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S 4 T3 y y r   x*a00aa 4 T\3 y y r3   z*a00aaH 4 0ηo~ ? ̙3380___PPT10.pU(X p\x(  \ \ N$#]e]e     p* AAA \ N,%]e]e %    r* AAA  \ Th']e]e    p* AAA \ T;]e]e %   r* AAAH \ 0ηo~ ? ̙3380___PPT10.CP)U 0  (   X   0A?`m"   6  2 Numerical Enzyme Kinetics using DynaFit softwaren33333 33XB   0D  $   < W 4  >Petr Kuzmi , Ph.D. BioKin, Ltd.^      XB   0D@0@H   0޽h ? ̙33y___PPT10Y+D=' = @B +V  0L0 e](     <]"`{    XB  0D`X  0A?`m   <U`&  MThere are no traditional (algebraic) rate equations for many important cases:4N )F  <؃     Time-dependent inhibition in the general case substrate depletion enzyme deactivation Tight binding inhibition in the general case impurities in inhibitors dissociative enzymes Auto-activation inhibition e.g., protein kinases Many other practically useful situations. !O T()H  0޽h ? ̙33y___PPT10Y+D=' = @B +N  0L0  r(     <<}"`t   XB  0D`X  0A?`m*  <@X p Abandon traditional algebraic formalism of enzyme kinetics Deploy numerical (iterative) fitting modes instead2qE# l ` 0P   ` 0P ,$D 0  <` D  fThis is approach is not new: SOFTWARE D. Garfinkel (1960 s - 1970 s) BIOSYM C. Frieden (1980 s - 1990 s) KINSIM P. Kuzmic (2000 s - present) DynaFit K. Johnson (2010 s - present) Kinetic ExplorerZ P, WTB   c $D  0 TB   c $D ` P "   0 8 ,$D  0H  0޽h ? ̙33___PPT10+PYD' = @B Ds' = @BA?%,( < +O%,( < +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?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +  0L0 n(     B"`u   X  0A?`m^  6^  6^  6H  0޽h ? ̙33y___PPT10Y+D=' = @B +  0L0 Pl(     <h"`r   XB  0D`X  0A?`m  <l SFROM A VARIETY OF ALGEBRAIC EQUATIONS TO A UNIFORM SYSTEM OF DIFFERENTIAL EQUATIONS<T= 3 33  T< ? 'EEXAMPLE: Determine the rate constant k1 and k-1 for A + B ABF33333333pB  H DjJ?pjB  B D?0    T` ?$  IALGEBRAIC EQUATIONS   T ?0e  LDIFFERENTIAL EQUATIONSpB   H D? @0 pB  @ H D?<@0<   TD ? 80 Lk1.  H ?l@`@ Mk-1.~  H A ?"`^4 ~  H A ?"`` ' M  H  ?6  d[A]/dt = -k1[A][B] + k-1[AB]   M  H ?   d[B]/dt = -k1[A][B] + k-1[AB]   l  H ? 6   <d[AB]/dt = +k1[A][B]  k-1[AB]   z p@    @ p ,$D  0rB  B D?p@ @   T( ?  ^Applies only when [B] >> [A]&  T- ?4    ^Applies under all conditions&  T  V?"` ,$D 0H  0޽h ? ̙33og___PPT10G+dD+' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+?  0L0   A (     <9"`   XB  0D`X  0A?`m  <l=  l&THERE IS NO SUCH THING AS A FREE LUNCH*'& 33pB  H DjJ?jB  B D?`   TA ?`P  gALGEBRAIC MODEL<  pB   H DjJ?` 9   TF ?D` X  gcan be derived for any molecular mechanism can be derived automatically by computer can be applied under any experimental conditions can be evaluated without specialized software requires very little computation time does not always require an initial estimate is resistant to truncation and round-off errors has a long tradition: many papers published2hz   TN ?<`P  \- - - + + + + +* 3   TV ?`   A ADVANTAGE 3z `(T    `(T ,$D  0  T\ ?`( jDIFFERENTIAL MODEL<  $  Tb ?@T  + + + - - - - -f333  Z  8c?"`` @,$D 0H  0޽h ? ̙33___PPT10+ D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+H  0  ''(  x  c ${``   XB  0D`[z j   j ,$D 0;  0}J* T  G E + S ---> ES : k1 ES ---> E + S : k2 ES ---> E + P : k3 pH   3   `  0`   <Hpjf> JInput (plain text file):`B  0D C   <,$D 0  d[E ] / dt = X n   0@,$D  0  - k1 [E] [S]X   0A?`m   <   v0HOW DYNAFIT PROCESSES YOUR BIOCHEMICAL EQUATIONS*10 33R   s *A` JX  00` z     ,$D 0,  <   k1 [E] [S]`  0 z      ,$D 0  0TU z  k2 [ES]n 33333`  0  z l \   l  \ ,$D 0  0 v J  k3 [ES]n `  0l \  z  `@@  ` @@,$D 0`B  0D j @  <| ` 4 = Rate terms: `B  0D @z @`@  `@@,$D 0`B  0D@@@  <&`4 ARate equations:`B  0D@R   <0t ,$D   0 + k2 [ES] 33333N ! <L < ,$D   0 + k3 [ES]| D " < p ,$D  0 d[ES ] / dt = X  $z ,   #  , ,$D   0B $ 0<    + k1 [E] [S]& % <@,\ 0  - k2 [ES] 33333" & <8   - k3 [ES]|  ' <e p ,$D   0 PSimilarly for other species...H  0޽h ? ̙33++___PPT10*+vD)' e= @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 $+e``  e XB  0D`[z j   j ,$ 0;  0/eJ* T  G E + S ---> ES : k1 ES ---> E + S : k2 ES ---> E + P : k3 pH   3   `  0`   <lepjf> JInput (plain text file):`B  0D X   0A?`m   <9e  v0HOW DYNAFIT PROCESSES YOUR BIOCHEMICAL EQUATIONS*10 33R   s *A` JX   00` z      ,$ 0,  <=e   k1 [E] [S]`  0 z      ,$ 0  06e z  k2 [ES]n 33333`  0  z l \   l  \ ,$ 0  0He v J  k3 [ES]n `  0l \  z  `@@  ` @@,$ 0`B  0D j @  <Qe ` 4 = Rate terms: `B  0D @z @`@  `@@,$ 0`B  0D@@@  <Ye&`4 ARate equations:`B  0D@R  C *Alego-001`  <Sep ."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   (  x  c $ ne``  e XB  0D`X  0A?`m  <,pe DMASS ACTION LAW AND MASS CONSERVATION LAW IS APPLIED IN THE SAME WAY*ED 33  <ve  EKinetics (time-course) Equilibrium binding Initial reaction ratesFF  <|eM t  eOrdinary differential equations (ODE) Nonlinear algebraic equations Nonlinear algebraic equationsffLB  c $DP@LB   c $D     <Le X  B EXPERIMENT     <ȅe M  SDYNAFIT DERIVES A SYSTEM OF ...  LB  @ c $D`    Z e ?PX  Ychemistry biophysics(  3  Ze ? 0  @ enzymology H  0޽h ? ̙33y___PPT10Y+D=' = @B +   0L0 P |\(  |X | 0A?`m^ | 6^ | 6^ | 6j | BȚe "`P  Example 1: Inhibition of HIV protease  Tight binding inhibition constant from initial rates Use Kiapp values, not IC50 s} 7   d z   |   ,$D 0 | <e"`  2Wha t wrong with IC50 s ?0 t  | 68c"` H | 0޽h ? ̙33~___PPT10^+-|DB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(+  0 pP(  x  c $e`  e XB  0D`X  0A?`m   <$eP2  01. Inhibition constant 2. Apparent K i 3. IC50T1%    <4e  hDepends on [S] [E]2 ^B  6DjJP^B  6DjJ ^B   6DjJ    <e ,   NO YES YESX    <(e t ,   NO NO YESX    < EI&>0;H  0޽h ? ̙33y___PPT10Y+D=' = @B +  0 = 5  (  x  c $z`  z XB  0D`X  0A?`m^   6p   S A  ??#" `?   (   <z@p IC50 = (1.3 0.13) nMh^  6Jl j  j ,$D  0x   S A  ??#" `?   N  <zpjD  Ki* = (0.10 0.05) nM|$RB @ s *D8c@p RB @ s *D8cPP  <z N E Fitting model  <0z: >Resultl \ j`  \ j` ,$D  0N  <0z\ j0  Ki* = (0.10 0.05) nM|$  < zf `  ~E + I <==> EI : Ki*, l p@ p@,$D 0nb  0"`p@  <z  >10 x !H  0޽h ? ̙33!  ___PPT10 +D ' = @B D ' = @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<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*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<*+9  0 `Xp(  x  c $z`  z XB  0D`X  0A?`m  <zP   Apparent inhibition constant K i* is preferred over IC50 Modified Morrison equation is preferred over four-parameter logistic equation: A symbolic model (DynaFit) is equivalent and more convenient:     ?5   <ze  k5MEASURE OF INHIBITORY POTENCY MATHEMATICAL MODELS 663x  <A  ?f?@P     <4zf"` @   E + I <==> EI : Ki*,  H  0޽h ? ̙33y___PPT10Y+D=' = @B +  0 O(  x  c $z`  z XB  0D`X  0A?`m   <z Patrick Chne et al. (2009) "Catalytic inhibition of topoisomerase II by a novel rationally designed ATP-competitive purine analogue" BMC Chemical Biology 9:1s>) 3$X  0A?@Kf  0A?"`0   <"`   IC50 = [E]/2 + Ki*J   H  0޽h ? ̙33y___PPT10Y+D=' = @B +T   0 <40(  x  c $H`   XB  0D`X  0A?`m   <D& p Legitimate need for continuity structure of existing corporate databases Simple inertia ( fear of the unknown ) Lack of awarenessD.<pl &  & ,$D  0ZB   s *D|`   <x&   POSSIBLE SOLUTIONS: Gradual transition (report both IC50 and Ki* for a period of time) Re-compute historical data: Ki* = IC50  [E]/2u$   5   ,?6H  0޽h ? ̙33___PPT10+?]D|' = @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     (  x  c $Pd`   XB  0D`X  0A?`m  < i`   >Sometimes [E] must be optimized, but sometimes it must not be:J?    <Xp4 `Kuzmic, P., et al. (2000)  High-throughput screening of enzyme inhibitors: Simultaneous determination of tight-binding inhibition constants and enzyme concentration Anal. Biochem. 286, 45-50    <t   j Robust regression analysis (exclusion of outliers):66  <hV  Kuzmic, P. (2004)  Practical robust fit of enzyme inhibition data Meth. Enzymol. 383, 366-381` 4 ,D   <4 n  s'Serial dilution is not always the best:0(,   <   Kuzmic, P. (2011)  Optimal design for the dose response screening of tight-binding enzyme inhibitors Anal. Biochem. 419, 117-122 V lH  0޽h ? ̙33y___PPT10Y+D=' = @B +  0L0 n(     BHz"`0z    X  0A?`m^  6^  6^   6H  0޽h ? ̙33y___PPT10Y+D=' = @B +   0L0 (     B"`7     0 HA  ?"`0:   XB  0D`X  0A?`m'  <d QNOTE THE EXCELLENT REPRODUCIBILITY: THESE ARE TWO REPLICATES ON TOP OF EACH OTHERNR. 3 3 33^  6^  6^   6lz @Q   @Q,$D 0  2  `A  ? ? @Q  n   0f"`0  TB   c $Df0 0 TB  c $Df @H  0޽h ? ̙33~___PPT10^+HfDB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+a  0L0 / ' 0 (     B"`P    XB  0D`X  0A?`m^  6^  6^  6f  0A?"`l   6jJ"` l   6jJ"`l   6Ԕ"` o   <xǃ0  rStein, R.  Kinetics of Enzyme Action (2011), sect. 2.5.4:: l )  ) ,$D 0   <̃   BStandard curven  0"` U  <<҃ )  O1 M of product (5-HT) corresponds to an increase in fluorescence of 1919.9 RFUTP  6 L  <ڃ6 &STANDARD APPROACH: FIT A STRAIGHT LINE TO THE  INITIAL PORTION OF EACH CURVEpN 3  3 3 3 33\l  ps   ps ,$D 0d  0"` ps  :Fluorescence change expected at 10% conversion: ~ 1000 RFUv;        7t  6Z"`P 0 H  0޽h ? ̙33___PPT10+tD~' = @B D9' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+p  0L0   Pw (     B"`}    0 HA  ?"`0P  XB  0D`X  0A?`m  <z |4IS THIS A  STRAIGHT LINE ?, 33^  6^  6^   6z 0p    pF ,$D 0ZB   s *D0  ZB   s *D0ppxB   HDPpP   <   q1000 RFU 10% conversion B  s *D1`P ,$D 0B  s *DjJP ,$D 0  <\"` "V ,$D 0 hslope cannot change abruptly0z  V    V ,$D 0n2  0"`    <"`  V  "slope must be changing continously0#  H  0޽h ? ̙33___PPT10 +䐦D ' = @B DX ' = @BA?%,( < +O%,( < +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<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+8+0+0 +  0L0  ~ p (     B$"`   XB  0D`X  0A?`m  <@(  /A NONLINEAR MODEL OF COMPLETE REACTION PROGRESSN0 3  $ 33^  6^  6^  6   </"`@` n[task] data = progress task = fit [mechanism] E + S <==> ES : kas kds ES ---> E + P : kdp [constants] kas = 1000 kds = 100000 ? kdp = 1 ? [concentrations] E = 0.01 [responses] P = 100 ? [data] sheet B01.txt column 2 | offset auto ? | concentration S = 60 [output] directory .../output/fit-B01 rate-file .../data/rates/B01v.txt D(  R  tP    <?"`   S DYNAFIT INPUT*  nz  5P     5P ,$D 0   C `A *data-model-t013-g001Data and model P    <$@"`5 TDYNAFIT OUTPUT* n  0"` ` H  0޽h ? ̙33___PPT10+yD|' = @B D7' = @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<* +j  0L0 yq  (     B4W"`    XB  0D`X  0A?`m  <|U  /A NONLINEAR MODEL OF COMPLETE REACTION PROGRESSN0 3  $ 33^  6^  6^  6J   <\"`f ~ R [mechanism] E + S <==> ES : kas kds ES ---> E + P : kdp SS >(f2   0"`Pf   0A f?"`0 H  0޽h ? ̙33y___PPT10Y+D=' = @B +  0L0 { s  (     BPp"`   XB  0D`X  0A?`m  <k 8THE SLOPE OF THE PROGRESS CURVE DOES CHANGE ALL THE TIMEN9  3 3 33^  6^  6^  6   C `A *data-model-t013-g001Data and modelPP    C XA *deriv-time-t013-g001DerivativeP@     <y4< ? fluorescence:   <\`@   arate of change in fluorescence:&    <H @ Gt = 0: rate ~ 1.0X2  0 X2  0`   < 0  It = 600: rate ~ 0.8G  <"` ` q,$D  0 Y20 % drop in reaction rate over the first 10 minutes (less than 10% substrate conversion)$ZVH  0޽h ? ̙33___PPT10+C)D' = @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 +  0L0 x(     BX"`pv   X  0A?`m^  6^  6^  6  <, &H  b suitable for routine processing of many compounds mechanism is assumed to be known independentlyccH  0޽h ? ̙33y___PPT10Y+D=' = @B +#  0L0 2*0 (  X  0A?`m^  6^  6^  6  B "`  xExample 2: Inhibition of 5a-ketosteroid reductase  Slow, tight binding Model discrimination analysisi H  0޽h ? ̙33y___PPT10Y+D=' = @B +0  0L0 ?7p- (     B0"`+   XB  0D`X  0A?`m^  6^  6^  6   <  9E + IRB   s *D@ ! @RB @ s *Dp ! p  <P  QE.I  <ܴ 8 @ <slowXB  0D`  <   9E + IRB  s *D   RB @ s *DH  H   <Ǝ p  QE.I  <ɎX   <fastRB  s *D 1  RB @ s *DH 1 H   <PΎ {  RE.I*  <ӎX    <slowXB  0D `  * <׎| S P  b"etc. (several other possibilities)$# , <0ݎ4v GSlow binding proper - <tp f2Rearrangement of initial enzyme-inhibitor complex 33H  0޽h ? ̙33y___PPT10Y+D=' = @B +r  0L0 | t   (       B@"`   XB   0D`X   0A?`m    <$[ FANY NUMBER OF ALTERNATE KINETIC MODELS CAN BE COMPARED IN A SINGLE RUN>G 3C 33^   6^   6^   6   <Dp ([task] data = progress | task = fit | model = one-step ? [mechanism] E + S ---> ES : kaS ES ---> E + P : kdP E + I <==> EI : kaI kdI ... [task] data = progress | task = fit | model = two-step ? [mechanism] E + S ---> ES : kaS ES ---> E + P : kdP E + I <==> EI : kaI kdI EI <==> EJ : kIJ kJI ...89    ]    " &q!x!   <"`  fDYNAFIT INPUT SCRIPT FILE:0 ll P    P ,$D 0t   6|"`t   6|"`` P ^B   6D8c ` ^B   6D8c`^B   6D8c`H   0޽h ? ̙33~___PPT10^+E,DB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+  0L0 $(  $ $  B"`:    X $ 0A?`m^ $ 6^ $ 6^ $ 6 $ < &  Z model selection criteria (AIC, BIC) residual analysis use common sense to check results[[ 8H $ 0޽h ? ̙33y___PPT10Y+D=' = @B +5   0 \T(  x  c $*`   XB  0D`X  0A?`m  <, ~<Benefits of using DynaFit in the study of enzyme inhibition:&=5  <1\@   No mathematical models, only symbolic models (E + I <==> EI) Everybody can understand this. This prevents making mistakes and facilitates  transfer of knowledge . Automation Can be used to process 1000 s of compounds in a single run. Automatic model selection (Bayesian Information Criterion). No restrictions on experimental design Not necessary to have large excess of inhibitor ( tight binding ) No restrictions on reaction mechanism Any number of interactions and molecular species(k &G'4:H  0޽h ? ̙33y___PPT10Y+D=' = @B +  0 D<(  x  c $H`   XB  0D`X  0A?`m  <TL z8Free support from BioKin Ltd included with site license:&9 -n  <Qb   Periodic data review via email Send your raw data, get results back in 72 hours (in most cases). Phone support Call +1.617.209.4242 any time during US (EST) business hours. Periodic on-site  DynaFit course Once a year (either in the Fall or Spring); one-day workshop format. Free upgrades DynaFit continues to evolve (e.g.,  Optimal Experimental Design )wAEC!N EH  0޽h ? ̙33y___PPT10Y+D=' = @B + 0 T(  d  c $4     s *I49 f   >@  H  0ηo~ ? ̙33, 0 |(  d  c $4     3 rss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 r|Ēss49 f    H  0ηo~ ? ̙33, 0  |(  d  c $4     3 r(ʒss49 f    H  0ηo~ ? ̙33, 0 @|(  d  c $4     3 rss49 f    H  0ηo~ ? ̙33, 0 `|(  d  c $4     3 rdԒss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 r,ڒss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 r Ւss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 r`ss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 r0ss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 rss49 f    H  0ηo~ ? ̙33, 0  |(  d  c $4     3 rdss49 f    H  0ηo~ ? ̙33, 0 @|(  d  c $4     3 r,ss49 f    H  0ηo~ ? ̙33, 0 `|(  d  c $4     3 r ss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 rss49 f    H  0ηo~ ? ̙33, 0 |(  d  c $4     3 r ss49 f    H  0ηo~ ? ̙33, 0  |(   d   c $4      3 rss49 f    H   0ηo~ ? ̙33, 0 (|(  (d ( c $4    ( 3 rtss49 f    H ( 0ηo~ ? ̙33, 0 `|(  d  c $4     3 r<ss49 f    H  0ηo~ ? ̙33  0   < (  d  c $4      s *49 f   & Points to make: Ki is the best, but laborious to get (need to vary both [S] and [I]). Kiapp is the next best. It "costs" as much as getting IC50 (vary [I] only), but is more informative than IC50 (does not depend on [E]). Of these three, IC50 is the least appropriate measure of potency, because... ... for tight binding inhibitors, IC50 shifts with [E]! That means, with a new protocol, a new staff person who changes [E] for some reason, in a different lab, etc., everyone will be getting a different IC50 for the same tight binding inhibitor (e.g., staurosporine) under otherwise identical conditions! Remember, "tight binding" has nothing to do with any particular value of Ki (picomolar, nanomolar, etc.). "Tight binding" is not a property of an inhibitor, but rather a characteristic of experimental conditions: whenever [E] is numerically close to Ki. For example, an inhibitor with Ki = 1 mM is "tight binding" when [E] = 500 nM (this could happen, if your substrate is really slow).@@    F     4   1   .   ^       Q  M           #    ' *   >Y v /H  0ηo~ ? ̙33z 0 :2(  d  c $4   &  s *U49 f   Points to make: How prevalent is tight binding? For how many compounds is IC50 really meaningless? This is a histogram of Kiapp for 10,000+ compounds. Two groups of compounds, centered at about 200 mM and 6 mM, respectively. About 400 (or 4%, or one in 25) are "tight binding", so for one compound out of 25, the IC50 has no meaning. @E@ @   .     H  \     }H  0ηo~ ? ̙33X 0 (  d  c $4     0y 49 f   Points to make: Can't fix the problem by the "nave" method: 1. Measure IC50 as usual (four-parameter logistic) 2. Subtract [E]/2 from resulting IC50. PROBLEM! The Kiapp is negative, which is a nonsensical result. We never know exactly what the enzyme concentration really is, so that's why the above "nave" method fails. __________________________ If there is time: Physical meaning of parameters in the four-parameter logistic equation: The Hill exponent (nHill = 1.4 in this case) has not physical meaning at all for a tight binding inhibitor. We do know independently that this compound is very "clean" mechanistically, with exactly 1:1 stoichiometry, a pure competitive inhibitor. The value nHill = 1.4 simply means that the original Hill equation (transformed into the "four parameters logistic") was derived under the assumption that no tight binding occurs! In other words, the basic assumptions of the four-parameter logistic equation are violated. It should not be used for tight binding..@@ A   J        <  t  ^           >%+H  0ηo~ ? ̙33 0 *(  d  c $4     s *49 f   fPoints to make: Here is how to fix the problem: - forget about IC50's completely - forget about the four-parameter logistic equation (4PLE) Instead of 4PLE, use a modification of the Morrison equation (paper #1 above). This will get you the Kiapp directly (it is, of course, positive). As a bonus, you may learn what your enzyme concentration really was. The conditions under which this simultaneous determination of [E] and Kiapp is possible are described in paper #2 above. In this case, the enzyme appears about 65% active (4.5 nM actual concentration, as opposed to 7.0 nM nominal concentration). ^@U@ 7   w  +       0  T         i  $   ,H  0ηo~ ? ̙33o 0 /'(  d  c $4     s *lҠ49 f   EPoints to make: Summarize: Let's stop talking about IC50's completely, and move to apparent inhibition constants (Kiapp) as the most basic measure of inhibitory potency. For (in this case) 95% of compounds, IC50 and Kiapp are the same number, but for the 5% of "tight binders", they are not. I call this the "modified Morrison" equation, because the original equation (Williams & Morrison, 1979) does not have background rate term (Vb). Not knowing [E] exactly is not a problem, because of an interesting "circular logic" situation: - If you can't determine [E] from the data, it does not matter, because under those circumstances [E] does not affect Kiapp ("classical" or weak binding). - If [E] is in fact important in the sense that it could affect your Kiapp ("tight binding") then you can determine it from the data. @4@@ *   ;     \                     -    2        ucdyH<H  0ηo~ ? ̙33, 0  |(  d  c $4     3 rss49 f    H  0ηo~ ? ̙33o 0 /'(  d  c $4     s *(49 f   EPoints to make: Summarize: Let's stop talking about IC50's completely, and move to apparent inhibition constants (Kiapp) as the most basic measure of inhibitory potency. For (in this case) 95% of compounds, IC50 and Kiapp are the same number, but for the 5% of "tight binders", they are not. I call this the "modified Morrison" equation, because the original equation (Williams & Morrison, 1979) does not have background rate term (Vb). Not knowing [E] exactly is not a problem, because of an interesting "circular logic" situation: - If you can't determine [E] from the data, it does not matter, because under those circumstances [E] does not affect Kiapp ("classical" or weak binding). - If [E] is in fact important in the sense that it could affect your Kiapp ("tight binding") then you can determine it from the data. @4@@ *   ;     \                     -    2        ucdyH<H  0ηo~ ? ̙33  0   < (  d  c $4      s *֡49 f   & Points to make: Ki is the best, but laborious to get (need to vary both [S] and [I]). Kiapp is the next best. It "costs" as much as getting IC50 (vary [I] only), but is more informative than IC50 (does not depend on [E]). Of these three, IC50 is the least appropriate measure of potency, because... ... for tight binding inhibitors, IC50 shifts with [E]! That means, with a new protocol, a new staff person who changes [E] for some reason, in a different lab, etc., everyone will be getting a different IC50 for the same tight binding inhibitor (e.g., staurosporine) under otherwise identical conditions! Remember, "tight binding" has nothing to do with any particular value of Ki (picomolar, nanomolar, etc.). "Tight binding" is not a property of an inhibitor, but rather a characteristic of experimental conditions: whenever [E] is numerically close to Ki. For example, an inhibitor with Ki = 1 mM is "tight binding" when [E] = 500 nM (this could happen, if your substrate is really slow).@@    F     4   1   .   ^       Q  M           #    ' *   >Y v /H  0ηo~ ? ̙33   0   < (  d  c $4      s * 49 f   & Points to make: Ki is the best, but laborious to get (need to vary both [S] and [I]). Kiapp is the next best. It "costs" as much as getting IC50 (vary [I] only), but is more informative than IC50 (does not depend on [E]). Of these three, IC50 is the least appropriate measure of potency, because... ... for tight binding inhibitors, IC50 shifts with [E]! That means, with a new protocol, a new staff person who changes [E] for some reason, in a different lab, etc., everyone will be getting a different IC50 for the same tight binding inhibitor (e.g., staurosporine) under otherwise identical conditions! Remember, "tight binding" has nothing to do with any particular value of Ki (picomolar, nanomolar, etc.). "Tight binding" is not a property of an inhibitor, but rather a characteristic of experimental conditions: whenever [E] is numerically close to Ki. For example, an inhibitor with Ki = 1 mM is "tight binding" when [E] = 500 nM (this could happen, if your substrate is really slow).@@    F     4   1   .   ^       Q  M           #    ' *   >Y v /H  0ηo~ ? ̙33o  0 /'(  d  c $4     s *LC49 f   EPoints to make: Summarize: Let's stop talking about IC50's completely, and move to apparent inhibition constants (Kiapp) as the most basic measure of inhibitory potency. For (in this case) 95% of compounds, IC50 and Kiapp are the same number, but for the 5% of "tight binders", they are not. I call this the "modified Morrison" equation, because the original equation (Williams & Morrison, 1979) does not have background rate term (Vb). Not knowing [E] exactly is not a problem, because of an interesting "circular logic" situation: - If you can't determine [E] from the data, it does not matter, because under those circumstances [E] does not affect Kiapp ("classical" or weak binding). - If [E] is in fact important in the sense that it could affect your Kiapp ("tight binding") then you can determine it from the data. @4@@ *   ;     \                     -    2        ucdyH<H  0ηo~ ? ̙33o  0 /'(  d  c $4     s *0{49 f   EPoints to make: Summarize: Let's stop talking about IC50's completely, and move to apparent inhibition constants (Kiapp) as the most basic measure of inhibitory potency. For (in this case) 95% of compounds, IC50 and Kiapp are the same number, but for the 5% of "tight binders", they are not. I call this the "modified Morrison" equation, because the original equation (Williams & Morrison, 1979) does not have background rate term (Vb). Not knowing [E] exactly is not a problem, because of an interesting "circular logic" situation: - If you can't determine [E] from the data, it does not matter, because under those circumstances [E] does not affect Kiapp ("classical" or weak binding). - If [E] is in fact important in the sense that it could affect your Kiapp ("tight binding") then you can determine it from the data. @4@@ *   ;     \                     -    2        ucdyH<H  0ηo~ ? ̙33o  0 /'@(  d  c $4     s *49 f   EPoints to make: Summarize: Let's stop talking about IC50's completely, and move to apparent inhibition constants (Kiapp) as the most basic measure of inhibitory potency. For (in this case) 95% of compounds, IC50 and Kiapp are the same number, but for the 5% of "tight binders", they are not. I call this the "modified Morrison" equation, because the original equation (Williams & Morrison, 1979) does not have background rate term (Vb). Not knowing [E] exactly is not a problem, because of an interesting "circular logic" situation: - If you can't determine [E] from the data, it does not matter, because under those circumstances [E] does not affect Kiapp ("classical" or weak binding). - If [E] is in fact important in the sense that it could affect your Kiapp ("tight binding") then you can determine it from the data. @4@@ *   ;     \                     -    2        ucdyH<H  0ηo~ ? ̙33x] xTE{{_[ D6DaG JHfHBQ&ӧ,ʢ8>t\pGq|fupTD ېwKs:UZNss'_[D guD(Xڙf$/?߀3 v$SJZRG' [)sv=Ε?O?O?ĺ1BoK=j[~Y+QE!)5dY~'6T}K~JdЂyv~A{ '2z?w0,G!=_t!` D 1au&:' Ht\ Nh$.\00Ⱦ#)TP@``8``$``4` jBcB&L"t^B:i t@&`kYm?C_&<.GSFxz98Ε?OӃ1~wX0`,N!CʥhPό}sxRAO?)UA/q^}M@)q*$o[-"XKʈh+R)ʲОR+K_,;Wvy69o˼xS]ryGNRiw~Ǥk*h)BFK'd,_E*\}sebJҼ%iWzei_˞6Ѽԋ ,R.>ayC.>$O5}vvoLi9F6AZzIHC88$' v[|7ݽ6>9.s۽*+VVwCC`^w0m?ߖǛAoU.W\>tW-kEֻ]|>4Zi"he[>%j%ނ@2'b}8?{O *W0TV~-<],W G91NOm|n<}> ψͧ?; sUw|:vTV[\ʉ!Suj굪a> T_WFru!;*w7w0U]kUߪ81{NWta(PW s'ka8>VS}fTYm0S|m> 4 Dke6a6'C^ެq>ËP{=|hlohaQ0{W|np`^=> Jrܦ9M|ʌݚ70b|Φ|~0Ia:0'ie(&5 SU8&_KV0|h9fjnzAe~ӼsʴÇaygzOo {ͯzl sWHxm/䄇cZ&x|v$lIa8p{ ~{N֝[}o0lj嶯|֯81LYo||w؆|٪? 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