MODELING THE AIRWAY SURFACE LIQUID REGULATION IN HUMAN LUNGS. Peiying Zuo

Transcription

1 MODELING THE AIRWAY SURFACE LIQUID REGULATION IN HUMAN LUNGS Peiying Zuo A dissertation submitted to the faulty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Dotor of Philosophy in the Department of Mathematis. Chapel Hill 2007 Approved by: Chair of Committee: Dr. M. Gregory Forest Advisor: Dr. Timothy C. Elston Advisor: Dr. Rihard C. Bouher Reader: Dr. Jingfang Huang Reader: Dr. Rihard M. MLaughlin

2 2007 Peiying Zuo ALL RIGHTS RESERVED ii

3 ABSTRACT PEIYING ZUO: Modeling the Airway Surfae Liquid Regulation in Human Lungs. (Under the diretion of Timothy Elston and Rihard Bouher) The researh in this dissertation is aimed at understanding the pathogenesis of Cysti Fibrosis whih is a life-threatening disorder that auses severe lung damage and nutritional defiienies. Patients with ysti fibrosis exhibit defiient muoiliary learane due to enhaned thikness and adherene of the muus in their airway. In the past a few deades signifiant progress has been made in understanding the ause of the disease as well as ways to treat it. Besides onventional treatments for ysti fibrosis the addition of adenine triphosphate (ATP) to the airway surfae of the lung was reently found to be effetive to restore muoiliary learane. Even as sientists begin to understand the signaling pathways that regulate the airway surfae liquid (ASL) there are still many parts of this omplex system that remain unlear. The ultimate goal of this work is to put together several important puzzle piees and try to understand how proper regulation of the ASL is ahieved. iii

4 ACKNOWLEDGEMENTS I am deeply indebted to my advisors Drs. Timothy Elston and Rihard Bouher who guided this work and helped whenever I was in need. Without their onstant support and enouragement this work would not have been possible. I am also very grateful to a group of fantasti people from Cysti Fibrosis Pulmonary Treatment & Researh Center at UNC. The beautiful experimental results from Drs. Maryse Piher and Eduardo Lazarowski provided a nie starting point and bakbone for this work. The enlightening disussions with Drs. Brian Button Seiko Okada and Robert Tarran have helped me in understanding different aspets of this work. Without strit training by Dr.Jak Stutts and Mrs. Leslie Fulher on Ussing hamber and ell ulture tehniques I wouldn t have been able to present my own experimental data in this dissertation. I had a really good time working with all of them over these years. Sinere thanks are also extended to the faulty members in the Department of Mathematis for their support; espeially to my ommittee members Drs. Gregory Forest Jingfang Huang and Rihard MLaughlin. My parents who raised me to be the person I am today deserve the most aknowledgements. Finally I thank my beloved husband Yihao for understanding supporting and loving me. iv

5 TABLE OF CONTENTS LIST OF TABLES.vii LIST OF FIGURES..viii Chapter I. INTRODUCTION History and motivation Outline.. 9 II. E XT RACE LLULAR NUCLE OTI ( SI) DE AND NUCLE OSIDE METABOLISM Introdution Methods Results Disussion..30 III. ION/WATER TRANSPORT MODEL Introdution Mathematial equations Parameter estimation Model validation Conlusion..55 IV. AIRWAY SURFACE LIQUID REGULATION Introdution...57 v

6 4.2 Miroeletrode studies Experimental results with ATP Experimental results with UTP Modeling the response 85 APPENDICES...91 REFERENCES vi

7 LIST OF TABLES Table 1. Comparison between parameters of ASL nuleotide release and metabolism funtionally measured and estimated from the nonlinear model without fitting or inluding parameters of ADP and AMP release Steady-state nuleotide onentrations alulated from the linear model without or with parameters of ADP and AMP release Diffusion onstants of ATP in different media Comparison of in vivo measurements of membrane permeabilities to ions and water with estimated values Comparison of variables at steady-state before and after parameter estimation Experimental observations and numerial simulation alulated by the ion/water transport model in the experiment in whih apial sodium hannel is bloked by amiloride Experimental sheme for measuring the hloride urrent with single-dose ATP in the apial side of the CF HBE ells Experimental sheme for measuring the hloride urrent with umulative-dose ATP in the apial side of the CF HBE ells Experimental sheme for measuring the sodium urrent with single-dose ATP in the apial side of the CF HBE ells Experimental sheme for measuring the sodium urrent with umulative-dose ATP in the apial side of the CF HBE ells Experimental sheme for measuring the transmembrane urrent that is omposed of both sodium and hloride ions Different senarios for testing the integrated model 87 vii

8 LIST OF FIGURES Figure 1. The struture of the human respiratory system 2 2. Gene loation of CFTR.3 3. Regulation of PCL layers by ative ion transport.6 4. Diagram of nuleotide transport/metabolism on the apial surfae of human airway epithelia Comparison of model predition with experimental measurements for steady state ATP and ADO Model validation of the transient and steady-state onentration profiles generated by the nonlinear model without data fitting Model validation of the transient and steady-state onentration profiles generated by data fitting using the Matlab least square program and without (A B) or with (C D) a fixed rate of ATP release Validation of the transient and steady-state onentration profiles generated by data fitting using the nonlinear model inluding parameters of ADP and AMP release Sensitivity analysis of the nonlinear model inluding ADP and AMP release for low-affinity NS AP and high-affinity E-NTPDase Relative ontribution of Eto 5 -NT and NS AP to airway adenosine regulation Layered struture of the ASL in human lungs The ativities of nuleotides and nuleosides in the ASL The averaged ATP onentration in the ASL when varying the diffusion rate in muus layer D M with respet to the diffusion rate in PCL D P Initial ondition of aerosol ATP delivery to the ASL The loal ATP onentration at epithelial ell membrane numerially solved from the partial differential equation system The transport proesses in human airway epithelium Voltage-lamp iruit representing the equilibrium state of transmembrane urrents...48 viii

9 18. Comparison of the in vivo measurement (blak) and simulation results (red) for ion onentration and membrane potentials before (A) and after (B) the parameter estimation Simulation of ATP depletion in human airway The signaling pathways ativated by ATP and adenosine in the normal and CF human epithelia Polyarbonate snapwells for ell ulturing Profusion Ussing hamber setup for measurement of transepithelial short iruit urrent Measurements of sodium urrent indued by umulative doses of ATP on P2 epithelial ells from CF patients Measurements of hloride urrent with umulative doses of ATP ranging from 10-9 M to 10-4 M Measurements of hloride urrent with single dose of ATP ranging from 10-6 M to 10-4 M Measurements of hloride urrent with umulative doses of ATP ranging from 10-6 M to 10-4 M Quantitative analysis of the hloride urrent measurement with a single dose of ATP Quantitative analysis of the hloride urrent measurement with umulative doses of ATP Cumulative dose-response urves for sodium urrent with ATP indued by ATP (10-9 M to 10-4 M) on P1 ultures of CF bronhial epithelial ells Measurements of sodium urrent measurement with a single apial dose of ATP on CF epithelial ells Quantitative analysis of the sodium urrent measurement with single dose of ATP on P2 CF epithelial ells Sodium urrent measurements with umulative doses of ATP on apial surfae of CF epithelial ells Quantitative analysis of the data from sodium urrent measurement with umulative doses of ATP ix

10 34. Single dose response of mixed urrent (I Na +I Cl ) to ATP ranging from 10-6 M to 10-4 M on P2 epithelial ells Measurement of sodium urrent indued by various doses of ATP on P0 (A B C) P1 (D E F) and P2 (G H I) ultures of bronhial epithelial ells Measurements of hloride urrent indued by various doses of ATP on P0 (A B C) P1 (D E F) and P2 (G H I) ultures of bronhial ells Measurements of hloride urrent and mixed urrent indued by various doses of UTP on P2 human epithelial ells Measurements of sodium urrent measurements indued by various doses of UTP on H441 ells Hypertoni saline test on the ion/water transport model with parameters from CF airways x

11 ABBREVIATION AC ADO ADP AMP AP ASL ATP CaCC AMP i CF CFTR CNT DAG Eto-AK Eto 5 -NT ENaC E-NPP HBE HPLC HNE KBR MTE INO IP3 Adenylyl ylase Adenosine Adenosine diphosphate Adenosine monophosphate Alkaline phosphatase Airway surfae liquid Adenosine triphosphate Calium-ativated hloride hannel Intraellular yli-amp Cysti fibrosis Cysti fibrosis transmembrane regulator Conentrative Na + -dependent nuleoside transporter Diaylglyerol Eto-adenylate kinase Eto 5 -nuleotidase Epithelial sodium hannel Eto-nuleotide pyrophosphatase/phophodiesterase Human bronhial epithelial High-performane liquid hromatography Human nasal epithelial Krebs-biarbonate ringer Murine traheal epithelial Inosine Inositol trisphosphate xi

12 MCC NS AP ENTPDase PCL PIP2 PKA PKC PLC UTP Muoiliary learane Non-speifi alkaline phosphatase Eto-nuleoside triphosphate diphosphohydrolase Periiliary layer Phosphatidylinositol 4 5-biosphosphate Protein kinase A Protein kinase C Phospholipase C Uridine triphosphate xii

13 CHAPTER 1 INTRODUCTION 1.1 HISTORY AND MOTIVIATION The prinipal funtion of the human lung is to transport oxygen from the atmosphere into the bloodstream and to exrete arbon dioxide from the bloodstream into the atmosphere. Respiration ours in a series of steps. Air is brought into the body via the airways from the nose to the pharynx the larynx the trahea bronhi bronhioles and the alveolar sas forming the terminal branhes of the respiratory tree (Figure 1). The exhange of gases is aomplished by the sas of speialized ells that form millions of tiny exeptionally thin-walled air sas alled alveoli. The airways also present natural defense mehanisms against infetions. The iliated epithelial surfaes of the airways are shielded by a muus layer whih traps inhaled partiles and is ontinuously removed from the airways by iliary beating ativity. The muus sereted by superfiial epithelium and goblet ells is normally lear and think filtering air during inhalation. During times of infetion muus an hange olor as a result of trapped bateria while in some other diseases suh as ysti fibrosis a onsisteny hange an our due to water loss and high salt onentrations. Lung disease is the number three killer in Ameria responsible for one in seven deaths. Along with other breathing problems it is also the number one killer of babies younger than one year. Today more than 35 million Amerians are living with hroni

14 lung diseases suh as asthma emphysema and hroni bronhitis. In this dissertation our fous is the lung disease alled ysti fibrosis. In medieval folklore infants with salty skin a symptom of ysti fibrosis are Figure 1: The struture of the human respiratory system (from onsidered "bewithed" beause they routinely die an early death. As sienes advaned more about this disease has gradually been revealed. Cysti fibrosis (CF) is an inherited hroni disease that affets the lungs and digestive systems of about hildren and adults in the United States (70000 worldwide). It is most prevalent amongst European and Ashkenazi Jews. One in twenty-two people of European desent arries one gene for CF making it the most ommon geneti disease among them. CF does not follow the same pattern in all patients but affets different people in different ways and to varying degrees. It affets the entire body but symptoms begin mostly in the lungs. Some ommon symptoms inlude oughing repeated lung infetions shortness of breath poor growth intestinal blokage and infertility all dominated by funtional abnormalities in the glands that produe or serete sweat and muus. Sweat ools the body; muus lubriates the respiratory digestive and reprodutive systems and prevents tissues from 2

15 drying out proteting them from infetion. The lungs of CF patients produe exess thik stiky muus that logs the airways ausing breathing problems and providing a breeding ground for bateria to grow whih leads to frequent lung infetions damages to the lungs and ontributes to early death. Thik fluid may also log panreati duts and prevent digestive fluids from reahing the small intestine whih auses digestive problems and slows growth. The onventional treatments for CF-related lung ompliations are hest perussion or other ways of learing muus. Antibiotis are often used to fight infetion. There is no ure for CF and most patients die young many in their 20s and 30s from lung failure. A Lung transplant is often neessary as CF progresses. Besides the onventional treatments sientists are also working on finding a gene-based therapies based on the identifiation of CF gene two deades ago. A B Figure 2: Gene loation of CFTR. The approximate gene loation of CFTR is based on Chromosome 7 map from NCBI Entrez Map Viewer (A). Figure2B: The F508 deletion is the most ommon ause of ysti fibrosis. The isoleuine (Ile) at amino aid position 507 remains unhanged beause both ATC and ATT ode for isoleuine (From Genomis.energy.gov) The identifiation of ysti fibrosis disease is traed bak to the 1930s when it was first referred to as ysti fibromatosis with bronhietasis. Andersen et al. developed the first omprehensive desription of ysti fibrosis symptoms in About fifteen years later di Sant Agnese formally reported exessive amounts of salt in the CF 3

16 patients sweat. In 1985 Tsui and o-workers disovered the gene responsible for CF and named its protein produt Cysti Fibrosis Transmembrane Condutane Regulator (CFTR) whih was mapped to the long arm of hromosome 7q (Fig2A). Both opies of the gene need to be defetive for a person to develop the disease. CFTR is an essential protein found in the epithelial ells that line the body's internal passageways inluding the lungs panreas olon and genitourinary trat. It is responsible for moving hloride ions (Cl - ) through the ell membrane. In 70% to 80% of all CF ases three of the base pairs in the gene are deleted and the amino aid that the triad odes for (phenylalanine) is not generated. The abnormal protein is alled F508 CFTR (Fig2B). The other 20% to 30% of CF ases result from one of hundreds of other possible mutations that an lead to abnormal CFTR funtion. The finding of the CF gene makes gene therapy a natural andidate for treatment of ysti. Gene therapy is the insertion of genes into an individual's ells and tissues to treat a disease. Cysti fibrosis ultimately ould be ured if safe and effetive methods are found to replae the defetive CFTR gene with an intat gene in affeted tissues. In the ase of ysti fibrosis gene therapy would involve inhaling a spray that delivers normal DNA to the lung. During suh a treatment shuttle vehiles alled vetors deliver a funtional opy of the defetive gene-in this ase CFTR-either to ells throughout the airways. One the new CFTR gene has entered the ell the biohemial mahinery must reognize it and use it as a template for the prodution of funtional protein. However despite an impressive amount of researh in this area there is little evidene to suggest that an effetive gene-transfer approah for the treatment of CF lung disease is imminent. The inability to produe suh a therapy reflets in part the learning urve with respet to vetor tehnology and the failure to appreiate the apaity of the airway epithelial ells 4

17 to defend themselves against the penetration by moieties inluding gene-therapy vetors from the outside world. Meanwhile the general reognition that CF lung disease reflets a failure of the innate defense of airways against baterial infetion leads to a searh fousing on identifying the nature of the normal innate defense of the airways against baterial infetions and how mutations in the CF transmembrane ondutane regulator (CFTR) gene perturb these mehanisms. It is generally believed that airway surfae dehydration produes leads to muus adhesion inflammation and baterial biofilm formation The haraterization of well-differentiated ultures of airway epithelial ell ulture revealed that the airway surfae liquid (ASL) is divided into a well-defined periiliary liquid (PCL) layer and a muus layer. Reent studies have shown that liquid an be added to or removed from the muus layer without altering the height of the PCL layer. Speifially the studies showed that removing approximately 50% of the liquid from the ASL ompartment led to seletive redution in the volume of the muus layer with preservation of the PCL layer and at least partial preservation of muus transport. Conversely when the ASL volume was doubled liquid entered the muus layer the PCL layer maintained its volume and interestingly the muus transport rates inreased. Further studies revealed that when 70% or more of the volume was removed from the ASL ompartment the muus layer ould no longer effetively donate liquid to the PCL layer volume was lost from the PCL and muus transport eased. The upper limit of volume addition to the muus layer was not determined in these studies. One impliation of these findings is that as liquid in vivo onverges onto a single airway from two smaller airways the exess liquid deposited on the single airway from two distal airways may be transiently stored in the muus layer with preservation of PCL layer height and muus transport. Presumably the exess liquid (salt and water) will be 5

18 removed by transepithelial ion transport from the muus layer as the ASL moves up the singe airway. In ontrast when water loss ours at the surfae of proximal airways due to exerise-indued evaporation the volume is seletively lost from the muus layer with preservation of PCL and muus transport. Figure 3: Regulation of the volume of periiliary liquid (PCL) layer by ative ion transport. a) Shema desribing routes of Na + Cl and H 2 O transport and ion transport elements that mediate these flows. The luminal surfae ontains the epithelial Na + hannel (ENaC) and two Cl hannels: ysti fibrosis transmembrane regulator (CFTR) and the Ca 2+ -ativated "alternative" Cl hannel (CaCC). CFTR is depited as a Cl hannel and a regulator of ENaC. The basolateral surfae ontains the Na + /K + pump the K + hannels and the loop diureti sensitive Na + -K + -2Cl otransporter. b) Regulation of "exess" PCL volume by Na + absorption and maintenane of PCL at funtionally relevant height (7 µm defined by the height of extended ilia) by a mix of the Na + absorption and Cl seretion. ) Interonversion of normal human airway epithelia between absorptive and seretory ion transport modes. When exess airway surfae liquid (ASL) is present Na + absorption mediated via ENaC is dominant (left panel). Cl is absorbed passively via the paraellular path due to the lak of eletrohemial driving fore (DFaCl ) favoring Cl exit from the ell. In ontrast both the negative apial membrane potential (V a ) and low intraellular Na + ativity (~20 mm) favour Na + entry into the ell. When ASL volume is low (right panel) ENaC is inhibited whih makes the apial membrane potential more negative and generates a driving fore for Cl seretion. Information regarding ASL volume is postulated to be "enoded" within the ASL. Despite the good understanding of the role of the muus layer as a reservoir there are still surprisingly large gaps in our knowledge of the physiology and biophysis of this layer. For example it is still not lear how this layer is formed in vivo nor what are the proesses that maintain it as a physial layer. Older theories suggesting that the muus 6

19 layer was reated by the thixotropi 1 ation of beating ilia appear to be inaurate. There are very likely important phase transitions that our as a funtion of the onentration of the gel-forming muins in ASL. Furthermore as noted above it is not known what the water storage apaity of the muin layer is or the biophysial priniples that govern the apaity of this layer to absorb or donate liquid. Finally it s not yet lear how the addition of liquid to airway surfaes inreases muus transport as the biophysial properties of the muus layer may be less important than the properties of the PCL layer. The prinipal determinant of ASL volume is the mass of the salt on the airway surfae 7. This fat reflets the highly water permeable nature of the airways epithelium that rapidly restores/maintains ASL volume in a near-isotoni state 8. The mass of salt I the ASL is determined in part by the movement of liquid along epithelial surfaes and in part by the ative ion transport mehanisms loated within that airway region. Reent studies have emphasized the importane of the role of the PCL layer volume (height) in the maintenane of effetive muus learane. A useful model for studying PCL physiology has been the well-differentiated ulture that has had the muus layer removed and a volume of liquid that mimis the properties of PCL plaed on its surfae. A onvenient paradigm has been to start experiments with an exess of PCL that might mimi the height found at the onvergene point of two airways. As shown in Figure 3 normal human airway epithelia absorb rapidly the exess PCL. But as the PCL layer approahes physiology height (7m) ative volume absorption eases and a steady state is reahed. Sine the original detetion of a raised potential differene (PD) aross CF airway epithelia in vivo 9 there has been the notion that abnormal eletrolyte transport is a key 1 Thixotropi adjetive form of thixotropy. Thixotropy is the property of various gels of beoming fluid when disturbed (as by shaking) 7

20 omponent of CF lung pathogenesis. Early PD studies deteted an inrease in the amiloride 2 -sensitive omponent of the PD whih suggested an aelerated Na + transport. However the PD measurements also deteted a failure to serete Cl - ions under basal onditions and β-adrenergi 3 stimulation whih predited a seond defet 10. Subsequent studies with freshly exised tissues and ultured ells established evidene for both Na + transport (upregulated) and Cl - transport (downregulated) defets in CF airway epithelia ompared with normal ell ultures. It suggested that the CFTR protein has a dual funtion in airway epithelia i.e. to ondut Cl - ions and to regulate Na + hannel. The absene of CFTR thus auses an up-regulation of Na + absorption through ENaC and a failure of Cl - seretion via CFTR. This finding lead to novel therapeuti approahes for the CF lung disease. Other than onventional anti-infetive and the antiinflammatory drugs the alternative approah is to restore normal ion transport properties in CF airway epithelia. Compounds that appear to possess ations that inhibit exessive Na + transport and trigger Cl - seretion are nuleoside triphosphates: ATP or UTP. They interat with speifi reeptors on apial epithelial surfaes and ativate signaling pathways leading to the inhibition of ENaC-mediated Na + absorption and stimulation of Ca 2+ -atived Cl - seretion by CaCC in normal and CF airway epithelia These ellular responses ause liquid efflux and an inrease in ASL volume on CF airway epithelia. Similarly reent data suggest that the loal formation of adenosine a dephosphorylation produt of ATP interating with A 2B reeptors on the apial surfae stimulates the ativity of CFTR. Extraellular nuleoside triphosphates and nuleosides not only partiipate in signaling transdution proesses on airway surfaes but are also atively regulated by 2 Amiloride bloks the epithelial sodium hannel (ENaC) thereby inhibiting sodium reabsorption in the distal onvoluted tubules and olleting duts in the kidneys. 3 β-adrenergi 3 reeptors are a lass of G protein-oupled reeptors. They stimulate hloride seretion in epithelial ells. 8

21 various enzymes in the ASL. Beause ASL ATP and UTP onentrations affet Na + and Cl - urrents and thus PCL height we an think of the biohemial network involving the nuleotides (ATP and/or UTP) and their dephosphorylated produts as an eletroni iruit regulating muoiliary learane. Beause the enzymes that atalyze nuleotide metabolism have been identified and biohemially haraterized an emerging idea is to develop a preditive mathematial model that desribes in detail the behavior of this biohemial network and then ouple it to a model of ion ondutanes aross the epithelium. 1.2 OUTLINE This dissertation onsists of three major parts: the biohemial network model that desribes the degradation of ATP the ion and water transport model and results from eletrophysiologial experiments that are required to ouple the two models. Chapter 1 gives a brief introdution on the physiologial bakground of this problem. Chapter 2 3 and 4 over eah of the three topis respetively. Chapter 2 mostly fouses on the biohemial network in a homogenous solution. However we also disuss some results from a spatial model of this network to address some interesting harateristis of ATP regulation in the ASL and its potential appliation in pharmaologial drug study of ysti fibrosis. 9

22 CHAPTER 2 EXTRACELULLAR NUCLEOTIDE AND NUCLEOSIDE METABOLISM 2.1 INTRODUCTION Muoiliary learane (MCC) onstitutes the first line of defense against the establishment of hroni airway infetion. Inhaled pathogens are interepted by a muin layer maintained above iliated epithelia by a periiliary (PCL) layer. Together muin and PCL form the ASL whih is ontinuously displaed upward by ilia beating ativity. In lung diseases like ysti fibrosis and primary ilia dyskinesia dysfuntional MCC leads to severe ompliations related to airway obstrution and tissue damage by inflammatory responses to persistent infetions Adenine nuleotides have been shown to stimulate all major epithelial funtions supporting MCC through ell surfae P2 reeptors: eletrolyte/ water efflux by ENaC to maintain optimum ASL height 15 muus seretion 1617 and ilia beating ativity They are sereted by the epithelium under basal onditions and at higher rates in response to mehanial stress suh as pathogen interation rhythmi breathing or oughing Nuleotidemediated epithelial responses are terminated by ell surfae enzymes onverting ATP into adenosine This nuleoside initiates a seond wave of signaling through A 2B reeptor-mediated ilia beating 29 and ion/water efflux by the ysti fibrosis transmembrane regulator (CFTR) 30. Despite the importane of this regulatory system for airway defenses it has not been possible to design a mathematial model to desribe this system due to the 10

23 unavailability of quantitative information regarding ASL nuleotide onentrations and release rates as well as the kineti properties of the enzymes and uptake mehanisms. In the past deade extensive work has been onduted to haraterize basal and stimulated ATP release on human airway epithelia In addition members from all three families of etoatpases eto-nuleoside triphosphate diphosphohydrolases (E- NTPDases) alkaline phosphatases (APs) and eto-nuleotide pyrophosphatase/phophodiesterases (E-NPPs) 3435 have been identified on the apial surfae of human bronhial epithelial ells along with an eto-adenylate kinase (Eto-AK; 2ADP ATP + AMP) The enzymes supporting the onversion of AMP to adenosine were identified as eto 5 -nuleotidase (Eto 5 -NT) and nonspeifi alkaline phosphatase (NS AP) 26 whereas airway adenosine is eliminated by adenosine deaminase 1 and onentrative nuleoside transporters (CNT2 and CNT3) 41. A mathematial model of nuleotide regulation on the apial surfae of human airway epithelia was built based on the above empirial data. The kineti oeffiients were optimized by fitting the model s output to experimental parameters of ATP metabolism adenosine/ inosine uptake 41 nuleotide release and ell surfae onentrations Sensitivity analyses reprodued major aspets of airway nuleotide regulation inluding the respetive ontributions of high- and low-affinity etonuleotidases to the regulation of steady-state and transient nuleotide onentration. This study provides a first mathematial approah to the investigation of an important defense mehanism in human airways. 2.2 METHODS Funtional Measurements of ATP Levels and Metabolism The model was validated by funtional assays onduted on polarized primary 11

24 ultures of human bronhial epithelial ells grown at air-liquid interfae as previously desribed 42. Steady-state ATP levels were measured by luminometry using soluble luiferase or himeri Staphyloous aureus protein A-luiferase (SPA-lu) attahed to antigens on the epithelial surfae 32. The time-ourses of ATP metabolism were obtained from high-performane liquid hromatography (HPLC) analysis of apial buffer samples olleted over time after the addition of M ATP to the apial surfae 27. The kineti parameters of airway NS AP for ATP and ADP were obtained as we previously desribed for AMP 26 in the presene of 0.5 mm Ap 5 A to prevent transphosphorylation events through eto-ak ativity 30. (4) (3) (-) (1 2) (1 2) ATP ADP AMP ADO INO (3) (-) (5) (6) Airway surfae Epithelial ells (7) Figure 4: Diagram of nuleotide transport/metabolism on the apial surfae of human airway epithelia. Released from the epithelium ATP undergoes a series of dephosphorylation and rephosphorylation reations atalyzed by etonuleotidases. The end produts adenosine (ADO) and inosine (INO) return to the ytosol via onentrative transporters. The model also inorporates feed forward inhibition of ADO prodution by ATP and ADP. (1 2) E-NTPDases APs; (3) Eto-AK; (4) E-NPPs; (5) Eto 5 - NT; (6) ADA1; (7) CNT2 CNT3. Kineti Model of Airway ATP /Adenosine Regulation This setion outlines the theory and methodology behind the mathematial model designed to simulate nuleotide regulation on the apial surfae of human airway epithelia. A biohemial network was derived using quantitative information gathered from the literature on nuleotide release 2532 and metabolism by ultured human bronhial epithelial ells (Figure 4). Beause UTP levels are about 15% 12

25 that of ATP 43 in the ASL the influene of uridine nuleotides on ATP metabolism was onsidered negligible. Therefore the reations supporting ATP dephosphorylation to adenosine and adenosine deamination are: ATPADP Pi (2.1) ADPAMP Pi (2.2) AMPADO Pi (2.3) ADO INO (2.4) ATP AMP PPi (2.5) Mihaelis-Menten kinetis is used to model these reation rates in the form: reation rate V max j S K M j S (2.6) where S is the substrate onentration and V maxj and K Mj designate the maximum reation veloity and Mihaelis onstant respetively. Beause several reations are atalyzed by more than one enzyme the subsript j is used to index the multiple enzymes. Adenosine and inosine uptake by CNTs also follows Mihaelis-Menten kinetis 41. In ontrast the reversible Eto-AK reation: ATP AMP 2ADP (2.7) whih involves two substrates was assumed to follow a Ping-Pong mehanism 44: reation rate V max forward 1 K ATP /ATP K AMP /AMP - V maxbakward 1 2K ADP /ADP (2.8) The Ping-Pong mehanism is a generalization of Mihaelis-Menten kinetis that relies on the same underlying assumptions. Experimental evidene indiates that ATP and ADP ompetitively bind to enzymes that atalyze AMP dephosphorylation The following equation was used to model this effet: 13

26 - reation rate K M j V max j AMP (2.9) 1 ATP ADP K iatp AMP K iadp Although it is possible that the inhibition onstants K iatp and K iadp may differ for eto 5 -NT and NS AP a single value was assigned for simpliity. The remaining elements to inorporate into the model are the rate of ATP release and steady-state ASL nuleotide onentrations. In aordane with experimental observations 25 the basal (unstimulated) rate of ATP release (J ATP ) was onsidered onstant. However one of the funtions of nuleotide release is to stimulate fluid efflux whih in turn may affet ASL nuleotide onentrations. Under steady-state onditions while basal release rates do not sustain ATP levels suffiiently high to ativate P2 reeptors the steady-state adenosine level generated from ATP metabolism stimulates fluid efflux into the ASL by the A 2B reeptor-cftr pathway 30. The equation was therefore derived to take into aount time-dependent ASL volume hanges during basal ATP release. We onsidered this ase in whih ATP is released into the ASL layer at a rate of J ATP moleules per seond and then hydrolyzed by enzyme E. The surfae area of the epithelium is denoted by A and E T represents the surfae density of E generally expressed in moles/m 2. If V indiates the volume the equation governing ASL ATP onentration is: d ATP dt J V KatA E T ATP V ATP K ATP V M dv dt ATP (2.10) where the last term in the equation models hanges in ATP onentration due to the hanging volume. The fat that ATP flux and V max designated by k at (A/V) E T sale inversely with volume predits that steady-state ATP levels are independent of ASL 14

27 volume. The biohemial steps desribing ASL nuleotide metabolism are modeled by the equations: datp dt dadp dt 1 V J ATP V (1) maxatp K (1) M ATP V max forward 1 K ATP ATP 1 V (1) max ATP V K (1) M ATP 2V max forward 1 K ATP ATP K AMP AMP V (2) maxatp K (2) M ATP V (3) maxatp K (3) M ATP V maxbakward 1 2K ATP dv ADP dt ADP V (2) maxatp K (2) M ATP K AMP AMP V (3) maxatp K (3) M ATP 2V maxbakward 1 2K ADP dv ADP dt ADP V (10) max ATP K (10) M ATP V (4) maxadp K (4) M ADP V (5) maxadp K (5) M ADP (2.11) (2.12) damp dt 1 V (4) max ADP V K (4) M ADP K M (6) K M (8) V (5) maxadp K (5) M ADP V (6) max AMP 1 ATP ADP AMP K i1 K i2 V (8) max AMP 1 ATP ADP AMP K i1 K i2 V (10) max ATP K (10) M ATP K M (7) AMP dv dt V max forward 1 K ATP ATP K AMP AMP V (7) max AMP 1 ATP ADP AMP K i1 K i2 V maxbakward 1 2K ADP ADP (2.13) dado dt 1 V V (9) maxado K (9) M ADO K M (7) ADO dv dt V t1ado K t1 ADO K M (6) V (7) max AMP 1 ATP ADP AMP K i1 K i2 V (6) max AMP 1 ATP ADP AMP K M (8) K i1 K i2 V (8) max AMP 1 ATP ADP AMP K i1 K i2 (2.14) dino 1 V (9) max ADO dt V K (9) M ADO V t2ino K t2 INO INO dv dt (2.15) The independene of nuleotide onentrations on ASL volume under steady-state onditions determined by setting time derivates to zero was verified by simulations and funtional assays. The model predits that an inrease in ASL volume autely redues 15

28 ATP and ADP onentrations followed by a rapid return to steady-state levels (Figure 5A). This model feature was validated experimentally using ultures of human bronhial epithelial ells (Figure 5B). Steady-state ATP levels measured 60 min after the addition of l phosphate-buffered saline to the apial surfae 32 were not affeted by liquid volume. When fitting the model random sets were generated using a multivariate Gaussian distribution with means equal to the experimental data and standard deviations equal to 25% of the mean. These parameter sets were used as initial guesses in MATLAB nonlinear least square routines. After the modeling fitting the estimated parameter sets are olleted and residuals are ompared (Table 1). A set that orresponds with the minimum residual is hosen to be the best fitting. Figure 5: Comparison of model predition with experimental measurements for steady state ATP and ADO. (A) Model predition for steady-state ATP and ADO with onstant J ATP before and after addition of a 20 l volume to the ASL layer. (B) Measurement of basal ATP with SA-luiferase or soluble luiferase on human bronhial ultures over a wide range of phosphate-buffered saline (PBS) added to the apial surfae. Linear Model for the Steady-State Nuleotide Conentrations Experimental observations indiated that under physiologial onditions steadystate nuleotide onentrations are orders of magnitude lower than the K M values of the 16

29 enzymati reations 25. Therefore to a good approximation the Mihaelis-Menten reation rates an be simplified (linearized) as follows: - V (k ) S max j K (k ) j M j S ~ j V (k ) max j K (k ) M j S P(k) S (2.16) where the parameter P (k) denotes the sum of the ratios of V (k) maxj to K (k) Mj for all the enzymes that atalyze the same reation. The expressions for adenosine and inosine uptake an be simplified in a similar way. Furthermore model simulations revealed that the non-linear parameters the reversible Eto-AK reation given in Eq.(2.9) and the inhibition of AMP hydrolysis by ATP and ADP (Table 1) do not signifiantly affet the steady-state behavior of the model (data not shown). They were therefore exluded from the linear model. Using these simplifiations Eq.(2.11) -(2.15) an be approximated under steady-state onditions by the following set of linear algebrai equations: J - P 1 ³ATP ss = 0 (2.17) P 1 ³ATP ss - P 2 ³ADP ss = 0 (2.18) P 2 ³ADP ss - P 3 ³AMP ss = 0 (2.19) P 3 ³AMP ss - P 4 ³ADO ss - U 1 ³ADO ss = 0 (2.20) P 4 ³ADO ss - U 2 ³INO ss = 0 (2.21) where U 1 and U 2 result from linearizing the expressions for adenosine (Eq. (2.20)) and inosine (Eq. (2.21)) uptake respetively. Sensitivity Analysis An important tool for analyzing differential equation models of biohemial pathways is sensitivity analysis. This tehnique determines the influene eah parameter has on the system and identifies whih omponents of the pathway an be perturbed to produe the 17

30 largest effet. Briefly if the elements of the vetor x(t) are solutions to the model equations: dx dt f (xt ; p) (2.22) where the elements of the vetor p are the model parameters the ratio S i j (t) x i (t) x i (t) Perent hange in x i(t) (2.23) p j Perent hange in p j p j =is used as a measure of the sensitivity of the i th model variable to perturbations in the j th parameter value. The sensitivities S i j (t) are time dependent and require knowledge of the quantityx i (t) p j. The partial derivatives x i (t) p j satisfy a set of M by N differential equations that involve the time-dependent Jaobian of the model equations and the f x t t p p. After determining the best parameter set for the non-linear quantity ( ) ; i j model of ASL nuleotide regulation sensitivity analyses were performed to test the importane of high- and low-affinity enzymes on the regulation of transient and steadystate onentration profiles as well as the physiologial relevane of the feed forward inhibition of adenosine prodution by ATP RESULTS Analysis of the Linear Steady-State Model We started our investigations using the multi-omponent model shown in Figure 4 and desribed by Eq.(2.11) -(2.15). Experimental measurements were available for all model parameters exept for the K M of AMP hydrolysis by Eto-AK (Eq.(2.8); kf12 in Table 1) and inosine uptake. Initially these were taken as free parameters to fit timedependent hanges in nuleotide ASL onentrations after the addition of 100 mm ATP. 18

31 Under these onditions onsiderable disrepanies were found between the model simulation and experimental data for both transient Figure 6A and steady-state Figure 6B onentration profiles. Figure 6: Model validation of the transient and steady-state onentration profiles generated by the nonlinear model without data fitting. (A) The smooth urves are simulation results and the symbols are experimental data for ATP ( ) ADP ( ) AMP ( ) adenosine ( ) and inosine () onentration obtained for buffer samples olleted after the addition of 100 M ATP to the apial surfae of bronhial epithelial ultures. (B) Steady-state ATP ADP AMP and adenosine onentrations obtained by funtional measurements (filled bar ± SEM) and predited by the equations (empty bars). The model was onsiderably improved by using the experimental data as initial guesses then fitted using the nonlinear least square routine of the MATLAB software (Mathworks Natik MA). This simulation reprodued losely the transient (Figure 7A) and steady-state (Figure 7B) onentration profiles. Furthermore among the 14 experimental V max only two remained 2-fold different from estimated values: the low-apaity ATPase ativity (v1) and adenosine deamination (v9) (Table 1). However large disrepany (15-fold) persisted between measured and predited rates of basal ATP release (Table 1). Comparable values were obtained by different researh groups using various methods thereby ruling out experimental error. On the other hand if the rate of ATP 19

32 release was held fixed and the other parameters left free to be determined by fitting the data the model reprodued the transient behavior of the system after the addition of 100 M ATP (Figure 7C) but not the steady-state onentration profile (Figure 7D). Figure 7: Model validation of the transient and steady-state onentration profiles generated by data fitting using the Matlab nonlinear least square program and without (AB) or with (CD) a fixed rate of ATP release. (AC) The smooth urves are simulation results and the symbols are experimental data for ATP ( ) ADP ( ) AMP ( ) adenosine ( ) and inosine () onentration obtained for buffer samples olleted after the addition of 100 M ATP to the apial surfae of bronhial epithelial ultures. (B D) Steady-state ATP ADP AMP and adenosine onentrations obtained by funtional measurements (filled bar ±SEM) and predited by the equations (empty bars). Model simulations were onduted to test whether the non-linear equations desribing eto-ak (Eq.(2.8)) and the feed forward inhibition of AMP dephosphorylation (Eq.(2.9)) influene steady-state nuleotide onentrations. The forward and bakward reation rates 20

33 of Eto-AK were approximated based on the 35-fold higher steady-state AMP onentration ompared to ATP (Table 2) while the inhibition of AMP dephosphorylation still followed the nonlinear sheme given by Eq. (2.9). This manipulation did not influene the steady-state onentration profile. Therefore we developed an approximate linear model to simulate steady-state nuleotide levels and the basal rate of ATP release (Eq. (2.17)-(2.21)). The simulation from nonlinear model suggested a minor ontribution to the steady state from the reversible reation the inhibition of ATP and ADP to AMP hydrolysis and the reation of ATP onverting to AMP. Therefore these three mehanisms were negleted from the linear model. We first alulated the reation rate onstants P i s and U i s in the linear model from the experimental measurements of the Mihaelis Menten parameters. When these rate onstants were plugged into the linear equations this model was also inonsistent with the experimental rate of ATP release (Table 2). Then we tried the opposite approah by plugging the experimental level of all the metabolites exept the unavailable INO level into the model and solving for parameter set. The ATP release rate and uptake rates of adenosine and inosine are assumed to be onstant parameters in this proedure. When we used this rate onstants derived from solving the linear equation to alulate the inosine onentration at steady state we reahed a negative value whih is biologially impossible (data not shown). Altogether these maneuvers suggested that no hoie of parameter values ould apture the empirial data and raised the possibility that the model was missing a key omponent. 21

34 Reations Parameters Experimental Data ATP ADP ADP AMP AMP ADO ADO INO ATP AMP ATP + AMP 2ADP ATP + AMP 2ADP ATP release ADP release AMP release ADO uptake INO uptake v1 k1 v2 k2 v3 k3 v4 k4 v5 k5 v6 k6 v7 k7 v8 k8 v9 k9 v10 k10 vf11 kf11 kf12 vr12 kr13 J ATP J ADP J AMP vt1 kt1 vt2 kt2 ki1 ki N/A N/A N/A N/A N/A REF Estimations (No ADP-AMP release) Estimations (ADP-AMP release) Ki for ATP Ki for ADP Table 1: Comparison between parameters of ASL nuleotide release and metabolism funtionally measured and estimated from the linear model without fitting or inluding parameters of ADP and AMP release. Unknown experimental values are labeled N/A. The units for V max and K M are nmoles.min -1.ml - 1 and M REF designates the referenes. Empirial data Linear model Linear model with ADP/AMP release ATP ADP AMP ADO Table 2: Steady-state nuleotide onentrations alulated from the linear model without or with parameters of ADP and AMP release. Predited release of ADP and AMP Our urrent knowledge of nuleotide release mehanisms is limited to ATP beause the etonuleotidase inhibitor oktail 32 interferes with measurements of ADP 22

35 and AMP by ethenyl derivatization and fluoresene hromatography (Lazarowski E.R. pers. omm.). However emerging studies suggest that mehanial stimulations indue the release of ATP ADP and AMP through exoytosis as a general mehanism in mammalian ells inluding polarized epithelia During maturation seretory vesiles aumulate ATP and UDP-sugars in onentrations up to 50-fold above ytosoli onentrations whih are onverted to ADP and UDP and eventually to AMP and UMP 47. Therefore vesile fusion to the apial membrane would release ATP ADP and AMP. These observations motivated the addition of terms desribing ADP and AMP release to the mathematial model. Constant fluxes for ADP and AMP were added to the linear equations (Eq. (2.17)-(2.21)) and adjusted so that the model generated steady-state onentrations similar to the experimental data (Table 2). With these modifiations the model aurately aptured the basal rate of ATP release and steady-state nuleotide onentrations exept for a two-fold higher adenosine onentration. Estimated release rates for ADP (0.013 M.min -1 ) and AMP (0.014 M.min -1 ) were ten-fold higher than for ATP whih would be onsistent with their relative steady-state levels 88. Reanalysis of the Full Model This multi-enzyme model with nonlinear Mihaelis-Menten kinetis (Eq.(2.11) -(2.15)) was revisited with the parameters of ADP and AMP release determined above. The new model losely reprodued both transient and steady-state behaviors. First the predited metaboli profile for 100 M ATP followed losely the experimental data exept for a slight deviation in adenosine aumulation after 30 min (Figure 8A). This disrepany is explained by the assumption of Mihaelis-Menten kinetis whih requires the substrate onentration to be higher than the K M of the reation (Eto 5 NT; 14 M Table 1). Seond this model eliminated the 15-fold differene between measured and estimated 23

36 rates of ATP release (Figure 8B). Finally this model provided the best fit of all V max and K M values (Table 1) exept for 2- to 3-fold differenes in the feed-forward inhibition onstants. Colletively these data demonstrate that the mathematial model losely reprodues the omplex biohemial network regulating adenine nuleotides on human airway epithelia. Figure 8: Validation of the transient and steady-state onentration profiles generated by data fitting using the non-linear model inluding parameters of ADP and AMP release. (A) The smooth urves are simulation results and the symbols are experimental data for ATP ( ) ADP ( ) AMP ( ) adenosine ( ) and inosine () onentration obtained for buffer samples olleted after the addition of 100 M ATP to the apial surfae of bronhial epithelial ultures. (B) Steady-state ATP ADP AMP and adenosine onentrations obtained by funtional measurements (filled bar ±SEM) and predited by the equations (empty bars). Sensitivity Analyses The apaity of the omputational model to reprodue the non-linear omponents of ASL nuleotide regulation was tested by sensitivity analysis of high-affinity Eto-AK. Figure 9A shows that bloking Eto-AK (vf11 kf11 kf12 vr12 and kr13; Table 1) aelerates the metabolism of ATP in the M range as demonstrated by funtional 24

37 Figure 9: Sensitivity analysis of the non-linear model inluding ADP and AMP release for low-affinity NS AP and high-affinity E-NTPDase 1. (A C) Time-dependent onentration profiles from 10 M ATP before (solid line filled symbols) and after (dashed line open symbols) bloking Eto-AK or NS AP parameters. The lines are simulations and the symbols experimental data obtained by monitoring the metabolism of 10 M ATP on bronhial ultures in the absene/presene of inhibitors of Eto AK (0.5 mm Ap 5 A) or NS AP (10 mm levamisole) (N = 3; SEM omitted for larity; ATP; ADP; AMP; ADO; INO ). The simulations also tested the impat of bloking (B) Eto-AK or (D) NS AP inhibition on steady-state nuleotide onentrations expressed as fold hange after blokage. assays onduted in the absene or presene of 0.5 mm Ap 5 A 40. Aordingly Eto- AK ativity is not predited to influene steady-state nuleotide onentrations (Figure 9B). These data suggest that the role of airway Eto-AK would be to prolong P2 reeptormediated responses within an optimum range of ATP onentrations 41. Sensitivity analyses were also onduted to asertain the ontribution of NS AP to the regulation of ASL nuleotides. Although onsidered a low-affinity enzyme (K M > 300 M) when assayed at ph NS AP has been shown to exhibit both low (K M > 25

38 400 M) and high (K M ~ M) affinities for adenine nuleotides at ph 7.5 in various tissues inluding airway epithelia 26. We previously determined that airway NS AP hydrolyzes AMP with K M values of 36 M and 717 M 26. Sine the kineti parameters of airway NS AP for ATP and ADP were unavailable we performed these experiments on primary ultures of human bronhial epithelial ells as we previously desribed 26. Two sets of kineti parameters were identified for ATP and ADP hydrolysis (Table 3) with K M values in the ranges reported for total airway etoatpase (k1 and k3) and etoadpase (k4 and k5) ativities (Table 1). The impat of bloking NS AP ativity on ASL nuleotide regulation was simulated for a physiologial ATP onentration (10 M) by reduing the fitted rate onstants for ATP (v1 v3) and ADP (v4 v5) hydrolysis by the V MAX values of NS AP (Table 3) and setting the parameters of NS AP for AMP hydrolysis (v7 v8) 26 at zero. Figure 9C shows that bloking NS AP redues the rate of ATP elimination as well as ADP and AMP aumulation by 2- and 3-fold. A stronger effet is predited on adenosine prodution depited by a 4-fold derease in aumulation rate and a 2-fold derease in maximum onentration. These simulation data were losely reprodued by funtional assays on bronhial epithelial ultures performed in the absene/presene of 10 mm levamisole 26 (Figure 9C). Furthermore this sensitivity analysis predits that NS AP influenes steadystate ADP and AMP but not ATP or adenosine (Figure 9D). Colletively sensitivity analyses and funtional assays suggest that NS AP ontributes signifiantly to the regulation of transient and steady-state ASL nuleotide onentrations with potential effets on the amplitude and duration of P1 (adenosine) reeptor-mediated responses following mehanial stimulation. The relative ontribution of NS AP and eto 5 -NT to the prodution of airway adenosine was investigated by sensitivity analyses omparing time-ourses of adenosine 26

39 aumulation from M ATP. The simulations were onduted before and after bloking the kineti parameters of Eto 5 -NT (v6 k6; Table 1) or NS AP as above (Figure 9) and validated experimentally by paired funtional assays on bronhial epithelial ultures before and after inhibiting Eto 5 -NT (10 mm onanavalin A) 2658 or NS AP (10 mm levamisole) The simulations losely reprodued the adenosine profiles obtained from bronhial ultures as shown in Figure 10A-C for M ATP. These experiments also onfirmed that both enzymes ontribute signifiantly to the prodution of ASL adenosine from physiologial ATP onentrations loally enountered after a mehanial stimulation Interestingly the rate of adenosine aumulation from Eto 5 -NT but not from NS AP dereased with inreasing ATP onentration resulting in a reversal of their relative ontributions. A mathematial model designed to desribe the regulation of adenine nuleotides on endothelial ells provided evidene for a physiologial role of feed forward inhibition by ATP on the regulation of vasular adenosine levels To test this possibility in the airways the above time-ourses of adenosine aumulation from ATP were repeated before and after bloking the feed forward inhibition onstants (ki1 ki2; Table 1). Based on the vasular model the data were first analyzed in terms of initial delay to the aumulation of 0.3 M adenosine whih approximates the EC 50 of A 2B reeptors for CFTR ativation on human bronhial epithelial ells Figure 10C shows that the lag phase to 0.3 M adenosine was not affeted by feed forward inhibition at physiologial ATP onentrations ( 10 M) Although not funtionally relevant in the airways the 5-fold redution in lag phase predited for Eto 5 -NT with 1 mm ATP is in agreement with this enzyme s response on endothelial ells The simulations were also analyzed for the impat of feed forward inhibition on the onversion rate of AMP to adenosine. The model predits that Eto 5 -NT is signifiantly 27

40 inhibited by physiologial ATP onentrations (1-10 M) beause bloking feed forward inhibition inreased the rate of AMP hydrolysis by 3-fold (Figure 10E). This regulatory mehanism is expeted to onsiderably affet the overall rate of adenosine prodution on airway epithelia after a mehanial stress as shown by the signifiant effet on total etoampase ativities (Figure 10E). In ontrast NS AP ativity was not affeted by ATP onentrations. This sensitivity analysis demonstrates for the first time that the feed forward regulation of ASL adenosine is speifi for Eto 5 NT. On the other hand the simulations showed that both enzymes regulate steady-state adenosine levels (Figure 10F) in agreement with their relative ativities in the presene of 0.1 M ATP (Figure 10A). The lak of effet on the steady-state adenosine level suggests an effiient regulation by ell surfae elimination. Altogether these sensitivity analyses demonstrate that the proposed omputerized model reprodues the linear and non-linear omponents of ASL nuleotide regulation and provides novel information that will improve our understanding of nuleotide-mediated signaling in human airways. 28

41 Figure 10: Relative ontribution of Eto 5 NT and NS AP to airway adenosine regulation. (A-C) Simulated (lines) time-ourses of adenosine aumulation from M ATP without/with isolating Eto 5 -NT or NS AP ativity by reiproal blokage. The symbols are experimental data from HPLC analysis of ADO aumulation on bronhial epithelial ultures from 1 or 10 M ATP with/without an inhibitor of Eto5 -NT (10 mm onanavalin A) or NS AP (10 mm levamisole). The time-ourse simulations were analyzed for the impat of feed forward inhibition by ATP on (D) the delay to 0.3 M adenosine and (E) the initial linear rate of ADO prodution from AMP. (F) Impat of bloking NS AP or Eto 5 -NT ativity on steady-state nuleotide levels (* N = 3-5; SEM < 10% of the mean omitted for larity). 29

42 2. 4 DISCUSSION The importane of understanding the dynami hanges in nuleotide onentrations taking plae on airway epithelia after a mehanial stimulation is highlighted by the pivotal role asribed to purine signaling in the regulation of baterial learane The ontinuous (basal) release of ATP from airway epithelia into the ASL 20 onstitutes a metaboli soure of adenosine maintaining baseline MCC through A 2B reeptor-mediated ion/water efflux by CFTR and ilia beating ativity Mehanial stress suh as physial interation with a pathogen reruits additional defense mehanisms through enhaned ATP release and P2 reeptor-mediated ion/water efflux by the Ca 2+ -ativated Cl - hannels muin seretion to onfine the partile and aelerated ilia beating ativity to lear the infetion 14. The airways alertness is then rapidly restored by the onversion of ATP to adenosine. Purine signaling on airway epithelia therefore represents an exeptional example of the intriate relationships that evolved between nuleotide regulation and purinoeptor ativation to protet the airways against the development of a hroni infetion. This study presents the first mathematial model of ASL nuleotide regulation on the apial surfae of human airway epithelia. The equations inorporate the linear reations mediating the sequential dephosphorylation of ATP to adenosine the reversible Eto-AK ativity the feed forward inhibition of adenosine prodution by ATP and ADP adenosine onversion to inosine ATP release and adenosine/inosine uptake. All kineti parameters were extrapolated from funtional experiments onduted on the apial surfae of polarized primary ultures of human bronhial epithelial ells. The simulations losely reprodued the steady-state nuleotide onentrations and the transient onentration profile measured on ultured bronhial epithelial ells after the addition of 100 M ATP. However regardless of the fitting strategy a 15-fold differene remained 30

43 between the simulated and experimental rates of ATP release suggesting that the model was missing a key omponent. Reent efforts to eluidate the mehanisms of ATP release led to the proposition that adenine nuleotides other than ATP are also sereted from mammalian ells 47. Mehanial stress has been shown to stimulate vesiular ATP release in a variety of mammalian ells inluding endothelial and epithelial ells For instane disruption of vesile traffiking by brefeldin A inhibited basal and mehaniallystimulated ATP release from ooytes 62. Seretory vesiles aumulate ATP and UDPsugars at onentrations 50-fold higher than in the ytosol 47. During maturation they are onverted to ADP and UDP respetively and eventually to AMP and UMP 47. Vesile fusion to the apial membrane is therefore expeted to release not only ATP but also ADP and AMP. Aordingly modifiation of the model to inlude parameters of ADP and AMP release provided the best fit of experimental transient and steady-state onentrations profiles and resolved the differenes between predited and estimated rates of ATP release. The mathematial model reprodued an important property of ASL nuleotide regulation whih is the independene of steady-state nuleotide onentrations on dynami hanges in ASL volume. A volume doubling whih orresponds to the maximum response of the ASL to mehanial stress 23 disrupted the steady-state ATP onentration during < 3 min. Hene the model simulation predits that a single mehanial stimulation will sustain P2 reeptor ativation during < 3 minutes before purinergi signaling returns to baseline A 2B reeptor-mediated MCC. Sine ATP but not adenosine indues muin release 6364 this rapid on-and-off swith system may represent a protetive mehanism against muin overprodution and airway obstrution. In addition as P2 reeptor-mediated MCC onstitutes an emergeny response to airway 31

44 insults the rapid essation of eah signal may represent an evolutionary means to optimize the airways alertness to subsequent invasions. The omplexity of the multi-enzyme system suggests that several etonuleotidases ompete for the same metaboli steps (NS AP: ATP ADP AMP; E-NTPDase1 or 3: ATP ADP AMP: E-NPPs; ATP AMP) 35. This apparent redundany may be resolved by sorting the etonuleotidases in two kinetially-distint groups regulating different nuleotide onentrations: high-affinity (E-NTPDase 1 E- NPPs eto-ak NS AP) and low-affinity (AP NTPDase 3 NS AP) Among them the reversible transphosphorylating reation of eto-ak (ATP + AMP 2ADP) has been suggested to prolong the effetive onentrations of the P2 reeptor agonist ATP on the apial surfae of human airway epithelia 40. This proposition was onfirmed in the present study by sensitivity analysis and funtional assays against 10 M ATP. The inhibition of Eto-AK ativity suppressed ATP elimination within M whih maximally ativates P2Y 2 reeptors on human airway epithelia 31. Colletively these findings demonstrate that the omputerized model was able to apture the ontribution of Eto-AK to the biohemial network regulating ASL nuleotides. Non-speifi alkaline phosphatase represents a unique enzyme exhibiting both low (K M > 400 M) and high (K M ~ M) affinities for adenine nuleotides when assayed at physiologial ph We previously showed that airway NS AP hydrolyzes AMP with K M values of 717 M and 36 M 26. In order to determine the role of NS AP in the regulation of ASL nuleotides we determined the kineti parameters of NS AP toward ATP and ADP on primary ultures of human bronhial epithelial ells. In agreement with the known harateristis of NS AP two parameter sets were identified for eah substrate with low and high affinities respetively. Based on this information sensitivity analyses were onduted by bloking all kineti parameters of NS AP for ATP 32

45 ADP and AMP and validated by funtional assays onduted with the seletive inhibitor levamisole on primary ultures of human bronhial epithelial ells. The orresponding simulation reprodued the impat of NS AP inhibition on the transient onentration profile generated by an ATP level (10 M) reahed loally in response to mehanial stress The elimination of 10 M ATP was redued by 20% as previously demonstrated with a higher substrate onentration (1 mm ATP) 27. Altogether these data suggest that NS AP plays a minor role in the regulation of ASL ATP. On the other hand the simulations and experimental data indiated that bloking NS AP auses larger perturbations on the transient adenosine profile with a 4-fold derease in the aumulation rate and a 2-fold derease in maximum onentration. The lower impat on ATP than adenosine is onsistent with the biohemial properties of purified NS AP exhibiting relative maximal veloities in the following order: AMP > ADP > ATP Altogether these results suggest that NS AP regulates the amplitude and duration of P1 (adenosine) reeptor-mediated responses following mehanial stimulation. In the vasular system the omplex purinergi regulation of thrombus formation motivated the development of a mathematial model desribing the regulation of nuleotide metabolism on endothelial ells The vessel walls are exposed millimolar ADP and ATP onentrations loally disharged by ativated platelets. While ADP ativates nearby platelets through P2Y 1 and P2Y 12 reeptors ATP and adenosine suppress platelet ativation through P2X 1 and A 2A reeptors respetively Platelet aggregation and thrombus formation are regulated by adenine nuleotide metabolism taking plae on nearby endothelial ells by the oordinated ativities of E-NTPDase 1 and Eto 5 -NT 69. Gordon et al. demonstrated that the dynami hanges in nuleotide onentrations taking plae on endothelial surfaes exposed to > 100 M nuleotides ould only be simulated if the model inluded parameters of feed forward inhibition of 33

46 adenosine prodution by ADP 60. In essene extensive loal nuleotide release due to tissue damage and platelet degranulation reates a time gap between ADP- and adenosine-mediated responses to allow suffiient time to onsolidate the thrombus while minimizing spread beyond the site of damage. Biohemial assays onduted on purified enzyme preparations showed that Eto 5 -NT is inhibited by ATP and ADP The regulation of adenosine on airway epithelial surfaes is further ompliated by the presene of an additional etonuleotidases supporting the ell surfae onversion of AMP to adenosine: NS AP. We therefore tested whether feed forward inhibition plays a signifiant role in the regulation of adenosine by the omplex biohemial network of airway epithelia. However sine most P2 reeptor-mediated responses are initiated by ATP rather than ADP 18 the present study foused on the ability of mehaniallyindued ATP to regulate adenosine prodution. The omputational model and funtional assays both demonstrated the existene of a signifiant negative relationship between ATP onentration and adenosine aumulation. The time lag required for the aumulation of 0.03 M adenosine whih approximates the EC 50 of A 2B reeptors for CFTR ativation 2930 was signifiantly inreased by ATP onentrations > 100 M. While these results are onsistent with the vasular model 6061 airway epithelial surfaes are not expeted to enounter nuleotide onentrations above 10 M under normal onditions Possibility remains that this regulatory mehanism may beome relevant during massive ATP release from extensive epithelial damage or baterial killing in hroni lung diseases suh as emphysema. Feed forward inhibition beame physiologially relevant for ASL nuleotide regulation when analyzed in terms of the rate of adenosine aumulation. Model simulations and experimental data showed that 1-10 M ATP signifiantly inhibits Eto 34

47 5 -NT ativity as previously reported on airway epithelia 26. In ontrast NS AP was unaffeted by ATP onentration on human airway epithelia. The overall effet on ASL adenosine regulation was a reversal in the relative ontribution of the two enzymes at ATP onentrations 1 M as the onentration profile for adenosine aumulation beame ditated primarily by NS AP. These results are in ontradition with the previously reported dominane of Eto 5 -NT established on these epithelial surfaes for 100 M AMP 26 whih did not aount for the feed forward inhibition by ATP. The present study illustrates the importane of investigating the physiologial role of a single etonuleotidase within an integrative setting inluding all fators regulating ASL nuleotides. This feed forward mehanism in biohemial networks where NS AP is absent may be important to prevent A 2B reeptor desensitization 72. On the other hand hroni lung diseases inluding ysti fibrosis hroni pulmonary disease and primary iliary dyskinesia are haraterized by enhaned NS AP ativity and expression 27. The lak of feed forward regulation of NS AP may ontribute to the vulnerability of the airways to the development of hronially-elevated adenosine in pathologial onditions assoiated with exessive ATP release whih is known to exaerbate inflammation and tissue damage 73. In onlusion this study provides a robust mathematial model for the regulation of two powerful signaling moleules: ATP and adenosine. The model predits that P2 and A 2B reeptor-mediated epithelial responses will be sequentially ativated by an insult aording to the relative onentrations of ATP and adenosine within the ASL layer. The present study also demonstrates that the physiologial importane of a single etonuleotidase may be tissue speifi depending on the biohemial network regulating extraellular nuleotides and on the loal onentrations enountered under normal and pathologial onditions. This demonstration onstitutes a first step toward the 35

48 understanding of nuleotide-mediated MCC. In the near future these equations will be refined to inlude parameters desribing the regulation of P2 and P1 reeptor ativation as well as the epithelial responses supporting baterial learane FUTURE APPLICATION Layered Struture of Airway Epithelium Under in vivo ondition the airway epithelium in human lung is overed by two liquid layers: the periiliary layer (PCL) and the muus layer (Figure 11). Among them the periiliary layer (PCL) is the losest to the epithelial ell membrane. Nature designs the PCL in a way that it has approximately same height of ilia a hair-like organelle that is rooted on epithelial membrane so that ilia an ondut onstant beating in the PCL. The fore on the tip of ilia transports the muus layer atop along with the bateria trapped in the muus in an upward motion and eventually out of our body through nose and throat. In physiology the muus layer and PCL together is alled airway surfae liquid or ASL. Figure 11: Layer struture of airway surfae fluid (ASL) in human lungs. ASL is omposed of two major layers: the muus layer and the periiliary layer (PCL). PCL has similar thikness as ilia whih is about 7 miron. Muus layer is approximately twie as thik as PCL. 36

49 Epithelial ells are able to serete enzymes to its membrane whih form a very thin layer within PCL (Figure 11). When ATP is released from epithelial ells it diffuses through the enzyme layer first where it interats with enzymes and gets hydrolyzed. At the same time some ATP moleules are able to esape and diffuse upward through the rest part of PCL and then to muus layer. When the loal onentration of ATP lose to the epithelial ell membrane beomes less and less ATP moleules beyond the enzyme layer will diffuse downward due to the onentration gradient (Figure 12). Model Equations As diffusion tends to drive ATP and its metabolites away from enzyme layer to prevent it from getting degraded we are interested in how diffusion ould possibly affet the metabolism of ATP and the metabolites. Therefore we built up a partial differential equation system that desribes the motion of ATP in the ASL. Beause only the total amount of enzymes has been measured and we have no idea about the distribution of enzymes at epithelial ell membrane under in vivo onditions we assume even distribution for enzymes in the spatial model. That means the diffusion happens only in the vertial diretion or the diretion of ASL height. The thikness of different layers in this model is speified aording to the in vivo measurements 86. Due to the lak of information on thikness of enzyme layer it is assumed to be 3 m. Eq. (2.24) desribes the motion of the five speies of nuleotides and nuleosides in the model. The variable C is a vetor representing the onentrations of all the metabolites in the ASL. The ativity of all the speies in the enzyme layer 0 L E is desribed by reation-diffusion equation. Reation diffusion systems are mathematial models that desribe how the onentration of one or more substanes hanges under the 37

50 influene of two proesses: hemial reations in whih the substanes are onverted into eah other and diffusion whih auses the substanes to spread out in spae. Figure 2.9: The ativities of nuleotides and nuleosides in ASL. Mathematially reation diffusion systems take the form of semi-linear paraboli partial differential equations. In Eq. (2.24) 2 C v D P y and 2 R(t C) v are related to diffusion along the ASL height and reation in the enzyme layer respetively. In the rest of the PCL and muus layer ATP and its metabolites follow Brownian diffusion. Therefore only the diffusion equation is used to desribe their motion in these two regions. The property of PCL and muus are quite different from eah other. The former is has a texture that is similar to water (true?) while the muus layer is more like gel. The value of D P the diffusion onstant in the PCL was hosen to be the same as the ATP diffusion rate in bulk water while its diffusion in muus layer D M was assumed to be 10 times slower. The differene between ATP ADP AMP and nuleoside adenosine (ADO) is the numbers of phosphate and adenosine (ADO) and inosine (INO) only differ in an amino group. Therefore we assume they have the same diffusion oeffiient. The model equations are: 38

51 C v t D 2 C v P y R(t C) v y 0 L 2 E C v t D 2 C v P y y L 2 E L P C v t D 2 C v M y y L 2 P L M (2.24) To solve the equations requires the speifiation of boundary onditions (Eq. (2.25)). The boundary onditions of the equation system are set up in suh a way that there is onstant exhange in epithelial ell membrane desribing the release of nuleotides and uptake of adenosine (ADO) and inosine (INO). At the other end of boundary i.e. the surfae of ASL zero flux is assumed. We also assume ontinuous flux between eah two of the three layers. The initial ondition is defined aording to the situation we want to simulate. C v D P v J t y0 C v D M 0 t ylm C v D P t yle C v D P t ylp D P v C t yle D M v C t ylp (2.25) Numerial Methods Operator-Splitting method is a ommon way to numerially solve reation/onvetion diffusion equations where reation/onvetive and diffusive fores are aounted for in separate sub-steps. It is widely used in solving initial value problems for partial differential equations. That involves more than one operator on the right-hand side of the equation. We tried to use the Strang Operator Splitting Method whih is a seond order numerial sheme (for details see Appendix 1). Due to the disontinuity of 39

52 the reation term along y axis the noise around disontinuity gets larger with time and eventually grows unbounded. To minimize the noise we have to start with a really small delta t or big delta x. Small time steps result in a fairly big matrix and time-onsuming matrix operation. Big spae steps lead to rough lattie and less information about the spatial distribution of nuleotide and nuleoside onentrations. However the diffusion model doesn t favor a rough lattie. If we onsider a 21 mirons (m) height for ASL and the enzyme layer is only a ouple of mirons the size of grid an not exeed 1 miron. This results in slow omputation. Meanwhile the nonlinearity of the boundary ondition for adenosine and inosine uptake makes the Strang Splitting Method less appliable to our problem. The defiieny of Splitting Method led us to try other numerial methods for solving reation-diffusion equations. We swithed to a Finite Element Method whih is a method for solving the equations by approximating ontinuous quantities suh as the flux at disrete points regularly spaed on a grid or mesh. Beause finite element methods an be adapted to problems of great omplexity and unusual geometry they are an extremely powerful tool in the solution of important problems in heat transfer fluid mehanis and mehanial systems. We use a modeling pakage alled COMSOL Multiphysis (formerly FEMLAB) to solve the reation-diffusion equation system. COMSOL Multiphysis is a software for solving different types of PDE s with finite element method in onjuntion with adaptive meshing and error ontrol as well as with a variety of numerial solvers whih allows us to use really fine grid in the enzyme layer and rougher grid in other regions. 40

53 Justifiation of Model Simplifiation for the in vitro Experiments The in vivo studies showed that most of enzymes that atalyze nuleotide metabolism were loalized at the surfae of epithelial ells in a layer about two mirons high. Considering the height of airway surfae liquid (7-21 mirons 86) whih is about 10 to 20 times higher it is reasonable to expet the existene of vertial gradients in NT/NS. As the diffusion onstant of the moleules also determines if a spatial model is needed we estimated the time required for an ATP moleule to diffuse aross the ASL. Table 3 shows various diffusion oeffiients for a ATP moleule in different media. As an be seen from Table 3 ATP diffuses in endothelium-fluid interfae from pig aorti endothelial ells at a slightly slower rate than it does in bulk water. For a medium with higher visosity similar to the ytoplasm the speed is redued by half. This means the speed for a single ATP moleule to diffuse in the PCL is on the order of 10-6 m 2.se -1. Beause no one has ever measured ATP diffusion in the muus layer we first onsider the ase in whih ATP diffuses equally fast in muus as in PCL. By the relation T~O (L 2 /D) the time it takes to diffuse from the ell membrane to the surfae of ASL ould be estimated to be a ouple of seonds. Compared to the time for a pharmaologial dose of ATP (100m) to hydrolyze in ASL whih is about 10 seonds the ASL an be onsidered a well-mixed solution and diffusion in this ase is negletible. Media in whih ATP diffuses Diffusion Coeffiients (m 2 /se) Referenes Cytoplasm 1.5 x Bulk water 3x Endothelium-fluid interfae from pig aorti endothelial ells Table 3: Diffusion onstants of ATP in different media 2.36x We then onsidered the situation in whih ATP diffuses at a different rate than it does in the PCL. Considering the muus layer is similar to gel it is very likely the ATP diffuses slower in this layer. We varied the diffusion rate D M ompared to D P the 41

54 diffusion in PCL and observed the behavior of the averaged ATP onentration in ASL shown in Figure 13. As we slow down the diffusion of ATP in muus layer the time for ATP to reah the steady state beomes longer. However not until the diffusion in muus layer is 100 times slower than that of PCL does the average ATP level in ASL show muh of a differene. This simulation along with the alulation earlier provides strong justifiation for negleting diffusion in the in vitro experiments we are about to model. In those experiments the muus layer was removed for the onveniene of measuring the ATP level. With the presene of only the PCL the media an be onsidered as well stired solution and only enzyme reations are neessary to desribe the dynamis of ATP and its metabolites. Figure 13: The averaged ATP onentration in ASL when varying the diffusion rate in muus layer D M with respet to the diffusion rate in PCL D P. The initial ondition here is zero for all the metabolites. Simulation for Aerosol Delivery One of the future appliations for the ATP regulation model is to study the aerosol drug delivery to the airway of CF lungs. However one symptom of CF is the 42

55 aumulation of muus layer due to the infetion and inflammation. In this ase the muus layer is so thik that diffusion will affet the ATP delivery to the airway surfae and eventually to the interation with membrane reeptors. The validation of ATP regulation model without spatial onsideration enables us to use it as the reation term in the spatial model we derived earlier. The initial ondition here is assumed to be a step funtion representing a layer of ATP at the ASL surfae and steady state elsewhere. To minimize the numerial error introdued by the disontinuity in the initial ondition we use the funtion fl2hs in COMSOL Multiphysis to smooth out the jump (Figure 14). Figure 14: Initial ondition of aerosol ATP delivery to the ASL. fl2hs is a smoothed Heaviside funtion with a ontinuous seond derivative. y=fl2h (xsale) approximates the logial expression y=(x>0) smoothing the transition within the interval sale<x<sale. We numerially solve the equations and alulated the loal ATP at the epithelial membrane where reeptors loate. Figure 15 shows that with high muus heigt ATP is diluted in the larger volume so the ATP at ell surfae is too low to ativate the reeptor (The effetive range of ativation is 1uM to 100nM). This simulation will be very helpful for studying the effetive dose of ATP when designing the inhaling drugs for CF. 43

56 Figure 15: The loal ATP onentration at epithelial ell membrane numerially solved from the partial differential equation system. The three urves represent the numerial solution when we vary the ASL thikness while keeping the PCL height fixed. 44

57 CHAPTER 3 ION/WATER TRANSPORT MODEL 3.1 INTRODUCTION Epithelial ells make up the lining of the lungs panreas liver digestive trat and reprodutive system and are also found in the sweat glands and sinuses. As mentioned earlier one of the symptoms of CF is to have salty sweat due to the impaired salt absorption in the sweat dust aused by the absene or malfuntion of CFTR Cl - hannel in the apial membrane of dust ells 77. One of many treatments for CF is saline inhalation. Two studies published by Donaldson and Bouher et al. 78 reported that CF patients who inhaled hypertoni saline solution at least twie a day were hospitalized half as often for lung problems and showed signifiantly improved muus learane. Hypertoni saline inreases the ion gradient in the ASL and therefore leads to rehydration of the airway surfae. The potential therapeuti drug we are interested in ATP restores the ASL through a different mehanism but with same result. ATP binds to membrane- bound reeptors and ativates a seond hloride seretion pathway by opening Calium-ativated Chloride Channel (CaCC). This mehanism also results in an enhaned ion gradient in the airway surfae and ontributes to the re-hydration of the ASL. The balane of airway surfae liquid aross the epithelial ell membrane involves the ompliated interations of various transport proesses. The three major types of transport proesses in this system are passive diffusion down eletrohemial gradients otransport and ative transport whih onsumes energy. These transport proesses are

58 inter-related through diret or indiret ways. They at in onert to produe a strongly oupled and highly nonlinear system. Therefore to understand this system requires mathematial modeling. We built a omputational model based on a model for the epithelium of dog trahea proposed by Novotny and Jakobsson We have onverted the original ion and water transport model of Novotny et al. into MatLab and re-set the input parameters to math the data from human bronhial epithelial ells reported by Willumsen et al To humanize the system basolateral membrane hloride hannels were inluded in the model. 3.2 MATHEMATICAL EQUATIONS Figure 16: The transport proesses in human airway epithelium The model of human airway epithelium is omposed of three ompartments: the airway surfae intraellular region and basolateral region (Figure 16). Transport proesses aross the apial membrane are haraterized by passive sodium and hloride movement. The basolateral membrane ontains passive potassium and hloride transport 46

59 along with ative sodium-potassium transport and sodium-potassium-hloride otransport. Both membranes are permeable to water exept the paraellular pathway whih only transports salt. Passive ion transport not only depends on onentration gradients but also the membrane potential differene and therefore is onsidered eletrodiffusion. To model this effet we used the Goldman-Hodgkin-Katz equation (Eq (3.1)) whih desribes the urrent produed by an ion speies moving from ompartment x to y. The urrent depends on the transmembrane potential V m the onentrations in eah ompartment (C ix and C iy ) the permeability of the membrane to this ion (P i ) and the absolute temperature. This formula also has several onstants suh as the valene of ion z i the Faraday onstant F and the ideal gas onstant R. The ion flux is: - J Passixy P i Z i FV RT C ix C iy exp Z FV i m RT 1 exp Z ifv m RT (3.1) The flow of water only depends on the ion gradients and transmembrane permeability to water moleules. Therefore the mathematial representation of water flux takes a simple form as in Eq. (3.2). J P H2 Oxy H 2 O C ix C iy i i (3.2) where the i C i x and C i y i are total ion onentrations inluding the impermeant anions in the two ompartments. The ative transport of sodium and potassium through energy-dependent pumps is modeled aording to Mihaelis-Menten kinetis with a pump ratio of three sodium ions per two potassium ions. A term was inluded to represent the 47

60 dependene of the pump on membrane potential ( V mb +1.25). This term was derived from the pump reversal potential. This leads to the following expressions for ative ion fluxes: Na J pumpbasoell J ell pumpmax Na ell K pumpna 3 K baso K baso K pumpk V mb 1.25 (3.3) J pumpnabasoell 3J pumpbasoell (3.4) J pumpkellbaso 2J pumpbasoell (3.5) The flux through otransporter was modeled aording to Mihaelis Menten theory (Eq. (3.6)) as well. J otmax is the maximum ioni flux through the otransporter (in mol.m -2.s -1 ). The otransporter ratio is one sodium ion to one potassium ion to two hloride ions. Therefore the ion flux through this pathway remains eletro-neutral at all times. The flux through the otransporter is: Na J otxy J x K otmax x Cl x Cl x Na x K otna K x K otk Cl x K otcl1 Cl x K otcl2 Na y K y Cl y Cl y Na y K otna K y K otk Cl y K otcl1 Cl y K otcl2 (3.6) The rate of hange of the ion onentrations in eah ompartment is given by the sum of the fluxes into that ompartment. For example the rate equation for sodium onentration in ytoplasm is desribed by Eq (3.7). where J pass Na a and J pass Na b are passive sodium flux from apial and basolateral regions while 3 J and pump Na b J ot b are ative transport and otransport sodium fluxes respetively. The intraellular ell volume is inluded in the equation to aount for dilution effets aused by the water flux. 48

61 dna dt 1 Vol J passnaa J passnab 3J pumpnab J otb dvol dt Na (3.7) Following the same onsideration we build up a system of equations whih desribes the ion onentrations and volume in eah ompartment. A omplete list of equations in the model is shown in Appendix II. The relaxation times for different proess in this model are quite different from eah other. The fastest time sale in the system is that for the membrane potential to respond to hanges in ion onentration. The membrane potential responds with a harateristi time on the order of milliseonds determined by the resistane-apaitane time onstant of the membrane. The time sale for water movement is slightly faster than 1 seond and that for hanges in ion onentrations is on the order of tens of seonds. Therefore the system is stiff. We used ode15s the stiff ODE solver in MATALB to numerially solve the system. At equilibrium the transmembrane urrents satisfy Kirhhoffs loop and node laws suh that if the ell were represented by the eletrial iruit in Figure 17 then at any juntion of the iruit the algebrai sum of the urrents must be zero (Eq. (3.8)). In this figure I A I B and I P are the urrents aross the apial membrane (positive into the ell) the basolateral membrane (positive into the ell) and the paraellular pathway (positive toward basolateral surfae) respetively. V ma and V mp are the apial and transepithelial membrane potentials referened to the muosal surfae. V mb is the basolateral membrane potential referened to the submuosal muosal surfae. 49

62 Figure 17: voltage-lamp iruit representing the equilibrium state of transmembrane urrents. I a (V ma ) I p (V mp ) 0 I b (V mb ) I p (V mp ) 0 V mp V ma V mb (3.8) At eah time step t we first solve the nonlinear equation system (Eq (3.8)) for the equilibrium state of membrane voltages based on the ion gradients and membrane potentials from previous time step. These new values are then used as onstants in the equations desribing the rate of hange in ion onentrations and volumes. We make sure the units of the fluxes in the equations are onsistent. All fluxes amounts and volumes were normalized to the epithelial surfae area. Fluxes were in units of moles per seond per square meter amounts in eah ompartment in moles per square meter and volumes of eah ompartment in ubi meters per square meter. The equilibrium value for apial volume per surfae area was hosen to be 7 m so that the apial fluid has a height equal to the length of the ilia For ell the equilibrium ell volume per surfae area was hosen to be 20 m the volume of the ell if it were ylindrial with dimensions shown in eletron mirographs Our strategy is to benhmark the modified Novotny model of ion and water fluxes without inluding nuleotide regulation. In the absene of suh regulation the Novotny 50

63 model leads to a state of either omplete absorption or unbounded inrease in the ASL. Although the former has been observed from experiment the unbounded ASL volume is an unphysiologial feature. To overome this effet Novotny added volume regulation to the permeability of the apial membrane Cl - hannel and to the maximum flux of the basolateral membrane otransporter. Unfortunately they did not speify a mehanism for how the hannels and transporters ould detet apial and ell volumes and assumed a linear oupling to the volume with presribed upper and lower bounds on the permeability and maximum flux. In Chapter 4 we are going to address this problem and assume a more realisti nonlinear oupling that does not require speifying artifiial upper and lower bounds. The ultimate goal is to develop a model that is apable of homeostati regulation by oupling the ion and water flux model to the nuleotide regulation model. 3.3 PARAMETER ESTIMATION The model desribed above is initial-ondition-dependent meaning that varying the initial ion onentrations in eah ompartment will produe different steady state onentrations volumes and membrane potential. Mathematial analyses revealed that this feature is a onsequene of the quasi-steady state approximation used for the membrane potential. Therefore we searhed for parameter sets that are biologially meaningful and produe steady state that is onsistent with the experimental observations. We fixed the apial and intraellular volumes and ran the simulation to steady state. If the steady state is lose to the experimental observations we then let the volume hange as a result of onentration gradients. The ion hannel permeabilities (Table 4) were olleted from literature on human epithelium. When these values were used in the simulations the model produed disrepanies in the steady state of ions and 51

64 membrane potentials (Figure 18A). Therefore we optimized the permeabilities suh that the model produed steady state that mathes the experimental observations (Figure 18B Table 5). A B Na + a K + a Cl - a V ma Na + a K + a Cl - a V ma Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Na + i K + i Cl - i V mb Na + i K + i Cl - i V mb Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Time(hr) Na + b Time(hr) K + b Time(hr) Cl - b Time(hr) Na + b Time(hr) K + b Time(hr) Cl - b Time(hr) Figure 3.3: Comparison of the in vivo measurements (blak) and simulation results (red) for ion onentrations and membrane potentials before (A) and after (B) the parameter estimation. As shown in Table 5 the parameter estimation produes a set of ion onentrations and membrane potentials that has smaller differene from the in vivo measurements. There is signifiant derease in the disrepanies in the apial hloride onentration and basolateral membrane potential. However the apial sodium onentration remains 16% lower than the in vivo ondition despite a small improvement after the estimation. On the other hand the differenes of the estimated permeabilities (Table 4) and in vivo measurement are all less than 2 folds suggesting the model equations do not have major defets. It is well known that the movement of hloride aross the apial membrane involves the CFTR Cl hannel; however ondutive pathways for Cl movement aross the basolateral membrane have been little studied. Willumsen et al. 84 had found out that Cl- transport aross the basolateral membrane in the CF epithelium ours mainly 52

65 through the bumetanide 4 -sensitive otransport system but also through a Cl- ondutane whih suggested that a hloride hannel is available to the CF airways. We took this into onsideration and estimated this permeability along with other parameters. The estimated basolateral hloride permeability is m/s whih is slightly smaller than the apial peramebilty to Cl -. We will ompare this estimation with experimental measurements when it is available. Apial Membrane (10-8 m/s) Basolateral Membrane (10-8 m/s) Paraellular Membrane (10-8 m/s) Exp. Opt. Exp. Opt. Exp. Opt. P Naa P Nab 0 0 P Nap P Ka 0 0 P Kb P Kp P Cla P Clb P Clp P H2Oa P H2Ob P H2Op 0 0 Table 4: Comparison of in vivo measurements of membrane permeabilities to ions and water with estimated values. Airway Surfae Cytoplasm Basolateral Region Exp. Opt. Exp. Opt. Exp. Opt. Na mm 101 mm 20 mm 23 mm 140 mm 149 mm K + 20 mm 24 mm 100 mm 84 mm 5 mm 5.4 mm Cl mm 123 mm 40 mm 41 mm 105 mm 116 mm V m -26 mv -24 mv -36 mv -41 mv Table 5: Comparison of variables at steady state before and after parameter estimation. 3.4 MODEL VALIDATION We then validated the model by testing it against the in vitro experiments in whih the salt onentrations in bilateral ompartments were perturbed. Data from human 4 Bumtanide is a potent diureti that used to inhibit the Na + -K + -2Cl otransporter. 53

66 nasal epithelial ells were hosen beause there are little experimental measurements from human bronhial ell available. The nasal membrane permeabilities to ions are also very similar to bronhial ells. All of these the experiment was onduted using an Ussing hamber setup so that both the apial and basolateral volumes are fixed. So when modeling the experiments we set these two parameters onstants and only hange the initial ondition of the ions in different ompartments. Shown in Table 6 is the omparison of the measurements from one experiment 82 and the simulation results from the model. In this experiment 82 apial addition of amiloride (10-4 M) hyperpolarized the apial membrane potentials and dereased transepithelial urrent. The dose used for amiloride (10-4 M) has been tested to able to blok nearly 100% of the sodium flux aross the apial membrane on the area of the ell ulture. To simulate this ondition we set the apial sodium permeability to zero and ran the model to steady state. Our model suessfully predited the trend of hange in membrane potentials (V ma V mb ) and transmembrane short urrent (I eq ) after the bloking of apial sodium hannel. V ma (mv) V mb (mv) I eq (A/m 2 ) Exp. Control Amiloride Sim. Control Amiloride Table 6: Experimental observations and numerial simulation using the ion water transport model in the experiment where apial sodium is bloked by amiloride. We then started from the model from steady state and allowed the volumes in apial and ytoplasm region vary. Without any regulation mehanisms in the model the simulation results shows a dereasing apial volume (Figure 19) whih agrees with the in vivo observation of un-regulated human airway 88. Due to the inreased ion onentration inside the ell its volume in the inreases without bound in the simulation. 54

67 In reality the ell ouldn t grow forever. At a ertain volume the surfae tension on the ell membrane fails to hold the ytoplasmi solution and the ell lyses. However it is very likely that the ell volume an be regulated and kept under ontrol when the airway surfae liquid is subjet to the ATP regulation. Figure 19: Simulation of ATP depletion fin the airway. The system was started from the steady state that is generated by estimated parameter set. The initial volumes for apial fluid and ytoplasm are 7 and 20 m per surfae area. The apial volume dereases to zero within 100 minutes while the volume of epithelial ell tends to grow without bound. 3.5 CONCLUSION The ion/water transport model was based on the physiologial theory of ion/water transport. The proedure used to perform parameter estimation is very similar to that of ATP regulation model. We used the measure parameter values as initial guesses and searhed for a set of parameters that ould produe the best fit for the model ompared to the resting level of ion onentrationsand membrane potentials in the different ompartments of airway epithelium. The positive predition of the model i.e. the bloking of apial sodium hannel and test of default state without any regulation both 55

68 suggest that the ion/water model aurately aptures key features of ion and water movement in the airway epithelium and therefore serves as a good model for integration with the ATP regulation model. 56

69 CHAPTER 4 AIRWAY SURFACE LIQUID REGULATION In this hapter we fous on studying the signaling pathways initiated by ATP and UTP in epithelial ytoplasm. A series of experiments designed to investigate different pathways are performed to show how triphosphate nuleotides (ATP and UTP) and their metabolite might by up-regulating hloride seretion to the airway surfae and inhibiting absorption of sodium ions bak to ytoplasm be potential therapeuti targets. 4.1 INTRODUCTION The pathogenesis of ysti fibrosis is very ompliated. As desribed in earlier hapters it is haraterized by abnormal regulation of the airway surfae liquid (ASL). The results are ahieved by the dual effets of down-regulation of hloride seretion due to the mutations in ysti fibrosis transmembrane ondutane regulator (CFTR) as a hloride hannel and hyper-absorption of epithelial sodium ions. Further experimental evidene showed that there is a seond hloride hannel in the apial membrane of airway epithelia whih is regulated by inreases in intraellular free alium (Ca 2+ i) There is experimental evidene showing the release of triphosphate nuleotides to the airway under normal ondition. Along with their metabolites they are able to initiate the autorine and pararine regulation on ion transport There are two major signaling pathways indued by ATP in normal epithelium (Figure 20). Intraellular ATP are sereted in response to diverse stimuli (loal stress

70 addendum) and are hydrolyzed by eto-nuleotidases and other enzymes on airway epithelium to adenosine (ADO) and inosine (INO) whih are taken bak into the ytoplasm by transporter proteins (see Figure 20: The signaling pathways ativated by ATP and adenosine in the normal and CF human epithelia. A desribes the P2Y 2 reeptor-dependent pathway ativated by ATP or UTP. B is the pathway ativated by binding of adeosine to reeptor A 2b. C ombines the two pathways with nuleotides and nuleosides metabolism in the airway surfae. D represents the signaling pathway in CF human epithelium. Chapter 2). While on the airway surfae ATP binds to the purinergi reeptor P2Y 2 -R whih is a G-protein-oupled (G q ) reeptor and ativates its downstream target phospholipase C (PLC). Ativated PLC hydrolyzes the membrane lipid phosphatidylinositol 4 5-biosphosphate (PIP 2 ) produing inositol 145-trisphossphate (IP 3 ) and diaylglyerol (DAG). IP 3 is water-soluble and diffuses through the ytoplasm to the endoplasmi retiulum (ER) where it binds to and opens a hannel that releases alium from stores inside the ER. A alium-sensitive hloride hannel (CaCC) is then 58

71 ativated and transports Cl - ions from the ytoplasm to apial region. DAG the other produt of PIP 2 hydrolysis interats with both alium and the protein kinase C (PKC) and mediates the hloride urrent through CFTR. This is the first pathway that not only up-regulates apial hloride urrents by separate routes from PLC ativation but also inhibits ENaC due to the derease in PIP 2 onentration The seond pathway is initiated by adenosine (ADO) binding to the G-protein-oupled reeptor A 2b. This reeptor ativates adenylyl ylase (AC) whih in turn raises the loal onentration of intraellular yli-amp (AMP i ). AMP i ativates protein kinase A (PKA) whih by phosphorylation ativates CFTR and inativates the epithelial Na + hannel (ENaC) 30. There is evidene showing that ativation of the epithelial Na + hannel (ENaC) requires CFTR Cl - hannel funtion 96. In CF airway epithelium both the regulation of CFTR through PKC-dependent and AMP i -dependent pathways fail due to a lak of funtional CFTR in apial membrane. However the pathway of CaCC ativation and ENaC remains intat and thus beomes a viable target for CF therapy. The regulation on these two types of ion hannels by extraellular nuleotides and their metabolites has been shown to help reovery of the airway surfae liquid (ASL) 97. The signaling pathways ats like a link that ties extraellular nuleoti(si)des metabolism and the hange of ion and water flow together. Therefore it is very important to study in detail the regulationof this pathway to enable the oupling of the two mathematial models desribed in the previous hapters. Many previous studies have foused on this area. Paradiso and Bouher investigated Ca 2+ i release and influx in polarized human nasal epithelial monolayers using ATP administration to stimulate P 2 purinoreeptors 98. In Ca 2+ -ontaining NaCl ringer solutions ATP added to either the muosal or serosal side indued an instant peak in Ca 2+ i. The intraellular alium onentration then gradually dereased bak to near the 59

72 basal levels. Ca 2+ signaling was also studied in normal and CF human bronhial epithelial (HBE) by UTP and a similar intraellular alium response was reported 99. Cysti fibrosis airway epithelial Ca 2+ i signaling: the mehanism for the larger agonist-mediated Ca 2+ i signals in human ysti fibrosis airway epithelia. The up-regulation of CaCC and down-regulation of ENaC have been studied together and separately in reent years. Mason et al. 100 studied the transepithelial short iruit urrent (I s ) whih reflets the regulation of both CaCC and ENaC in human normal and CF airway epithelium and presented rpresentative traings of the effet on I s of extraellular ATP applied to the apial or basolateral membrane. A study on the regulation of CaCC alone was onduted using the same ultures and pretreating the ells with amiloride to blok ENaC. Meausurements of the hloride urrent through CaCC resembled the Ca 2+ i response indued by extraellular ATP in either of the ompartments. These two observations provide information on the individual responses of CaCC and ENaC. Later measurements of the response for CaCC to UTP were reported by Tarran et al. 97 whih showed a similar response to that of ATP but a bigger response in CF than normal murine traheal epithelial (MTE) monolayers. This paper also showed evidene that CaCC plays a role in regulating ASL height in response to released agonists (e.g. muosal nuleotides). Despite a lot of researh on signaling pathways in HNE ells there is little work on HBE ells. Beause our extraellular nuleotide and nuleoside metabolism model (Chapter 2) was built based on the measurements from HBE ells we deided to use traditional bioeletrode tehniques i.e. modified profusion Ussing hamber experiments to investigate ion transport in these ells. And we used HBE ells from CF patients so that CaCC (Cl - urrent) and ENaC (Na + urrent) pathways ould be studied individually without any effet on I s from CFTR. 60

73 4.2 MICROELETRODE STUDIES To study how ATP affets ion and water flow aross the membrane of epithelial ells we designed a series of in vitro eletrophysiologial experiments to measure the regulation of ATP on the Calium Ativated Chloride Chanel (CaCC) and Epithelial Na Channel (EnaC) individually. Initially we wanted to qualitatively learn how ATP regulates these two hannels. That is how differently the hannels respond to ATP the time span of eah response and how sensitive the hannels are to an inreasing dose of ATP. After more information was gathered we studied ATP regulation quantitatively by measuring the dose response urves of ATP on the hannels. These measurements haraterize the interation of ATP and muosal membrane reeptors and the signaling pathways they initiate. Therefore this information is essential for integrating the biohemial network model and the ion/water flux model TISSUE CULTURING AND PREPARATION All the ells used were CF bronhial epithelial ells. Bronhial speimens were obtained from CF subjets and removed for linial reasons. All proedures were approved by the University of North Carolina Committee for the Protetion of the Rights of Human Subjets. Detahment from speimen/thawing and plating In brief ells were detahed from freshly reseted speimens by inubation at 40 o C in modified Eagle's medium (MEM) ontaining 0.1% Protease 14 (Sigma Chemial Co. St. Louis MO) and 100 Mg/ml DNAase (Sigma Chemial Co.). Cells were isolated after h by entrifugation (800 g) protease neutralized (10% FBS) after whih the 61

74 ells were washed twie in MEM and suspended in a base medium (Ham's F-12) that was supplemented with the following hormones and growth fators (F12-7Xm): insulin (5 pg/ml) holera toxin (1 rig/ml) transferrin (7.5 pg/ml) hydroortisone (10-6 M) triiodothyronine (T3 3 x 10-8 M) endothelial ell growth substane (7.5 pg/ml) and retinoi aid (5 x 10-8 M). For those ells that were frozen before being used they need to be thawed in 37 o C and then go through the same proedure above. Human epithelial ells are onsidered to be preious sine it s hard to get. Instead of being passaged to the snap-wells diretly freshly reseted or previously frozen epithelial ells were firstly plated onto 100mm ollagen oated (10mg Collagen type IV (Sigma C or Fisher # OB S.5mg/ml 20 ml distilled water 40ul onentrated Aeti Aid) plasti plates. The ells were washed every other day with phosphate-buffered saline (PBS) solution and then fed with BEGM. The total number of the ells inreased through growing and dividing until ells beame onfluent (meaning they are densely distributed over the plate). By then enough number of ells were ultured for passaging to the snap-wells ( millions ells/snap-well). This proess might take a ouple days to one week and it makes sure that relatively small amount of ell ultures an be utilized for more experiments. Passaging ells to snap-wells After the ells reahed onfluene the media was replaed with Trypsin solution ontaining 1mM EDTA and 0.1% trypsin (Sigma Chemial St. Louis MO) to detah the ells from the ollagen oat. After inubation at 37 o C for 10 minutes most ells were detahed and were treated with an equal volume of Soybean Trypsin Inhibitor 1 mg/ml in F12 (STI) to neutralize Trypsin. The tube with the ell suspension was put into the 62

75 entrifuge at 1500RPM for 5 minutes. Then the supernatant was aspirated and resuspended in the tube in a known volume of media (ALI for bronhial epithelial ells). A B Figure 21: Polyarbonate snapwells for ell ulturing. Epithelial ell ultures are grown on a polyarbonate plate and lipped to the suspending well (A). The snapwells are then inserted into the 6-well tissue ulture plate (B). Cells were ounted using Trypan Blue dye to determine viability before they were passaged onto substrata affixed to polyarbonate ups housed in six-well ontainers (Costar Cambridge MA) ontaining media in both basal and apial ompartments. For the miroeletrode studies the substratum was a polymerized ollagen sheet; for optial studies it was a Falon Cylopore membrane (Beton Dikinson Linoln Park NJ). The ideal amount of ells is approximately 0.25 million per snap-well. The media ALI is fed to both apial and basal ompartments on the seond day and then every other day until the ells reah onfluene. After that only the basal ompartment needs media. One a week ells were washed with phosphate-buffered saline (PBS) solution whih was aspirated after a few minutes. The ells were monitored daily by measurement of the transepithelial potential differene (V t ) using alomel eletrodes interfaed to an eletrometer (WPI EVO-M Sarasota FL). Cell preparations were routinely studied within 1-2 days of the development of the maximal V t (21 ~28 days from passaging). 63

76 Depending on the time when epithelial ells are passaged they are name as P0 the primary ells that are grown on the snapwells right after disseting from speimen P1 the primary ells after one passage to the 10mm plate and then to the snapwells and P2 ells passaged twie in 10mm plate before growing in the snapwells. For bronhial epithelial ells from human lungs they an be at most passaged twie before moving to the snapwells. Some researh shows that the surfae metabolism of ATP on ultured human airway epithelia deays through passage and is redued by more than 50% in passage 2 ells (Piher M. pers. omm.) Therefore we also onduted a ontrast study for different ell passage type in the experiments SOLUTIONS AND DRUGS For the study of hloride urrents the epithelia were mounted in Ussing Chambers with Krebs-biarbonate Ringer (KBR; in mm 140 Na Cl K + 25 HCO HPO H 2 P Ca Mg 2+ and 5.2 gram gluose) on both theapial and basolateral sides. KBR solution resembles the fluid enviroment of the airway surfae liquid and blood on top and underneath bronhial epithelial ells in human lungs. The CF lungs also have this property. Amiloride (Sigma) was present in the apial bath of all the experiments at 10-4 M to inhibit sodium absorption before addition of ATP as it s an inhibitor of sodium hannel ENaC (there is little sodium urrent through the basolateral membrane). Different onentrations of ATP were dissolved in KBR at 10-2 or 10-1 M and diluted into the appropriate bath. After this proedure all the measured trans-epithelial urrent omes from hloride transport through CaCC beause 1) CFTR is mutated in the CF epithelial ells; 2) there are no potassium hannel present in the apial membrane; 3) the apial and basal bath have the same omposition so there will be no ontribution of transepithelial urrent oming from shunt ompartment. 64

77 Chloride-free KBR was used in the study of sodium urrents in order to distinguish from hloride urrents. The only differene of this solution is the replaement of hloride ions with gluonate. To get rid of the influene of the hloride out flux from intraellular ompartment the epithelia needed to be mounted for at least 30 to 40 minutes before adding ATP. Although potassium hannels are rare in the apial membrane postassium urrents were observed in some epithelia after adding ATP 102. Chloride-free KBR was then modified to inlude 5mM Ba 2+ to inhibit potassium hannel. Sine Ba reats with SO 4 in the original solution and preipitates the latter was replaed with Gluonate. (Protools of making KBR Chloride-free KBR and Chloride-free KBR with 5mM Ba 2+ are shown in the appendix III) USSING CHAMBERS Polyarbonate Ussing hambers were milled to fit the plasti ups that supported the permeable ollagen matrix on whih the ells were grown as desribed previously. The luminal and basolateral sides of the ultures were ontinually perfused with solutions that were warmed (37 o C) and gassed (95% O 2-5% CO 2 ). Primary ultures were mounted vertially in modified Ussing hambers for the measurement (VCC 600 voltage lamp; Physiologial Instruments San Diego CA) of transepithelial potential differene (Vt). The eletrial potential of the basolateral side of the tissue with respet to the apial side was defined as positive. The transepithelial PD (Vt) was measured by alomel eletrodes onneted to the half-hambers via 3M KC1 agar bridges. The luminal bridge served as the ommon ground for the maro- and miroeletrode systems. A seond pair of 3 M KC1 agar 65

78 A B C Figure 22: Profusion Ussing hamber setup for measurement of transepithelial membrane short urrent. A is one set of profusion Ussing hambers. The polyarbonate snapwell that grows ell ultures (Figure 21) is inserted between the two hambers. B shows the hambers during the experiments with both hambers filled with buffer solution and eletrodes in both sides to detet the hanges in the transmembrane short iruit urrent and membrane potential differene. C is the setup with multiple pairs of Ussing hambers and the data aquiring system that is onneted to the omputer. bridges onneted a pair of Ag-AgCl eletrodes to the bath whih permitted passage of 0.5-s urrent pulses (I ~40 miroamp.m -2 ) every 6 s with a duration of 0.5 s via a stimulator World Preision Instruments (WPI) 301-T onneted to a stimulus-isolation unit (WPI 305). The transepithelial resistane (R t ) was alulated from the ohmi relationship between the defletion of V t and the urrent passed. The equivalent shortiruit urrent (I eq ) was obtained from V t and R t aording to Ohm s Law and ontinuously reorded (Aquire; Dataq Instruments) and stored on a omputer hard drive. Beause the transepithelial urrent voltage relationships are linear and time independent in the physiologi range of potentials the I eq aurately estimates the true short iruit urrent I s. 66