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Enzymol. 467, 248-280^. ,H  0޽h ? ̙33y___PPT10Y+D=' * = @B +H  0  p'' (   x  c $G``   XB  0D`[z j    j ,$D 0;   0IJ* T  G E + S ---> ES : k1 ES ---> E + S : k2 ES ---> E + P : k3 pH   3   `   0`    < Rpjf> JInput (plain text file):`B  0D C  <V,$D 0  d[E ] / dt = X n  0`@,$D  0  - k1 [E] [S]X  0A?`m  <8j  v0HOW DYNAFIT PROCESSES YOUR BIOCHEMICAL EQUATIONS*10 33R  s *A` JX  00` z      ,$D 0,   <lp   k1 [E] [S]`   0 z       ,$D 0   0$z z  k2 [ES]n 33333`   0  z l \    l  \ ,$D 0   0l v J  k3 [ES]n `   0l \  z  `@@   ` @@,$D 0`B   0D j @   < ` 4 = Rate terms: `B   0D @z @`@   `@@,$D 0`B   0D@@@   <D&`4 ARate equations:`B   0D@R  <X0t ,$D   0 + k2 [ES] 33333N ! <DL < ,$D   0 + k3 [ES]| D " < p ,$D  0 d[ES ] / dt = X  $z ,   #   , ,$D   0B $  0쭅<    + k1 [E] [S]& %  <,\ 0  - k2 [ES] 33333" &  <̿8   - k3 [ES]|  ' <Xȅ p ,$D   0 PSimilarly for other species...H  0޽h ? ̙33++___PPT10*+vD)' ؅= @B D=)' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*! %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*! D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*! DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*" %(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*# %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*# D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*# D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*' %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*' D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*' +P+0+ 0 ++0+ 0 ++0+ 0 ++0+! 0 ++0+" 0 ++0+' 0 +H  0 og// (   x  c $``   XB  0D`[z j    j ,$ 0;   0J* T  G E + S ---> ES : k1 ES ---> E + S : k2 ES ---> E + P : k3 pH   3   `   0`    <pjf> JInput (plain text file):`B  0D X  0A?`m  <p  v0HOW DYNAFIT PROCESSES YOUR BIOCHEMICAL EQUATIONS*10 33R  s *A` JX  00` z      ,$ 0,   <   k1 [E] [S]`   0 z       ,$ 0   0| z  k2 [ES]n 33333`   0  z l \    l  \ ,$ 0   0 v J  k3 [ES]n `   0l \  z  `@@   ` @@,$ 0`B   0D j @   <\ ` 4 = Rate terms: `B   0D @z @`@   `@@,$ 0`B   0D@@@   <&`4 ARate equations:`B   0D@R  C *Alego-001`  <L p ."The LEGO method" of deriving rate equations</&X  0 R ! s *p R " s *p R # s *p t X $ 0 P R % s *P @ R & s *P 0 R ' s *P X ( 0l P \ R ) s * @ l R * s * 0 l R + s * l dB , <Dp0 0 dB - <Dp@ P @ dB . <Dp P  R / C *AlegologoZH  0޽h ? ̙33y___PPT10Y+D=' * = @B +   0 4, (   x  c $}``   XB  0D`X  0A?`m5  <0 OMASS ACTION LAW AND MASS CONSERVATION LAW IS APPLIED TO DERIVE DIFFERENT MODELS^P 3 3 3& 33  <9X  o5Reaction progress Initial rates Equilibrium binding66  <2` BL  iFirst-order ordinary differential equations Nonlinear algebraic equations Nonlinear algebraic equationsjjLB  c $D  LB  c $D@   <x: ` B EXPERIMENT   <F ` SDYNAFIT DERIVES A SYSTEM OF ... 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(1981)  Design and Analysis of Enzyme and Pharmacokinetics Experiments 6%!#,2 B._H  0޽h ? ̙33y___PPT10Y+D=' * = @B +f  0 P (   x  c $|r``   XB  0D`X  0A?`m  <Lt5  -HUNDREDS OF ARTICLES, INCLUDING IN ENZYMOLOGY`.  3 3 3  33f  0A?"`(:f  0A?"`` RB  s *Do  RB  s *Do  H  0޽h ? ̙33y___PPT10Y+D=' * = @B +!  0 \T` (   x  c $T``   XB  0D`X  0A?`mx  <`  D-OPTIMAL DESIGN: MAXIMIZE DETERMINANT OF THE FISHER INFORMATION MATRIX^J  3 3  3! 33  <D LFisher information matrix:X  0A? ^  <` 4 b"EXAMPLE: Michaelis-Menten kinetics$#^  6l T   T ,$D 0r   S A  ??"?T      <4 >Model:l  h    h ,$D 0@@ h   h t2   6>"` t2   6>"`H h    < a  ltwo parameters (M=2)<   l @ G    @ G  ,$D  0   < @ G   !Design: four concentrations (N=4)B"   <  0   [S]1, [S]2, [S]3, [S]4     ^  6^  6dl  p2    p2 ,$D  0   < p <Derivatives: ( sensitivities )( r   S A  ??"? p P2   r   S A  ??"? 0    H  0޽h ? ̙33___PPT10+SUD' = @B D_' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +r  0   ) / (   x  c $ē``   XB  0D`X  0A?`mx  <Ɠ  D-OPTIMAL DESIGN: MAXIMIZE DETERMINANT OF THE FISHER INFORMATION MATRIX^J  3 3  3! 33t  <ϓ \Approximate Fisher information matrix (M M):/ ^  6^  6^  6^  6j   S A  ??"?  ^  6//  <Xړ  b"EXAMPLE: Michaelis-Menten kinetics$#  <x"`X L`,$D  0 P D-Optimal Design: Maximize determinant of F over design points [S]1, ... [S]4.S   ^ " 6++^ $ 6++l # !  &  #! ,$D 0 #  2A   ?8c?#" `?#     %  <p6 ! h  C determinant ^ ) 6//p (  S A!  ??#" `?B   H  0޽h ? ̙33{ s ___PPT10S +޸D ' = @B D ' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*& %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*& D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*& D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +8+0+ 0 +,!  0  p" (   x  c $T``   XB  0D`X  0A?`mQ  <D   /DUGGLEBY, R. (1979) J. THEOR. BIOL. 81, 671-684n0 3 3 3 3  33$X  0A ? F T    0$r   S A  ??"?T      < 4 >Model:  <0 P0 u V = 1 K = 1N l B `p   `B p ,$D 0`B   0D     < "`B `p 4 t[S]max0^  6   >A   ?jJ?#" `? 0 8  $D 0  6z"` P ,$D 0l `    `  ,$D 0   < "`   t[S]opt0`B   0D@` @ l x   x ,$D 0`B  B 0DxH 8H `B  B 0D ZB   s *D@@0 n   0"`@0 n   0"`@`  l  @ "  @,$D 0t2   6jJ"`   !  <  @ gK is assumed to be known !0  H  0޽h ? ̙33___PPT10+6+D{' * = @B D6' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*" %(D' =-o6Bdissolve*<3<*" +  0  O(   x  c $/ ``   XB  0D`X  0A?`m  <0 D<4___PPT9 xAssumed mathematical model is correct for the experiment A fairly good estimate already exists for the model parametersty    @`!  <6 j ;OPTIMAL DESIGN FOR ESTIMATING PARAMETERS IN THE GIVEN MODEL^< 3  3 3  33  <,J Jx <   <tM  x PTWO FAIRLY STRONG ASSUMPTIONS:\l       ,$D  0`   0 ` x   <K "`    Designed experiments are most suitable for follow-up (verification) experiments.4T- H  0޽h ? ̙33___PPT10+k=GD|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +   0 z (   x  c $] ``   XB  0D`X  0A?`mI  <_  AIN MANY KINETIC EXPERIMENTS THE OBSERVATION TIME CANNOT BE CHOSENB 3 3 3 3 3 33  <h  CONVENTIONAL EXPERIMENTAL DESIGN: Make an optimal choice of the independent variable: - Equilibrium experiments: concentrations of varied species - Kinetic experiments: observation time#  - O  <+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +8+0+ 0 +  0 rj (   x  c $ ``   XB  0D`X  0A?`m  <9   |$EXAMPLE: CLATHRIN UNCOATING KINETICS<% 3 33   6ؓ  >[task] task = design data = progress [mechanism] CA + T  > CAT : ka CAT  > CAD + Pi : kr CAD + T  > CADT : ka CADT  > CADD + Pi : kr CADD + T  > CADDT : ka CADDT  > CADDD + Pi : kr CADDD  > Prods : kd [data] file run01 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run02 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run03 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run04 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run05 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run06 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run07 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100) file run08 | concentration CA = 0.1, T = 1 ?? (0.001 .. 100)Z  )())))))u  j  < p b 8[constants] ka = 0.69 ? kr = 6.51 ? kd = 0.38 ?v9    ,    6jJ"` ,$D 0v  <  ns ,$ 0  Choose eight initial concentration of T such that the rate constants ka, kr, kd are determined most precisely. s'        ! ,K"H  0޽h ? ̙33___PPT10+s|vD:' * = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +8+0+ 0 +  0    M (   x  c $ ``   XB  0D`X  0A?`m<  < + dEXAMPLE: CLATHRIN UNCOATING KINETICS  ACTUAL DATAP3 3  3  33X  0A ?P P   <t @ < !Actual concentrations of [T] (M)Z"  <l 0 m 90   < pp  <0.25   < p   ;0.5   < `   91   <    92   <  ]  94   < "`p Qj ,$D  0 YSix different experiments$LB  c $D    < TZ( D|Rothnie et al. (2011) Proc. Natl. Acad. Sci USA 108, 6927 6932? $!H  0޽h ? ̙33___PPT10+ aD'  = @B DD' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +8+0+ 0 +c  0    Z (   x  c $H ``   XB  0D`X  0A?`m  <   |$EXAMPLE: CLATHRIN UNCOATING KINETICS<% 3 33X  0A ?0P LB  c $D` `   <  T ] = 0.70 M, 0.73 MR LB  c $D`   <|# \   #[T] = 2.4 M, 2.5 M, 2.5 M p$ LB  c $D `   <, 0 )  [T] = 76 M, 81 M, 90 Mp   <5  v i!D-Optimal initial concentrations:," @  <: "`  ,$D  0 8Just three experiments would be sufficient for follow-up>9/2l 0    0  ,$D 0t   6jJ"`0  :   <A d   ~ maximum feasible concentration upswing phase no longer seen,@!  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