- Email: [email protected]
Targeting proteins in vivo: in vitro guidelines
Nuclear Medicine and Biology 33 (2006) 161 – 164 www.elsevier.com/locate/nucmedbio
Editorial
Targeting proteins in vivo: in vitro guidelines The previous definitions of molecular imaging initially separated anatomy and function and identified molecular imaging with functional studies, which included external measurements of high- and low-capacity sites [1]. The highcapacity imaging procedures use contrast media and radiopharmaceuticals whose biodistribution does not have a strong mass dependency, and include measurements of blood flow, blood volume, perfusion, glomerular filtration, phagocytosis, hepatocyte clearance and bone adsorption. A recent publication by Thakur and Lentle [2] refined the definition of molecular imaging by eliminating several approaches such as MRI using the blood oxygen leveldependent technique, MR diffusion tensor sequences and magnetoencephalography, to name a few. A further refinement on the possible probe classifications is molecular targeting, which addresses specific and saturable binding of a probe to a target protein. This implies lowcapacity targets such as enzymes and receptors. There is a pregenomic component of probe development where the choice was based on autopsy studies, genetic linkage studies and drug efficacy studies. This approach led to the development of several classes of compounds including receptor binding radiotracers and enzyme inhibitors or substrates. In the postgenomic era, more approaches involving proteomics, genomics, antisense mRNA, reporter genes, protein–protein interactions and increased targets (500 to 5000 instead of 100) became available. Molecular targeting is the basis of the Aims and Scope of Nuclear Medicine and Biology [3]. Experiments at the beginning of the 20th century led to the hypothesis that there must be a specific binding site for a specific biological action. This was applied to both enzymes and receptors. The lock and key analogy of specificity has been in the vernacular since the time of Fischer who in 1895 studied two different enzyme preparations, emulsin and maltase, and examined their ability to hydrolyze synthetic glucose derivatives that had been prepared in his laboratory. When one derivative reacted with emulsin but not maltase and another reacted with maltase but not emulsin, the lockand-key analogy was born [4]. The concept of receptor binding ligands and receptors has an equally long history. The interaction of targeted molecules with a specific binding site has been postulated for some time. As early as the first century, Lucretius addressed 0969-8051/$ – see front matter D 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.nucmedbio.2006.01.010
this issue of targeted sites in general by proposing that differences in taste and smell are related to differences in the bpores with some smaller than others, some triangular, some square, some round and others of various polygonal shapesQ [5]. The molecular biology approach led to the discovery of the odorant receptors and the organization of the olfactory system and the Nobel Prize in Medicine/Physiology for Richard Axel and Linda Buck in 2004 [6]. Modern targeted chemotherapy has been dated to the work of Paul Ehrlich who, at the turn of the century, discovered effective agents to treat trypanosomiasis and syphilis. He discovered prosaniline, which has antitrypanosomal effects, and arsphenamine, which is effective against syphilis. Ehrlich postulated that it would be possible to find chemicals that were selectively toxic for parasites but not toxic to humans. Ehrlich also realized that this same concept was operative in his study of the interaction of antigens with specific, complementary, preformed receptors. Agents that are specific for a particular site were described by him as bmagic bulletsQ [7]. In 1906, Langley [8] postulated the existence of breceptive substancesQ on cell surfaces, and from that point on, this concept defined the action of a minute amount of substrate on a particular target organ. The use of radiolabeled ligands to measure receptors in vitro has a shorter history. Jensen and Jacobson [9] identified estradiol receptors using high specific activity [3H]estradiol. The use of radiolabeled ligands was slowed by the inability to produce high specific activity radioligands such that the low concentration of isolated receptor would not be saturated, but today there are receptorbinding radiotracers for in vitro use for many of the known receptors and their subtypes. The history of radioligands for the muscarinic system demonstrates the evolution of radiotracers for in vitro use. The muscarinic acetylcholine receptor (mAChR) was one of the earliest receptors studied with in vitro techniques. As early as 1973, Farrow and O’Brien [10] described the use of [3H]atropine to define the mAChR. A year later, Beld and Ariens [11] reported the use of stereospecific binding of benzetimide using the (+) and () isomers. They reported that [3H]atropine had a specific activity of 0.4 Ci/mmol and [3H]benzetimide had a specific activity of 0.6 Ci/mmol compared with the maximal value of 30 Ci/mmol for one tritium per molecule [11]. They were able to show specific binding for (+) benzetimide and atropine,
162
Editorial / Nuclear Medicine and Biology 33 (2006) 161–164
but not for () benzetimide. This was the first demonstration in the muscarinic receptor field of stereospecific binding. With the development of higher affinity and higher specific activity radioligands such as [3H]quinuclidinyl benzilate, receptor distribution was mapped in isolated tissue [12]. Today, receptor theory in pharmacology has moved past the simple bimolecular reaction. The ternary complex model and the probability model have replaced the bimolecular reaction model. Constitutive activity and reverse agonists have been added to the traditional agonists and antagonists, and some 85% of competitive antagonists are now classified as reverse agonists. Such concepts as spontaneously occurring active states, organ selective and ligand selective agonists, auxiliary coupling proteins, allosterism and receptor dimerization have been introduced to explain the varied actions of receptors [13]. The development of targeted molecules for in vivo imaging is a natural outgrowth of the development of targeted biochemicals and pharmaceuticals used in vitro. The original in vitro studies were dose–response curves using a biological end point. With the definition of a receptor, the field evolved into measuring dose-binding curves as well. Fortunately, receptor binding and enzyme inhibition are mathematically similar in the simplest case of the law of mass action for a ligand and a single binding site. The enzyme velocity, v, equals V max[S]/([S]+K), whereas specific binding, B, equals B max[L]/([L]+K d). Motulsky [14] notes a number of important differences. Receptor ligand interactions take from minutes to hours to reach equilibrium, whereas enzyme assays reach steady state (defined as a constant rate of product accumulation) in seconds. The specific binding equation is valid at equilibrium; the equation used to analyze enzyme kinetic data is valid when the rate of product formation is constant, so product accumulates at a constant rate. Whereas K d is an equilibrium dissociation constant, K m is not since its value includes the affinity of substrate for enzyme and the kinetics by which the substrate bound to the enzyme is converted to the product. Krohn and Link [15] have analyzed the similarities and differences between receptors and enzymes. They discuss two situations where the K in the equation v =V max[S]/([S]+K) has different meanings depending on which of the k’s in the enzyme action is rate determining. The general equation is E þ SfESYE þ P where E denotes an enzyme and S is a substrate and they form a reversible intermediate, ES, with a forward rate constant of k 1 and reverse rate constant of k -1 which then breaks up at a rate k p to form product P. If there is an equilibrium between ES and E+S, then the K is written as K eq. If, on the other hand, the second step in the reaction is irreversible, then the process is thought to be in steady state (d[ES]/dt = 0), and K = (k 1+k p)/k 1, which is commonly written as the Michaelis constant, K m, applicable under the circumstances of irreversibility. In vitro studies of receptor binding are analyzed at equilibrium. Most analysis of in vitro data has been restricted to a second-order equation with nonspecific binding added. There
are various transformations of the simple binding equation with various assumptions. Second-order equation should not be analyzed by linear regression. Given the powerful computers with the capacity to analyze nonlinear regressions, analyzing data using linear transformations, e.g., the Scatchard equation, should not be used and should be reserved for plot presentation after the parameters have been determined using nonlinear regression. As the model becomes more complicated, some variables need to be fixed and because parameters are often covariant, initial values need to be chosen. For example, the K d and B max are covariant and multiple combinations can be found to fit the data depending on the initial values. Inspection of the data after nonlinear regression analysis is always important to determine whether the values are reasonable since multiple answers may fit the regression equally well depending on the initial values chosen. Rodbard and Feldman [16] had addressed many of these issues earlier, and, more recently, Motulsky and Christopoulos [17] have described these issues in conjunction with the computer program GraphPad PRISM. In subsequent editorials, we will discuss the choice of the target system. Having chosen a receptor or an enzyme crucial to a specific disease, the use of a mathematical model to choose potential receptor-specific radiopharmaceuticals is key. A simple model has been put forth by Katzenellenbogen et al. [18] and Eckelman [19] as a first approximation. At high specific activity, the maximal B/F ratio will be B max/K d. The second term in the Scatchard transformation (B/F = B max/ K dB/K d) is negligible. Certainly, distribution factors, nonspecific protein binding, metabolism and other interactions will decrease the maximal B/F ratio when the molecular probe is used in vivo. Therefore, this criterion is necessary but not sufficient. This estimation is especially important as targeting of receptor systems with low nanomolar to picomolar concentration becomes more prevalent. It is incorrect to only address the issue of K d when referring to potential targeted molecules. Only the combination of B max/ K d will accurately estimate the probability of obtaining a reasonable ratio in vivo. Table 1 gives three examples of transporters at different concentrations in the brain and the K d of compounds of affinities such that the radiotracers have specific binding ratios in vivo [20]. Furthermore, this B max/K d of the target protein and targeted probe cannot be considered in a vacuum. If the B max/K d for other low-density sites is comparable, there will be competition for the molecular probe. Under some conditions, even Table 1 Comparing the K d requirements for the B max of the dopamine transporter (DAT), the serotonin transporter (SERT) and the norepinephrine transporter (NET)
DAT SERT NET
B max (fmol/mg protein or 0.1 nM)
Kd (nM)
Compound
B max/K d
2000 in rat striatum 194 in rat frontal cortex 55 in rat frontal cortex
10 0.13 0.05
[99mTc]TRODAT [125I]ADAM 2-[125I]INXT
20 149 110
Editorial / Nuclear Medicine and Biology 33 (2006) 161–164
nonspecific binding can compete for the probe. Katzenellenbogen et al. [18] addressed this for estradiol binding nonspecifically to albumin. When the K d is weak (5 to 10 AM), but the B max is enormous at 400–650 AM, the B max/K d ratio [(400 to 650)/(5 to 10)] is competitive with so-called specific binding. Katzenellenbogen et al. quotes an equation derived by Hansch for neutral molecules binding to albumin as log (1/C)=0.751 log P+2.301. If the log P is increased by one unit, then the binding to serum albumin will increase by 5.6-fold where C is the molar concentration of a variety of neutral compounds needed to achieve a 1:1 complex with albumin. For compounds with a log P of between 1 and 3, 1/C ranges between 3.052 and 3.993 or a concentration of between 0.33 and 0.25 M. This is not relevant to the no-carrier-added situation, but shows the trend in nonspecific binding as a function of log P. The preparation of a series of nonradioactive substituted ligands is often the next step. This avoids the problems with no-carrier-added synthesis until the substituted ligand is shown to be a true tracer for the unsubstituted receptor binding ligand, especially in those cases where the substitution of the radionuclide introduces a substantial perturbation. This also produces the necessary reference compounds for the radiolabeled compound. The preparation of the nonradioactive compound better defines the radioactive compound because classical analytical methods can be used, whereas with the high specific activity compound, chromatography is the only analytical tool usually available for identification and quantification, although the increasing sensitivity of mass spectrometry is making it a necessity in the modern radiochemistry laboratory. In the current regulatory climate, the nonradioactive compound is also needed to carry out the necessary toxicology and pathology studies. Just as structure–activity relationships have been the foundation of classic drug design, structure–distribution studies are the backbone of radiopharmaceutical development. The use of both theoretical and experimental parameters can direct the choice of radioligand. Many of the earlier radiopharmaceuticals were water-soluble, polar compounds that are excreted by the kidneys [21]. As radioligands were developed that cross cell membranes, the properties of these compounds were often correlated with a particular physicochemical property. Most often, the property is lipophilicity determined by either measuring the organic–aqueous partition coefficient or using a related technique such as reversed-phase high-pressure liquid chromatography [22]. In the radiopharmaceutical context, the percentage dose per gram of tissue gives a value proportional to the permeability coefficient. A comprehensive review of radiotracer uptake in normal brain and the uptake in tumors have both been shown to have a parabolic relationship that peaks between log P of 2 and 3 [23,24]. Much of the structure–activity relationships is now modeled with various programs using homology modeling. The protein data base is growing rapidly, but is still at only 1–2% of the known proteins, whereas advances in sequence
163
comparison, fold recognition and protein-modeling algorithms have been instrumental in closing the bsequence–structure gapQ [25]. For the G-protein-coupled receptors, homology modeling approaches are still based on the bovine rhodopsin structure. These homology models have been able to identify agonists and antagonists of G-protein receptors. Another important aspect of homology modeling is the comparison of different species based on the differences in sequence. Homology modeling can also be used to determine whether the proposed ligands will be substrates for the cytochrome P450s involved in metabolism. Only ~10 hepatic P450s are responsible for 90% of the metabolism of known drugs. Although the crystal structures of all 10 are not known, by homology modeling, the metabolism of various drugs can be proposed. Recently, The National Biomedical Library has included Pub Chem at the Entrez home page and an increasing number of drug–protein crystal structures. These have been beneficial in designing analogs of the parent compound. Most compounds are either chemically unstable and/or metabolized in vivo. Therefore, the stability of the new derivative should be determined in plasma and in liver. The most convenient model for the enzymatic activity of the liver is commercially available cryopreserved hepatocytes [26]. One difficulty with using the nonradioactive compound for stability testing is caused by the large concentrations used, which will mostly likely result in a secondorder reaction, whereas the high specific activity ligand will most likely be in a pseudo first-order reaction. This problem has been solved with the use of a combination liquid chromatography/mass spectrometry (LC/MS) analysis where picograms of material can often be analyzed [27]. Another benefit of this technique is that an extraction procedure that allows the isolation of unmetabolized parent compound can be developed from the knowledge of the metabolite structures. In summary, there are two advantages of using LC/MS to define the metabolites of a potential radiopharmaceutical: (1) the identity of the metabolites is known and therefore questions about the presence of metabolites in the target tissue can be answered; (2) simple extraction procedures can be developed to determine the percentage of parent in the plasma. Such a method allows rapid determination of the parent fraction in plasma and does not require less sensitive, time-consuming chromatographic analysis. This procedure is best carried out before in vivo experiments, although for expediency sake, it is often carried out if the in vivo experiments are not as expected. In the next edition of this newsletter, we will discuss specific examples of the issues addressed here. William C. Eckelman Molecular Tracer LLC Bethesda, MD 20814, USA Chester A. Mathis University of Pittsburgh Medical Center Pittsburgh, PA, USA
164
Editorial / Nuclear Medicine and Biology 33 (2006) 161–164
References [1] Weissleder R, Mahmood U. Molecular imaging. Radiology 2001; 219(2):316 – 33. [2] Thakur M, Lentle BC. Report of a summit on molecular imaging. Radiology 2005;236(3):753 – 5. [3] http://www.nucmedbio.com. [4] Clardy J. Borrowing to make ends meet. Proc Natl Acad Sci U S A 1999;96(5):1826 – 7. [5] Lucretius. On the nature of the universe. In: Latham RE, editor. London7 Penguin Books; 1951. p. 149 – 52. [6] Miller G. 2004 Nobel Prizes. Axel, Buck share award for deciphering how the nose knows. Science 2004;306(5694):207. [7] Himmelweit F, Marquardt M, Dale H. The collected papers of Paul Ehrlich, vol. II–IV. London7 Pergamon Press; 1957. [8] Langley JM. On nerve endings and special excitable substances in cells. Proc R Soc B 1906;8:170. [9] Jensen E, Jacobson H. Basic guides to the mechanism of estrogen action. Recent Prog Horm Res 1962;18:387. [10] Farrow JT, O’Brien RD. Binding of atropine and muscarone to rat brain fractions and its relation to the acetylcholine receptor. Mol Pharmacol 1973;9(1):33 – 40. [11] Beld AJ, Ariens EJ. Stereospecific binding as a tool in attempts to localize and isolate muscarinic receptors: Part II. Binding of (plus)benzetimide, (minus)-benzetimide and atropine to a fraction from bovine tracheal smooth muscle and to bovine caudate nucleus. Eur J Pharmacol 1974;25(2):203 – 9. [12] Yamamura HI, Kuhar MJ, Snyder SH. In vivo identification of muscarinic cholinergic receptor binding in rat brain. Brain Res 1974;80(1):170 – 6. [13] Kenakin T. Principles: receptor theory in pharmacology. TIPS 2004; 25:186 – 92. [14] Motulsky H. Analyzing data with GraphPad Prism. San Diego (CA)7 GraphPad Software Inc; 1999. p. 333. [15] Krohn KA, Link JM. Interpreting enzyme and receptor kinetics: keeping it simple, but not too simple. Nucl Med Biol 2003;30(8):819– 26.
[16] Rodbard D, Feldman HA. Theory of protein–ligand interaction. Methods Enzymol 1975;36(00):3 – 16. [17] Motulsky HJ, Christopoulos A. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. San Diego (Calif)7 GraphPad Software Inc; 2003. http://www.graphpad.com. [18] Katzenellenbogen JA, Heiman DF, Carlson KE, Lloyd JE. In vitro and in vivo steroid receptor assays in the design of estrogen radiopharmaceuticals. In: Eckelman WC, editor. Receptor binding radiotracers, vol. 1. Boca Raton (FL)7 CRC Press; 1982. p. 93 – 126. [19] Eckelman WC. Radiolabeled adrenergic and muscarinic blockers for in vivo studies. In: Eckelman WC, editor. Receptor binding radiotracers, vol. 1. Boca Raton (FL)7 CRC Press; 1982. p. 69 – 92. [20] Kung MP, Choi SR, Hou C, Zhuang ZP, Foulon C, Kung HF. Selective binding of 2-[125I]iodo-nisoxetine to norepinephrine transporters in the brain. Nucl Med Biol 2004;31(5):533 – 41. [21] Eckelman WC, Reba RC. The classification of radiotracers. J Nucl Med 1978;19(10):79 – 81. [22] Dischino DD, Welch MJ, Kilbourn MR, Raichle ME. Relationship between lipophilicity and brain extraction of C-11-labeled radiopharmaceuticals. J Nucl Med 1983;24:1030 – 8. [23] Waterhouse RN. Determination of lipophilicity and its use as a predictor of blood–brain barrier penetration of molecular imaging agents. Mol Imaging Biol 2003;5(6):376 – 89. [24] Tu Z, Dence CS, Ponde DE, Jones L, Wheeler KT, Welch MJ, et al. Carbon-11 labeled sigma2 receptor ligands for imaging breast cancer. Nucl Med Biol 2005;32(5):423 – 30. [25] Hillisch A, Pineda LF, Hilgenfeld R. Utility of homology models in the drug discovery process. DDT 2004;9:659 – 69. [26] Ma Y, Kiesewetter D, Lang L, Eckelman WC. Application of LC-MS to the analysis of new radiopharmaceuticals. Mol Imaging Biol 2003; 5(6):397 – 403. [27] Korfmacher WA. Principles and applications of LC-MS in new drug discovery. Drug Discov Today 2005;10(20):1357 – 67.
Editorial
Targeting proteins in vivo: in vitro guidelines The previous definitions of molecular imaging initially separated anatomy and function and identified molecular imaging with functional studies, which included external measurements of high- and low-capacity sites [1]. The highcapacity imaging procedures use contrast media and radiopharmaceuticals whose biodistribution does not have a strong mass dependency, and include measurements of blood flow, blood volume, perfusion, glomerular filtration, phagocytosis, hepatocyte clearance and bone adsorption. A recent publication by Thakur and Lentle [2] refined the definition of molecular imaging by eliminating several approaches such as MRI using the blood oxygen leveldependent technique, MR diffusion tensor sequences and magnetoencephalography, to name a few. A further refinement on the possible probe classifications is molecular targeting, which addresses specific and saturable binding of a probe to a target protein. This implies lowcapacity targets such as enzymes and receptors. There is a pregenomic component of probe development where the choice was based on autopsy studies, genetic linkage studies and drug efficacy studies. This approach led to the development of several classes of compounds including receptor binding radiotracers and enzyme inhibitors or substrates. In the postgenomic era, more approaches involving proteomics, genomics, antisense mRNA, reporter genes, protein–protein interactions and increased targets (500 to 5000 instead of 100) became available. Molecular targeting is the basis of the Aims and Scope of Nuclear Medicine and Biology [3]. Experiments at the beginning of the 20th century led to the hypothesis that there must be a specific binding site for a specific biological action. This was applied to both enzymes and receptors. The lock and key analogy of specificity has been in the vernacular since the time of Fischer who in 1895 studied two different enzyme preparations, emulsin and maltase, and examined their ability to hydrolyze synthetic glucose derivatives that had been prepared in his laboratory. When one derivative reacted with emulsin but not maltase and another reacted with maltase but not emulsin, the lockand-key analogy was born [4]. The concept of receptor binding ligands and receptors has an equally long history. The interaction of targeted molecules with a specific binding site has been postulated for some time. As early as the first century, Lucretius addressed 0969-8051/$ – see front matter D 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.nucmedbio.2006.01.010
this issue of targeted sites in general by proposing that differences in taste and smell are related to differences in the bpores with some smaller than others, some triangular, some square, some round and others of various polygonal shapesQ [5]. The molecular biology approach led to the discovery of the odorant receptors and the organization of the olfactory system and the Nobel Prize in Medicine/Physiology for Richard Axel and Linda Buck in 2004 [6]. Modern targeted chemotherapy has been dated to the work of Paul Ehrlich who, at the turn of the century, discovered effective agents to treat trypanosomiasis and syphilis. He discovered prosaniline, which has antitrypanosomal effects, and arsphenamine, which is effective against syphilis. Ehrlich postulated that it would be possible to find chemicals that were selectively toxic for parasites but not toxic to humans. Ehrlich also realized that this same concept was operative in his study of the interaction of antigens with specific, complementary, preformed receptors. Agents that are specific for a particular site were described by him as bmagic bulletsQ [7]. In 1906, Langley [8] postulated the existence of breceptive substancesQ on cell surfaces, and from that point on, this concept defined the action of a minute amount of substrate on a particular target organ. The use of radiolabeled ligands to measure receptors in vitro has a shorter history. Jensen and Jacobson [9] identified estradiol receptors using high specific activity [3H]estradiol. The use of radiolabeled ligands was slowed by the inability to produce high specific activity radioligands such that the low concentration of isolated receptor would not be saturated, but today there are receptorbinding radiotracers for in vitro use for many of the known receptors and their subtypes. The history of radioligands for the muscarinic system demonstrates the evolution of radiotracers for in vitro use. The muscarinic acetylcholine receptor (mAChR) was one of the earliest receptors studied with in vitro techniques. As early as 1973, Farrow and O’Brien [10] described the use of [3H]atropine to define the mAChR. A year later, Beld and Ariens [11] reported the use of stereospecific binding of benzetimide using the (+) and () isomers. They reported that [3H]atropine had a specific activity of 0.4 Ci/mmol and [3H]benzetimide had a specific activity of 0.6 Ci/mmol compared with the maximal value of 30 Ci/mmol for one tritium per molecule [11]. They were able to show specific binding for (+) benzetimide and atropine,
162
Editorial / Nuclear Medicine and Biology 33 (2006) 161–164
but not for () benzetimide. This was the first demonstration in the muscarinic receptor field of stereospecific binding. With the development of higher affinity and higher specific activity radioligands such as [3H]quinuclidinyl benzilate, receptor distribution was mapped in isolated tissue [12]. Today, receptor theory in pharmacology has moved past the simple bimolecular reaction. The ternary complex model and the probability model have replaced the bimolecular reaction model. Constitutive activity and reverse agonists have been added to the traditional agonists and antagonists, and some 85% of competitive antagonists are now classified as reverse agonists. Such concepts as spontaneously occurring active states, organ selective and ligand selective agonists, auxiliary coupling proteins, allosterism and receptor dimerization have been introduced to explain the varied actions of receptors [13]. The development of targeted molecules for in vivo imaging is a natural outgrowth of the development of targeted biochemicals and pharmaceuticals used in vitro. The original in vitro studies were dose–response curves using a biological end point. With the definition of a receptor, the field evolved into measuring dose-binding curves as well. Fortunately, receptor binding and enzyme inhibition are mathematically similar in the simplest case of the law of mass action for a ligand and a single binding site. The enzyme velocity, v, equals V max[S]/([S]+K), whereas specific binding, B, equals B max[L]/([L]+K d). Motulsky [14] notes a number of important differences. Receptor ligand interactions take from minutes to hours to reach equilibrium, whereas enzyme assays reach steady state (defined as a constant rate of product accumulation) in seconds. The specific binding equation is valid at equilibrium; the equation used to analyze enzyme kinetic data is valid when the rate of product formation is constant, so product accumulates at a constant rate. Whereas K d is an equilibrium dissociation constant, K m is not since its value includes the affinity of substrate for enzyme and the kinetics by which the substrate bound to the enzyme is converted to the product. Krohn and Link [15] have analyzed the similarities and differences between receptors and enzymes. They discuss two situations where the K in the equation v =V max[S]/([S]+K) has different meanings depending on which of the k’s in the enzyme action is rate determining. The general equation is E þ SfESYE þ P where E denotes an enzyme and S is a substrate and they form a reversible intermediate, ES, with a forward rate constant of k 1 and reverse rate constant of k -1 which then breaks up at a rate k p to form product P. If there is an equilibrium between ES and E+S, then the K is written as K eq. If, on the other hand, the second step in the reaction is irreversible, then the process is thought to be in steady state (d[ES]/dt = 0), and K = (k 1+k p)/k 1, which is commonly written as the Michaelis constant, K m, applicable under the circumstances of irreversibility. In vitro studies of receptor binding are analyzed at equilibrium. Most analysis of in vitro data has been restricted to a second-order equation with nonspecific binding added. There
are various transformations of the simple binding equation with various assumptions. Second-order equation should not be analyzed by linear regression. Given the powerful computers with the capacity to analyze nonlinear regressions, analyzing data using linear transformations, e.g., the Scatchard equation, should not be used and should be reserved for plot presentation after the parameters have been determined using nonlinear regression. As the model becomes more complicated, some variables need to be fixed and because parameters are often covariant, initial values need to be chosen. For example, the K d and B max are covariant and multiple combinations can be found to fit the data depending on the initial values. Inspection of the data after nonlinear regression analysis is always important to determine whether the values are reasonable since multiple answers may fit the regression equally well depending on the initial values chosen. Rodbard and Feldman [16] had addressed many of these issues earlier, and, more recently, Motulsky and Christopoulos [17] have described these issues in conjunction with the computer program GraphPad PRISM. In subsequent editorials, we will discuss the choice of the target system. Having chosen a receptor or an enzyme crucial to a specific disease, the use of a mathematical model to choose potential receptor-specific radiopharmaceuticals is key. A simple model has been put forth by Katzenellenbogen et al. [18] and Eckelman [19] as a first approximation. At high specific activity, the maximal B/F ratio will be B max/K d. The second term in the Scatchard transformation (B/F = B max/ K dB/K d) is negligible. Certainly, distribution factors, nonspecific protein binding, metabolism and other interactions will decrease the maximal B/F ratio when the molecular probe is used in vivo. Therefore, this criterion is necessary but not sufficient. This estimation is especially important as targeting of receptor systems with low nanomolar to picomolar concentration becomes more prevalent. It is incorrect to only address the issue of K d when referring to potential targeted molecules. Only the combination of B max/ K d will accurately estimate the probability of obtaining a reasonable ratio in vivo. Table 1 gives three examples of transporters at different concentrations in the brain and the K d of compounds of affinities such that the radiotracers have specific binding ratios in vivo [20]. Furthermore, this B max/K d of the target protein and targeted probe cannot be considered in a vacuum. If the B max/K d for other low-density sites is comparable, there will be competition for the molecular probe. Under some conditions, even Table 1 Comparing the K d requirements for the B max of the dopamine transporter (DAT), the serotonin transporter (SERT) and the norepinephrine transporter (NET)
DAT SERT NET
B max (fmol/mg protein or 0.1 nM)
Kd (nM)
Compound
B max/K d
2000 in rat striatum 194 in rat frontal cortex 55 in rat frontal cortex
10 0.13 0.05
[99mTc]TRODAT [125I]ADAM 2-[125I]INXT
20 149 110
Editorial / Nuclear Medicine and Biology 33 (2006) 161–164
nonspecific binding can compete for the probe. Katzenellenbogen et al. [18] addressed this for estradiol binding nonspecifically to albumin. When the K d is weak (5 to 10 AM), but the B max is enormous at 400–650 AM, the B max/K d ratio [(400 to 650)/(5 to 10)] is competitive with so-called specific binding. Katzenellenbogen et al. quotes an equation derived by Hansch for neutral molecules binding to albumin as log (1/C)=0.751 log P+2.301. If the log P is increased by one unit, then the binding to serum albumin will increase by 5.6-fold where C is the molar concentration of a variety of neutral compounds needed to achieve a 1:1 complex with albumin. For compounds with a log P of between 1 and 3, 1/C ranges between 3.052 and 3.993 or a concentration of between 0.33 and 0.25 M. This is not relevant to the no-carrier-added situation, but shows the trend in nonspecific binding as a function of log P. The preparation of a series of nonradioactive substituted ligands is often the next step. This avoids the problems with no-carrier-added synthesis until the substituted ligand is shown to be a true tracer for the unsubstituted receptor binding ligand, especially in those cases where the substitution of the radionuclide introduces a substantial perturbation. This also produces the necessary reference compounds for the radiolabeled compound. The preparation of the nonradioactive compound better defines the radioactive compound because classical analytical methods can be used, whereas with the high specific activity compound, chromatography is the only analytical tool usually available for identification and quantification, although the increasing sensitivity of mass spectrometry is making it a necessity in the modern radiochemistry laboratory. In the current regulatory climate, the nonradioactive compound is also needed to carry out the necessary toxicology and pathology studies. Just as structure–activity relationships have been the foundation of classic drug design, structure–distribution studies are the backbone of radiopharmaceutical development. The use of both theoretical and experimental parameters can direct the choice of radioligand. Many of the earlier radiopharmaceuticals were water-soluble, polar compounds that are excreted by the kidneys [21]. As radioligands were developed that cross cell membranes, the properties of these compounds were often correlated with a particular physicochemical property. Most often, the property is lipophilicity determined by either measuring the organic–aqueous partition coefficient or using a related technique such as reversed-phase high-pressure liquid chromatography [22]. In the radiopharmaceutical context, the percentage dose per gram of tissue gives a value proportional to the permeability coefficient. A comprehensive review of radiotracer uptake in normal brain and the uptake in tumors have both been shown to have a parabolic relationship that peaks between log P of 2 and 3 [23,24]. Much of the structure–activity relationships is now modeled with various programs using homology modeling. The protein data base is growing rapidly, but is still at only 1–2% of the known proteins, whereas advances in sequence
163
comparison, fold recognition and protein-modeling algorithms have been instrumental in closing the bsequence–structure gapQ [25]. For the G-protein-coupled receptors, homology modeling approaches are still based on the bovine rhodopsin structure. These homology models have been able to identify agonists and antagonists of G-protein receptors. Another important aspect of homology modeling is the comparison of different species based on the differences in sequence. Homology modeling can also be used to determine whether the proposed ligands will be substrates for the cytochrome P450s involved in metabolism. Only ~10 hepatic P450s are responsible for 90% of the metabolism of known drugs. Although the crystal structures of all 10 are not known, by homology modeling, the metabolism of various drugs can be proposed. Recently, The National Biomedical Library has included Pub Chem at the Entrez home page and an increasing number of drug–protein crystal structures. These have been beneficial in designing analogs of the parent compound. Most compounds are either chemically unstable and/or metabolized in vivo. Therefore, the stability of the new derivative should be determined in plasma and in liver. The most convenient model for the enzymatic activity of the liver is commercially available cryopreserved hepatocytes [26]. One difficulty with using the nonradioactive compound for stability testing is caused by the large concentrations used, which will mostly likely result in a secondorder reaction, whereas the high specific activity ligand will most likely be in a pseudo first-order reaction. This problem has been solved with the use of a combination liquid chromatography/mass spectrometry (LC/MS) analysis where picograms of material can often be analyzed [27]. Another benefit of this technique is that an extraction procedure that allows the isolation of unmetabolized parent compound can be developed from the knowledge of the metabolite structures. In summary, there are two advantages of using LC/MS to define the metabolites of a potential radiopharmaceutical: (1) the identity of the metabolites is known and therefore questions about the presence of metabolites in the target tissue can be answered; (2) simple extraction procedures can be developed to determine the percentage of parent in the plasma. Such a method allows rapid determination of the parent fraction in plasma and does not require less sensitive, time-consuming chromatographic analysis. This procedure is best carried out before in vivo experiments, although for expediency sake, it is often carried out if the in vivo experiments are not as expected. In the next edition of this newsletter, we will discuss specific examples of the issues addressed here. William C. Eckelman Molecular Tracer LLC Bethesda, MD 20814, USA Chester A. Mathis University of Pittsburgh Medical Center Pittsburgh, PA, USA
164
Editorial / Nuclear Medicine and Biology 33 (2006) 161–164
References [1] Weissleder R, Mahmood U. Molecular imaging. Radiology 2001; 219(2):316 – 33. [2] Thakur M, Lentle BC. Report of a summit on molecular imaging. Radiology 2005;236(3):753 – 5. [3] http://www.nucmedbio.com. [4] Clardy J. Borrowing to make ends meet. Proc Natl Acad Sci U S A 1999;96(5):1826 – 7. [5] Lucretius. On the nature of the universe. In: Latham RE, editor. London7 Penguin Books; 1951. p. 149 – 52. [6] Miller G. 2004 Nobel Prizes. Axel, Buck share award for deciphering how the nose knows. Science 2004;306(5694):207. [7] Himmelweit F, Marquardt M, Dale H. The collected papers of Paul Ehrlich, vol. II–IV. London7 Pergamon Press; 1957. [8] Langley JM. On nerve endings and special excitable substances in cells. Proc R Soc B 1906;8:170. [9] Jensen E, Jacobson H. Basic guides to the mechanism of estrogen action. Recent Prog Horm Res 1962;18:387. [10] Farrow JT, O’Brien RD. Binding of atropine and muscarone to rat brain fractions and its relation to the acetylcholine receptor. Mol Pharmacol 1973;9(1):33 – 40. [11] Beld AJ, Ariens EJ. Stereospecific binding as a tool in attempts to localize and isolate muscarinic receptors: Part II. Binding of (plus)benzetimide, (minus)-benzetimide and atropine to a fraction from bovine tracheal smooth muscle and to bovine caudate nucleus. Eur J Pharmacol 1974;25(2):203 – 9. [12] Yamamura HI, Kuhar MJ, Snyder SH. In vivo identification of muscarinic cholinergic receptor binding in rat brain. Brain Res 1974;80(1):170 – 6. [13] Kenakin T. Principles: receptor theory in pharmacology. TIPS 2004; 25:186 – 92. [14] Motulsky H. Analyzing data with GraphPad Prism. San Diego (CA)7 GraphPad Software Inc; 1999. p. 333. [15] Krohn KA, Link JM. Interpreting enzyme and receptor kinetics: keeping it simple, but not too simple. Nucl Med Biol 2003;30(8):819– 26.
[16] Rodbard D, Feldman HA. Theory of protein–ligand interaction. Methods Enzymol 1975;36(00):3 – 16. [17] Motulsky HJ, Christopoulos A. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. San Diego (Calif)7 GraphPad Software Inc; 2003. http://www.graphpad.com. [18] Katzenellenbogen JA, Heiman DF, Carlson KE, Lloyd JE. In vitro and in vivo steroid receptor assays in the design of estrogen radiopharmaceuticals. In: Eckelman WC, editor. Receptor binding radiotracers, vol. 1. Boca Raton (FL)7 CRC Press; 1982. p. 93 – 126. [19] Eckelman WC. Radiolabeled adrenergic and muscarinic blockers for in vivo studies. In: Eckelman WC, editor. Receptor binding radiotracers, vol. 1. Boca Raton (FL)7 CRC Press; 1982. p. 69 – 92. [20] Kung MP, Choi SR, Hou C, Zhuang ZP, Foulon C, Kung HF. Selective binding of 2-[125I]iodo-nisoxetine to norepinephrine transporters in the brain. Nucl Med Biol 2004;31(5):533 – 41. [21] Eckelman WC, Reba RC. The classification of radiotracers. J Nucl Med 1978;19(10):79 – 81. [22] Dischino DD, Welch MJ, Kilbourn MR, Raichle ME. Relationship between lipophilicity and brain extraction of C-11-labeled radiopharmaceuticals. J Nucl Med 1983;24:1030 – 8. [23] Waterhouse RN. Determination of lipophilicity and its use as a predictor of blood–brain barrier penetration of molecular imaging agents. Mol Imaging Biol 2003;5(6):376 – 89. [24] Tu Z, Dence CS, Ponde DE, Jones L, Wheeler KT, Welch MJ, et al. Carbon-11 labeled sigma2 receptor ligands for imaging breast cancer. Nucl Med Biol 2005;32(5):423 – 30. [25] Hillisch A, Pineda LF, Hilgenfeld R. Utility of homology models in the drug discovery process. DDT 2004;9:659 – 69. [26] Ma Y, Kiesewetter D, Lang L, Eckelman WC. Application of LC-MS to the analysis of new radiopharmaceuticals. Mol Imaging Biol 2003; 5(6):397 – 403. [27] Korfmacher WA. Principles and applications of LC-MS in new drug discovery. Drug Discov Today 2005;10(20):1357 – 67.