Fitting Michaelis-Menten directly to substrate concentration data

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Analytic numeric solution for S(t)?◮{ ( )}S0 S0 − V max tS(t) = K m W expK m K mwhere Lambert’s W : y = W (x) such that ye y = x◮ Expansion <strong>to</strong> give (approximate) Lambert’s W :
Analytic numeric solution for S(t)?◮{ ( )}S0 S0 − V max tS(t) = K m W expK m K mwhere Lambert’s W : y = W (x) such that ye y = x◮ Expansion <strong>to</strong> give (approximate) Lambert’s W :◮ See Golicnik, Analytic Biochemistry (2010), andreferences therein.maximum error < 0.02% (Barry et al., 2000)
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Fitting Michaelis-Menten directly t
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OutlineEnzyme KineticsMichaelis−M
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OutlineEnzyme KineticsMichaelis−M
Page 7 and 8:
Enzymes‘Little’ molecular machi
Page 9 and 10:
An enzyme reactionk 1S + E 0 ⇋ E
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An enzyme reactionk 1S + E 0 ⇋ E
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Enzyme kineticsScientists wish to
Page 15 and 16:
Enzyme kineticsScientists wish to
Page 17 and 18: Reaction rates . . .k 1S + E 0 ⇋
Page 19 and 20: k 1S + E 0 ⇋ E 1k−→2E0 + Pk
Page 21 and 22: k 1S + E 0 ⇋ E 1k−→2E0 + Pk
Page 23 and 24: Reaction rates . . .dSdt= −k 1 SE
Page 25 and 26: ... which give...dSdt= (k 2E T S( )
Page 27 and 28: ... which give...dSdt= (k 2E T S( )
Page 29 and 30: The Michaelis-Menten equation.v = V
Page 31 and 32: How good is the steady-state approx
Page 33 and 34: Traditional estimation of V maxand
Page 39 and 40: Fit directly to concentration data,
Page 41 and 42: Fit directly to concentration data,
Page 43 and 44: Solution to S(t){ ( )}S0 S0 − V m
Page 45 and 46: Estimation strategies using (S, t)
Page 47 and 48: Estimation strategies using (S, t)
Page 49 and 50: Transform (S, t) to (v, S ∗ )?v i
Page 51 and 52: Note that{ }Si+1 − S iVar(V i ) =
Page 53 and 54: Fitting v = V maxS ∗K m +S ∗ ,
Page 55 and 56: Transforming (S, t) to (v, S ∗ )
Page 57 and 58: Direct fit to (S, t) data: S(t) num
Page 65 and 66: Euler’s solution to S(t)Simple to
Page 67: Analytic numeric solution for S(t)?
Page 71 and 72: "Fit Michealis-Menten (following Go
Page 73 and 74: Semi-parametric method?Represent S(
Page 75 and 76: Semi-parametric method?Represent S(
Page 77 and 78: Semi-parametric methodFit spline to
Page 83 and 84: 4. OptionsPRINT = stringPLOT = stri
Page 85: MICHAELIS CONC=S; TIME=ElapsDays357
Page 88 and 89: MICHAELIS CONC=S; TIME=ElapsDaysRGR
Page 90: MICHAELIS CONC=S; TIME=ElapsDaysRGR
Page 93 and 94: Fix K 1 = 0 (original Michaelis-Men
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Fitting Michaelis-Menten directly to substrate concentration data

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