2.5 The Fӧster distance and The Overlap Integral ...... 33 2.6 Measuring FRET ...... 35

Chapter 3: Two-Photon FRET Microscopy to Quantify Mycobacterium Phagosomal Rupture in Macrophages ...... 38 3.1 Background Knowledge...... 38 3.2 Mechanism for Tracking Phagosomal Rupture ...... 39 3.3 Experimental Procedure ...... 40 3.4 Results ...... 43 3.5 Conclusions ...... 46

Chapter 4: Functional Imaging of Drosophila Brain Using Two-Photon Microscopy ...... 47 4.1 Visualization of dopaminergic neurons in the protocerebrum ...... 47 4.2 Functional imaging using the fluorescent calcium reporter GCaMP5G ...... 49 4.3 Imaging Drosophila cerebral trachea with two-photon fluorescence microscopy....52 4.4 Conclusions ...... 57

iv Bibliography ...... 58

Vita…...... 59

v List of Tables

Table 1.1: Transverse and axial resolution calculated based on the PSF ...... 10 Table 1.2: Lines per image corresponding to each frame rate...... 16 Table 1.3: Configuration of the control inputs A, B, C, D, E and F for each frame rate...... 18 Table 4.1 Comparison of tracheal volume for the structures shown in figure 4.8 (c and d)...... 57

vi List of Figures

Figure 1.1: Process of one-photon absorption described by Eq. 1.13...... 4 Figure 1.2: Convention followed for labeling the various levels for two-photon absorption...... 5 Figure 1.3: Approximation of from Eq. (1.20) as a Dirac delta function...... 6 Figure 1.4: Fluorescence intensity generated at each z-plane as a function of the distance from the focal plane...... 11 Figure 1.5: Schematic of the Two-Photon Laser Scanning Fluorescence Microscope developed in the Biophotonics Laboratory of the Physics Department at UTEP...... 13 Figure 1.6: Schematic of the synchronization electronic circuit...... 17 Figure 2.1: Diagram describing the decay process in terms of the rates...... 23 Figure 2.2: Diagram describing FRET and showing decaying and transfer rates...... 24 Figure 2.3: Plot of equation (2.9) ...... 25 Figure 2.4: Dipole moments in a Cartesian coordinate system...... 29 Figure 2.5: Four possible relative orientations between D and A...... 32 Figure 2.6: Representation of the overlap integral ...... 34 Figure 3.1: Stages of Mtb infection...... 39 Figure 3.2: Fluorescence Emission Spectra of CCF4 (two-photon excitation at 700 ) ...... 41 Figure 3.3: Mechanism for tracking phagosomal rupture...... 41 Figure 3.4: Images acquired after 48 and 96 hours of infection...... 44 Figure 3.5: Comparison at 48 and 96 hours...... 45 Figure 3.6: Comparison with Ms after 96 hours...... 45 Figure 4.1: TH-GAL4 expressing neurons in the Drosophila brain...... 48 Figure 4.2: Maximum intensity projections of two Drosophila brains generated with Imajej. .... 49 Figure 4.3: GCaMP5G fluorescent spectra...... 50 Figure 4.4: Three-dimensional reconstructions of two adult brains expressing calcium sensor GFP...... 52 Figure 4.5: Three-dimensional reconstructions of one adult brain (a, b, c) and one third instar larvae brain (d,e,f) autofluorescence upon excitation with 710 ...... 53 Figure 4.6: Maximum intensity projections of tracheal branches in two different brains showing correlation between GFP expression and autofluorescence...... 54 Figure 4.7: Treshholded images using Imagej...... 55 Figure 4.8: Three-dimensional reconstruction of the ROI...... 56

vii Chapter 1: Two-Photon Microscopy

1.1 THEORY OF TWO-PHOTON ABSORPTION

The simultaneous absorption of two photons by an atom was first predicted by Maria Gӧppert-Mayer in 1931. The probability for such quantum event is proportional to the square of the excitation intensity and to the molecular cross section. In order to calculate this probability the laws of quantum mechanics must be taken into consideration, more specifically, time- dependent perturbation theory should be applied to the interaction of atomic electrons with a classical radiation field.

To begin we write the Hamiltonian ̂ of the system as the sum of the unperturbed

Hamiltonian ̂ and the interaction energy with the applied optical field ̂( )

̂ ̂ ̂( ). (1.1) The interaction energy can be defined as

̂( ) ̂ ̃( ), (1.2) where ̂ ̂. The field is considered as a monochromatic wave of the form

̃( ) (1.3) that is turned on at .

Assuming that the wavefunctions ( ⃗ ) associated with the energy eigenstates ( ⃗) for the unperturbed system are known, it can be represented by,

( ⃗ ) ( ⃗) , where . (1.4)

Also, ( ⃗) satisfies the eigenvalue equation

̂ ( ⃗) ( ⃗). (1.5) The general problem is to solve the time-dependent Schrӧdinger equation in the presence of a time-dependent interaction potential ̂( ) ( ⃗ ) ( ̂ ̂( )) ( ⃗ ). (1.6)

The solution to this equation can be expressed as a linear combination of the energy eigenstates given that they form a complete set

( ⃗ ) ∑ ( ) ( ⃗) . (1.7) Substituting Eq. (1.7) into Eq. (1.6)

∑ ( ⃗) ∑ ( ) ( ) ( ⃗) ∑ ( ) ( ⃗)

∑ ( ) ̂ ( ⃗) .

Since , the expression can be simplified as

∑ ( ⃗) ∑( ) ( ) ( ⃗)

∑ ( ) ( ⃗) ∑ ( ) ̂ ( ⃗)

∑ ( ⃗) ∑ ( ) ̂ ( ⃗) .

Making use of the orthonormality condition we can simplify it even further

∫ ( ⃗) ( ⃗)

∑ {∫ ( ⃗) ( ⃗) } ∑ ( ) {∫ ( ⃗) ̂ ( ⃗) }

∑ ( )

( ) ∑ ( ) ( )

( ) ∑ ( ) , (1.8)

where ∫ ( ⃗) ̂ ( ⃗) are the matrix elements of the interaction Hamiltonian ̂( ) and . In order to solve Eq. (1.8) we must use perturbation techniques. Using and expansion parameter which varies continuously between zero and one we obtain the following expansion for ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) . (1.9)

Using Eq. (1.9) on both sides of Eq. (1.8), replacing by , and equating powers of we get the set of equations (1.10), ( )( ) ( )( ) ( )( )

( ) ( ) ( ) ( ) ∑ { ( ) ( ) ( ) }

2 ( )( ) ( )( ) ( )( )

( ) ( ) ( ) ∑ ( ) ( ) ∑ ( )

( ) ( ) ( ) ∑ ( )( )

( )( ) ( ) ∑ ( )( ) (1.10)

To describe linear absorption we set in Eq. (1.10) and assume that in the absence of an applied field the atom is in the ground state

( ) ( ) ( ) ( ) . We have that, ( )( ) ( ) ( )( ) ( ) ( )( ) (1.11)

where, using Eq. (1.2) and (1.3), can be represented as

( ). Equation (1.11) becomes, ( ) ( ) ( ) { }

( )( ) ( ) { ( ) ( ) }.

Integrating,

( ) ( ) ( ) ( ) ( ) ∫ { }

( ) ( ) ( ) ( ) [ ] [ ]. (1.12) ( ) ( )

If we restrict our attention to driving frequencies that are very close to the transition frequency , the first term in Eq. (1.12) dominates and we are left with

( ) ( ) ( ) [ ]. (1.13) ( ) Eq. (1.13) can become resonant for the process of one-photon absorption illustrated schematically in figure 1.1.

The process of two photon absorption can be described setting

Figure 1.1: Process of one-photon absorption described by Eq. 1.13.

( )( ) ( ) ∑ ( )( ) ( ) ∑ ( )( ) (1.14)

where can be expressed as follows:

( ) . (1.15) The term has been neglected since, as discussed before, it will not produce terms

( ) in ( ) related to the absorption of a photon. Substituting Eq. (1.13) and (1.15) into (1.14):

( ) ( ) ( ) ∑ { [ ( ) ]} { } ( )

( ) ( ) ( ) ∑ { [ ( ) ]} ( ) ( )

( ) ( ) ( ) ∑ [ ( ) ( ) ] ( )

( )( ) ( ) ( ) ( ) ∑ [ ]. ( ) The second term in square brackets does not lead to two-photon absorption, so it can be dropped, ( )( ) ( ) ( ) ∑ [ ]. ( ) Integrating,

( )( ) ( ) ∑ [∫ ( ) ] ( )

4 ( ) ( ) ( ) ∑ [ ]. (1.16) ( ) ( ) The process of two photon absorption is represented in figure 1.2.

푛

휔 푚

휔

푔

Figure 1.2: Convention followed for labeling the various levels for two-photon absorption.

( ) ( ) Since ( ) is a probability amplitude, the probability ( ) that the atom is in state at time is given by

( ) ( ) ( ) ( ) | ( )| |∑ | | | . (1.17) ( ) ( ) The numerator of the second term can be transformed as

| ( ) | ( ( ) )( ( ) )

| ( ) | ( ) ( )

| ( ) |

( ) ( )

( ) | | ( ( ) ) ( ) | ( ) | [ ]. (1.18)

Rewriting Eq. (1.17),

( ) ( ) |∑ | ( ) (1.17.1) ( ) where ( ) [ ]

( ) . (1.19) ( )

Figure 1.3: Approximation of ( ) from Eq. (1.20) as a Dirac delta function.

In order to have a better understanding of Eq. (1.19) we can do the following substitution ( )

so that, [ ] ( ) . (1.20) ( ) From the graph of ( ) in figure 1.3 we can see that the peak value is reached when

and that the width of the central peak is of the order of ; the area can be approximated as

For large , ( ) becomes highly peaked and it can written in terms of a Dirac delta function

6 ( ) ( ). So, Eq. (1.17.1) can be written as

( ) ( ) |∑ | ( ). (1.17.2) ( )

If we assume that the state is spread into a density of final states ( ), defined such that ( ) is the probability that the transition frequency lies between and

( ) . The probability ( ) must be averaged over all possible values of the transition frequency

( )( ) |∑ | ∫ ( ) ( ) ( )

( ) ( ) |∑ | ( ). ( ) For convenience, this result can be written in terms of a two-photon cross section in the following form,

( ) ( ) ( ) ( ) (1.21)

where | | is the intensity of the incident light beam and

( ) ( ) |∑ | ( ) (1.22) ( ) ( ) From Eq. (1.21) it can be seen one of the main features of the process we have been describing, the probability of a two-photon absorption event depends on the square of the excitation intensity. As we will discuss later, the non-linearity of two-photon absorption has important consequences for optical sectioning.

A typical order of magnitude for the cross section defined in Eq. (1.22) is which is defined as 1 Gӧppert-Mayer (GM). The molecular cross section has been measured for the most common fluorescent molecules in a wide range of wavelengths. As we can see from Eq.

(1.22) a fluorophore should have a cross section local maximum corresponding to double the wavelength used for single photon excitation. However, this rule is only applicable for very symmetric molecules; there are more complex structures like some green fluorescent protein (GFP).

7 In order to compensate for this small cross section, high photon flux densities from the radiation source are required at the focal volume. This can be achieved by a tight focusing of the excitation beam coming from a high power continuous wave laser but the thermal effect on the sample would be significant. The best way to avoid this problem is by using a short-pulsed laser and to combine the spatial and the temporal focusing of the excitation beam. Short pulses allow to reduce the average power delivered, thus decreasing the damage on the sample caused by the incident light.

1.2 TWO-PHOTON FLUORESCENCE INTENSITY

The two-photon fluorescence intensity ( ) is proportional to the square of the excitation ( ) intensity ( ), to the molecular cross section, , and to the quantum yield : ( ) ( ) ( ) (1.23) The relation between the excitation intensity ( ) and the instantaneous power ( ) delivered at the illumination area is ( ) ( ) (1.24)

where [ ] , is the wavelength of the excitation radiation, NA is the numerical aperture of the objective lens, is the speed of light in the vacuum and is the Planck’s constant.

Substituting Eq. (1.24) and using as the proportionality constant, the Eq. (1.23) reads as,

( ) ( ) ( ) [ ]

When a pulsed laser is used, the time averaged two-photon fluorescence intensity ( ) can be expressed in terms of the peak laser power ( ) in the following way,

( ) 〈 〉 [ ] ∫ ( )

Considering the relation between the peak laser power and the average laser power ,

( )

8 where is the pulse width and is the pulse repetition rate, the expression for the two-photon fluorescence intensity ( ) can be rewritten in terms of the average laser power ,

〈 〉 ( ) [ ] ∫ ( ) [ ]

1.3 AXIAL RESOLUTION IN TWO-PHOTON MICROSCOPY

A remarkable consequence of the dependence of two-photon absorption on the square of the excitation intensity is the optical sectioning capability. The excitation volume is confined within a subfemtoliter which allows the imaging of consecutive planes separated by a fraction of a micrometer. The collection of these images is commonly regarded as “z-stacks” due to the fact that they are taken from parallel planes across the axial direction while the x-y coordinates are fixed. The acquisition of fluorescence from neighbor planes serves to construct three dimensional images of the sample under observation, which has important applications in biological research. In the literature, the sectioning capability of two-photon microscopy is commonly presented as a comparison with conventional single photon microscopy. I will follow the same approach given that it provides a better understanding of this important feature. The point spread function (PSF) supply information about the distribution of intensity of a point source at the focal region in the axial and radial coordinates. Under the paraxial approximation, it is defined for single photon and two-photon microscopes as

( ) ( )

( ) ( ) where the quadratic dependence of two-photon has become evident. The variables and are the radial and axial optical coordinates which are related to the real coordinates by

( )

9 where is the numerical aperture of the objective. The function ( ) is defined under the same approximation by

( ) | ∫ ( ) |

The resolution of an optical system in the transverse and axial directions can be measured in terms of the half-width of the PSF. These values have been calculated for conventional one- photon and two-photon fluorescence microscopes and they are shown in table 1.1.

Table 1.1: Transverse and axial resolution calculated based on the PSF

Half-width of PSF Conventional one-photon Conventional two-photon

1.17 2.34

5.56 8.02

The sectioning capability of two-photon does not clearly stand up from these values due to the fact that the PSF involves only a point source. In order to demonstrate this property it is necessary to calculate the three dimensional optical transfer function (OTF) to describe the image formation. This is done by means of the Fourier transform of the PSF. Since we are interested in the axial image of a planar fluorescent layer, the transverse coordinate in the OTF is set to zero and the inverse Fourier transform of this axial cross-section is calculated to obtain the intensity as a function of at the focal plane. This is plotted in figure 1.4 and normalized to unity for one-photon (dark curve) and two-photon (light curve) microscopes. From the graph it can be seen that the intensity for two-photon drops fast as the distance from the focal plane increases, while in the case of single photon equal fluorescence intensity is observed in all planes and there is no optical sectioning.

Figure 1.4: Fluorescence intensity generated at each z-plane as a function of the distance from the focal plane.

1.4 SCATTERING AND ABSORPTION

In two-photon fluorescence microscopy, near-infrared (NIR) light is used to create excited states with photons of half the nominal excitation energy. An advantage of using this portion of the spectrum for excitation is that NIR light can penetrate more deeply into tissue than the corresponding one-photon excitation wavelength. The reason for this is that tissue adsorption and scattering are substantially reduced in this spectral region. When light is transmitted into tissue it is either scattered or absorbed. It has been shown experimentally that the penetration depth increases with wavelength. The main NIR absorbers in biological tissues are water and hemoglobin. The absorption takes place when the energy of the incident photon is equivalent to the energy difference between two allowed electronic states. The energy absorbed is lost by the emission of a less energetic photon or by vibrations and rotations within the molecule. As a result the photon propagation is terminated. In a homogeneous absorbing medium, the Beer-Lambert extinction law relates the absorption of light to the properties of the material through which the light is traveling

where is the intensity at a depth , is the intensity of the incident light and is a constant known as the absorption coefficient. In the NIR spectral region scattering is generally much more important than absorption. This phenomenon arises from variations in the refractive index of the constituent parts of the tissue. Two types of scattering can be distinguished in biological tissues. The first one is Rayleigh scattering which is produced by small particles like organelles, mitochondria and large proteins with diameters much smaller than the wavelength of the light. This is an elastic process where only the trajectory of the photons is changed. The other type is known as Mie scattering and it is produced by large particles with diameters much greater than the wavelength of light such as cells. In this case light is scattered in a highly anisotropic manner with most of the light scattered in the forward direction. Due to the fact that biological tissues are a mixture of small and large particles, an approximation can be made considering scattering inversely proportional to wavelength.

The scattering coefficient for a scattering medium consisting of one type of particle with number density which is the number of particles per unit volume, is given by

where is the total scattering cross section of a particle, in other words, the effective area presented to the incident light.

12 1.5 TWO-PHOTON LASER-SCANNING FLUORESCENCE MICROSCOPE

Figure 1.5: Schematic of the Two-Photon Laser Scanning Fluorescence Microscope developed in the Biophotonics Laboratory of the Physics Department at UTEP.

13 1.5.1 Light Source

The microscope developed in our lab is based on a femtosecond titanium-sapphire

(Ti:Sapphire) laser source. This system provides pulses with duration on the order of 100 with a repetition rate of 80 . It delivers peak powers of over 300 while the average power can reach above 2.5 . This laser also possesses a wide tuning range from 690 to 1040 allowing selective excitation of a wide variety of fluorophores. The most abundantly used fluorophores have single photon excitation wavelength ranging from 350 to 690 . Considering that for two-photon absorption the excitation wavelength can be approximated as twice the wavelength used for single photon, we are transported to the near-infrared region of the spectrum. Another important characteristic of the range of wavelengths provided by our laser source is that the absorption coefficients of most biological specimens are minimized in this range. In other words, the fact that there is low absorption and scattering in this wavelength range accounts for greater penetration depth in biological samples.

1.5.2 Waveplate and Polarizer

The light coming out of our laser source is linearly polarized in the horizontal direction.

Right after the source there is a half waveplate attached to a rotary mounting that allows us to shift the polarization direction by rotating the fast and slow axis of the waveplate. A typical half waveplate introduces a phase shift of between the polarization components. For linearly polarized light this translates into a rotation of , where is defined as the angle formed by the polarization vector and the fast axis of the waveplate. Following the half waveplate there is a linear polarizer that splits the beam into two parts with different linear polarization. This type of polarizer is more suitable for use with our femtosecond laser since it does not need to absorb the high intensity light; instead it allows a particular polarization direction to go through parallel to the direction of the beam while all other polarization directions are deflected perpendicular to the beam path.

14 We use this combination of waveplate and polarizer to effectively control the average power of our laser beam. Usually, the polarizer is kept in a fixed position while the wave plate is rotated to obtain the desired average power. This can be easily understood from Malus’ law which describes the intensity of a beam when a perfect polarizer is placed in its path and is given by

( ) where and are the intensities of the laser beam before and after the polarizer and is the angle formed between the polarization vector coming out of the waveplate and the axis of the polarizer. In an ideal situation the full intensity is transmitted when while the light beam is blocked if .

1.5.3 Scanning Platform

The scanning mechanism and its timing circuitry form an essential part of our two-photon system. It provides the fast scanning capability necessary to image dynamic cellular processes and makes it suitable for live animal studies. Currently it is possible to image a full frame of

320 by 320 at a rate of 30 frames per second. Additionally, an electronic circuit allows tuning the frame rate to 60 and 120 frames per second, which can be used to image even faster processes. The field of view is decreased in the vertical direction by one half of its full frame dimension in the case of 60 frames per second and by one fourth for 120 frames per second. The scanning platform is composed of a galvanometer mounted mirror and a spinning polygonal mirror to produce a unidirectional raster scan pattern. The galvanometer mounted mirror scans the vertical direction or axis while the horizontal direction or axis is scanned by the spinning polygonal mirror. The later consists of a disk with 36 facets equally distributed along the edge; its constant rotational speed is 480 revolutions per second. Each facet corresponds to a line in the image parallel to the axis. It is straight forward to calculate the line

15 scanning rate for the polygonal mirror, which is fixed to 17280 . Table 1.2 summarizes the amount of lines per image calculated for each frame rate.

Table 1.2: Lines per image corresponding to each frame rate.

Frame Rate ( ) Lines per Image

30 576

60 288

120 144

The fact that the number of lines per images are integer multiple of the number of facets (36) guarantees that the same facet scans the same line on every successive frame avoiding vertical scrolling effects. Unlike the polygonal mirror, whose scanning rate is fixed, the galvanometer-mounted mirror can be scanned in the vertical dimension at 30, 60 or 120 , therefore setting the scanning rate of the microscope. In order to synchronize the galvanometer and polygonal mirrors a bicell photodiode is used to count the number of facets (lines) and generate an electronic signal that is used by the circuitry to drive the galvanometer at a specific frequency. The photodiode is able to generate the synchronization signal by means of a 650 laser diode that shines on the polygonal scanner in a way that its reflection scans across the bicell photodiode.

1.5.4 Synchronization Electronic Circuit

As it was described in the previous section the electronic circuit is vital to synchronize the polygonal mirror and the galvanometer mounted mirror. Figure 1.6 shows a diagram of the electronic design used in our microscope. The signal generated by the photodiode is differentially amplified (Analog Device:AD811) before being converted to TTL levels by Schmitt-triggered NOT gates (74ACT14). Each TTL pulse corresponds to a fixed position within

Figure 1.6: Schematic of the synchronization electronic circuit. a horizontal line and it is designated as HSYNC. This signal is transmitted to the frame grabber and therefore it is used as a master synchronization signal. Every HSYNC pulse increments a 12-bit binary counter (74HC4040). Table XX shows the number of lines (HSYNC pulses) that corresponds to each frame rate. Depending on which frame rate has been selected, the 12-bit binary counter should reinitiate the count every time the maximum number of lines per frame has been reached. In order to do that two multiplexers (SN74ALS151N) are employed; these data selectors provide full binary decoding to select one- of-eight data sources. For each multiplexer the data selection is achieve by means of three control inputs that are connected to external switches; they can be arranged in eight different combinations between low and high levels and therefore forward only one of the eight inputs into a single output line. The purpose of having two multiplexers is that one of them selects the

17 more significant bit (MSB) while the other one picks the less significant bit (LSB). The MSB multiplexer receives as input lines 3 to 10 while the LSB multiplexer takes as input lines 1 to 8. Table 1.3 shows the different configurations of the control inputs for each frame rate.

Table 1.3: Configuration of the control inputs A, B, C, D, E and F for each frame rate.

Frame Lines Lines MSB Multiplexer LSB Multiplexer Rate (Decimal base) (Binary base) A B C D E F 30 576 1001000000 H H H H H L 60 288 100100000 H H L H H L 120 144 10010000 H H L H L H The output of each multiplexer is connected to the inputs of a NAND gate. Every time the NAND gate has both inputs on high level its output will go low, therefore activating the output of a monostable timer (555). The pulse signal generated by the 555 circuit will register an event every time a frame has been completely scanned and it is designated as VSYNC. Simultaneously, the low output of the first NAND gate is connected to both inputs of a second NAND gate which purpose is to reset the 12-bit counter and initiate a new frame. The counter binary value is directly converted to a proportional voltage by a digital to analog chip (Analog device: AD7392). The output of this chip is a periodic linear voltage ramp that drives the galvanometer mounted mirror (vertical axis).

1.5.5 Dichroic Mirrors and Filters

A dichroic mirror can be used to separate laser beams with different wavelengths. They have the property of transmitting a certain range of wavelengths while reflecting others. As we can see in figure 1.5, our microscope has three dichroic mirrors labeled as a, b and c. The dichroic mirrors in our set up are positioned in a way that the angle formed between the incident light and the mirror is close to 45 degrees. Dichroic a transmits all the wavelengths above 660 while reflecting wavelengths below it. This allows that the excitation light reaches the objective lens while the fluorescence emitted by the sample is reflected in a perpendicular direction to the initial beam path. The next two dichroic, b and c, separate the fluorescent signal, redirecting specific ranges of wavelengths to each detector (PMT). For example, dichroic b

18 reflects wavelengths below 495 , allowing the blue range of wavelengths to reach the PMT designated for the blue channel. The transmitted fluorescence continues a straight path until it reaches the dichroic c, where it is separated one more time; wavelengths below 580 , containing the green portion of the spectrum, are reflected towards the green channel detector while the remaining fluorescent signal is transmitted towards the red channel detector. With the purpose of narrowing down the range of wavelengths and selectively detect fluorescence from the sample corresponding to the blue, green and red portions of the visible spectrum, there are a couple of band pass filters in front of each detector. They are represented in figure 1.5 and labeled as d, e and f.

1.5.6 Objective Lens

The selection of the objective lens depends on specific needs of a given experiment. In our laboratory we count with two Olympus objective lenses differing mainly in the numerical aperture (NA) and the working distance. The NA is a unitless number that characterizes the range of angles over which the objective lens can accept or emit light. It is defined as

where is the refractive index of the objective immersion liquid and is the half angle of the maximum cone of light that can enter or exit the lens. The working distance, on the other hand, is defined as the distance from the front lens element of the objective to the closest surface of the coverslip when the specimen is in sharp focus. As a general rule, the objective working distance decreases as the magnification and NA both increases. Our two objective lenses have a magnification factor of 60X and a NA of 1 and 1.2. The working distance specified by the manufacturer is XX ( ) and XX ( ). They are both water immersion objective lenses ( for pure water). The characteristics of the objective lens play an important role in determining the resolution of an imaging system. As it was explained before, optical sectioning is an intrinsic

19 property of a two-photon system, giving it the capability of 3D imaging. The lateral resolution of our microscope can be approximated using Abbe’s equation

where is the minimum distance between distinguishable objects in an image and is the wavelength of the light used for illuminating the sample. This formula has its origin in the diffraction of light and the finite aperture of the optical elements; it represents a limit for the resolution of an optical system.

One of the experiments performed in our laboratory involves imaging of dopaminergic neurons expressing a green fluorescent protein (GFP) in the fly brain which, depending on the age, may range from 100 to 200 microns. If we use our objective lens and an excitation wavelength of 920 , the lateral resolution of our microscope can be estimated as 0.46 . If we use our objective instead, for the same excitation wavelength the resolution turns out to be 0.38 . The choice of objective lens in this particular case depends on how deep we want to image inside the brain; even though the gives a better resolution, it has a shorter working distance than the objective which can cover more of the specimen.

1.5.7 Photomultiplier Tube (PMT)

The photomultiplier tubes are one of the critical components of our system. They possess a photosensitive surface that captures incident photons and generates electronic charges that are sensed and amplified. The output of a PMT is a current proportional to the number of photons striking the photosensitive surface. The quantum efficiency (QE) of these devices, which is the percentage of photons that are detected, is a function of the illumination wavelength and dependable on the chemical composition of the surface. The values for QE may range between 20% and 40%. PMTs are able to respond to changes in the input photon flux within a few nanoseconds which makes them suitable for detection and recordings of extremely fast events. The dynamic

20 range of these devices is also considerably wide yet the electrical output current accurately reflects the incident photon flux. The signal to noise (SN) ratio is another measurement that serves to describe the performance of electronic imaging sensors. In the case of PMTs the SN ratio is very high because the dark current, which arises in electronic devices in the absence of light, is considerably low. In our system, each PMT is coupled with a Hamamatsu C7950 socket which converts the small-current high-impedance output of the PMT into a low-impedance voltage output with a conversion factor of 0.3 . Additionally, each C7950 is connected to a +/-15 and a variable power supply (0 V to +3.6 V) for high voltage adjustments. The latter is used to manually control the gain of the amplification circuit inside each C7950. The large area of the photocathode or photosensitive surface is another advantage of PMTs because it allows efficient collection of fluorescence. In our set up this fluorescence comes from a point in the sample at a time and each PMT is able to handle a maximum count rate of about 1 .

1.5.8 3D Stage

As explained before, the combination of the polygonal mirror and mounted galvanometer mirror produces a two dimensional image at a given z-position. In order to create a three dimensional reconstruction of the sample it is necessary to obtain images at different points in the axial direction. Our 3D motorized stage (Shutter Instrument, model MP-285) provides this capability. It can travel one inch on all three axes and provides a low resolution of 0.2 and a high resolution of 0.04 . Typically in our lab a stack of images is taken with a separation of 1 between planes. In terms of speed the maximum value specified by the manufacturer for this stage is 2.9 which contributes to a small acquisition time.

21 Chapter 2: Fluorescence Resonance Energy Transfer

Fluorescence resonance energy transfer (FRET) is the physical mechanism describing the energy transferred from one chromophore, termed as the donor (D), to another chromophore, regarded as the acceptor (A), by means of intermolecular long-range dipole-dipole coupling. It falls within the category of long-range because the donor and acceptor are not in contact and the transfer can occurs over several molecular diameters (1 to 10 nm). The donor can be excited either by means of single-photon or multiphoton absorption; however, it does not emit a photon in return; instead there is a non-radiative transfer of energy to the acceptor. There are several important requirements to guarantee the efficiency of FRET. As mentioned before, the distance between D and A must be in the range of 1 to 10nm. Additionally, the emission spectrum of D should overlap with the absorption spectrum of A, the quantum yield of D should be sufficient (usually ) and the transition dipoles of D and A must be oriented favorably relative to each other.

2.1 THE RATE OF ENERGY TRANSFER

The rate constant of FRET between a particular D-A pair was described by Fӧster to be

( ) (2.1)

where is the fluorescence lifetime of the donor in the absence of acceptor; is the distance between D and A; and is a distance parameter known as “Fӧster distance” and it is calculated from the spectroscopic and mutual dipole orientation parameters of D and A when .

2.1.1 Fluorescence Life Time

The fluorescence lifetime measures the average time a molecule spends in the excited state prior to returning to the ground state (see figure 2.1). The former can be achieved either by emitting fluorescence or through other relaxation processes. The diagram in figure 2.1 shows the rate for the transition from to via fluorescence emission, Г, and all the other transitions that do not result in fluorescence emission are represented by the rate .

Figure 2.1: Diagram describing the decay process in terms of the rates.

For the system described in figure 2.1 the fluorescence lifetime is defined as

(2.2)

If a sample containing a large number of fluorophore molecules is excited at , an initial population will go into the state . The excited state population will decay according to the relation ( ) ( ) ( ) (2.3)

( ) being the number of excited molecules at a given time and ( ) . The fluorescence intensity ( ) is proportional to the number of molecules in the excited state ( ) so Eq. 2.3 can be written in terms of the intensity ( ) ( ) ( ) (2.4)

Solving Eq. 2.4,

( ) ( ) (2.5) where is the initial intensity. This expression serves to understand the physical meaning of the fluorescence lifetime . When , 63% of the molecules have decayed and 37% will decay after .

The natural fluorescence lifetime ( ) is obtained in the absence of non-radiative processes, ,

(2.6)

23 The fluorescence lifetimes are usually in the order of a few nanoseconds but they can be modified by several factors like interaction with the solvent, collisions with other molecules or ions, electron transfer or radiationless energy transfer to a suitable acceptor like in the case of FRET.

2.2 THE EFFICIENCY OF ENERGY TRANSFER

The efficiency of energy transfer is a quantitative measure of the number of photons absorbed by the donor that are transferred to the acceptor.

Figure 2.2: Diagram describing FRET and showing decaying and transfer rates.

According to figure 2.2, is the ratio of to the total decay rate of D

(2.7)

If we consider the fluorescence lifetime of D in the absence of A,

(2.8)

Substituting Eq. (2.1) we obtain

(2.9) ( )

From the plot of Eq. (2.9) in figure 2.3 it can be seen that changes dramatically in the range . The efficiency quickly increases to 1 when decreases below , however, when the distance between D and A is the efficiency decreases below 0.1.

Figure 2.3: Plot of equation (2.9)

2.3 SEMI-CLASSICAL DERIVATION OF FRET

The rate of energy transfer from D to A can be derived from a semi-classical stand point. First, we will assume that only the dipole that corresponds to the donor is oscillating. To obtain an expression for the electric field ⃗⃗ we start from Maxwell’s equation ⃗ ⃗⃗ (2.10)

In order to obtain ⃗⃗ we need to find the scalar potential and the vector potential ⃗. The former can be expressed in the Lorentz gauge as ⃗( ⃗ ) | ⃗ ⃗ | ⃗( ⃗⃗⃗⃗ ) ∫ ∫ ( ) (2.11) | ⃗ ⃗ | where the current density is assumed to have a sinusoidal time dependence

⃗( ⃗ ) ⃗( ⃗) (2.12) The Dirac delta function can help us to express the vector potential in a more convenient fashion

⃗( ⃗ ) | ⃗ ⃗ | ⃗( ⃗⃗⃗⃗ ) ∫ ∫ ( ) | ⃗ ⃗ | | ⃗ ⃗ | ⃗( ⃗ ) ( ) ⃗( ⃗⃗⃗⃗ ) ∫ | ⃗ ⃗ | ⃗ | ⃗ ⃗ | ( ⃗ ) ⃗( ⃗⃗⃗⃗ ) { ∫ } | ⃗ ⃗ |

| ⃗⃗⃗ ⃗⃗⃗ | ⃗( ⃗⃗⃗⃗ ) { ∫ ⃗( ⃗ ) } (2.13) | ⃗ ⃗ | where is the wave number. If the source of current is confined to a small region of order and we are interested in a region where , then we can approximate

| ⃗ ⃗ | therefore

⃗( ⃗⃗⃗⃗ ) { ∫ ⃗( ⃗ ) } (2.14)

The integral term can be transformed using integration by parts

⃗( ⃗ ) ⃗⃗ ⃗( ⃗ ) ⃗

∫ ⃗( ⃗ ) ⃗ ⃗( ⃗ ) ∫ ⃗ ( ⃗⃗ ⃗( ⃗ )) ∫ ⃗ ( ⃗⃗ ⃗( ⃗ )) and from the continuity equation

⃗⃗ ⃗

∫ ⃗( ⃗ ) ∫ ⃗ ( ⃗ ) ⃗ (2.15) where

⃗ ∫ ⃗ ( ⃗ ) (2.16) is the electric dipole moment. Finally, the vector potential takes the form

⃗( ⃗⃗⃗⃗ ) { ⃗ } (2.17)

To determine the scalar potential we proceed in a similar manner as we did for ⃗( ⃗⃗⃗⃗ ). The scalar potential can be obtained from

( ⃗ ) | ⃗ ⃗ | ( ⃗⃗⃗⃗ ) ∫ ∫ ( ) (2.18) | ⃗ ⃗ | and assuming that the charge distribution has a sinusoidal time dependence

( ⃗ ) ( ⃗) (2.19) Then, ( ) | | ⃗ ⃗ ⃗ ( ⃗⃗⃗⃗ ) ∫ ∫ ( ) | ⃗ ⃗ |

26 | ⃗ ⃗ | ( ) ( ⃗ ) ( ⃗⃗⃗⃗ ) ∫ | ⃗ ⃗ | | ⃗ ⃗ | ( ⃗ )

( ⃗⃗⃗⃗ ) { ∫ } | ⃗ ⃗ | | ⃗⃗⃗ ⃗⃗⃗ |

( ⃗⃗⃗⃗ ) { ∫ ( ⃗ ) } (2.20) | ⃗ ⃗ | Here we will use the approximation

| ⃗ ⃗ | ̂ ⃗ And Eq. 2.20 can be written as ̂ ⃗

( ⃗⃗⃗⃗ ) { ∫ ( ⃗ ) } ̂ ⃗ ̂ ⃗

( ⃗⃗⃗⃗ ) { ∫ ( ⃗ ) } ̂ ⃗

̂ ⃗ ̂ ⃗ Expanding ̂ ⃗ and ̂ ⃗⃗⃗ we have

̂ ⃗ ( ⃗⃗⃗⃗ ) { ∫ ( ⃗ )( ̂ ⃗ ) ( ) }

̂ ⃗ | ̂ ⃗ | ( ⃗⃗⃗⃗ ) { ∫ ( ⃗ ) ( ̂ ⃗ ) }

Keeping only the electric dipole terms, ̂ ⃗ ( ⃗⃗⃗⃗ ) { ∫ ( ⃗ ) ( ̂ ⃗ ) }

( ⃗⃗⃗⃗ ) { ̂ ∫ ( ⃗ ) ⃗ ( ) }

( ⃗⃗⃗⃗ ) { ̂ ⃗( )} (2.21)

Substituting Eq. (2.17) and (2.21) into Eq. (2.10) we can calculate the electric field of an oscillating dipole

⃗⃗ [{ ̂ ⃗( )} ] [{ ⃗ } ]

⃗⃗ { [ ( ̂ ⃗) ( ̂ ⃗)] ⃗ } (2.22)

( ) ( ) ( ) Using the identity ( ( ) ̂ ⃗) ⃗ ( ̂ ⃗) ̂ ( ) for both terms with a nabla operator in Eq. (2.22) we obtain

( ̂ ⃗) ⃗ ( ̂ ⃗) ̂ ( )

( ̂ ⃗) ⃗ ( ̂ ⃗) ̂ ( ) (2.23)

and

( ̂ ⃗) ⃗ ( ̂ ⃗) ̂ ( )

( ̂ ⃗) ⃗ ( ̂ ⃗) ̂ ( ) (2.24)

Substituting Eq. (2.23) and (2.24) back into Eq. (2.22) and rearranging terms

⃗⃗ { [ ⃗ ( ̂ ⃗) ̂ ( ) ( ⃗ ( ̂ ⃗) ̂ ( ))]

⃗ }

⃗⃗ { [ ⃗ ( ̂ ⃗) ̂ ( ) ( ⃗ ( ̂ ⃗) ̂ ( )) ⃗ ]}

⃗⃗ { [ ⃗ ( ̂ ⃗) ̂ ( ̂ ⃗) ̂ ⃗ ( ̂ ⃗) ̂ ( ̂ ⃗) ̂

⃗ ]}

⃗⃗ { [ ⃗ ( ̂ ⃗) ̂ ⃗ ( ̂ ⃗) ̂ ( ̂ ⃗) ̂ ⃗ ]}

⃗⃗ { [ ( ⃗ ( ̂ ⃗) ̂) ( ( ̂ ⃗) ̂ ⃗) ( ( ̂ ⃗) ⃗)]}

⃗⃗ { [ ( ̂ ⃗) ̂ ( ( ̂ ⃗) ̂ ⃗) ( )]} (2.25)

When or , the term containing ( ) dominates and it is the only one contributing to the radiation of the energy or far field. For the near field we have that or

and the term ( ) leads the expression; apart from its oscillations in time, it has the same form as the static dipole field ⃗⃗ [( ( ̂ ⃗) ̂ ⃗) ( )] (2.26)

Figure 2.4: Dipole moments in a Cartesian coordinate system.

From figure 2.4 we can see that ̂ is the unit vector in the direction of ⃗ and equivalent to the radial unit vector ̂. The z axis has been oriented in the same direction as the donor dipole moment ⃗ . We can rewrite the equation for the electric field of the donor ⃗⃗ in spherical coordinates replacing ̂ by ̂, calculating the dot product between ̂ and ⃗ noticing that the angle between them is and expressing ⃗ in terms of its components in the ̂ and ̂ directions;

⃗ , ̂ and ̂ are all in the same plane.

⃗⃗ [( ̂( ̂ ⃗ ) ⃗ ) ( )]

⃗⃗ ̂ [( ̂(| ⃗ | ) ̂| ⃗ | | ⃗ | ) ( )]

⃗⃗ ̂ [( ̂(| ⃗ | ) | ⃗ | ) ( )] (2.27)

If a second dipole ⃗ corresponding to the acceptor is in the near field of the donor, it is going to interact with the field we have just obtained. The interaction energy can be calculated as the dot product between ⃗⃗ and ⃗

29 | ⃗⃗ | ⃗

̂ [( ̂(| ⃗ | ) | ⃗ | ) ( )] ⃗

⃗⃗ | ⃗ | ̂ | | ⃗ ( ) [( ( ̂ ⃗ ) ( ⃗ ) )] (2.28)

Looking back at figure 2.4 we can see that ⃗ is not in the same plane as ⃗ , so we need to find first its projection onto the ̂, ̂ plane. The angle between ⃗ and ( ̂) is and the angle between the projection of ⃗ and ̂ is . | ⃗ || ⃗ | ⃗⃗ | | ⃗ ( ) [( )]

⃗⃗ | ⃗ || ⃗ | | | ⃗ ( ) (2.29)

where is an orientation parameter of the two dipoles interacting. At this point we can incorporate quantum mechanics to our derivation. In chapter the probability amplitude for linear absorption was found to be

( ) ( ) ( ) [ ] ( ) We can introduce some minor changes to adapt this probability amplitude to our current situation. First, the interaction energy should be replaced by and the frequency necessary to go from state to state is now the frequency to take the acceptor molecule to an excited state.

The probability amplitude for a transition from to takes the form ( ) ( ) ( ) [ ] (2.30) ( ) The transition probability can be obtained as

( ) ( ) | ( )| [ ] | | ( ) and, like before, we do the substitution ( ) | ( ) | [ ]

so that

30 ( ) [ ]

[ ] [ ] ( )

As we saw in chapter 1 the term inside square brackets can be approximated to a Dirac delta function for large

[ ] ( ) (2.31)

Since the probability for a transition from to increases linearly with time, the transition rate can be defined as

[ ] ( ) (2.32)

Substituting Eq. (2.29) into (2.32)

| ⃗ | | ⃗ | ( ) ( ) (2.33)

From this analysis we can imply several important characteristics of FRET. The transition rate dependence on ( ) arises because the energy transfer process occurs in the non- radiative near-field zone of the oscillating dipole D. Also, when we considered the interaction energy between A and the field generated by D, the orientation factor arised. The Dirac delta function in this expression serves to highlight the fact that FRET is a resonance process. The transition rate for A to be excited is zero unless the frequency of the field produced by D coincides with that of a transition from to . Basically, the energy lost by D is gained by A.

2.4 ORIENTATION FACTOR

In Eq. (2.29) we defined in terms of the sines and cosines of the angles , and . These angles are shown in figure 2.4 and they describe the orientation between the two dipoles D and A. Depending on the relative orientation of these two dipoles, can range from 0 to 4. Figure 2.5 shows four possible orientations with their respective values of .

Figure 2.5: Four possible relative orientations between D and A.

In a situation in which D has a unique static orientation (like in figures 2.4 and 2.5) and A is rapidly and randomly oriented we can expand the expression for

{ }

Since all possible orientations of A have equal probability, can be averaged over the rotational space of the acceptor; considering a sphere of radius 1

∫ ∫

〈 〉

∫ ∫

Substituting the expression for and performing the integration results in

〈 〉 { }

According to this expression there is a maximum for when and a

minimum when . The assumption of a randomly oriented A and a fixed D has

32 reduced the difference between the maximum and minimum values of from 3 for two fixed dipoles to 1.

As we can see the value of 〈 〉 depends on for a randomly oriented A. However, in many situations there is no sufficient information about the orientation of the dipoles and the calculations of FRET efficiency and distance estimates are greatly simplified if is assumed constant for all D-A pairs. In order to do this the expression for 〈 〉 is averaged over any specific distribution of angles and

∫ ∫ 〈 〉 〈 〉 〈 〉

∫ ∫

The integration leads to

〈 〉〈 〉

This approximation for the average value of is typically used for systems with fast rotational dynamics for D and A, where it is possible to expect full dipole randomization before the energy transfer occurs. However, it does not apply to systems where the mobility of donor and acceptor is significantly limited.

2.5 THE FӦSTER DISTANCE AND THE OVERLAP INTEGRAL

The Foster distance appeared for the first time in this chapter when the concept of energy transfer was introduced. Here it will be written in a different form that explicitly shows its relation with the emission and absorption spectra of the donor and acceptor molecules as well as the quantum yield of the donor.

From a classical point of view, can be viewed as the distance at which the rate of radiation of one dipole (donor) and the rate of absorbance of a second dipole (acceptor) are equal. When , Eq. (2.1) takes the form

which means that the rate of energy transfer is equivalent to the rate at wich the donor molecule would decay from excitation in the the absence of acceptor. Furthermore, from this it is

33 possible to conclude that at 50% of the donor energy is transferred to the acceptor while the other 50% is release through radiative and non-radiative processes.

The expression derived by Foster quantum mechanically for is

( ) ( ) ( ) [ ] (2.34)

where is Avogadro’s number, relates to the orientation factor introduced before, is the quantum yield of the donor, is the refractive index of the medium and ( ) is the overlap integral defined as

( ) ( ) ( ) (2.35) ∫ where ( ) is the normalized fluorescence intensity of the donor and ( ) is the extinction coefficient of the acceptor at . This integral expresses the extent of spectral overlap between the donor emission and the acceptor absorption (figure 2.6). The extinction coefficient ( ) is a measurement of how strongly the acceptor absorbs light and it can be considered an intrinsic property of the fluorophore. Fluorescence spectra ( ), on the other hand, are usually sensitive to the fluorophore environment; therefore the overlap integral depends on the medium in which the fluorophore is embedded.

As we can see in expression (2.34) the index of refraction appears as , which makes

any small change in have a big effect on the value of . The value of in biological tissue is typically from 1.33 to 1.6.

Figure 2.6: Representation of the overlap integral ( ).

34 2.5.1 Fluorescence Quantum Yield

The fluorescence quantum yield is defined as the number of emitted photons relative to the number of absorbed photons. Looking back at figure 2.1, where the depopulation of the excited state is performed by both, the emission rate and the non-radiative rate , we define the quantum yield as

(2.36)

If dominates over , the quantum yield will be close to unity. The quantum yield can also be strongly dependent on the surrounding environment of the fluorophore. However, because depends on the sixth root of , a small change in the quantum yield will not have a significant impact.

2.6 MEASURING FRET

Several approaches to determine the efficiency of FRET are based on steady-state spectra analysis. A common denominator in most steady state methods is that the absorption and emission spectrum of the donor and acceptor alone do not change in the energy transfer system.

The efficiency of energy transfer defined in section 2.2 can be determined experimentally from donor and acceptor steady-state spectra analysis. The fluorescence of donor and acceptor in the absence of each other is defined upon single photon excitation as

( ) ( )

( ) ( ) where is the intensity of the excitation light, ( ) and ( ) are the extinction coefficients for donor and acceptor at the excitation wavelength, ; and are the concentrations of donor and acceptor respectively; and and are the quantum yields. In the presence of FRET part of the energy of the donor will be transferred to the acceptor. To account for this transfer we introduce the efficiency of energy transfer into the fluorescence equations for donor and acceptor

( ) ( ) ( ) ( )( )

35 ( ) ( ) ( ) ( ) ( ) ( ) ( ) From these equations it can be seen that is obtained from the donor or acceptor emission when they are both excited; however, it is required to measure the emission spectra of donor and acceptor when no energy transfer is present. It is important to notice that for most common fluorophores the red edge of the emission spectrum of the donor extends over the acceptor emission causing contamination of the FRET signal (figureXX). This is known as spectral bleedthrough (SBT) signal into the acceptor (FRET) channel. The donor SBT can be calculated and corrected collecting the emission spectrum from samples labeled with donor only and with both, donor and acceptor, and using different computational algorithms. In biological systems the distance between donor and acceptor is not fixed. It is a range of values that depending on the molecular motion can be wider or narrower. It can be represented by a probability function ( ), whose distribution would be sharply peaked for D-A pairs attached to specific sites in a well-defined macromolecule while for systems with more spatial flexibility the distribution broadens. From Eq. (2.9) it can be seen that depends on the ratio

( ) and in the context of a distance distribution it can be averaged as

( ) ∫ ( )

By using different values, it is possible to select a distribution of distances in flexible molecules. Small values will include only the closely spaced D-A pairs while increasing will incorporate the contributions of all D-A pairs. A way to manipulate is by taking advantage of its dependence on the quantum yield of the donor (Eq. 2.34). Introducing specific molecules in the solution that will increase the non-radiative decay of the donor trough collisions will decrease ; this process is known as dynamic quenching. However, the amount of quenching should not exceed a reasonable amount due to it will reduce FRET signal.

The distribution of distances ( ) has a considerable effect on the fluorescence decay of the donor. For well-defined D-A distances (sharply peaked ( )) there is a single transfer rate for all the donors and the exponential decay becomes shorter. On the other hand, for systems

36 with a broader range of D-A distances there will be a mixture of transfer rates. Pairs that are closely spaced will display shorter decay times while those that are further apart will show much longer decay times. Time-resolved analysis of the donor decay is a common method for determining distance distributions in biological systems.

37 Chapter 3: Two-Photon FRET Microscopy to Quantify Mycobacterium Phagosomal Rupture in Macrophages

Mycobacterium tuberculosis (Mtb) is one of the most studied pathogens belonging to the family of Mycobacterium and yet the disease caused by it still represents a major threat to human health. It is estimated that one-third of the world population is latently infected by Mtb. The transition from latency to active tuberculosis (Tb) requires Mtb to penetrate subcellular phagosomal membrane and translocate to the cytosol of the host macrophage, termed as “cytosolic translocation”. In our laboratory we employ two-photon microscopy and FRET to study the mechanism of cytosolic translocation of Mycobacterium marinum (Mm), an organism genetically similar to Mtb. The method we use is based on a -lactamase fluorescent substrate that allows measurement of cytosolic translocation.

3.1 BACKGROUND KNOWLEDGE

Tuberculosis is effectively transmitted by the inhalation of small aerosol droplets produced in large quantities when persons with the active disease cough or speak. A single droplet of 0.5 to 5 in diameter contains enough bacteria to cause the infection. Typically, 5% of the patients will enter the active stage of the disease following the exposure to Mtb; but, the majority of individuals (95%) will transition to a non-infectious latent disease. The latent phase can persist for decades and the patients do not present symptoms or transmit the disease. Approximately 5% of individuals in the latent stage will develop the active disease at some point in life and this is accentuated (50%) when there is immunosuppression such as in the case of HIV. Most of the patients with active Tb that are treated will recover (95%), whereas 5% of them might relapse; if untreated, high mortality results (figure 3.1).

Figure 3.1: Stages of Mtb infection.

Macrophages constitute the principal host cell niche for the growth and survival of Mtb. Their main role is to engulf and then digest cellular debris and pathogens. This process is known as phagocytosis and it starts with the ingestion of the cellular pathogen trapping it inside the phagosome, a subcellular membrane compartment. The fusion of the phagosome with the lysosome produces the phagolysosome which is where the digestion of the pathogen takes place. Mtb is known for avoiding lysosomal fusion which is linked to the capacity of the bacteria to persist and replicate within the macrophage.

3.2 MECHANISM FOR TRACKING PHAGOSOMAL RUPTURE

As mentioned in the introduction of this chapter, the capability of Mtb to escape the phagosome is a key factor to study the transition from latent to active Tb. The study of cytosolic contact of selected mycobacteria at different time points serves to link phagosomal rupture with the pathogenic potential of the tested bacterial species. In our research we focused on Mycobacterium marinum (Mm) which is a model organism typically used to study mycobacterial

39 pathogenesis. We tested wild type Mm as well as several strains of Mm and compared their ability to escape the phagosome after 48 and 96 hours of infection. Similarly, we compared Mm with Mycobacterium smegmatis (Ms) which is generally considered a non-pathogenic microorganism.

Mycobacteria produce beta-lactamase enzymes that provide them with resistance to - lactam antibiotics like penicillins. These antibiotics have a common element in their molecular structure known as -lactam. The lactamase enzymes break this ring open therefore deactivating the molecule’s antibacterial properties. This property was used for the creation of a chemical probe that is trapped within the host cytoplasm and that exhibits FRET when beta-lactamase activity is present. The FRET-based fluorescent substrate CCF4 consists of two fluorophores, coumarin and fluorescein, and a cephalosporin core that contains a -lactam ring. CCF4 is trapped in the cytosol of macrophages and excluded from endosomes and other organelles. The use of this probe relies on the bacterial expression and exposure of beta-lactamase. Cleavage of CCF4 by beta-lactamase-expressing bacteria causes a switch of the FRET signal from 535 to 450 upon two photon excitation with 700 (figure 3.2 and 3.3).

3.3 EXPERIMENTAL PROCEDURE

1. Mouse macrophages (RAW 264.7) were loaded with CCF4 dye.

2. Wild-type and mutant strains cultures of Mm and Ms were prepared and deployed to the CCF4 loaded cells.

3. Cells were incubated at 37°C for bacterial invasion.

4. Image acquisition was performed at after 48 and 96 hours of infection. A two-photon laser scanning fluorescence microscope was used with a 60x (1.2 Numerical Aperture (NA), 0.28mm Working Distance (WD)) water objective. The excitation wavelength was adjusted to 700 nm and the fluorescence emission was detected in three channels (red, green and blue).

Figure 3.2: Fluorescence Emission Spectra of CCF4 (two-photon excitation at 700 )

Figure 3.3: Mechanism for tracking phagosomal rupture.

41 5. Subsequently, images were analyzed using CellProfiler, a computer software that allows automated scoring of the fluorescence signal for each individual cells. By using this software it is possible to calculate the ratio between the 450nm and 535nm emission signals and export the results to a text file. Ratios greater than 1 were considered positive for translocation.

6. Histograms showing the blue/green ratio distribution were generated for each assay using Minitab.

3.3.1 Image Processing Using CellProfiler

The images acquired with our two-photon microscope were saved as 24-bit RGB TIF files. Each of them displays 256 values in the red, green and blue channel. They were quantitatively analyzed using CellProfiler software. A pipeline was created in order to identify cells properly and calculate the ratio of the mean intensity in the blue and green channel per individual cell. The sequence of steps followed in order to create the pipeline can be listed in order as image pre-processing, cell identification, measurement, math calculation, image post- processing and storing of results. 1. RGB color images were converted to a grayscale image by combining the three channels together. The relative weight was set to 1 for each channel to ensure that

they contribute equally to the final image. 2. RGB color images were converted to a grayscale image by splitting the three channels into three individual grayscale images. 3. Using the images generated in step one cells were identified based on diameters in the

range of 10 to 80 pixels (6.4 to 51.2 um). Cells outside this range were discarded. Similarly, cells lying on the border of the image were not taken into account to avoid measurements from a portion of an object. A global threshold strategy was used to

classify pixel intensities as foreground or background. Since the distribution of cells varies substantially from image to image, the Otsu approach was employed to calculate the threshold separating the two classes of pixels based on splitting the image into three classes: foreground, mid-level, and background. The middle

42 intensity class was assigned to the foreground. Each image was smoothed with a Gaussian filter before thresholding in order to remove noise in the acquired images. 4. The average pixel intensity was measured within each cell identified in step three based on the grayscale images obtained for the red, blue and green channels in step two. 5. The ratio of (mean blue intensity) / (mean green intensity) was calculated for each cell based on the measurements from step four.

6. Images with ratios above 1 were flagged. 7. The average pixel intensities measured in step four were converted from CellProfiler default scale (0 to 1) to grayscale (0 to 255). 8. The cell outlines produced in step three where placed on the original RGB color images. 9. The ratios calculated in step five were placed on top of every cell from the images generated in step seven. 10. RGB color images displaying cell outlines and ratios (from steps 8 and 9) were saved

as TIF files. 11. The grayscale mean intensities generated in step 7 together with the ratios from step 5 and the flagged images from step 6 were exported to text files.

3.4 RESULTS

Figure 3.4 shows typical images of cell cultures infected with Mm and strains pMV261 and Q5K after 48 and 96 hours. The three fluorescent channels are shown separately. Bacteria was labeled with the red fluorescent protein mCherry. Histograms of the ratio blue / green are shown in figures 3.5 and 3.6. The former is a comparison of the same bacteria after 48 and 96 hours, while the later compares each bacteria mentioned above with the non-pathogenic Ms.

43 a)

Figure 3.4: Images acquired after 48 and 96 hours of infection.

(a) Mm, (b) strain pMV261, (c) strain Q5K

44 a) b)

Figure 3.5: Comparison at 48 and 96 hours.

Graphs show and increase in the higher ratios after 96 hours of infection for Mm (a), strain pMV261 (b) and strain Q5K (c).

a) b)

Figure 3.6: Comparison with Ms after 96 hours.

(a) Mm (b) strain pMV261 and (c) strain Q5K.

45 3.5 CONCLUSIONS

The histograms in figure 3.5 show an increase in the higher ratios after 96 hours when compared to 48 hours. There is indication of phagosomal rupture and cytosolic contact at both time points; however, after 96 hours the presence of blue fluorescence is more significant. Similarly, the comparison with the non-pathogenic Ms (figure 3.6) after 96 hours indicates that Mm, pMV261 and Q5K have a higher capability of translocation to the cytosol. The use of sensitive cytoplasmic FRET reporter CCF4-AM combined with our two photon laser scanning fluorescence microscope provides quantitative analysis of phagosomal rupture and cytosolic entry of cellular pathogens. This interdisciplinary project applies a frontier optical technique developed in Physics Department on an important infectious disease study.

46 Chapter 4: Functional Imaging of Drosophila Brain Using Two-Photon Microscopy

4.1 VISUALIZATION OF DOPAMINERGIC NEURONS IN THE PROTOCEREBRUM

Dopamine plays an important role in the brain of mammals. It functions as a neurotransmitter released by nerve cells to send signals to other nerve cells playing an important role in motion, motivation and cognition. In humans, abnormal levels of dopamine have been linked to Parkinson’s disease and schizophrenia. Reward studies have shown an increase in the levels of dopamine in the brain and several addictive drugs such as cocaine, amphetamine and methamphetamine produce an amplification of the effects of dopamine. In our laboratory we used Drosophila as a model organism to study putative dopaminergic neurons in the adult protocerebrum. We focused our attention on tyrosine hydroxylase (TH) neurons; TH is an enzyme that participates in the production of L-DOPA, a direct precursor of dopamine. In order to visualize TH neurons we used a biochemical method termed as GAL4-UAS System, which is widely employed to study gene expression and function in the fruit fly. The system is divided into two parts: the GAL4 gene and the UAS (Upstream Activation Sequence), an enhancer to which the Gal4 protein binds to activate gene expression. The line we used is TH-GAL4, which expresses GAL4 in TH neurons. The presence of GAL4 by itself is not visible since its main effect is to bind to a UAS region and most cells have no UAS regions. The other part of this system are the reporter lines; strains of flies with a special UAS region next to the desired gene. Once the UAS is activated, the gene next to it is turned on and starts producing its resulting protein. For our experiments we used TH-GAL transgene to drive the expression of UAS-mCD8::GFP; basically a green fluorescent protein (GFP). Similar experiments were performed by a group of scientist from Baylor College of Medicine in Houston, Texas; and published in July, 2009. They used confocal microscopy to image TH neurons in the protocerebrum and were able to identify and quantify eight clusters of TH neurons according to the cell size, shape, location and projection pattern (figure 4.1).

Figure 4.1: TH-GAL4 expressing neurons in the Drosophila brain.

Based on the classification of TH neuron clusters shown in figure 4.1 we proceeded to identify them in dissected fly brains using our two-photon fluorescence microscope. In order to identify these clusters we carefully analyzed stack of images as well as three dimensional reconstructions of the fly brain using Imagej. Figure 4.2 shows some of the images we were able to obtain.

48 a) b)

c) d)

Figure 4.2: Maximum intensity projections of two Drosophila brains generated with Imajej.

(a,b) Anterior portion of the right hemisphere where PAM and PAL clusters of neurons can be seen. (c,d) Several clusters located in the posterior area of the right hemisphere. (a,c) Images obtained in the green fluorescent channel of our two-photon fluorescent microscope. (b,d) Same images as in a) and c) in a gray scale. All scale bars are equivalent to 30 .

4.2 FUNCTIONAL IMAGING USING THE FLUORESCENT CALCIUM REPORTER GCAMP5G

Calcium is an important messenger that serves to regulate many aspects of neuronal function. Measuring the concentration of free inside neurons can lead to quantification of action potentials and synaptic inputs. The concentration of intracellular in neurons can

49 change due to different factors such as the receipt of a neurotransmitter signal from another neuron or some other form of stimulation including odor presentation or electrical shock.

Calcium ions can enter the cells during action potentials that open voltage-sensitive calcium channels. There are several genetically encoded calcium indicators (GECI) that are used to measure changes. Some of them are based on FRET indicators or on the single wavelength sensor family GCaMP. The former is created from the fusion of a green fluorescent protein (GFP), calmodulin (CaM) and the /CaM-binding M13 peptide. CaM is a calcium sensor that transduces the signal into specific changes in cellular function. In the presence of CaM undergoes a conformational change and the GFP fluorescence increases. However, in the absence of there is a higher probability of quenching by the solvent and therefore a decrease in the fluorescence signal. GCaMP5G is an engineered GECI that has shown high performance in terms of the ( ) dynamic range of the fluorescence response ( ), lower -free fluorescence and higher -bound fluorescence (figure 4.3)

Figure 4.3: GCaMP5G fluorescent spectra.

One-photon emission (left) and two-photon excitation (right) spectra. Calcium-free spectra are depicted by dashed blue lines and calcium-saturated spectra by solid red lines. Dashed green lines depict ( ) ,

plotted on the right axis. GCaMP5G have been used in reward and functional imaging studies in Drosophila to measure the activation and fluorescence response of or certain regions inside the brain. An article published in 2012 [reference] presented data related to the measurement of calcium signal in

50 PAM neurons using GCaMP3 (a predecessor of GCaMP5G). The results showed that these neurons are activated by sugar ingestion and starvation. As we can see in figure 4.2 PAM neurons form a dopaminergic cluster located close to the anterior part of the brain. This cluster innervates the horizontal lobes of the mushroom body where appetitive olfactory associative memory is formed. Another study from 2012 used GCaMP5 in Drosophila larval neuromuscular junction (NMJ) and adult antenna lobe (AL). Drosophila larvae NMJ showed considerable fluorescence changes upon electrical activation of motor neuron axons. On the other hand, adult

Drosophila fluorescence response in AL was measured when presented to different concentrations of octanol. In our laboratory we have started using GAL4/UAS system to drive the expression of calcium sensors in the adult mushroom body. GAL4-OK107 is expressed in the larval and adult mushroom body alpha'/beta', alpha/beta and gamma neurons and the Kenyon cells in the calyx. This line was crossed with UAS-GCaMP5G and the dissected brains were imaged under our two-photon microscope using 920nm as the excitation wavelength. The three-dimensional reconstructions can be appreciated in figure 4.4. We obtained expression of the calcium sensor

GCaMP5G in the Kenyon cells, calyx and peduncle of the mushroom body. In the mushroom body calyx, Kenyon cells receive olfactory input from projection neurons on their dendrites. The fact that we can visualize these structures under our microscope opens the possibility of performing in vivo calcium in Drosophila.

4.2.1 Future work

Before moving forward to live imaging it is necessary to run several experiments and measure the fluorescence response in dissected brains expressing GCaMP5G upon the application of some action potential. The baseline fluorescence can be averaged over a few seconds before the application of the stimulus. Subsequently, the mean response can be calculated as the average of during the time the stimulus is being applied.

51 a) b)

c) d)

Figure 4.4: Three-dimensional reconstructions of two adult brains expressing calcium sensor GFP.

(a,c) GCaMP5G expression in Kenyon cells and calyx. (b,d) Lateral view of images in a) and c); peduncle of mushroom body visible from this angle.

4.3 IMAGING DROSOPHILA CEREBRAL TRACHEA WITH TWO-PHOTON FLUORESCENCE MICROSCOPY

The respiratory system in Drosophila melanogaster is constituted by trachea, a branched network of epithelial tubes that spreads throughout the body carrying oxygen into tissues. The cerebral trachea in Drosophila is a branch of the first segmental trachea of the embryo. Previous studies have identified five primary tracheal branches that originate during the larval stages and grow around the neuropile. However, the trajectories and branching pattern of brain trachea is very variable in comparison with the well-defined pattern of dorsal trachea. More analysis is

52 required to evaluate brain tracheation and the development of methods to reconstruct its variable patterns is of particular importance. In our laboratory we have obtained fluorescence emission from tracheal branches in dissected brains without introducing any artificial fluorescent indicators. Using our two-photon fluorescence microscope and adjusting the excitation wavelength to 710 we can capture autofluorescence signal from trachea under the blue channel (figure 4.5).

a) b) c)

d) e) f)

Figure 4.5: Three-dimensional reconstructions of one adult brain (a, b, c) and one third instar larvae brain (d,e,f) autofluorescence upon excitation with 710 .

(a,d) Blue and green channels combined in one image. (b,e) Blue channel. (c,f) Green channel.

In order to corroborate that the autofluorescence signal detected in the blue channel in fact comes from tracheal branches of the brain we used btl-GAL4 to drive the expression of

UAS-mCD8::GFP in the tracheal system. Images were obtained simultaneously in the green and blue channels upon two-photon excitation with 920 and 710 respectively. The correlation between the structures observed in both channels is evident from figure 4.6.

a) b)

53 c) d)

e) f)

g) h)

Figure 4.6: Maximum intensity projections of tracheal branches in two different brains showing correlation between GFP expression and autofluorescence.

(a,e) RGB images obtained upon two-photon excitation with 920 . (b,f) Green channel ( 920 excitation wavelength). (c,g) Blue channel (920 excitation wavelength). (d,h) Blue channel (710 excitation wavelength).

54 4.3.1 Quantification of the volume of tracheal branches

In order to compare the autofluorescence signal and the GFP signal expressed in the tracheal system we can calculate the volume of the branches at a randomly chosen region of interest (ROI). Using Imagej it is possible to count the number of voxels in a ROI throughout an entire stack of images. In the same way that a pixel is the smallest element in a raster image, a voxel represents the smallest volume on a regular grid in a three-dimensional space. We have previously established that in our system 1 pixel is equivalent to 0.64 , therefore the volume represented by 1 voxel is approximately equal to 0.26 . The approach that we will follow in order to count the number of voxels contained in tracheal branches in a specific ROI starts with the conversion of 8-bit gray scale images to binary images. This can be achieved by using Imagej threshold tool making sure that most tracheal structures are preserved while the background signal is minimized (figure 4.7).

a) b) c)

d) e) f)

Figure 4.7: Treshholded images using Imagej.

(a,b,c) Same location and different threshold for GFP signal. As the range of threshold is increased more pixels turn black (tresholded pixels). (a) Treshold range : 0 to 27. (b) Treshold range : 0 to 30. (c) Treshold range : 0 to 39. (d,e,f) Same location and different threshold for autofluorescence signal. (d) Treshold range : 0 to 30. (e) Treshold range : 0 to 40. (f) Treshold range : 0 to 55. Scale bars equivalent to 30 .

55 The applied threshold range for the stack of images expressing GFP signal was selected according to figure 4.7 (c) while for the stack of images showing autofluorescence signal the same range as in figure 4.7 (f) was chosen. Figure 4.8 (c,d) shows the final stacks to be analyzed for voxels counting.

a) b)

c) d)

Figure 4.8: Three-dimensional reconstruction of the ROI.

(a) GFP expression upon 920 excitation. (b) Autofluorescence signal upon 710 excitation. (c) Tresholded stack for a). (d) Tresholded stack for b). Imagej provides a plugin named Voxel Counting that counts the treshholded voxels in a stack and displays the count, the average count per slice and the volume fraction (ratio of thresholded voxels to all voxels). The results obtained using this tool are shown in table 4.1.

56 Table 4.1 Comparison of tracheal volume for the structures shown in figure 4.8 (c and d).

GFP Signal Autofluorescence

Tracheal Volume (μm3) 2903.51 5458.10 Volume fraction % (Tracheal Branches) 0.07 0.14

4.4 CONCLUSIONS

Throughout this chapter we have covered several applications of our two-photon system to the study of Drosophila brain. The quantification of dopaminergic clusters of neurons discussed in section 4.1 represents an important advance towards a more meaningful study. For example, it allows the investigation of any variation in the number of neurons of each individual cluster upon exposing flies to different concentrations of alcohol. On the other hand, the expression of GFP given by the calcium sensor GCaMP5G in Kenyon cells, calyx and peduncle but not in the mushroom body lobes when using GAL4- OK107 pose an interesting discussion. It is possible that because Kenyon cells and calyx serve as an input to the neuronal circuit, this region is activated most of the time. However, it is necessary to perform more experiments, mainly, the application of action potentials like potassium in dissected brain and observe if there is any expression of GFP in the lobes. Finally, the procedure described in section 4.3.1 to quantify the volume of tracheal structures obtained through autofluorescence could be used to examine the plasticity of these branches under hypoxia conditions. Before studying this phenomenon in live brain a preliminary experiment could be done in the laboratory using dissected brains and obtaining autofluorescence signal at different time points after the dissection is performed. The goal would be to quantify the volume of tracheal branches in the region close to the mushroom body; looking at both hemispheres of the protocerebrum. From this analysis it would be possible to determine whether or not there is any correlation between tracheal volume and hypoxia in dissected brains.

57 Bibliography

1. Robert W. Boyd 2008. Nonlinear Optics. 3rd ed. Academic Press/Elsevier: pp. 549-559. 2. Xue Feng Wang and Brian Herman 1996. CHEMICAL ANALYSIS VOL. 137, Fluorescence Imaging Spectroscopy and Microscopy. Willey-Interscience Publication: chapter 7. 3. Ammasi Periasamy and Richard N. Day 2005. Molecular Imaging, FRET Microscopy and Spectroscopy. New York: Oxford University Press. 4. Ammasi Periasamy 2001. Methods in Cellular Imaging. Oxford University Press. 5. Alberto Diaspro 2010. Nanoscopy and Multidimensional Optical Fluorescence Microscopy. CRC Press. 6. David J. Griffiths 2005. Introduction to Quantum Mechanics. 2nd ed. Pearson Prentice Hall. 7. John David Jackson 1999. Classical Electrodynamics 3rd ed. John Wiley & Sons, Inc. 8. Max Born and Emil Wolf 1999. Principles of Optics 7th (expanded) ed. Cambridge University Press. 9. C. J. Joachain, N. J. Kylstra and R. M. Potvliege 2012. Atoms in Intense Laser Fields. Cambridge University Press. 10. E. Hanamura, Y. Kawabe and A. Yamanaka 2007. Quantum Nonlinear Optics. Springer. 11. Lukas Novotny and Bert Hecht 2006. Principles of Nano-Optics. Cambridge University Press. 12. Israel Veilleux, Joel A. Spencer, David P. Biss, Daniel Cˆot´e, and Charles P. Lin 2008. In Vivo Cell Tracking With Video Rate Multimodality Laser Scanning Microscopy. IEEE Journal of Selected Topics in Quantum Electronics, VOL. 14, NO. 1. 13. Simeone R, Bobard A, Lippmann J, Bitter W, Majlessi L, et al. (2012) Phagosomal Rupture by Mycobacterium tuberculosis Results in Toxicity and Host Cell Death. PLoS Pathog 8(2): e1002507. doi:10.1371/journal.ppat.1002507 14. Keller, C., Mellouk, N., Danckaert, A., Simeone, R., Brosch, R., Enninga, J., Bobard, A. Single Cell Measurements of Vacuolar Rupture Caused by Intracellular Pathogens. J. Vis. Exp. (76), e50116, doi:10.3791/50116 (2013). 15. Jasper Akerboom, Tsai-Wen Chen, Trevor J. Wardill 2012. Optimization of a GCaMP Calcium Indicator for Neural Activity Imaging. The Journal of Neuroscience. 16. Anil Koul, Eric Arnoult, Nacer Lounis, Jerome Guillemont and Koen Andries 2011. The challenge of new drug discovery for tuberculosis. Published by Nature, VOL 469.

58 Vita

Yassel Acosta was born and raised in Havana, Cuba. In 2005 he obtained a B.S. in Electronic

Engineering from the Institute of Technology of Juarez City in Mexico. His passion for science, Physics in particular, led him to pursue a M.S. in Physics at the University of Texas at El Paso. While completing the courses of the master’s program, Yassel got involved in research activities at the Biophotonics

Laboratory of the Physics Department. There he worked in interdisciplinary projects mainly focused in the applications of a Two-Photon Laser Scanning Fluorescence Microscope to study interesting biological problems. He recently got accepted into the Applied Physics Program for doctoral students at the

University of Michigan where he expects to continue performing research in the field of optics. During his academic life, Yassel has interacted with a large number of students and professors with different backgrounds; therefore he is very comfortable working with heterogeneous research groups.

Permanent address: 625 Londonderry El Paso, Texas, 79907

This thesis was typed by Yassel Acosta.