Methods and kits for detecting non-luminescent or weakly luminescent metals
10908141 ยท 2021-02-02
Assignee
Inventors
- Stewart Russell (New York, NY, US)
- Edward A. FISHER (Scarsdale, NY, US)
- Youssef Zaim Wadghiri (New York, NY, US)
- Ryan Casey (New York, NY, US)
Cpc classification
G01N21/6428
PHYSICS
A61K49/0021
HUMAN NECESSITIES
International classification
Abstract
The invention provides methods and kits for detecting the presence of, the amount of, or the concentration of a substantially non-emitting metal in a sample by a) providing a sensitizer to a chelator of the substantially non-emitting metal thereby creating a sensitized-metal complex; b) adding an unsensitized chelate, and c) detecting a signal from the unsensitized chelate. The substantially non-emitting metal may be gadoliniumn and may exist in complex with a chelator. The unsensitized chelate may be terbium (Tb) or europium (Eu) and the detecting a signal may be performed by fluorescence.
Claims
1. A method for detecting presence of or amount of a substantially non-emitting metal in a solution comprising: a) binding a first compound to the substantially non-emitting method in the solution to form a complex that is substantially non-emitting; b) exposing the substantially non-emitting complex to a source of illumination to cause the first compound to enter into an excited state while the metal in the complex remains substantially non-emitting; c) contacting the illuminated complex in the solution with a second compound; d) detecting energy transferred to the second compound from the excited state of the first compound in the illuminated complex; and e) correlating the detected transferred energy to a presence or amount of the substantially non-emitting metal in the solution.
2. A method according to claim 1 wherein the substantially non-emitting metal is gadolinium.
3. A method according to claim 1 wherein the first compound is carbostyril124-diethylenetriaminepentaacetic acid (cs124-DTPA).
4. A method according to claim 1 wherein the substantially non-emitting metal exists in a complex with a chelator.
5. A method for detecting presence of a substantially non-emitting metal bound to a chelator in a solution, comprising: a) binding a sensitizer to the chelator of the substantially non-emitting metal thereby creating a sensitized-metal complex in the solution; b) exposing the complex to a source of illumination to cause the sensitizer to enter into an excited state while the metal in the complex remains substantially non-emitting; c) adding an unsensitized chelate to the solution; d) detecting a signal from the unsensitized chelate which represents energy transferred from the excited state of the sensitizer; and e) correlating the detected signal from the unsensitized chelate to a presence of the substantially non-emitting metal in the solution.
6. A method according to claim 5 wherein the substantially non-emitting metal is gadolinium.
7. A method according to claim 5, further comprising the step of complexing the substantially non-emitting metal with the chelator.
8. A method according to claim 5 wherein the sensitizer is carbostyril124 (cs124).
9. A method according to claim 5 wherein the unsensitized chelate is selected from the group consisting of terbium (Tb) and europium (Eu).
10. A method according to claim 5 wherein the signal being detected is a fluorescent signal.
11. A method according to claim 5 wherein the detecting a signal is performed by electron plasma resonance (EPR).
12. A method according to claim 5 wherein the detecting a signal is performed by nuclear magnetic resonance (NMR).
13. A method according to claim 5 wherein the sensitizer and the unsensitized chelate are conjugated to a phospholipid.
14. A method for detecting amount of or concentration of a substantially non-emitting metal bound to a chelator in a solution comprising: a) binding a sensitizer to the chelator of the substantially non-emitting metal thereby creating a sensitized-metal complex in the solution; b) exposing the complex to a source of illumination to cause the sensitizer to enter into an excited state while the metal in the complex remains substantially non-emitting; c) adding an unsensitized chelate to the solution; d) detecting a signal from the unsensitized chelate which represents energy transferred from the excited state of the sensitizer; and e) correlating the detected signal from the unsensitized chelate to an amount or concentration of the substantially non-emitting metal in the solution.
15. A method according to claim 14 wherein the substantially non-emitting metal is gadolinium.
16. A method according to claim 14, further comprising the step of complexing the substantially non-emitting metal with the chelator.
17. A method according to claim 14 wherein the sensitizer is carbostyril124 (cs124).
18. A method according to claim 14 wherein the unsensitized chelate is selected from the group consisting of terbium (Tb) and europium (Eu).
19. A method according to claim 14 wherein the signal being detected is a fluorescent signal.
20. A method according to claim 14 wherein the detecting a signal is performed by electron plasma resonance (EPR).
Description
BRIEF DESCRIPTION OF THE FIGURES
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DETAILED DESCRIPTION OF THE INVENTION
(6) Before the present methods are described, it is to be understood that this invention is not limited to particular methods and experimental conditions described, as such methods and conditions may vary. It is also to be understood that the terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting, since the scope of the present invention will be limited only by the appended claims. As used in this specification and the appended claims, the singular forms a, an, and the include plural references unless the context clearly dictates otherwise. Thus, for example, references to the method includes one or more methods, and/or steps of the type described herein and/or which will become apparent to those persons skilled in the art upon reading this disclosure and so forth in their entirety.
(7) Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the invention, the preferred methods and materials are now described. All publications mentioned herein are incorporated herein by reference I their entireties.
Definitions
(8) The terms used herein have the meanings recognized and known to those of skill in the art, however, for convenience and completeness, particular terms and their meanings are set forth below.
(9) Agent refers to all materials that may be used to prepare a composition, including, for instance, pharmaceutical and diagnostic compositions, or that may be compounds such as small synthetic or naturally derived organic compounds, nucleic acids, polypeptides, antibodies, fragments, isoforms, variants, or other materials that may be used independently for such purposes, all in accordance with the present invention.
(10) Analog as used herein, refers to a chemical compound, a nucleotide, a protein, or a polypeptide that possesses similar or identical activity or function(s) as the chemical compounds, nucleotides, proteins or polypeptides having the desired activity or effect of the present invention, but need not necessarily comprise a compound that is similar or identical to those compounds of the preferred embodiment, or possess a structure that is similar or identical to the agents of the present invention.
(11) Derivative refers to the chemical modification of molecules, either synthetic organic molecules or proteins, nucleic acids, or any class of small molecules such as fatty acids, or other small molecules that are prepared either synthetically or isolated from a natural source, such as a plant, that retain at least one function of the active parent molecule, but may be structurally different. Chemical modifications may include, for example, replacement of hydrogen by an alkyl, acyl, or amino group. It may also refer to chemically similar compounds which have been chemically altered to increase bioavailability, absorption, or to decrease toxicity. A derivative polypeptide is one modified by glycosylation, pegylation, or any similar process that retains at least one biological or immunological function of the polypeptide from which it was derived.
(12) A small molecule refers to a molecule that has a molecular weight of less than 3 kilodaltons (kDa), preferably less than about 1.5 kilodaltons, more preferably less than about 1 kilodalton. Small molecules may be nucleic acids, peptides, polypeptides, peptidomimetics, carbohydrates, lipids or other organic (carbon-containing) or inorganic molecules, as those skilled in the art will appreciate. A small organic molecule is normally an organic compound (or organic compound complexed with an inorganic compound (e.g., metal)) that has a molecular weight of less than 3 kilodaltons, and preferably less than 1.5 kilodaltons, and more preferably less than about 1 kDa.
(13) Subject or patient refers to a mammal, preferably a human, in need of or undergoing treatment or screening for a condition, disorder or disease.
(14) Non-emitting or substantially non-emitting as used herein means non-fluorescent or substantially non-fluorescent, or non-light emitting, or substantially non-light emitting, in any range from UV to IR
General Description
(15) The present methods provide a sensitive, convenient, and cost effective method to detect low concentrations of gadolinium based contrast agents (GBCA). The present methods include adding a sensitizing molecule to the GBCA, and using a detecting reagent for fluorescent reading.
(16) Gadolinium (Gd) belongs to the lanthanides, a family of rare-earth elements. GBCA are formed by the complexation of Gd with a chelator. If a light-absorbing sensitizer is covalently bound to the chelator, some lanthanides, such as terbium (Tb) and europium (Eu), display luminescent properties. That is, they will emit light if exposed to the excitation wavelength of the sensitizer, and they have been used as energy donors in luminescence resonance energy transfer (LRET) applications. GBCA are not sensitized, and are non-luminescent, and therefore have not been used before for fluorescence or LRET. In addition, sensitized chelates of gadolinium, in solution, are non-luminescent.
(17) The present methods use existing methods to attach a sensitizer to the chelator of the GBCA, to create a sensitized-GBCA (s-GBCA) and detect the concentration of the complex by the addition of a trace amount of unsensitized chelate, such as, for example Tb chelate. The fluorescent signal from the resulting complex (e.g. Tb complex) is directly proportional to the concentration of s-GBCA, and independent of the concentration of the unsensitized chelate, e.g. Tb. The mechanism behind this signal may be energy transfer or transmetallation. Previous lanthanide FRET work has all used light-emitting metals, and the triplet-emitter work has all been done in the solid state for light emitting diodes (LED).
(18) The concentration of s-GBCA in solution may be determined by absorption spectroscopy down to 1.sup.3M using the molar extinction coefficient of the sensitizer, s-GBCA has magnetic and biological characteristics that are identical to the original GBCA and may be used directly for MR experiments. Blood samples may be withdrawn from the animal at time intervals appropriate to the experiment at hand, whereupon the detector molecule is added, and the concentration of the non-fluorescent metal is read in a fluorescent plate reader. Detection sensitivity of s-GBCA in the plate reader is on the order of 1.sup.7M.
(19) When the GBCA is incorporated in a dendrimer or nanoparticle, the Tb signal may be used similarly to LRET to evaluate the size and composition of the nanoparticle. This agent and method may be used in a small animal experimental model, as it provides a method sufficiently sensitive to measure the concentration of GBCA in small plasma sample volumes.
(20) The methods described herein provide the following: i) an improvement over previous methods in sensitivity and convenience of measurement of contrast agents in small animal imaging; ii) a method for obtaining a measureable signal from a non-fluorescent or weakly-fluorescent metallic complex; iii) an application to generate aFRET signal from s-GBCA to a non-sensitized lanthanide chelate; iv) a formulation of a spin-label: v) a method to elicit and detect a change in the electronic configuration of an MR contrast agent; vi) a method to elicit and detect a change in the electronic configuration of an injected complex by infrared excitation and emission; vii) a formulation of a photoactivable chelator conjugated to a phospholipid; viii) incorporation of the photoactivable phospholipid-chelator in a nanoparticle, and a method to detect nanoparticle integrity and composition
(21) In some instances the methods provide conjugation of carbostyril124 (cs124) to Gadolinium-DTPA (the commercial GBCA Magnevist). The resulting compound has a well defined absorption spectrum in water with maxima at 328 nm and 341 nm. When the sample containing cs124-Gd-DTPA is excited at 341 nm, the characteristic emission spectrum of Tb can be detected by time-resolved fluorescence on a fluorescent plate reader, and is proportional to the concentration of Gd. The clinical dose of Magnevist may be 1.sup.4 mol per kg body weight, with a distribution half-life of 12 minutes, and a plasma clearance half-life of approximately 81 min. Typical plasma concentrations range from 6.0.sup.4 M at 3 min post injection, to 2.44 M at 60 minutes post injection. When sensitized, the compound can be detected on a standard laboratory fluorescence plate reader at 2.5.sup.7 M in a volume of 100 mL, allowing accurate detection from a plasma sample volume of 1 mL at 60 minutes post injection, and can be detected from undiluted samples up to 4 hours post injection. This is in contrast to relaxometry which requires a 200 mL plasma sample and is at the limit of detection for time points longer than 1 hour. Plasma samples are diluted in a buffer containing a non-sensitized chelate of Terbium.
(22) In some instances, different sensitizers and different chelators may be provided. In some instances a contrast agent may be provided where the concentration may be detected by Electron Plasma Resonance (EPR). In such a system, the agent may function as a spin-label. In some instances the concentration may be detected by nuclear magnetic resonance (NMR). In such a system, the photo-excited state can be differentiated from the ground state of the complex by a change in magnetic resonance. In some instances, the composition may be provided so as to shift the excitation and emission wavelengths, particularly in the infrared region. In addition to Gadolinium, Lanthanum, Ytterbium. and Lutetium also have stable 4f electron configurations, and as a result, do not have low-lying energy states that allow fluorescent emission by an excited sensitized chelate. The choice of an organic dye may be made so as to allow excitation by infrared radiation (IR). The long-lived excited state of the complex will be at a lower-energy level, that is, one farther infrared Detection of this complex may be made by energy transfer to an appropriate infrared fluorescent species such as Europium or Cerium or by EPR or NMR. The complex thus formed may be both excited and detected by infrared radiation, thereby allowing whole-animal imaging by infrared detection, or allowing the initiation of excited EPR or NMR states during experiment by infrared radiation.
(23) In some instances, the sensitizer and chelate may be conjugated to a phospholipid. This molecule may be incorporated into nanoparticles for imaging such as is described in, for example, Fisher et. al., U.S. Pat. No. 7,947,307, the disclosure of which is herein incorporated by reference, and used to detect and quantify the concentration of the nanoparticle contrast agent. In some instances, the fluorescent detector may be incorporated into the nanoparticle along with the sensitized chelate, which can be used to quantify the concentration of the sensitized chelate. Since the fluorescent energy transfer does not occur across large distances, this also indicates that the nanoparticle is intact.
(24) These methods allow for the rapid measurement of plasma kinetics parameters of s-GBCA formulations, using a standard laboratory fluorescent reader equipped for time resolved fluorescence. Currently, GBCA is measured by relaxometry, which has low sensitivity, requiring large sample volumes, or ICP-MS, which is expensive and time consuming. The present methods reduce experimental costs, facilitate efficient screening protocols, reduce experimental variability, and reduce the number of animals required for experimentation.
(25) Determination of plasma kinetics parameters requires the collection of serial samples from a single test subject, at concentrations as low as 10 nM. For a blood sample of 50 L or less, a typical volume for a mouse study, the only option is ICP-MS. Alternatively, in relaxometry, larger volume requirements preclude serial sampling in small animals.
(26) Current FRET and LRET systems using metal donor-acceptor detection systems can use only fluorescent donors and fluorescent acceptors. The present methods describe fluorescent detection of non-fluorescent donors.
(27) Recognizing the need for alternative testing modalities for GBCA, in 2011 BioPAL introduced a 96-well format colonmetric ELISA assay which purports to measure a GBCA excreted in urine by reaction with rabbit antiserum raised against Gd-DTPA. This kit can only be used for urine testing, not for plasma. The present methods are less expensive to manufacture, more sensitive, specific for Gd content, and may be used for plasma studies.
(28) The present methods expand the utility of existing CA. The sensitizer can be conjugated directly to an existing FDA-approved GBCA, allowing direct detection of the compound. At present, there is no GBCA which can be directly detected by fluorescence.
(29) The high sensitivity of the present methods also means that plasma samples may be further diluted, allowing the use of standard size exclusion chromatography methods of plasma lipoprotein research for characterization of particle plasma biodistribution.
(30) The present methods solve the problem of quantifying, rather than merely detecting GBCA. In the present methods, the excited state is maintained on the donor complex only, which is in solution, and physically separated from the acceptor. A related method termed co-fluorescence relies on the formation of solid crystal aggregates of donor and acceptor, making it quantitative only the concentration of acceptor. The present methods also avoid the problem of spectral bleed through, in which the donor fluorescent signal must be subtracted from the acceptor signal.
(31) When the sensitized chelate is on a phospholipid, and incorporated into a nanoparticle, the present methods solve the problem of determining the labeling efficiency of the nanoparticle synthesis process. The observation and quantification of emitted light from this system can be used to determine a) the concentration of the donor complex, b) the integrity of the nanoparticle, and c) the size of the particle.
(32) The present methods also provide a way to determine if particle components remain associated with the nanoparticle, or dissociate over time. There is currently no direct method to do this.
(33) The present methods provide many advantages in the field of small animal experimentation in GBCA. Animal labs that use GBCA for angiography in neurology, nephrology, cardiology, oncology, and other research areas are now able to accurately measure GBCA concentrations at any experimental time point, with a turnaround of minutes. This allows for rapid identification of GBCA delivery and clearance, and allow for real-time adjustment of experimental conditions.
(34) The present methods may be used to measure the concentration of GBCA on nanoparticles such as those described by Fisher et al., U.S. Patent Publication 2006/0099148, the disclosure of which is incorporated herein by reference in its entirety, such as those used for atherosclerosis MRI studies. There is currently no fluorescence-based method to do this.
(35) The present methods have broad applicability in physical chemistry for the detection of small quantities of ionic metals. It also has broad applicability in nanomedicine, for nanoparticle compositional analysis, to identify the presence and concentrations of two or more target molecules on the same nanoparticle
(36) Synthesis and Characterization of cs124-DTPA-Gd
(37) Synthesis follows the method of (Li, et al., Bioconjug Chem, 1997, 8(2): 127-132).
(38) The relaxivity of cs124-DTPA-Gd was the same as that of DTPA-Gd, showing a decrease in r1 relative to Gd.sup.3+. Size and diffusivity, as revealed by dynamic light scattering (DLS) were similar although sensitized chelates are, predictably, slightly larger than unsensitized chelates. Shown in Table 1.
(39) TABLE-US-00001 TABLE 1 Physical properties of the experimental and reference compounds. Diffusivity Absorbance and Fluorescence Relaxivity Compound D (cm.sup.2/s) A.sub.max (nm) Ex.sub.max (nm) Em.sub.max (nm) r1 (M.sup.1 ms.sup.1) DTPA-Tb 3.5 10.sup.6 280 300 365 cs124 328 310 370 cs124-DTPA-Gd 2.5 10.sup.6 328 341 375 3.32 1.4 Magnevist 3.4 Gd3+ 8.0 10.sup.6 9.16 0.96
(40) When xylenol orange coordinates Gd.sup.3+ ion, absorption at 573 decreases relative to that at 433. Samples of cs124-DTPA-Gd, incubated with 50 mM xylenol orange show that free Gd.sup.3+ is detectable when the concentration of the chelated complex is above 1.75 mM, indicating a free ion concentration of 0.06%.
(41) In Vitro Detection of Sensitized Gadolinium Chelates
(42) To assess the ability of DTPA-Tb to generate a fluorescent signal when in solution with cs124-DTPA-Gd, a fluorescent plate reader capable of detecting the integrated fluorescent signal from 600 to 2100 s was used. The concentration of cs124-DTPA-Gd was determined by absorption spectroscopy, and dilutions of the complex from 10.sup.2 to 10.sup.10 were placed in a black 96 well plate. 10.sup.9M of DTPA-Tb was added to each well and excited at 341 nm. The integrated signal was read at 545 nm. Evaluation of Tb fluorescence showed that the time-resolved Tb signal was a function of the concentration of Gd, demonstrating a marked quenching effect at concentrations higher than 10.sup.3M, shown in
(43) To determine the stability of the chelate in solution as a function of time, readings were made at different time points. If there is an exchange of Tb with Gd on the sensitized chelate, then a dramatic increase in signal should be observed. The intensity of cs124-DTPA-Tb is 10000 fold higher than the equivalent concentration of cs124-DTPA-Gd. No significant change of intensity was observed at 5, 30, and 60 minutes, indicating that exchange of metals between sensitized and unsensitized chelates was undetectable during the time course of the experiment.
(44) In Vivo Detection of Sensitized Gadolinium Chelates
(45) To evaluate the in vivo properties of cs124-DTPA-Gd quantification accuracy in whole body experiments, five C57-Black6 mice were given metered injections of 0.1 mmol/kg, the clinical dose for Magnevist, via the saphenous vein, and allowed a 7-minute time period for uniform plasma distribution. To determine the pharmacokinetic parameters, 50 L blood samples were taken from each mouse so that no more than 200 L total blood volume was removed from a single mouse during the experiment. Sampling time points were arranged so that time points were sequential, with the average time between points being 3 minutes for the first 30 minutes, and 10 minutes for the remainder of the experiment, up to 2 hours. Blood was centrifuged at 13000g for 5 minutes, and approximately 25 L of plasma isolated from each sample. Of these samples, 101 L was diluted in 100 L deionized water containing 10M DTPA-Tb, and read according to the in vitro protocol, against a standard curve of known concentration. The results, shown in
(46) In Vivo Imaging
(47) To evaluate the imaging efficacy of the sensitized contrast agent, c57-Black6 mice were injected as for clearance studies, and imaged in a custom small-animal coil. Maximum intensity projections are shown in
Discussion
(48) Small animal studies form the bulk of experimental innovation in contrast media GBCA are currently the most effective clinical agent, and offer the clearest route to translational applications. The introduction of a sensitive and convenient method for quantification will allow the leaders in innovation to perform rapid pharmacokinetic studies and provide a new standard for in vivo screening. The data demonstrate that a sensitizing the chelator used in the formulation of GBCA can allow quantitative detection of the concentration of metal with minimal alteration of the characteristic imaging and pharmacokinetic properties of the agent. In future work, systematic analysis of the effect of varying sensitizer and chelate may reveal new applications of this system.
EXAMPLES
(49) The following examples are set forth to provide those of ordinary skill in the art with a description of how to make and use the methods and compositions of the invention, and are not intended to limit the scope thereof. Efforts have been made to insure accuracy of numbers used (e.g., amounts, temperature, etc.) but some experimental errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, molecular weight is average molecular weight, temperature is in degrees Centigrade. and pressure is at or near atmospheric.
Example 1
(50) Sensitized Chelate: Synthesis and Characterization
(51) Cs124-DTPA (
(52) Chelation Studies: Comparison of Chelation Affinity by Fluorescence and Xylenol Orange
(53) Absorption and fluorescence experiments were conducted on a SpectraMax M5 plate reader (Molecular Devices, Sunnyvale, Calif.). For fluorescence, the excitation source was a xenon flash lamp with monochromators employed to tune excitation and emission wavelengths. Automatic cutoff filters were used for all emission and excitation spectra. The excitation maximum for cs124 is 341 nm, 9 nm excitation and 15 nm emission slits were used. For time resolved fluorescence (TRF), a delay time of 600 s and an integration time of 1000 s were used. Peak fluorescence at 545 nm and 485 was recorded.
(54) The white powder from lyophilization was suspended in 1 mL deionized water and stirred for 1 hour at RT, with occasional sonication to disperse observed aggregates. The solution was filtered in a 10 kD MWCO filter (Millipore) and the absorption spectrum measured between 250 and 450 on a nanodrop (Thermo Scientific). Concentration was determined by using the Beer-Lambert Law Abs=Cl, where is the molar extinction coefficient, l is the path length, and C is concentration. The molar extinction coefficient for cs124-DTPA-Ln was determined by diluting a sample with a known absorption value over 3 orders of magnitude, titrating in increasing amounts of Tb.sup.3+, and measuring the increase in Tb emission. A linear increase in emission was observed that reached a plateau. The point of intersection between the linear increase and plateau marks the concentration at which all chelation sites are occupied. Plotting the ratio Abs.sub.(341)cs124-DTPA:Tb concentration v. fluorescence, gives c(cs124-DTPA-Tb)=1.0710.sup.4 M.sup.1 cm.sup.1. It is assumed that, since all lanthanides have extremely small absorption cross-section, the extinction coefficient is the same for all cs124-DTPA chelates.
(55) For determination of free Gd.sup.3+ in solution after chelation. 3 mg xylenol orange was dissolved in 50 mM acetic acid pH 5.8, and 90 L added to each well of a clear 96 well plate. Triplicate samples of 10 L 10.sup.3M cs124-DTPA were added to each well, and increasing amounts of Gd.sup.3 titrated in. Absorption was read at 573 and 433, against a standard of known Gd.sup.3+ concentration.
(56) The stock solution was diluted to 10.sup.3M and absorption of a 1:1000 dilution measured at 328 and 341 nm to confirm concentration. In a clear 96 well plate, cs24-DTPA was provided
(57) In Vitro Detection Studies
(58) The concentration of cs124-DTPA-Gd was determined by absorption spectroscopy, and samples diluted to 510.sup.3M, pH 7.4. Triplicate samples were placed in a black 96-well plate, and serial dilutions prepared to 110.sup.9M, in 1001 L deionized water. 10 L of 110.sup.9M DTPA-Tb was added to each well, and incubated for 10 minutes. The plate was read as for the chelation studies. A 1:1 molar ratio of Gd3+ was added to each well, and incubated for 30 minutes, and read.
(59) Derivation of Model:
(60) Both the donor and acceptor are free to diffuse by Brownian motion throughout the solvent, and whenever the distance of closest approach between two particles is small enough that it is possible for a transfer to occur, we define a collision. The result of this collision is either a success, if a transfer, or a failure if no transfer. The fluorescence of a single acceptor will be proportional to the total number of successful transfers to it from colliding donors. We write
F=
where is the fluorescence yield per collision, and
and substituting into Equation S1:
F(
(61) Upon normalization by a, we obtain Equation 1.
(62)
(63) All that remains is to determine the number of donor and acceptor collisions. We start with a number concentration of particles P composed of donor D and acceptor A:
(64)
(65) where N.sub.i is number of the respective species and V is the total volume. The rate of collision per unit volume can be expressed as
(66)
where .sub.P=(2d).sup.2/4 is the collisional cross section, for a particle of diameter d,
(67)
(68) The quantity in parentheses defines an interaction volume. V.sub.C=.sub.P{square root over (2)}
(69)
we can see that the number of donor collisions is
where C.sub.D and C.sub.A are the molar concentrations of donor and acceptor, respectively, and =6.02210.sup.26 L.Math.m.sup.3.Math.mol.sup.1 is a unit conversion constant. Substituting into Equation 1 gives the normalized fluorescence distribution as a function of donor concentration:
{circumflex over (F)}(C.sub.D)=V.sub.CC.sub.D(1p).sup.V.sup.
for a fixed concentration of acceptor C.sub.A. For low concentration, where the interparticle distance is greater, the chance of transfer to an acceptor is proportional to the chance of collision, i.e the number of donors per acceptor. As the concentration of donor increases, the number of transfers to an acceptor increases, but the per-donor chance of transfer to another donor also increases, eventually becoming more likely than the probability of transfer to an acceptor, as observed in experiment.
In Vivo Plasma Kinetics Studies
(70) All animal procedures were approved by the NYU Institutional Animal Care and Use Committee. C57-Black6 mice were anesthetized by isofluorene inhalation, and the hair removed from the anterior surface of the left hindlimb to reveal the superficial saphenous vein. A microcannula formed from #10 polyeurethane tubing was prepared by heating then stretching the tubing. The caudal end of the microcannula was attached to a 1 mL tuberculin syringe, and the distal end inserted into the saphenous vein. A total of 54 L of contrast agent was infused via syringe pump at a rate of 50 L/min. After the infusion was stopped, the cannula was removed and the site of cannulation sealed with a cyanoacrylate adhesive. A recovery time of 7 minutes was allowed to ensure uniform plasma distribution and to allow the animal to regain normal functioning. Also at this time, a local anesthetic (proparacaine) was applied to both eyes. 5 L heparain PBS (10 U/mL) was introduced to one end of a 50 L borosilicate glass microcapillary tube (Fisher), and blood samples were withdrawn from the retro-orbital plexus of awake mice at measured intervals. Blood was centrifuged at 13000g for 5 minutes, and 25 L of plasma recovered from the sample. 10 L of each plasma sample was evaluated as in the in vitro detection method, against a known concentration diluted in an equal concentration of heparinized PBS and control mouse plasma (no contrast agent infusion).
(71) Mathematical Modeling of Plasma Clearance
(72) The solution of the transport equations that describe concentration as a function of time for a two-compartment open mamillary system is the bi-exponential equation
C(t)=Ae.sup.t/.sup.
(73) Where C it concentration, t is time, A and B are the initial concentrations of each compartment, and .sub.a and .sub.b are the characteristic times for compartments A and B respectively. Plasma kinetics of most GBCA can be described by this equation. Data was linearized by taking the natural logarithm of the concentration, and a least-squares method was employed to find the coefficients of equation 2. Goodness of fit was determined by the combined Pearson's R-squared value. Normalized residuals were plotted against predicted quantiles of a normal distribution to determine if measurement errors are normally distributed relative to the model, using built in libraries of the R statistical programming language.
Example 2
(74) Background
(75) The use of gadolinium-based contrast agents (GBCA) is integral to the field of diagnostic magnetic resonance imaging (MRI). Strategies to combine fluorescent detection with MRI have relied on bifunctionalized particles, conjugating a fluorescent element and a magnetic contrast agent on the same compound. However, most multi-modal compounds are not designed to demonstrate a coupled effect between the two detection methods. By exploiting the heavy-ion effect, we developed a compound that maintains a nonemittive excited triplet state on a fluorescent label only in the presence of chelated Gadolinium. The nonemittive triplet allows the compound to become a dark donor, transferring energy to a second, fluorescent, detector molecule. The compound, carbostyril-124-diethylenetriaminepentaacetic acid-Gadolinium (cs124-DTPA-Gd), can be quantified on a standard laboratory plate reader, with a lower limit of detection of 10-7 M.
(76) Results
(77) We examined the effect of single and double cs124 labels on detection sensitivity. In fluorescent applications that consist of only organic molecules, both the intersystem crossing rate and the triplet radiative decay rate are small, and luminescence is observed only from the decay of the singlet excited state. However, increased spin-orbit coupling between an organic-labeled chelate and a coordinated heavy metal ion increases the rate of intersystem crossing, enriching the lowest triplet energy level of the organic label. For small interparticle distance, R, this triplet energy can transfer to another molecule by non-radiative electron exchange.
(78) We showed that this energy transfer can be made to a fluorescent acceptor molecule, and used to detect the presence of the GBCA in tissue. Conversely, identification of the location of the GBCA by MRI identifies a region of tissue to which energy transfer can be stimulated by directed fluorescent excitation. One drawback to this technique is that efficiency of energy transfer attenuates for high concentrations of donor. We demonstrated that increasing the number of organic labels can correct this problem. For a donor with a single organic label, the probability of transfer is proportional to the probability of the first collision being between a donor and an acceptor, and decreases sharply with high concentration as donor-donor collisions become dominant. A donor with two organic labels may sustain an excited triplet state for a second collision, thereby increasing the fluorescent signal of the acceptor even for high concentrations of donor.