RotatablebondsinDrugsIoniza3onvsDrugPermeability
Henderson–Hasselbalchequa1on
SolventAccessibleSurfaceArea(SASA)ofaroundhydrophobicatoms
• Thehydrophobicenergycanbees3mated,whereσ issurfacetension20to40calA-2mol-1andAreaistheSolventAccessibleAreaaroundatomswithhydrophobicproper3es
• Onemethylgroupburiesabout30A2thatcorrespondstoσ=0.6-1.2kcal/mol
Ehp =σ ⋅Areahp
TypesofDrugIsomers
Newmanpj
ChirallypureRitalinThalidomideisomersOmepgazole/PrilosecvsNexium
• IsomersofdrugswillactDIFFERENTLY• Abilityand3mingtointerconvertdependsontheenergybarrierandiscri3calfordrugac3on
Chair/boat
Definingrotatablebonds• Drugswithrotatablebondsundergoconforma3onalchanges
• Rotatablebond:single,acyclic.• Excludesinglebondstoaterminalatomorbondstolineargroups,e.g.CH3-C≡N.
• Highlyrestrictedrota3on,e.g.esterlinkages.
• SinglebondsinsidecyclesmayundergoRESTRICTEDROTATION(ringpuckering)
Torsionangle
Conforma3onalEntropyLossassociatedwithtargetbinding
• Uponbindinglosesmostofitsrotamersandonlytheonecompa3blewiththebindingsiteischosen,italsolosestransla3onalandrota3onalDFs
• Fullmethod:definealllowenergystatesandassignPi,
• Simplemethodforcoun3ngrotamers:3perbond:3x3x3…
• Simpleandadvancedentropices3mates
• Realcoun3ngneedstoincludeenergy(clashing)andprobabilityes3mates
torsionsNrotN 3∝
Sconf _ entropy = R ln3Ntor = RNtor ln3 ≈ RNtor
Gconf _ entropy ≈ −RTNtor ≈ −0.6Ntor[kcal /mol]
Sconf _ entropy = −R Pi lntorsions∑ Pi
Smoleculeconf _ entropy = kB ln(NstatesIn1molecule )
Smoleconf _ entropy = R ln(NstatesIn1molecule ) =
−R ln(1 / N ) = −R (1 / N )N∑ ln(1 / N )
Smoleconf _ entropy = −R Pi lnstates∑ Pi
Popula3onsofconformers
• Thepopula3onofdifferentconformersfollowsaBoltzmanndisribu3on
• Consequencesfordrugbinding
• UsingPiforentropycalculatons
• Usingconforma3onalstrainEiintheenergybalancecalcula3onfordrugbinding
RTEE
j
iji
eNN −
−=
RTEE
j
iji
ePP −
−=
€
Sconf _ entropy = −R Pi lnstates∑ Pi
Posi3onalentropylossupondrugbinding:Entropyoffusion
• Theentropylossuponcrystalliza3onfromtheliquidphasecanbees3matedasTΔS ~ 1.2-1.5 kcal/mol
• enthalpyoffusion(mel3ng)forwater1.44,forethanol1.2
• Asimilarentropylossisassociatedwiththedrugbinding
Mostdrugshaveionizablegroups
• Fromabout55KdrugsinWDI,63%(~32K)areionizable.• 2/3rdshaveoneormorebasicgroup.
From:TimMitchellandRyszardKoblecki,MillenniumPharmaceu3calsLtd.
E.g.:Carboxylicacid
E.g.:Amine
Acid⇔H+ +Base
AminesinDrugs:Examples
• Chlorpheniramine:anan3histamine.• Chlorpromazine:atranquillizer• Ephedrineandphenylephrine:decongestants.• Amphetamine,methamphetamine,andmethcathinone:
psychos3mulantamines• Amitriptyline,imipramine,lofepramineandclomipramine:
tert.amines,tricyclicsad.• Nortriptyline,desipramine,andamoxapine:secondary
amines,tricyclican3depressants
LonepairorH+dependingonthepH
VariabilityofDrugAc3on• Solubilityandabsorp3onofadrugarehighlyvariableandrequireoppositeproper3es
• Itdependsonthechemicalnatureofthedrug,pH,concentra3ons
• Dissolu3on,absorp3onanddistribu3ondependonthechargeofthedrug
• Onlytheneutralformofadrugcanpassivelypermeatethemembrane
• Everyexposedchargemaiers(ratherthanthemean).Zwiierionsdonothelp
• Ac3vetransportmaychangethings:hijackingthebio-traffic
Absorp3on• Transcellulartransportisthemostcommonwayofdrugabsorp3onanddistribu3on
• Small~100-550andnonpolarcompoundscangothroughthetranscellularroute(logP>0)
• Thebiggesteffect:ioniza1on.Polarity:thesecond
Source:Drugdiscoverytoday
BloodBrainBarrier.Astrocytessurroundingcapillariesinthebrain.Transportispassive(PSA<75)ortransporter-mediated
Acidity,BodyandDrugs
• Litmustest(pHindicator)• Itisallaboutthesmallestnucleus,asingleproton
belowpH4.5 abovepH8.3 4.5 ↔ 8.3
Litmusisawater-solublemixtureofdifferentdyesextractedfromlichens.Chemicalstructureof7-hydroxyphenoxazone,thechromophoreoflitmuscomponents
Lichens:Fungus+Algaorcyanobacterium
Mostatomsstaycovalentlybonded,buthydrogenisanexcep3on
Hydrogenionsjump:• Betweenwatermolecules• Betweendrugsandwatermolecules• Betweenbothandacids/basesinsolu3on
Acid-BaseBalance• NormalmetabolismproducesH+,(acidity)• Dissocia3onofwater:2H2O→[OH-]+[H3O+],i.e.hydroxide+hydro[xo]niumions
• High[H+]isacidic,low[H+]isbasic• ThreeHomeosta3cmechanisms:– Buffersystems,-instantaneous;temporary– Exhala3onofCO2-operateswithinminutes;cannotcompletelycorrectseriousimbalances
– Kidneyexcre3on-cancompletelycorrectanyimbalance(eventually)
+
Dealingwithahugerangeofconcentra3ons
Hydroxoniummolari1esrangefrom1to10-14M
Usethe“p”(power)operator:
p⇒−log10pH = −log10[H3
+O]
pH• pH(powerofHydrogenion)isameasureof[H3O+]molarity.
• pH≡−log10[aH+],• aH+isac3vityofwater• aH+≈[H+],i.e.molarityofhydroxoniumions,inM=mol/L
• Example:lemonadehas[H+]~0.005M,pH≈-log10(0.005)≈2.3
Self-ioniza3onofwater
• 2H2O→[OH-]+[H3O+]• Kw=[H30+][OH-],dissocia3onconstantviamolari3esoftwoions.
• Warning!Duetoaconven3on,KwisNOTastandardequilibriumconstant,sincethe[H2O]2isomiied.WatermolaritywillalsobeomiiedinKalater
• Kw=10-14(mol/L)2
LowpH,highpH
• pHofpurewater[H3O+]=[OH-]=c:• Kw=c2,,
[H3O+]purew=10-7M
• pH=7• LowpHmanyions• HighpHfewions
Acid-BaseImbalances
• Acidosis– Highblood[H+]– LowbloodpH,<7.35
• Alkalosis– Lowblood[H+]– HighbloodpH,>7.45
Absorp3oninGItract
Stomach
1.4-2.1
3-7
Ileum
6.8-8.0
6.8-8.0
Colon
5-8
5-8
fastedstate
fedstate
Jejunum 4.4-6.65.2-6.2
0.1m2
0.3m2
Dressman,Amidon,Reppas,Shah,Pharm.Res.1998,15,11.
0.5-3.5hr 3-4hr
1-3d
120m2
acids bases
pH
AcidsandBases
We’llconsideronlyBronstedequilibria.E.g.,
or,moregenerally,whichhastheacidityconstantKa([H2O]isomiied,asinKw)
-32 AcOHOH HAc +⇔+ +
€
NH4+ + H2O⇔ H3O
+ + NH3
BaseOHOH Acid 32 +⇔+ +
€
Ka =a H3O
+( )a Base( )a Acid( )
pH,pKaandlog10
Nowusethe“p”operator:
10-logp⇒a10a -logp KK =
↑⇒↓ donatingproton p aK
][-logp 310 OHH +=
pKaofsomefunc3onalgroups
phosphates(DNA)1.5,6.5purineN(DNA)9pyrimidineN(DNA)9carboxylates(a.a.,asp,glu,C-ter)3.5-5phenols(a.a.,tyr)9.5-11sul}ydryls(a.a.,cys)8.5hydroxyls(a.a.,ser,thr)13.5amines(DNA,ade,cyt)3.5-4imidazole(a.a.,his)6.5-7amino(a.a,lys,N-terminus)10guanidinium(a.a.,arg)13
Solubility• Likedissolveslike• Polarsolutesdissolveinpolarsolvents.
• Nonpolarsolutesdissolveinnonpolarsolvents.
• NeedtopredictormeasurepKa(s)sincechargedgroupshelpwatersolubilityandconflictwithfatsolubility.
µ 0aq + RT lnSW = µ 0s
From:LMLiu,A.LaioandA.MichaelidesPhys.Chem.Chem.Phys.,2011,13,13162
DrugSolubility• Foreachdrug,waterandfatsolubilityvary.• Rela3vesolubili3esdependon
ChemicalstructureofthedrugpHofthesolu3onpKaofthedrug
• Solubilitypercentagesdependonioniza3onra3os
Ace3c-acid-dissocia3on
SolubilityandpKa
DrugpKa Solu1onpH
<7(Acidicsolu3on) >7(Basicsolu3on)
<7(Acidicdrug,chargeis-1or0)
pKa>pHUn-ionized,Fatsoluble
pKa<pH(-)Ionized,Watersoluble
>7(Basicdrug,chargeis0or+1)
pKa>pH(+)Ionized,Watersoluble
pKa<pH(0)Un-ionized,Fatsoluble
[H+]Excess [H+]Deficiency
Cau3on:Inmostinforma3onsourcesanddatabasesthedruggroupsionizedatpH=7.4groupswills3llbeshownasneutral.
Norepinephrineinitsunnaturalneutralform
Henderson-Hasselbalch• ThedifferencebetweenthepHofthesolu3onandthepKaofthedrugisthecommonlogarithmofthera3oofionizedtounionizedformsofthedrug.
• ForaciddrugsLog(Ionized/Unionized)=pH-pKa,or[I]/[U]=10(pH-pKa) Deriva1on:
Ka=[H+][A-]/[HA]-logKa=-log([H+][A-]/[HA])-logKa=-log[H+]-log([A-]/[HA])pKa=pH-log([A-]/[HA])log([A-]/[HA])=pH-pKa
H.H.:aquan3ta3vepicture
• Mostdrugsareweakacidsorweakbases
• Itisnotallornothing,therearealwaysseveralspeciesatdifferentconcentra3ons pKapH
BHB
pKapHHAA
−=⎟⎟⎠
⎞⎜⎜⎝
⎛
+
−=⎟⎟⎠
⎞⎜⎜⎝
⎛ −
][][log
][][log
Frac3onIonizedasafunc3onofpKaandpH
+ -
0 0
Weakacidismostlyneutralinstomach
Adrugisaweakacid,hasapKaof5.5.Takenorally,itisinastomachsolu3onofpH3.5.
pH–pKa=3.5–5.5=-2Foranacid,weuse:ionized/unionized=10-2/1=1/100
Forevery1moleculeofthedrugthatisionized,100areunionized.Thisdruginthestomachishighlyfatsoluble.
BasicDrugsForbasicdrugs,everythingisthe
sameexceptthatthera=oreverses:
Log(Unionized/Ionized)=pH–pKa
Examples:Chlorpheniramine,chlorpromazine,ephedrineandphenylephrine,amphetamine,methamphetamine,andmethcathinone,amitriptyline,imipramine,lofepramineandclomipramine,nortriptyline,desipramine,andamoxapine.
pKapHBHB
pKapHHAA
−=⎟⎟⎠
⎞⎜⎜⎝
⎛
+
−=⎟⎟⎠
⎞⎜⎜⎝
⎛ −
][][log
][][log
NH2+[Cl-]
Amphotericdrugs
• Ordinaryampholytes,e.g.m-aminophenol• pKaacidic>pKabasic.pKaA=9.8,pKaB=4.4• IncreasingpH:1.NH3+2.Neutral3.O-
Zwiierionicampholytes
• E.g.Aminoacids,pep3des
• pKaacidic<pKabasic
Distribu3onofionicspeciesforthezwiierionicampholytelabetalol.fromA.Pagliara,P.-A.Carrupt,G.Caron,P.GaillardandB.Testa,Chem.Rev.,97,3385(1997).
IsoelectricPoint• pI=pH=½(pKaacidic+pKabasic)• Itcanbebothunchargedandzwiierionicormul3plycharged
• Forabsorp3oneverychargecounts(notthetotalcharge)
• pIisusedforisoelectricfocusing(Agarosegelelectrophoresis)
Zwiieriondrugs:Examples
Calcula3onofthepHofdrugsolu3ons
• Thedrugsolu3onitselfcandevelopitsownpH
• ThepHcanbederivedfromitspKaandconcentra3on,C
Aweaklyacidicdrug:HA+H2O=[A-]+[H30+](1-a)cacaca–degreeofdissocia3on
a<<1ac=[H+]atc>≈10-7M
Note:thisapproxima=on
breaksatinfinitesimalconcentra=ons.
cpKpH a log21
21 −=
Ka =a2c2
(1− a)c≈ a2c
a2 = Ka / ca2c2 = Kac
[H+]= (Kac)12
− log([H+]) = − log((Kac)12 )
− log([H+]) = − log(Ka )− log(c)12
Deriva1on:
Forthesolu1onofaweaklyacidicdrug:
Note:loghereislog10
Weaklybasicdrugs• Similarlyitcanbeshownthat
• Example:codeinemonohydrate(MW=317.4),pKa=8.2
C=0.026MpH=7+4.1-0.79
cpKpHcpKpKpH
a
aw
log7log
21
21
21
21
21
++=
++=
BasicAmineischargedatneutralpH
Note:loghereislog10
IonTrappingofanacidicdrugThesamehighlyfatsolubledrugreadilycrossesthestomachmembranesandentersbloodplasma,whichhasapHofapproximately7.5
pH–pKa=7.5–5.5=2[I]/[U]=102/1=100/1Forevery100moleculesofthedrugthatareionized,only1isunionized.Thedruginthebloodisnotveryfatsoluble.
Thisphenomenoniscallediontrapping.
Example:NaproxenpKa=5neutralinstomach(pH<5)(absorbed)chargedinblood(pH>7)
Absorp3onisquan3ta3vetoo
• Permea3onrate,RP=PAreaΔC• Amountabsorbed=RP•Time
– Pismembranepar33oncoefficient(relatedtoLogP)
– Areaiseffec3vesurfaceareaofmembrane
– ΔCisconcentra3ondifferencefortheneutralformofthedrug
• Astomach/Aileumdiffer10003mes.Thatmeansthatevenifthefrac3onofneutralspeciesinstomachis1003mesgreater,s3ll103mesmorecompoundwillbeabsorbedinthegut.Theeffectof3mecomesontop.
Cout
Cin
A=120m2
A=0.1m2
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