pset07_soln

# pset07_soln - Problem 1 The binding of protein P with...

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Unformatted text preview: Problem 1. The binding of protein P with ligand L to form complex C is reversible, as told C L P on k ⎯→ ⎯ + and L P C off k + ⎯→ ⎯ We are given a table with various initial concentrations of L in order to estimate k on and k off and also K d for the reaction. C off L P on C C k C C k dt dC − = Also from material balances and stoichiometry, we have C P +C C =C P0 and C L +C C =C L0 , therefore C off C L0 C P0 on C C k ) C )(C C- (C k dt dC − − = In this problem, we can safely assume that C L0-C C ≈ C L0 since C L0 >> C P0 in all three cases of different C L0 . Thus, the integrated analytic expression for C C becomes )t]} k C exp[-(k 1 { K C C C )t]} k C exp[-(k- {1 k C k C C k C off L0 on d L0 L0 P0 off L0 on off L0 on L0 P0 on C + − + = + + = where on off d k k K ≡ Therefore, if we plot C C w.r.t time for each cases of C L0 , we can fit according to an exponential y=a[1-exp(-bt)], where b is k on C L0 +k off , and a is d L0 L0 P0 K C C C + . Values for a and b are shown in the following table. L (uM) a b 1 0.903 1.1113 5 1.0436 4.7047 15 0.9932 15.1079 One important observation in this table is that parameter a does not change much when initial ligand concentration is changed, indicating C L0 =1 μ M is already above the saturating value. M is already above the saturating value....
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• Fall '04
• ClarkColton
• Reaction, Trigraph, MIT OpenCourseWare, Massachusetts Institute of Technology, Biological Reaction Engineering, 10.37 Chemical and Biological Reaction Engineering, K. Dane Wittrup

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pset07_soln - Problem 1 The binding of protein P with...

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