Many patterns of Nature are so irregular and fragmented, that, compared with Euclid-- a term used in this work to denote all of standard geometry-- Nature exhibits not simply a higher degree but an altogether different level of complexity.

Benoit Mandelbrot (1987)

The Fractal Geometry of Nature

4.1 Introduction to Fluorescence Spectroscopy

An atomic or molecular species which is capable of absorbing photons of a particular wavelength is called a chromophore. The optical absorption spectrum of a chromophore depends on the energy states available in that particular chromophore, and when an energy difference of DE exists between two states of the species, photons of energy E = DE = hn may be absorbed, where h is Plank's constant, and n is the frequency of the incident photon. Hence, photons of wavelength l = c/n = hc/DE may be absorbed. When the photon is absorbed by a loosely bound p-electron in the molecular cloud, the electron often returns to ground state by reemission of another photon of slightly lower energy some time later. This process is known as optical fluorescence, and is depicted schematically in Figure 4.1. [84]

The emitted photon has energy E = E₂ -E₃ and hence wavelength l = hc/(E₂-E₃ ). Thus, depending on the available energy states of the electron E₂, and E₃ , the photon may be emitted at different wavelengths. The energy levels E₂ and E₃ , in turn depend on the local molecular environment in which the excitable electron exists. Many factors (including pH, temperature, and the presence of other molecules, atoms, or functional groups) influence these energy levels and hence the fluorescence spectrum of a molecule. For this reason, fluorescent molecules, or fluorophores, are an extremely useful class of indicators, since appropriate optical interrogation of these molecules can provide detailed information about the environment in which they reside [84].

Figure 4.1: Jablonski Diagram Depicting the Optical Phenomenon of Fluorescence.

4.2 Fluorescent Metal Ion Indicators

One particularly useful class of fluorescent indicators are the metal ion indicators. These dyes are capable of accurately indicating the presence and concentration of metal ions down to the nanomolar (10^-9 moles per liter) level in aqueous and other solutions [8]. In general, these dyes are chelators which contain one or more aromatic carbon rings with loosely associated p-electrons and an ion binding site of varying specificity. A chelation occurs when finger-like binding sites in the chelator conjugate with the empty outer electron shells of metal ions. The specificity of the chelation site is determined largely by the charge of the bound species and by stereochemistry of the binding site. The presence of a bound metal ion species in the core of such a molecule influences the available energy levels of electrons which are in the vicinity of the metal, and hence the fluorescence spectrum of the molecule. If the binding process is reversible with dissociation constant K_D , then the population of chelated (and hence fluorescently altered) fluorophores will depend on K_D and the concentration of the chelated species. Hence a method of quantification of metal ion concentration exists based on measurement of the fluorescence spectrum of the indicator.

A number of these chelator dyes are available for the sensing of cationic calcium, Ca²⁺ [8]. All of these dyes consist of a multi-ring aromatic fluorophore with a calcium-specific binding site. In general, these dyes may exhibit several fluorescent responses to the binding of calcium including: 1) an increase in a particular fluorescence resonance, 2) a decrease in a particular fluorescence resonance, 3) a shift in the wavelength of the emitted photon, 4) a shift in the wavelength of the excitation photon which is absorbed, or 5) some combination of the above. Table 4.1 below summarizes several commonly used fluorescent dyes.

Table 4.1: Some Common Fluorescent [Ca²⁺ ] Indicators (source: Haughland [8]).

A further advantage of the fluorescent indicators listed in Table 4.1 is that they tend to become compartmentalized either inside or outside of a living cell [8, 85]. This compartmentalization stems from the fact that most of these types of dyes exhibit negatively charged moieties which make them hydrophilic and prevent them from crossing the hydrophobic phospholipid bilayer of the cellular membrane. This exclusion allows for specificity in monitoring both intra- and extra-cellular ion concentrations. Dye indicators which are present in the extracellular fluid stay in the extracellular fluid and provide measures of extracellular ion concentrations, while dye indicators which are internal to the cell (as is the case when they are injected directly into the cytosol) provide ionic concentration measures of intracellular ionic species. This distinction is not as straight-forward with other techniques like quantitative NMR spectroscopy.

A significant advance in the measurement of intracellular ion concentrations is the ability to esterify typical chelator dyes with an acetoxymethyl (AM) ester [85, 8]. This ester, shown below, is attached to the negatively charged hydroxyl sites on the fluorophore via an ester bond. The hydrophobic AM group now allows the fluorophore/AM compound to cross the cellular membrane via passive diffusion. Once inside the cell, however, naturally occurring esterases in the cytosol cleave off the AM portion and again leave exposed negatively charged sites [85]. The indicator is now trapped inside the cell, and if the remaining extracellular dye is washed away, measurement of only intracellular calcium can be made. This process is dubbed AM loading and is depicted schematically in Figure 4.2.

Figure 4.2: Schematic Representation of AM Loading . The cell permeant version of fluo-3 freely crosses the hydrophobic cellular membrane. However, once inside the cytosol, naturally occurring esterases (shaded triangles) cleave off the acetoxymethyl ester and leave the negatively charged fluo-3 molecule trapped inside the cellular compartment.

4.3 Tissue Autofluorescence

In in vivo fluorescence spectroscopy applications, an important source of signal noise and/or interference is autofluorescence. Autofluorescence is the fluorescence of chromophores intrinsic to the sample under study. For in vivo tissue samples, the largest contributors to autofluorescence are the pyridine nucleotides (NAD⁺ and NADH, the oxidized and reduced forms of nicotinamide adenine dinucleotide, NADP⁺ and NADPH, the oxidized and reduced forms of nicotinamide adenine dinucleotide phosphate) and the flavins (FAD and FADH₂ , flavin adenine dinucleotides, FMN and FMNH₂ , flavin mononucleotides) [86]. Of these, by far the most abundant are the pyridine nucleotides.

The concentrations of NAD⁺/NADH and NADP⁺/NADPH should be constant under constant metabolic and tissue oxygenation states and therefore should contribute an autofluorescence spectrum which is constant too. Since this autofluorescence spectrum is constant, it can be corrected for via reference to a simple background spectrum. This technique is rather common in in vivo fluorescence studies, and a popular technique is to fit the background spectrum to a fifth order polynomial and use this for subsequent spectral correction [87].

When the tissue oxygenation state changes, the fluorescence background may change significantly as the tissue concentration of NADH (the primary fluorophore) changes [88, 89]. This will most certainly be the case for our studies since we will be deliberately inducing hypoxic cardiac stress. In this case, there are four readily available solutions to the problem.

First, since simultaneous NMR measurements are being made, we could correlate tissue autofluorescence to NMR measures which correlate to tissue metabolic state in the absence of other (deliberately introduced) fluorophores. Then we can use NMR data and the corresponding recorded autofluorescence spectra to make baseline corrections. Secondly, if fluorescence spectra and not just single wavelength intensity measures are collected, we can use spectral shape identification and/or multivariate calibration methods to extract the desired spectrum and eliminate confounders [90]. Having a priori information about the shapes of the fluorescence spectra of both NADH and our dye will allow us to extract the extent of spectral contribution from each. A third unique feature of the measurements we propose is that while NADH fluorescence may vary along with tissue oxygenation state, intracellular calcium concentration (and hence Ca ²⁺ indicator fluorescence) changes through out a single cardiac cycle. Thus, by changing the gating time of our fluorescence acquisition window, we can measure calcium levels at different times during the cycle. We would then expect for the calcium-indicator fluorescence levels to change, but for the background NADH fluorescence to remain the same. This offers another method to extract signal contributions from our desired variable and could even work with single wavelength recording systems. Finally, the fourth and simplest solution is to avoid autofluorescence to the greatest extent possible and thus minimize its contribution to our signal. NADH is typically monitored by measuring the intensity of its 450 nm emission peak due to 366 nm excitation [88]. In contrast, the dye used in this study, fluo-3, fluoresces at 530 nm when excited at 488 nm [8]. With 488 nm excitation, NADH will not be excited (since this wavelength is longer than its emission wavelength), and autofluorescence will be minimized. In addition, the emission peak of NADH is sufficiently removed from that of fluo-3 that they should not interfere.

4.4 Dye Choice

Table 4.1 lists a number of dyes capable of providing calcium concentration measurements. Of these, fluo-3 was chosen for this study because it offers several advantages over other dyes. Of primary importance is the availability of an AM ester form of the dye. Secondly the excitation wavelength is well into the visible region of the spectrum where sensitive CCD cameras are readily available and where optical fluorescence of the fiber-optics themselves is minimal. This allows for spectral imaging of the entire fluorescence spectrum with an imaging spectrograph and a CCD array. Though a dye like indo-1 has an AM ester and offers the advantage of dual emission and hence absolute quantitation, indo-1 has very short excitation and emission wavelengths which require PMT's or specially coated CCD arrays for detection. The primary disadvantage of fura-2 is that it is a dual excitation dye and thus requires complicated optics and collection gating. Other dyes like Calcium Green or Rhodamine either have small quantum yields or have poor specificity for calcium over other ionic species (like magnesium) [8]. Finally, fluo-3 has the advantage that it may be combined with fura-red to create a single-excitation, dual-emission combination. Since fluorescence of fura-red decreases with increasing [Ca²⁺] and since fluo-3 and fura-red share an excitation band, the pair can be used ratiometrically in a fashion similar to indo-1 and fura-2 [8, 91].

The molecular structure of fluo-3 is shown below in Figure 4.3. The R- moiety is either an O^- group in the case of ionic fluo-3 or the acetoxymethyl ester

-O-CH₂-O-C(=O)-CH₃ in the case of fluo-3/AM [8].

Figure 4.3: Chemical Structure of Calcium Chelator Dye fluo-3. Glycine, N-[4-[6-[(acetyloky)methoxy]-2,7-dichloro-3-oxo-3H-xanthen-9-yl]-2-[2-[2-[bis[2-[(acetyloxy)methoxyl]-2-oxyethyl]amino]-5-methylphonoxy]ethoxy]phenyl]-N-[2-(acetyloxy)methoxy]-2-oxyethyl]-,(acetyloxy)methyl ester.

Figure 4.4 illustrates typical fluo-3 fluorescence with varying concentrations of [Ca²⁺]. The product data sheets for fluo-3 are included in APPENDIX B.

Quantitative levels of free calcium ion are related to the intensity of fluo-3 fluorescence by the equation below:

where F is the observed fluo-3 fluorescence intensity at 525 nm, F_Max is the maximum observed fluorescence intensity when the dye is saturated with calcium, F _Min is the minimum observed fluorescence intensity when no free calcium is present, and K_D is the dissociation constant for the calcium binding dye and is dependent to some extent on the local chemical environment [8].

4.5 Instrument Design

The problem of measuring calcium concentration during an NMR experiment is essentially one of remote sensing. An instrument must be designed which allows for fluorescence measurements to be made of a sample which is inside the bore of a high field magnet. Fiber optics provide a mechanism of optical interrogation which is particularly compatible with the NMR environment. A second consideration is that the instrument should be versatile and be capable of making a wide range of optical measurements. In this case, the cost of developing an NMR compatible optical instrument will be offset if it is sufficiently versatile. A CCD camera and imaging spectrograph ensure such versatility by allowing measurements to be made at many wavelengths and over very short time spans. Figure 4.5 shows a diagram of the system which was created for these experiments. The instrument consists of a long fiber optic probe which allows for delivery of light to and collection of light from the sample. This probe fiber is coupled to excitation and collection fibers near the spectrograph. Light from an arc lamp is band-pass filtered at 500 nm and coupled into the excitation fiber. It travels through the probe fiber and excites the fluorescent indicator in the sample. Fluorescent photons are collected at the distal tip of the probe fiber and return through the collection fiber into the imaging spectrograph. Figure 4.6 shows a detail of the coupled fiber probe which consists of two 400 mm fibers coupled to a single 600 mm fiber. The imaging spectrograph linearly disperses the light from the fiber using a ruled diffraction grating, and this image is recorded on the imaging CCD array. Thus, a horizontal line on the CCD read out indicates the intensity versus wavelength fluorescence spectrum of the sample.

The portion of the spectrum which is recorded depends on the focal length f of the spectrometer, the rule spacing of the grating a , the angle q_D at which diffracted light leaves the grating, the order of light being observed m, and the width of the CCD array W according to law of linear reciprocal dispersion below [92].

Figure 4.5: Schematic of Optical Setup.

Figure 4.6: Fiber Optic Coupler Detail.

The theoretical resolution of the instrument depends on the rule spacing of the grating, the focal length of the spectrometer, and the illuminated width of the diffraction grating [93]. However, since a discrete pixel array is used in the CCD system, the actual resolution is limited by the pixel spacing and can be found by again using linear reciprocal dispersion, this time substituting with the CCD pixel width P.

In this instrument an f/4 270 mm focal length SPEX 270M imaging spectrograph was used. The spectrograph creates, at its focal plane, an image of the entrance slit with a 1.24 magnification ratio [93]. A ruled grating with 600 lines/mm and blazed at 500 nm was used yielding a dispersion in the imaging plane of approximately 7.6 nm/mm. (Note: in earlier experiments including the one described in section 6.3.1 a 150 lines/mm grating was used.) The CCD imaging array was 9.1 mm wide, thus a spectrum roughly 70 nm wide could be collected in a single scan. This completely covers the range of interest. The spectral resolution is also quite sufficient with about 0.27 nm per pixel on the 256 pixel wide CCD array. Figures 4.7 and 4.8 are photographs of the complete optical system and fiber-optic chuck, respectively. Collection of optical spectra was accomplished using a PC-compatible computer connected to the camera and running the vendor supplied WinSpec version 1.4.3 software. In order to increase signal to noise in the experiment, a long-pass filter with cut-on at 500 nm was used inside the spectrograph to insure rejection of the back reflected excitation light. Spectra were generally saved in ASCII format and loaded into the Matlab or OCTAVE computing environments for processing.

4.6 Preliminary Experiments

Two sets of preliminary experiments were performed to evaluate the performance of optical calcium measurement. First, a fluo-3 calibration experiment was performed inside of a high-field magnet in order to verify operation of the CCD based instrument and to ensure that the fluo-3 fluorescence resonance was not significantly altered by the magnetic field. Since in a polarizing magnetic field, electron spins become preferentially aligned, such a field can cause shifts in observed optical resonance frequencies or in the intensity of fluorescence bands as certain quantum mechanical transitions are ``not allowed'' [84, 94].

A second preliminary experiment was performed to assess the effectiveness of fluo-3/AM in vivo and to see if fluo-3/AM could effectively be loaded into the specific cells under investigation. Since loading of AM esterified dyes into the heart is usually accomplished in vivo by adding the dye solution to a perfusate being circulated through the organ [12, 16, 41, 42], it remained to be demonstrated that the passive pericardial bathing of these cells could be used to effectively load fluo-3/AM. The details and results of both of these preliminary experiments are presented in Chapter VI.