Cellular kinetic models of the antiviral agent (R)-9-(2-phosphonylmethoxypropyl)adenine (PMPA)

PDF

Download

Open document

Flip pages

Download a page range

Download transcript

Copy asset link

Request this asset

Request accessible transcript

Transcript (if available)

Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality o f the copy subm itted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back o f the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f CELLULAR KINETIC MODELS OF THE ANTIVIRAL AGENT (R)-9-(2-PHOSPHONYLMETHOXYPROPYL)ADENINE (PMPA) by Rajesh K. Raman A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment o f the Requirements for the Degree MASTER OF SCIENCE (Biomedical Engineering) August 1997 ©1997 Rajesh K. Raman Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. U M I Number: 1387843 UMI Microform 1387843 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This thesis, written by ____RA_JESH_K.__RMA!L________________________ under the guidance o f his/her F aculty Committee and approved by all its members, has been presented to and accepted by the School o f Engineering in partial fu lfillm e n t o f the re quirem ents fo r the degree o f -MASTER ■ QF Sr.TE’.NQJ’ --_________________________ NfiEB IttG.______________________ D a te___AusiiSi_5._J.427_________________________ Faculty Committee Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS I wish to thank Dr. David Z. D’Argenio for all his guidance and support in completion of this report. I also wish to acknowledge Dr. John Rodman at the S t Jude Children’s Research Hospital, Pharmaceutical Department, in Memphis, TN for suggesting this project and providing all the data used in this report ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONTENTS Acknowledgments ii List of Tables iv List of Figures v A bstract vi I. Introduction 1 A. AIDS/HIV 1 B. Life Cycle o f HIV 2 C. Immune System Collapse 5 D. HIV Vaccines and Drugs 8 1. Chemokine Therapy 8 2. Protease Inhibitors 8 3. Regulatory Protein Therapy 10 4. Reverse Transcriptase Inhibitors 11 E. Objectives o f the Study IS n . Methods 17 A. In Vitro Data 17 B. In Vivo Data 19 C. ADAPT Software 23 HI. Results 24 A. In Vitro Data 24 B. In Vivo Data 46 C. Dose Regimen Simulations 53 IV. Discussion 57 A. Summary and Conclusions 57 B. Further Research 60 References 62 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. L ist o f Tables Table 1. Data for st48_utwo. Table 2. Data for st24_woa. Table 3. Data for st24_wob. Table 4. Data for st24_woc. Table 5. Data for us48_utwo. Table 6. Data for us24_wo. Table 7. Data for us24_woa. Table 8. Data for us24_wob. Table 9. Data table for in vivo experiment (Note: Unit of time is hours and unit o f drug concentration is pM/106 cells; unit of Plasma PMPA is in pM). Table 10. Model estimates and criterion values for stimulated experiments with Kout. All rate constants are in units o f hrs'1 . Table 11. Model estimates and criterion values for stimulated experiments without K out All rate constants are in units o f hrs*1 . Table 12. Model estimates and criterion values for unstimulated experiments with K out All rate constants are in units o f hrs*1 . Table 13. Model estimates and criterion values for unstimulated experiments without K out Ail rate constants are in units o f hrs*1 . Table 14. Model estimates and criterion values for decoupled (Exponential Input Model) and coupled (Systemic/Cellular) systems with Kout. All rate constants are in units o f hrs'1 . Table 15. Model estimates and criterion values for decoupled (Exponential Input Model) and coupled (Systemic/Cellular) systems without Kout. All rate constants are in units of hrs*1 . Table 16. Results from simulation experiments. All values except Peak Plasma PMPA and Total Dosage are in units of pM/106 cells. Peak Plasma PMPA and Total Dosage are in units o f pM. 18 18 18 18 20 20 20 20 22 27 27 37 37 48 48 56 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. r List of Figures Figure 1. Life Cycle o f HTV. Figure taken from [2]. 3 Figure 2. Graph depicting CD4 lymphocyte depletion in HTV patients 3 overtime. Figure taken from [9]. Figure 3. Sites o f action o f some anti-HIV drugs currently in clinical 9 trials. Not shown is AZT which is used as a reverse transcriptase inhibitor. Figure taken from [13]. Figure 4. Kinetic model for cellular metabolism o f PMPA. In the in 25 vitro experiments, R (l) was the concentration o f PMPA in the medium. In the in vivo experiment, R (l) was replaced with the exponential function, Cp(t). PMPAb represents the bound PMPA. Figure 5. Systemic/Cellular model, (cc is the central compartment and 26 pc is the peripheral compartment representing all other perfusing tissues in the body. R(t) is the drug infusion rate as described in the text). Figure 6. Model predictions for st48_utwo. 28 Figure 7. Model predictions for st24_woa. 29 Figure 8. Model predictions for st24_wob. 30 Figure 9. Model predictions for st24_woc. 31 Figure 10. Model predictions for st48_utwo without Kout. 32 Figure 11. Model predictions for st24_woa without K out 33 Figure 12. Model predictions ibr st24_wob without Kout. 34 Figure 13. Model predictions for st24_woc without Kout. 35 Figure 14. Model predictions for us48_utwo. 38 Figure 15. Model predictions for us24_wc. 39 Figure 16. Model predictions for us24_woa. 40 Figure 17. Model predictions for us24_wob. 41 Figure 18. Model predictions for us48_utwo without K out 42 Figure 19. Model predictions for us24_wo without K out 43 Figure 20. Model predictions for us24_woa without K out 44 Figure 21. Model predictions for us24_wob without K out 45 Figure 22. Plot for Plasma PMPA modeling. 47 Figure 23. Results of using an exponential function as input 49 Figure 24. Results of using an exponential function as input (Kout = 0). 50 Figure 25. Results from systemic/cellular model. 51 Figure 26. Results from systemic/cellular model without K out 52 Figure 27. Model predictions for I week observation. 54 Figure 28. Results for dose regimen simulation experiments. 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT The cellular kinetics o f the antiviral nucleoside (R)-9-(2- Phosphonylmethoxypropyl)adenine (PMPA) were modeled using intracellular measurements o f PMPA and its mono- and diphosphate derivatives in lymphoid cells. Data obtained from in vitro experiments were used to devise kinetic models describing the intracellular metabolism o f PMPA. These models were then used to determine the kinetics of PMPA in data obtained from in vivo experiments on monkeys. By coupling the systemic disposition processes with the cellular events, simulation experiments were conducted to elucidate the effect o f changes in PMPA dose regimen on cellular PMPA and its mono- and diphosphate derivatives. vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [ I. INTRODUCTION A. AIDS/H IV In the decade since the identification o f the human immunodeficiency virus (HIV) as the causative agent of acquired immunodeficiency syndrome (AIDS), the global epidemic has continued to spread with alarming speed. More than 18 million HIV infections are estimated to have occurred worldwide since the beginning o f the epidemic in 1981. If the present trend continues, by the year 2000 there will be a cumulative total o f30-40 million HTV infections in the world, with 90% o f these infections occurring in developing countries. A safe, effective and affordable HIV preventive vaccine will be essential for the future control o f this pandemic [1]. AIDS is caused by two different strains o f the virus, HIV-1 and HIV-2, which belong to the lentivirus family o f retroviruses. The virus responsible for the great majority o f AIDS cases in the United States, Europe and Africa is HIV-1. A second virus related to HIV-1 has also been isolated in Africa, HTV-2. HIV-2 also appears to cause AIDS [2]. In this report, we will refer to the AIDS virus simply as HIV, and this will always mean HIV-1. Another large group o f related lentiviruses has also been discovered in nonhuman primates, and designated as simian immunodeficiency virus (SIV). 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. B. LIFE CYCLE OF HIV Retroviruses are enveloped, single-stranded ribonucleic acid (RNA) viruses whose replication depends on the integration o f a double-stranded deoxyribonucleic acid (DNA) intermediate (termed the provirus) into the host cell genome. The replication cycle o f all retroviruses compromises the same series o f steps [3]. Infection is initiated by the binding o f the viral envelope to a specific receptor or receptors located on the surface o f target cells. Receptor binding is quickly followed by the internalization o f the virus core, containing its genome and several virally encoded enzymes. Once this happens, a unique virus-specified enzyme called reverse transcriptase is quickly activated. Reverse transcription of the viral RNA ensues, leading to the stable integration o f its double-stranded DNA copy into the host cell chromosome. As the viral genes are subsequently expressed, viral RNAs and proteins are produced, processed, and assembled at the cell membrane. This viral RNA is then used for two purposes: 1) some of the viral RNA moves to the cytoplasm and functions as viral messenger RNA to program the formation of viral proteins; 2) the rest of the viral RNA becomes genetic material for new virus particles by moving to the cytoplasm and combining with viral proteins. New virus particles are formed at the cell surface and leave the cell by a process called budding (Figure 1). Throughout these events, the virus behaves as a parasite, utilizing multiple functions o f the cell machinery to its own benefit [2,4]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ® Binding to vlnlONA (4) Integration Mo Host chromosomal DNA Penetration and uncoatmg Synthaaia A J U M in M ire l *bua and budding bum tha eal Figure 1. Life c y c le o f HIV. Figure taken from [2 ]. 900 m H ♦ 2 AiOS u Time from HIV exposure Figure 2. Graph depicting CD 4 lymphocyte depletion in HIV patients over time. Figure taken from [9]. JL Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. There are several important characteristics o f the retrovirus life cycle. First, most retroviruses do not kill the cells they infect Second, the fact that these viruses integrate their DNA into host chromosomes means that they establish a stable carrier state within the infected cell. As a result, once cells are infected with most retroviruses, they will continually produce virus without dying. For some retroviruses, a latent state may also be established, in which the retroviral DNA is integrated into the host chromosomes, but it does not program the formation o f new virus particles. However, at a later time (sometimes years later), the latent viral DNA may become activated by some means, and virus will be produced. This latency process is probably important in AIDS [2]. The course of an HIV-infected individual is extraordinarily complex and is both mutifactorial and multiphasic. Following primary infection there is a burst of viremia which results in the wide dissemination o f virus and seeding of lymphoid organs. Within a period o f weeks following the initial burst o f viremia there is a potent immune response which markedly downregulates the level o f virus in both plasma and individual cells. Of particular note is the fact that although the virus is markedly downregulated, it is never completely cleared. Recent studies have demonstrated that HIV replication occurs in the lymphoid tissues throughout the entire course of HIV disease even during the prolonged period o f clinical latency [5]. This persistent plasma viremia is probably the most important component of HTV disease which distinguishes it from other retroviral infections. O f particular 4 J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. importance is the fact that the immune system is maintained in a persistent state of activation, most likely in response to the presence o f replicating virus. It is this persistent virus replication with its concomitant maintenance of cellular activation that is one of the major driving forces o f the pathogenesis of HTV disease [6]. C. IMMUNE SYSTEM COLLAPSE In contrast to most retroviral infections, infection o f T-lymphocytes with HIV results in cell death [2]. T-lymphocytes are white blood cells that make receptor proteins that are similar to antibodies, in that these proteins recognize specific antigens. Unlike B-lymphocytes, which release their antibodies into the circulatory system, T-lymphocytes hold the receptors on their cell surfaces. As a result, the T- lymphocytes themselves recognize and bind to foreign antigens. T-lymphocytes and some macrophages have a characteristic protein on their surfaces called the CD4 receptor proteins. HIV uses the CD4 receptor on the T-lymphocyte to infect host cells [7,8]. T-lymphocytes are the primary target o f HIV since they are the predominant cell type that have the CD4 receptor protein on their surface. Depletion of CD4 T-lymphocytes is a cardinal feature of infection by HIV [9] (Figure 2). The mechanisms o f CD4 depletion in HIV disease are complex and vary among patients. The simplest explanation for the loss of CD4 cells is direct killing by HIV. The virus might induce “lysis” (causing infected cells to implode or burst) or it might 5 i I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. cause cells to fuse together into clumps called syncytia [10]. But many researchers think that direct mechanisms are inadequate to explain all o f the devastation caused by HIV. A fundamental paradox o f HIV disease is the steady decline in CD4 lymphocytes, despite direct infection by HTV of only a small fraction o f circulating T cells [11]. Other mechanisms of cell death include direct cytotoxicity by viral products, immune and autoimmune destruction of infected and uninfected cells by the host, and cell signaling aberrations leading to anergy and apoptosis [9]. Infection by HTV may somehow cause another set of immune cells know as killer cells to go “haywire” and eliminate uninfected CD4s. It is possible that even more exotic destructive immunologic cascades are unleashed because parts of HIV mimic parts o f immune cell molecules, leading the body to see its own immune cells as foreign. The elaborate notion o f apoptosis, a word coined to described programmed death in cells, is also being considered. This theory claims that HIV can cause CD4 cells to destroy themselves [10]. In HIV's initial clasp with T-lymphocytes, the viral protein gpl20 on the virus’s surface binds to the host cell’s CD4 receptor. But studies in 1986 revealed that HIV required an additional factor-most likely a second receptor on the cell surface— to breach the cell membrane [8]. The identity o f this missing receptor is now known as CXCR4. Based on its amino acid sequence, researchers have surmised that CXCR4 6 i l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. belongs to the chemokine family. Chemokines, which are produced by a wide variety o f cell types, are the paging system o f the inflammatory process, recruiting white blood cells to injured or ailing tissues [7]. Researchers speculate that after CD4 and gpl20 bind, the complex goes through a “conformational change”, twisting to expose different parts o f the protein. This conformational change is what allows the complex to bind to the chemokine receptor. After the chemokine receptor has fused with the CD4-gpl20 complex, the bottom part of HIV’s envelope protein, gp41, pops away from gpl20 and, in effect, gaffs the cell membrane. The chemokine receptor completes the process by “chaperoning” the gpl20-CD4 complex into the cell [8]. Scientists at the National Institute o f Allergy and Infectious Diseases have discovered that CXCR4 seems to provide a point o f entry for HIV’s grown in cell lines, but not primary HTVs. In addition, they have reported that primary HIV’s use a different chemokine receptor, now dubbed CCR5 [7]. This receptor normally binds three chemokines known as RANTES, M IP -la, and MIP-lf}. Tests done by researchers at the National Cancer Institute on patients have shown that these three chemokines have an ’’ uncanny knack” for inhibiting strains o f HIV. These chemokines inhibit HIV by blocking some o f its entrances to the cell. A great deal o f work now has connected the dots between different strains o f HTV and the chemokine receptors they rely on. HIV’s that cause the initial infection Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f predominantly use CCR5, while the HIV's that predominate in the final stages o f disease resemble the viruses grown in T-cell lines and bind to CXCR4 [7]. D. HIV VACCINES AND DRUGS 1. Chemnldwe Thgranv Many pharmaceutical companies are now using the newly found knowledge about chemokines to develop vaccines and drugs to treat people already infected with HIV. Like most o f its competitors, Bristol-Myers is looking for a small molecule “antagonist” that blocks CCR5 and ideally can be given as a pill. Some companies are looking for an “agonist” that, by mimicking natural chemokines, would not only block CCR5 but would also trigger the receptor to send out a signal to tell the cell to slow down and express fewer of it CCR5’s— the same signal normally generated by a chemokine [7]. 2. Protease Inhibitors In developing antiretroviral drugs against AIDS, several stages o f the HTV replication cycle have been considered as targets for therapeutic intervention. In addition to chemokine therapy, researchers are also looking for other forms of treatments such as protease inhibitors, regulatory proteins, and nucleoside reverse transcriptase inhibitors (Figure 3). When the host cell, under HIV's direction, makes 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. CD4BA SED THERAPIES HYPERICIN I Panatralron Uncoating R avarsa Transcription -----------I I--------- II------------------------ \ HlVPartida ANTISENSE GLYCOSYLATION OLIGONUCLEOTIDES INHIBITORS TAT ANTAGONISTS PROTEASE INHIBITORS INTERFERON a Integration Transcription Translation Assambly an d R elaasa I I ||-------------- 1| -------------1|----------------------------- —| Host Ctiromoioma Provtral f Ooubte-strandad^ umntagratad DNA ^ Ganorwc RNA cONA \ f V hsI mRNA ovwal I >N A a * Y ~ . Cytoplasm Nucleus Y o— C o f n p l M HIV P arte* Glycosylalion and Cleavaga Cytoplasm Buddmg • « Q Pamela o r M i' Qtycoprotem Knods Figure 3. Sites of action of some anti-HIV drugs currently in clinical tr ia ls. Not shown is AZT which is used as a reverse transcriptase Inhibitor. Figure taken from [13]. VO the components o f a new virus, it begins by turning out several large proteins that must be cut in pieces before a new virus particle assembles itself. A protease does the cutting, and without that enzyme, the new virus particle is malformed and noninfectious [10]. Clinical trials have shown that a new protease inhibitor, indinavir, when used with two other anti-HIV drugs that attack a different target, can reduce the amount of HIV in people so dramatically that the most sensitive tests could not detect any virus in more that 85% o f the patients [12]. 3. R egulatory Protein Theranv Other promising targets are HIV’s regulatory proteins, which govern viral replication. Once the HIV provirus is integrated into host cell DNA, cellular and viral factors help regulate viral gene expression and replication. One HIV regulatory protein, Tat, is a unique target for antiviral therapy in both in vitro and in vivo. It acts to stabilize the elongation of RNA transcripts and to increase initiation of transcription [13]. A drug that could block Tat’s action may stop viral replication. A second viral regulatory protein, known as Rev, works downstream from Tat to help transport RNA from the nucleus to cytoplasm, where it is packaged as viral genetic material in new HTV particles. While HTV can replicate with little Tat, the virus seems to need much higher levels o f Rev to copy itself. Hence, in theory, a drug would only have to lower Rev production slightly to reduce replication [10]. 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. Reverse Transcriptase Inhibitors Most o f the clinical success in treating HIV has come from focusing on one step in the life cycle o f the virus: the point where HIV’s genetic material (RNA) is “reverse transcribed” into DNA, which then infiltrates the host cell’s genes (Figure 3). The reverse transcriptase inhibitor zidovudine (3 ’-azido-3 ’-deoxythymidine, AZT) was first tried in infected humans in 1985. AZT is very similar in chemical structure to thymidine, one of the building blocks o f DNA. However, when AZT is incorporated in place o f thymidine during the DNA assembly process, it aborts further DNA assembly because o f its structure. This inactivates any growing DNA molecule which has incorporated AZT. During HTV infection, if AZT is present, HIV reverse transcriptase will readily incorporate it into the viral DNA. This will inactivate the viral DNA. It is important that the enzymes responsible for m aking the chromosomal DNA o f the cell (cellular DNA polymerases) do not efficiently incorporate AZT into their own DNA. As a result, the cell can continue to grow and make its own genetic material, but HIV cannot replicate efficiently. Initially, patients who are given AZT show increased levels of T-lymphocytes and CD4 cells. However, the modest increases typically fade within a year, probably because the virus quickly mutates into new forms that are resistant to the drug’s action. In addition, AZT has other limitations. During prolonged treatment, cellular DNA polymerases do incorporate some AZT into cell DNA at low levels. This can 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. lead to the death o f normal cells. Anemia is a common side effect in individuals taking AZT, and results from the killing of blood cells by the drug [2]. When AZT is taken up by a cell, it must be modified chemically (phosphorylated) before it can be incorporated into DNA. This modification takes place in T- lymphocytes, so the drug is effective against HIV infection in these cells. However, there are some indications that this modification may not take place efficiently in macrophages. In this case, AZT will not be incorporated into viral DNA as efficiently in infected macrophages, and it may not prevent infection in these cells. This is o f particular concern since macrophages are probably the reservoirs of infection in HIV-infected people [2]. So far, HIV has been able to mutate into forms that evade every other antiretroviral drug tested in people. As a result, researchers have concluded that in order to beat HIV, they will have to bombard the virus with several drugs at once, since even HTV may not be able to mutate fast enough to become resistant to a multidrug combination. Scientists at the Wellcome Research Laboratories in England have been studying the effects of combining AZT with other drugs that aim at precisely the same target, the viral enzyme reverse transcriptase. They reason that when HIV has developed resistance to one drug and a new drug with the same target is added to the mix, the virus will mutate so as to resist the second drug. Somehow, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. by a mechanism that is not fully understood, the presence o f the second mutation make the virus again susceptible to the action o f the original drug [10]. The acyclic adenosine (another building block o f DNA) analogue, (R)-9-(2- Phosphonylmethoxypropyl)adenine (PMPA), has shown to be an potent viral DNA reverse transcriptase inhibitor in the simian immunodeficiency virus (SIV) [14]. Though HIV differs significantly from SIV, it is hoped that PMPA’s powerful effect in monkeys may one day help prevent and treat HTV infection in people. Using the host cell’s DNA as a template, HIV “reverse transcribe” their genetic material from viral RNA to viral DNA one nucleotide at a time. AZT and PMPA block this process by acting as decoy nucleotides which prematurely terminates the viral DNA chain synthesis. PMPA is taken up by the cells through a process resembling endocytosis, as it is temperature dependent and inhibited by endocytosis inhibitors such as sodium azide and cytochalasin [15]. Following their uptake by the cells, PMPA is converted to its monophosphate (PMPAp) and diphosphate (PMPApp) derivatives. PMPApp is the potent inhibitor o f the DNA reverse transcriptase. As discussed above, PMPApp acts as a chain terminator in the RNA-directed DNA polymerization reaction. The antiviral efficacy o f PMPA is based on the capacity o f its diphosphate derivative to preferentially inhibit viral DNA replication with relative sparing of host DNA synthesis [16]. 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. O f particular importance is the prolonged antiviral activity o f PMPA, which may last for several days. Although the compound penetrates the cell rather slowly, once inside they may be “trapped” in the form o f their active metabolites (PMPAp and PMPApp). The persistence o f these active metabolites may then explain the prolonged antiviral action. This prolonged antiviral activity conferred by PMPA makes it possible to sustain an antiviral response with infrequent dosing or even a single dose o f the compound [16]. An urgent need for new antiretroviral drugs has become evident as more people worldwide are exposed to and become infected with HIV. Unfortunately, AZT has had limited efficacy against HIV infection, and treatment can lead to drug toxicity and the emergence of drug-resistant strains o f the virus. Drugs that are more efficacious and less toxic than AZT are clearly needed. PMPA is a promising candidate for anti-HIV treatment and prophylaxis with PMPA could have a significant impact on preventing HTV infection. In vitro studies done by researchers at the University o f Washington with PMPA showed that it was 100 times less toxic than AZT. Also, the following in vivo studies on long-tailed macaques were conducted: (1) IS monkeys were injected with PMPA 48 hours before they were inoculated with SIV; (2) five others started the drug 4 hours after inoculation; (3) another five began treatment 24 hours after inoculation. All the monkeys continued receiving PMPA for 4 weeks. Eight months into the study, none o f the animals 14 J L Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. showed any sign o f infection or drug toxicity. In contrast, 10 untreated animals given the same dose o f SIV all became persistently infected [14,17]. E. OBJECTIVES O F THE STUDY For a clinician to successfully treat a patient’s disease with a new therapeutic drug, such as PMPA, requires, among other things, the understanding of a drug’s pharmacokinetics in the patient under treatment. Pharmacokinetics is the study of the absorption, distribution, biotransformation and excretion o f drugs. It is these processes that determine, for a given dose o f the drug, the concentration of the drug at its sites o f action in the body. The conversion o f PMPA to its active metabolites (PMPAp and PMPApp) is carried out by cellular enzymes. However, the exact pathway and kinetics responsible for this activation to PMPApp remain unclear. The m ain focus of this paper is to study the metabolic pathways and cellular kinetics o f PMPA in lymphoid cells. A quantitative understanding of the intracellular kinetics o f this compound is central to the development o f informed therapeutic strategies. In the present study, plasma and cellular measurements are used to develop a kinetic model for the intracellular metabolism of PMPA. The work has three parts: (1) First, in vitro data were obtained from stimulated and unstimulated lymphoid cells exposed to PMPA. The objective here was to develop candidate models that describe the cellular kinetics o f PMPA. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2) Second, in vivo data were obtained from monkeys injected with PMPA. The models developed in part (1) were used to fit the in vivo data. In addition, models that describe both the cellular and systemic kinetics of PMPA were also explored. (3) Using the systemic/cellular models developed in part (2), simulation experiments were conducted in order to determine the effect o f c h an ging the dose regimen o f PMPA on its cellular metabolites. 16 J L Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II. METHODS A. I N VITRO DATA Two different in vitro data sets were analyzed. One set o f data was from lymphoid cells that had been stimulated with phytohemaglutinen to increase cell proliferation. These include data from four different experiments: (a) st48_utwo, (b) st24_woa, (c) st24_wob, and (d) st24_woc. Tables 1-4 show the experimental data from all four experiments. In the stimulated, 48 hour uptake/washout (st48_utwo) experiment, lymphoid cells were exposed to lOpM concentration PMPA at 37 °C in media for 24 hours (uptake). For the final 24 hrs o f the experiment, the cells were resuspended in a medium lacking PMPA (washout). The intracellular concentrations o f PMPA and its metabolites (PMPAp and PMPApp) were measured during the uptake and washout phases at 7 different time points as shown in Table 1. Details o f the assay o f PMPA in cells is provided in [18]. In the three remaining stimulated experiments, measurements were made only during the washout (wo) phase. The protocol for the washout experiments was as follows: (1) expose cells to 10 pM concentration o f PMPA for 24 hrs at 37 °C; (2) “ice’ * cells to halt transport (of PMPA into cells); (3) quickly wash cells free of PMPA; (4) return cells to a medium lacking PMPA (at 37 °C); (5) take 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Time PMPA PMPAp PMPAdp Time PMPA PMPAp PMPApp 3 0.2625 0.0240 0.0292 24 0.1989 0.0833 0.1738 6 0.4309 0.0621 0.0988 28 0.0731 0.0545 0.0992 12 0.6590 0.0924 0.2029 32 0.0595 0.0377 0.0829 24 0.5542 0.0770 0.2431 36 0.0263 0.0291 0.0495 28 0.1173 0.1045 0.2727 48 0.0079 0.0159 0.0162 32 0.0936 0.1064 0.2328 36 0.0593 0.0775 0.1477 Table 2. Data for st24 woa. 48 0.0209 0.0363 0.0717 Table 1. Data for st48_utwo. Time PMPA PMPAn P M P A d p 24 0.3835 0.1182 0.3126 28 0.1859 0.1347 0.2338 32 0.1637 0.1250 0.2064 36 0.1396 0.1232 0.2044 48 0.0832 0.0670 0.1093 Table 3. Data for st24 wob. (Note: In all data sets, unit of time is hours cells.) Time PMPA PMPAd PMPApp 24 0.2267 0.0788 0.2216 28 0.1365 0.1223 0.2424 32 0.1040 0.1140 0.1457 36 0.1307 0.0957 0.1799 48 0.0453 0.0604 0.0788 Table 4. Data for st24 woe. unit of drug concentration is pM/106 18 S L Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurements during drug free exposure after “loading” cells. In sum m ary, measurements were taken only for final 24 hrs of the experiment Measurement were taken at the following time points: 24,28,32, 36, and 48 hrs. In comparing to the uptake/washout experiment, it means that the 24 hr time point in the washout and uptake/washout experiments should be similar since all o f the experiments were done under similar conditions. The other data set was from unstimulated lymphoid cells. These also include data from four different experiments: (a) us48_utwo, (b) us24_wo, (c) us24_woa, and (d) us24_wob. Tables 5*8 show the experimental data obtained for these four experiments. The experimental procedure for the unstimulated (us), 48 hour uptake/washout (utwo) experiment was similar to that o f st48_utwo. The only difference was that in the unstimulated experiment, an additional measurement of PMPA and its metabolites (PMPAp and PMPApp) was made at 24.1 hrs. The protocol for the three remaining unstimulated washout experiments was the same as for the stimulated washout experiments. B. I N VIVO DATA Data were obtained from a long-tailed macaque that was ad m in istered PMPA (105fiM concentration) as a short (0.1 hr) intravenous infusion. Measurements were made over a 48 hr period which included plasma PMPA, together with 19 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I Time PMPA PMPAd PMPAd d 3 0.3271 0.0249 0.0654 6 0.3988 0.0503 0.1560 12 0.4585 0.0933 0.3103 24 0.5180 0.1381 0.4865 24.01 0.2881 0.1414 0.4631 28 0.1648 0.1410 0.3550 32 0.1630 0.1222 0.4654 36 0.1466 0.1087 0.4062 48 0.1015 0.0874 0.3395 Table 5. Data for us48 utwo. Time PMPA PMPAp PMPApo 24 0.1263 0.0591 0.1610 28 0.1124 0.0579 0.1855 32 0.0817 0.0473 0.1570 36 0.0769 0.0474 0.1600 48 0.0507 0.0361 0.1094 Table 6. Data for us24_wo. Time PMPA PMPAp PMPApp 24 0.3270 0.1305 0.3973 28 0.1650 0.1033 0.3087 32 0.1163 0.0786 0.2804 36 0.1218 0.0831 0.3165 48 0.0997 0.0705 0.2945 Table 7. Data for us24 woa. Time PMPA PMPAd PMPApp 24 0.2335 0.1204 0.2503 28 0.0866 0.0651 0.1562 32 0.1023 0.0674 0.2201 36 0.1069 0.0652 0.1952 48 0.0608 0.0373 0.1296 Table 8. Data for us24 wob. (Note: In all data sets, unit of time is hours and unit of drug concentration is |iM/106 cells.) 20 it Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurements o f PMPA and its metabolites in lymphoid cells. Table 9 shows the data obtained from the in vivo experiment Details o f the assay of PMPA in plasma and cells are provided in [18]. The purpose o f the in vivo analysis was to study the cellular metabolism of PMPA (in vivo) and to determine the effect o f changing the dose regimen o f PMPA. In our first modeling approach, we decoupled the systemic disposition processes from the cellular metabolic processes. This was accomplished by first modeling the plasma PMPA data using an empirical exponential model. The plasma concentration function so obtained, Cp (t), was then used as the input concentration for the cellular metabolic model [19]. In our second modeling approach, we coupled the systemic and cellular processes to compare the pharmacokinetics o f PMPA in this system with those observed in the decoupled system. The input to this compartment model was an intravenous infusion as described above. This approach enabled us to predict the changes in plasma PMPA concentration, in addition to changes in cellular PMPA and its metabolites. Models that describe the pharmacokinetics o f drugs have shown that drug effects are better predicted by the plasma concentration o f the drug than by the actual amount o f drug administered. In such cases, when both the therapeutic and toxic effects o f the chug parallel its concentration in blood, the administration of the drug is generally manipulated so as to achieve a specified target plasma concentration. 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Time PMPA PMPAd PMPApp Plasma PMPA 1 1.3540 0.0332 0.0408 56.980 3 0.6696 0.0538 0.1183 16.450 7 0.1695 0.0532 0.1219 1.297 16 0.1644 0.0397 0.1793 0.149 24 0.1396 0.0305 0.1748 0.065 36 0.0895 0.0443 0.1235 0.0236 48 0.0899 0.0456 0.1638 0.007 Table 9. Data table for in vivo experiment. (Note: Unit of time is hours and unit of drug concentration is jiM/106 cells; unit of Plasma PMPA is in jiM). J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Simulation experiments were then conducted on this compartment model to assess the effects o f different dose regimens on the cellular kinetics o f PMPA and its metabolites. In the decoupled system, the input to the cells was a sum o f exponentials. In the coupled system, we simulated PMPA administration as short (0.1 hr), repeated intravenous infusions o f concentration, lOSpM. To determine optimum dose regimen, we simulated PMPA administration at 4 different dose intervals (every 48,72,96 and 120 hours). C. ADAPT SOFTWARE The modeling (estimation and simulation) was performed using the ADAPT software package. ADAPT consists o f high-level programs for sim ulation, parameter estimation and sample schedule design, developed primarily for pharmacokinetic and pharmacodynamic modeling and data analysis applications. It is a computational tool for basic and clinical research scientists involved in therapeutic drug development, designed to facilitate the discovery, exploration and application o f the underlying pharmacokinetic and pharmacodynamic properties of drugs. In the present study, maximum likelihood estimates o f the model parameters were obtained using the ADAPT II modeling software package [20]. 23 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in . RESULTS A. IN VITRO DATA The model and mass balance equations used to describe the kinetics o f PMPA in lymphoid cells are shown in Figure 4. This model was fitted to the lymphoid cell data obtained from each in vitro experiment An option in ADAPT allows the user to specify a model for the variance o f the additive error o f measured data. Measurements o f PMPA and its metabolites taken at the discrete times stated above include experimental errors. In ADAPT, experimental error is assumed to be normally distributed, with zero mean and variance assigned by the user. For each measurement made in both the in vitro and in vivo data sets, an error of 10% of the measured quantify (i.e., 10% coefficient of variation) was assigned when implementing ADAPT. In the analysis o f the stimulated experiments, two different models were obtained. One model includes a first-order pathway (Kout) for the removal o f cellular PMPA and other model does not. Table 10 and Figures 6-9 sum m arize the maximum likelihood estimates and corresponding model predictions for the model with Kout For clarify, CLup represents the rate (hrs*1 ) o f uptake o f PMPA by the lymphoid cell. Table 11 shows the estimates for the model without Kout, and Figures 10-13 show 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PMPA K b\^\K u PMPAb) PMPA PMPA Q . Kout dPMPA dt = <Kp + Kdirect + Kb + Kout) PMPA + (Ku) PMPAb + (CLup) R (l) dPMPAp dt = (Kp) PMPA - (Kpp) PMPAp dPMPApp dt = (Kpp) PMPAp + (Kdirect) PMPA - (Kpp-d) PMPApp dEMPAfa dt = (Kb) PMPA - (Ku) PMPAb Figure 4. Kinetic model for cellular metabolism of PMPA. In the in vitro experiments, R(1) was the concentration of PMPA in the medium. In the in vivo experiment, R(1) was replaced with the exponential function, Cp(t). PMPAb represents the bound PMPA. 25 4 J Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R(t) (PMPAcc) l^Z^fPMPApc) Kel C L u p\ Kdirect Kout K n ^ n n PMPA -£+»PMPAp — -^PM PAk K b \\K u [PMPAb] = -(Kp + Kdirect + Kb + Kout) PMPA + (Ku) PMPAb + (CLup) PMPAcc 0 1 dPMPAp dt = (Kp) PMPA - (Kpp) PMPAp dPMPAPP = (Kpp) PMPAp + (Kdirect) PMPA - (Kpp-d) PMPApp dt dPMPAh = (Kb) PMPA - (Ku) PMPAb dt dPMPAce - <Kel + Kcp) PMPAcc + (Kpc) PMPApc + R(t) dt dPMPAPC » (Kcp) PMPAcc - (Kpc) PMPApc dt Figure 5. Systemic/Cefluar model, (cc is the central compartment and pc is the peripheral compartment representing a l other perfusing tissues in the body. R(t) is the drug infusion rate as descrbed in the text). 26 £ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Kp Kpp Kpp-d Kdirect Kb Ku CLup Kout C W A1C st48_utwo 0.03062 0.09283 0.1233 0.04997 0 2231 0.1252 0.03467 0.5195 -49 0882 -82.176 st24_woa 0.0451 0.1102 0.3498 0 2739 0.3126 0 2341 0 007864 0.06677 -51.8897 -87.779 st24_wob 0.03974 0.07726 0.2013 0.1524 0.6665 0.1415 0.01703 0.1522 -44.7516 -73.503 st24_woc 0.04491 0.07241 0.1819 0.1528 0.4653 0.2309 0.006792 0.01253 -33 6454 -51.291 Average 0.04009 0.08817 0.21407 0.15726 0.41687 0.18292 0.01658 0.18775 ------- ------- Std. Dev. 0.00678 0.01707 0.09636 0.09157 0.19414 0.05764 0.0129 0.22851 ------- ------- Table 10. Model estimates and criterion values for stimulated experiments with Kout. All rate constants are in units of hrs'1 . Kp Kpp Kpp-d Kdirect Kb Ku CLup C W AiC St48_utwo 0.03902 0.1124 0.1504 0.06001 0.2328 0.00527 0.01703 -27.7114 -41.423 St24_woa 0.04867 0.1141 0.3933 0.3331 0 3606 0.2567 0.00745 -51.4441 -88 882 St24_wob 0.04405 0.08391 0 242 0.1955 0.4723 0.1489 0.01147 -44.4457 -74 891 st24_woc 0.0357 0.06019 0.1506 0.1171 0.1638 0.1474 0.00531 -30.5224 -47 045 Average 0.04186 0.09265 0 23407 0.17642 0.30737 0.13956 0.01031----------- ------- Std. Dev. 0.00569 0.02569 0.11457 0.11829 0.13688 0.10312 0.00515 ------- ------- Table 11. Model estimates and criterion values for stimulated experiment without Kout. All rate constants are in units of hrs'1 . 27 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) v* Tim* (st4flLuUf0.dat) ai - 90 1 0 Y(2) v* Tim* (st4A_utwe.dat) 0. 1 • 0 * 1 • 10 Y(3) v* Tim* (st44_utwo.dat) 0.1 • 40 Figure 6. Model P red iction s for st48 utwo. I J L Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tim* (ot24_woa.dat) « L l 0. 01 Y(2) vs Time (st24.woo.dat) 0. 1 • o o i ■ 40 Y(3) vs TTmo (st24_woo.dat) 0.1 < O O I ■ 2 0 90 Figure 7. Model predictions for st24 woa. 29 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tims (at24_wob.dat) si ■ 9 0 Y(2) vs Tims (st24_wob.dat) 0. 1 ooi as 40 Y(3) vs Tims (st24.wob.dot) i 0.1 O O I 40 Figure 8. Model predictions for st24_wob. 30 i l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tim* (st24_woc.dat) 0 .1 20 3 0 Tima (hour*) « 0 Y(2) v* Tim* (st24_woc.dat) 0.1 • 30 Tima (hours) Y(3) v* Tim* (st24.wec.dat) 0.1 ooi 90 Figure 9. Model predictions for st24 woe. " 3 1 i i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Timo (ot44_utwo.dat. Kout ■ 0) a o t • 20 Y(2) vo Tim# (st4fl_utwo.dat. Kout “ 0) 0 . 1 ■ 10' s o 40 Y(3) vo Timo (st4flLutwo.dat. Kout 0 .1 • ooi • 2 0 Figure 10. Model predictions for st48_utwo without Kout. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) v* Tim# (st24_woo.dat. Kout “ 0) at • 40 Y(2) vs Tim# (st2f_woo.dat. Kout “ 0) 0 .1 • 0. 01 • o 1 0 30 40 90 1 0 Tim* (hour#) Y(3) vs Tim# (st24-ooa.dat. Kout - 0} 0.1 • Figure 11. Model predictions for st24_woa without Kout. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tims (st24_wob.dat. Kout “ 0) o n 0 4 1 10 S O Y(2) vs Tim* (st24_wob.dat. Kout “ 0) 0. 01 - 10 J O 4 0 S O Y(J) vs Tims (st24_wob.dat. Kout “ 0) 0.1 O O I Figure 12. Model pred iction s for st24_wob without Kout. ~ 34 ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I I Y(1) vs Tims (»t24_*roc.dot. Kout * 0) 0.1 ■ s Y(2) vs Tims (st24_woc.dot. Kout « 0) 0. 01 Y(3) vs Tims (st24.woc.dot. Kout ■ 0) &• - O O I « 0 Figure 13. Model predictions for st24_woc w ithout Kout. 3 5 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the resulting model predictions. In the figures, Y (l) represents the concentration (pM/106 cells ) of PMPA, Y(2) is the concentration (pM/106 cells) o f PMPAp, and Y(3) is the concentration (pM/106 cells) of PMPApp in the lymphoid cells. In addition to model parameters, the tables also contain the estimator criterion value, the negative o f the log o f the likelihood (O nll) and the Akiake Information Criterion (AIC). ADAPT calculates the parameter values that minimize O nll- The AIC value takes into account the O nll and the number o f parameters being used to fit a given data set, such that addition o f unnecessary parameters increases the value of the AIC. When evaluating two competing model fits to the same data set, the model with the smaller AIC should be selected. In analyzing the unstimulated experiments, two different models were obtained, as in the stimulated experiments. Table 12 lists the maximum likelihood estimates of model parameters for the model with Kout, and Figures 14-17 show the resulting model predictions. Table 13 and Figures 18-21 show the m axim um likelihood estimates and corresponding model predictions for the model without K out In the one uptake/washout (us48jutwo) experiment the model shown in Figure 4 was modified to include an additional first-order pathway (Wout) to compensate for the washing o f the cells after the 24 hr uptake period. As described earlier, lymphoid cells were placed in a medium containing PMPA for 24 hrs. Then the cells were “washed” and resuspended in a medium without PMPA for another 24 hrs. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Kp Kpp Kpp-d Kdirect Kb Ku CLup Kout Wout C W AIC us48_utwo 0 02879 0.06514 0.0679 0.0811 1236 0.04934 0.07095 0.7733 22.1 -73 8038 -129 61 u«24jwo 008507 0.1608 0.1731 0.2015 5.178 0.4717 0 009621 0.1488 — -55 0242 -94 048 us24_woa 005728 0.1154 0 07314 0 07834 2 229 0 05942 0.0481 0.574 — -39 5587 -63 117 us24_wob 0.1032 0.1977 0.1161 0 05388 3.59 0 0857 0.0576 1.381 — -39 622 -63 244 Average 0 06858 0.13476 0.10756 0.10370 3.05625 0.16654 0 04656 0.71927 — ------- ------ Std Dev. 0.03256 0 05733 0.04873 0.06633 1.71117 0 20401 0 02635 0 51229 — ------- ------ Table 12. Model estimates and criterion values for unstimulated experiments with Kout. All rate constants are given in units of hrs'1 . Kp Kpp Kpp-d Kdirect Kb Ku CLup Wout O iu AIC us48_utwo 0.02879 0.06294 0 06532 0.07897 231 0.01902 008505 20 66 -69 8793 -123.76 us24_wo 0.08432 0.1594 0.1734 0 2027 3.361 0 4928 0 00629 ------ •55 0318 •96.064 us24_woa 0.04503 0 08514 0 06762 0 08226 0.3832 0 03764 0 01092 ------ -39412 •64 824 us24_wo6 0.2759 0.4768 0.2512 0.1089 1.287 0 1235 0 01316 ------ •36.1105 •58 221 Average 0.10851 0 19607 0 13938 0.1182 1 8353 016824 0 02885 ------ ------ ------ Std. Oev. 0.1140 0.19164 0.0899 0 0579 1 2861 0 2211 0 03757 - - — Table 13. Model estimates and criterion values for unstimulated experiments without Kout All rate constants are in units of his'1 . 37 JL Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) v* Tim* (us48_utwo.dat) 0 . 1 • 40 Y(2) v* Timo (us4S_utwo.dat) a n • I O 9 0 Y(3) vs Timo (us48_utvo.dat) a n ■ 40 Figure 14. Model Predictions for us48_utwo. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) »* Tim# (us24_wo.dat) 0 4 oos 0.04 so Y(2) vs Timo (us24_»o.dot) oos o o i 40 S O r(3 ) vs Timo (us24_oo.dat) oi • Figure 15. Model p r e d ic tio n s fo r us24_wo. 39 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) v* Time (ua24_aoa.dat) Y(2) v» Time (us24_»oo.dot) 0 .1 • 90 Y(3) vs Time (us24_woa.dat) u 40 Figure 16. Model p r e d ic tio n s for us24_woa. 40 i 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) v* Tim* (us24_wob.dat) 2 0 40 90 Y(2) vs Timo (us24.wob.dot) 0 . 1 * Y(3) vs Tims (us24_wob.dat) u 0.1 • J O 40 Figure 17. Model p r e d ic tio n s for us24_wob. 41 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tim# (us48_utwo.dat. Kout — 0) Oil • & o i 30 Tima (hour*) 40 S O T(2) vs Tima (us44Lutsro.dat. Kout “ 0) O l I • oat so Timo (hours) Y(3) vs Tim* (us*€Lut»o.dct, Kout " 0) 0 . 1 • so Figure 18. Model p red ictio n s fo r us48_utwo w ithout Kout. JU Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tims (us24.we.dot. Kout m 0) o 1 0 » ao w 40 Tim s (hows) Y(2) vs Timo (us24.wo.dot. Kout m 0) 0.1 i o 10 90 90 » 40 Ti Y(3) vs Timo (us24.wo.d0t. Kout ■ 0) 90 Figure 19. Model p red ictio n s for us24_wo w ith out Kout. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tim* (uo24_*oo.dot. Kout ■ 0) 0.1 • 20 40 Y(2) vo Timo (uo24_woa.dat, Kout » 0) 0.1 ■ a m 90 Y(3) vo Tima (us24_woo.dat, Kout “ 0) 0.1 90 40 Figure 20. Model p red ictio n s fo r us24_woa w ith ou t Kout. 4 4 jL Reproduced with perrnission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tim* (us24_wob.dat. Kout ■ 0) 0. 1 • 0 * 1 to x Tim* (hovri) i 1 9 0 Y(2) v» Tim* (us24.wob.dat. Kout “ 0) Y(3) vs Tim* (us24_wob.dat. Kout “ 0) Out Figure 21. Model p red ictio n s fo r us24_wob w ith ou t Kout. 45 ill Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. B. IN VIVO DATA The result o f modeling the plasma PMPA data using an empirical exponential model is shown in Figure 22. Statistics showed that the correlation coefficient (R2 - value) for this plot was 0.999, indicating that data and prediction were highly correlated. Using this plasma concentration function (Cp (t)) as the input concentration for the cellular model (Figure 4), the maximum likelihood estimates for the model parameters were obtained. Again, two different models were obtained, one with Kout (Table 14) and one without Kout (Table IS). Figures 23 and 24 show the resulting model predictions for exponential inputs with and without Kout, respectively. The model and mass balance equations for the systemic/cellular coupled system are shown in Figure 5. Compartment C represents the systemic circulation and Compartment P represents all peripheral tissues in the body other than lymphoid cells. The dashed line in the figure (CLup) represents the negligible amount of PMPA from the systemic circulation that is taken up by the lymphoid cells. Again, two models were analyzed, one with Kout (Table 14) and one without Kout (Table IS). Figures 25 and 26 show the resulting model predictions. In these plots, Y(4) represents the plasma PMPA concentration. Not shown in the tables are the parameter estimates for Kel, Kcp and Kpc. In the model with Kout (Table 14), the following estimates were obtained: Kel = 0.6620, Kcp = 0.0203, Kpc = 0.0976. In 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. Plasm a PMPA Modeling 1 0 0 - c o S c u 3 5 0 - 30 40 20 50 10 0 Time (hours) Figure 22. Plot for Plasma PM PA modeling. Kp Kpp Kpp-d Ksyn K b Ku CLup Kout O nll AIC EIM 0.0235 0.0818 0.0499 0.03357 2.187 0.0459 0.0549 0.3059 -39.812 -63.623 S/C 0.018 0.0609 0.0402 0.03046 3.538 0.053 0.1137 0.926 -57.411 -90.821 Avg. 0.0208 0.0714 0.045 0.03202 2.863 0.0494 0.0843 0.616 ------ ------ STD. 0.0039 0.0148 0.0069 0 .0 0 2 2 0.955 0.005 0.0416 0.4385 ------ . Table 14. Model estimates and criterion values for decoupled (Exponential Input Model) and coupled (Systemic/Cellular) systems with Kout. All rate constants are in units of hrs'1 K p Kpp Kpp-d Ksyn K b K u CLup O nll AIC EIM 0.0212 0.0782 0.04818 0.03293 2.762 0.0358 0.0622 -38.376 -63.752 S/C 0.0193 0.0714 0.04389 0.03114 4.62 0.0337 0.1139 -53.751 -85.502 Avg. 0.0203 0.0748 0.04604 0.03204 3.691 0.0348 0.0881 ---------- ---------- STD. 0.0014 0.0048 0.00303 0.00127 1.314 0.0014 0.0365 - ---- Table IS. Model estimates and criterion values for decoupled (Exponential Input Model) and coupled (Systemic/Cellular) systems without Kout. All rate constants are in units o f hrs'1 . 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tim* (Exponential Input) O S ax at • 9 0 Tim* (houn) 40 Y(2) vs Tim* (Exponential Input) ai aax 40 Y(3) vs Tim* (Exponential Input) ax at 90 90 Tim* (h a m ) Figure 23. R esu lts o f using an exponential fu n ction a s Input. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tims (Exponential Input. Kout ■ 0) as si • 30 3 0 Y(2) vs Tims (Exponential Input. Kout - 0) st sos 30 Tima (hours) S O Y(3) vs Time (Exponential Input. Kout “ 0) si • to Figure 24. R esults o f u sin g an exponential fu n ction as Input (Kout * 0 ) . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(1) vs Tims (In vwo oystsm /csH modsl) Y(2) vs Tims (In vivo sy stsm /cslt modsl) si i os is m 90 Y(3) vs Tims (In vivo systsm/csM modsl) Y(4) vs Tims (In vivo sy stsm /csil modsl) s i 4 to 90 to 40 9 0 Figure 25. Results from sy stem ic/cellu la r model. 51 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I . Kout - 0) Y(1) vs Tims (In vivo (ystsm /csM os is Y(2) vs Tims (In vivo systsm /csH 0»1 I , Kout - 0) o o i • m Y(3) v i Tims (In vivo ty stom /coi I. Kout - 0) Y(4) vo Timo (In li. Kout • 0) 0 2 1 0 • 0.1 * • 0 10 9 0 Figure 26. Results from sy ste m ic/c e llu la r model without Kout. 52 JL Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ! the model without Kout (Table IS), the following estimates were obtained: Kel = 0.6367, Kcp = 0.0198, Kpc = 0.0966. (Units for these parameters are in hrs*1 ). C. DOSE REGIM EN SIMULATIONS To determine the effect o f changing the dose regimen for PMPA, simulation experiments were conducted on the coupled system. Figure 27 shows the resulting model predictions for a one week observation when PMPA adm inistration was simulated as a short (0.1 hr) intravenous infusion of concentration, lOSpM. Figure 28 shows the resulting model predictions for the rate o f change o f PMPApp concentration (Y(3)) when intravenous infusions were repeated every 48, 72,96, and 120 hrs (administration of PMPA was simulated as short (0.1 hr) repeated infusions of concentration 105pM for 600 hrs). Table 16 lists the following values for each simulation experiment: (1) peak value o f PMPApp after the last dose; (2) trough value o f PMPApp after the last dose; (3) total amount o f dosage given for each time increment; (4) peak value for plasma PMPA concentration during the experiment; and (5) (peak-trough) value. 53 J L Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I I 1 Y(2) vs Tims (1 s t m SB Y(1) vs Tims (1 obssrvotisn) os 0 2 a o 40 Y(4) vs Tims (1 SO too Figure 27. Model predictions for 1 week observation. 54 j£l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y(3) v t Tim* (Dosog* *vsry 48 hrs) Y(3) v* Tim# (Dosog* i w y 72 hr*) a * 120 hrs) Y(3) vs Tim# (Deaog* Y(3) vs Tims (Dosog* svsry 96 hrs) o s si si« 4 0 * T im * (to i m i s Figure 28. Results for dose regimen sim ulation experim ents. 55 I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 hrs (Peak Value) 0.481 (Trough Value) 0.398 (Total Dosage) 1365 (Peak Plasm a PMPA) 101.49 (Peak - Trough) 0.083 72 hrs 0.325 0.234 945 101.5 0.091 96 hrs 0.245 0.152 735 101.48 0.093 120 hrs 0.196 0.104 630 101.48 0.092 Table 16. Results from simulation experiments. All values except Peak Plasma PMPA and Total Dosage are in units of pM/106 cells. Peak Plasma PMPA and Total Dosage are in units of pM. 56 [ J L Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f IV. DISCUSSION A. SUMMARY AND CONCLUSIONS While several kinetic models were considered, the model shown in Figure 4 best fit the data collected from the in vitro experiments. The inclusion o f two o f the pathways shown in the figure was necessitated by specific qualitative patterns in the raw data o f PMPA in lymphoid cells. First, to account for the biphasic time course of the cellular concentration o f PMPA, a reversible intracellular binding process was postulated (Kb/Ku). This compartment in the model suggests that there is a certain amount o f unspecified binding o f PMPA such that all o f the PMPA is not metabolized right away. Second, to account for the rapid formation o f the diphosphate derivative (more rapid than the formation o f the monophosphate), a direct (Kdirect) formation pathway between free cellular PMPA and its diphosphate derivative was included [19]. Tables 10 and 11 list the maximum likelihood estimates for the stimulated experiments with and without Kout, respectively. Both tables show that the estimates for the key model parameters (Kp, Kpp, Kpp-d, and Ksyn) have a standard deviation close to 10%. This suggests that, given some experimental error in the data collection, the values for these rate constants are reliable. To determine the 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. better model, the model with Kout or the one without Kout, the criterion values were considered. By comparing the O nll and AIC criterion values, it was noted that in two o f the data sets (st48_utwo and st24_woc), the model that included the additional parameter Kout was the better model. It should also be noted that in the uptake/washout data set, the model with Kout is overwhelmingly a better model. But in the other two data sets (st24_woa and st24_wob), the O nll and AIC criterion values are very similar. In these two data sets, it appears that the model without Kout is slightly better than the model with Kout. This conclusion is the result of comparing the AIC values since this estimator already takes into account the O n ll- Figure 6-9 and Figures 10-13 show the resulting model predictions for model with and without Kout, respectively. Tables 12 and 13 list the maximum likelihood estimates for the unstim ulated experiments with and without Kout, respectively. Statistical analysis of the kev parameters (Kp, Kpp, Kpp-d, and Ksyn) shows that for the most part, these values are within a standard deviation of 10% for both models. It can be concluded that given experimental error, these estimates are reliable. In analyzing the O nll and AIC criterion values for the two data sets, us48_utwo and us24_wob, it is concluded that the model which includes Kout is the better model. In the data sets, us24_wo and us24_woa, the criterion values for both models are very similar. In these two data sets, it appears that the model without Kout is slightly better than the model with 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Kout when the AIC values are compared. Figures 14-17 and Figure 18-21 shows the resulting model predictions for models with and without Kout, respectively. Tables 14 and 15 list the maximum likelihood estimates o f the model parameters for the decoupled and coupled systems, with and without Kout, respectively. Statistical analysis of both models show that for both systems, the key model parameter estimates are within a standard deviation of 10%. To determine the better model, analysis of the two criterion values showed that the model with Kout is the better model. Figures 23 and 25 show the model predictions for both systems for the model with Kout. Figures 24 and 26 show the model predictions for both systems for the model without Kout To determine the effect o f changing the dose regimen, we first simulated an infusion (as described earlier) to observe the rate of removal o f PMPA from plasma (Y(4) plot in Figure 27). Next, simulation experiments with repeated infusions at discrete time intervals (48,72,96, and 120 hrs) were conducted. Table 16 lists the results of PMPApp concentration after the administration o f the last dose for each time interval. Since PMPApp is the key metabolite that is directly incorporated into the viral DNA, it is imperative that its concentration be kept constant during treatment Table 16 shows that the (peak-trough) value is lowest in the 48 hr dose interval, indicating that this dose interval might be used for therapeutic treatment In the other three dose intervals, the (peak-trough) value is relatively constant. From 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 28, we see that in all four dose intervals, the trough value o f PMPApp is maximal at approximately 400 hours. This indicates that steady-state for PMPApp is reached around 400 hours. In addition, Table 16 also lists the peak plasma PMPA concentration for all four dose intervals. It was discovered that the peak value returned to same value in all four dose interval simulations. As discussed earlier, plasma concentration of a drug is critical since toxic effects of the drug parallel its concentration in blood. B. FURTHER RESEARCH The use o f ADAPT has provided some preliminary details o f the pharmacokinetics o f PMPA, both in vitro and in vivo. Before clinical trials on patients with HIV can be conducted, some important issues, such as PMPA toxicity levels and the PMPApp concentration required for maximal viral elimination, still need to be resolved. Our analysis of the in vitro and in vivo data showed that for most part, the model which included Kout yielded better results, both statistically and graphically. However, for two of the data sets, the results are inconclusive and require further exploration. Additional experiments, both in vitro and in vivo, need to conducted in order to verify the results found in this study. Many scientists believe that in order to control HIV, treatment with several drugs will be essential since even HIV may not be able to mutate fast enough to become 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resistant to a multidrug combination. In light o f this, a multidrug study with PM PA and other reverse transcriptase inhibitors such as A Z T , may provide valuable insights to the combination therapy theory. The kinetic modeling software, ADAPT, may prove useful for pharmacokinetic analysis o f the multidrug combination treatment 61 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I REFERENCES [1] Saladin, Osmanov, et al. HIV-1 Genetic Variability: Implications for the Development of HIV Vaccines. Antibiotics & Chemotherapy. 48:30(1996). [2] Fan, Hung, et al. The Biology o f AIDS. Jones and Bartlett Publisher, Boston, MA, 1989. [3] Varmus, H. E. Replication o f Retroviruses. RNA Tumor Viruses, ed. 2. Cold Spring Harbor, N.Y., Cold Spring Harbor Laboratory, 1985, p74. [4] Trono, Didier. Molecular Biology o f HIV. Clin. Lab. Med. vl4:2, p203-220 (1994). [5] Fauci, Anthony, S. Host Factors in the Pathogenesis o f HIV Disease. A ntibiotics & Chemotherapy. 48:4-6(1996). [6] Laughlin, Mark, A. Cellular Latency in HIV-1 Infection. Clin. Lab. Med. vl4:2, p239-255 (1994). [7] Cohen, Jon. Exploiting the Chemokine Nexus. Science. 275:1261-1264 (1997). [8] Cohen, Jon. Investigators Detail HIV’s Fatal Handshake. Science. 274:502 (1996). [9] Schattner, Elaine. HTV-Induced T-lymphocytes Depletion. Clin. Lab. Med. vl4:2, p221-238 (1994). [10] Cohen, Jon. AIDS Research: The Mood is Uncertain. Science. 260:1254-1261 (1993). [11] Ho, D. D. Quantitation of HIV-1 in the Blood o f Infected Persons. New Eng. J. M ed. 321:1621-1625(1989). [12] Cohen, Jon. Protease Inhibitors: A Tale o f Two Companies. Science. 272:1882-1883 (1996). [13] Kaplan, Joan, C., et al. Therapy Other Than Reverse Transcriptase Inhibitors for HIV Infection. Clin. Lab. Med. vl4:2, p367-391 (1994). 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [14] Cohen, Jon. New Drug Shows Promise in Monkeys. Science. 270:1121 (1995). [15] Palu, G. Mechanism o f Cellular Uptake of Phosphonylmethoxyalkyl Purine Derivatives. The Third Int’I Conference on Antiviral Research, Brussels, Belgium, 22-27 April 1990. Antiviral Res. Suppl. 1, p86, No. 90,1990. [16] De Clerco, Erik. Broad-Spectrum Anti-DNA Virus and Anti-Retrovirus Activity of Phosphonylmethoxyalkyl Purines and Pyrimidines. Biochem. Pharmacology. 32.962:912 (1991). [17] Tsai, Che-Chung. Prevention o f SIV Infection in Macaques by (R)-9-(2- Phosphonylmethoxypropyl)adenine. Science. 270:1197-1199(1995). [18] Robbins, B. L. Metabolic Pathways for Activation o f the Antiviral Agent 9-(2- Phosphonylmethoxyethyl)adenine in Human Lymphoid Cells. Antimicrob. Agents Chemother. 139:2304-2308 (1995). [19] D’Argenio, David, Z., Schumitzky, Alan. ADAPT II: Pharmacokinetic/ Pharmacodynamic Systems Analysis Software. User’s Guide to Release 4, March 1997. Biomedical Simulations Resource, University o f Southern California. [20] D’Argenio, David, Z., Rodman, John H., Robbins, Brian L., and Fridland, Arnold. Modeling the Cellular Kinetics of the Antiviral Agents PMEA and PMPA. Proceedings o f the IEEE Engineering in Medicine and Biology, 18t h Annual Conference, p649-650. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Asset Metadata

Creator Raman, Rajesh K. (author)

Core Title Cellular kinetic models of the antiviral agent (R)-9-(2-phosphonylmethoxypropyl)adenine (PMPA)

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Master of Science

Degree Program Biomedical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, pharmaceutical,engineering, biomedical,OAI-PMH Harvest

Language English

Advisor D'Argenio, David (committee chair), Khoo, Michael C.K. (committee member), Singh, Manbir (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-17484

Unique identifier UC11341237

Identifier 1387843.pdf (filename),usctheses-c16-17484 (legacy record id)

Legacy Identifier 1387843.pdf

Dmrecord 17484

Document Type Thesis

Rights Raman, Rajesh K.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA