Multivalent interactions in human biology

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1 Cooperativity

2 Multivalent interactions in human biology

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7 Multivalent interactions in supramolecular chemistry

8 Additivity (?) Multivalent interactions in supramolecular chemistry In order to obtain a strong recognition between the host and the guest using weak non covalent interaction, multiple interactions must be used. NH N K ass = 25 M 1 G = 7.9 kj mol 1 NH NH N N K ass = M 1 G = 21.6 kj mol 1 K ass = M 1 G = 35.3 kj mol 1

9 Additivity (?) In some cases however, binding constant are much lower: H bond acceptors and donors are also charge centers! K ass = 10 4 M 1 K ass = 10 2 M 1 Each H bond contributes with 7.8 kj mol 1, each secondary interaction with ± 2.9 kj mol 1

10 Chelate effect Host with multiple binding sites results in more stable complexes than multiple unidentate ligand (chelate cooperativity) H 3 N NH 3 NH 3 H 3 N NH 3 NH 3 H 2 N NH 3 NH 2 NH 2 H 2 N NH 2 H 2 N NH 2 NH 2 M = Ni 2+ log K = Greater basicity of primary amines 2. Weaker solvatation of primary amines 3. Decreased repulsive interaction between binding sites 4. Steric interactions and strain in the complex ΔH = 29 kj mol 1 TΔS = 25 kj mol 1 1.Conformational changes 2.Greater number of free species

11 Enthalpy Positive cooperativity is due to entropic and enthalpic contributions to binding. Enthalpy: secondary functional groups interactions, conformational changes, ring strain, polarization of the interacting groups

12 Entropy Positive cooperativity is due to entropic and enthalpic contributions to binding. Entropy: loss of motion of the molecule, including internal rotation and vibrations (contribution already paid for in connecting together the recognition elements)

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14 Multiple interactions in binding: definitions (reference: ) receptor ligand complex multiple binding sites: receptor interacts with a multivalent ligand multiple binding sites: receptor interacts with a monovalent ligand

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16 Measuring cooperativity: value!! this is a wrong comparison!!

17 degree of cooperativity positive cooperativity (synergistic) noncooperative (additive) negative cooperativity (interfering) in all cases overall binding constants increase! when talking about cooperativity (in binding) we often consider this one as the typical situation. On the contrary this is a rare situation! most of the available examples are characterized by Don t be fooled by the overall strength of binding which is always larger: poly mono G G RT N K poly N K mono ln( )

18 Case study see PDF

19 1. Hill equation imagine an enzyme with n binding sites for n substrates Koshland, Némethy and Filmer

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21 Hill plot the slope in the region of 50% saturation is called the Hill constant n>1: positive cooperativity n=2.8 n=1: no cooperativity n<1: negativecooperativity

22 2. Scatchard plot

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25 3. Binding curve a sigmoidal isotherm is indicative of cooperativity

26 But is Lehn s conclusion correct?

27 see PDF

28 K inter + K inter = microscopic H 1 G binding constant H 1 G H 1 G H 1 x G + K obs macroscopic binding constant K obs = H 3 G 3 H 3 x G 3 H 3 G H 3 G 3 in case of non cooperativity (indipendent binding sites) we can anticipate that K obs = K inter K inter K inter = K inter 3 but what about the individual binding steps?

29 1. complexation of the first guest + K obs,1 macroscopic binding constant K obs = H 3 G H 3 x G H 3 G H 3 G complex H 3 G has 3 sites for binding G, which are all identical What is the relation between K obs,1 and K inter? thus K obs,1 = 3K inter

30 2. complexation of the second guest + K obs,2 K obs = H 3 G 2 H 3 G x G H 3 G G H 3 G 2 What is the relation between K obs,2 and K inter? complex H 3 G has 2 sites available for G (x2) +, but each complex can be formed in 2 ways(/2) thus K obs,2 = 2K inter /2 = K inter

31 3. complexation of the third guest + K obs,3 K obs = H 3 G 3 H 3 G 2 x G H 3 G 2 G H 3 G 3 What is the relation between K obs,3 and K inter? complex H 3 G 2 has 1 site available for G (x1), but the final complex can be formed in 3 ways(/3) thus K obs,3 = 1/3 K inter

32 + K obs macroscopic binding constant K obs = H 3 G 3 H 3 x G 3 H 3 G H 3 G 3 K obs = K obs,1 K obs,2 K obs,3 = (3K inter )(K inter )(1/3K inter )=K inter 3

33 K i = K inter (m i+1)/i m: number of identical and indipendent binding sites 4 K inter 3/2 K inter 3 sites left but each complex can be formed in 2 ways 2/3 K inter 2 sites left but each complex can be formed in 3 ways 1/4K inter 1 sites left but final complex can be formed in 4 ways

34 this criterium is used to evaluate cooperativity and is at the basis of the Hill equation and Scatchard plot positive cooperativity: K i+1 > K i no cooperativity: K i+1 = K i negative cooperativity: K i+1 < K i however, it is only valid when comparing the same binding events to assess cooperativity, only virtually identical processes described by equilibrium constants having the same dimensions should be compared.

35 L 3 binding sites M 2 binding sites assembly S assembly S has stoichiometry: L 8 M 12 (or L pl M pm ) N: number of molecules in assembly S = pl + pm = 20 B: number of bonds = plm = 24 To form the assembly 19 (N 1) intermolecular bonds are required (defined by K inter ) The amount of intramolecular bonds is given by B N+1 (defined by K intra )

36 inter K 1 = 2 K inter intra K 2 = 2 K intra,2 intra K 3 = 1/2 K intra,3 In the example illustrated in Scheme 2, since there is only one intermolecular interaction, the processes relevant to cooperativity are those intramolecular. Thus if the closure of the first ring facilitates the closure of the virtually identical second ring, there is positive cooperativity or, in other words, K intra,3 > K intra,2 (or K intra,3 /K intra,2 >1) This implies K 3 /K 2 > 1/4

37 positive cooperativity: K obs > K S no cooperativity: K obs = K S negative cooperativity: K obs < K S

38 see PDF

39 Cooperativity allosteric cooperativity: chelate cooperativity: interannular cooperativity: