Review Session. The concentration of substrate that results in 50% of the maximal growth rate is 100 mg/ml.

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1 ReviewSession Problem1 Acultureofcellsisinitiatedwith0.2mg/mlofcellmass.Theinitialglucose concentrationis1mg/ml.whatisthevalueofthemonodconstantassuming externalgrowthcontrolafter7daysofgrowth?howmuchloweristhemonod constantatthistimepointthanthegrowthconstantforunconstrainedgrowth?you arealsogiventhefollowingadditionalinformation: Yieldforglucose(thelimitingsubstrateinthiscase)=0.8 Theconcentrationofsubstratethatresultsin50%ofthemaximalgrowthrateis 100mg/ml. TheMonodequationisvalidforthiscultureofcellsandisrepresentedbythe followingexpression: µ = (0.06day 1 )[ S] S 0 = S + X X 0 ( ) Y bx X(t) = 0 e bt ax 0 + b ax 0 e bt a = k Y b = ks 0 + kx 0 Y + S ( ) k = µ m

2 Problem2 Ingenetherapyresearch,itiscommontousereportergenestoquantifytheability ofacellpopulationtoproduceaforeignprotein.thesereportergenestypically encodeforeitheraproteinthatfluorescesorluminescesoranenzymethatwill convertasubstrateintoacolored,fluorescent,orluminescentproduct(,diagram below).onesuchgeneencodesfortheenzymebeta galactosidase.thisisan enzymethatturnsthesubstrateonpgintotheyellowproducto nitrophenol. Measuringthelightabsorbanceofthesolutionthatthecellpopulationwasgrownin at420nmandcomparingthisvaluetotheabsorbancevaluesofaseriesof standardsofknownbeta galactosidaseconcentrationallowsyoutoquantifythe amountofproductproducedbythecellpopulation. Assumethattheconsumptionofthesubstrate,ONPG,occursviaMichaelis Menton kineticswherebeta galactosidaseistherelevantenzymeandthatthefollowing informationisknownaboutthereactionwithsubstrate: Total=3µg S0=2millimol/liter KM=0.161millimol/liter kcat=0.006millimol/(liter µgenzyme min). Whensubstrateconcentrationhasdroppedto50%ofitsinitialvalue,whatfraction oftheenzymepresentinthereactionisboundtosubstrate?whatistherateof productformationatthistimepoint? [ S] = cell k 1 [ Total ][ S] ( k 1 + k cat ) + k 1 [ S] ( K M = k + k 1 cat ) k 1 ONPG [ S] K M t = S 0 + ln S 0 k cat Total k cat S Total

3 Problem3 BasicFibroblastgrowthfactorisaddedtoculturemediumataconcentrationof 1000molesperliter.Onemilliliterofculturemediumisaddedtoacultureof fibroblastsseededat1x10 6 cellsperdish.(a)after0.5secondswhatfractionof receptorsarenotboundtoligand?(b)atsteady statewhatfractionofreceptors wouldbeboundtoligand?(c)xplainwhattypeofexperimentalchangeyoucould maketoincreasethefractionofreceptorsboundatsteady state. [ LR] = k f k f [ R Total ] 1 exp k f [ ] + k r + k r ( [ ( )t]) Y = [ ] [LR] = k f [ ][ R Total ] [ ] + K D k f [ ] + k r

4 Problem4:AcontinuationofHW3problem2 Astudentleavingforavacationaskedhisfriendtotakecareofhisendothelialcells whileheisgone.whenchangingthemedia,thefrienddecidestoadd4mlofmedia tothedishes(insteadof2ml)becausemoremediameansmorenutrients,which meansthathedoesn thavetochangethemediaasoften.however,whenthe studentreturns,hefindstohisdismaythatsomeofhiscellshavedied.the disgruntledstudentdoessomecalculationstodeterminewhetherornotthecells diedduetoalackofoxygen.forthecalculationsthatfollowyoumayassumethat diffusionoccursinonedimensionatsteady state.thepartialpressureofoxygenin theambientincubatorairis150mmhg(ps).thepartialpressureofoxygenin equilibriumwiththeconcentrationofdissolvedoxygenatthecellsurfaceisgivenby thevariable P δ.cellviabilityiscompromisedforvaluesof P s < 0.5mmHg.Adiagram isgivenbelow: Youmayusethefollowingadditionalinformation: K=1.19nmol/(ml mmhg)where, C equilibrium = KP equilibrium D=2x10 5 cm 2 /s(diffusivityofoxygenthroughculturemediumat37 o C) Thefluxisgivenbythefollowingexpression: ( ) Flux = D K P " P s # # where " istheheightoftheculturemedium. Whilenotaboundaryconditionperse,atthecellsurfaceyoudoknowthatcells consumeoxygenatarateequaltothatdescribedbymichaelis Mentenkinetics: V m P δ + P δ wherevm=3x10 7 nmol/(s cell)andkm=0.5mmhg. Whatoxygentensionintheambientincubatorairwouldbenecessaryto sustaincelllifewiththeconditionsusedbytheundergraduatestudent(4ml ofmedia,areaofculturedish=21cm 2 )?

5 Problem4 BasicFibroblastgrowthfactorisaddedtoculturemediumataconcentrationof 1000molesperliter.Onemilliliterofculturemediumisaddedtoacultureof fibroblastsseededat1x10 6 cellsperdish.after0.5secondswhatfractionof receptorsareboundtoligand? [ LR] = k f k f [ R Total ] 1 exp k f [ ] + k r + k r ( [ ( )t]) Y = [ ] [LR] = k f [ ][ R Total ] [ ] + K D k f [ ] + k r