Fitting Michaelis-Menten directly to substrate concentration data

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Semi-parametric method?Represent S(t) by f (t) = Φ(t)β,RequireMinimizen∑{s i − f (t i )} 2 + λi=1f ′ (t) ≃ V maxf (t)K m + f (t) .n∑i=1e.g. beta spline{f ′ (t i ) − V }maxf (t i ) 2K m + f (t i )
Semi-parametric method?Represent S(t) by f (t) = Φ(t)β,RequireMinimizeorn∑{s i − f (t i )} 2 + λi=1i=1f ′ (t) ≃ V maxf (t)K m + f (t) .n∑i=1e.g. beta spline{f ′ (t i ) − V }maxf (t i ) 2K m + f (t i )n∑∫ {{s i − f (t i )} 2 + λ f ′ (t) − V }maxf (t) 2dtK m + f (t)
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Fitting Michaelis-Menten directly t
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OutlineEnzyme KineticsMichaelis−M
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OutlineEnzyme KineticsMichaelis−M
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Enzymes‘Little’ molecular machi
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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
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Enzyme kineticsScientists wish to
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Reaction rates . . .k 1S + E 0 ⇋
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k 1S + E 0 ⇋ E 1k−→2E0 + Pk
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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 and 68: Analytic numeric solution for S(t)?
Page 69 and 70: Analytic numeric solution for S(t)?
Page 71 and 72: "Fit Michealis-Menten (following Go
Page 73: 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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