Download Review of Thermodynamics

CH3F5 Bioorganic Chemistry
Lecture 9
Molecular Interactions
Dr Andrew Marsh, C515
[email protected]
Dr Ann Dixon, A102
[email protected]
Dr Rebecca Notman, G Block Room 2
[email protected]
Overview
Week 15 Lecture 9
Lecture 10
Week 16 Lecture 11
Lecture 12
Lecture 13
Week 17 Lecture 14
Lecture 15
Lecture 16
Week 18
Lecture 17
Introduction to molecular interactions
Quantifying strengths of interactions
Examples Class Estimation of association constant
Computer Workshop 3 – Assessed work 1
Estimation of association constants
Hydrogen bonding; π-interactions
Electrostatic interactions
Hydrophobic effect and protein folding
Thermodynamics & Isothermal titration calorimetry
Physical methods to measure interactions
Membrane protein folding and assembly
Assessed Workshop feedback 1
Week 19
Computer Workshop 4 [–> assessed work 2]
Weeks 20, 21
Revision Sessions
Week 30 Term 3, Mon 20 Apr 4 pm Hand in assessed work 2
Week 32 Term 3 Fri 8 May Feedback 2
Recommended reading: Modern Physical Organic Chemistry
2
E Anslyn J Dougherty
QD1611.A6
Example: β-adrenergic receptor
Adenylate cyclase, Ca2+ channels
See Nature, 2009, 459, 356 and 3sn6.pdb and PDBe QUIPS summary
3
Review of Thermodynamics:
Recommended reading
• Chemical Structure and Reactivity, J Keeler, P
Wothers Chapter 6 “Thermodynamics and the
Second Law” QD471.K43
• Atkins’ Physical Chemistry, P W Atkins, J de Paula
e.g. 8/e; Chapters 2 and 3 First Law and Second
Law of Thermodynamics QD453.3.A74
• Molecular Driving Forces K A Dill, S Bromberg
1/e Chapters 10, 12, 30 *** highly recommended! ***
QC311.5.D55
Review of thermodynamics
• Consider the general reaction:
A+B⇌ C+D
• The equilibrium constant for this reaction is given by:
C  D 

Ka
 A B 
May also report Kd = 1/Ka
• Standard state, report ΔGo and by choosing Kao = KaC0
• Conventionally, C0 = 1 M and concentrations are usually
expressed as M = mol dm-3
• We will expect that you can all deduce the units of K for
any given reaction
5
Review of thermodynamics
• If a mechanism involves successive reaction steps, the
overall equilibrium constant is a product of the stepwise
equilibrium constants (often denoted ).
• e.g. for the reactions:
A+B⇌C+D
C⇌E+F
• The overall K is given by:
C  D   E  F   D  E  F 

K  1   2 


 A B  C 
 A B 
1
2
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Review of thermodynamics
• Amount of energy capable of doing work
= change in the Gibbs free energy
• G of reaction is related to the equilibrium constant by:
G = –RT ln(K)
• Where Ideal gas constant R = 8.314 J mol-1 K-1; T =
temperature, Kelvin
– Calculated this way, G will have units of J mol-1.
– Convert to kJ mol-1 by dividing by 1000.
• Alternatively, divide expression by (–RT) on both sides and
take exponential of both sides to get:
 G 
K  exp 

RT


7
Review of thermodynamics
• The Gibbs free energy, G, is energy available in a form
that can be used to do work.
• Cane be broken down into two further components:
enthalpy H; and entropy S for a given temperature T (in
Kelvin):
G (kcal mol-1 or kJ mol-1)= H–TS
– H is heat of reaction at constant pressure (kcal mol-1 or kJ mol-1).
– S relates to increase/decrease in system disorder; has several
components: e.g. bulk translation and rotation, configurational, etc.
•
Caution: enthalpy and entropy are not fundamental
properties of a system and decomposition of ΔG into ΔH
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and ΔS are model dependent.
Review of thermodynamics
Potential energy, U(x) is the fundamental property changed by
e.g. ligand binding to receptor, where x is the microscopic
configuration (including receptor, ligand, solvent degrees of
freedom)
At equilibrium, the distribution of configurations with specific
volume of cell or flask is given by the Boltzmann distribution:
p(x) µ e
-
((U (x )+ pV ( x))
kBT
Hence although we may like to discuss entropy and enthalpy
for explaining spontaneous reactions, equilibria and phase
behaviour, we must be aware that they are intrinsically linked
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Supramolecular Chemistry, Bioorganic Chemistry,
Molecular Interactions?
Scientists have long sought to explain biological
processes through understanding fundamental
interactions at the molecular level. One approach has
been the use of simplified chemical ‘model’ compounds
and this is one strand of supramolecular chemistry.
What is Supramolecular Chemistry?
Often defined as the chemistry of non-covalent
interactions or literally “chemistry beyond the molecule”
What do we mean by Molecular Interactions?
10
Molecular Interactions…
Main classes of interaction (convention is —ve = more free energy)
to be considered are:
- electrostatic interactions
ion-ion
(strength - 100 - 350 kJ mol-1)
ion-dipole
(+/- 50 - 200 kJ mol-1)
dipole-dipole
(+/- 5 - 50 kJ mol-1)
quadrupole-quadrupole (+/- 5 kJ mol-1)
- induction (dipole - induced dipole)
- dispersion (-2.5 kJ mol-1 per atom)
- repulsion (+1.5 kJ mol-1 per atom)
Compare to covalent bonds e.g. C-C single bond 348 kJ mol-1
ref: Steed and Atwood Supramolecular Chemistry pp. 19-30
11
…are ingredients for the following
Hydrogen bond
e.g. for H2O dimer gas phase: electrostatic 118 %,
induction 37 %, dispersion 42 %, repulsion –97 %
π-π interactions
Benzene – benzene T-shaped gas phase: electrostatic
127 %, induction 82%, dispersion & repulsion –109%
Cation-π interactions
K+ benzene gas phase: electrostatic 65 %, induction
47 %, dispersion & repulsion –12 %
Van der Waals’ interactions
argon dimer at equilibrium distance gas phase:
dispersion 194 %, repulsion –94 %
MP2 calculations, TR Walsh
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Ion-ion interactions
+
-
- effective over a long range (1/r dependence)
qq
- recall Coulombic interaction
1 2
 where e, e0 permittivity of medium & vacuum)
4 pee0 r
- Non-directional, high strength 100 - 350 kJ mol-1
- Many receptors for cations and anions use
electrostatic interactions to hold a guest in place
N
Anion e.g. I-
Ka [Cl-] 50 [Br-] 1020 [I-] 500 M-1
N
5
N
N
13
Dipole-dipole interactions
d+
dO
O
d-
dipole magnitude = qr
q is charge of each point
r is distance between
d+
Dipole – dipole (brought about by inherent bond polarity) interactions
have a strong orientational dependence, producing attractive or repulsive
forces of the order 5 – 50 kJ mol-1
Distance dependence follows 1/r3
Often seen in solid state and evident in protein crystal structures.
(For recent review see Angew. Chem. Int. Ed. Engl. 2005, 44, 1788)
55o
θ
mB
r
mA
(3cos2 θ – 1)
-2
+2
+1
-1
0
x
m AmB
4peor 3
14
Ion-dipole interactions
d+
dO
Directional (dipole aligned for optimal binding) and strong
(50 - 200 kJ mol-1)
Not as long ranged as ion-ion (1/r2 dependence)
+
H
N
O
O
O
O
O
NH
O
O
HN
M
+
O
O
O
O
O
O
NH
O
HN
O
O
X-ray molecular structure of
valinomycin - K+ complex
O
O
N
H
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e.g. valinomycin (macrocyclic depsipeptide antibiotic isolated from Streptomyces)
What is a quadrupole?
Charge separation over two sites (1+ve,1-ve) gives a dipole;
Charge separation over four sites (2+ve,2-ve) gives a
quadrupole.
For an aromatic ring, the quadrupole passes through the centre
of the ring.
(in very simple shape terms, it approximates to a dz2 orbital).
d-
H
H
d+
H
H
d+
H
H
Represented symbolically as:
d-
 (capital theta) is the magnitude of the
quadrupole moment
16
Quadrupole-quadrupole interactions
Distance dependence follows 1/r5
Strong directional dependence
e.g. controls phenyl ring relative orientation
H
H
d-
d+
H
H
d+
Represented
schematically as:
dd-
H
H
H
d+
H
H
55o
d+
H
H
d-
H
(end on)
r
+6
-3
+2 1
4
AJ Stone The Theory of Intermolecular Forces 2/e 2013, OUP
+ 3
4
-2 7
16
x
Q AQB
4peor 5
17
Induction
Induction effects arise from the distortion of a
molecule in the electric field of its neighbours.
i.e. a permanent dipole inducing a dipole
molecules approach
induced dipole
18
Dispersion
Sometimes referred to as van der Waals’ interactions, first quantified by
London, F. (1930):
induced dipole – induced dipole
instantaneous
dipole
induced
Dispersion is attractive everywhere (all distances and orientations).
Is not strongly orientation dependent.
Follows 1/r6 distance dependence (short-ranged)
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Repulsion
Electron-electron repulsion.
Can use van der Waals’ atomic radii described by Pauling (1960) as
first estimate
e.g. argon dimer at
equilibrium
separation
potential energy
close approach is repulsive
Computational models for repulsion
take many forms.
Examples are 1/r12 or exp(-r) at simple
level.
Rm separatuion at min. energy
Rm
internuclear distance
Lennard-Jones potential
20
Bringing interactions together
This set of archetypal interactions can be likened to a set of
ingredients that when combined create a menu that we observe as
molecular recognition properties of molecules.
Bringing two or more molecules together results in preferences for
particular orientations that can lead to particular reactivity or expressed
properties.
These resultant structures are highly dependent on amongst other
factors:
- solvent
- temperature
- other solutes
21
Shape and interaction
complementarity
These interactions between molecules are only important if they fit
together correctly. This was recognised by Emil Fischer in 1894 and is
called the
Lock and Key Principle
Although it was first use as an explanation for the specificity of enzymes
for their substrates, the same ideas hold for many other stucture
including designed and evolved supramolecular receptors.
O
H3 C
O
Ph
NH
O
O
OH
Paclitaxel (Taxol®)
potent and broad spectrum
antitumour activity
O
Ph
O
O
H
OH O
OH
O
CH 3
O
Ph
Originally derived from the bark
of the Pacific Yew, T axus
Br evif olia
O
22