Chelate effect and cooperativity Flashcards
Chelate effect
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
Why is an ethylene diamine complex 10^8x more stable than an ammonia complex?
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
Macrocyclic effect
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
Pre-organisation
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
Macrocyclic complexes are…
…even more stable than would be expected from cooperative/chelate effects alone
Cooperativity
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
Positive cooperativity
If the overall stability of the complex is greater than the sum of the interaction energy of the guest with the binding sites individually
Negative cooperativity
If unfavourable steric/electronic effects cause the overall binding energy for the complex to be less than the sum of its parts
“All or nothing” behaviour
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
Positive cooperativity at the molecular level
Any individual molecule is likely to be fully bound or fully unbound - it spends little time in intermediate states
Positive cooperativity at the macroscopic level
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
Allosteric ligand binding
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 *
Alpha
= K2/K1
Interaction parameter
Describes the cooperativity of the system at the molecular level
Alpha = 1
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
ThetaA
Binding occupancy of the receptor
Defines the total fractions of receptor sites bound to ligand
Speciation curve for no cooperativity
Alpha = 1
K1 = K2
The ThetaA curve is identical to that of the one-site reference system
Speciation curve for negative cooperativity
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
Speciation curve for positive cooperativity
Alpha = 100
K2 > K1
Intermolecular interactions in the fully bound state are more favourable than in the intermediate
In the limit of alpha»_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
How is cooperativity in allosteric systems characterised?
In a Hill plot
Hill coefficient, nH
The slope of the Hill plot measured at log[ThetaA/(1-ThetaA)] = 0
i.e. 50 % saturation
nH = 1
Given by a simple reference receptor with one binding site
nH < 1
Indicates negative cooperativity
nH > 1
Indicates positive cooperativity
Why does the slope return to 1 at the extremes of the Hill plot?
Because changes in ThetaA are caused by only the first binding event at low [B] and only the second binding event at high [B]
Switching window
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
Effect of positive cooperativity on CR
Reduces the value of CR
The bound-free transition takes place over a narrower conc. range
Effects of negative cooperativity on CR
Increases the value of CR
The bound-free transition takes place over a wider conc. range
Chelate cooperativity
The interaction between 2 multivalent binding partners
Observed in protein folding/dsDNA formation
Difference between allosteric and chelate cooperativity
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
Why are chelate systems more complicated than allosteric systems?
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)
What is the key feature that defines the properties of a chelate system?
The intramolecular binding interaction that leads to the cyclic 1:1 complex c-AA.BB
This interaction is defined using the effective molarity (EM)
Effective molarity equation
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
KEM
The key molecular parameter that defines the cooperativity of self-assembled systems
KEM = 0.01
The partially bound (open) intermediate is more stable than the cyclic complex
The behaviour is identical to that found for monovalent ligands
KEM = 100
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
For KEM = 100, when does c-AA.BB open to form AA.(BB)2?
Only when 2[BB] > EM
i.e. EM = the concentration at which simple monovalent intermolecular interactions compete with cooperative intramolecular ones
Kinetic definition of EM
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
Kintra
First order rate constant of an intramolecular reaction
Kinter
Second order rate constant of the corresponding intermolecular reaction (to Kintra)
How is the relationship between allosteric and chelate cooperativity illustrated?
By considering free energies
i.e. by comparing the free energy of formation of the complexes AA.B2 and c-AA.BB
Free energy of formation of AA.B2
DeltaG(AA.B2) = -RTln(aK^2)
= 2DeltaG(A.B) - RTlna
Free energy of formation of c-AA.BB
DeltaG(c-AA.BB) = -RTln(2EMK^2)
= 2DeltaG(A.B) - RTln(2EM)
= DeltaG(A.B) - RTln(2KEM)
When does positive cooperativity (alpha > 1) arise?
When the free energy of formation of the assembly is more than the sum of the free energies of the isolated interactions
