Chelate effect and cooperativity

Question 1

Chelate effect

Answer 1

Multidentate ligands result in more stable complexes than comparable systems with multiple monodentate ligands
This enhanced stability arises from a combination of enthalpic and entropic factors

Question 2

Why is an ethylene diamine complex 10^8x more stable than an ammonia complex?

Answer 2

Entropic factors: intramolecular ring formation - as one N from ethylene diamine binds, it is easy for the second N to ‘swing round’ and bind
Enthalpic factors: N in ethylene diamine has a higher electron density than N in NH3 due to induction from the alkyl chains, therefore forms a stronger bond with the metal centre
Ethylene diamine complex also kinetically stabilised - K-1 is very small, because it is easier for the dissociated N to add back on than it is for the second N to break off

Question 3

Macrocyclic effect

Answer 3

Refers to the high affinity of metal cations for macrocyclic ligands compared to their acyclic analogues - macrocyclic hosts with multiple binding sites result in even more stable complexes
Stabilisation arises from the chelate effect plus the pre-organisation of the macrocyclic ligand

Question 4

Pre-organisation

Answer 4

A host is said to be pre-organised if it requires no significant conformational change to bind a guest species
Pre-organisation results in a significant increase in the stability of complexes

Question 5

Macrocyclic complexes are…

Answer 5

…even more stable than would be expected from cooperative/chelate effects alone

Question 6

Cooperativity

Answer 6

Arises from the interplay of 2 or more interactions, so that the system as a whole behaves differently from expectations based on the properties of the individual interactions acting in isolation

Question 7

Positive cooperativity

Answer 7

If the overall stability of the complex is greater than the sum of the interaction energy of the guest with the binding sites individually

Question 8

Negative cooperativity

Answer 8

If unfavourable steric/electronic effects cause the overall binding energy for the complex to be less than the sum of its parts

Question 9

“All or nothing” behaviour

Answer 9

As a system approaches the limit of strong positive cooperativity, only the extreme states (unbound/bound) are populated (i.e. very low conc of intermediates)
The key consequence of positive cooperativity
Occurs widely in biology where switching between ‘on’ and ‘off’ states results from a small change in conditions

Question 10

Positive cooperativity at the molecular level

Answer 10

Any individual molecule is likely to be fully bound or fully unbound - it spends little time in intermediate states

Question 11

Positive cooperativity at the macroscopic level

Answer 11

The behaviour of the ensemble is characterised by a population switch from mainly free to mainly bound over a small change in conditions - leading to sigmoidal curves/sharp transitions between states e.g. binding of O2 to Hb
Under most conditions, one state predominates

Question 12

Allosteric ligand binding

Answer 12

2 monodentate ligands (B) interacting with a receptor with 2 covalently-connected binding sites (AA)
Receptor has 3 possible states:
Free (AA)
Partially bound (AA.B)
Fully bound (AA.B2)

• equations *

Question 13

Alpha

Answer 13

= K2/K1
Interaction parameter
Describes the cooperativity of the system at the molecular level

Question 14

Alpha = 1

Answer 14

No cooperativity
Association constants (K1 and K2) are identical to the value for the corresponding reference receptor with one binding site i.e. K1 = K2 = K

Question 15

ThetaA

Answer 15

Binding occupancy of the receptor

Defines the total fractions of receptor sites bound to ligand

Question 16

Speciation curve for no cooperativity

Answer 16

Alpha = 1
K1 = K2
The ThetaA curve is identical to that of the one-site reference system

Question 17

Speciation curve for negative cooperativity

Answer 17

Alpha = 0.01
K1 > K2
The intermolecular interaction in the intermediate AA.B is stronger than in the fully bound state AA.B2
Formation of the fully bound complex takes place over a wider conc range than for the reference system
AA.B is the dominant species at intermediate concs

Question 18

Speciation curve for positive cooperativity

Answer 18

Alpha = 100
K2 > K1
Intermolecular interactions in the fully bound state are more favourable than in the intermediate
In the limit of alpha&raquo_space; 1, the intermediate is never populated and “all or nothing”, two-state behaviour is observed
Assembly and disassembly of the complex takes place over a narrower conc range than for the reference system

Question 19

How is cooperativity in allosteric systems characterised?

Answer 19

In a Hill plot

Question 20

Hill coefficient, nH

Answer 20

The slope of the Hill plot measured at log[ThetaA/(1-ThetaA)] = 0
i.e. 50 % saturation

Question 21

nH = 1

Answer 21

Given by a simple reference receptor with one binding site

Question 22

nH < 1

Answer 22

Indicates negative cooperativity

Question 23

nH > 1

Answer 23

Indicates positive cooperativity

Question 24

Why does the slope return to 1 at the extremes of the Hill plot?

Answer 24

Because changes in ThetaA are caused by only the first binding event at low [B] and only the second binding event at high [B]

Question 25

Switching window

Answer 25

CR The factorial increase in ligand concentration required to change the bound:free receptor ratio from 1:10 to 10:1 i.e. a measure of the sharpness of the bound-free transition

Question 26

Effect of positive cooperativity on CR

Answer 26

Reduces the value of CR | The bound-free transition takes place over a narrower conc. range

Question 27

Effects of negative cooperativity on CR

Answer 27

Increases the value of CR | The bound-free transition takes place over a wider conc. range

Question 28

Chelate cooperativity

Answer 28

The interaction between 2 multivalent binding partners | Observed in protein folding/dsDNA formation

Question 29

Difference between allosteric and chelate cooperativity

Answer 29

Chelate cooperativity is the interaction between 2 multivalent binding partners, whereas allosteric cooperativity is the effect of one binding event on the next for monovalent guests in a multivalent host or vice versa

Question 30

Why are chelate systems more complicated than allosteric systems?

Answer 30

Because there are more possible bound states (but if the ligand is present in a large excess compared to the receptor then complexes that involve more than one receptor can be ignored because they will not be significantly populated)

Question 31

What is the key feature that defines the properties of a chelate system?

Answer 31

The intramolecular binding interaction that leads to the cyclic 1:1 complex c-AA.BB This interaction is defined using the effective molarity (EM)

Question 32

Effective molarity equation

Answer 32

1/2 KEM = [c-AA.BB] / [o-AA.BB] This equation implies that the ratio of open and closed 1:1 complexes is independent of the ligand concentration The product KEM determines the extent to which the cyclic complex is populated

Question 33

KEM

Answer 33

The key molecular parameter that defines the cooperativity of self-assembled systems

Question 34

KEM = 0.01

Answer 34

The partially bound (open) intermediate is more stable than the cyclic complex The behaviour is identical to that found for monovalent ligands

Question 35

KEM = 100

Answer 35

The cyclic complex is more stable than the partially bound intermediate, and is the major species over a wide conc. range o-AA.BB is barely populated Formation of AA.(BB)2 is suppressed c.f. the corresponding monovalent ligands

Question 36

For KEM = 100, when does c-AA.BB open to form AA.(BB)2?

Answer 36

Only when 2[BB] > EM i.e. EM = the concentration at which simple monovalent intermolecular interactions compete with cooperative intramolecular ones

Question 37

Kinetic definition of EM

Answer 37

The ratio between the first order rate constant of an intramolecular reaction and the second-order rate constant of the corresponding intermolecular reaction EM(kinetic) = Kintra / Kinter High EM = greater ease of intramolecular processes

Question 38

Kintra

Answer 38

First order rate constant of an intramolecular reaction

Question 39

Kinter

Answer 39

Second order rate constant of the corresponding intermolecular reaction (to Kintra)

Question 40

How is the relationship between allosteric and chelate cooperativity illustrated?

Answer 40

By considering free energies | i.e. by comparing the free energy of formation of the complexes AA.B2 and c-AA.BB

Question 41

Free energy of formation of AA.B2

Answer 41

DeltaG(AA.B2) = -RTln(aK^2) = 2DeltaG(A.B) - RTlna

Question 42

Free energy of formation of c-AA.BB

Answer 42

DeltaG(c-AA.BB) = -RTln(2EMK^2) = 2DeltaG(A.B) - RTln(2EM) = DeltaG(A.B) - RTln(2KEM)

Question 43

When does positive cooperativity (alpha > 1) arise?

Answer 43

When the free energy of formation of the assembly is more than the sum of the free energies of the isolated interactions