Back to molecular interac/ons Quantum theory and molecular structure

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Philomena Gray
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Atoms in one molecule are connected by strong covalent bonds that are not easily broken by thermal fluctua1ons

1 Back to molecular interac/ons Quantum theory and molecular structure Atoms are arranged in 3D to cons1tute a molecule. Atoms in one molecule are connected by strong covalent bonds that are not easily broken by thermal fluctua1ons (>40kcal/mol vs thermal 0.6 kcal/mol) Bond length and bond angles are well defined by the covalent geometry Single bonds are rotatable Drug molecule can get transformed by cell enzymes and ionized before it becomes bioac1ve

2 Boltzmann s factor and probability If we have two states, A and B, say two rotamers of a drug, the probability to find a higher energy state is If you have two energies differing by 0.6 kcal/mole the higher energy state will be found e (2.71) 1mes less frequently. 1.4 kcal/mol 10 1mes less ΔG = 1.4*pKd = -Log(Kd, 10) ln K = Δ rg o RT G [A] [B] = A G B e RT p e ΔE RT

. They use covalent mechanism and may be considered irreversible or reversible depending on kine1cs.

3 Two classes of drugs: covalent and non-covalent Covalently bound to the target (the minority). Examples: aspirin, alkyla1ng agents, rivas1gmine,.. They use covalent mechanism and may be considered irreversible or reversible depending on kine1cs. Cys, Ser/Thr, Tyr, Asp/Glu, N+,.. Non-covalently bound to the target. The majority To understand chemical reac1vity and forma1on of covalent bonds we need to study the molecular orbitals and electronic transi1ons.

4 Non-covalent Interac1ons Drug gets converted into its ac1ve form Atoms get par1al of full charges (pka + electrosta1c field ) Drug atoms interact with atoms of the following main molecules: Other atoms of the same molecule Water molecules Lipids Receptor atoms

5 Main contribu1ons to molecular energe1cs G = H-TS Quantum effects covalent bonds (bonding orbitals) atom repulsion (Pauli exclusion principle) Electrosta/c interac/ons Interac1ons between full charges, dipoles, induced dipoles, hydrogen bonds, agrac1ve part of the Lennard-Jones poten1al Entropic effects a part of the hydrophobic effect Conforma1onal entropy changes upon binding.. Concentra1on-dependent entropies of mixing Other energy terms are either subtypes of the main class, or combina1ons of the main types (e.g. hydrophobic interac1ons)

Electrosta1c Interac1ons Coulomb s poten1al energy, in

distance in meters, charges in C (1 Coulomb = Ampere x

agract one another The force of repulsion/agrac1on get

6 Electrosta1c Interac1ons Coulomb s poten1al energy, in SI units q q U = 1 2 el 4πε ε r 0 Energy in Joules, distance in meters, charges in C (1 Coulomb = Ampere x second) Like charges repel one another Opposite charges agract one another The force of repulsion/agrac1on get weaker as the charges are farther apart. 1 Coulomb, Charles Augus1n

7 A more prac1cal formula Charges in electron units (-1,1,-0.5), distance in Ångstroms, energy in kcal/ mol, C = 332 ε is dielectric constant of the medium ε=1 for vacuum +1 and -1 charges at 3 A get 100 kcal/ mol!!! (10nM drug ~ 10kcal/mol) U = C q 1 q 2 εr

8 Polariza1on, solva1on and ε Electrosta1c interac1ons are reduced by ε because of the polariza1on of the media. U = C q q 1 ε r 2 ε=80 in water at 300K. Electronic polariza1on, dipole relaxa1on. Water is a strong dipole In the hydrocarbon layer of membranes ε~2 to 4 in proteins ε~ 4 to 10

9 Dielectric constants at 25C Water 78.5 Methanol 33.0 Ethanol 24.3 Ammonia 16.9 Benzene 2.3 Cyclohexane 2.0 Methane 100K 1.8

10 A Charge in a fog Dipoles reorient, electron density flows to compensate the charge Le Chatelier principle screened Na + Na + ε

11 Three consequences of high ε Charged atoms are almost completely screened in water (U w =U vacuum /80=U fat /40) Direct charge-charge interac1on is weak in water (Na+)(Cl-): d=2.5a, E= -1.7km Charged (and polar) atoms are extremely happy in water (low energy) and do not want to go to media with smaller ε. screened Na + ε Ignoring fellow charges ε Na+ Cl- Sorry, I feel nothing Happy Na + ε = 80 charge is screened Unhappy Na + ε = 4

12 Solva1on Energy of Charges Born formula for the solva1on energy of a charge with radius r q, C=332 The solva1on energy of the ion: water U solv q when moved from apolar solvent to water (U is nega1ve) ε = C 2 q r 2 ε 1 w 1 ε Na + ε w Apolar medium e.g. membrane ε If ε = 2 and r =2A, U = -332./8. ~ -40 kcal/mol

13 Mnemonic device What is the Coulomb energy of interac1on of ion with itself? To compare between two media with ε w and ε : U 1-2 = U 1 -U 2 If one compares with the ion in vacuum, ε = 1 U U w m U solv = = Cq 2r C q 2 q 2r q R ε 1 ε w q (2 2 r q 1 ε ε 2 Cq 1 = 1 2rq ε w )

14 Even simpler for water-fat transfers Transfer from water to a medium with ε=4 (membrane, or protein interior): r q - is the Born radius of an ion, and Z is its charge in electron units: U transfer = 40 Z r q 2 [ kcal / mol]

15 Solva1on energies of important ions Δ G solv (Na + ) = ~100 kcal/mol (water/vapor) Δ G solv (K + ) = ~ 80 kcal/mol Standard state solva1on free energy data from: Noyes RM. Thermodynamics of ion hydra1on as a measure of effec1ve dielectric proper1es of water. J Am Chem Soc 84 (4) , Inside membrane Δ G memb (Na+) is only a frac1on of 100 kcal/mol. Biological membranes are pracacally impermeable to anything charged Even polar compounds can not go through (rule of 5)

16 How mosquito calms you down? Histamine: Arousal, inflamma1on biogenic amines and drugs Serotonin Happiness, appe1te Dopamine Parkinsons, Schizophrenia cocaine, methamphetamine are amplifiers Adrenaline Fight or flight

Energy and Force U = C q 1 q 2 εr Don t mix

Force is a nega1ve gradient of the Energy

17 Energy and Force U = C q 1 q 2 εr Don t mix up Energy and Force Energy is primary, Force is literally a derivaave of the Energy du = Fd x F = U F = C q 1 q 2 εr 2 Force is a nega1ve gradient of the Energy func1on (a slope) Force causes instability and accelera1on

18 Charges in Drug Molecules Ibuprofen, pka=4.91 Which atoms in ibuprofen are charged? At neutral ph ibuprofen s oxygens in solu1on are charged In stomach the carboxyl gets uncharged The neutral form gets absorbed Then it gets charged again and binds to its target COX2 In both charged and uncharged forms the electron density is redistributed with respect to the posi1vely charged nuclei. The balance projected on the nuclei can be described as par1al charges.

Formal and Par1al atom charges Physical reality: a molecule can have a different number of protons and electrons. The integer difference gives the formal charge of the molecule.

19 Formal and Par1al atom charges Physical reality: a molecule can have a different number of protons and electrons. The integer difference gives the formal charge of the molecule. The orbitals may be distributed and both atomic formal charges and par1al charges are simplifica1ons Formal Charge (FC): If an atom has more or less electrons in a molecule than in a free, neutral state, FC +1, -1, +2,..-1/2 Frac1ons result from a redistribu1on of an integer number between several atoms. Lewis structures (electron dot diagrams) FC=N valence els N lone_pair_els - ½ N shared els ) Par1al charges: the formal charge gets redistributed so each atom gets an effec1ve frac1onal charge. -1/2-1/2

20 The Bond Spliyng Method Draw a Lewis structure, e.g. Split bonds into two electrons Count electrons and compare with the valence number (C:4, N:5, O:6,..) Be aware of the resonance structures, e.g. -1/2-2/3

21 An implicit solvent electrosta1c model Water is replaced by a polarizable con1nuum with ε = 80 Proteins, membrane,.. are geometric shapes with low dielectric medium ε=2-10 ε=80 ε=4 ε=4 Atomic charges are immersed in low dielectric medium at a par1cular loca1ons inside or on the surface of the shapes

22 Poisson-Boltzmann Equa1on Input: shapes with different dielectric constant and charges at certain loca1ons Output: the electrosta1c poten1al Φ at any point in space Energy of one charge is E i = q i Φ ε=80 ε=4 ε=4

23 Numerical Solu1on of the Poisson Equa1on Goal: calculate polariza1on charges at each element of the molecular surface

Biochemistry,530:,, Introduc5on,to,Structural,Biology, Autumn,Quarter,2015,

Biochemistry,530:,, Introduc5on,to,Structural,Biology, Autumn,Quarter,2015, Course,Informa5on, BIOC%530% GraduateAlevel,discussion,of,the,structure,,func5on,,and,chemistry,of,proteins,and, nucleic,acids,,control,of,enzyma5c,reac5ons.,please,see,the,course,syllabus,and,