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Levulinic Acid & Enhanced Nicotine Binding Capacity

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The following document was first revealed by Greg Conolly of Massachusetts Tobacco Control at a press conference in St. Paul, MN in 1998. It is an RJ Reynolds scientific report from 1989 describes how RJR's additives nicotine levulinate and levulinic acid enhance the binding capacity of nicotine in the brain by 20-50%. Other documents show RJR added these chemicals to Winston ultra lights. Type of Document: RJ Reynolds scientific report Authors: Patrick M. Lipello and Key G. Fernandes Date: Sept. 25, 1989 Starting Bates No. 508295794 Total No. of Pages: 27 Site: RJ Reynolds Document Site http://www.rjrtdocs.com URLs: [Note: I think I have found a way to bookmark documents on the RJR site now. I hope these URLs work--if not, this document can be found by entering as combined text the phrase 'Enhancement of Nicotine Binding to Nicotinic Receptors.') This is a lengthy report, so I will give you the most effective pages. The first page contains a succinct summary of the research: http://www.rjrtdocs.com/imaging.jsp'SIZE=774&LOCATION=0 Quotes from the Summary: Nicotine levulinate and levulinic acid significantly increased the amount of L[3H] nicotine bound to nicotinic receptors in rat brain tissue. The observed increase ranged from 20-50%, with a mean value of around 30%...According to the model, levulinic acid binds to a...class of low-affinity receptors and increases the affinity of these receptors to nicotine. Page 20: A chart, titled Figure 2: Levulinic Acid Enhancement of [3H]-Nicotine Binding to Nicotinic Receptors in Rat Brain (page is Bates No. 508295813 -- this is useful as an overhead at presentations to demonstrate what this study is about): http://www.rjrtdocs.com/imaging.jsp'SIZE=774&LOCATION=20 Page 23: Figure 5 - Theoretical Model for Levulinate Enhancement of Nicotine Binding to Nicotine Receptors (the left pie chart represents nicotine binding without levulinate, the right pie shows the amount of enhancement of binding with the additive -- also makes a good overhead for presentations) (Page is Bates No. 508295817): http://www.rjrtdocs.com/imaging.jsp'SIZE=774&LOCATION=23 The following document shows that RJR scientific affairs evaluated nicotine levulinate as a cigarette additive in their Winston Ultra Light cigarettes: Type of Document: Interoffice Memorandum Title: Scientific Affairs Evaluation of Nicotine Levulinate as a Tobacco Ingredient Author: Dr. Scott Appleton Recipient: Jerry Lawson Date: 01/09/1987 Bates No. 506826449 No. of Pages: 1 URL: http://www.rjrtdocs.com/imaging.jsp'SIZE=774&LOCATION=0 (if this can also be found by entering the Bates No. in the document ID field).

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Public Affiars approves the evaluation of Winston Ultra low tar cigarettes containing up to 5% nicotine levulinate by focus groups providing each panel member smokes only one (1) cigarette.

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R001251 tiiiimi RJMR&D SCIENTIFIC INFORMATION SERVICES LIBRARY Authors: Patrick M. Lippiello Kay G. Fernandes Date: September 25, 1989 Group: Biochemical/Biobehavioral R&D R&DM, 1989, No. 267 Notebook Pages: 383909-383929 424156-424166 No. of Pages: 27 Dated: 4/2/87-9/8/87 Project: 0201 - Biobehavioral 0213 - Analog Research 6/10/88-4/18/89 Enhancement of Nicotine Binding to Nicotinic Receptors by Nicotine Levulinate and Levulinic Acid OBJECTIVE: To characterize the effects of nicotine levulinate and levulinic acid on the binding of L-[3H] nicotine to nicotinic receptors in membrane preparations derived from rat brain tissue, and to develop a plausible model that accounts for the observed effects. SUMMARY: Nicotine levulinate and levulinic acid significantly increased the amount of L- [3H] nicotine bound to nicotinic receptors in rat brain tissue. The observed increase ranged from 20-50 %, with a mean value of around 30 %. The total amount of radiolabeled nicotine bound to receptors was more than could be accounted for by binding to high affinity receptors alone. The maximal effect, which was observed at concentrations of nicotine levulinate and levulinic acid in the low nanomolar range, was reversed at higher concentrations. A computer model consistent with the results was developed and tested. According to the model, levulinic acid binds to an allosteric site on a class of low-affinity receptors and increases the affinity of these receptors for nicotine. At higher concentrations this effect is reversed by levulinic acid itself, with the assumption that it also has a reasonable affinity for the nicotine binding sites. Octanol:water partition coefficients, determined for nicotine levulinate by Dr. Corwin Hansch (Pomona College) suggest that nicotine levulinate can exist as an ion pair in nonpolar environments. Thus, the receptor effects observed in vitro may also be significant in vivo where partitioning of the compounds across the blood-brain barrier would become a factor. STATUS: NMR studies have been initiated in the laboratory of Dr. Huw Davies (Wake Forest) to further characterize ion pairing of nicotine levulinate. Dr. Allan Collins (U. of Colorado) is planning studies to measure in vivo levels of nicotine levulinate in rodent brain. Studies to measure behavioral effects in rodents are already under way in Dr.Collins' laboratory. .;-KEYWORDS: Nicotine (54-11-5), levulinic acid (123-76-2), nicotinic receptors, nicotine receptors, brain, central nervous system, octanol:water partition coefficients. C) 0 C) C) 0 © CV 0 0 1
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INTRODUCTION Levulinic acid (4-oxopentanoic acid) is primarily a breakdown product of starch, cane sugar and other cellulosic materials. It has been identified in a number of consumer products, including beer, bread volatiles, lettuce, hydrolyzed soy protein, and roasted coffee (1,2). Average daily intake from these sources has been estimated at around 25 mg. Levulinic acid has also been reported to be one of the primary aromatic constituents responsible for the odor of smoke from burley tobacco (3), and the calcium salt of the acid has been used therapeutically to treat disorders of calcium metabolism (4). Levulinic acid has been granted GRAS status by FEMA and is approved for food use by the FDA (172.515). Recent studies have demonstrated that low to moderate levels of levulinic acid (0.2- 0.8 %), when applied to tobacco in the casing for drying, can significantly reduce the harshness af srnoke#rom-hig~-nicotine-products(RJRT produvt-Researvh-Report MDII$6- - 31238). A possible explanation for this phenomenon is that levulinic acid directly affects sensory receptors that mediate nicotine's sensory impact. We have extended the concept of potential receptor effects to include the possibility that there are pharmacological interactions between nicotine and levulinic acid at the level of nicotinic cholinergic receptors in the brain. There is almost no scientific literature in this area, although there is some evidence suggesting that levulinic acid may interact with cholinergic systems, by virtue of its ability to reverse acetylcholinesterase inhibition in vitro (5). Similarly, it has been shown that there are some compounds which enhance the binding of nicotine to its receptors in brain tissue (6). However, nicotine salts have not been explored. The present report summarizes a series of in vitro receptor binding studies which were designed to test the effects of levulinic acid on the binding of nicotine to pharmacological receptors in rat brain tissue. Based on the results, a mathematical model has been derived that represents a potential mechanism for levulinic acid's observed effects on receptor binding. The question of access to receptor sites in vivo is also discussed, in light of data from ex-house collaborative laboratories on the partitioning of nicotine levulinate into nonpolar solvents. 2 C) il- Lr) O C>
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METHODS Tissue Preparation - Female Sprague-Dawley rats (200-300 g) were anesthetized with 70 % CO2 prior to killing by decapitation. Whole brains minus cerebellum were homogenized at 0° C in 10 volumes of buffer (w/v) using a Brinkman Polytron, setting 6, for 10 sec. The preparative buffer consisted of Na2HPO4, 8 mM; KH2PO4, 1.5 mM; KCI, 3 mM; NaCI, 120 mM; EDTA, 2mM; Hepes, 20 mM; iodoacetamide, 5 mM; Phenylmethylsulfonyl fluoride (PMSF), 0.1 mM, pH 7.4. The homogenate was sedimented by centrifugation (20 min; 50,000 x g at 0°). The pellet was resuspended in distilled, deionized water (5 %, w/v) and incubated for 1 h on ice prior to centrifugation as above and resuspension in assay buffer (ca. 1 mg/ml). The assay buffer was the same as the preparative buffer, with the addition of MgC12, 1 mM and CaC12, 2 mM, and the elimination of EDTA, iodoacetamide, and PMSF. A more detailed description of the above procedures has appeared elsewhere (7). Binding Assays (Rats)- Assay mixtures typically contained 200-400 ug of membrane protein, 30 nM L-[3H] nicotine (specific activity 80 Ci/mMole), and variable concentrations of unlabeled competing compounds in a final incubation volume of 0.5 ml assay buffer. Competing compounds included nicotine salicylate (0-100 uM), nicotine levulinate, 3:1 salt (0-100 uM) and levulinic acid (0-100 nM). Incubations were carried out on ice in the cold (0- 4° C) for 2 h. Incubations were terminated by adding 5 ml of ice cold assay buffer, followed by rapid filtration under vacuum through a double thickness (ca. 0.9 mm) of Gelman type A/E glass fiber filters (pore size 0.3 um) soaked in 0.5 % polyethyleneimine, using a Brandel multi-manifold tissue harvester. Filters were then washed three times with 5 ml assay buffer and air dried prior to placing them in counting vials, mixing them vigorously with 20 ml of liquid scintillation cocktail and quantifying tissue-bound radioactivity using a Beckman LS- 7000 counter (40-50 % efficiency). For additional details, see reference (7). Binding Assays (Mice) - Studies were conducted by Drs. Michael Marks and Allan Collins (University of Colorado) to determine the effects of nicotine levulinate and levulinic acid on the binding properties of two major nicotinic receptor subtypes in mouse brain. Their assays, which are based on the binding of [3H]-nicotine to high affinity receptors and [125n_ bungarotoxin to low affinity receptors, have been previously described (8). The experiments described in the present report utilized female C57BL mice (whole brain membrane homogenate minus cerebellum). The concentrations of radiolabeled compounds used were: L-[3H] nicotine, 5.6 nM and [125I]-bungarotoxin, 0.47 nM. Solvent Partitioning Studies - LogP values for the partitioning of nicotine, nicotine levulinate and levulinic acid between octanol and water were determined by Dr. Corwin Hansch (Pomona College), using previously published methods (9). cv O C-) 0 C) © t.n tV ` C) O 3
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RESULTS AND DISCUSSION Binding Experiments (Rat Brain) A standard method for assessing the relative potency of various ligands with respect to their affinity for a receptor site is the inhibition binding assay. In the case of nicotine, one can compare the ability of various unlabeled compounds to inhibit the binding of radiolabeled nicotine to nicotinic receptors in vitro. The result which is normally observed is illustrated by the lower curve (filled circles) in Figure 1, where the binding of L-[3H] nicotine has been plotted as a function of increasing concentrations of unlabeled nicotine salicylate. In the absence of inhibitor there is some level of [3H]-nicotine binding which is arbitrarily taken to be 100 %. As increasing concentrations of inhibitor are added there is a drop off in binding until the bound nicotine is completely displaced. In the experiment shown, this occurred at around 1 uM nicotine salicylate. The point at which 50 % inhibition occurs, the IC50, can be determined graphically and various compounds can be compared according to their IC50 values, i.e. less potent compounds would have higher values. In ex3eriments where nicotine levulinate (3:1 salt) was used as the competitive inhibitor of [ H]-nicotine binding to rat brain receptors an unexpected phenomenon was observed. Over the concentration range of around 1 to 20 nM we consistently observed an increase in binding above the level of 100 % control binding. This amounted to an increase of from 20% to as much as 50% above control binding, with a mean of 30%. A representative experiment is shown in Figure 1 (open circles). Note that at higher concentrations of nicotine levulinate the expected inhibition of binding was eventually expressed. This was probably due to the presence of unlabeled nicotine in the nicotine levulinate salt which displaced radiolabeled nicotine from the receptors at higher concentrations. At this point it was hypothesized that the enhanced binding effect could be assigned to some binding property of the levulinate moiety or of an unusual nicotine levulinate ion pair, since the effect was not observed with the nicotine salicylate salt under the same conditions. Changes in binding could not be attributed to pH effects because the maximal effect was observed in the low nM range. This concentration of levulinic acid was not sufficient to change the pH of the buffers used, including phosphate buffered saline (pH 7.4) and TRIS hydrochloride (pH 7.4). To confirm that enhanced receptor binding was due to the levulinate moiety, binding assays were performed with varying concentrations of pure levulinic acid. A typical experiment is shown in Figure 2. It can be seen that a similar, but somewhat less pronounced enhancement of binding was produced. Control experiments indicated that the additional binding could not be attributed to nonspecific binding to the glass fiber filters, used in the binding assay, in the presence of levulinate (compare dotted circles and triangles in Figure 2). The enhancement occurred in the same concentration range as that observed with the nicotine levulinate salt (compare Figure 1). However, in the absence of unlabeled nicotine, the levulinic acid was not capable of inhibiting [3H]-nicotine binding below the 100% control level. It was somewhat unexpected that the enhanced binding was reversible at all in the absence of unlabeled nicotine. If the enhancement were due simply to an allosteric effect of the levulinate one would predict binding to increase and level off at some plateau value. The 'inverted U' effect suggests that levulinate enhances binding at lower concentrations, but eventually inhibits its own effect at higher concentrations. A possible explanation for this phenomenon is offered in the receptor binding model discussed below. M 0 c.) O C1 t.n CV C1 CO 4
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Binding Experiments (Mouse Brain) Experiments by Drs. Michael Marks and Allan Collins (University of Colorado) were based on [~H]-nicotine binding to high-affinity nicotinic receptors and [125I]-alpha- bungarotoxin binding to low-affinity nicotinic receptors in mouse brain. Some representative results for inhibition of [3H]-nicotine binding by nicotine levulinate are shown in Figure 3. The results indicate a definite trend toward enhanced binding by nicotine levulinate in the low nM range, as in the rat. This effect was more pronounced at higher nicotine concentrations. However, the magnitude of the enhancement was significantly lower in mice, compared to rats. The maximum enhancement seen was around 10-12 %, compared to 50 % in rats. There was some evidence that the enhanced binding of [3H]-nicotine to receptors might result from positive cooperativity effects at low-affinity nicotinic receptors. Scatchard plots of alpha-bungarotoxin binding at different nicotine levulinate concentrations are shown in Figure 4. The upward concavity of the curves is a clear indication of positive cooperativity at low nanomolar concentrations of nicotine levulinate. It should be noted, however, that a number of different compounds show similar cooperativity effects at this receptor. Therefore, nicotine levulinate should not be considered unique in this respect. Solvent Partitioning Experiments Although the possible physiological significance of enhanced receptor binding cannot be determined solely from in vitro receptor binding studies, the potential for in vivo effects can be assessed in part by the partitioning of nicotine levulinate and levulinic acid between polar and nonpolar solvents. This approach has been developed by Hansch (9) as a method to compare the relative lipid solubilities of various pharmacological compounds. Membrane solubility becomes particularly important for nicotinic receptors in brain since the access of ligands to these sites depends on their ability to pass across the blood-brain barrier. Solvent partitioning studies carried out in Dr. Hansch's laboratory were based on the distribution of compounds between octanol and water. The parameter used for comparisons is logP, the log of the ratio of concentrations in octanol and water (logP = log ([octanol]:[water])). Dr. Hansch has defined the'ideal' value for pharmacological compounds to be 2.0, which says that the solubility of the compound in the more nonpolar phase should be roughly 100-fold higher than that in water. The results of studies with nicotine, nicotine levulinate and levulinic acid are presented in Table 1. The values of logP were determined using phosphate buffer, pH 7.4 as the aqueous phase. The value of 0.45 for nicotine indicates that approximately 74 % of the nicotine is present in the octanol phase at equilibrium. By comparison, levulinic acid by itself is only sparingly soluble in octanol, with greater than 99 % present in the aqueous phase. However, logP= -0.16 for the nicotine salt of levulinic acid. This indicates that roughly 41 % of the nicotine levulinate has partitioned into the nonpolar phase. Dr. Hansch suggested that some form of ion pairing between nicotine and levulinate would be necessary for this to occur. It further indicates that, although nicotine appears to partition into octanol less effectively as the salt, the levulinate moiety has increased its partitioning by nearly 500-fold compared to levulinic acid. This might provide a potential mechanism for nicotine levulinate to gain access to receptors in vivo. However, studies have been designed to test this hypothesis more directly by measuring brain levels following in vivo administration of nicotine levulinate. Studies have also been planned in collaboration with Dr. Huw Davies (Wake Forest University) to measure the presence of nicotine levulinate ion pairs in solution, using NMR techniques. 0 © t.n N 0 O 5
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Receptor Binding Model It is likely that the enhancement of nicotine binding to receptors by levulinate results from one of two things. Either the levulinic acid increases the affinity of the receptor sites to which nicotine is already binding, or it induces positive cooperativity at an additional class of receptor sites. The latter could occur if levulinate binds to an allosteric site, resulting in a significant increase in affinity at a low-affinity nicotinic receptor. This would be observed experimentally as an apparent increase in receptor number and the expression of [3H]- nicotine binding above the level normally observed. This hypothesis is supported by the following experimental observations: 1. The level of radiolabeled nicotine used in these studies was around 30 nM. This concentration of nicotine is sufficient to almost completely saturate the known high-affinity sites present in the tissue (i.e. > 90%). Thus, any additional binding would be likely to represent another class of sites. 2. At low concentrations levulinic acid increases binding above the normally observed maximum level but at higher concentrations does not inhibit binding beyond the 100% control level, suggesting again that the effect is additive with binding sites already present. 3. Scatchard plots from experiments with levulinic acid are curvilinear, consistent with the presence of an additional class of low-affinity sites. Similarly, the extrapolated Bmax value is significantly higher than that determined from control binding studies, consistent with the presence of additional binding sites. 4. Scatchard plots of alpha-bungarotoxin binding in the presence of nicotine levulinate are concave upward, consistent with a positive cooperativity (i.e. enhanced affinity) effect at these sites. Alpha-bungarotoxin binding sites have been well characterized as low-affinity nicotinic receptors. Their Kd for nicotine has been estimated at around 1 uM. This is nearly three orders of magnitude lower than the Kd of high-affinity sites measurable in [3H]- nicotine binding assays. In other words, the low-affinity sites would not normally be observable using nicotine as the ligand unless their affinity were enhanced allosterically by the presence of some other compound. Based on all of the evidence presented, a model has been formulated which offers a plausible explanation for levulinic acid's effects (A detailed mathematical derivation of the model is presented in Appendix A). According to the model (see Figure 5), nicotine binds to two populations of receptor sites, one having high affinity for nicotine (H) and the other low affinity for nicotine (R). H and R could represent two alpha subunits of the same receptor molecule or completely different receptor proteins. The formal derivation of the model is mathematically identical for either situation. The results of the mouse studies suggest that the low affinity nicotinic receptors labeled by alpha-bungarotoxin may be a potential candidate. In that case the two classes of sites in the model would be on completely different proteins, as depicted in Figure 5. The model further allows for an allosteric site on the low-affinity receptor that binds levulinate (L) with reasonably high affinity. This site may or may not be physically close enough to the nicotine binding site to allow direct interaction with nicotine. Therefore, ion pairing between nicotine and levulinate is not an absolute requirement of the model. t.O O O O O 0 !n N _.: O O 6
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When levulinate binds to its site it produces a positive cooperativity effect that increases the affinity of nicotine (N) for its binding site on the low-affinity receptor (R). This would increase the total binding observed and predict the experimental observation that the total binding is more than the maximum amount which can be accounted for by binding to the high affinity sites (H) alone. Finally, the model allows the levulinate to also have some affinity for the low affinity nicotine binding site itself. Therefore, at high enough concentrations levulinate can directly inhibit nicotine binding to that site. This would predict the 'inverted U' effect on nicotine binding and would restrict levulinate's enhancement of binding to a limited range of concentrations. This model represents the simplest mechanism that can account for all of the experimental observations. In order to test the compatibility of the model with experimental results a computer program was developed, based on the mathematical solution shown in Appendix A. For reference, the program has been listed in Appendix B. Manual iteration of the binding parameters resulted in a reasonable fit to the data. The theoretical curves have been plotted together with the data in Figures 6 and 7. Figure 6 shows the best manual fit for the enhancement of nicotine binding by levulinic acid concentrations in the range of 0-20 nM. The peak effect is around 3-4 nM levulinic acid. Note in particular how the data conform to the rapid rise in enhancement followed by the predicted gradual decline. Scatchard plots of the data are presented in Figure 7. The curvilinear plot represents the theoretical curve superimposed on the data (closed circles). Control nicotine binding is shown for comparison (open circles). The binding parameters which were used to obtain all of the theoretical curves are listed in Table II. Acknowledgments The authors thank Drs. Sam Simmons and Carr Smith for their efforts in obtaining logP values from Dr. Hansch and Dr. William Caldwell for his contributions to the design and implementation of experiments to test the solvent partitioning properties of nicotine levulinate and levulinic acid. .Q O a O C) lh N O O 7
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REFERENCES 1. Flavor and Extract Manufacturers Association of the United States. Scientific literature review of aliphatic keto- and hydroxy- acids with oxygen functions and related compounds in flavor usage. (1984). 2. Nakabayashi,T. The Quality of Coffee VII. Formation of Organic Acids from Sucrose by Roasting. Nippon Shakuhin Kogyo Gakkaishi 25: 257-261 (1978). 3. Fredrickson, J.D. The Study of Burley Smoke Condensate III. Constituents of the strong acid fraction. RDR 64-005. (1964). 4. Haynes, R.C. and Ferid Murad. Agents Affecting Calcification: Calcium, Parathyroid Hormone, Calcitonin, Vitamin D and other Compounds. In Goodman and Gilman's Pharmacological Basis of Therapeutics, Seventh Edition. Eds. A.G. Gilman, L.S. Goodman, T.W. Rall, F. Murad. Macmillan Publishing Co., NY p. 1521 (1985). 5. Neuhoff, V. and H. Kewitz. Reactivation of Alkylphosphorylated Cholinesterase by a Constituent of Liver. Int.J.Neuropharmacol. 1: 169-171 (1962). 6. Sloan, J.W., Martin, W.R., Hook, R. and J Hernandez. Structure-Activity t*.-.. 0 Relationships of some Pyridine, Piperidine, and Pyrrolidine Analogues for Enhancing and 3 0 Inhibiting the Binding of (+/-)-[ H] Nicotine to the Rat Brain P2 Preparation. J.Med.Chem. 28: 1245-1251 (1985). ca 7. Lippiello, P.M. and K.G. Fernandes. The Binding of L-[3H] Nicotine to a Single Class of High Affinity Sites in Rat Brain Membranes. Mol.Pharmacol. 29: 448-454 (1986). 8. Marks, M.J. and A.C. Collins. Characterization of Nicotine Binding in Mouse Brain and Comparison with the Binding of Alpha-bungarotoxin and Quinuclidinyl Benzilate. Mol. Pharmacol. 22: 554-564 (1982). O Lf) N 9. Hansch, C.. Experimental Determination of Partition Coefficients. In Strategy of Drug Design: A Guide to Biological Activity. Eds. Purcell, W.P., Bass, G.E. and J.M. Clayton. John Wiley and Sons, NY 126-143 (1972). O 0 8
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APPENDIX A: Mathematical Solution of Receptor Binding Model The model depicted in figure 5 was derived from a steady-state solution of the following equations: d(RN)/dt = kl(R)(N) + k4(RLN) - k2(RN) - k3(RN)(L) d(RL)/dt = k3(R)(L) + k6(RLN) + k8(RLL) - k4(RL) - k5(RL)(N) - k7(RL)(L) d(RLN)/dt = k5(RL)(N) + k3(RN)(L) - k6(RLN) - k4(RLN) d(RLL)/dt = k7(RL)(L) - k8(RLL) Where R = receptor concentration N = nicotine concentration L = levulinic acid concentration and RN, RL, RLN, and RLL are the concentrations of receptor with various combinations of nicotine and levulinate bound. The amount of nicotine bound to the receptors at equilibrium is RN + RLN, where RN = D1/DET and RLN = D2/DET where 131,132 and DET are the solutions of the following determinants: O O O O D1 = I I kl(N)(Bm) k3(L)(Bm) kl(N) k3(L)+k4+k5(N)+k7(L) kl(N)-k4 k3(L)-k6 kl(N) k3(L)-k8 I I LA tV I 0 k5(N) -(k4+k6) 0 I I 0 k7(L) 0 -k8 I O D2 = I I kl+k2+k3(L) k3(L) kl(N) k3(L)+k4+k5(N)+k7(L) kl(N)(Bm) k3(L)(Bm) kl(N) k3(L)-k8 I I O I k3(L) k5(N) 0 0 I I 0 k7(L) 0 -k8 I DET = I I I kl+k2+k3(L) k3(L) k3(L) kl(N) k3(L)+k4+k5(N)+k7(L) k5(N) kl(N)-k4 k3(L)-k6 -(k4+k6) kl(N) k3(L)-k8 0 I I I I 0 k7(L) 0 -k8 I and kl,k2...k8 are the rate constants for the various forward and reverse binding reactions, and Bm is the maximum possible receptor binding (i.e., Bm = R+RN+RL+RLN+RLL). 9
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APPENDIX B: Computer Program of Receptor Binding Model 0 © 0 0 10

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