non-covalent interacruben.ucsd.edu/19/r12.pdf · • lewis structures (electron dot diagrams) •...
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Non-covalentInterac.ons• Drugatomsinteractwithatomsofthefollowingmainmolecules:
• Otheratomsofthesamemolecule
• Watermolecules• Lipids• Receptoratoms
Maincontribu.onstomolecularenerge.csG=H-TS
• Quantumeffects– covalentbonds(bondingorbitals)– atomrepulsion(Pauliexclusionprinciple)
• Electrosta0cinterac0ons– Interac.onsbetweenfullcharges,dipoles,induceddipoles,
hydrogenbonds,aLrac.vepartoftheLennard-Jonespoten.al• Entropiceffects
– apartofthehydrophobiceffect– Conforma.onalentropychangesuponbinding– ..Concentra.on-dependententropiesofmixing
• Otherenergytermsareeithersubtypesofthemainclass,orcombina.onsofthemaintypes(e.g.hydrophobicinterac.ons)
Threesourcesofelectriccharges
• Formalcharges:protonsandelectronsnotbalanced
• Par.alcharges:redistribu.onofelectrondensitytomoreelectronega.venuclei
• Inducedpolariza.oncharges:addi.onalredistribu.on(orevenformalcharge)causedbyproximityofothercharges.
+
Lidocaine
MOA:inac.va.onofthefastvoltage-gatedNa+channels.(otherblockers:mexile.ne,tocainide,andphenytoin).Toxins:ac.vatethechannels
Electrosta.cInterac.ons• Coulomb’spoten.alenergy,inSIunits
• EnergyinJoules,distanceinmeters,chargesinC(1Coulomb=Amperexsecond)
• Likechargesrepeloneanother• OppositechargesaLractoneanother• Theforceofrepulsion/aLrac.onget
weakerasthechargesarefartherapart.
Coulomb,CharlesAugus.n
rqqUel επε21
041
=
Amoreprac.calformula
• Chargesinelectronunits(-1,1,-0.5),distanceinÅngstroms,energyinkcal/mol,C=332
• εisdielectricconstantofthemediumε=1forvacuum
• +1and-1chargesat3Aget100kcal/mol!!!(10nMdrug~10kcal/mol)
U =C q1q2εr
Polariza.on,solva.onandε
• Electrosta.cinterac.onsarereducedbyε becauseofthepolariza.onofthemedia.
• ε=80inwaterat300K.• Electronicpolariza.on,dipolerelaxa.on.Waterisastrongdipole
• Inthehydrocarbonlayerofmembranesε~2to4
• inproteinsε~4to10
rqqCUε
21=
Dielectricconstantsat25C
• Water 78.5• Methanol 33.0• Ethanol 24.3• Ammonia 16.9• Benzene 2.3• Cyclohexane 2.0• Methane100K 1.8
AChargeinafog
• Dipolesreorient,• electrondensityflowstocompensatethecharge
• LeChatelierprinciplescreened
εNa+
Na+
Threeconsequencesofhighε
• Chargedatomsarealmostcompletely“screened”inwater(Uw=Uvacuum/80=Ufat/40)
• Directcharge-chargeinterac.onisweakinwater
• (Na+)(Cl-):d=2.5A,E=-1.7km• Charged(andpolar)atomsareextremelyhappyinwater(lowenergy)anddonotwanttogotomediawithsmallerε.
εNa+
screened
4=εNa+
charge is screened
εNa+
Ignoring fellow charges
Cl-
80=εNa+
Happy Unhappy
“Sorry, I feel nothing”
Solva.onEnergyofCharges• Bornformulaforthe
solva.onenergyofachargewithradiusrq,C=332
• Thesolva.onenergyoftheion:
whenmovedfromapolarsolventtowater(Uisnega.ve)
εNa+
wε
⎟⎟⎠
⎞⎜⎜⎝
⎛−=εε11
2
2
wqsolv r
qCU
ε
Apolar medium e.g. membrane
water
If ε = 2 and r =2A, U = -332./8. ~ -40 kcal/mol
Mnemonicdevice
• Fieldenergy:WhatistheCoulombenergyofinterac.onofionwithitself?
• Tomoveanionfrommedia(orvacuum)towater:
• Ifthefirstmediumisvacuum,thenεm=1
Um→w =Uw −Um =Cq2
2rq1εw
−1εm
⎛
⎝⎜
⎞
⎠⎟
U =C q2
ε(2rq )
q 2r q R ε
⎟⎟⎠
⎞⎜⎜⎝
⎛−= 11
2
2
wqsolv r
CqUε
Evensimplerforwater-to-fattransfers
• Transferfromwatertoamediumwithε=4(membrane,orproteininterior):
• rq-istheBornradiusofanion,andZisitschargeinelectronunits:
Umolartransfer = 40
Z 2
rq[kcal /mol]
Solva.onenergiesofimportantions
• ΔGsolv(Na+)=~100kcal/mol(water/vapor)• ΔGsolv(K+)=~80kcal/mol• Standardstatesolva.onfreeenergydatafrom:NoyesRM.Thermodynamicsofionhydra.on
asameasureofeffec.vedielectricproper.esofwater.JAmChemSoc84(4)513-22,1962.• InsidemembraneΔGmemb(Na+)isonlyafrac.onof100kcal/mol.
• Biologicalmembranesareprac=callyimpermeabletoanythingcharged
• Evenpolarcompoundscannotgothrough(ruleof5)
Howmosquitocalmsyoudown?biogenicaminesanddrugs
SerotoninHappiness,appe.te
Histamine:Arousal,inflamma.on
DopamineReward.LackinginParkinsons,Schizophrenia
cocaine,methamphetamineareamplifiers
EnergyandForce
• Forceisanega.vegradientoftheEnergyfunc.on(aslope)
• Forcecausesinstabilityandaccelera.on
F =C q1q2εr2
U =C q1q2εr dU = −
Fdx
F = −
∇U
• Don’tmixupEnergyandForce
• Energyisprimary,Forceisliterallyaderiva=veoftheEnergy
Whichatomsinibuprofenarecharged?• AtneutralpHibuprofen’soxygensinsolu.onarecharged• Instomachthecarboxylgetsuncharged• Theneutralformgetsabsorbed• ThenitgetschargedagainandbindstoitstargetCOX2• Inbothchargedandunchargedformstheelectrondensityisredistributedwithrespecttotheposi.velychargednuclei.• Thebalanceprojectedonthenucleicanbedescribedas‘par.alcharges’.
Ibuprofen,pKa=4.91
ChargesinDrugMolecules
FormalandPar.alatomcharges• Physicalreality:amoleculecanhaveadifferent
numberofprotonsandelectrons.Theintegerdifferencegivestheformalchargeofthemolecule.
• Theorbitalsmaybedistributedandbothatomicformalchargesandpar.alchargesaresimplifica.ons
• FormalCharge(FC):Ifanatomhasmoreorlesselectronsinamoleculethaninafree,neutralstate,FC+1,-1,+2,..-1/2…Frac.onsresultfromaredistribu.onofanintegernumberbetweenseveralatoms.
• Lewisstructures(electrondotdiagrams)• FC=Nvalenceels–Nlone_pair_els-½Nsharedels)• Par.alcharges:theformalchargegets
redistributedsoeachatomgetsaneffec.vefrac.onalcharge.
-1/2
-1/2
TheBondSpliwngMethod• DrawaLewisstructure,e.g.• Splitbondsintotwoelectrons• Countelectronsandcomparewiththevalencenumber(C:4,N:5,O:6,..)
• Beawareoftheresonancestructures,e.g.
-1/2-2/3
Animplicitsolventelectrosta.cmodel
• Waterisreplacedbyapolarizablecon.nuumwithε=80
• Proteins,membrane,..aregeometricshapeswithlowdielectricmediumε=2-10
• Atomicchargesareimmersedinlowdielectricmediumatapar.cularloca.onsinsideoronthesurfaceoftheshapes
ε=80
ε=4
ε=4
Poisson-BoltzmannEqua.on
• Input:shapeswithdifferentdielectricconstantandchargesatcertainloca.ons
• Output:theelectrosta.cpoten.alΦ atanypointinspace
• EnergyofonechargeisEi=qiΦ
ε=80
ε=4
ε=4
SiméonPoisson
NumericalSolu.onofthePoissonEqua.on
• Goal:calculatepolariza.onchargesateachelementofthemolecularsurface
PolarSurfaceArea(PSA)forCNSandsystemicdrugs
• ChargedcompoundsdonotcrossBBB
Evenapar.alchargeisanobstacle:• Oral:PSA<140A2safe:PSA<120A2
• Blood-brainbarrier:40<PSA<75(90?)A2
• Addi.onalCNSfilters:– logP<3,logD<2,MW<360,HbD<0.5,basicpKa<8
– Needatleast4oufof6 BBBOrallimits
Umolartransfer = 40
Z 2
rq[kcal /mol]