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SolutionSet2 2008

# SolutionSet2 2008 - BMB100B Winter 2008 Rubin Problem Set#2...

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BMB100B Winter 2008 Rubin Problem Set #2 Due Tuesday, January 22 nd 10:00 A.M. 1) In class, we noted that the specificity of a protein for a particular ligand in a mixture of ligands depends on the relative affinities of the protein for each ligand. In this problem, you will explore how it can also depend on the relative concentrations of ligands. a) Consider a protein P and two ligands L 1 and L 2 . P can bind either ligand, but not both simultaneously. Derive algebraic expressions for the concentration of P bound to L 1 and L 2 ([P-L 1 ] and [P-L 2 ]) as a function of total protein and ligand concentrations and the dissociation constants ([P] t , [L 1 ] t , [L 2 ], K d1 , and K d2 ). Assume that the concentration of each ligand is much greater than protein so that you can take [L]=[L] t . b) Calculate [P-L 1 ] and [P-L 2 ] for the following three situations: [P] t [L 1 ] t K d1 [L 2 ] t K d2 1 nM 1 μ M 1 μ M 1 μ M 10 μ M 1 nM 1 μ M 1 μ M 10 μ M 10 μ M 1 nM 0.1 μ M 1 μ M 1 μ M 10 μ M c) What can you conclude about the effect on ligand preference of [L] and K d ?

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BMB100B Winter 2008 Rubin
BMB100B Winter 2008 Rubin

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BMB100B Winter 2008 Rubin
BMB100B Winter 2008 Rubin 2) The sigmoidal properties of positive cooperative ligand binding make the concentration of protein-ligand complex (or fraction of ligand bound Y) much more sensitive to the concentration of ligand when Y is near 0.5. Show this for the following example: a) Using the Hill equation for n=1, calculate Y when [L] = [L] 50 /2 and when [L]=2[L] 50 . Recall from class, we defined [L] 50 as the concentration of L when Y=0.5. By what factor (let’s call it φ29 does Y increase with this four-fold increase in [L] (i.e. calculate φ =Y([L]=2[L] 50 )/ Y([L]=[L] 50 /2)).

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