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]