J. Water Resource and Protecton, 009,, 6- do:0.6/warp.009.500 Publshed Onlne ovember 009 (http://www.scrp.org/ournal/warp) Effects of Estrogen Contamnaton on Human Cells: Modelng and Predcton Based on Mchaels-Menten Knetcs Abstract F. IBRAHIM, B. HUAG, J. Z. XIG, W. ROA, Stephan GABOS Chemcal and Materals Engneerng Unversty of Alberta, Edmonton, Alberta, Canada Department of Laboratory Medcne and Pathology, Unversty of Alberta, Edmonton, Canada Department of Oncology, Cross Cancer Insttute, Edmonton, Canada Alberta Health and Wellness, Edmonton, Alberta, Canada E-mal: stephan.gabos@gov.ab.ca Receved July, 009; revsed August 8, 009; accepted August 7, 009 In ths paper, we propose a novel preventon strategy to alert ctzens when water s contamnated by estrogen. Epdemologcal studes have shown that chronc exposure to hgh blood level of estrogen s assocated wth the development of breast cancer. The preventve strategy proposed n ths paper s based on the predcton of estrogen effects on human lvng cells. Based on frst prncple nsghts, we develop n ths work, a mathematcal model for ths predcton purpose. Dynamc measurements of cell prolferaton response to estrogen stmulaton were contnuously montored by a real-tme cell electronc sensor (RT-CES) and used n order to estmate the parameters of the model developed. Keywords: Water Protecton, Early Warnng, Estrogen, Mathematcal Modelng, Parameter Estmaton, Predcton. Introducton Some chemcals, both natural and man-made, can nterfere wth endocrne glands and ther hormones where the hormones act on the target tssues. These chemcals are called endocrne dsruptors or endocrne dsruptng chemcals (EDCs) []. EDCs nduce harmful effects that have been observed on reproducton, growth and development n certan speces of wldlfe and t has been proven that there are ncreases n some human reproductve dsorders and some cancers whch could be related to dsturbance of the endocrne system. Estrogen and estrogen-lke chemcals are a maor part of EDCs. Estrogen s essental for lfe and ts maor bologcal functon s modulatng a woman s reproductve process. Estrogen affects the reproductve tract, the urnary tract, the heart and blood vessels, bones, breasts, skn, har, mucous membranes, pelvc muscles and the bran. Secondary sexual characterstcs, such as pubc and armpt har also begn to grow when estrogen levels rse. Many organ systems ncludng the musculoskeletal and cardovascular systems and the bran are affected by estrogen The short verson of ths paper was presented n EPPH009. []. In addton to ts postve effects, however, unregulated quantty of estrogen may lead to health dsaster due to ts capacty to stmulate some tumors to grow. The epdemologcal and n vtro studes have shown that chronc exposure to hgher blood level of Estrogen s assocated wth the development of breast cancer []. Whle estrogen s present n both men and women, t s usually present at sgnfcantly hgher levels n women of reproductve age []. Thus, the lkelhood of women havng a serous excess of estrogen-lke substances n the body s much greater than for men. In addton to the natural presence of estrogen n human body, a number of EDCs ncludng estrogen have been detected n envronmental sources partcularly n drnkng water and food. Estrogen may exst accdentally n water due to reecton of detergents and brth control plls n water system and by addng pestcdes [5]. The water contamnaton of EDCs s becomng hghly publczed concerns. Therefore, we study n ths paper the case where water s the source of estrogen and we develop a preventon strategy related to water protecton. The ultmate obectve s to develop an early warnng system such that ctzens are alerted as early as possble when water s contamnated by an excess of estrogen. Copyrght 009 ScRes.
F. IBRAHIM ET AL. 7 More precsely, an alarm s trggered when the concentraton of estrogen exceeds certan value. Ths value s determned by studyng a predcted human cells response to estrogen stmulaton. Ths predcton s then used by medcal experts n order to assess the bologcal consequences of estrogen n water contamnaton. In order to acheve ths goal, an analytcal system must be developed to accurately measure estrogen at very low levels and to dentfy ts bologcal effects. The system should also provde dynamc nformaton about bologcal effects that can be used to predct the bologcal consequences of the contamnaton n longer perod. Ths analytcal system s based on the predcted human cells response usng mathematcal modelng. The parameters of the proposed model are estmated usng dynamc measurements. Theses measurements represent cell prolferaton dynamc response to estrogen stmulaton and have been accurately measured wth a real-tme cell electronc sensor (RT-CES) n our recent work. The RT-CES s wdely used for many cell-based toxcty and stmulaton assay n clncal laboratory and other related applcatons [7,8]. The preventon strategy proposed n ths paper s based on mathematcal modelng of cell populaton dynamc response to estrogen stmulaton rather than modelng of contamnant molecules transport n water canalzaton system as usually done n other water preventon strateges such as n [9]... The Proposed Preventon Strategy As mentoned prevously, the goal of our proposed preventon strategy s to protect ctzens as early as possble when water s contamnated by estrogen. Ths goal s acheved by buldng a predcton strategy whch gves us early nformaton about the effect of estrogen on human cells n a dynamc fashon. The early nformaton ncludes the followng three predcton features:... Predcton of Cell Response to Estrogen Stmulaton of Dfferent Doses The dynamc cell response to estrogen stmulaton shows dfferent patterns when changng the estrogen concentraton. The predcton of cell response to dfferent estrogen doses stmulaton helps the medcal experts to decde whether the concentraton level of estrogen exceeds the allowed lmt. For ths predcton purpose, we develop a mathematcal model for descrbng the estrogen effect on human cell. To obtan a dynamc model, one usually needs to determne the model structure usng fundamental prncples and then estmate the model parameters. The parameter estmaton procedure s evolved usng the least squares approach whch looks for parameters that mnmze the ntegral of the squared predcton error. The predcton error s the dfference between the mathematcal model output and the dynamc measurements whch may be provded by a sutable sensor such as the Real-Tme Cell Electronc Sensor (RT-CES).... Fast Determnaton of Estrogen Concentraton Usng modelng strategy, we provde the possblty of determnng the concentraton of estrogen usng only small part of cell response measurements. Ths allows medcal experts to determne an estrogen concentraton wthout watng for collectng all possble measurements responses. Ths feature helps n the case where an early determnaton of the concentraton s needed.... Future Predcton of Cell Dynamc Response to Dfferent Estrogen Doses Stmulaton Ths feature helps medcal experts to decde early whether an alert needs to be trggered usng only short tme measurements. Usng only ntal data, a local (ntermedate) model s dentfed on-lne to predct future evoluton of cell response under dfferent estrogen doses stmulaton. We refer to ths model as local (ntermedate) because t s dentfed from specfc ntal dynamc response and used to predct ts future evoluton. The model developed for the frst predcton feature s consdered as a unversal or global one because t s dentfed off-lne from complete tme-hstory data and valdated for predctng cell prolferaton response to dfferent estrogen concentratons as well as beng used n the second predcton feature for rapd determnaton of estrogen concentraton. The model determned from the thrd feature s consdered as a local model. Due to the fact that our preventon strategy s based on mathematcal modelng framework, t s necessary to dscover the related exstng modelng strateges. We look for methods to descrbe estrogen effects on cells populaton dynamcs. Unregulated exposure of cells to estrogen may lead to uncontrolled cells prolferaton whch s strongly related to cancer development. The descrpton of estrogen effects on cells populaton dynamcs belongs to tumor growth descrpton area. Mathematcal modelng of uncontrolled cells prolferaton (tumor growth) has a long hstory [0]. One of the man obectves of such modelng s to fnd a way to optmze the anttumor therapy. At least three dfferent phenomenologcal models have been proposed n the lterature namely: the Logstc model, the Bertalanffy model and the Gompertz model []. The synthess of these models s purely mathematcal so that no bologcal nsghts are consdered and there were several proposals to provde a bologcal ratonale for these functons, as n [] for nstance, where the theory of cellular energy s used. In addton to the mathematcal models mentoned above, the so-called two compartments cell dynamc model s proposed for tumor growth []. Ths model s based on knowledge about the cell cycle []. Whle our proposed preventon strategy s based on predcton of the effects of estrogen concentratons on Copyrght 009 ScRes.
8 F. IBRAHIM ET AL. cell prolferaton response, we need a mathematcal model whch ncludes a term that reflects estrogen concentraton. one of the models proposed above has consdered t. To the best of our knowledge, there exst no mathematcal models n the lterature that have ths characterstc. As a result, we develop n ths paper a mathematcal modelng strategy that s able to reflect the effect of the concentraton on cell prolferaton response. Ths modelng strategy s based on some bologcal nsghts about the estrogen effects on the human cells as shown n Secton. The organzaton of ths paper s as follows. The experments procedure and the developed mathematcal modelng approaches are presented n Secton and Secton respectvely. Secton shows smulaton results ncludng model predcton valdatons. Dscusson and concludng remarks are gven n Secton 5 and Secton 6 respectvely.. Materal and Method.. Experment Setup Equpments: The RT-CES system (ACEA Boscences, CA, U.S.A.) used for ths study s set up n Alberta Laboratory for Envronment and Cancer Rsk Assessment (ALECRA) and was descrbed prevously n [7]. Brefly, t conssts of a 6x mcroelectronc sensor devces havng 6 plastc wells n mcrotter plate format, a devce staton and an electronc sensor analyzer. Cells are grown onto the surfaces of mcroelectronc sensors. In operaton, the sensor devces wth cultured cells are mounted to a devce staton placed nsde a CO ncubator. Electrcal cables connect the devce staton to the sensor analyzer. Under the control of RT-CES software, the sensor analyzer automatcally selects wells to be measured and contnuously conducts measurements on wells. The electronc mpedance can then be transferred to a computer and recorded. A schematc dagram of the nstrument (RT-CES) s shown n Fgure. A parameter termed cell ndex ( CI) s derved to represent cell status based on the measured electrcal mpedance. The frequency dependent electrode mpedance (resstance) wthout or wth cells present n the wells s represented as R ( b f ) and Rcell ( f), respectvely. The CI s calculated by: Rcell ( f ) CI max [ ] () R ( f ) where s the number of the frequency ponts at whch the mpedance s measured. Several features of the CI can be derved: ) Under the same physologcal condtons, f more cells attach onto the electrodes, the mpedance value becomes hgher, leadng to a larger CI. If no cells are present on the electrodes or f the cells are not well-attached onto the electrodes, R cell (ƒ) s the same as R b (ƒ), leadng to CI=0; Thus, CI s a quanttatve measure of the number of cells attached to the sensors; ) For the same number of cells attached to the sensors, changes n cell status, such as morphologcal change, may also lead to a change n CI. In addton to cell numbers, the mpedance also depends on the extent to whch cells attach to the electrodes. For example, f cells spread, there wll be a greater cell/electrode contact area, resultng n larger mpedance. Thus, the cell bologcal status ncludng cell vablty, cell number, cell morphology and cell adheson may all affect the measurements of electrode mpedance that s reflected by CI on the RT-CES system. Therefore, a dynamc pattern of a gven CI curve can ndcate sophstcated physologcal and pathologcal responses of the lvng cells to a gven toxc compound [7]. Chemcals and Cell Cultures: Human gloma GH cell lne (ATCC, USA) was mantaned n F- Kaghhn s (FK) meda contanng 0 % FCS, 00 g ml penclln and 00 unts ml streptomycn. The cells o were culture at 7 C and 5 % CO. Beta- Estrogen 7 acetate was purchased from Sgma-Aldrch Inc. (St Lous, USA)... Experment Method and Dynamc Growth wth Estrogen Stmulaton GH was plated onto 6x sensor devce at densty of 8000 well n trplcate n FK wth 0 % FBS and cultured for hours. Then the culture meda was replaced wth FK wthout FBS. After (hrs), two l estrogen solutons wth dfferent concentratons were added nto cell culture. The concentratons of estrogen at culture meda were at range of 0.005 (nm) - (nm). Fgure shows that the dynamc cell prolferaton response to estrogen stmulaton s dose dependant and ncreasng dose leads to ncreasng cell ndex ( CI ). b. Model Development Fgure. The real-tme cell electronc sensor (RT-CES). As we mentoned n the ntroducton, the preventon strategy we develop s based on the predcted human Copyrght 009 ScRes.
F. IBRAHIM ET AL. 9.5 C e : Estrogen concentraton C e nm Estrogen receptor CI.5 C e 0. 5nM C e 0. 0nM Estrogen Proten.5 C e 0. 05nM C e 0. 0nM C e 0. 005nM 0.5 0 5 0 5 0 5 0 5 Tme [hrs] Fgure. Dynamc prolferaton response of GH cells to dfferent doses of estrogen: 0.005; 0.0; 0.05; 0.; 0.5; [ nm ]. These data are measured by the real-tme cell electronc sensor (RT-CES). cells response to estrogen stmulaton. A mathematcal model whch s able to predct ths response s then needed. In order to buld ths mathematcal model, we explore n the next secton some bologcal nsghts whch descrbe the estrogen transport mechansm from outsde to nsde the cell and whch quantfy the estrogen stmulatve effects on cells. Wth bologcal nsghts, followng the approach of [6] the model structures can then be determned. Experment data from RT-CES such as the ones shown n Fgure can be used to ft the model parameters... Estrogen Transport and Stmulatve Effects Estrogen crculates n the bloodstream and enters target cells by a non-energy-dependant process and the cell membrane provdes a favourable lpd-rch envronment for passage of estrogen by passve dffuson [5]. When estrogen enters a cell, t bnds to hgh-affnty ntracellular receptors (Fgure ). An estrogen receptor s a proten molecule found nsde those cells that are targets for estrogen acton. Estrogen receptors contan a specfc ste to whch only estrogens (or closely related molecules) can bnd [5]. The target tssues affected by estrogen molecules all contan estrogen receptors; other organs and tssues n the body do not. Therefore, when estrogen molecules crculate n the bloodstream and move throughout the body, they exert stmulatve effects (cell prolferaton) only on cells that contan estrogen receptors. From ths ntroducton, we can hypothesze that a mathematcal modelng strategy whch reflects the effect of the estrogen concentraton on cell prolferaton response may consder two mechansms, namely, the mechansm of estrogen transport nto cell and the stmulatve mechansm of estrogen nsde the cell. Mathematcal modelng of both mechansms s presented next. Target gene Fgure. A schematc [6] of an estrogen target cell (breast, uterne, lver, etc).... Mathematcal Modelng for Estrogen Transport Mechansm The cell membrane functons as a sem-permeable barrer, allowng some molecules to cross t whle fencng others outsde the cell. Ths means that estrogen concentraton outsde the cell (refereed to as extracellular concentraton c e ) s not at mmedate equlbrum wth estrogen concentraton nsde the cell (refereed to as ntracellular concentraton c ) and a passve dffuson process takes place [5]. On the other hand, n a related area of pharmacoknetcs and pharmacodynamcs where the effect of drug s of man nterest, t was accepted that passve dffuson transport of a toxcant (Doxorubcn) s descrbed by relatng the extracellular and the ntracellular concentraton by the followng pharmacoknetc model [7]: dc kce k( kce c ) () dt k c In ths equaton, the dynamcs of the ntracellular concentraton are a combnaton of a lnear dffusve component and a saturable, carrer-medated component (Mchaels-Menten lke knetcs). The parameters k, k, k, k, are postve and constant. Due to the fact that estrogen enters cell by passve dffuson, we can assume that estrogen transport mechansm nto the cell may be descrbed by Equaton ().... Mathematcal Modelng for Estrogen Stmulatve Effects As mentoned prevously, when estrogen enters a cell, t bnds to ntracellular receptors and then starts exertng stmulatve effects leadng to cell prolferaton. By observng the related experment shown n Fgure, we can conclude that the prolferaton rate s proportonal to es- e Copyrght 009 ScRes.
0 F. IBRAHIM ET AL. trogen concentraton. In addton, due to the presence of the receptors nsde the cell, the ntracellular concentraton c stmulates cell prolferaton rather than the extracellular concentraton. Mathematcally, the proportonalty of the cell prolferaton rate to the ntracellular concentraton of estrogen can be expressed as follows: d k f ( c ) () dt Ths equaton s nspred from cell populaton dynamcs under toxcty effect gven by [8]: d k kc () dt where s cell populaton, k s prolferaton rate and kc s cell kllng rate whch we replace by the functon f ( c ) n the Equaton (). The functon f ( c ) represents a term whch reflects the effect of ntracellular estrogen concentraton on cell prolferaton rate.... Mathematcal Modelng for Cell Prolferaton Dynamc under Estrogen Stmulaton As mentoned above, we am to develop a preventon strategy when water s contamnated by estrogen. Ths preventon straggly s based on predcted cell prolferaton response to estrogen stmulaton. A mathematcal model whch reflects the extracellular concentraton of estrogen n water and relates t to cell populaton dynamcs s needed. Puttng together the transport equaton (Equaton ()) and the cell populaton dynamc equaton (Equaton ()), we obtan the desred model: dc kce k( kce c) dt k c d k 5 f ( c ) (5) dt The remanng step s to know n whch manner the ntracellular concentraton affects the prolferaton rate,.e. how to choose the functon f ( c )? We may consder that ths functon s an unknown non-lnear functon. As a second order approxmaton, t s found the followng structure s approprate: f c k c c ( ) 6 ( ) where the parameter k 6 must be constant and set to be postve n order to ensure the proportonalty between cell prolferaton dynamcs and the ntracellular concentraton as observed from the related experments (Fgure ). Ths approxmaton s chosen after several structure search steps based on experment data and we concluded that usng ths approxmaton provdes better results than usng other general functons such as f ( c) k6c or k7 f ( c ) k c k c k for nstance. The crteron of the 6 7 8 e structure search s based on the confdence ntervals of the parameters determned from the experment data. Smulaton results wll demonstrate the success of ths choce. The calculaton of the confdence ntervals of the model parameters s necessary n order to have an dea on the qualty of the estmaton. The dervaton of the confdence nterval s presented n the next secton.... The Confdence Interval In order to have a measure of the overall qualty of the estmaton and the uncertanty assocated wth a specfc estmate, one needs to calculate the confdence ntervals of the estmated parameters. A confdence nterval s a regon around an estmated value, and the true value of the parameters wll be n ths regon wth a confdence or probablty of 00 ( ) ( s the sgnfcance level). Consder the model (5). Let a state vector be expressed T T as X [ x x] [ c ] R and let the parameters vector be expressed as [ k k6] R. The 6 model (5) may be wrtten n a compact form as: kc e g( X) k( kce x) X G( X) where G( X) k c e g ( X ) k 5 f( c ) (6) wth the observaton equaton : y f( X) where f( X) (7) The confdence nterval for a parameter k s gven by: kˆ t ˆ ˆ C t C where { 6 k k } s the parameter ndex and t s the crtcal value whch equal to.960 for a 95% confdence nterval [9]. The varance matrx C and the standard error are gven by: n ( y ˆ y) T C ( J J) n p where n s the number of data ponts and p s the number of the parameters. J s the senstvty matrx whch s gven by : y y y y f( X) f( X) X J [ ] where { 6} k k k k X k (8) 6 f( X) f( X) f( X) f( X) 0 [ ] [0 ] { 6} k X x x x k X s y s 0 [0 ] k x s k s k s { 6} The term X k represents the senstvtes of the state to the parameter k. The senstvty matrx can be expressed by: Copyrght 009 ScRes.
F. IBRAHIM ET AL. On the other hand, s J [ s s (9) ] 6 s s X G G X d X G G X G G ( ) k k X k dt k k X k s k s X g g g x (0) s s s (0) 0 k x x k k x x k (0) g g g x (0) s s s s (0) 0 () In order to calculate the senstvtes s, whch s necessary for calculaton of the senstvty matrx J, we solve the system equatons (Equaton (5)) together wth the senstvty equatons (Equaton (0)) and (Equaton ()).. Results The results presented n ths secton demonstrate the ablty of our proposed preventon strategy to meet the features mentoned n the ntroducton. For ths purpose, we need to estmate the parameters of the proposed model (Equaton (5)) from the experments data provded by the RT-CES. These measurements represent cell populaton dynamcs n response to dfferent nput concentratons of estrogen as shown n Fgure. In our model dentfcaton procedure, part of these data s used for estmatng the model parameters (for fttng) and the other part s compared to the predcted output of the proposed model for valdaton. The choce and the number of the data ponts used n the estmaton procedure s done accordng to the requested bomedcal scenaro as mentoned n the ntroducton. Table. The model estmated parameters. 95% confdence nterval lower bound.5.5.5 ˆk 95% confdence nterval upper bound 0.007 0.0088 0.0 6.69 6.856 7.566.9059 6.567 9.77 0.00778 0.0575 0.07-0.0009 0.000 0.00079 Cross valdaton C e 0. 5nM C e 0. 05nM C e 0. 005nM 0.5 0 50 60 70 80 90 00 0 0 Tme [hours] Fgure. The model (5) wth the estmated parameters (Table ) predcts three sets of data correspondng to [0.5 0.05 0.005] ( nm ) estrogen concentratons. These data were not used n parameter estmaton procedure. Ths demonstrates the ablty of the model to predct cell prolferaton response when concentraton vares... Predcton of Cell Response to Estrogen Stmulaton of Dfferent Doses As we mentoned prevously, the frst feature of our proposed preventve strategy s the ablty to predct cell response to dfferent estrogen concentratons. The obectve of ths scenaro s to valdate the model developed as shown n Equaton (5). Ths valdaton s also a demonstraton of the frst feature for the preventve strategy. We use three sets of data shown n Fgure whch correspond to [ 0. 0.0] ( nm ) estrogen concentraton for estmatng the model parameters. Usng three sets of measurements s equvalent to usng 99 data ponts. The remanng three sets of data correspondng to [0.5 0.05 0.005] ( nm ) estrogen concentraton are used to valdate the model. The parameter estmaton procedure results n the parameters values and ther confdence ntervals whch are presented n Table. It was notced durng the parameter estmaton procedure that the optmzer sets the parameter k 5 to zero. Ths adds to our bologcal nsghts about the process that the.5.5.5 Self valdaton C e nm C e 0. nm C e 0. 0nM 0.5 0 50 60 70 80 90 00 0 0 Tme [hours] Fgure 5. The model (5) fts the three sets of data correspondng to [ 0. 0.0] ( nm ) estrogen concentraton. These data are provded by the real-tme cell electronc sensor RT-CES and used to estmate the model parameters presented n Table. Copyrght 009 ScRes.
F. IBRAHIM ET AL. cell prolferaton rate depends only on the ntracellular concentraton and not on the populaton varable tself. Ths leads us to consder that the estrogen stmulaton effect should be represented by the followng model nstead: dc kce k( kce c) dt k c d ( k 6 c c ) () dt The predcton performance of the proposed model usng the estmated parameters n Table s presented n Fgure and Fgure 5. In Fgure 5 the proposed model fts the data whch s used n parameter estmaton phase. In Fgure the model predcts the remanng data whch does not partcpate n model fttng. These valdatons demonstrate the ablty of the model to predct cell prolferaton response when concentraton vares... Rapd Determnaton of Estrogen Concentraton In ths scenaro, we use the model (5) wth the estmated parameters presented n Table to estmate estrogen concentraton from short term measurements. The concentraton s treated as an unknown parameter for the model and s estmated from a short perod of response. Examples of these concentratons correspond to 0.5 ( nm ) and 0.005 ( nm ). As shown n Fgure 6, the proposed model s able to provde an estmaton of the concentraton that equals to 0.5, whch s close to the real value 0.5 ( nm ), wthn 88 hours. Fgure 7 shows that the model s also able to provde an estmaton of the concentraton that equals to 0.07 ( nm ) wthn 8 hours, whch s close to the real value 0.05 ( nm ). Ths scenaro provdes the second feature of our preventve strategy whch helps n the case where an early determnaton of the concentraton s needed... Future Predcton of Cell Response to Dfferent Estrogen Doses Stmulaton In ths scenaro, we dentfy a set of parameters for the model (5) usng short tme measurements. The obectve s to predct the future evolutons of cell responses based on the ntal response. The purpose of ths scenaro s to provde the thrd feature of the proposed preventon strategy whch helps medcal experts to decde early whether an alert needs to be trggered usng only short tme measurements. We refer to ths model as local or ntermedate model and t s dentfed on-lne after collectng some ntal response data and then the model s used to predct the future evoluton. Ths model s only e.5.5.5 Self valdaton Cross valdaton 0 50 60 70 80 90 00 0 0 Tme [hours] Fgure 6. The model (5) s able to provde a close estmaton of the concentraton usng short tme data (up to 88 [hr]). The real concentraton value equals to 0.5 ( nm ) and the estmated value equals to 0.5 ( nm )..6.5.... Self valdaton Cross valdaton 0.9 0 50 60 70 80 90 00 0 0 Tme [hours] Fgure 7. The model (5) s able to provde a close estmaton of the concentraton usng short tme data (up to 8 [hr]). The real concentraton value equals to 0.05 ( nm ) and the estmated value equals to 0.07 ( nm ). Table. The model estmated parameters. 95% confdence nterval lower bound ˆk 95% confdence nterval upper bound 0.00006 0.007 0.058 6.888 0..6075.876 5.8956 76.99 0.06 0.0 0.07-0.0000 0.0007 0.0007 for predcton purpose and the values of the estmated parameters vary wth dfferent length of data used, also Copyrght 009 ScRes.
F. IBRAHIM ET AL..5.5.5 0.5 0 50 60 70 80 90 00 0 0 Tme [hours] Fgure 8. Usng only a part of hstory data (up to 9 [hr]); a set of parameters s estmaton (Table ). Usng ths set of parameters, the model (5) s able to predct the future evoluton. known as adaptve estmaton. As an example, usng short tme data (up to 9 [hr], whch s equvalent to 8 data ponts) n parameter estmaton procedure, we obtan the parameters values and ther confdence ntervals shown n Table. Fgure 8 shows that, usng the set of estmated parameters presented n Table () for the model (5), the model s able to predct the future evoluton of the data startng from t 9 (hrs). 5. Dscussons C e nm C e 0. 5nM C e 0. nm C e 0. 05nM C e 0. 0nM C e 0. 005nM The strategy presented n ths paper has three man features whch represent real scenaros n an early warnng context. We have successfully acheved the obectve through mathematcal modelng and predcton based on data obtaned from RT-CES experments. The heart of our preventon strategy s the mathematcal modelng and predcton. Therefore the success of ths strategy depends on the qualty of the used model. The model we developed (Equaton (5)) s able to provde a good cross valdaton wth several choces of f ( c ). However only the structure f( c ) k6 ( c c ) provdes a reasonable confdence nterval as shown n Tables [,]. Therefore n Secton we ponted out that ths approxmaton s chosen after several structure search steps and the crteron for ths structure search s based on the confdence ntervals of the parameters determned from the expermental data. All other terms of the model are derved drectly from fundamental bologcal nsghts. More understandng of the cell stmulaton mechansm by estrogen doses wll lead to a more precse expresson of f ( c ). However, n absence of such deep knowledge so far, data-based structure search s the best choce. 6. Conclusons The man contrbuton of ths work s the development of a preventon strategy composed of three predcton features for water protecton area. Ths strategy s based on mathematcal models. Theses models are able to descrbe estrogen effects on human cell dynamc response and they are cross valdated usng data whch s not used n the model dentfcaton phase. The calculated confdence ntervals of the parameters for the developed models show a good estmaton qualty. The ultmate obectve of our preventon strategy s to protect ctzens as early as possble when water s contamnated by estrogen. Ths strategy s composed of three predcton features, namely, predcton of cell response to dfferent stmulatons of estrogen concentraton, early determnaton of estrogen concentraton and predcton of future evoluton of cell response usng short tme measurements. It s mportant to menton that the proposed strategy s not lmted to the case when water s contamnated by estrogen. The same methodology may be adopted when water s contamnated wth other toxns. The work presented here s our frst step toward buldng a hgh performance early warnng system for water protecton. 7. Acknowledgment The authors gratefully acknowledge the support of the atural Scences and Engneerng Research Councl of Canada (SERC), Alberta Health (Water for Lfe Proect) and Alberta Laboratory for Envronment and Cancer Rsk Assessment (ALECRA). 8. References [] J. S. Patrck, J. A. Frankln, and J. J. C. James, The envronmental scence of drnkng water, ISB-: 978 0 7506 7876 6, 005. [] K.. Raesh, Endocrne dsruptors: Effects on male and female reproductve systems, CRC Press, st Edton ISB-0: 0896, 999. [] P. Lemeux and S. Fuqua, The role of the estrogen receptor n tumor progresson, The Journal of Sterod Bochemstry and Molecular Bology, Vol. 56, o. 87 9, 996. [] R. A. Hess and K. Carnes, The role of estrogen n tests and the male reproductve tract: A revew and speces comparson, Anmal Reproducton, Vol., pp. 5 0. 00. [5] M. L. Johnson, A. Salveson, L. Holmes, M. S. Denson, and D. M. Fry, Envronmental estrogens n agrcultural dran water from the central valley of Calforna, Journal Bulletn of Envronmental Contamnaton and Toxcology, Vol. 60, pp. 609 6, 998. [6] B. Huang and J. Z. Xng, Dynamc modelng and Copyrght 009 ScRes.
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