CH3F5 Bioorganic ChemistryLecture 9

Molecular Interactions

Dr Andrew Marsh, C515a.marsh@warwick.ac.uk

Dr Ann Dixon, A102ann.dixon@warwick.ac.uk

Dr Rebecca Notman, G Block Room 2r.notman@warwick.ac.uk

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OverviewWeek 15 Lecture 9 Introduction to molecular interactions

Lecture 10 Quantifying strengths of interactionsExamples Class Estimation of association constantComputer Workshop 3 – Assessed work 1

Week 16 Lecture 11 Estimation of association constantsLecture 12 Hydrogen bonding; π-interactionsLecture 13 Electrostatic interactions

Week 17 Lecture 14 Hydrophobic effect and protein foldingLecture 15 Thermodynamics & Isothermal titration calorimetryLecture 16 Physical methods to measure interactions

Week 18Lecture 17 Membrane protein folding and assembly

Assessed Workshop feedback 1 Week 19 Computer Workshop 4 [–> assessed work 2]Weeks 20, 21 Revision SessionsWeek 30 Term 3, Mon 20 Apr 4 pm Hand in assessed work 2Week 32 Term 3 Fri 8 May Feedback 2

Recommended reading: Modern Physical Organic Chemistry E Anslyn J Dougherty QD1611.A6

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Example: β-adrenergic receptor

See Nature, 2009, 459, 356 and 3sn6.pdb and PDBe QUIPS summary

Adenylate cyclase, Ca2+ channels

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:

• 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

C D

KA B

aMay also report Kd = 1/Ka

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Review of thermodynamics

• If a mechanism involves successive reaction steps, the overall equilibrium constant is a product of the stepwise equilibrium constants (often denoted β).

• e.g. for the reactions:

A + B ⇌ C + D

C ⇌ E + F

• The overall K is given by:

1 2

C D E F D E FK

A B C A Bβ β

β1 β2

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Review of thermodynamics• Amount of energy capable of doing work

= change in the Gibbs free energy• ΔG of reaction is related to the equilibrium constant by:

• Where Ideal gas constant R = 8.314 J mol-1 K-1; T = temperature, Kelvin– Calculated this way, ΔG 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:

expG

KRT

Δ

ΔG = –RT ln(K)

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Review of thermodynamics• The Gibbs free energy, ΔG, is energy available in a form

that can be used to do work.• Cane be broken down into two further components:

enthalpy ΔH; and entropy ΔS for a given temperature T (in Kelvin):

ΔG (kcal mol-1 or kJ mol-1)= ΔH–TΔS

– ΔH is heat of reaction at constant pressure (kcal mol-1 or kJ mol-1).– ΔS 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 and ΔS are model dependent. 8

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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

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:

Review of thermodynamics

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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?

Supramolecular Chemistry, Bioorganic Chemistry,

Molecular Interactions?

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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

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…are ingredients for the followingHydrogen bonde.g. for H2O dimer gas phase: electrostatic 118 %, induction 37 %, dispersion 42 %, repulsion –97 %

π-π interactionsBenzene – benzene T-shaped gas phase: electrostatic 127 %, induction 82%, dispersion & repulsion –109%

Cation-π interactionsK+ benzene gas phase: electrostatic 65 %, induction 47 %, dispersion & repulsion –12 %

Van der Waals’ interactionsargon 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)- recall Coulombic interaction - where e, e0 permittivity of medium & vacuum)

- Non-directional, high strength 100 - 350 kJ mol-1 - Many receptors for cations and anions use electrostatic interactions to hold a guest in place

Ka [Cl-] 50 [Br-] 1020 [I-] 500 M-1

Dipole-dipole interactions

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)

dipole magnitude = qrq is charge of each pointr is distance between

(3cos2 θ – 1) 14

θ

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Ion-dipole interactionsDirectional (dipole aligned for optimal binding) and strong (50 - 200 kJ mol-1)Not as long ranged as ion-ion (1/r2 dependence)

e.g. valinomycin (macrocyclic depsipeptide antibiotic isolated from Streptomyces)

X-ray molecular structure of valinomycin - K+ complex

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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 dz

2 orbital).

Represented symbolically as:

Θ (capital theta) is the magnitude of the quadrupole moment

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Quadrupole-quadrupole interactions

Distance dependence follows 1/r5

Strong directional dependence e.g. controls phenyl ring relative orientation

Represented schematically as:

AJ Stone The Theory of Intermolecular Forces 2/e 2013, OUP

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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

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Dispersion

Sometimes referred to as van der Waals’ interactions, first quantified by London, F. (1930):induced dipole – induced dipole

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

Computational models for repulsion take many forms.Examples are 1/r12 or exp(-r) at simple level.

e.g. argon dimer at equilibrium separation

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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

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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.