Mathematical Modeling of Biosensors: An Introduction for Chemists and Mathematicians PDF
Preview Mathematical Modeling of Biosensors: An Introduction for Chemists and Mathematicians
9 Springer Series on Chemical Sensors and Biosensors Methods and Applications Series Editor: G. Urban Springer Series on Chemical Sensors and Biosensors Series Editor: G. Urban Recently Published and Forthcoming Volumes Optical Guided-wave Chemical FrontiersinChemicalSensors andBiosensors II NovelPrinciplesandTechniques VolumeEditors:Mohammed Z., VolumeEditors:OrellanaG.,Moreno-BondiM.C. LakhtakiaA. Vol.3,2005 Vol.8,2009 UltrathinElectrochemical Optical Guided-wave Chemical Chemo-andBiosensors andBiosensors I TechnologyandPerformance VolumeEditors:Mohammed Z., VolumeEditor:MirskyV.M. LakhtakiaA. Vol.2,2004 Vol.7,2009 OpticalSensors HydrogelSensorsandActuators Industrial,Environmental VolumeEditors:GerlachG.,ArndtK.-F. andDiagnosticApplications Vol.6,2009 VolumeEditors: NarayanaswamyR.,WolfbeisO.S. PiezoelectricSensors Vol.1,2003 VolumeEditors:SteinemC.,JanshoffA. Vol.5,2006 SurfacePlasmonResonanceBasedSensors VolumeEditor:HomolaJ. Vol.4,2006 Mathematical Modeling of Biosensors An Introduction for Chemists and Mathematicians Volume Authors: Romas Baronas · Feliksas Ivanauskas Juozas Kulys 123 Chemical sensors and biosensors are becoming more and more indispensable tools in life science, medicine,chemistryandbiotechnology.Theseriescoversexcitingsensor-relatedaspectsofchemistry, biochemistry, thin film and interface techniques, physics, including opto-electronics, measurement sciencesandsignalprocessing.Thesinglevolumesoftheseriesfocusonselectedtopicsandwillbe editedbyselectedvolumeeditors.TheSpringerSeriesonChemicalSensorsandBiosensorsaimsto publishstate-of-the-artarticlesthatcanserveasinvaluabletoolsforbothpractitionersandresearchers activeinthishighlyinterdisciplinaryfield.Thecarefullyeditedcollectionofpapersineachvolumewill give continuous inspiration for new research and will point to existing new trends and brand new applications. ISSN1612-7617 ISBN978-90-481-3242-3 e-ISBN978-90-481-3243-0 DOI:10.1007/978-90-481-3243-0 SpringerDordrecht HeidelbergLondonNewYork LibraryofCongressControlNumber:2009931246 (cid:176)c SpringerScience+BusinessMediaB.V.2010 Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby anymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework. Coverdesign:SPi Publisher Services Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Series Editor Prof.Dr.GeraldUrban IMTEK-LaboratoryforSensors InstituteforMicrosystemsEngineering Albert-Ludwigs-University Georges-Ko¨hler-Allee103 79110Freiburg Germany [email protected] Volume Authors Romas Baronas Feliksas Ivanauskas Vilnius University Dept. Mathematics & Informatics Naugarduko 24 LT-03225 Vilnius Lithuania [email protected] [email protected] Juozas Kulys Vilnius Gediminas Technical University Fac. Fundamental Sciences Dept. Chemistry & Bioengineering Sauletekio Ave. 11 LT-10223 Vilnius Lithuania [email protected] Preface Biosensors are analytical devices in which specific recognition of the chemical substancesisperformedbybiologicalmaterial.Thebiologicalmaterialthatserves as recognition element is used in combination with a transducer. The transducer transforms concentration of substrate or product to electrical signal that is ampli- fiedandfurtherprocessed.Thebiosensorsmayutilizeenzymes,antibodies,nucleic acids, organelles, plant and animal tissue, whole organism or organs. Biosensors containing biological catalysts (enzymes) are called catalytical biosensors. These typeofbiosensorsarethemostabundant,andtheyfoundthelargestapplicationin medicine,ecology,andenvironmentalmonitoring. The action of catalytical biosensors is associated with substrate diffusion into biocatalytical membrane and it conversion to a product. The modeling of biosen- sorsinvolvessolvingthediffusionequationsforsubstrateandproductwithaterm containing a rate of biocatalytical transformation of substrate. The complications ofmodelingarise duetosolvingofpartiallydifferentialequationswith non-linear biocatalyticaltermandwithcomplexboundaryandinitialconditions. The book starts with the modeling biosensors by analytical solution of partial differential equations. Historically this method was used to describe fundamental features of biosensors action though it is limited by substrate concentration, and is applicable for simple biocatalytical processes. Using this method the action of biosensorswasanalyzedatcriticalconcentrationsofsubstrateandenzymeactivity. Thesubstratesconversioninsingleandmultienzymemembraneswasstudied.The different schemes of substrates conversion which found practical application for biosensorsconstructionwereanalyzed.Thebiosensorsdynamicswasconsideredat thesimplestschemeofbiocatalyzeraction. Theotherpartofthebookcoversdigitalmodelingofbiosensors.Thebiosensors basedonamperometricaswellaspotentiometrictransducersareconsidered.Theac- tionofbiosensorscontainingsingleandmultienzymesweremodeledusingthefinite differencetechniqueatnonstationaryandsteadystate.Specialemphasiswasplaced to model biosensors utilizing a complex biocatalytical conversion and biosensors withmultiparttransducersgeometryandbiocatalyticalmembranesstructure. Thefinalpartofthebookisdedicatedtothebasicconceptsofthetheoryofthe difference schemes for the digital solving of linear diffusion equations which are basisforbiosensorsmodeling. vii viii Preface Thebookcanberecommendedforthemasteranddoctoralstudiesaswellasfor specialstudiesofbiosensorsmodeling.ThePart3canalsobeusedforindependent studyofdigitalsolutionofdifferentialequations. The book was prepared for the period of students teaching by R. Baronas and F.IvanauskasatVilniusUniversityandbyJ.KulysatVilniusGediminasTechnical University. The authors acknowledge particular universities for the support of the manuscriptpreparation.Thecontributionofthecoauthorsofthecitedpublications ishighlyappreciated. Vilnius, RomasBaronas February2009 FeliksasIvanauskas JuozasKulys Acknowledgements The authors acknowledge Vilnius University (Romas Baronas and Feliksas Ivanauskas) and Vilnius Gediminas Technical University (Juozas Kulys) for the supportofmonographpreparation. ix Contents Introduction ....................................................................... xvii PartI AnalyticalModelingofBiosensors BiosensorAction .................................................................. 3 1 KineticsofBiocatalyticalReactions......................................... 3 2 TransducerFunction.......................................................... 5 3 SchemeofBiosensorAction ................................................. 6 ModelingBiosensorsatSteadyStateandInternalDiffusionLimitations.. 9 1 BiosensorsContainingSingleEnzyme ...................................... 9 2 BiosensorsContainingMultienzymes ....................................... 10 2.1 ConsecutiveSubstratesConversion .................................. 10 2.2 ParallelSubstratesConversion........................................ 14 2.3 BiosensorsUtilizingCyclicSubstratesConversion ................. 15 3 BiosensorsUtilizingSynergisticSubstratesConversion.................... 16 4 BiosensorsBasedonChemicallyModifiedElectrodes..................... 18 ModelingBiosensorsatSteadyStateandExternalDiffusion Limitations ........................................................................ 21 1 BiosensorUsingSingleEnzyme............................................. 21 2 BiosensorswithMultienzymes............................................... 22 3 BiosensorUtilizingNonMichaelis–MentenEnzyme....................... 23 ModelingBiosensorsUtilizingMicrobialCells ................................ 27 1 MetaboliteBiosensor......................................................... 27 2 BODBiosensor ............................................................... 30 ModelingNonstationaryStateofBiosensors................................... 33 1 PotentiometricBiosensors.................................................... 33 2 AmperometricBiosensors.................................................... 34 xi
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