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Intrinsicallydisorderedlinkerscontroltetheredkinasesviaeffectiveconcentration
MateuszDyla1,2andMagnusKjaergaard1-4*
1DepartmentofMolecularBiologyandGenetics,AarhusUniversity2TheDanishResearchInstituteforTranslationalNeuroscience(DANDRITE),NordicEMBLPartnershipfor
MolecularMedicine3CenterforProteinsinMemory-PROMEMO,DanishNationalResearchFoundation4AarhusInstituteofAdvancedStudies,AIAS,AarhusUniversity*Correspondingauthor:magnus@mbg.au.dk
Abstract:
Kinasespecificityiscrucialtothefidelityofsignallingpathways,yetmanypathwaysuse
thesamekinasestoachievewidelydifferenteffects.Specificityarises inpart fromthe
enzymaticdomain,butalso from thephysical tetheringofkinases to their substrates.
Suchtetheringcanoccurviaproteininteractiondomainsinthekinaseorviaanchoring
and scaffoldingproteins, and candrastically increase the kinetics of phosphorylation.
However,wedonotknowhowsuchintra-complexreactionsdependonthelinkbetween
enzyme and substrate. Here we show that the kinetics of tethered kinases follow a
Michaelis-Menten like dependence on effective concentration. We find that
phosphorylationkineticsscalewiththelengthoftheintrinsicallydisorderedlinkersthat
jointheenzymeandsubstrate,butthatthescalingdiffersbetweensubstrates.Steady-
statekineticscanonlypartiallypredictratesoftetheredreactionsasproductreleasemay
obscure the rate of phospho-transfer. Our results suggest that changes in signalling
complexarchitecturenotonlyenhancetheratesofphosphorylationreactions,butmay
alsoalter therelativesubstrateusage.Thissuggestsamechanismforhowscaffolding
proteinscanallostericallymodifytheoutputfromasignallingpathway.
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Introduction
Cellular signalling relies on cascades of enzymes such as protein kinases and
phosphatases.Signallingfidelityrequireskinasestousespecificsubstrates,althoughthe
samekinasescantakepartindifferentpathwayswithdifferentsubstrates.Forexample,
proteinkinaseA(PKA)isinvolvedinsignallingpathwaysthroughoutcellbiology.1Kinase
specificity arises in part from the linear motifs surrounding the phospho-accepting
residue.However,invivosubstrateusagecanonlybepredictedpartiallyfromsequences
motifsaskinasesignallingisalsoregulatedthroughthelocalabundanceofenzymes.2The
latterclassofeffectsismuchlessunderstoodquantitatively.
The localabundanceof signallingenzymes is regulatedatmany levels.At thecellular
level,kinasesare targeted toe.g.anorganelleor thecellmembrane.At themolecular
level, enzymes are targeted to a subset of their potential substrates by tethering to
scaffolding proteins. In multidomain enzymes, such tethering occur via protein
interaction domains attached to the catalytic domain.3 Alternatively, enzymes can be
tetheredbyscaffoldingproteins thatbind theenzymeandsubstratesnon-covalently.4
PKA isregulatedbymore than50differentAkinaseanchoringproteins(AKAPs) that
directthekinasetodifferentpathways.5PKAmaydissociatefromitsregulatorysubunit
andthusAKAPsuponactivation,butrecentlyitwasdemonstratedthatactivePKAmay
remaintetheredtoAKAP.6TheintrinsicallydisorderedAKAPsthusrestrictthekinaseto
aregionwhosedimensionsaredefinedbythelengthandcompactnessoftheanchoring
protein.7 Similarly, disordered linkers of variable length regulate the activity of the
dodecamerickinaseCaMKIIbycontrollingthebalancebetweeninter-andintra-subunit
phosphorylation.8Manykinasesignallingreactionsthusoccurinternallyinproteinsorin
proteincomplexes.
Whenakinaseisphysicallyassociatedtoitssubstrate,thetetheredsubstrateisdistinct
fromallother substrates in the reactionmixtureand isusuallyphosphorylatedmuch
faster.Thekineticsofsuchreactionsdifferfromsteady-stateenzymekineticsastethered
catalysisiseffectivelysingleturnover.Duetotheswitch-likefunctionsofmanykinases,
theymayonlyneedtophosphorylateasinglesubstratetoexertabiologicalfunction.9
This canbe seen e.g. in thenegative feedback loop formedbyAKAP79-tetheredPKA,
whichinactivatesadenylatecyclasebyphosphorylation.10Therateofintramolecular(or
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intra-complex) reactions isexpected tobeconcentration independentalthough this is
rarely tested for tethered kinases. Instead, the encounter rate is determined by the
connection between enzyme and substrate. The quantitative description of tethered
catalysisishinderedbythelackofframeworktodescribetheconnectioninkineticterms.
Wepropose thatmany linkers canbe accounted for by the effective concentrationof
substratetheyenforce.Enzymescaffoldingproteinsandinterdomainlinkersinkinases
are often intrinsically disordered as they allow the kinase domain to search for its
substrates.11Forfullydisorderedlinkers,theeffectiveconcentrationscanbeestimated
frompowerlawscalingwiththelengthofthelinker.12Kinasestetheredbydisordered
protein linkers thus offer a chance to understand the general principles that govern
tetheredcatalysis.
Hereweinvestigatehowtheconnectionbetweenakinaseanditssubstrateaffectsthe
phosphorylationkinetics.Weuseamodelsystemconsistingofthecatalyticdomainof
PKAtetheredtoasubstrateviavariableintrinsicallydisorderedlinkers.Weshowthat
phosphorylationratevariesbyseveralordersofmagnitudedependingonthesubstrate
and the linker. We show that phosphorylation rate follows a Michaelis-Menten like
dependence on the effective concentration enforced by the linker, with steady-state
parameterspartiallypredicting theratesof tetheredsingle turnoverphosphorylation.
Thisprovidesabaselineforinterpretinghowsignallingcomplexarchitectureregulates
tetheredenzymes.
Materials and Methods
Preparation of DNA constructs: The plasmid containing the catalytic domain of PKA
(PKAc)wasagiftfromSusanTaylorviaAddgene(#14921).13Theotherplasmidswere
synthesized by Genscript and codon optimized for expression in E. coli. The coding
regionswereclonedintopET15bvectorsusingtheNdeI/XhoIsites.ThedisorderedGS
linkers from the linker library generated previously12 were cloned into the protein
constructsusinguniqueNheI/KpnIsites.Thesequencesofproteinconstructsaregiven
intheSI.
Proteinexpressionandpurification:Proteinconstructscontainingthecatalyticdomainof
PKA linked by variable length linkers to the MBD2 coiled-coil domain (MBD2-(GS)n-
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PKAc)wereexpressedinC41(DE3)cellsinLBmediumwith100µg/mLampicillinat37°C
andshakingat120RPM.Thecultureswereinducedwith1mMIPTGatOD600=0.6-0.8
andthetemperaturewasdecreasedto30°Cforovernightexpression.Proteinconstructs
containingPKAsubstrateslinkedtothep66αcoiled-coildomain(p66α-(GS)n-substrate)
wereexpressed inBL21(DE3) cells in ZYM-5052auto-inductionmedium14 containing
100µg/mLampicillinat37°Candshakingat120RPMovernight.
The cells were harvested by centrifugation (15 min, 6000 g), bacterial pellets were
resuspendedinbindingbuffer(20mMNaH2PO4,0.5MNaCl,5mMimidazole,0.1mM
TCEP,0.2mMPMSF,50mg/Lofleupeptin,50mg/Lpepstatin,50mg/Lchymostatin,pH
7.4)andlysedbysonication(50%dutycycle,maximumpowerof75%,sonicationtime
of6min).Thelysatewascentrifuged(20min,27000g)andthesupernatantwasapplied
to gravity flowcolumnspackedwithNi-NTASuperflow (QIAGEN).The columnswere
washedwithbufferscontainingincreasingconcentrationsofimidazole(20-50mM)and
wereelutedwithelutionbuffer(20mMNaH2PO4,0.5MNaCl,500mMimidazole,0.1mM
TCEP).ElutedproteinsamplescontainingPKAsubstratesweredialyzedagainstbinding
bufferwithoutimidazoleovernight,followedbycleavageofHis-tagbythrombin(1:1000
thrombintosubstrateratio)at37°Candshakingat300RPMfor30min.Cleavedsamples
wereappliedtogravityflowcolumnspackedwithNi-NTASuperflow(QIAGEN)andflow-
throughwascollected.Allproteinsampleswereadditionallypurifiedbysize-exclusion
chromatography(SEC)inTBSbuffer(20mMTris-base,150mMNaCl,0.1mMTCEP,pH
7.6)usingSuperdex200IncreaseandSuperdex75Increasecolumns(GEhealthcare)to
purifyPKAcanditssubstrates,respectively.
Quench-flow measurements: Single-turnover kinetic measurements were performed
usingaKinTekCorporationRQF-3Rapidquench-flowinstrumentat30°C.MBD2-(GS)n-
PKAc and p66α-(GS)n-substrate were diluted to 10x final concentration in enzyme
dilutionbuffer(50mMTris-base,0.1mMEGTA,1mg/mlBSA,1mMTCEP,pH7.6)and
TBS (20mMTris-base,150mMNaCl,pH7.6), respectively.Quench flowexperiments
were executed by loading the catalytic domain of PKA and its substrates (final
concentration0.5µMunlessindicatedotherwise)intoonesampleloopand[γ-32P]ATP
(finalconcentration0.1mMof100-200countsperminute(c.p.m.)pmol-1)intotheother.
Phosphorylationreactionswerecarriedoutinthereactionbuffercomposedof50mM
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Tris-base,0.1mMEGTA,10mMmagnesiumacetate,150mMNaCl,pH7.6.Thereactions
werequenchedusing150mMphosphoric acidusing the “constantquench”option to
limit the total quenched reaction volume to 70 µL. Phosphorylated substrates were
separated from unreacted ATP by spotting the quenched reactions onto P81
phosphocellulosedisks(JonOakhill,St.VincentInstitute,Melbourne).Thefilterswere
washed3timeswith75mMphosphoricacid,rinsedwithacetone,dried,andcountedon
the32Pchannelinscintillationcounterasc.p.m.Controlexperimentswereperformedto
determinebackgroundphosphorylationlevelofsubstratemotifsintheabsenceofPKAc,
aswellasautophosphorylationofPKAcintheabsenceofsubstrates.Backgroundvalues
(typicallynegligible)weresubtractedfromtherawdata.Specificphosphorylationwas
determinedasamountof32P-incorporatedsubstrate(pmol)basedon32P-ATPstandard
curve,wherec.p.m.valuesofknownamountsofspiked32P-ATPweremeasured.
Steady-statekinetics:PKAc(withouttheMBD2dimerizationdomain)wasdilutedto10x
finalconcentrationinenzymedilutionbuffer(50mMTris-base,0.1mMEGTA,1mg/ml
BSA,1mMTCEP,pH7.6)andp66α-(GS)n-substratewasdilutedto5xfinalconcentration
inTBS(20mMTris-base,150mMNaCl,pH7.6).Steady-stateexperimentswereexecuted
bymanualadditionof[γ-32P]ATP(finalconcentration0.1mMof100-200c.p.m.pmol-1)
into reactionmixcontaining1nMPKAcandp66α-(GS)n-substrate (final concentration
10-1820µM)inareactionbuffer(50mMTris-base,0.1mMEGTA,10mMmagnesium
acetate,150mMNaCl,pH7.6)at30°C.Everyminute5µlofthereactionmixwasspotted
ontoaP81filterdiskandplacedinto75mMphosphoricacidtoquenchthereaction.The
filterswerewashed3timeswith75mMphosphoricacid,rinsedwithacetone,dried,and
countedonthe32Pchannel inscintillationcounterasc.p.m.Controlexperimentswere
performedinthesamewayasinquench-flowexperiments,andspecificphosphorylation
was determined likewise. Initial velocities at different substrate concentrationswere
derived froma slopeof a linear regressionaspmolof 32P-incorporated substrateper
minute.ThedatawerethenfittedbyaMichaelis-Mentenmodel,andkcatwascalculated
bydividingVmaxby0.005pmolofPKAcandby60(min/s).
Results
To probe the linker dependence of tethered catalysis, we designed a model system
composedofthecatalyticdomainofproteinkinaseA(PKAc)tetheredtoitssubstratevia
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disorderedlinkers(Fig.1A,S1).WeusedtheoptimalPKAsubstrateKemptide(WTinthe
following)16andvariedsubstratequalitybymutagenesis.Thekinaseandsubstratewere
made as separate proteins and joined non-covalently using heterodimeric coiled-coil
domains.Weusetheanti-parallelcoiled-coilformedbetweenp66αandMBD215asithas
lownMaffinity,andisstableonthetimescaleofthetetheredreaction.Thecoiled-coil
domains were joined to the PKAc/substrate by an exchangeable linker flanked by
restriction sites compatible with our library of disordered linkers.12 To approximate
passive,entropicspacers,weusedglycine-serinerepeatlinkerscontaining2,20,60and
120residues.
Figure1:Areductionistmodelsystemfortetheredphosphorylation.(A)ThecatalyticdomainofPKAanditsconsensussubstratemotifarejoinedtothecoiled-coildomainfromMBD2andp66α,respectively.MBD2andp66αformananti-parallelheterodimerwithnanomolaraffinity.15Substratequalitywasvariedbymutationawayfromtheconsensusmotif,andthelinkerwasvariedbyincludingGS-repeatsofvariablelength.(B)Quench-flowwasusedtomeasuresingle-turnoverkineticsbyfollowingincorporationof32Pintothesubstrate.Tetheringofenzymeusingcombinedlinkerlengthof40residuesincreasedtherateby~300-fold at a substrate and enzyme concentrations of 0.5 µM. (C) The rate of the tethered catalysisdecreasedslightlywithincreasingconcentrationofsubstrateandenzyme.
We followed single-turnover phosphorylation in an equimolar mix of kinase and
substrateusingquench-flow.Thereactionwasstartedbyadding[γ-32P]ATP,quenched
byphosphoricacidatreactiontimesfrom2.5msto330s,andfollowedfromtheamount
of32Pinthesubstrate.Initially,wecomparedidenticaltetheredanduntetheredreactions,
wheretetheringincreasedreactionratebymorethan100-fold(Fig.1B).Intra-complex
reactions are concentration independent, whereas the rate of bimolecular reactions
increaseswithconcentration.Therefore,wetestedhowtheconcentrationoftheenzyme
andsubstrateaffected thephosphorylationrate.WhileremainingbelowtheKMof the
substrate, the concentration was increased 10-fold, which led to a slightly slower
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phosphorylation(Fig.1C).Theseobservationssuggestthatphosphorylationoccursintra-
complexwithnegligiblecontributionsfromtrans-phosphorylation.
Totesthowlinkersaffectphosphorylation,wevariedthelengthsoftheGSrepeats.By
combiningkinaseandsubstratevariants,wecreated6complexeswithacombinedlinker
lengthspanningfrom20to180disorderedresiduesinadditiontothe17residuesfrom
restriction sites and the short extra linker in the substrate. For all variants the
phosphorylationreactioncouldbedescribedwellwithasingleexponentialmodel,where
thephosphorylationratedecreasedmonotonicallywithincreasedlinkerlength(Fig.2A,
S2). This suggests that kinase linkers and anchoring proteins directly regulate intra-
complexkinasereactions.
Next, we tested whether substrate quality affects the linker dependence of
phosphorylation.PKArecognizespositiveresiduesinpositions-2and-3relativetothe
phosphorylationsitewithapreferenceforarginineoverlysine.16Toweakenthesite,we
mutatedeachofthetwoarginineresidues inthesubstratemotif to lysineresulting in
variantsR-2KandR-3K.Thephosphorylationratedecreasedmonotonicallywithlinker
lengthforbothmutants,althoughwithdifferentmagnitudes(Fig.2B).Phosphorylation
oftheWTsubstrateonlyslows2-foldfromtheshortesttothelongestlinkers,whereas
theR-3Ksubstrateslowsbymorethan10-fold.Thissuggeststhatsubstratesareaffected
differentlyby tethering, and that thepropertiesof the linkerandsubstrate shouldbe
consideredtogether.
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Figure2:Linkerdependenceofsingle-turnoverphosphorylationrates.(A)Quench-flowkineticsofthephosphorylationreactionsoftheR-3Ksubstratewithdifferentlinkerlengths.ThelinkerlengthisthecombinednumberofGS-repeats in the two linkers. (B)Theobserved rateofphosphorylationof threedifferentsubstratesasafunctionofthecombinedlinkerlength.(C-E)Phosphorylationratesasafunctionoftheestimatedeffectiveconcentrationenforcedbythelinker.EffectiveconcentrationsareestimatedfromthepowerlawmeasuredpreviouslyforGS-linkers12assumingthatthepresenceofthecoiled-coildomainisnegligible.(F)KineticschemeofthetetheredsystemundersaturatingconcentrationofATP.O·ATP–openstateofthetetheredsystem,ATP-bound;C·ATP–closedcatalyticallycompetentstate,ATP-bound;CP·ADP – closed phosphorylated state, ADP-bound; OP – open, nucleotide-free state. Nucleotide andphosphorylationareshownasorangemoietiesinthecartoon.
TheattenuatedlinkerdependenceoftheWTsubstratecouldinprinciplebecausedby
ATP binding becoming the limiting factor at high phosphorylation rates. To test this
possibility,wecarriedoutquenchflowexperimentsata1mMATPinsteadof100µM.
Theamountof[γ-32P]ATPwaskeptconstanttostaywithinpermittedradioactivitylevels,
andsoweincreasedtheproteinconcentrationto5µM,whichhadaminimaleffecton
kinetics (Fig. 1C), tomaintain a robust signal. For theWT substrate, phosphorylation
rates increased by ~30% (Fig. S3) for all linker combinations. A uniform rate
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enhancementat1mMATPisexpectedifthekinaseisnotfullysaturatedwithATPat100
µM.PreviousstudiesreportaKMforATPof10µMatdifferentbuffercondition,17sothe
kinasemaynotbefullysaturatedat100µM.Totestthisexplanation,wealsotesteda
slowerR-3Kvariantwith1mMATP,andsawasimilarincreaseintheobservedrate(Fig.
S2)consistentwithanincreaseinlevelofboundATP.Thissuggeststhattheattenuated
linkerdependencefortheWTisnotduetoATPbindingbecomingkineticallylimiting,but
ratherrepresentssaturationofthetetheredsubstrate.
Tetheredreactionsareexpectedtofollowfirstorderkineticswiththecontactfrequency
of reactants determinedby their physical connection.18 The contact frequency canbe
expressed as an effective concentration, which in our case corresponds to the
concentrationoffreesubstratethatwouldencountertheenzymeasoftenasthetethered
substrate. Such effective concentration can occasionally bemeasured by competition
experiments,12,19,20althoughinmostproteinshastobeestimatedtheoretically.21–23Our
group previouslymeasured the scaling of effective concentrationswith the length of
disordered linkers including the sequences used here.12 To estimate the effective
concentration of the tethered substrate, we used the power law determined for GS-
linkers previously, and plotted phosphorylation rates as a function of effective
concentration (Fig.2C-E).The tether inourkinase-substrate systemalso includes the
coiled-coil domain, which act as a rigid link in the flexible linker. Previous effective
concentration measurements suggest a similar scaling with linker length for such a
system,sowedisregardthecontributionofthecoiled-coildomainalthoughitpotentially
introducesasystematicerror.19
Thephosphorylationratesaturatedathigheffectiveconcentrationforallvariants.The
WT substrate was close to saturation already at the concentrations enforced by the
longest linkers. Incontrast,R-2Konlysaturatedat thehighesteffectiveconcentration
enforced by the shortest linkers, whereas R-3K has not plateaued yet at the highest
effectiveconcentration.Themaximalratealsodifferedstronglybetweenthesubstrates,
astheR-2KandR-3KvariantssaturatedatmuchlowerratesthantheWTsubstrate.In
total, this suggests that the single turnover reaction canbedescribedby aMichaelis-
Mentenlikedependenceontheeffectiveconcentrationwithahalfwaysaturationpoint
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andmaximal turnover characteristic of each substrate,wherektet,max is themaximum
phosphorylationrateandCeff,50isaneffectiveconcentrationathalf-saturation:
𝑘"#" =𝑘"#",&'(𝐶#**𝐶#**,+, + 𝐶#**
(1)
Todescribethekineticsoftetheredphosphorylationreactions,wederivedrateequations
(SItext)basedonaproduct-releaselimitingmodelforPKA(Figure2F).17,24Underthe
assumptionthatphosphorylation(k2)andproductrelease(k3)areirreversibleandthe
closed,catalyticallycompetentcomplex(C)isinarapidequilibriumwithanopenform
(O), the rate of phosphorylation in the tethered system (ktet) follows the following
relationshiponeffectiveconcentration(Ceff):
𝑘"#" =𝑘2𝐶#**𝐾4 + 𝐶#**
(2)
The rate of phosphotransfer (k2) is directly obtained from the maximum rate of
phosphorylation in the tetheredsystem(ktet,max) andKd isobtained fromaneffective
concentrationathalf-saturationCeff,50,basedonthefitofexperimentaldatatoEquation
1. The fittingparameters are given inTable 1.Kd determined in thisway for theWT
substrateisequalto142µM,similartotheliteraturevalueof200µM17,anditincreased
to837µMand8400µMforR-2KandR-3K,respectively.
Table1:Kineticparametersobtainedfromfitsofexperimentaldata
WT 1mM ATP
WT R-2K R-3K
Tethered ktet,max (s-1) 415 ± 47 307 ± 21 40.0 ± 3.5 = 14.1
Ceff,50 (µM) 107 ± 59 142 ± 42 837 ± 150 8400 ± 910
Untethered kcat (s-1) 37.3 ± 0.8 33.5 ± 0.4 14.1 ± 0.3
KM (µM) 24.0 ± 2.1 200 ± 5.2 973 ± 43
To test whether the rates of tethered catalysis can be predicted from steady-state
kinetics, we recorded a matching untethered steady-state enzyme kinetics for each
substrate(Fig.3).TheKMoftheuntetheredreactionincreasedfrom24.0µMintheWT
substrateto200and973µMinR-2KandR-3K,respectively.KMvaluesforallsubstrates
are an order of magnitude below the corresponding Kd values. To quantify the
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relationshipbetweenKMandKd,wederivedsteady-stateparametersasafunctionofrate
constantsinuntetheredsystem(SItext),whichresultedinthefollowingequation:
𝐾6 = 𝐾4𝑘7
𝑘2 + 𝑘7(3)
KMisexpectedtobesmallerthanKdwhenthesteady-statereactionislimitedbyproduct
dissociation(k3<k2).Inturn,thissuggeststetheredanduntetheredphosphorylationwill
have different half saturation points, as kinases are often limited by product
dissociation.25,26
Figure3.QuantifyingthequalityofPKAsubstratevariants.(A)Rawdatafromasteady-statekineticexperimentperformedat1nMPKAcandanindicatedconcentrationoftheR-2Ksubstrate.Theinsetshowsaschematiccartoonoftheexperiment.(B)Steady-statekineticdataof3substratesfittedbyaMichaelis-Mentenmodel.
Thekcatvaluesdecreasedslightlyfrom37.3s-1inWTto33.5s-1and14.1s-1inR-2Kand
R-3K, respectively. In contrast, there was a big difference in ktet,max between the
substrates:itwas8-foldfasterthankcatforWT(307s-1),roughlythesameforR-2K(40.0
s-1) and seemed to be slower (~3 s-1) for R-3K. As ktet,max corresponds to the rate of
phosphotransferitcannotbelowerthankcat.TheinconsistencyforR-3Kislikelydueto
thepoorlydefinedplateauinthedatafortetheredR-3K,andthusweconstrainedktet,max
toitslowerlimitequaltokcatuponfittingoftheR-3Kdata.Totesthowreactionswith
widelydifferentratesofphosphotransfercanconvergeonsimilarsteady-stateturnover
rates, we simulated kcat as a function of ktet,max for different values of the product
dissociationrateconstant(Fig.4A)asbelow:
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𝑘9'" =𝑘2𝑘7𝑘2 + 𝑘7
(4)
Fig.4Ashowsthatkcatislargelyindependentoftherateofphospho-transfer,whenthe
steady-statereactionislimitedbyproductdissociation.Theobservedvaluesofkcatcan
thus roughly be explained assuming the same rate of product dissociation. Product
dissociationrateswillbesimilar ifADPdissociation is limiting,butmaydiffer for the
peptides,soaperfectfitisnotexpected.Crucially,however,Fig.4Ashowsthatsteady-
statekineticsonlyhavealimitedabilitytopredicttherateofatetheredreaction,andby
extension it cannot predict the relative substrate usage in signalling events that only
requireasingleintra-complexphosphorylation.
Figure4.Simulatedpredictionsfortetheredcatalysis(A)Simulationsofkcatfromktet,maxandk3basedonEquation4inaproductreleaselimitedreaction.Athighktet,maxvalues,kcatisdecoupledfromatherateofthetetheredreactionandmaydisguiselargedifferencesinthetetheredphosphorylationrate.(B)FittingcurvesfromFigure2C(WT)and2E(R-3K)showunequalincreaseinktet(2.1xand9.0x,respectively)uponincreasingCefffrom100to1000µM.
Discussion
Wehavedevelopedareductionisticmodelforphosphorylationbyatetheredkinasethat
mimicskeyfeaturesofkinasesthatcontaindisorderedlinkersorbindflexiblescaffolding
proteins.Themodelsystemomitsthecomplexityofnaturalsignallingcomplexes,butin
returnallowssystematicvariationofthelinkerarchitectureandsubstrate.Thisallowed
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ustodemonstratethatphosphorylationcanbeenhanceddramaticallybytethering,and
this enhancement depends strongly on the linker architecture. We have shown that
single-turnovertetheredphosphorylationcanbedescribedbyaMichaelis-Mentenlike
dependence on the effective concentration, but that the kinetic parameters can only
partiallybedescribedfromsteady-statekinetics.
We have shown that the rate of tethered phosphorylation reaches a plateau at high
effectiveconcentrations,butissuchsaturationrelevantforkinasereactionsinnatural
signalling complexes? Saturation occurs when the effective substrate concentration
exceedstheaffinityofthekinase.Theaffinityofkinasesforshortsubstratemotifscan
typicallyreachlowµM values,althoughmanybiologicallyimportantsubstratesarefar
fromtheoptimalsequencemotifandmayhaveevenloweraffinities.Modelsystemsand
computationalmodellingsuggestthattheeffectiveconcentrationsinproteincomplexes
reach the lowmM range.12,20,27 This suggests that signalling complexes can reach the
saturation regime, where e.g. the shortening of a linker will no longer enhance the
reaction.
Saturationathigheffectiveconcentrationsprovidesamechanismforhowchangesinthe
linkerarchitecturecanchangetherelativerateoftetheredsubstrates,andthusalterthe
substrateusageofakinase.Forexample,considertwoadjacentphosphorylationsites
corresponding to the WT and R-3K substrates tethered at the same effective
concentration(Fig.4B).Ifthescaffoldingproteinchangesstructureduetoe.g.effector
bindingoralternativesplicing,theeffectiveconcentrationmaychangefrom100µMto1
mM, corresponding to GS-linkers of 257 and 53 residues, respectively. These values
roughlymatchthedifferenceinlinkersbetweenthea andb-isoformsofCaMKII.28Asthe
WTsubstrateisnearsaturation,thephosphorylationrateofR-3Kwillbeenhanced4.3-
fold more. This suggests that changes in linker architecture that increase effective
concentrationsshiftrelativesubstrateusagetowardslowaffinitysubstrates.
Tetheredkinasesareoftenpartofswitch-likefunctions,wherethebiologicaleffectonly
requiresphosphorylationof fewsubstrates.Examples includeautophosphorylationof
kinases such as CaMKII or activation by transphosphorylation of receptor tyrosine
kinases.Furthermore,activatorystimuliareoftentransientsuchase.g.thebriefburstof
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted April 4, 2020. . https://doi.org/10.1101/2020.04.04.023713doi: bioRxiv preprint
Dyla&Kjaergaard(2020) www.biophysics.dk-14-
Ca2+ triggered by opening Ca2+-channels. In such switches, the number of substrates
processedpertimeislessimportantthanthetimerequiredforthefirstphosphorylation.
Yet steady-state kinetics remains themainmodeof evaluating substrates, even if the
nativephysiologicalcontextisatetheredcomplex.Weshowthatsteady-stateparameters
candisguisebigdifferencesintherateoftetheredphosphorylation:TheWTandR-2K
substrateshada8-folddifferenceinktet,maxeventhoughthekcatvaluesaresimilar.This
occurs because product dissociation limits the steady-state reaction, but not the
phosphorylationof tetheredsubstrate.The latter ismorerelevant to tetheredkinases
withswitch-likefunctions,whichsuggeststhatsubstratepropertiesshouldbeevaluated
insingleturnoverexperiments.
Kinasesareoftentetheredtosubstratesvianon-covalent interactions,whichsuggests
that dissociation and rebinding should be considered. Themodel proposedhere only
considersastaticconnection,eventhoughthefitteddatausesanon-covalentconnection
betweenkinaseandsubstrate.Wesuggestthattheinteractioncanbeapproximatedas
static,whenitslifetimeismuchlongerthanthecatalyticcycle.Assuchourmodelsystem
describeshigh-affinityscaffoldinginteractionsinadditiontolinkersthataretrulystatic,
such as in kinase auto-phosphorylation reactions. For weaker interactions, single-
turnover and steady-state kineticmodels start toblend andwill accordinglybemore
complex.Webelievethatstaticmodelwillprovideabaselineforsuchefforts.
Duringthepreparationofthismanuscript,apre-printappearedwithsimilaraims,but
verydifferentresults.29Inagreementwithourresults,SpeltzandZalatanfoundthatfor
tethered PKAc shorter linkers increased the rate of phosphorylation. Despite the
similaritybetweenthemodelsystemsused,thereactionoccurredinadifferentkinetic
regimewithamaximalktetof~0.002s-1.Theunexpectedlyslowphosphorylationrate
was explained by effective concentrations of ~80 nM, which is 50.000-fold below
predictionfromasimplegeometricmodel.29Thesystemsdiffermainlyinthesubstrate
andthelinkersused.Itispossible,thatthekineticssimplyreflectthedifferentsubstrates,
assubtledifferencesinthemotifmayhaveabigeffectontherateofthetetheredreaction.
Additionally, Speltz and Zalatan use short linkers that also contain a folded domain.
Likely,thediscrepancybetweenexperimentalandpredictedvaluesshowsthelimitation
ofsimplepolymermodels forshort linkers.Suchsystemscaneasilybecomesterically
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted April 4, 2020. . https://doi.org/10.1101/2020.04.04.023713doi: bioRxiv preprint
Dyla&Kjaergaard(2020) www.biophysics.dk-15-
limitedbytheexcludedvolumefromfoldeddomainsandsequence-specificinteractions
that lead to internal friction. In contrast, long disordered linkers allow almost free
orientation of domains,30 and are likely to provide the most robust architecture for
engineeredscaffoldingproteins.
Tetheredreactionsarenotjustimportantforkinases.Tetheringisarguablyevenmore
importantforphosphatasesasthesubstratemotifcontributeslittlespecificity.Instead,
phosphatasesareregulatedbyanchoringproteins,ande.g.proteinphosphatase-1hasat
least 200 different regulatory subunits that target it to different substrates.31 These
anchoringinteractionslikelydisplayasimilardependenceforlinkerarchitectureasseen
here.Tetheringisalsoincreasinglyusedasatherapeuticinterventionstrategy.Enzymes
tetheringisimportantine.g.PROTACsthattargetproteinsfordegradationbytethering
themtoubiquitinligase.32Tetheringhasalsobeenusedpharmacologicallytoenhance
otherclassesofenzymesincludinge.g.proteases33andphosphatases.34Suchconnector
moleculeswilllikelydisplayasimilardependenceonconnectiontothesystemsstudied
here, and mechanistic studies of tethered catalysis is thus both of fundamental
importance to understand signalling pathways and to optimize pharmaceutical
interventionstrategies.
Acknowledgments
ThisworkwassupportedbygrantstoM.K.fromthe“YoungInvestigatorProgram”ofthe
Villum Foundation, the AIAS COFUND program funded by the EU FP7 programme
(Agreementno.754513)andPROMEMO–Center forProteins inMemory,aCenterof
Excellence funded by the Danish National Research Foundation (grant number
DNRF133). We would like to thank XavierWarnet and Sujata Mahapatra for critical
commentstothemanuscript.
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