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Solution Set 2_2011

# Solution Set 2_2011 - Bioc100B Winter 2011 Rubin Solution...

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Bioc100B Winter 2011 Rubin Solution Set #2 Due Tuesday, January 18 th 4:00 P.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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Bioc100B Winter 2011 Rubin
Bioc100B Winter 2011 Rubin

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Bioc100B Winter 2011 Rubin
Bioc100B Winter 2011 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)). b) Repeat these calculations for n=2. c) A biosensor is a device that uses a biochemical interaction to detect the presence of a chemical compound (referred to as an analyte). In most biosensor designs, the detected signal scales with the fraction of sensor protein bound with analyte (i.e. Y). If you were to design a protein biosensor to monitor small changes in the concentration of an analyte (say the amount of lead in drinking water), would you want to exploit a positive cooperative ligand-protein interaction? Why?

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Bioc100B Winter 2011 Rubin
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Solution Set 2_2011 - Bioc100B Winter 2011 Rubin Solution...

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