non-covalent interactionsruben.ucsd.edu/20/r12.pdf · non-covalent interactions electrostatics,...
TRANSCRIPT
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Non-covalent interactions
Electrostatics, Solvation, Transfer to a membrane or to a solvent
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A Charge in a fog
• Dipoles reorient, • electron density flows to
compensate the charge• Le Chatelier principle
screened
eNa+
Na+
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Three consequences of high e
• Charged atoms are almost completely “screened” in water (Uw=Uvacuum/80=Ufat/40)
• Direct charge-charge interaction 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 e.
eNa+
screened
4=eNa+
charge is screened
e Na+
Ignoring fellow charges
Cl-
80=eNa+
Happy Unhappy
“Sorry, I feel nothing”
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Solvation Energy of Charges• Born formula for the
solvation energy of a charge with radius rq , C=332
• The solvation energy of the ion:
when moved from apolar solvent to water (U is negative) eNa+
we
÷÷ø
öççè
æ-=ee11
2
2
wqsolv r
qCU
e
Apolar mediume.g. membrane
water
If e = 2 and r =2A, U = -332./8. ~ -40 kcal/mol
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Mnemonic device
• Field energy: What is the Coulomb energy of interaction of ion with itself?
• To move an ion from media (or vacuum) to water :
• If the first medium is vacuum, then em = 1
Um→w =Uw −Um =Cq2
2rq1εw
−1εm
⎛
⎝⎜
⎞
⎠⎟
U =C q2
ε(2rq )
q 2r qR e
÷÷ø
öççè
æ-= 11
2
2
wqsolv r
CqUe
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Even simpler for water-to-fat transfers
• Transfer from water to a medium with e=4 (membrane, or protein interior):
• rq- is the Born radius of an ion, and Zis its charge in electron units:
Umolartransfer = 40
Z 2
rq[kcal /mol]
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Solvation energies of important ions
• Δ Gsolv(Na+) = ~100 kcal/mol (water/vapor)• Δ Gsolv(K+) = ~ 80 kcal/mol • Standard state solvation free energy data from: Noyes RM. Thermodynamics of ion hydration
as a measure of effective dielectric properties of water. J Am Chem Soc 84 (4) 513-22, 1962. • Inside membrane Δ Gmemb(Na+) is only a fraction of
100 kcal/mol.• Biological membranes are practically impermeable to
anything charged• Even polar compounds can not go through
Lipinski’s rule of 5– No more than 5 hydrogen bond donors– No more than 10 hydrogen bond acceptors (all nitrogens
and oxygens– Gut: PSA < 120-130 A2 , BBB: PSA < 70 A2
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How mosquito calms you down?biogenic amines and drugs
SerotoninHappiness, appetite
Histamine:Arousal, inflammation
DopamineReward.Lacking in Parkinsons,Schizophrenia
cocaine, methamphetamine are amplifiers
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Energy and Force
• Force is a negative gradient of the Energy function (a slope)
• Force causes instability and acceleration
F =C q1q2εr2
U =C q1q2εr dU = −
Fdx
F = −
∇U
• Don’t mix up Energy and Force
• Energy is primary, Force is literally a derivative of the Energy
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Which atoms in ibuprofen are charged?• At neutral pH ibuprofen’s oxygens in solution 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 positively charged nuclei. • The balance projected on the nuclei can be described as ‘partial charges’.
Ibuprofen, pKa=4.91
Charges in Drug Molecules
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Formal and Partial atom charges• Physical reality: a molecule can have a different
number of protons and electrons. The integerdifference gives the formal charge of the molecule.
• The orbitals may be distributed and both atomic formal charges and partial charges are simplifications
• 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 … Fractions result from a redistribution of an integer number between several atoms.
• Lewis structures (electron dot diagrams)• FC=Nvalence els –Nlone_pair_els - ½ Nshared els)• Partial charges: the formal charge gets
redistributed so each atom gets an effective fractional charge.
-1/2
-1/2
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The Bond Splitting 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
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An implicit solvent electrostatic model
• Water is replaced by a polarizable continuum with e = 80
• Proteins, membrane, .. are geometric shapes with low dielectric medium e=2-10
• Atomic charges are immersed in low dielectric medium at a particular locations inside or on the surface of the shapes
e=80
e=4
e=4
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Poisson-Boltzmann Equation
• Input: shapes with different dielectric constant and charges at certain locations
• Output: the electrostatic potential F at any point in space
• Energy of one charge isEi = qi F
e=80
e=4
e=4
Siméon Poisson
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Numerical Solution of the Poisson Equation
• Goal: calculate polarization charges at each element of the molecular surface
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Polar Surface Area (PSA) for CNS and systemic drugs
• Charged compounds do not cross BBB
Even a partial charge is an obstacle:• Oral: PSA < 140A2 safe:
PSA < 120A2
• Blood-brain barrier: 40 < PSA < 75 (90?) A2
• Additional CNS filters:– logP<3, logD<2, MW<360,
HbD<0.5, basic pKa < 8– Need at least 4 ouf of 6 BBB Oral limits
Umolartransfer = 40
Z 2
rq[kcal /mol]
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• Drugs fit very well into their binding pockets
• They also fit well into water
• Why?
Van der Waals Interactions
Oseltamivir with Flu-viral Neuraminidase
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Two parts of Van der Waals interactions
• Repulsive– Quantum Principles
• Attractive– Electrostatic of
mutually induced dipoles
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Van der Waals Interactions
• Interaction between any two atoms including the uncharged ones
• Consists of two parts:– Strong repulsion after atoms bump
into each other (Pauli principle)– Attraction at contact distances and
quickly vanishing weak attraction at larger distances (fluctuating dipoles)
Johannes Diderik van der Waals
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Atomic composition of drugs
• H,C,N,O - in most drugs• S (222)• P(25) usually in pro-drugs• Halogens: F, Cl, Br, I
– F (105) Halothane, Gefitinib (Iressa)– Cl (170) Midozolam, Iressa– Br (12) Brompheniramine– I (7) Diatrizoate, Levothyroxine, Amiodarone
Thyroxine with the human thyroxinebinding globulin (large iodines)
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Van Der Waals radii• Atom size depends on the electron
orbitals interacting with the nuclei . • The radius of an atom is not a
uniquely defined property
• Radii increase as principle quantum number, n, increases
• Radii decrease as effective nuclear charge increases
• Some radii:– H 1.– C 1.7– O 1.5– N 1.6– S 1.8
+ +
6e–
Nucleus
Electroncloud of C
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Repulsion is steep
• The Lennard-Jones form of the repulsive potential:
12rAErepulsionvw =
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Van der Waal’s attraction
• The weak attraction is due to two mutually fluctuating dipoles.
6rBEattractivevw -=
rqqCECoulomb 21=
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Full Lennard Jones Potential• Properties
– Strong repulsion at r < rA+rB
– Weak attraction at r ≈ rA+rB
– Zero at large distances
• AIJ , and BIJ values are tabulated for different I and J pairs of atom types, e.g. sp3 carbon and sp2 nitrogen.
• EIJ ≈ -0.15 kc/ m at the vw contact distances for two methane molecules (vaporization enthalpy of 2kcal/mole), n_packing ~ 12
612 rB
rAEvw -=
Stable distance
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VdW and shape complementarity
• Van der Waals interactions are weakbut there are many of atom pairs.
• Shape complementarity between a drug and a receptor shallow