DrugStability&Kine1cs

•  Ratesofdrugdissolu/on,permea/on,diffusion,metabolism,bindingarecontrolledbythelawsofchemicalkine/cs

•  Liquid(andevensolid)dosagedrugformissuscep/bleto:–  Hydrolysis–  Oxida1on–  Isomeriza/on–  Photochemicaldecomposi/on–  Polymeriza/on–  Precipita/on–  …

Time

Kine1csvsThermodynamics

•  Rate=Changeperunit/me,e.g.mol/s

•  Rateofreac/on=therateatwhichthereactantsaretransformedintotheproducts

•  Thermodynamicsestablishesconcentra/onatanequilibrium(infinite/me).“Diamondsareforever” UnboundBound

Diffusion:netflow•  Diffusionisarandomprocessandthelawsdescribethenetflow

Diffusionvsconcentra1on

gradient

•  Diffusionisthenetac/onofmaQer,heat,light,..whoseendistominimizeaconcentra/ongradientinspace

•  Flux,J,istheamountofsubstanceflowingthroughunitareapersecond

•  J[molm-2s-1]•  Ques/on:HowdoesJdependonthe

concentra/ondifference?

Drug

Concentra1onGradient

α β

Membrane

Concen

tra/

on

Fick’sLawsofDiffusion•  Relatesthefluxandtheconcentra/on(C)gradient(differenceperunitlength)

•  1stLaw:SteadyState•  2ndLaw:/medependence•  Ddependsonthediffusionac/va/onenergy(barrier).

dxdCDJ −=

AdolfEugenFick,1829-1901,aGermanphysiologist,inventedcontactlenses

RTEa

eDD−

= 0

2

2

xCD

tC

∂

∂=

∂

∂

Diffusionasafunc1onofmoleculesize•  Largepar/cleshavesmallerdiffusioncoefficients:

D~1/R

MW D(m2s-1)Smallmoleculeinwater 1-1.5x10-9E.g.hydroxybenzoate 152Da 8.44x10-10

Smallproteininwater 10-10E.g.albumin 66kDa 0.46x10-10Phospholipidinmembrane 10-12Proteininmembrane 10-14

Totalamountdiffused•  E.g.fromtheintes/nestothebloodstreamthroughintes/nalwalls

•  Thetotalamountofdrugabsorbedis

Flux(J)•Area(A)•Time•  J[molm-2s-1];J×A[mols-1];J×A×t[mol]•  FluxisJ=–P(Cα–Cβ)=–PΔC

–  wherePispermeability(relatedtodiffusioncoefficient)

Ax0

● RateLawsandRateConstants

● IntegratedRateLaws● Zero-orderReac/ons

● First-orderReac/ons

● Second-orderReac/ons

● Temperaturedependenceofthe

Reac/onRates(Arrhenius)

RatesofChemicalReac1ons

Reac1onRates•  Moleculesoratomsofreactantsmustcollidewitheachotherinchemicalreac/ons(concentra/ons).

•  Themoleculesmusthavesufficientenergy(discussedintermsofac/va/onenergy)toini/atethereac/on.Thatleadstok(T)

•  Insomecases,theorienta/onofthemoleculesduringthecollisionmustalsobeconsidered.

RateofConsump/on

RateofForma/on

[ ] [ ] [ ] [ ]dtDd

dtCd

dtBd

dtAd

+=+=−=−31

21

Example:A+2B→3C+D

[ ] [ ]dtBd

dtAd

21

−=−

[ ] [ ]dtDd

dtCd

=31

RateofChemicalReac1on

Reversiblereac1ons•  Examples:

–  Epimeriza/onoftetracyclines

–  Chiraltransi/onofthalidomide

BA ⎯→←kf

kr

€

d[A]dt

= −k f [A]+ kr[B] = 0

Keq =[B][A]

=k fkr

Atequilibrium

RatesandEquilibriumConstant

•  AóB•  Forwardrate:kf[A]•  Reverserate:kr[B]•  Equilibrium:

kf[A]=kr[B]

•  P+LóPL•  Forwardrate:kon[P][L]•  Reverserate:koff[PL]•  Equilibrium:

kon[P][L]=koff[PL]

€

Keq =[B][A]

=k fkr

€

Kbind =[PL][P][L]

=konkoff

Kd =[P][L][PL]

=koffkon

TheuniqueRateofReac/onisdefinedas:

[ ]dtJdrate

jν1

=

whereJisagenericpar/cipanttothereac/onandνjitsstoichiometricnumber.Reac/onRatesarereportedin[molL-1s-1]

TheUniqueRate

RateLawsTheRateLawisanexperimentallydeterminedequa/onthatexpressestherateofreac/onasafunc/onofconcentra/ons:

€

ν = k⋅ f A[ ], B[ ],etc.( )Thecoefficientkiscalledrateconstant.It is o0en possible to write the func/on as aproduct of concentra/ons with constantexponents:

€

v = k A[ ]x B[ ]y C[ ]z

€

v = k A[ ]x B[ ]y C[ ]z

The reac/on is said to be of order x withrespect to [A], etc. The overall order of thereac/onis

x+y+zThe orders are generally unrelated to thestoichiometric coefficients in the reac/onequa/on.E.g.,

[ ]522252 ONkv ,)g(O)g(4NO)g(ON2 =+→

Reac1onOrder

MolecularityvsReac1onOrderTheMolecularity(uni-,bi-,etc.)referstoanelementaryreac/onproposedasastepinamechanismTheReac/onOrderisanempiricalquan/ty,andobtainedfromtheexperimentalRateLawE.g.,Ifthereac/onisanelementarybimolecularprocess,thenithasasecond-orderkine/csBUT,ifthekine/csaresecond-order,thenthereac/onmightbecomplex.

Zero-orderIntegratedRateLaw

IntegratedRateLawsIntegratedRateLawsgivetheconcentra/onsofreactantsandproductsasfunc/onof/meZero-order reac/ons doNOT depend on theconcentra/onandare limitedbyanexternal(constant)concentra/onoffactor.

€

d[A]dt

= −k0, k = mol L-1 s-1[ ]

€

[A] = [A]o − kt

Half-lifeoftheZero-thOrderReac1on•  t½=A0/2k0

•  Examples:•  Degrada/onofsuspensionsorsolidstate

•  Dissolu/onofdrugcrystals(assuminginfinitedilu/on)

FirstOrderreac1on•  Therateispropor/onaltothe

concentra/on.•  Example,radioac/vedecay:

•  kisrateconstant•  1storderIntegratedRateLaw:

•  Half-life

€

d[A]dt

= −k[A], k = s-1[ ]

2lne21e

21e[A][A]

21

2/1oo2/12/12/1 =⇒=⇒=⇒= −−− ktktktkt

t½=ln2/k=0.693/k

kt−= e[A][A] o

CyclopropaneCitalopramR

PropeneCitalopramS

Uni-molecularReac/ons

Racemic mixture Single-enantiomer Amphetamine (Benzedrine) dextroamphetamine (Dexedrine) Bupivacaine (Marcain) levobupivacaine (Chirocaine) Cetirizine (Zyrtec / Reactine) levocetirizine (Xyzal) Citalopram (Celexa / Cipramil) escitalopram (Lexapro / Cipralex) Methylphenidate (Ritalin) dexmethylphenidate (Focalin) Modafinil (Provigil) armodafinil (Nuvigil) Ofloxacin (Floxin) levofloxacin (Levaquin) Omeprazole (Prilosec) esomeprazole (Nexium) Salbutamol (Ventolin) levalbuterol (Xopenex) Zopiclone (Imovane) eszopiclone (Lunesta)

Enan1omericdrugformsandtransi1ons

Thalidomide:Oneenan/omeriseffec/veagainstmorningsickness,whereastheotheristeratogenic.However,theenan/omersareconvertedintoeachotherinvivo.Dosingwithasingle-enan/omerformofthedrugwills/llleadtoboththeDandLisomerseventuallybeingpresentinthepa/ent'sserumandthuswouldnotpreventsideeffects(thoughitmightreducethemiftherateofinvivoconversioncanbeslowed).Ethambutol:Whereasoneenan/omerisusedtotreattuberculosis,theothercausesblindness.Naproxen:Oneenan/omerisusedtotreatarthri/spain,buttheothercausesliverpoisoningwithnoanalgesiceffect.

TheTimingofDangeroustransi/ons

TheChemicalDecomposi/on:Hydrolysis

•  Thehalflifeisindependentontheini/alconcentra/on,i.e.firstorder

•  Pseudo-firstorderkine/cs:oneofthereactantsisinlargeexcess

•  Liquiddosageform+drugdecomposi/oninvivo

Hydrolysis:Ester•  R-C(=O)O-R’•  Methyldopate,tetracaine,procaine,etc.

•  FasteratacidicpHPhysos/gmine(cholinesteraseinhibitor)isusedtotreatglaucomaanddelayedgastricemptying

TimingofEsterHydrolysisofAspirin

•  InventedbyFelixHoffman,patentedbyBayerin1899

•  CleavageoftheAspirinesterisapartofitsCOX-1/2inac/va/onmechanism

•  1%adayhydrolysisofsuspensionofaspirin

AspirinAcetylatesSerine530inCox2

Hydrolysis:Lactones,Amide

•  Amide:R-C(=O)NH2

•  Thereac/oniscatalyzedbyeitheracidorbase

β-propiolactoneγ-butyrolactone(GBL)gluconodelta-lactone(GDL)Caprolactone

•  Acyclicester•  Lactonesarehydrolyzed

Hydrolysis:Lactam

•  Acyclicamide.•  Beta-lactaman/bio/cs

Penicillin-core

Hydrolysis:Imide

•  R-C(=O)NHC(=O)-R’•  Someimide-containingdrugs

1stOrderreac1on:t½andk

•  PlotLog10(Percentage)vs/me•  Ifitisastraightline,thereac/onfollowsthe1storderkine/cs

•  Calculatetheslope•  k1=Slope/ln10=Slope/2.3•  t½=0.69/k1

Log

Exampleproblem:1storderreac/on•  Q:Thalidomideundergoesspontaneousconversionfrom(+)formto(-)formandvice-versa,withtherateofconversiondependingonthecomposi/onofthesolu/on.Forexample,thehalf-lifeof(+)Thalidomideinhumanplasmais11.5minutes.Es/matetherateconstantforthereac/onofconversionof(+)Thalidomideinto(-)Thalidomideinhumanplasma.

•  Hints:–  Enan/omerconversionis1storder;henceconstantt1/2–  Asksforrateconstant(k),notrate(d[A]/dt=–k[A])

•  S:usekt1/2=ln2.t1/2=11.5min=690s.Therateconstantisk=ln2/t1/2=ln2/690~0.001s-1

•  A:0.001s-1

SecondOrderreac/ons

•  Rateisdeterminedbytheconcentra/onsoftworeac/ngspecies

•  Ifbothini/alconcentra/onsarethesame,orbothcomponentsarethesamereactant

[ ]1-1-2 sM ,A][B][

dd[A]

=−= kkt

[ ]1-1-2 sMk ,A][ktd

d[A]=−=

[ ] [ ]tk

AA 20

11=−

Secondorder•  A+Btoproducts•  2Atoproducts•  E.g.[P]+[L] ↔[PL](in1:1stoichiometry)

•  IntegrateRateLaw:

•  Halflife(changing): [ ]022/1

1Ak

t =

Exampleproblem:2ndorderreac/on•  Q:The1:1bindingreac/onbetweenadruganditsproteintarget

isfirstorderineachofthereactants.Inthesolu/onof1nMproteinand100nMdrug,theini=alrateofcomplexforma/onwasfoundtobe12pM/s.Whatwillbetheini/alrateofcomplexforma/oninthesolu/onof1µMproteinand1µMdrug?

•  Hints:–  Firstorderineachofthereactantsmeansthatd[PD]/dt=k[P][D].The

reac/onis2ndorderaltogether.–  Asksforrate(d[PD]/dt)

•  S:When[P]isincreasedfrom1nMto1µM(1000-foldincrease),and[D]isincreasedfrom100nMto1µM(10-foldincrease),theratemustincrease10000-fold.Thenewratewillthenbe12pM/sx104=120nM/s.

•  A:120nM/s

Arrhenius•  Therateconstantofchemicalreac/on,k

•  Pfisthepre-exponen/alfactor(pre-factor),

•  Risthegasconstant

RTGactivation

ePfk−

= )( SvanteArrhenius,Swedishphysicalchemist.In1903hebecamethefirstSwedetobeawardedtheNobelPrizeinchemistry.

€

K = e−GAB

RTJacobusvan’tHoff

Review•  Thechemicalpoten/alofcomponentJ:–  Gas–  Liquidmixture–  ΔGandentropyofmixing.

•  Thechemicalequilibrium–  Kviaconcentra/onsandreac/onstoichiometry

–  FromK,toΔGo

–  FromKatT1andT2,toΔHo,Van’tHoff RT

GKo

rΔ−=ln

⎟⎟⎠

⎞⎜⎜⎝

⎛−

Δ−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

212

1 11lnTTR

HKK o

0

ln0

ccRT ic

ii += µµ

]][[][..,

1 BABAKgeaK

n

iii

•==∏

=

ν

)ln(0

0

PPRT iP

igi += µµ

ai is molar fraction xi or concentration ci or activity depending on the standard state and ideality

RS

RTHK

or

or Δ

+Δ

−=ln

Review•  Chemicalpoten/alofthesamemoleculein

differentphasesorcompartments(osmosis)mustbeequal

•  Chemicalpoten/alofwaterislower(beQer)insolu/onIfxsolutesissmall:

•  Osmo/cpressure:Posm=MRT,whereMismolaritycorrectedbydissocia/on,i,M=iM0

•  Osmosis:semipermeablemembranes.•  OsmolarityandTonicity:coun/ngsolutes

thatcannotcrossthemembraneandtakingdissocia/onintoaccount(i,van’tHoff’sfactor).

•  Boilingpointeleva/on•  Freezingpointdepression(Kfdoesnot

dependonsolutes!).Kf=1.858Kkg/mol•  Waterpressurereduc/on:Raoult’slaw•  Gasdissolu/oninwater:Henry’slaw•  Theeffectsareentropicandtothefirst

approxima/ondonotdependonthenatureofsolutes(colliga/veproper/es)

€

µw _ in _ solution = µw _ pure + RT ln(xw )Δµw = RT ln(1− xsolutes) ≈ −RTxsolutesΔSw ≈ Rxsolutes

Posm =ΔnsolV

RT = iMRT

ΔTboiling = KbxsolutesΔTfreezing = K f xsolutesPw_ vap_ solution = Pw_ vap_ purexwaterPsolute_ in_ gas = KHenry

solutexsolute_ in_water

ReviewofEnergyContribu1onstothenon-covalentBindingEnergy

•  q-q:Coulomb:(+)or(-),stronginnon-polarmediumandweakinwater.Longrange(r-1).C=332(kcal/mol)Å(eu)-2

•  q-water:IonanddipoleSolva/on.Large(-):.

•  D-H..A:Hbonds.Medium,shortrange.

•  A-A:VanderWaalsinterac/onWeak(-0.2km),butmany.Shortrange(r-6).

•  Apolar-ApolarHydrophobicenergy,waterentropycontribu/on

Ehb = f (rHA,αALPHD)

Evw =Ar12

−Br6

Ehp =σ ⋅Area

⎟⎟⎠

⎞⎜⎜⎝

⎛−=−

mwq

solvmw r

CqEεε11

2

2

rqqCEel ε21=

H.H.:aquan1ta1vepicture•  Mostdrugsareweakacidsorweakbases

•  Itisnotallornothing,therearealwaysseveralspeciesatdifferentconcentra/ons

pKapHBHB

pKapHHAA

−=⎟⎟⎠

⎞⎜⎜⎝

⎛

+

−=⎟⎟⎠

⎞⎜⎜⎝

⎛ −

][][log

][][log

])log([

)log(

,[Acid][Base]][H

a

+

+

−=

−=

=

HpHKpKa

K

a

cpKpH a log21

21 −=

pH = 7+ 12 pKa + 1

2 logc

DrugSolu/ons(acidicandbasic)

BindingReac1on

•  PL↔P+L;Kd=[P][L]/[PL];Ka=1/Kd•  x=[PL];(P0-x)(L0-x)=x•Kd•  x=½•(P0+L0+K0-((P0+L0+K0)2-4P0L0)½)•  P0<<Kd:[PL]/[P]≈L0/Kd(50%inh.@L0=Kd)•  [PL]<<P0(proteininexcess):[PL]/[L]≈P0/Kd,frac/on_drug_bound≈P0/(P0+Kd)

Kine1csandDiffusion

•  [Drug]=Flux(J)•Area(A)•Time

RTGactivation

Aek−

=

J = −D dCdx

≈ ΔC€

[A] = [A]o − kt

€

[A] = [A]oe−kt

€

1A[ ]

−1A[ ]0

= k2t

€

Keq =[B][A]

=k fkr

€

Kbind =[PL][P][L]

=konkoff

Kd =[P][L][PL]

=koffkon