AFLUORESCENCE CORRELATION SPECTROSCOPY STUDYOFTHE CRYOPROTECTIVE MECHANISMOF GLUCOSEON HEMOCYANIN
By
Eric J. Hauger
A THESIS
Submitted to the faculty of the Graduate School of Creighton University in Partial Fulfillment of the Requirements for the degree of Master of Science in the Department of Physics.
Omaha, NE May 6, 2014
Abstract
Cryopreservation is the method of preserving biomaterials by cooling and storing them at very low temperatures. In order to prevent the damaging effects of cooling, cryoprotectants are used to inhibit ice formation. Common cryoprotectants used today include ethylene glycol, propylene glycol, dimethyl sulfoxide, glycerol, and sugars. However, the mechanism responsible for the effectiveness of these cryoprotectants is poorly understood on the molecular level. The water replacement model predicts that water molecules around the surfaces of proteins are replaced with sugar molecules, forming a protective layer against the denaturing ice formation. Under this scheme, one would expect an increase in the hydrodynamic radius with increasing sugar concentration. In order to test this hypothesis, two-photon fluorescence correlation spectroscopy
(FCS) was used to measure the hydrodynamic radius of hemocyanin (Hc), an oxygen-carrying protein found in arthropods, in glucose solutions up to 20wt%. FCS found that the hydrody- namic radius was invariant with increasing glucose concentration. Dynamic light scattering
(DLS) results verified the hydrodynamic radius of hemocyanin in the absence of glucose. Al- though this invariant trend seems to indicate that the water replacement hypothesis is invalid the expected glucose layer around the Hc is smaller than the error in the hydrodynamic radius mea- surements for FCS. The expected change in the hydrodynamic radius with an additional layer of glucose is 1nm, however, the FCS standard error is ±3.61nm. Therefore, the water replacement model cannot be confirmed nor refuted as a possible explanation for the cryoprotective effects of glucose on Hc.
i Acknowledgements
I would like to first thank the Creighton University Physics Department for all of the knowl- edge and guidance that they have provided over the years. With their help, my understanding of the world has grown deeply and I will be forever grateful for having them be part of my journey.
To my advisor, Dr. Michael Nichols, thank you for your patience, for your kindness, and for inspiring me to pursue biophysics.
Finally, I would like to thank my family, for their loving support and encouragement to achieve my goals.
ii Contents
1 Cryopreservation and Motivations 1
1.1 Motivations ...... 1
1.1.1 Organ Preservation ...... 1
1.1.2 Human Reproductive Medicine ...... 1
1.1.3 Conservation of Endangered Species ...... 2
1.2 Modern Preserving Methods ...... 2
1.3 Protein Structure and Function ...... 3
1.3.1 Primary Structure ...... 3
1.3.2 Secondary Structure ...... 3
1.3.3 Tertiary Structure ...... 5
1.3.4 Quaternary Structure ...... 5
1.3.5 Loss of Protein Structure ...... 5
1.4 Cryopreservation Theories ...... 5
1.4.1 Vitrification Theory ...... 6
1.4.2 Water Replacement Theory ...... 7
1.5 Model Systems ...... 8
1.6 Previous Work ...... 10
1.7 Conclusion ...... 12
2 Optical Techniques to Evaluate the Water Replacement Model 13
2.1 Verifying the Water Replacement Model ...... 13
2.2 Fluorescence Correlation Spectroscopy (FCS) ...... 14
2.2.1 Multiphoton Excitation ...... 15
2.2.2 Diffusion ...... 18
2.2.3 Particle Fluctuations ...... 19
iii CONTENTS iv
2.2.4 FCS Design ...... 21
2.2.5 Filter Set ...... 22
2.2.6 FCS Correlation Function ...... 23
2.2.7 Photobleaching ...... 26
2.3 Dynamic Light Scattering (DLS) ...... 26
2.3.1 Rayleigh Scattering ...... 27
2.3.2 Interference ...... 28
2.3.3 DLS Correlation Function ...... 30
2.4 Conclusion ...... 31
3 Materials and Methods 33
3.1 Approach Overview ...... 33
3.2 Apparatus ...... 34
3.2.1 FCS System Preparation ...... 34
3.2.2 DLS System Preparation ...... 34
3.3 Methods ...... 34
3.3.1 Solution Preparation ...... 35
3.3.2 FCS Measurements ...... 36
3.3.3 DLS Measurements ...... 38
3.3.4 Data Analysis Procedure ...... 39
3.4 Conclusion ...... 40
4 Results and Discussion 41
4.1 FCS Results ...... 41
4.1.1 Power Dependence Study ...... 41
4.1.2 Detection Sensitivity Study ...... 42
4.1.3 Experimental Focal Volume ...... 44
4.1.4 Hemocyanin Studies ...... 47
4.2 DLS Results ...... 52
4.3 Evaluating the Water Replacement Hypothesis ...... 54
4.4 Conclusion ...... 57
Appendices CONTENTS v
A Optics Protocols 65
A.1 FCS Laser Alignment ...... 65
A.2 Cleaning Optical Equipment ...... 65
B Solution Preparation 67
B.1 Hemocyanin ...... 67
B.2 10xCMFPBS ...... 69
B.3 1xCMFPBS ...... 69
B.4 20wt% glucose 1xCMFPBS ...... 69 List of Figures
1.1 Schematic of Generic Amino Acid Structure ...... 4
1.2 Formation of a Dipeptide ...... 4
1.3 Phase diagram for H2O and Glucose Solution...... 6 1.4 Diagram of Vitrification Model ...... 7
1.5 Diagram of Water Replacement Model ...... 8
1.6 Fluorescent Amino Acid Spectra ...... 9
1.7 Diagram of Water Replacement Model ...... 11
2.1 Focal volume, intensity trace and FCS correlation function diagrams ...... 14
2.2 Schematic of 2PE process ...... 16
2.3 IPSF2 diagram ...... 17
2.4 Fluorescence intensity trace ...... 20
2.5 Schematic diagram of 2PE FCS setup ...... 21
2.6 Plot of System Transmission and L-tryptophan Fluorescence ...... 22
2.7 FCS example autocorrelation function ...... 25
2.8 Schematic diagram of DLS setup ...... 27
2.9 Relative scattering intensity of 5nm and 50nm particles ...... 29
2.10 Interference pattern for DLS ...... 29
2.11 DLS example autocorrelation function ...... 31
3.1 Screenshot for a FCS data run with 50nM Hc...... 37
3.2 Screenshot for a DLS data run with 50nM Hc...... 38
3.3 Autocorrelation graph showing timescales for various processes...... 40
4.1 L-tryptophan power dependence study ...... 42
vi LIST OF FIGURES vii
4.2 Fluorescence Intensity vs Concentration plot for L-tryptophan, avidin spheres,
and hemocyanin...... 43
2 4.3 Plot of χυ vs lateral-to-axial 2PE focal volume aspect ratio...... 45 4.4 Fits and residuals for 50nM Hc ...... 48
4.5 FCS autocorrelations of Hc in glucose ...... 49
4.6 Plot of τD vs concentration of glucose of 50nM Hc...... 50 4.7 Viscosity plot of buffer solution vs the concentration of glucose...... 50
4.8 FCS plot of RH vs the concentration of glucose of 50nM Hc...... 51 4.9 DLS autocorrelations of Hc in solution at varying concentrations...... 53
4.10 DLS plot of RH vs the concentration of Hc...... 53 4.11 FCS histogram of Hc ...... 55
4.12 DLS histogram of Hc ...... 55
4.13 FCS and DLS plot of RH vs the concentration of glucose of 50nM Hc...... 57
A.1 Photograph of the 2PE FCS system ...... 66 List of Tables
1.1 Amino Acid Fluorescence Data ...... 9
4.1 Average Hydrodynamic Radius of Hc from FCS ...... 52
4.2 Average Hydrodynamic Radius of Hc from DLS ...... 54
viii Chapter 1
Cryopreservation and Motivations
1.1 Motivations
1.1.1 Organ Preservation
Every day 18 people die waiting for an organ transplant [1]. Organ preservation is consid- ered the “supply line for organ transplantation” [2]. The continuing shortage of donor organs and changes in donor demographics have propelled the need for achieving an optimal and effica- cious approach to organ preservation [3]. Currently the length of time an organ can be preserved depends on the organ but most cannot be kept viable for more than 24 hours [3]. If the viability of organs could be extended for months or even years then donor organs could be stored until patients in need, who best match the tissue being stored, could be prepped and placed into trans- plant surgery. Optimal storage would also help alleviate transplant complications due to delayed function rates of organs. Additionally, promising developments being made in tissue engineer- ing would increase our supply of available organs but ultimately effective storage techniques would be necessary [4]. Besides organ transplantation, developing and understanding optimal cryopreservation methods is an invaluable tool for human reproductive medicine and the con- servation of endangered species. Therefore, advancements made in cryopreservation have the potential to have great impacts in diverse areas of the scientific community.
1.1.2 Human Reproductive Medicine
In the case of human reproductive medicine, techniques such as in vitro fertilization (IVF) and intracytoplasmic sperm injection (ICSI) along with advancements in female gamete acquisition have resulted in an increased need for sperm and oocyte cryopreservation methods to be devel-
1 CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 2 oped [5, 6]. Advances in human reproductive medicine allow cancer patients undergoing toxic chemotherapy or radiation treatment, those with degenerative diseases or traumatic injury that effect reproduction and those that are opting to have a vasectomy or tubal ligation, to retain the possibility of reproduction at a later date [5]. By developing a better understanding of the mechanisms of cryopreservation, patients can be assured that fertility can be maintained in spite of health conditions that have a negative effect on reproductive capabilities.
1.1.3 Conservation of Endangered Species
Cryopreservation development in combination with assisted reproduction techniques not only helps retain human fertility but it gives hope to many endangered species on the brink of ex- tinction. Typically, the spermatozoa of a given endangered species are preserved and utilized for breeding purposes. Preserving spermatozoa is a valuable tool if protocols are adapted for the required conditions for optimum preservation for each species [7]. By exploring the mecha- nisms of cryopreservation and conducting species-specific studies, the appropriate protocols and conditions for optimum cryopreservation will be able to be determined. The advances made in our understanding of these mechanisms will greatly improve the stability of endangered species populations.
1.2 Modern Preserving Methods
The discovery of cryopreservation occurred accidently in 1948 when C. Polge, A.U. Smith, and
A.S. Parkes found that glycerol would allow fowl spermatozoa to survive freezing to −37◦ C [8].
Low temperature storage of living cells is essential for stopping biological time. Currently,
◦ liquid N2 (T=-196 C) is typically used for storage and at that temperature only two states of water can exist (crystalline or glassy) both of which have a viscosity so high (> 1012 Pa· s) that
diffusion is almost non-existent [9]. If the crystalline phase of water occurs, intracellular ice
formation (IIF) is the most likely cause of cell death during the various freezing, storage and
thawing protocols associated with cryopreservation [10]. Recent studies suggest that IIF is more
likely in tissues than in suspended cells in solution which explains why organ preservation is
more difficult than the cryopreservation of human gamete cells [11].
Today, the most common cryopreserving agents (CPAs), contain additives which prevent
cell destruction, such as ethylene glycol, propylene glycol, dimethyl sulfoxide, glycerol, and CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 3 sugars [12]. Essentially, at the cellular level these CPAs prevent ice crystals from forming by lowering the freezing point of water and inhibiting crystal formation. However, at the molecular level the actual protective mechanisms of CPAs, in particular sugars, are poorly understood [13].
1.3 Protein Structure and Function
Changes at the molecular level must be studied within biological systems that are much smaller than individual cells, namely proteins and amino acids. During the freezing process, as water containing buffer salts and proteins forms ice crystals, the concentration of these solutes can increase causing changes in protein stability. If selective precipitation of buffer salts, such as mixed phosphate buffer occurs, localized pH shifts can cause denaturing (loss of normal protein activity) [14].
The structure of a protein determines its activity or function [15]. Biochemists break a protein’s structure into several levels of structural organization. The primary structure of a protein is defined by the amino acid sequence, the secondary structure comes from the localized arrangements of adjacent amino acids as the protein folds, and tertiary structure is considered to be the overall three-dimensional shape of the protein [16].
1.3.1 Primary Structure
Amino acids are small organic molecules made up of a central carbon atom, an amino group, a carboxyl group, a hydrogen atom, and a side chain called the R group [15]. A rendering of the general structure of an amino acid can be seen in Figure 1.1. The R group (green) varies from one amino acid to the next but the other molecular structure is the same for all amino acids.
Amino acids can be linked together to form polypeptide chains. When two amino acids come together to form a dipeptide a water molecule is released and the two amino acids are linked by what is known as a peptide bond. This reaction is the beginning of a polypeptide chain.
1.3.2 Secondary Structure
When several amino acids come together as a continuous and unbranched chain they form a polypeptide. Secondary structure consists of several repeating patterns in polypeptides, the most common being the α-helix and the β-pleated sheet. Both of these patterns are stabilized CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 4
Figure 1.1: Rendering of the generic amino acid structure with the amino group (blue), carboxylic group (red) and variable R group (green).
Figure 1.2: Two amino acids come together to form a dipeptide and a water molecule is released. This reaction is the beginning of a polypeptide chain (Adapted from [15]). by localized hydrogen bonding between the amine (N-H) and carbonyl (C=O) groups [16].
The α-helix structure forms when a polypeptide chain twists into a spiral conformation.
Hydrogen bonding takes place between the N-H of each amino acid and the C=O of the amino acid four residues down the polypeptide chain. All of the R groups face outward from the
α-helix [16].
In the case of the β-pleated sheet, two or more polypeptides line up next to each other and
are not coiled but fully extended. Segments of the polypeptides that hydrogen bond with each
other are called β-strands. Hydrogen bonds are always between the N-H and C=O of adjacent
chains [16]. CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 5
1.3.3 Tertiary Structure
The tertiary structure of a protein consists of the unique three-dimensional shape the protein assumes while folding into its biologically functional native structure. This complex, organized structure comes about as a result of interactions between the R groups in the primary structure and is called protein folding [16]. It is this folding which is essential for a protein to function properly. The nature of the folding process is not completely understood but it is known that protein folding is a thermodynamically favorable process which has an negative Gibbs free energy change (∆G). However, the magnitude of ∆G is the equivalent of several hydrogen bonds ( 0.1 eV/bond) therefore the protein folding process is a delicate balance that requires favorable environmental conditions to occur [16].
1.3.4 Quaternary Structure
When a protein is made up of several polypeptide chains (or subunits) noncovalent interactions can occur between these subunits resulting in an even more intricate structure than that of a protein with a single polypeptide chain. These interactions include the hydrophobic effect, electrostatic interactions, hydrogen bonds, and covalent cross-links [16]. This additional higher order structure is known as quaternary structure.
1.3.5 Loss of Protein Structure
As has been mentioned in Section 1.3.3 the small magnitude of ∆G associated with protein folding means that protein structure is very dependent on environmental factors. When con- ditions are not ideal, protein denaturing can occur. Protein denaturing is a disruption of the protein structure that may or may not include unfolding [16]. A few environmental factors that can cause denaturing are: exposure to strong acids or bases, high salt concentrations, and tem- perature changes [16]. In most cases, the denaturing process is irreversible and thus a denatured protein permanently loses its biological function.
1.4 Cryopreservation Theories
The environmental factors discussed in Section 1.3.5 that can lead to permanent denaturing of a protein are all important to consider with regards to cryopreservation. Selective precipitation of buffer salts, pH fluctuations, and temperature changes all can occur during the freezing process. CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 6
The use of CPAs helps to alleviate these environmental stresses but the question is how? There are several current theories that attempt to explain how CPAs, especially sugars, protect biotissue during cryopreservation.
1.4.1 Vitrification Theory
One theory, vitrification, suggests that CPAs help to inhibit ice formation completely by turning the solution into a highly viscous glassy state. It is known that as solutes, such as sugar, are added to water the colligative properties such as the boiling point and freezing point of the solution change. The freezing point of the solution decreases and as more sugar is added the system changes from a liquid to a solid as a sole result of an increase in viscosity, without any crystallization and therefore without any ice formation [8]. This process of solidification without ice formation is known as vitrification and the system is considered to be in a glassy state.
Figure 1.3: Phase diagram for water and glucose solution. As the concentration of glucose is increased the melting temperature (Tm, red dotted) decreases while glass transition temperature (Tg, black solid) increases. The highest glucose concentration 20wt% used in the Hc study is shown (black dashed). Adapted from [17]. CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 7
Figure 1.3 depicts how both the melting temperature (Tm) and the glass transition temper-
ature (Tg) change as a result of the increase in the concentration of glucose. The Tm decreases while the Tg increases as the concentration of glucose is increased. For very low glucose con- centrations it is unlikely that a glucose solution would form a glass but as the concentration increases the liquid can move directly to the glass state as long as the solution is cooled rela- tively quickly [18]. However, above 80wt% glucose any cooling below a certain point no matter how slow will result in vitrification.
Figure 1.4: The diagram above is a representation of vitrification theory which predicts no change in the protein size. When vitrification occurs the water and sugar system moves into a glass state.
Figure 1.4 shows an illustration of the vitrification model. Glucose molecules are shown as the larger red dots and water molecules are given by the smaller blue dots. The system turns into a glass or vitrified state without altering the salt distribution or the pH and therefore the protein is protected. However, depending on the cooling conditions and the concentration of CPAs it is possible that vitrification does not occur but rather ice crystals form.
1.4.2 Water Replacement Theory
In the case of ice crystals forming, water replacement theory, states that the protein is maintained in a viable state by glucose replacing the water bound to the outside of the protein via hydrogen bonding [19]. As the temperature is lowered buffer salts concentrate in the remaining unfrozen liquid. Figure 1.5 depicts the water replacement model. The glucose circles (red) bind to the protein, replacing the ice crystals (blue). As a result, the glucose forms a protective layer around the protein and keeps any pH fluctuations and precipitating buffer salts from damaging the protein. This protective layer would add about 2nm to the diameter of the protein and therefore, CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 8 in principle, this could be measured.
Figure 1.5: Diagram depicting the water replacement model. The glucose molecules bind to the protein and protect it from the ice crystals.
1.5 Model Systems
The structure of the protein is what determines its function and that structure is made up of amino acids. There are 22 naturally occuring, protein-building amino acids that can come together in a variety of combinations to form millions of unique proteins. With so many choices, criteria are needed to help narrow the search for a potential model system for testing the water replacement model.
The most important criteria is that the experimental techniques used to study the cryopro- tective effects of sugars on amino acids and proteins are able to detect possible changes in the diameter of these molecules and proteins. Two techniques that are especially adept at measuring minute changes in molecular size are fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS). Both techniques require small molecules to be suspended in solution and
FCS requires molecules to be fluorescent (able to emit light after absorbing light). Therefore, these are the constraints on the amino acid and protein model systems.
Looking to the available amino acids only three are fluorescent: tryptophan, tyrosine, and phenylalanine. These three amino acid residues contribute to the intrinsic fluorescence of pro- teins and thus a model protein should contain one of these three residues in order to be utilized for FCS measurements. Looking at the properties of these amino acids, the choice becomes clear.
As can be seen in Figure 1.6 tryptophan has a shifted fluorescence peak compared to tyrosine CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 9
Figure 1.6: The graph above gives the spectra for tryptophan (black solid), tyrosine (red dashed), and phenylalanine (blue dotted). Tryptophan has a shifted fluorescence peak compared to tyrosine and pheny- lalanine. Fluorescence data was obtained from [20].
Table 1.1: Amino Acid Fluorescence Data [21]
Amino Acid Absorption Wavelength (nm) Fluorescence Wavelength (nm) Quantum Yield Tryptophan 280 348 0.20 Tyrosine 274 303 0.14 Phenylalanine 257 282 0.04 and phenylalanine and looking at Table 1.1 tryptophan also has a larger fluorescence quantum yield (ratio of the number of photons emitted to the number of photons absorbed) than either tyrosine or phenylalanine. Typically, tyrosine fluorescence is quenched in the presence of tryp- tophan via resonance energy transfer [21]. Phenylalanine is weakly fluorescent and can only be detected if tryptophan and tyrosine are not present. Therefore, the ideal amino acid in terms of
fluorescence is tryptophan.
For proteins the choices are narrowed down to those that contain tryptophan or that can be labeled with an exogenous fluorescent probe. One such example of a strongly fluorescent tryptophan-containing protein is avidin. Avidin is a basic glycoprotein found in egg-white and contains 16 tryptophan residues per protein molecule [22]. The tetrameric form of avidin has CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 10 been found to have a molecular weight of 66-69kDa (1Da= 1.66 × 10−27kg), which would make the hydrodynamic radius of a tetrameric avidin protein 2.7nm [23]. This protein can be purchased as avidin-coated polystyrene spheres which exhibit much more fluorescence than tryptophan alone and are readily available. However, the synthetic spheres may not be the model of choice because they do not represent a protein in its natural state. Another fluorescent tryptophan-containing protein is hemocyanin. A readily available form of hemocyanin (Hc), is keyhole limpet hemocyanin (KLH). KLH is a very large protein and can exist in various unit sizes including decamers, multidecamers, flexible tubules of varying length and if prepared correctly it is able to dissociate into subunits [24]. Decamers have an approximate molecu- lar weight of 5×106Da which corresponds to a hydrodynamic radius of 11nm while multide- camers can have molecular weights up to 15×106Da or a hydrodynamic radius of approximately
16nm [25]. KLH is an oxygen-carrying protein that contains 148 tryptophan residues per protein
and is found in the hemolymph of the giant keyhole limpet, Megathura crenulata, that lives off
the coast of California [24, 26]. One final protein that should be mentioned because of its wide
use in fluorescence studies is green fluorescent protein (GFP). GFP fluorescence does not origi-
nate from tryptophan but rather from an internal 4-(p-hydroxybenzylidene)-imidazolidin-5-one
structure [27]. GFP and its various mutants have been used with FCS to study a wide range
of intracellular processes both in vitro and in vivo [28]. GFP is unique in that its fluorescence
does not require any cofactors or substrates, fusion of GFP to another protein does not affect the
protein’s activity or mobility, it’s nontoxic, resistant to heat, alkaline pH, photobleaching, and
salts [29].
1.6 Previous Work
Initial studies aimed at understanding cluster growth in aqueous sugar solutions using DLS
were conducted by Dr. David Sidebottom and Tri Tran. Their results suggested that sugars
(glucose, maltose, and sucrose were used) form clusters at any concentration level, even those
too dilute for vitrification to occur. They concluded that proteins, which interact via hydrogen
bonding, would only promote the cluster formation because they would serve as a nucleation
site and thus the results were supportive of the water replacement model [30]. Studies were
continued by Yuli Wang using FCS and DLS to monitor the hydrodynamic radius of avidin-
coated polystyrene spheres in sugar solutions. These studies found that FCS and DLS showed CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 11 inconsistent trends for the hydrodynamic radius as a function of sugar concentration. DLS data showed an invariant hydrodynamic radius with increasing sugar concentration while FCS data indicated a decreasing trend of the hydrodynamic radius with increasing concentrations of glucose, maltose, and raffinose.
Figure 1.7: The hydrodynamic radius of avidin-coated polystyrene spheres in glucose, maltose, and raf- finose solutions as a function of sugar concentration. DLS data shows no variation with increasing sugar concentration. FCS data shows the hydrodynamic radius decreases with increasing sugar concentration. (Adapted from [18])
As a result of the trends found in Figure 1.7 it is obvious that further investigation into the effect of sugar on the hydrodynamic radius of proteins is necessary. From water replacement theory we expect that sugar molecules bind to the outside of the protein. Therefore, by measur- ing the size of the protein before and after the addition of glucose we would be able to verify if water replacement is actually occuring. In the experiment described in the following chapters, the hydrodynamic radius of the Hc protein was measured as a function of glucose concentra- tion. FCS was used to determine the hydrodynamic radius of the Hc protein with and without glucose and DLS was utilized to verify the size of the Hc protein in solution. If vitrification was occuring instead of water replacement glucose would not bind to the outside of the Hc protein CHAPTER 1. CRYOPRESERVATION AND MOTIVATIONS 12 and therefore there would be no change in the protein’s hydrodynamic radius.
1.7 Conclusion
By gaining a deeper understanding of the cryoprotective mechanisms of glucose on proteins at a molecular level, advancements in organ preservation, human reproductive medicine, and the conservation of endangered species can be made. Two prominent theories explaining the protective effects of glucose on proteins are the vitrification theory and the water replacement theory. The experiments presented herein focus on testing the water replacement theory which states that water surrounding proteins is replaced by glucose and this sugar coating protects the protein from denaturing. The details of our methods to verify the water replacement model will be presented in the subsequent chapter. Chapter 2
Optical Techniques to Evaluate the Water Replacement Model
The importance of studying the molecular mechanisms of cryopreservation, current preserving methods, and two competing theories describing these molecular mechanisms have been de- scribed in Chapter 1. It is now a question of the method to test the water replacement model and the best techniques for this analysis. The following discussion will help build the proper foundation for understanding the experiment and the results obtained by it.
2.1 Verifying the Water Replacement Model
The purpose of this study is to test the water replacement model of cryopreservation. The water replacement model states that the mechanism behind the protection of a protein during cryopreservation is the replacement of the hydrogen bonded water-protein interaction with a sugar-protein hydrogen bond [19]. Sugar coats the outside of the protein and protects it from the denaturing pH fluctuations due to selective precipitation of buffer salts. This sugar coating much like the candy shell of an M & M®, adds a thin layer of protection. Previous work done at a temperature of 20◦ C has shown that sugars form clusters at all concentrations [30]. Since
sugars form clusters near room temperature one would also expect them to cluster and form a
coating around proteins near room temperature. If we were able to measure the size of a protein
in solution with and without glucose we would be able to verify that this coating exists and prove
the water replacement model. The coating thickness on an M & M® could be easily measured
with a good set of calipers but the glucose layer on the outside of a protein is at least 6 orders of
13 CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL14 magnitude smaller and therefore we need a technique that is able to measure single molecules.
One such technique is fluorescence correlation spectroscopy (FCS).
2.2 Fluorescence Correlation Spectroscopy (FCS)
FCS was originally developed by Magde, Elson, and Webb in 1972 as a new form of relaxation analysis [31]. FCS is a high-resolution optical technique which utilizes fluctuations in fluo- rescence intensity to gain information about the random movement (diffusion) of fluorescent particles in solution [32]. When light of a particular wavelength is absorbed by a fluorophore it moves into a higher energy electronic excited state and then eventually returns to the ground state and may emit light. The light emitted as the particle returns to the ground state is known as fluorescence [33]. In the simplest case, fluorescence intensity fluctuates due to Brownian motion of the particles and it fluctuates around an average background value. The movement of these particles occurs in a very small volume of focused laser light.
Figure 2.1: Fluorophores diffusing through the focal volume fluoresce (A) and produce intensity fluc- tuations (B) as they enter and leave the focal volume. These fluctuations are then utilized to produce a correlation function (C).
Let us consider a single particle diffusing into the focal volume. As the particle enters CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL15 it absorbs the laser light and then fluoresces, contributing to the fluorescence intensity signal.
When the particle moves out of the focal volume the fluorescence intensity drops. An illustration of the focal volume and a diffusing particle is given in Figure 2.1 (A). Fluorescence intensity
fluctuations, which can be seen in Figure 2.1 (B), reveal when a particle enters and exits the focal volume. These intensity spikes are used to calculate the average intensity for the entire time trace and also the fluctuations of that intensity from the average. Fluorescence intensity fluctuations are analyzed by looking at the fluctuations at some initial time (τ1) and then at some time later (τ2). By comparing the fluorescence fluctuations the correlation function is determined, from which diffusion parameters can be measured. An example correlation function is given by
Figure 2.1 (C).
Fluorescent proteins are one type of fluorophore that can be analyzed with FCS. The analysis of proteins with FCS will give the average number of fluorescent proteins in the focal volume and the average diffusion time, which is the time it takes for the protein to pass through the volume that is being observed. More in-depth analysis will yield the concentration and the size of the protein. When glucose is added to the protein solution, assuming glucose binding occurs, the effective size of the protein increases as a result of the glucose layer and the viscosity of the solution increases. Both of these events would cause slower protein diffusion and increase the diffusion time through the focal volume.
2.2.1 Multiphoton Excitation
As fluorescent molecules (in this case proteins) enter the focal volume they absorb a photon of the required energy to boost them into an excited state and then emit fluorescence as they fall back down to their ground state. Another method to get these fluorescent proteins to reach an excited state is by simultaneously absorbing two photons, each containing half of the required energy to reach the excited state. The excitation of a molecule by simultaneous absorption of two photons was predicted by Maria Göppert-Mayer in 1931 [34]. Thirty years later, in 1961,
2+ her prediction was verified by a group at Bell Telephone Laboratories using a CaF2:Eu crys- tal [35]. This excitation process (2PE) occurs by two photons simultaneously (within 10−16s) exciting the molecule to a virtual intermediate state and to its final state [36]. This process is shown in Figure 2.2.
The probability of an absorption process occurring is defined by the absorption cross-section. CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL16
Figure 2.2: Schematic representation of the 2PE process. Two excitation photons γ1 and γ2 each con- taining half the required energy must simultaneously excite the molecule to an electronic excited state. Vibrational relaxation occurs where some of the excitation energy is transferred to other vibrational modes as kinetic energy. As the molecule returns to the ground state it can emit a fluorescence photon (γ3).
The two-photon absorption cross-section (σ2) for L-tryptophan has been measured to be
−50 cm4s 32.0mGM±1.2mGM (1GM= 10 photon ) at 532 nm [37]. This cross-section is an important parameter when estimating the fluorescence of the system. An approximation of the average
fluorescence for a 2PE diffraction-limited focus is given by Equation 2.1 [36],
1 8.8 < P (t) >2 < F (t) >≈ g(2)φηCσ n , (2.1) 2 2 0 πλ where g(2) = 1 for a CW laser, φ is the collection efficiency, η is the fluorescence quantum
efficiency (for L-tryptophan η=0.20), C is the concentration, σ2 is the two-photon absorption
cross-section, n0 is solution’s index of refraction, < P (t) > is the average excitation power and λ is wavelength of excitation light. Equation 2.1 indicates that < F (t) > is proportional
to < P (t) >2. This quadratic dependence is a defining characteristic of 2PE and like most
nonlinear processes 2PE requires high intensities, usually 1020 to 1030photons/(cm2s) to achieve
two-photon absorption [36]. As a result of the necessity for high intensities 2PE only occurs in
the very small and well-defined focus of a high NA lens. CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL17
Theoretical Focal Volume
The high NA lens focuses the laser beam (directed along the optical z-axis) down to a well- defined high intensity focus at the focal volume where 2PE occurs and where the image plane
(x-y plane) is located at the sample. Since we are using 2PE the squared illumination point spread function IPSF2 is used to describe the intensity distribution everywhere in space near the focus. Lateral (x) and axial (z) views of the IPSF2 are given in Figures 2.3 (a) and (b).
Figure 2.3: (a) Lateral (x) and axial (z) views of IPSF2 which theoretically describes the 2PE volume. (b) Axial (z) profile of IPSF2 (solid red line) with a Gaussian function overlayed (dashed black line). Adapted from [38].
As can be seen from Figure 2.3 (b) the IPSF2 (solid red line) fits a Gaussian function profile
(dashed black line). Using the work of [38] we can estimate the lateral (ωxy) and axial (ωz) 1/e radii of the IPSF2. For NA>0.7, these equations turn out to be given by [38]
0.325λ ωxy = √ , and (2.2) 2NA0.91
" # 0.532λ 1 ωz = √ p . (2.3) 2 n − n2 − NA2 CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL18
Our experimental setup has a laser with a wavelength of λ = 0.532µm, an objective with nu- merical aperature (NA =1.15), and buffer solution with index of refraction n=1.33. Using these values and Equations 2.2 and 2.3 we obtain values of ωxy = 0.108µm and ωz = 0.302µm. The excitation volume can be approximated by integrating the three-dimensional Gaussian over all space, which yields
3 2 VTPE = π 2 ωxyωz. (2.4)
Equation 2.4 is a good approximation of the IPSF2 but results in a value 68% of that found by a more comprehensive numerical integration [38]. Therefore, in order to make a more accurate theoretical determination of the size of our focal volume let’s take into account that equation
2.4 is only 68% of what it truely should be,
V V = TPE (2.5) Corrected 0.68
.
If we insert our values for ωxy and ωz into Equation 2.5 then we obtain a result of VCorrected = 0.0288µm3 = 0.0288fL. This value is the theoretical focal volume size given the parameters of our setup. It should be noted that this is an ideal value given a perfectly aligned laser without any optical aberations.
2.2.2 Diffusion
Determining the size of the focal volume is very important to the discussion because the fluores- cent proteins are undergoing diffusion in solution and therefore the larger the focal volume the longer it will take for them to diffuse from one side to the other. The theory of Brownian motion presented by Einstein in one of his famous 1905 papers [39] explains the mechanisms behind the movement of particles near thermal equilibrium. One of the most important properties of a diffusing particle is its diffusion coefficient (D) which contains information about the size and mass of the particle. Effectively, D determines how far a particle will move in solution due to the random walk of diffusion. For example, a protein in water will take a random walk because of a series of small collisions with water molecules. As a result each particle will have a random trajectory, ~r(t). As D increases, the speed, |v(t)|, of the particle increases. The particle’s path may be described by its mean squared displacement (MSD) < r2 >, which gives the area the CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL19 particle will cover in some time. The MSD is given by the following equation,
< r2 >= 6Dτ. (2.6)
Along with Einstein’s explanation of the microscopic mechanisms behind Brownian motion, he also derived a relation that relates D to the properties of the particles and the solution that they move in,
k T D = B . (2.7) 6πηRh
−23 2 −2 −1 Equation 2.7 is known as the Stokes-Einstein equation, where kB = 1.38×10 m kg s K is Boltzmann’s constant, T is the absolute temperature, η is the viscosity of the solution and Rh is the radius of a sphere that would have the same D as the molecule undergoing Brownian motion. The hydrodynamic radius (Rh) will be slightly larger than the true radius of the sphere because D also includes the effects of the solvent molecules being dragged along with the molecule of interest [40].
2.2.3 Particle Fluctuations
In FCS, particles in solution are diffusing in and out of the observation volume where the laser light is exciting them. Fluorescence intensity peaks while the molecules are in the focal volume and decreases when the molecule leaves the focal volume. Therefore, in FCS fluorescence
fluctuations are measured and used to determine the diffusion time of the particle. We can split up the total fluorescence intensity F (t) into two components,
F (t) =< F > +δF (t), (2.8) where < F > is the average fluorescence intensity of the fluorophores in the focal volume and
δF (t) are the fluorescence intensity fluctuations [40]. For FCS analysis, the fluctuations δF (t) are what we are interested in. The fluorescence intensity trace in Figure 2.4 shows what a typical set of fluctuations might look like.
Fluctuations (δF (t)) are centered about the average fluorescence intensity (< F >). The total fluorescence intensity F (t) is proportional to the total number of particles N(t) in the focal volume [40]. Therefore, the greater the intensity, the more particles are being excited. Informa- CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL20
Figure 2.4: Fluorescence intensity trace showing the fluctuations of Hc entering and leaving the focal volume. δF (t) represents the fluctuations (dotted green line) about the average intensity < F (t) > (solid green line). Data is from a 600s run of 50nM Hc solution.
tion about the movement of molecules is collected by analyzing the fluctuations in fluorescence
intensity δF (t) which correspond to fluctuations in the number of particles in the focal volume
δN(t). Since we would like to gain information about the movement of single particles we have
to be able to detect single particle fluctuations where δN(t) = 1. Imagine being at a rock con-
cert with thousands of people and trying to determine if your friend was in the venue or outside
waiting to buy tickets. Unless you text or call him it would be next to impossible to know if
he was inside. Now imagine sitting in your car waiting to pick up your friend at their home.
In this case it would be very obvious if they got into or out of your car. This basic principle is
fundamental for FCS to detect single molecules. If there are only a few particles (small N(t))
in our small focal volume then it will be easy to detect one particle moving in or out. However,
as the average number of particles < N > or our focal volume increases it becomes more and
more difficult to be able to observe the fluctuation associated with a single particle moving into
and then out of the focal volume. Modern implementations of FCS using high NA objectives
(NA> 0.9) focus excitation light to a diffraction limited spot resulting in a focal volume of
approximately 0.0288µm3 = 0.0288fL for a NA=1.15 [38, 41]. Assuming that we would like
to detect a single molecule in the focal volume we can estimate the concentration needed to CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL21 achieve this condition. The concentration given by Equation 2.9 reveals that we should expect to be in the nM range.
1molecule 1mole = 5.77 × 10−8M = 57.7nM (2.9) 2.88 × 10−17L 6.022 × 1023molecules
2.2.4 FCS Design
Figure 2.5: Schematic diagram of the 2-photon FCS setup. Laser light (green) reflects off the dichroic mirror and fluorescent light (purple) transmits through the dichroic mirror.
In the schematic diagram of Figure 2.5 laser light from a continuous wave (CW) laser at
λ = 532nm (VerdiTM V-5, Coherent®, Santa Clara, CA) is sent through a beam expander to increase the beam diameter and to “overfill" the back aperature of the objective. Then the beam is reflected by a short pass dichroic mirror (485dcsp, Chroma Technology Corp, Bellows Falls,
VT). The dichroic mirror has a high reflectivity for wavelengths above 485nm and high transmis- sion for wavelengths below 485nm [18]. Our laser light at 532nm is therefore reflected upwards to the high numerical aperature water immersion objective (UAPO 340 40/1.15W, Olympus, CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL22
Center Valley, PA). The objective focuses light through a low UV emission fused silica cover slip (R425000, Bioindustrial Products, Universal City, TX) and into the sample solution. Flu- orescence from the sample is collected by the objective and passes through the dichroic mirror and into a series of filters. A single-band bandpass filter (357/44 Brightline®, Semrock Inc.,
Rochester, NY) and two colored glass uv transmitting filters (FGUV11, Thorlabs Inc., New- ton, NJ) helps to isolate the peak emission spectrum of L-tryptophan. A plano-convex uv lens
(LA4052, Thorlabs Inc., Newton, NJ) focuses fluorescence light onto a channel photomultiplier tube (C983P CPM, Perkin Elmer Inc., Waltham, MA).
2.2.5 Filter Set
Figure 2.6: Plot of the system transmission spectrum (left axis, black dashed line) and the L-tryptophan fluorescence intensity (right axis, blue solid line). The transmission at the laser excitation wave- length is approximately 3.69×10−17 while at the L-tryptophan emission peak of 355 nm transmission is 8.08×10−2.
Figure 2.6 plots the transmission spectrum (black) for fluorescence of all optical elements in the FCS setup, the fluorescence emission spectrum of L-tryptophan (blue), and the laser ex- citation light source (green). Knowing the transmission curve of each optical element and the
fluorescence spectrum of L-tryptophan we can calculate the percent of L-tryptophan fluores- CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL23 cence transmitted to the PMT,
R T(λ)F(λ)dλ %collected = × 100. (2.10) R F(λ)dλ
In Equation 2.10, T (λ) is the transmittance at wavelength λ and F (λ) is the fluorescence at wavelength λ. The result gives a value of 3.9% of L-tryptophan emission is incident on the detector. L-tryptophan’s emission peak is within the pass band of the filter set and it is easily transmitted. The PMT has a quantum efficiency of 20% at 350nm and thus the total amount of L-tryptophan fluorescence collected is 0.8%. Laser excitation light on the other hand is maximally blocked. Assuming a scattered laser power is 1.00W at 532nm there would be about
18 photons 2.7×10 s being emitted into the filter set. Given the transmission of the filter set at −17 photons 532nm to be 3.69×10 there are 100 s incident on the detector from the laser source. The quantum efficiency of the PMT at 532nm is about 8% therefore the expected contribution to background from the laser source should be about 8Hz. During the experiments, background count rates at 1.00W with buffer typically were 12Hz.
2.2.6 FCS Correlation Function
It has been discussed previously that molecules diffusing through the focal volume create fluo- rescence intensity fluctuations. These fluorescence intensity fluctuations however do not directly provide information about the diffusion parameters of the molecules. In order to extract infor- mation from the fluorescence intensity given by Figure 2.4 we must use a method known as autocorrelation analysis in which a special electronic card, known as a “correlator" calculates the autocorrelation function G(∆t) from the fluorescence intensity signal F (t) [40]. Mathemat-
ically, G(∆t) is given by the equation:
< F (t) · F (t + ∆t) > G(∆t) = . (2.11) < F >2
Conceptually, Equation 2.11 is the correlation (relationship) between the fluorescence intensity at some initial time t with the fluorescence intensity after a delay of ∆t. The autocorrelation
function is built upon the understanding that the fluorescence intensity at time t and at time
t + ∆t is correlated given a small enough value of ∆t.
An important property of randomly distributed processes, including diffusion, is that the
average of the square of the fluctuations in a parameter, let us call this parameter N, is equal to CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL24 the average of that parameter < N > [42]. This concept is shown by Equation 2.12.
< (δN)2 >=< N > (2.12)
Since N is proportional to the concentration C and the fluorescence intensity F , it follows that
< (δN)2 > < (δC)2 > < (δF )2 > 1 = = = . (2.13) < N >2 < C >2 < F >2 < N >
It is important to note that when ∆t = 0 Equation 2.11 becomes
< F (t) · F (t) > < F 2 > G(0) = = . (2.14) < F >2 < F >2
By substituting Equation 2.8 into the < F 2 > term in equation 2.14 we can come up with a new equation that gives the autocorrelation (when ∆t = 0) in terms of fluorescence intensity
fluctuations δF and the fluorescence intensity F .
2 < δF > < (δF )2 > G(0) = 1 + + (2.15) < F > < F >2
Recognizing that random processes have equal deviations above and below the mean we can
2<δF > <(δF )2> see that the
1 G(0) = 1 + . (2.16) < N >
A simple example of a correlation function taken from a solution of avidin-coated polystyrene spheres in buffer is given in Figure 2.7. The green line corresponds to the diffusion time (τD) for the particle in question. From Equation 2.16 we know that the amplitude of G(∆t) gives us
the concentration of the solution.
Physical and chemical changes in the molecules during FCS measurements can be complex
and the resulting fluorescence intensity and autocorrelations may need to be modified to ac-
count for this behavior. Three different models were fit to the data sets that will be presented in
Chapter 4 and the criteria for model selection were given by FCSXpertTM [42]. The process for CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL25
Figure 2.7: An example of a correlation function graph for FCS. Data taken from a 10nM solution of avidin spheres in buffer. model selection begins by fitting the data to the model with the fewest parameters (one compo- nent), examining the fit and the residuals, asking if the result makes physical sense, looking at
2 the goodness of fit quantitatively (χυ), and then repeating for a more complex model to see if these criteria improve in a statistically meaningful way.
Equation 2.17 describes diffusion of one size of protein in solution,
2 1 t −1 k t − 1 G(t) = 1 + (1 + ) (1 + ) 2 . (2.17) N1 τ1 τ1
The 1-component 3-D diffusion model assumes that the solution is homogeneous with the same monomers or multimers of the protein. In this case, N1 gives the number of fluorescing proteins in the focal volume, τ1 is the average diffusion time for a protein to diffuse across the focal volume, and k = ωxy is the lateral-to-axial aspect ratio of the focal volume. ωz Another appropriate model is the 1-component 3-D diffusion with system correction model which also takes into account possible rotational diffusion rates and afterpulsing [42],
2 −t 1 t −1 k t − 1 G(t) = 1 + (1 + Ae τc ) (1 + ) (1 + ) 2 . (2.18) N1 τ1 τ1 CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL26
These phenomena are described by an additional simple exponential function that is added to the 1-component 3-D diffusion model. In Equation 2.18, A is a correction coefficient and τc is the correlation time for these phenomena.
The last fitting model used was the 2-component 3-D diffusion model given by
2 2 1 t −1 k t − 1 1 t −1 k t − 1 G(t) = 1 + (1 + ) (1 + ) 2 + (1 + ) (1 + ) 2 . (2.19) N1 τ1 τ1 N2 τ2 τ2
This model assumes that there are two different types of aggregates (either monomers or multi- mers) of different sizes and that they will have two different diffusion times τ1 and τ2 and two
different concentrations N1 and N2, respectively [42]. Adjusting the fitting model can help to correctly account for molecular aggregation, rotational fluctuations, and afterpulsing [32].
2.2.7 Photobleaching
The high excitation intensities in the focal volume required by 2PE can cause fluorescent molecules
to undergo photochemical reactions that leave them nonfluorescent [32]. This process is known
as photobleaching and it is a limiting factor for all fluorescence studies. Photobleaching is char-
acterized by decreasing fluorescence intensity and shortening diffusion times [32]. In FCS it
is crucial to maximize the number of fluorescence photons emitted by molecules in order to
obtain an optimal S/N ratio. However, when striving for these optimal S/N ratios it is important
to note that increasing the excitation intensity may lead to photobleaching [43]. A useful mea-
surement that helps to determine optimal excitation intensity without photobleaching is to plot
a molecule’s fluorescence intensity vs the excitation power. This plot allows one to identify the
presence of photobleaching because above a certain excitation power the fluorescence intensity
will cease to follow the quadratic dependence that identifies 2PE [32]. A fluorescence intensity
vs excitation power plot will be presented in Section 4.1.1.
2.3 Dynamic Light Scattering (DLS)
The second technique that was used in this study to verify the hydrodynamic radius of Hc
in buffer was DLS. DLS is a laser light scattering technique which can measure the size of
particles in the sub-micron region [44]. One common application of DLS is particle size de-
termination of molecules undergoing Brownian diffusion in solution [45]. As discussed earlier CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL27
Brownian motion is the result of the random movement of particles caused by collisions with the solvent molecules of the solution. The larger the particle the less it will be effected by the solvent “kicks” and the slower it will move. Similar to FCS, the measured quantity that gives us information about the Brownian motion of a molecule is the diffusion coefficient, D.
In order to measure the diffusion coefficient, DLS uses information obtained by scattering laser light from a sample solution and then uses a photomultiplier tube (PMT) to collect the scattered light. The setup for a typical DLS experiment is given in Figure 2.8.
Figure 2.8: A typical DLS setup. Incident laser light scatters off of the sample particles (red) and scattered light exits at 90◦ with respect to incident light, through a collection lens, into a small aperature and then into a photomultiplier tube (PMT).
An incident source of monochromatic laser light (with incident wave vector k~i) is focused with a lens into a small vial of sample solution. Incident light then scatters isotropically in all directions. Scattered light (with scattered wave vector k~s) is focused with a collection lens onto a pinhole (50 µm diameter) and collected by a detector (PMT) [18]. Similar to FCS, the intensity of the scattered light is measured and then used to produce an autocorrelation function.
However, first it is important to discuss the light scattering process in order to understand the signal that is collected.
2.3.1 Rayleigh Scattering
When the protein scattering the light is much smaller than the wavelength of the incident light
λ (dprotein ≤ 10 ) then Rayleigh scattering occurs [46]. This type of scattering is isotropic (equal CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL28 in all directions) in the scattering plane. The wavelength of our laser is 532nm which means that our protein diameter should be on the order of 53.2nm. The solvent (water) molecules are 0.3nm in diameter and glucose molecules are about 1nm in diameter. Although the small diameter of the solvent and glucose molecules will not contribute much to the scattering intensity it should be noted that the concentration of the molecules should be kept as low as possible in order to keep their contributions to the scattering intensity as low as possible.
The intensity of scattered light for a setup with a coherent laser beam illuminating a liquid solution with small particles is given by [47]
4 6 2 2 c 2π d m − 1 2 Is = I0 (1 + cos (θ)), (2.20) 2r2 λ 2 m2 + 2
where c is the number of particles, d is the particle diameter, m is the refractive index of the
particle with respect to the solution, r is the distance to the particle, λ is the wavelength of
the laser, and θ is the scattering angle. The important piece of information to take away from
6 Equation 2.20 is that Is ∝ d . This result indicates that the larger the particle the greater the intensity of scattered light and therefore the stronger the signal. As a result of this if there is a
mix of small and large particles the large particles will mostly dominate the scattered signal and
the correlation function will reflect a diffusion coefficient related to the larger particle motion.
The three graphs in Figure 2.9 demonstrate this effect with a solution containing both 5nm and
50nm particles. The scattered light intensity of 50 nm particles is 1,000,000 times greater than
that of 5 nm particles. As a result, DLS would not be an appropriate technique for distinguishing
particles that are of similar size in a polydisperse solution because they would have roughly the
same intensity fluctuations.
2.3.2 Interference
Intensity fluctuations are the result of constructive and destructive interference of scattered light
which causes a speckle pattern to form (Figure 2.10C). Dark spots (Figure 2.10A) are where the
phase additions of the scattered light cancel each other out while bright spots are where light
scattered from proteins arrives in phase (Figure 2.10B) and adds constructively. As the pro-
teins undergo Brownian motion the speckle pattern fluctuates as the scatterers move in solution
and change the interference pattern. These fluctuations are what produce the DLS correlation
function. CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL29
Figure 2.9: Graph showing there are the same number of 5nm and 50nm particles in solution (A). Relative intensity graph of particles showing that 50nm particles will scatter 1,000,000 times more light than 5nm particles (B). Adapted from [46].
Figure 2.10: Diagram displaying scattering for constructive interference (A), destructive interference (B) and a typical interference pattern (C). Adapted from [44]. CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL30
2.3.3 DLS Correlation Function
From the fluctuations in scattered light intensity a correlator card (same as for FCS) produces the autocorrelation function for DLS,
< Iq(0)Iq(t) > 2 C(t) = 2 = 1 + Acoh|S(q, t)| . (2.21) < Iq >
Equation 2.21 is known as the Siegert relationship and it is what makes DLS a useful technique for monitoring slow dynamics [45]. If we remember the FCS autocorrelation function from
Equation 2.11 in Section 2.2.6 it looks very similar. The only real difference is the origin of the intensity fluctuations. In Equation 2.21, Iq(0) is the scattered intensity at time t = 0 and
Iq(t) is the scattered intensity at time t. The constant Acoh, known as the coherence factor, is determined by the particular experimental setup and determines the S/N ratio. The function
S(q, t) is known as the dynamic structure factor and is given by,
2 S(q, t) = S(q, 0)e−q Dt, (2.22) which represents the interference due to an arbitrary collection of point particles. In Equa- tion 2.22, ~q is the elastic scattering wave vector and D is the diffusion coefficient. The elastic scattering wave vector is given by,
~q = ~ki − ~ks 4πn θ = sin( ), (2.23) λ0 2
where n is the index of refraction of the solution (n ≈ 1.33),λ0 is the wavelength of incident laser light and θ is the scattering angle between ~ki and ~ks. Therefore using Equation 2.21 one can determine D and from there the hydrodynamic radius can be calculated from Equation 2.7.
in DLS is given by
1 τ = . (2.24) DLS Dq2 CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL31
Combining Equations 2.21, 2.22 and 2.24 we have the final form for our correlation function is
−2 t C(t) = 1 + βe τDLS , (2.25)
2 where β = Acoh|S(q, 0)| and τDLS is the characteristic time for DLS given in Equation 2.24. An example of a DLS correlation function is given in Figure 2.11. The black line corresponds to the characteristic time (τDLS). Using Equation 2.24 the diffusion coefficient can be calculated. Figure 2.11 is taken from a solution of 50nM hemocyanin in buffer.
Figure 2.11: DLS correlation function of 50nM hemocyanin protein in buffer.
2.4 Conclusion
In this chapter it has been determined that the water replacement model will be tested by mea- suring the size of a protein before and after the addition of glucose. A suitable technique for this analysis is FCS, which collects information about the diffusion of a protein (including particle size) by correlating the fluorescence intensity signal. In order to confirm our measurements with
FCS another technique, known as DLS, was utilized to measure the size of the protein. DLS CHAPTER 2. OPTICAL TECHNIQUES TO EVALUATE THE WATER REPLACEMENT MODEL32 is a technique that measures the fluctuations in scattered light intensity to build a correlation function which is used to determine the protein size. All of the necessary theory and techniques that must be used in order to verify the water replacement model have been discussed. Chapter 3 will discuss the relevant materials and methods for conducting this type of experiment. Chapter 3
Materials and Methods
Before conducting an FCS experiment careful attention must be given to the equipment available and the subsequent selection of the fluorophore to be used. The fluorophore being excited in all of our measurements is the common amino acid L-tryptophan which is essential in the diet of most animals, including humans [48]. We have used it in our experiment because of its preva- lence in many proteins and because its excitation peak (λ = 278nm) permits 2PE by a 532nm
laser. Three different solutions that contained L-tryptophan have been studied: L-tryptophan in
buffer, avidin-coated polystyrene spheres (also known as avidin spheres), and keyhole limpet
hemocyanin (Hc). The photostability of L-tryptophan in each of the above solutions was dif-
ferent and thus FCS data taken for each was significantly different. DLS was conducted on Hc
at a concentration of 50nM. The purpose of this chapter is to introduce the experimental design
used to test the water replacement model and the materials necessary for this experiment.
3.1 Approach Overview
The overall purpose of this experiment is to determine whether glucose replaces water surround-
ing the protein when it is added to protein solutions. This data was measured by determining
the hydrodynamic radius of hemocyanin protein at varying concentrations of glucose in solu-
tion using FCS. Fluorescence intensity fluctuations were correlated for 600s producing a distinct
correlation function. Diffusion times of hemocyanin were determined by fitting three models to
the FCS curves as discussed in Section 2.2.6 and these were averaged at each concentration of
glucose. Then using Equation 2.7 the hydrodynamic radius of hemocyanin is calculated from
the average diffusion time at each concentration. DLS studies were conducted on solutions of
33 CHAPTER 3. MATERIALS AND METHODS 34 hemocyanin without glucose as a baseline to determine the size of the protein.
3.2 Apparatus
3.2.1 FCS System Preparation
The FCS system (Figure 2.5) was prepared and aligned using two iris diaphrams inserted into the optical path, adjusting the beam until it went throught the center of both. The iris’s were moved and used to check centering at several locations along the optical axis and then the dichroic mirror was adjusted until the beam was centered on the back aperature of the objective. The beam at the focus of the objective was then checked with a fluorescent slide from Chroma®
(see Appendix A for alignment procedure). The fused silica coverslip was rinsed with Milli-Q® ultrapure water before and after every data run to clean any remaining sample and to remove dust and then the coverslip was dried with Kimwipes®. After being cleaned, 150µL of sample was placed on the coverslip and data collection was started.
3.2.2 DLS System Preparation
Our DLS system (Figure 2.8) was aligned by adjusting the telescope on the PMT to focus the scattered image from the sample onto the pinhole and then by adjusting the entrance lens until the laser was focused at the center of the sample. A test solution of polystyrene spheres was used to calibrate the system. The spheres produced a known scattering intensity and the system was adjusted slightly to obtain the highest scattering intensity. After that the test solution was replaced with a sample of Hc and data collection began.
3.3 Methods
Previously, FCS has been discussed as an appropriate technique for studying the diffusion char- acteristics of Hc in glucose solutions. Obtaining correlations to study these characteristics in- volved a series of careful preparations and procedures that allowed consistent results to be mea- sured. These involved dissolving the Hc in a calcium and magnesium free phosphate buffered saline (CMFPBS) solution (see Appendix B.2), diluting to the desired concentration, sonicating, and finally filtering the sample. DLS did not require any extra sample preparation procedures beyond those associated with FCS. Therefore, any of the preparations in the subsequent sections CHAPTER 3. MATERIALS AND METHODS 35 could be used for either technique.
3.3.1 Solution Preparation
L-tryptophan
A stock solution was made by measuring the required amount of L-tryptophan in a 50mL Falcon test tube and adding 1xCMFPBS to make a concentration of 106nM. Then the tube was warmed in a water bath for 60 minutes at 37◦C until the crystals were completely dissolved. Further dilutions were made from this stock solution for a period of up to a month. Dilutions of the stock solution were made using a serial dilution from 106nM down to 103nM. The method for this
process involved making 10mL dilutions where, for example, one would pipette 1mL of106nM
stock solution and 9mL of 1xCMFPBS into a 15mL BD (Franklin Lakes, NJ) FalconTM tube
and invert until mixed, which would create 10mL of 105nM solution. Then the same process would be repeated using 1mL 105nM and 9mL of 1xCMFPBS which would produce 10mL of
104nM solution.
Avidin spheres
Avidin spheres obtained from InvitrogenTM (Carlsbad, CA) were at a concentration of 470nM and were diluted using 1xCMFPBS to make a stock solution of 47nM to reduce the likelihood of aggregation. Dilutions were made by pipetting the required amount of 1xCMFPBS into a glass vial and then pipetting the stock solution of avidin spheres. For example, to prepare 1000µL of 1nM avidin spheres solution pipette 979µL of 1xCMFPBS and 21µL of 47nM stock into a vial. After pipetting, the vial was capped, inverted until mixed and then the top was wrapped in parafilm and the vial was placed in a sonicator for 60 minutes. Sonication appeared to help alleviate aggregation.
Hemocyanin
Since the molar mass of Hc is not well defined, the upper limit of 7.5×106 Da was taken as the molar mass when diluting to provide a baseline for estimating concentrations [24]. Stock solutions were made at a concentration of 667nM and were prepared by placing Hc crystals in a 15mL BD Tube and then pipetting 1xCMFPBS into the tube and slowly rocking the solution back and forth gently to prevent the formation of bubbles. After Hc is completely dissolved, CHAPTER 3. MATERIALS AND METHODS 36 further dilution is made with 1xCMFPBS (without glucose) for 0wt% glucose data collection and/or with 30wt% glucose in 1xCMFPBS to obtain the desired concentration of glucose and
Hc. Hc concentrations typically produced correlations at concentrations of 100nM, 50nM, and
25nM. After dilution, each sample was sonicated for 5 minutes in a Fisher Scientific FS60H
Ultrasonicator to aid in creating a uniform mixture. Then just before each measurement Hc solutions were filtered with a Millex® 0.45µm HV filter to remove any impurities and large aggregates.
3.3.2 FCS Measurements
Measurement of Fluorescence Intensity Power Law
Conducting fluorescence intensity power law studies is done in order to determine if two-photon excitation is occuring and to investigate the possibility of photobleaching. Solutions of L- tryptophan were investigated and used as a calibration for our system because they proved to be inexpensive, were easy to prepare and remained stable for up to one month. A concentration of
104nM L-tryptophan was made via the serial dilution method described above and then two 30s measurements were made at each laser power setting up to 1.00W.
Measurement of Detection Sensitivity
One easy method for comparing the fluorescence of L-tryptophan, avidin spheres, and Hc in solution is to conduct a detection sensitivity study where the concentration and the laser power are varied for each measurement. Detection sensitivity studies are necessary to investigate the ability of a fluorophore to produce correlations and to compare the relative brightness of dif- ferent solutions. L-tryptophan solutions were made at concentrations of 103 − 106nM, avidin sphere solutions with concentrations from 0.625−10nM and Hc solution concentrations ranged from 1.25 − 150nM. For each concentration two 30s measurements were made at each laser power setting. For example, a solution of 103nM L-tryptophan was pipetted onto the coverslip and measured for 30s at a laser power of 1.00W, then the coverslip was cleaned and another drop of 103nM L-tryptophan was pipetted and measured for 30s at 1.00W. CHAPTER 3. MATERIALS AND METHODS 37
Fluorescence Intensity Calibration Measurement
Calibration of the system was done using 1xCMFPBS and 104nM L-tryptophan. The 1xCMF-
PBS buffer was used to determine the background count rate and the 104nM L-tryptophan gave us a 2-photon absorber to check day-to-day count rate variations and make small adjustments to the optics if necessary. If samples of Hc contained glucose, the glucose-containing buffer background count rate was also measured.
Correlation Measurement
Fluorescence photons were collected by a Perkin Elmer® PMT. The signal was then sent through an amplifier and a TTL device to produce a digital pulse. Then, the pulse was sent into a
Correlator.com® Flex 02 correlator which created an autocorrelation function. Intensity traces
and the correlation functions were recorded by the software provided by the manufacturer. A
typical correlation function and trace intensity are seen in Figure 3.1.
Figure 3.1: Screenshot for a typical FCS data run with 50nM Hc.
The intensity trace in the upper right section shows the fluctuations in the intensity of inci- dent photons recorded by the PMT from the fluorescing Hc in the focal volume. Large spikes CHAPTER 3. MATERIALS AND METHODS 38 are the result of Hc proteins diffusing into the focal volume. Correlation functions correspond- ing to these intensity spikes are on the bottom of the image and they are both identical except for the range of the graphs. Duration times for each of the experiments for 50nM Hc were typically 600s. Theoretically, if compiled for a longer period of time the correlation function would smooth out and become better defined. However, it was found that experiments longer than 600s produced artifacts in the correlation function at long times scales (above 102s).
3.3.3 DLS Measurements
Correlation Measurement
Scattered light was collected by a PMT after being sent through a collection lens and a pinhole.
The signal was then amplified and autocorrelated with the same Correlator.com® Flex 02 cor- relator card that was used for FCS. The scattered light intensity trace and the autocorrelation function were recorded using software provided by Correlator.com®.
Figure 3.2: Screenshot for a DLS data run with 50nM Hc.
Comparing Figure 3.1 from FCS of 50nM Hc with Figure 3.2 from DLS of 50nM Hc there appear to be several important differences. The intensity trace at the upper right hand corner of CHAPTER 3. MATERIALS AND METHODS 39
Figure 3.1 has a steady baseline with several high intensity peaks corresponding to Hc diffusing into the focal volume while the intensity trace for Figure 3.2 has many peaks corresponding to the many Hc in the volume being monitored in DLS. Another important feature is the correlation function in the bottom left of Figure 3.2 is much smoother and better defined than in Figure 3.1.
This difference is a result of DLS monitoring many particles in a given period of time while FCS only monitors a few in that same time frame. DLS measurements were run for 150s in order to produce correlations.
3.3.4 Data Analysis Procedure
After data has been collected from the correlator card the data was analyzed using either Kaleidagraph® or Origin 9.0®. The first task when obtaining raw correlation data, whether from FCS or DLS, is to decide what data is to be selected for analysis. In FCS we want to limit detector noise, anti-bunching, rotational fluctuations, and triplet states. None of these signals are related to the diffusion of our protein but rather to other physical and photophysical processes outside the scope of this study. The affects of these processes can be limited by only analyzing data for times above 1ms [41]. Figure 3.3 shows the timescales for each process that can be measured with FCS.
Limiting the timescale is an essential step in getting the proper data to fit. Determining a
fitting routine can be somewhat ardous if your data has a low S/N ratio, as is the case with Hc when using FCS. In order to obtain a better quality fit and limit the possibility of the fitting tool
fitting excessively noisy data we weighted each data point by using the inverse of the variance,
1 winstrumental = 2 . (3.1) σi
2 The goodness of fit was determined by the reduced Chi-Square (χυ) fitting statistic,
n 2 1 X (yi − f(xi)) χ2 = = , (3.2) υ υ σ2 i=1 i
2 where n is the number of data points, σi is the variance related to measurement error for yi, yi is the observed mean, and xi is the predicted mean from the model. This quantity tells us how well a given model fits our data set. In this case, υ = n − p − 1 where p is the number of fitting
2 parameters [49]. Equation 3.2 is known as the reduced chi-square statistic. When χυ = 1 the fit 2 is “appropriate", if χυ < 1 we have either over estimated the errors or the data is correlated, and CHAPTER 3. MATERIALS AND METHODS 40
Figure 3.3: Autocorrelation graph showing timescales for various physical and photophysical processes that FCS can measure. Adapted from [41].
2 if χυ > 1 the errors are underestimated or we have chosen a poor model to represent our data. 2 The χυ statistic gives us a more quantitative method of determining if the fit is “appropriate." The results of these fitting routines will be discussed in Chapter 4.
3.4 Conclusion
In this chapter the experimental design used to test the water replacement model and the mate- rials used have been discussed. Solutions of L-tryptophan, avidin spheres and Hc were studied using FCS and DLS. FCS and DLS methods included calibration and correlation measurements.
Additional FCS measurements include checking the power dependence and the detection sen- sitivity to determine extent of 2PE and to investigate if a fluorophore will produce correlations.
Data analysis procedures involve limiting the timescale of the autocorrelation function, fitting
® ® 2 the data with either Kaleidagraph or Origin 9.0 and using χυ to determine the goodness of fit. In Chapter 4, results from these experiments using L-tryptophan, avidin spheres and Hc will be presented and discussed. Chapter 4
Results and Discussion
In this chapter, results from power dependence, detection sensitivity, focal volume, and Hc studies are discussed. Initial studies with L-tryptophan indicated that although it was able to be excited with 2PE the fluorescence intensity was not sufficient to produce correlations. As an alternative, avidin-coated polystyrene spheres were investigated by a previous researcher but results to verify the water replacement model turned out to be inconclusive. As a third option, Hc protein was investigated and used to test the water replacement model as a molecular mechanism for cryopreservation using both FCS and DLS. Calibration of the FCS focal volume was done using the value for the diffusion coefficient of Hc determined from DLS and using the amplitudes of the FCS correlations. In studies without glucose, FCS determined that the hydrodynamic radius of hemocyanin was 40.2nm±3.61nm. DLS obtained a similar result with a hydrodynamic radius of 29.1nm±0.44nm. FCS found that the hydrodynamic radius of Hc was invariant with increasing glucose concentrations of 5wt%, 10wt%, and 20wt%.
4.1 FCS Results
4.1.1 Power Dependence Study
Initial studies of FCS were conducted on L-tryptophan in buffer in order to determine if the
square-law dependence characteristic of two-photon-excited fluorescence was present. A solu-
tion of 104nM L-tryptophan in 1xCMFPBS was tested at varying laser powers (0.20-1.00W)
and the fluorescence intensity was recorded. These intensities at varying laser powers were used
to verify that 2PE was occuring. The equation for Figure 4.1 power vs fluorescence count rate is
given by y = 1.7864(±0.01878)x − 0.46513(±0.00743). In two-photon processes the fluores-
41 CHAPTER 4. RESULTS AND DISCUSSION 42 cence intensity is proportional to the square of the laser power and therefore doubling the excita- tion power quadruples the fluorescence signal. As a result of this dependence we would expect a slope of 2 for Figure 4.1 and although the slope is lower than expected, 1.7864(±0.01878), it still indicates that 2PE is occurring.
Figure 4.1: CW 2PE of 104nM L-tryptophan in 1xCMFPBS. The equation for the linear fit is y = 2 1.7864(±0.01878)x − 0.46513(±0.00743) with a reduced chi-squared of χυ = 0.94744. The slope of 1.7864 verifies the quadratic dependence of intensity on laser power which is characteristic of 2PE.
4.1.2 Detection Sensitivity Study
Besides achieving 2PE of L-tryptophan, a study comparing the relative brightness of each of our solutions was useful to determine the sensitivity of our system to each solution. With this, we can predict whether or not it will be possible to obtain an autocorrelation function. This study also determines how much fluorescence each solution should provide at a given concentration.
L-tryptophan was dissolved in buffer solution at high concentration to achieve intensity data for Figure 4.2; however, as the concentration was lowered the fluorescence intensity of L- tryptophan reached the background count rate before getting anywhere near the range needed for correlation curves to be generated (1 − 100nM). This problem can be seen in Figure 4.2 where CHAPTER 4. RESULTS AND DISCUSSION 43
Figure 4.2: Fluorescence Intensity vs Concentration plot for L-tryptophan, avidin spheres, and hemo- cyanin. Each solution was prepared in 1xCMFPBS and then run at varying excitation intensities [red= 1.00W, blue= 0.80W, green=0.60W, black=0.40W and purple=0.20W]. Avidin spheres are 100 times brighter than hemocyanin and hemocyanin is 1000 times brighter than L-tryptophan. a power of 1.00W (typical power level to obtain correlations) the intensity of L-tryptophan is far below background (due to detector noise and stray excitation light) at a concentration of
100nM. Correlations are a result of fluorescence intensity fluctuations and in order to produce these fluctuations, as discussed in Section 2.2.3, the solutions need to be dilute (< 100nM) and bright enough to be seen above background intensity fluctuations. L-tryptophan does not emit enough fluorescence intensity below 100nM to be distinguished from background effects and therefore would not produce a correlation. As a result of the low count rate (intensity) of
L-tryptophan in buffer, avidin spheres were investigated as an alternative.
Since avidin-coated spheres have 340 L-tryptophans per sphere one might expect avidin spheres to be about 340 (2 to 3 orders of magnitude) times brighter than L-tryptophan at the same concentration. However, as shown in Figure 4.2, avidin spheres are about 100, 000 times brighter than L-tryptophan in buffer. This large difference is due to the increased photostability of L-tryptophan in avidin. One L-tryptophan in buffer emits only 2 photons before photobleach- ing while an L-tryptophan residue in avidin immobilized on a polystyrene sphere emits 180 CHAPTER 4. RESULTS AND DISCUSSION 44 photons before photobleaching [26]. Since avidin-coated polystyrene spheres do not represent a protein in its natural state, Hc protein was investigated.
We would expect Hc to be about half as bright as avidin spheres however once again by looking at Figure 4.2 we see Hc is about 100 times dimmer than avidin spheres but still 1000 times brighter than L-tryptophan in buffer. This effect is once again a result of the number of
L-tryptophan residues per protein and the photostability of L-tryptophan in each environment.
Hc has a low count rate per Hc protein (4 − 5 counts) before photobleaching in buffer [26].
However, we can see that correlations with Hc should be possible since Figure 4.2 shows that at concentrations of 1 − 100nM (where FCS can be used) the fluorescence intensity is above background. The 50nM Hc was selected to be used for extensive study with glucose solutions because of its more consistent correlations (compared to 25nM) and higher amplitude (com- pared to 100nM). After selecting 50nM Hc as the ideal concentration, the characteristics of the experimental focal volume must be calculated in order to determine the size of the protein.
4.1.3 Experimental Focal Volume
Calculation of the Aspect Ratio
2 As discussed in Section 3.3.4 an important part of fitting is to minimize χυ as much as possible and in order to do that a study was conducted on the variable k which is the lateral-to-axial aspect ratio of the focal volume. Looking at the correlation Equations 2.17, 2.18, and 2.19 we see that k is a variable in each of them. In this study solutions of 50nM hemocyanin in
2 1xCMFPBS solution were fit with varying values of k between 0 and 1 in order to minimize χυ and thus give the best fit.
2 Figure 4.3 shows a plot of the χυ value of 1-component and 2-component fit models for varying values of the lateral-to-axial aspect ratio (k = ωxy ). The minimum value of χ2 for the ωz υ 2 1-component fit occurs at k = 0.2 however after that point χυ begins to increase again. The 2-component fit has an exponential decrease down to a minimum around k = 1. However, with k = 1, the focal volume becomes a sphere which is not physically realistic because of the nature of the squared illumination point spread function (IPSF2) which defines the light propogating through the high NA objective. Given our equipment, a value of k = 0.356 was calculated from the literature [38]. This value is not only physically realistic but comes close to the experimental
2 value for 1-component fits (that used χυ minimizing to determine the optimal k) of k = 0.20. CHAPTER 4. RESULTS AND DISCUSSION 45
All fits of the FCS correlation functions were therefore done with a fixed value of k = 0.356.
By determining the aspect ratio of the focal volume its size can now be calculated from FCS and DLS data.
2 Figure 4.3: Plot of χυ vs the lateral-to-axial 2PE focal volume aspect ratio, k. The value of k was varied 2 to obtain the lowest value of χυ for both 1-component (black) and 2-component (red) fits to experimental data.
Determination of Focal Volume Size
We have calculated the focal volume for a perfect, theoretical FCS setup with our parameters but experimental conditions can change its size and therefore an experimental value for our focal volume must be determined. The Stoke’s-Einstein diffusion relation for Brownian motion for
DLS [50] is given by,
1 kBT 2 = D = . (4.1) τDLSq 6πηRH
The value q is known as the “elastic scattering wave vector” and is related to the DLS laser and sample setup. For our DLS experiment θ = 90◦, n = 1.33, and λ = 5.32 × 10−7 m.
Using Equation 2.23 q = 2.22 × 107m−1. Equation 4.1 indicates the diffusion coefficient CHAPTER 4. RESULTS AND DISCUSSION 46
D is only dependent on the temperature T , viscosity η, and the hydrodynamic radius RH . It has been assumed that identical Hc sample preparation and ambient conditions will produce identical diffusion coefficients for both DLS and FCS. The diffusion relation for FCS is given by Equation 4.2.
ω2 D = xy (4.2) 4τFCS
If we combine Equations 4.1 and 4.2 we can begin to setup an equation that will allow us to find a value for ωxy.
2 ωxy 1 = 2 (4.3) 4τFCS τDLSq
The values for τFCS and τDLS are obtained by averaging experimental values for the dif- fusion times for each technique for 50nM Hc buffer solutions without glucose. Experimentally obtained values were calculated to be τFCS = 0.051s±0.005s and τDLS = (2.675 ± 0.008) ×
−4 10 s and using the value of q from Equation 2.23 we can calculate ωxy.
r 4τFCS ωxy = 2 τDLSq s (4)(0.051s) = (2.675 × 10−4s)(2.22 × 107m−1)2 = (1.24 ± 0.06) × 10−6m (4.4)
Recalling, that in our case the radial-to-axial aspect ratio is k = ωxy = 0.356 we can ωz calculate ωz.
ω ω = xy z 0.356 1.24 × 10−6m = 0.356 = (3.5 ± 0.2) × 10−6m (4.5)
Now that we have both ωxy and ωz from experimental measurements we can use the cor- rected focal volume Equation 2.5 to calculate our experimental focal volume size. CHAPTER 4. RESULTS AND DISCUSSION 47
3 2 π 2 ω ωz V = xy experimental 0.68 3 −6 2 −6 (π 2 )(1.24 × 10 m) (3.5 × 10 m) = 0.68 = 4.4 × 10−17m3 = 44µm3 = 44fL ± 6fL (4.6)
Comparing the experimental focal volume to our original theoretical calculation in Sec- tion 2.2.1 we see that our experimental focal volume is about 3 orders of magnitude larger than what it would be in the ideal case. Another method for determining the size of the focal volume, assumes a known concentration of Hc and uses the amplitude of the correlation function to cal- culate an effective focal volume. From Equation 2.16 the correlation function at t=0 is related to the average number (
1 1 G(0) = 1 + = 1 + . (4.7) < N > Veff < C >
Assuming that our Hc concentration is fixed at
Veff = 0.9fL±0.1fL. This effective focal volume is much closer to VCorrected = 0.0288fL obtained from the theoretical calculation in Equation 2.5. It should be noted that values for
τFCS, ωxy, ωz, Vexperimental, and V eff were obtained by averaging 15 trials and values for
τDLS were obtained by averaging 3 trials. Error values given for the measurements are the standard error.
4.1.4 Hemocyanin Studies
Now that we have discussed what parameters we fit our data to it is time to look at an example
data set. In Figure 4.4 we have the correlation curve of 50nM Hc without glucose in buffer
solution with our three different fitting models, the intensity trace (which shows the fluorescence
intensity spikes when an Hc protein diffuses through the focal volume), and the residuals which
show how well each model fits the data.
All three fits provide good residuals that oscillate about zero. Physically, the values of τ1 =
0.0582s±0.0013s (1-component), τ1C = 0.0583s±0.0014s (1-component with correction), and CHAPTER 4. RESULTS AND DISCUSSION 48
Figure 4.4: A fluorescence correlation data set for 50nM Hc in buffer solution. Three different models are fit to the curve: 1-component (red), 1-component with system correction (magenta), and 2-component (blue). Standardized residuals for each fit are also given.
2 τ2 = 0.0582s±0.0013s (2-component) are all reasonable values. Therefore, we look at the χυ to determine which model best fits our data. The 1-component 3-D diffusion model gives the
2 2 lowest value of χυ = 2.79 which is the lowest χυ out of the group and it is closest to the ideal 2 value of χυ = 1 (perfect fit). In this example, the 1-component 3-D diffusion model was chosen as the best fit.
2 2 It should be noted that almost all of the χυ values are larger than the ideal value of χυ = 1, which would indicate either that our model does not represent the data or we have underesti-
mated the errors. Since three fit models common to FCS 3-D diffusion were tested and with the
2 poor S/N ratio it is much more likely that these larger χυ values are due to underestimation of the errors rather than faulty models. After fitting all of the data with each of these three models
the 1-component model was chosen as the best to use for the rest of the data analysis because it
2 produced similar χυ values to the 1-component with correction model but was ultimately sim- pler and therefore preferred. The two component model was not suitable for our data because
none of the fits proved to have two distinct diffusion times.
After determining that our FCS setup is collecting two-photon fluorescence from L-tryptopohan CHAPTER 4. RESULTS AND DISCUSSION 49 and determining the size of our focal volume, now correlations of Hc must be taken with and without glucose to test the water replacement theory. All FCS correlations were obtained using collection periods lasting 600s at a laser output power of 1.00W. Examples of typical corre- lations given in Figure 4.5 show that the correlation function (G(t)) shifts to the right with increasing glucose concentration. From our previous discussion, the diffusion time is defined as the time it takes the particle to diffuse across the focal volume and it is typically indicated by the time directly below the inflection point of the correlation curve. Since the curve is shifting to the right we would expect the diffusion time to increase as well.
Figure 4.5: Examples of FCS correlations of Hc in glucose and buffer solutions shown as different colors. The glucose concentrations are 0wt% (black), 5wt% (red), 10wt% (purple), and 20wt% (blue).
In Figure 4.6 the average diffusion time for several trials of Hc is plotted as a function of the wt% of glucose. The diffusion time increases slightly with increasing glucose concentration, which would indicate that the Hc protein is taking longer to diffuse across the focal volume as more glucose is added to the solution. Now at first this might seem like the glucose is attaching to the outside of the protein and that we have verified the water replacement model, however, in order to calculate the hydrodynamic radius, the viscosity η of the solution must also be taken CHAPTER 4. RESULTS AND DISCUSSION 50
Figure 4.6: A plot of the diffusion time (τD) of Hc vs the concentration of glucose in buffer solution. Error bars represent the standard error of at least 7 measurements.
Figure 4.7: Viscosity plot of solution (y-axis) as a function of the concentration of glucose (x-axis). Error bars represent an estimated 10% error in the viscosity measurement. Data obtained from the CRC Handbook [51]. CHAPTER 4. RESULTS AND DISCUSSION 51
Figure 4.8: A plot of the hydrodynamic radius (RH ) vs the concentration of glucose in the Hc protein solution obtained by FCS. The concentration of Hc in each case is 50nM. Error bars represent the standard error in at least 7 measurements. into account. As we can see in Equation 4.8 the hydrodynamic radius depends on both the diffusion time τD and inversely on the viscosity η of the solution,
4kBT τD RH = 2 . (4.8) 6πηwxy
Viscosity as a function of glucose concentration is plotted in Figure 4.7. As the concen- tration of glucose increases the viscosity of the solution increases as well, therefore a change in the diffusion time does not necessarily indicate a change in the hydrodynamic radius. We must therefore look at the values for the hydrodynamic radius at each concentration of glucose to determine the viability of the water replacement model.
As discussed earlier, the water replacement theory, if correct, would suggest that the hydro- dynamic radius of a protein should increase when glucose is added to the solution. The increase in size is due to the replacement of the water surrounding the protein with a layer of glucose molecules. With the additional layer of glucose the effective size of the protein increases and therefore as the concentration of glucose increases, one would expect some increase in the hy- CHAPTER 4. RESULTS AND DISCUSSION 52 drodynamic radius of the protein. A 50nM Hc solution set with 0wt%, 5wt%, 10wt%, and
20wt% glucose were analyzed using 2-photon FCS and the average hydrodynamic radius of Hc as a function of glucose concentration is plotted in Figure 4.8.
Table 4.1: Average Hydrodynamic Radius of Hc from FCS
[Glucose], wt% [Hc], nM Avg. Rh, nm SE, nm 0 50 40.2 3.61 5 50 25.4 3.65 10 50 39.1 4.21 20 50 26.8 2.09
The FCS results for the average hydrodynamic radius of Hc in 0wt%, 5wt%, 10wt%, and
20wt% glucose solutions are summarized in Table 4.1. As can be seen from Figure 4.8 there appears to be no significant trend to the data. The apparent lack of a trend is somewhat muddied by the error in the measurements due to a poor S/N ratio inherent to the Hc’s low count rate per molecule before photobleaching, which is 5 counts per Hc before photobleaching occurs [26].
This low S/N ratio means that the photons being emitted by fluorescence of a particle diffusing into and out of the focal volume are difficult to distinguish from background noise not related to fluorescence.
4.2 DLS Results
In order to verify the hydrodynamic radius of Hc in solution a second study was conducted using Dynamic Light Scattering (DLS). Several concentrations of the protein were used in order to test for the presence of monomers and multimers. Solutions were prepared using the same
Hc preparation procedure as that for FCS measurements except no glucose was added to the solution. Correlation runs were conducted for 200s at a laser output power of 0.70W .
Solutions had protein concentrations of 6.25nM, 12.5nM, 25nM, and 50nM. The correla- tions recorded are shown in Figure 4.9, there appears to be very little change in the correlations other than a slight increase in amplitude as the concentration increases. These correlations show how little noise is associated with DLS because it is a technique that uses “ensemble averaging," unlike the single-particle fluctuations used for FCS. The overlapping correlations of Figure 4.9 would indicate a stable particle size.
The DLS results for the average hydrodynamic radius of Hc for 6.25nM, 12.5nM, 25nM, and
50nM Hc solutions without glucose are summarized in Table 4.2. A graph of the hydrodynamic CHAPTER 4. RESULTS AND DISCUSSION 53
Figure 4.9: DLS correlations of Hc at varying protein concentrations in buffer solution.
Figure 4.10: Verification of the hydrodynamic radius of Hc using DLS. The hydrodynamic radius is plotted (y-axis) as a function of protein concentration (x-axis). All measurements were taken in buffer without glucose. Error bars shown represent the standard error in 3 measurements. CHAPTER 4. RESULTS AND DISCUSSION 54
Table 4.2: Average Hydrodynamic Radius of Hc from DLS
[Glucose], wt% [Hc], nM Avg. Rh, nm SE, nm 0 6.25 36.3 1.85 0 12.5 26.3 0.45 0 25 23.9 0.18 0 50 29.1 0.44 radius (Figure 4.10) indicates that there are some slight discrepancies in the Hc protein size, however, as indicated by the correlations of Figure 4.9 the particle size is stable. The value for 50nM Hc of 29nm from DLS is similar to the value of 40nm obtained from FCS for 50nM solution without glucose. These results indicate that the proteins appear to have a 30-40nm radius in buffer solution.
4.3 Evaluating the Water Replacement Hypothesis
Other studies have found the diffusion coefficient of Hc from the tarantula E. californicum, using
2 2-photon FCS, to be 1.9 × 10−7cm /s [26]. Using the Stoke’s-Einstein relation this works out to give a hydrodynamic radius of 11nm. Additionally, experimenters conducting small-angle x-ray scattering on KLH from the marine gastropod Megathura crenulata have found the radius of gy- ration (typically similar in magnitude to the hydrodynamic radius) to be 163.8Å≈16.38nm [52].
Both studies were conducted at T = 20◦ C in buffer solutions. These values, which appear to be about half of the magnitude of those found from our FCS and DLS studies, might seem to indicate that our Hc solutions are actually homogeneous with Hc dimers, rather than monomers.
However, histogram plots of the FCS (red) and DLS (blue) hydrodynamic radii distributions for
Hc, seen in Figures 4.11 and 4.12 do not indicate the formation of dimers. Figure 4.11 shows a well-defined peak between 30nm-40nm and the DLS results of Figure 4.12 have a definite peak around 30nm. These histograms indicate that our samples are not aggregating because they appear to have one distinct distribution of the Hc protein’s hydrodynamic radius centered around 30nm. It should be noted that Figure 4.11 includes all FCS measurements including those with glucose. Using these measurements with glucose will not change the distribution of aggregates since dimers would show distinct doubling of the hydrodynamic radius from 30nm to 60nm while glucose layering would only increase the hydrodynamic radius by 2nm.
The working hypothesis of this study was that if the water replacement model were a valid mechanism of protein protection during cryopreservation, an increase in the hydrodynamic ra- CHAPTER 4. RESULTS AND DISCUSSION 55
Figure 4.11: Histogram from FCS showing the distribution of the hydrodynamic radius of Hc at all glu- cose concentrations. The peak between 30nm and 40nm indicates no evidence of two distinct distributions of monomers and dimers.
Figure 4.12: Histogram from DLS showing the distribution of the hydrodynamic radius of Hc without glucose. A definite peak at 30nm defines the distribution which indicates the solutions are homogeneous with Hc monomers. CHAPTER 4. RESULTS AND DISCUSSION 56 dius of the Hc protein would occur as a result of the replacement of the hydrogen bonded water- protein interaction with a sugar-protein hydrogen bond. Previous data shown in Figure 1.7 and discussed in Section 1.6 indicated, using FCS, that the hydrodynamic radius of avidin-coated polystyrene spheres decreased with increasing sugar concentration and using DLS indicated an invariant trend in the hydrodynamic radius of avidin-coated polystyrene spheres with increasing sugar concentration. However, the current study conducted using FCS found no change in the hydrodynamic radius of Hc with increasing glucose concentration. Although this would seem to indicate that a glucose layer is not preferentially binding to the outside of the Hc protein, the expected glucose layer around Hc is smaller than the error in the hydrodynamic radius mea- surements for FCS. The expected increase in the hydrodynamic radius of Hc with a glucose layer is 1nm, however the FCS standard error is ±3.61nm. Therefore, the water replacement model cannot be confirmed nor refuted as a possible explanation for the cryoprotective effects of glucose on Hc.
DLS studies were also conducted with Hc in the absence of glucose and they were similar to the results obtained with FCS for Hc without glucose. Using FCS the hydrodynamic radius of Hc was found to be 40.2nm±3.61nm and using DLS a result of 29.1nm±0.44nm was found.
Both of these measurements were taken with 50nM Hc concentrations in the absence of glucose.
Future studies of the hydrodynamic radius of Hc in glucose solutions should look into using
DLS to check if the size of Hc changes with increasing glucose concentration. An important piece of information to remember when conducting that study would be to remember that the intensity of scattered light (Is) is proportional to the concentration of the molecule (c) and its
6 diameter (d) by the relation Is ∝cd . In order to minimize sugar molecule contributions to the scattered light it would be ideal to have low sugar concentrations and high concentrations of large diameter proteins in order to get the highest intensity of scattered light from the proteins.
On the other hand, future FCS experiments should possibly look at a smaller protein than Hc in order to be able to detect a more significant size increase if glucose coats the outside of the protein. Additionally, a recent study [13] using computer simulations has shown that a naturally occuring dissacharide of glucose, trehalose, has an extraordinary ability to protect lysozyme in a manner that resembles the water replacement model but in fact traps a layer of water between the protein and the trehalose protective shell inhibiting both crystallization and keeping the protein hydrated. Therefore, future study of sugar-protein interactions should include trehalose because of its unique promise as a cryopreserving agent. CHAPTER 4. RESULTS AND DISCUSSION 57
Figure 4.13: A plot of the hydrodynamic radius (RH ) vs the concentration of glucose in the Hc protein solution obtained by FCS (red) and DLS (blue). The concentration of Hc in each case is 50nM. Error bars represent the standard error in at least 7 measurements for FCS and 3 measurements for DLS.
4.4 Conclusion
In this report we began by describing our motivation for studying the cryoprotective mechanisms
of sugars on biological molecules as they pertain to the relevant issues of organ preservation,
human reproductive medicine and the conservation of endangered species. The model of cryo-
preservation being tested is the water replacement model which states that as protein-sugar
solutions cool the sugar hydrogen bonds to the outside of the protein, replacing the water and
thus protecting the protein from the denaturing ice formation. This sugar coating could be
monitored by obtaining the size of the protein both with and without sugar in solution. It was
determined that FCS and DLS are suitable techniques for determining the hydrodynamic radius
of our protein.
Nevertheless, the current data appears to show no significant trend of an increasing hydro-
dynamic radius with the addition of glucose at 5wt%, 10wt%, and 20wt%. Additionally, DLS
results agreed with FCS studies on the hydrodynamic radius of Hc in the absence of glucose. Hc CHAPTER 4. RESULTS AND DISCUSSION 58 has proven to be a usable fluorophore for FCS studies and it is also a natural biological protein
(unlike the avidin coated polystyrene spheres), however it is not ideal because of its low S/N ratio and its large size in comparison to glucose molecules. Therefore, a much smaller protein with a higher S/N ratio must be used to test the water replacement model. Green fluorescent protein (GFP) is one such candidate currently being investigated with 2-photon FCS. Bibliography
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Optics Protocols
A.1 FCS Laser Alignment
Getting the FCS setup to function properly requires several optical components being aligned correctly in order to obtain the maximum fluorescence intensity from the fluorophore. In this section, the alignment techniques for FCS are presented. Initially, the laser must be aligned parallel to the table and therefore the height of the laser is checked at several locations along the beam path with a ruler. Adjusting the beam height is done by using at least 2 mirrors to direct the beam. After checking that the height is constant the beam can be aligned further with several mirrors and 2 movable pinholes. The goal is to center the beam through every optical component in the system in order to avoid diffraction effects and to maximize the intensity at the objective’s focus. Alignment starts at the mirror closest to the laser being adjusted until it goes through the center of the first permanent iris. Then the beam is adjusted or “walked" by the next two mirrors until it is centered through 2 movable pinholes. After that the alignment is checked by moving the pinholes onto the beam expander lenses to check to make sure the beam is stable. A final check is made at the objective with a fluorescent slide that reveals if the focus is distorted. Adjustments for the focus of the objective are done with a 90◦ mirror that directs the beam into the objective.
A.2 Cleaning Optical Equipment
All of the optical components of the system (mirrors, lenses, filters and the objective) should be cleaned as often as necessary to keep dust from distorting the beam. The method used to
65 APPENDIX A. OPTICS PROTOCOLS 66
Figure A.1: Photograph of the 2PE FCS system. This setup was used to take FCS data presented in Chapter 4 for L-tryptophan, avidin spheres and Hc. clean requires methanol and lens paper. Several drops of methanol should be placed on the lens paper (while careful attention is paid to avoid contaminating the paper with finger oils) and then the paper should be placed on top of the component being cleaned and gently dragged across several times until the component is clean. By using this non-abrasive method damage to delicate optical components is avoided. Appendix B
Solution Preparation
B.1 Hemocyanin
1. Obtain and label a 15mL BD tube fore each concentration.
2. Measure out 0.0050g of hemocyanin in a 15mL BD tube and then pipette in 1mL of
1xCMFPBS.
(a) Label “667nM Hemocyanin"
3. Slowly and CAREFULLY rock the BD tube back and forth until the hemocyanin crystals
dissolve (≈30 minutes).
4. PRECAUTIONS:
(a) ALL DILUTIONS SHOULD BE MADE IN THE BIO-HOOD WITH CARE TAKEN
TO PREVENT CONTAMINATION (i.e. wear gloves and sterilize anything you
bring into the hood with 70% ethanol).
(b) Immediately prior to pipetting a solution, invert vial 20 times to ensure it is thor-
oughly mixed.
(c) “Rinse" pipette with the solution that you are pipetting 3 times before using. This
helps to dilute possible contaminants in the pipette itself and helps to mix the solu-
tion to be used.
5. Now dilute your stock “667nM Hemocyanin" into the various 15mL BD tubes with
1xCMFPBS to the desired concentrations.
(a) Account for losing 600µL of each solution from filtering (to wet the filter).
6. The dilutions should be made as follows
(a) 100nM dilution (3000µL sample)
67 APPENDIX B. SOLUTION PREPARATION 68
i. Pipette out 4250µL of 1xCMFPBS into a 15mL BD tube.
ii. Pipette 750µL of “667nM Hemocyanin" (after inverting 20 times) and carefully
place into the tube with the 1xCMFPBS.
iii. Slowly invert the tube 20 times for optimal mixing (careful that bubbles do not
form).
(b) 50nM dilution (3000µL sample)
i. Pipette out 3000µL of 1xCMFPBS into a 15mL BD tube.
ii. Pipette 3000µL of “100nM Hemocyanin" (after inverting 20 times) and care-
fully place into the tube with the 1xCMFPBS.
iii. Slowly invert the tube 20 times for optimal mixing (careful that bubbles do not
form).
(c) 25nM dilution (3000µL sample)
i. Pipette out 3000µL of 1xCMFPBS into a 15mL BD tube.
ii. Pipette 3000µL of “50nM Hemocyanin" (after inverting 20 times) and carefully
place into the tube with the 1xCMFPBS.
iii. Slowly invert the tube 20 times for optimal mixing (careful that bubbles do not
form).
(d) 12.5nM dilution (3000µL sample)
i. Pipette out 3000µL of 1xCMFPBS into a 15mL BD tube.
ii. Pipette 3000µL of “25nM Hemocyanin" (after inverting 20 times) and carefully
place into the tube with the 1xCMFPBS.
iii. Slowly invert the tube 20 times for optimal mixing (careful that bubbles do not
form).
7. Now tightly close all of the lids on the samples and wrap the lids with parafilm (in order
to seal out any water).
8. Place samples in the sonicator and set for 5 minutes.
(a) While samples are sonicating find these items:
i. Millex 0.45µm PVDF disposable filters (4x).
ii. Henke Sass Wolf GmbH 1mL NORM-JECT disposable syringes (4x).
9. After taking the samples out of the sonicator begin laser startup and calibration.
10. With the laser ready and calibrated proceed with data collection but remember to complete
the following necessary steps: APPENDIX B. SOLUTION PREPARATION 69
(a) Invert samples carefully 20 times before filtering them for a run (in order to keep
them mixed and homogeneous).
(b) Wet the filter with 600µL of your concentration above a clean beaker.
i. Once the filter is wet push three more drops through.
(c) Place 4 filtered drops onto the quartz coverslip and place the plastic cover over the
objective (BE CAREFUL NOT TO DISTURB THE SLIDE).
i. Do one 10 minute data run per filtering.
ii. Repeat until you are out of sample.
iii. Repeat steps 10(c)i and 10(c)ii for each concentration.
B.2 10xCMFPBS
1. Dissolve the following in 800mL distilled H2O. Contents 1000mL (10x)
NaCl 8g
KCl 0.2g
Na2HPO4 1.44g
KH2PO4 0.24g 2. Adjust pH to 7.4 with HCl.
3. Adjust volume to 1L with distilled H2O. 4. Invert mixture 20 times to mix.
5. Sterilize by autoclaving.
6. This solution must be further diluted to obtain the desired concentration for use as a buffer.
B.3 1xCMFPBS
1. Measure 20mL 10xCMFPBS into a 500mL graduated cylinder.
2. Fill graduated cylinder up to 200mL mark with distilled H2O. 3. Pour contents of graduated cylinder into a 500mL media flask and invert 20 times to mix.
B.4 20wt% glucose 1xCMFPBS
1. Weigh out 10g of glucose.
2. Pour the glucose into a graduated cylinder with 30mL of 1xCMFPBS. APPENDIX B. SOLUTION PREPARATION 70
3. Swirl the graduated cylinder until the glucose has dissolved completely.
4. Add 1xCMFPBS up to the final 50mL mark.
5. This is now a stock 20wt% glucose 1xCMFPBS solution.