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Supramolecular > Chelate effect and cooperativity > Flashcards

Chelate effect and cooperativity Flashcards

1
Q

Chelate effect

A

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

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2
Q

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

A

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

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3
Q

Macrocyclic effect

A

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

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4
Q

Pre-organisation

A

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

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5
Q

Macrocyclic complexes are…

A

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

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6
Q

Cooperativity

A

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

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7
Q

Positive cooperativity

A

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

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8
Q

Negative cooperativity

A

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

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9
Q

“All or nothing” behaviour

A

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

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10
Q

Positive cooperativity at the molecular level

A

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

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11
Q

Positive cooperativity at the macroscopic level

A

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

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12
Q

Allosteric ligand binding

A 
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 *
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13
Q

Alpha

A

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

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14
Q

Alpha = 1

A 
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
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15
Q

ThetaA

A

Binding occupancy of the receptor

Defines the total fractions of receptor sites bound to ligand

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16
Q

Speciation curve for no cooperativity

A

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

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17
Q

Speciation curve for negative cooperativity

A

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

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18
Q

Speciation curve for positive cooperativity

A

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

19
Q

How is cooperativity in allosteric systems characterised?

A

In a Hill plot

20
Q

Hill coefficient, nH

A

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

21
Q

nH = 1

A

Given by a simple reference receptor with one binding site

22
Q

nH < 1

A

Indicates negative cooperativity

23
Q

nH > 1

A

Indicates positive cooperativity

24
Q

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

A

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

25
Q

Switching window

A

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

26
Q

Effect of positive cooperativity on CR

A

Reduces the value of CR

The bound-free transition takes place over a narrower conc. range

27
Q

Effects of negative cooperativity on CR

A

Increases the value of CR

The bound-free transition takes place over a wider conc. range

28
Q

Chelate cooperativity

A

The interaction between 2 multivalent binding partners

Observed in protein folding/dsDNA formation

29
Q

Difference between allosteric and chelate cooperativity

A

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

30
Q

Why are chelate systems more complicated than allosteric systems?

A

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)

31
Q

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

A

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

32
Q

Effective molarity equation

A

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

33
Q

KEM

A

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

34
Q

KEM = 0.01

A

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

35
Q

KEM = 100

A

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

36
Q

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

A

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

37
Q

Kinetic definition of EM

A

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

38
Q

Kintra

A

First order rate constant of an intramolecular reaction

39
Q

Kinter

A

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

40
Q

How is the relationship between allosteric and chelate cooperativity illustrated?

A

By considering free energies

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

41
Q

Free energy of formation of AA.B2

A

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

= 2DeltaG(A.B) - RTlna

42
Q

Free energy of formation of c-AA.BB

A

DeltaG(c-AA.BB) = -RTln(2EMK^2)

= 2DeltaG(A.B) - RTln(2EM)

= DeltaG(A.B) - RTln(2KEM)

43
Q

When does positive cooperativity (alpha > 1) arise?

A

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

Supramolecular (8 decks)

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