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(                      &1:D>phs?"-(./H&D$        5    ,*&:#$c+    D# (#'609 <e>02  9"7G55H#;  #&  (#  (0 '9  8  4 F#* "#,1  $-wI  "&-h7+4 d e-mE   2+! 21!4 [ $!   & "#  ! .!!H\# &20<OEaAO#?&        2$"Zlѫ|g"7Rb$a?Rb$ =ܰMi_q2rZPdo2$0&f-K̽eL"}]b$$k@8{0f}DPb$G9khWqY{-b$D o%pACK{342$:3hf (vX|!hb$g A-#gl j2$AMց7c֧oOCv2$uBT[L4vz2$~g]wb޹ !V2$ =M.4v͙#b$#RhSۉ~/j#b$d>.+ Vwb$ /h?|]x+a&b$?`]{JhM7b$!ݺ| b$J77ih+s!> b$'t83z] b$'!hQa*qwm:\b$Ԛ'~KۤDW$LYb$lby QS phb$1T4L+^*|v{b$n5 S:b$SȉwzO751b$"kgb1=M%(8b$S1)`ҮYЄh:]b$&LN`@pb$P9%f|P],b$f\ʪ&]1b$ؕsb$`슃۽~$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$b$F']#%<f, 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 333f33@dg4kdkd, x: 0ppp@  <4!d!d@ 0t<4BdBd@ 0tg4dddd" x: 0Pp poO ʚ;Xm8ʚ;<4dddd@U 0@r0___PPT10 2___PPT9/ 0?T, @BKEB Lec 3: Equilibrium - TheoryO =+  }Lecture outlineJt+Matrix representation of complex equilibria,,M?4 Complexes and  elements  \%Illustrative example: Arginine kinase,&%WzFormula matrix, F: XStoichiometric matrix, S: ^'Definition: Complex formation constants,('_Complex stability matrix, B: `5Complex stability matrix: Ambiguity in case of cycles:6$KuThermodynamic cycles]&Thermodynamic  box ,a&Thermodynamic boxes in the literature ''1i^DynaFit notation to  close the boxes properly 000hMultiple thermodynamic cyclesLv+Equilibrium composition of complex mixtures,,V/Composition of complex mixtures at equilibrium 00MwEquilibrium matrices in DynaFit $b/Why should you care about matrices in DynaFit ?00%c#Stoichiometric matrices in DynaFit $$&dFormula matrices in DynaFit 'e3Formula matrices: Sometimes not completely obvious 44,fStability matrices in DynaFit -g3Formula matrix derivation: how does DynaFit do it? 64Nx`Equivalent binding sites &  statistical factors 114jbEquivalent binding sites &  statistical factors 225k12 Equivalent binding sites: Equilibrium constants226l13 Equivalent binding sites: Equilibrium constants22Oy Nonspecific binding interactions!!7m'Nonspecific binding: How to identify it((8n1Nonspecific binding: How to analyze it in DynaFit229o#Nonspecific binding: Example - data$$:pVNonspecific binding: Example  input script,,;qZNonspecific binding: Example  results of fit..<r0Nonspecific binding: Sometimes it can be ignored61" =sSummary and conclusions/~!N ()*+./23>?@ABCDEFGPQRSTUX   0` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> <4(    6O  P   T Click to edit Master title style! !  0R     RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0HX  ``   X*  0H]  `    l*(    0d  `    `* H  0޽h ? ̙33 Default Design 0 P4 (  4 4 N y y .    p* a00aa 4 N@ y y 3 .   r* a00aad 4 c $ ?   4 4 N@ y y 9 f   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  4 T y y r    p* a00aa 4 T y y r3    r* a00aaH 4 0ηo~ ? ̙3380___PPT10.| >X \x(  \ \ N ]e]e     p* AAA \ N ]e]e %    r* AAA  \ Td# ]e]e     p* AAA \ T ]e]e %    r* AAAH \ 0ηo~ ? ̙3380___PPT10.|  0  @ (   X  0A?`m(  6z  p XBinding and Kinetics for Experimental Biologists Lecture 3 Equilibrium binding: TheoryNY0    <\ /  (Petr Kuzmi , Ph.D. BioKin, Ltd. WATERTOWN, MASSACHUSETTS, U.S.A.hB    7p  H A ? ` ~  H A] ?"` )9  Z  ?5U GI N N O V A T I O N L E C T U R E S (I N N O l E C)LH&    H  0޽h ? ̙33y___PPT10Y+D='  = @B +   0L0 *"3P (  P r P S b `    XB P 0D`X P 0A?`mH 3P  ` ?"0@NNN?N_  Theory of equilibrium binding analysis - matrix representation of simultaneous equilibria stoichiometric matrix formula matrix stability matrix - composition of complex biochemical mixtures: numerical method - thermodynamic cycles: inconsistent equilibrium mechanisms - multiple equivalent sites: statistical factors - nonspecific binding: representation as a single  weak binding site Applications in DynaFit scripting - Representing equilibrium binding mechanisms in DynaFit |3"       2(0 3 8 @`H P 0޽h ? ̙33y___PPT10Y+D='  = @B +   0L0 (  r  S  0     H  0޽h ? ̙33y___PPT10Y+D='  = @B +:  0L0 x'p' -Z &(   x  c $! `    XB  0D`X  0A?`m  <# +  m'TWO DISTINCT TYPES OF MOLECULAR SPECIES*(' 33  Z?"0@NNN?N '  `) ?"0@NNN?N[  ? Protein + DNA B ( TD?"0@NNN?N  B ) @ TD?"0@NNN?N   *  `N ?"0@NNN?N["  W Protein.DNA   8   B [  +  Z?"6@`NNN?N@ ,  Z?"6@`NNN?N  -   ` Q ?"0@NNN?N5`  >elements  %8 @   C [@  .  Z?"6@`NNN?N@    /   `= ?"0@NNN?N{   =complex 3/ 0  `A ?"0@NNN?N   g%Example 1: protein / DNA interactions&&   | :  `Dg ?"0@NNN?N ],$ 0 >Example 2: enzyme kinetics (partial noncompetitive inhibition)&?  4 l c  X  c ,$D 0 ;   `dV ?"0@NNN?N6   7E + S B <  TD?"0@NNN?N` ` B = B TD?"0@NNN?N   >   `T ?"0@NNN?N   4ES B @  TD?"0@NNN?N8 r X r  A   `j ?"0@NNN?NZ   7E + P B F  TD?"0@NNN?N  B G TD?"0@NNN?Np p " H   `@j ?"0@NNN?N   REI + S  I   ` ?"0@NNN?Nc p  5+ I B J  TD?"0@NNN?N- - B K B TD?"0@NNN?N] ]  L   `, ?"0@NNN?N  (  OESI B M  TD?"0@NNN?N8 ? X ? " N   `w ?"0@NNN?NZ  REI + P B O  TD?"0@NNN?N  B P TD?"0@NNN?N] ]  Q   `{ ?"0@NNN?NP ]  5+ I l  t :!  Y t :! ,$D  0 S   ` ?"0@NNN?N t !  ? elements:   U   ` ?"0@NNN?Nt :!  @ E, S, I, P  l  c   Z c  ,$D  0 T   ` ?"0@NNN?N d R  @ complexes:  3E V   `| ?"0@NNN?Nc   u ES, EI, ESI  3, W  `x ?"6@`NNN?N L,$D  0 @number of species = number of elements + number of complexesA         H  0޽h ? ̙33___PPT10+3DJ'  = @B D' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*: %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X %(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Y %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*Y D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Y Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Z %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*Z D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Z D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*W %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*W D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*W +p+0+: 0 ++0+W 0 +  0L0   ((  x  c $ `   XB  0D`X  0A?`m  <  `PHYSIOLOGICAL IMPORTANCE, 33  B ?"6@ NNN?N  B ?"6@ NNN?N  B ?"6@ NNN?N  N  ?"6@ NNN?N @ VArchives of Insect Biochemistry and Physiology 57, 166-77 (2004) Brown AE, Grossman SHNW.   & T   N  ?"6@ NNN?N   dL The kinetic mechanism and evaluation of several potential inhibitors of purified arginine kinase from the cockroach (Periplanta americana) were investigated. This monomeric phosphagen kinase is important in maintaining ATP levels during the rapid energy demands of muscle required for contraction and motility. [...] Arginine kinase could be a useful chemotherapeutic target for the control of cockroach proliferation. 1   f K "  tR    aZ  B8F  ?"6@ NNN?N0@ L"Phosphagen kinases catalyze the reversible transfer of a high-energy phosphoryl group from phosphorylated guanidino storage compounds known as phosphagens to ADP in the following general reaction: phosphagen + MgADP + H+ guanidino acceptor + MgATP. These reactions are typically found in cells that display high and variable rates of energy turnover, such as muscle fibers, neurons, spermatozoa and transport epithelia"      C    ;   +     BXX  ?"6@ NNN?N @ NJournal of Experimental Biology 206, 1545-1556 (2003) Compaan DM, Ellington WRNO   , ,6H  0޽h ? ̙33y___PPT10Y+D='  = @B +  0L0 X(  x  c $d `    XB  0D`X  0A?`m  <  ;DESCRIBES THE COMPOSITION OF COMPLEXES IN TERMS OF ELEMENTS,<; 33=  <d  ?"6@ NNN?N Example: Arginine Kinase<     g  H  ?"6@ NNN?N&0 %J. Exper. Biol. 206, 1545-1556 (2003)N&    D  H  ?"6@ NNN?N~  ArgP + ADPN     B   HD?"0@NNN?NB  @ HD?"0@NNN?NMM!   H8  ?"6@ NNN?NP} k Arg + ATP,      H& ?"0@NNN?NT 9[E]    < V?"6@`NNN?N@`   B ?"6@ NNN?N  B ?"6@ NNN?NYz 0r`  0r,$D 0  BA ?"6@ NNN?Nr`  H1  ?"6@ NNN?N` :  Relements.   3  Hp%  ?"6@ NNN?N0   A complexes  3  B ?"6@ NNN?NTz n  [  n ,$D  0  H<:  ?"6@ NNN?N  \ ;... E   H>  ?"6@ NNN?N*  `... ArgP    HB  ?"6@ NNN?N } =... ADP   H\h  ?"6@ NNN?N Z _... Arg   Hl  ?"6@ NNN?N*- =... ATP x  S A 7??#" `?n P[ 7H  0޽h ? ̙33___PPT10+3:Dg' = @B D"' = @BA?%,( < +O%,( < +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?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+  0L0 D< `(  x  c $8 `    XB  0D`X  0A?`m  <H S  /DESCRIBES INDIVIDUAL REACTIONS IN THE MECHANISMN0 3  3 33= Q <  ?"6@ NNN?N Example: Arginine Kinase<      R H  ?"6@ NNN?N& 1Arch. Insect. Biochem. Physiol. 57, 166-77 (2004)N2    , S 6A ?"6@ NNN?NPIz l PP ]PP,$D 0 T NA ?"6@`NNN?NP N Kd1, U N8 ?"6@`NNN?N N Kd4, V N ?"6@`NNN?NP0 N Kd3, W N ?"6@`NNN?N0r N Kd2, X N ?"6@`NNN?Nr P N Kd5, Y ND ?"6@`NNN?Nc   N Kd8, Z N ?"6@`NNN?Np 0  KKd7, [ N ?"6@`NNN?Nc0 KKd6,4 \ N ?"6@`NNN?N^P  p Keq,Ol m `m,$D 0 ^ BA ?"6@ NNN?N`m _ H^  ?"6@ NNN?Np A  ]reactants products.   H  0޽h ? ̙33d\___PPT10<+#D '  = @B D' = @BA?%,( < +O%,( < +D'' =%(D' =%(Dw' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<*]%(D' =-6B'blinds(horizontal)*<3<*]D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bdissolve*<3<*`+*6  0L0 $%% %>$(  x  c $h `    XB  0D`X  0A?`m  <j  JOVERALL EQUILIBRIUM CONSTANT = PRODUCT OF SEQUENTIAL EQUILIBRIUM CONSTANTS,KJ 33  H2  ?"6@ NNN?N/d  PTwo sequential reaction with known Kd s:B)$   #   H7  ?"6@ NNN?NB SABB  TD?"0@NNN?NRB @ ND?"0@NNN?N@R@  Hp>  ?"6@ NNN?N  ;A + B   <0  ?"6@ NNN?N  aKd1BC  HI  ?"6@ NNN?N (p Kd1 = [A][B]/[AB]>   HN  ?"6@ NNN?N UABCB  TD?"0@NNN?N|R|B @ ND?"0@NNN?NR    HtT  ?"6@ NNN?N:  WAB + C  ! <Y  ?"6@ NNN?NL aKd2BH " H(P  ?"6@ NNN?N ? Kd2 = [AB][C]/[ABC]>l @p  =/ ,$D 0B # HD?"0@NNN?N@Y $ N$   ?"6@ NNN?N p  ABCZ  B % ZD?"0@NNN?N 4 B &B TD?"0@NNN?N, 4,  ' N|  ?"6@ NNN?N] ` p  ? A + B + C 3 ( B"  ?"6@ NNN?N 1  {KdTBa ) N!  ?"6@ NNN?Ny +\  KdT = [A][B][C]/[ABC]>$ 0 N|q  ?"6@ NNN?N $  TTotal dissociation constant:  2 Hu  ?"6@ NNN?N  ,$ 0 KdT = Kd1 Kd2333333333 z  )p  4  /x,$D 0 5 H  ?"6@ NNN?N p  ? A + B + C B 6 TD?"0@NNN?N S B 7B ND?"0@NNN?N, S,  8 H  ?"6@ NNN?N| V p  UABC- 9 <؅  ?"6@ NNN?N3 P  {KaTB[ : Hh  ?"6@ NNN?Ny )\  KaT = [ABC]/[A][B][C]>$ ; H@  ?"6@ NNN?N   SComplex stability constant:  < H  ?"6@ NNN?N  ,$ 0 ,KA = 1 / ( Kd1 Kd2 )33 333333333H  0޽h ? ̙33___PPT10n+7;9=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@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =-o6Bdissolve*<3<*2Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<+p+0+20 ++0+<0 +(  0L0 =(  x  c $  `    XB  0D`X  0A?`m  <x  DESCRIBES OVERALL STABILITY CONSTANTS OF COMPLEXES IN TERMS OF BINARY Kd sNKG 3 3 33F=  <  ?"6@ NNN?N Example: Arginine Kinase<       HL   ?"6@ NNN?N& 1Arch. Insect. Biochem. Physiol. 57, 166-77 (2004)N2    ,  6A ?"6@ NNN?NPIT F PP   PP   Nh ?"6@`NNN?NP N Kd1,   N" ?"6@`NNN?N N Kd4,   N8. ?"6@`NNN?NP0 N Kd3,   N2 ?"6@`NNN?N0r N Kd2,  N6 ?"6@`NNN?Nr P N Kd5,  N@; ?"6@`NNN?Nc   N Kd8,  N9 ?"6@`NNN?Np 0  KKd7,  ND ?"6@`NNN?Nc0 KKd6,4  N@I ?"6@`NNN?N^P  p Keq,  BA ?"6@ NNN?N0 @ ,$D 0l p aP   paN ,$D 02  B ?"6@`NNN?N P B  TD?"0@NNN?Np    HG  ?"6@ NNN?N aP  &KA = 1/ (Kd7 Kd8)33333333  B ?"6@ NNN?N  s ,A %??#" `? ^ 8 %$D  0  NV ?"6@`NNN?N@,$D  0 =Can you spot anything suspicious about this stability matrix?<>  ( H  0޽h ? ̙33___PPT10z+&!D&' N = @B D' = @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<*%(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<*+8+0+0 +  0L0 0%[(  x  c $e `    XB  0D`X  0A?`m  <g  5TWO WAYS TO DEFINE THE STABILITY OF A TERNARY COMPLEX>6 3- 33=  <|n  ?"6@ NNN?N Example: Arginine Kinase<       Hs  ?"6@ NNN?N& 1Arch. Insect. Biochem. Physiol. 57, 166-77 (2004)N2    ,  6A ?"6@ NNN?N0) T F PP   0    N} ?"6@`NNN?NP N Kd1,   N ?"6@`NNN?N N Kd4,   N ?"6@`NNN?NP0 N Kd3,   N ?"6@`NNN?N0r N Kd2,  N ?"6@`NNN?Nr P N Kd5,  N ?"6@`NNN?Nc   N Kd8,  N ?"6@`NNN?Np 0  KKd7,  Nğ ?"6@`NNN?Nc0 KKd6,4  N̤ ?"6@`NNN?N^P  p Keq,  B ?"6@ NNN?N  N| ?"6@`NNN?N   B  l @@  !@@ ,$D 0B  ZDԔ?"0@NNN?N@ 0 B  ZDԔ?"0@NNN?N0 @0    H  ?"6@ NNN?N ` 4  (KA = 1 / (Kd4 Kd2) l @  %@ ,$D 0B " ZDԔ?"0@NNN?N@@ B # ZDԔ?"0@NNN?N@ $ Hd  ?"6@ NNN?N  (KA = 1 / (Kd3 Kd1)33 3333333H  0޽h ? ̙33___PPT10+I D~'  = @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<*%%(+  0L0   (  x  c $ 0     H  0޽h ? ̙33y___PPT10Y+D='  = @B +s  0L0    (  x  c $ `    XB  0D`X  0A?`m*  <  BOVERALL EQUILIBRIUM CONSTANTS AROUND A CYCLE MUST BE EQUAL TO 1.00`C' 3 3 3 33  6A ?"6@ NNN?N0 l     ,$D 0P  HD  ?"6@ NNN?N P  Kd1 Kd2d B  ND?"0@NNN?N@ P   H  ?"6@ NNN?N P  Kd3 Kd4d    H   ?"6@ NNN?N `  R= 1.320     H  ?"6@ NNN?N `  Z 1.002 3 3   NԮ  ?"6@ NNN?N0=m 1Arch. Insect. Biochem. Physiol. 57, 166-77 (2004)P2    ,E   H7  ?"6@ NNN?N00G 7Numerical values of binary dissociation constants (mM):88 3Q  NX ?"6@`NNN?N ] ,$D  0 a+This thermodynamic box is not quite closed!,, H  0޽h ? ̙33___PPT10+x|:Dt'  = @B D/' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*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<*+8+0+0 +  0L0   P G (  x  c $ ``    XB  0D`X  0A?`mn  <  THIS THIS NOT A  MADE UP ISSUE: ERRONEOUSLY CLOSED BOXES ARE IN FACT FOUND!NM! 3 3 3 3  TA?"6@`NNN?N    `<" ?"6@`NNN?N` Z Dinosine 5'-monophosphate dehydrogenase Biochemistry 38, 2295 (1999)BE(     >v   `) ?"6@`NNN?NF`,$D  0 tKeq 1 !, 33 z P      P ,$D  0   TA ?"6@`NNN?NP     `0/ ?"6@`NNN?N @  Ecalmodulin / plasma membrane Ca2+ pump Biochemistry 42, 12115 (2003)dF        <v    `L> ?"6@`NNN?N  t ,$D  0 tKeq 1 !, 33H  0޽h ? ̙33  ___PPT10g +/D '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* +p+0+0 ++0+ 0 +   0L0 < 4 ` @ (  @x @ c $M ``    XB @ 0D`X @ 0A?`m @ <O   q)COMES UP IN THE ANALYSIS OF KINETIC DATA,* 3 3 @ TA?"6@`NNN?N0/ i @  `lU ?"6@`NNN?N nY 1dihydrofolate reductase Science 239, 1105 (1988)N2      @ Z\ 3?"6@`NNN?N 0 ,$D  0 Z[constants] k1 = ... k2 = (k1 k3 k5 k7) / (k4 k6 k8) k3 = ... k4 = ... ...8[ 3z H$  @ H$,$D  00  @ Tf ?"0@NNN?N PH$ lLk2 = k1 k3 k5 k7 / k4 k6 k8 '33333333333333333333333333333  @ Z?"6@`NNN?NpH @ 0޽h ? ̙33aY___PPT109+]D'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =-m6Bbox(in)*<3<* @D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-m6Bbox(in)*<3<*@+8+0+@0 +  0L0   @8O (  8x 8 c $  ``    XB 8 0D`X 8 0A?`m 8 < Y  j"COME UP IN MORE COMPLEX MECHANISMS,#" 3 3 8 TA?"6@`NNN?N i 8  ` ?"6@`NNN?N > 1dihydrofolate reductase Science 239, 1105 (1988)N2       8 H  ?"6@ NNN?Nf SHow many cycles do you see? l @0  8@0 ,$D 0 8 Z?"6@`NNN?NP@ 8 Z?"6@`NNN?NP@@0  8 Z?"6@`NNN?N 8 H?"6@`NNN?NPp ,$D 0 8 H?"6@`NNN?N ,$D 0 8 H  ?"6@ NNN?Nt z n  @  8 Nؙ ?"6@`NNN?N  ,$D  0 enumber of constraints on rate / equilibrium constants = number of cycles in the reaction mechanism.f     $     H 8 0޽h ? ̙33___PPT10+@DJ'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bdissolve*<3<*8D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*8+8+0+80 +  0L0  @(  x  c $8 0     H  0޽h ? ̙33y___PPT10Y+D='  = @B +="  0L0  N(  ~  s *    XB  0D`X  0A?`m  <m   q+MATRIX FORMALISM - FREE ENERGY MINIMIZATION*,+ 33 10 C zA *? ?#" `?  *  c 3 Hs  ?"6@ NNN?N0  UFind a vector of species concentrations, c, that minimize the total Gibbs free energy<V)  , p 4 S A  +??#" `?  +p 8 S A  -??#" `?0 " - : H\{  ?"6@ NNN?NCq ;where p ; S A  .??#" `?@Uh . = H  ?"6@ NNN?N  b,subject to the mass-conservation constraints-- B > ND?"0@NNN?N 0 0 B ? ND?"0@NNN?N0 0 B @ ND?"0@NNN?N0 0 B A ND?"0@NNN?N B B ND?"0@NNN?NB C ND?"0@NNN?N E B ?"6@ NNN?Np D S A  /??#" `? ^  /l @  J @,$D  0 G T䅰  ?   4HRoyer, C.A.; Smith, W.R.; and Beechem, J.M. (1990)  Analysis of binding in macromolecular complexes: A generalized numerical approach Anal. Biochem., 191, 287-294.    3 T      >c H TT  ?@  2Royer, C.A. and Beechem, J.M. (1992)  Numerical analysis of binding data: advantages, practical aspects, and implications Methods Enzymol. 210, 481-505.j% V      >g I H  ?"6@ NNN?N@ 0  @DETAILS:  l @P  N@P ,$D  0 K H 8c?"6@`NNN?N0 WP  L B 8c?"6@`NNN?N{ M B 8c?"6@`NNN?N@H  0޽h ? ̙336 . ___PPT10 +V D ' = @B D ' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*JD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*JDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*N%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*ND' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*N+  0L0  `(  x  c $ 0    H  0޽h ? ̙33y___PPT10Y+D='  = @B +!  0L0 Z(  x  c $ `   XB  0D`X  0A?`m   <Y h DAT LEAST TO UNDERSTAND WARNING MESSAGES WHEN YOUR MECHANISM IS WRONG>E- 3 33~   `_ ?"0@NNN?N00 tExample of a  wrong mechanism: A closed thermodynamic box&; 3   `a ?"0@NNN?NtJH <    `h ?"0@NNN?Npw :M03   TA?"6@`NNN?N < ,$D  0zz +     +  ,$D 0    `jJ?"6@`NNN?N+      `4! ?"0@NNN?N`   Jinvalid mechanism! 3   TA?"6@`NNN?N  ,$D  0   `8c?"6@`NNN?N  ,$D 0  TA?"6@`NNN?N 0 ,$D  0   `4 ?"6@`NNN?N] ,$D 0 .DynaFit  understands that forming the ABC complex can legitimately involve only three unique equilibrium constants. It has decided to throw away Kac.`L ( 3  3 3 H  0޽h ? ̙33___PPT10+kbD1'  = @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<* %(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<*%(D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+0 +  0L0  <(  x  c $pF `   XB  0D`X  0A?`m"  <hH %  \ TABULAR TRANSCRIPT OF THE REACTION MECHANISM>/% 3  331   ` AB : Ka dissoc B + C <===> BC : Kc dissoc AB + C <===> ABC : Kca dissoc A + BC <===> ABC : Kac dissoc +    `* ?"0@NNN?N= BDynaFit input:    ` ?"0@NNN?N7 ,$  0 Stoichiometric matrix: as many rows as there are reactions as many columns as there are species entries reflect the stoichiometry of reactions negative entries represent  reactants positive entries represent  products (3     @`az    ,$D  0   TA?"0@NNN?N@P    `䴰 ?"0@NNN?N= CDynaFit output:     `l ?"6@`NNN?N ``9,$D 0 rWhat it means for you: Always check at least the species names (top row) and equilibrium constant names (leftmost column). This will assure that DynaFit  understood what you meant.@f  3< H  0޽h ? ̙33  ___PPT10i +ne,D '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +p+0+0 ++0+ 0 +j  0L0 ia (  x  c $Ͱ `   XB  0D`X  0A?`m#  <ΰ  =REACTING SPECIES ARE CLASSIFIED INTO COMPONENTS AND COMPLEXES^>% 3  3 3  33   `ڰ ?"6@`NNN?NJ 4 [mechanism] A + B <===> AB : Ka dissoc B + C <===> BC : Kc dissoc AB + C <===> ABC : Kca dissoc A + BC <===> ABC : Kac dissoc 333333+az n @  ` 2,$D  0  TA?"0@NNN?N @    `\ ?"0@NNN?Nn ?  CDynaFit output:      `H ?"0@NNN?N= BDynaFit input: 8    ` ?"0@NNN?N0 0 ,$  0 <*Formula matrix: as many rows as there are components as many columns as there are complexes entries reflect the composition ( formula ) of complexes3    @`    `x& ?"6@`NNN?N  ,$D 0 rWhat it means for you: Always check the  Model link in the output. Make sure that the formula matrix is derived correctly. This will assure that DynaFit  understood what you meant.R.  38 3< H  0޽h ? ̙33  ___PPT10i +-nD '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +p+0+ 0 ++0+ 0 +Y  0L0  -(   x   c $  `    XB   0D`X   0A?`mR   <  DYNAFIT IS FAIRLY GOOD AT  UNDERSTANDING WHAT IS A COMPLEX OR COMPONENT SPECIES*QP 33    `@ ?"6@`NNN?NJ  [mechanism] M1 + M2 <===> M3 : K1 dissoc M4 + M5 <===> M3 : K2 dissoc M4 + M6 <===> M1 : K3 dissoc M6 + M2 <===> M5 : K4 dissoc    ` ?"0@NNN?N]Z - JComponents: Complexes:    ` ?"0@NNN?NU I? ?*3     `" ?"0@NNN?N= BDynaFit input: az S     S  ,$D  0   TA?"0@NNN?N      `p& ?"0@NNN?NS  CDynaFit output: z vP    Pv ,$D  0+    `* ?"0@NNN?NP  [M6, M2, M4 M3, M5, M1* 3 B   TD?"0@NNN?N@@     `T/ ?"0@NNN?Nvi <  ABC X    `3 ?"6@`NNN?N | ,$D 0 VWhat it means for you: Always name your species  sensibly . This will assure that the formula matrix can be easily checked.@~&  3@ H   0޽h ? ̙33L D ___PPT10$ +rseD '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +8+0+ 0 +n   0L0 z((  (x ( c $hB `    XB ( 0D`X ( 0A?`m  ( <`D " EHERE IS WHERE DYNAFIT PUTS ANY WARNINGS ABOUT INCONSISTENT MECHANISMS>F. 3 331 (  `K ?"6@`NNN?NJ 4 c[mechanism] A + B <===> AB : Ka dissoc B + C <===> BC : Kc dissoc AB + C <===> ABC : Kca dissoc A + BC <===> ABC : Kac dissoc +  (  `T ?"0@NNN?N= BDynaFit input: az W  ( W ,$D  0  ( TA?"0@NNN?N P  (  `Y ?"0@NNN?NW = CDynaFit output: J  (  `` ?"0@NNN?N0  ,$  0 NStability matrix: as many rows as there are equilibrium constants in the mechanism as many columns as there are complexes entries reflect the total stability constants of complexes an empty row means a redundant step in the mechanism (e.g., a closed  box )3    ) @`Z  (  `X ?"6@`NNN?N O ,$D 0 XWhat it means for you: Always check the stability matrix for the presence of empty (shaded) rows. If any are found, see which redundant equilibrium constant was ignored by DynaFit. If you prefer to keep this constant, delete some other redundant step.>   z     (   ,$D 0 (  `>?"6@`NNN?N   (  `8 ?"0@NNN?N 0   KABC =Ka-1 Kca-1 33H ( 0޽h ? ̙33| t ___PPT10T +”\D '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-m6Bbox(in)*<3<*(D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =-m6Bbox(in)*<3<* (D' =%(D' =%(D@' =A@BB BB0B%(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<* (+p+0+ (0 ++0+ (0 +A  0L0  0 (  0x 0 c $ ``    XB 0 0D`X 0 0A?`mx 0 <  DYNAFIT  DOES A LOT OF LINEAR ALGEBRA AND  UNDERSTANDS A VERY NICE THEORY BOOK NRE 3  3 33 0  ` ?"0@NNN?N@ UW.R. Smith and R.W. Missen (1991) Chemical Reaction Equilibrium Analysis: Theory and Algorithms 2nd Edition, Krieger Publishing Malabar, Florida ISBN-10: 0894645846^# >    /  3,  0 HA Ԕ?"6@`NNN?N   0  ` ?"6@`NNN?N, f ,$D 0 [mechanism] M1 + M2 <===> M3 : K1 dissoc M4 + M5 <===> M3 : K2 dissoc M4 + M6 <===> M1 : K3 dissoc M6 + M2 <===> M5 : K4 dissocl P ` 0P `,$D 02 0 H V?"6@`NNN?N`P P 2 0 H V?"6@`NNN?N p 2 0 H V?"6@`NNN?N`b P B 0 ND?"0@NNN?Np pB 0 HD?"0@NNN?N  pB 0 HD?"0@NNN?NP p 0 H\  ?"6@ NNN?N@` B components H 0 0޽h ? ̙33___PPT10+`TD:'  = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-o6Bdissolve*<3<*0+8+0+ 00 +  0L0  (  x  c $ 0     H  0޽h ? ̙33y___PPT10Y+D='  = @B +  0L0   H (  Hx H c $ ``    XB H 0D`X H 0A?`m H TA?"6@`NNN?NuP H <   X INTRINSIC VS.  MACROSCOPIC RATE CONSTANTSp- 3  3 3  3 3 3G H  `d ?"0@NNN?N7 d -Two identical, non-interacting binding sites:6. H  `x ?"0@NNN?N   R L ka kdd    H  `L ?"0@NNN?N X  greceptor ligand binding site intrinsic association rate constant a intrinsic dissociation rate constanth  z   H ,$D 02  H  `8c?"6@`NNN?Ni<  H  ` ?"0@NNN?N l$two equivalent ways to come together,% 3" 3z  yRa   H y Ra ,$D 02 H  `8c?"6@`NNN?N yy iK H  `+?"0@NNN?N Ra  {!two equivalent ways to fall apart>"   H H 0޽h ? ̙33 ___PPT10+bD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bdissolve*<3<* HD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bdissolve*<3<* H+g  0L0 Pk(  Px P c $+``  + XB P 0D`X P 0A?`m P TA?"6@`NNN?Nu^ P <T+^ f INTRINSIC VS.  MACROSCOPIC EQUILIBRIUM CONSTANTSp4 3  3 3  3 3 3Y P  `P+?"0@NNN?N] d -Two identical, non-interacting binding sites:H. P  ` +?"0@NNN?N0   Kd2 = 2 kd / ka    P  `+?"0@NNN?NL   Kd1 = kd / 2 ka  333r  P  `?"0@NNN?N  0 r  P  `?"0@NNN?N0 00 z     P   ,$D  0  P Z?"6@`NNN?N0 p Y P  `+?"0@NNN?N    Kd2 = 4 Kd1b 33333z o@ . P @ o.,$D  0  P  `h+>?"6@`NNN?N@ . Jz[mechanism] R + L <==> R.L : K1 dissoc R.L + L <==> R.L.L : K2 dissoc [constants] K2 = 4 * K1 K1 = 1.2345J{a 3b  * P  `+?"0@NNN?NoT 0  GDynaFit notation: H P 0޽h ? ̙33___PPT10+$)D'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* P%(D' =-m6Bbox(in)*<3<* PD' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-m6Bbox(in)*<3<*P+W  0L0  |  X (  Xx X c $<+``  + XB X 0D`X X 0A?`mA X <@+ IA DYNAFIT SCRIPT TO DISTINGUISH BETWEEN INDEPENDENT AND INTERACTING SITESpJ 3  3  3 3 3 3 X ZH+?"6@`NNN?N J N[task] data = equilibria model = interacting sites ? [mechanism] P + L <===> P.L : K1 dissoc P.L + L <===> P.L.L : K2 dissoc P.L.L + L <===> P.L.L.L : K3 dissoc [constants] ; vary independently K3 = 1.23 ? K2 = 4.56 ? K1 = 7.89 ? ... [task] data = equilibria model = independent sites ? [constants] ; link via statistical factors K3 = 1 ? K2 = 3 * K3 K1 = 9 * K3 ...4 s 33- 4 33 3Y     X  f8c?"6@`NNN?N ,$D 0  X  `+?"6@`NNN?N@p,$D  0 eexercise: derive statistical relationships between equilibrium constants for four independent sites>f  E     X H 8c?"6@`NNN?N&Z   X H 8c?"6@`NNN?N| T H X 0޽h ? ̙33c[___PPT10;+9D'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-o6Bdissolve*<3<* XD' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-m6Bbox(in)*<3<* X+8+0+ X0 +  0L0  (  x  c $^+0   + H  0޽h ? ̙33y___PPT10Y+D='  = @B +  0L0 : 2 ` (  `x ` c $d+``  + XB ` 0D`X ` 0A?`m ` <f+  @HOW TO RECOGNIZE NONSPECIFIC BINDING IN ACTUAL EXPERIMENTAL DATA,A@ 3 3 ` TA?"0@NNN?N7 `  f`r+?"0@NNN?Np0 i3www.graphpad.com/prism/learn/binding%20analysis.pdf44! `  `8y+?"6@`NNN?NM Stotal binding $  `  `f+?"6@`NNN?N  Q nonspecific ( 33uz 0 L   ` 0 L ,$D 0B  ` TD|?"0@NNN?N  '  `  `l+?"0@NNN?N0 L  Wlinear increase, 3  3z 0    ` ,$D 0B ` TD|?"0@NNN?N  @ `  `hs+?"0@NNN?N0   p(a linear  component ,    H ` 0޽h ? ̙33 ___PPT10+bD'  = @B D' = @BA?%,( < +O%,( < +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<* `+j   0L0 y q h (  hx h c $T+``  + XB h 0D`X h 0A?`m9 h <L+ ADEFINE AN EXTREMELY WEAK BINDING SITE WITH A HUGE RESPONSE FACTORpB  3 3 3  3 3 3P h  `$ ?"0@NNN?N D<4___PPT9 <introduce a second  specific binding site this will represent many very weak (nonspecific) sites assign to it an extremely weak binding affinity many orders of magnitude higher Kd treat the weak nonspecific Kd as a fixed constant optimize only the specific binding constants assign a very large response factor corresponding to  many simultaneous sites treat the response factor as an adjustable parameter this represents the  number of weak sites J 8 !       L*  , @`H h 0޽h ? ̙33y___PPT10Y+D='  = @B +  0L0   p(  px p c $+``  + XB p 0D`X p 0A?`m p <Q+g @HIV-1 Rev RESPONSIVE ELEMENT (LABELED RNA FRAGMENT) / NEOMYCIN B>A 3$ 3 3p p H A ?0P v p Z,  ? 0 2Lacourciere et al. (2000) Biochemistry 39, 5630-413          2 B p TD?"0@NNN?N` ` `   p  `4 ?"0@NNN?N pQ  @[Neomycin], M B  p HD?"0@NNN?Npp   p  `& ?"0@NNN?Nv8  <1.5 M z  0l  p 0 l,$D  0  p TA?"0@NNN?N 0lB p TD8c?"0@NNN?NB p TD8c?"0@NNN?N J JB p TD8c?"0@NNN?Nz 0P  p 0P ,$D  0 p TA?"0@NNN?N0P B pB HD?"0@NNN?N    p  `C ?"0@NNN?N q <200 M H p 0޽h ? ̙33___PPT10+^*D'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =-m6Bbox(in)*<3<* pD' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-m6Bbox(in)*<3<*p+  0L0 t l @ x (  xx x c $HL ``    XB x 0D`X x 0A?`m x <TN g @HIV-1 Rev RESPONSIVE ELEMENT (LABELED RNA FRAGMENT) / NEOMYCIN B>A 3$ 3 3 x ZT ?"6@`NNN?N`  [mechanism] R72 + Neo <===> R72.Neo : K1 dissoc R72.Neo + Neo <===> Neo.R72.Neo : K2 dissoc [constants] ; uM K1 = 0.1 ? K2 = 10000 [concentrations] ; uM R72 = 0.1 [responses] R72 = 10 ? R72.Neo = 5 ? Neo.R72.Neo = -5 ? m 3 "3z T x T,$D  0_ x  `b ?"6@`NNN?NP T  Kd2 = 10 mM@  3 B  x ND?"0@NNN?NP  x  `j ?"0@NNN?N A Hextremely weak binding z     x   ,$D  0  x  `o ?"6@`NNN?Nf   ~ straight line binding curve continues to high negative values$@+  B  xB ND?"0@NNN?N p H x 0޽h ? ̙33___PPT10+jND'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-m6Bbox(in)*<3<*xD' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* x%(D' =-m6Bbox(in)*<3<* x+  0L0 ` Z(  x  c $z ``    XB  0D`X  0A?`m  <| g @HIV-1 Rev RESPONSIVE ELEMENT (LABELED RNA FRAGMENT) / NEOMYCIN B>A 3$ 3 3  TA?"0@NNN?NP p   TA?"0@NNN?N Bd   `؃ ?"0@NNN?NT Z( K1 = (266 30) nML     `jJ?"6@`NNN?N`  "    `܋ ?"0@NNN?N  Zspecific binding component$ H  0޽h ? ̙33y___PPT10Y+D='  = @B +  0L0  U(  x  c $ ``    XB  0D`X  0A?`m  < g @HIV-1 Rev RESPONSIVE ELEMENT (LABELED RNA FRAGMENT) / NEOMYCIN B>A 3$ 3 3d   `| ?"0@NNN?NT Z( K1 = (290 70) nML    `, ?"0@NNN?N 2 Uspecific binding only$  TA ?"0@NNN?N  p    `jJ?"6@`NNN?N`     TA!?"0@NNN?NP p H  0޽h ? ̙33y___PPT10Y+D='  = @B +a   0    (  x  c $ `    XB  0D`X  0A?`m  T,  ? D<4___PPT9 FWe need to understand the matrix representation of complex equilibria at least enough to be able to read DynaFit warning messages. DynaFit will happily work even with inconsistent mechanisms, but it will ignore redundant equilibrium constants ( closed thermodynamic box ) Equivalent sites require a proper use of statistical factors. Nonspecific binding looks like a  linear component superimposed onto the usual nonlinear (hyperbolic) binding curve. Nonspecific binding is modeled in DynaFit as  specific binding characterized by very high dissociation constant  fixed in the regression model. DynaFit is not a  silver bullet : You must still use your brain a lot.X< (  '  !A B  ! 33 @`H  0޽h ? ̙33y___PPT10Y+D='  = @B +  0 T p(  T ^ T S 4     T # lp  ss49 f     H T 0ηo~ ? ̙33+ 0 P T(   d  c $4     s *P 49 f   >@  H  0ηo~ ? ̙33,? 0   |(   d  c $4     3 r$9 ss49 f    H  0ηo~ ? ̙33,V 0  |(  d  c $4     3 r> ss49 f    H  0ηo~ ? ̙33,X 0  |(  d  c $4     3 r\D ss49 f    H  0ηo~ ? ̙33,\ 0  |(  d  c $4     3 rJ ss49 f    H  0ηo~ ? ̙33,] 0  |(  d  c $4     3 rO ss49 f    H  0ηo~ ? ̙33,^ 0 |(  d  c $4     3 r8U ss49 f    H  0ηo~ ? ̙33,_ 0  |(  d  c $4     3 rZ ss49 f    H  0ηo~ ? ̙33,` 0 @|(  d  c $4     3 rx` ss49 f    H  0ηo~ ? ̙33,a 0 `|(  d  c $4     3 rj ss49 f    H  0ηo~ ? ̙33,b 0  |(   d   c $4      3 ro ss49 f    H   0ηo~ ? ̙33,c 0 |(  d  c $4     3 rt ss49 f    H  0ηo~ ? ̙33,d 0 |(  d  c $4     3 rPz ss49 f    H  0ηo~ ? ̙33,e 0 $|(  $d $ c $4    $ 3 r ss49 f    H $ 0ηo~ ? ̙33,f 0 ,|(  ,d , c $4    , 3 r ss49 f    H , 0ηo~ ? ̙33,g 0 04|(  4d 4 c $4    4 3 r$ ss49 f    H 4 0ηo~ ? ̙33,h 0 P<|(  <d < c $4    < 3 rȐ ss49 f    H < 0ηo~ ? ̙33,i 0 pD|(  Dd D c $4    D 3 r ss49 f    H D 0ηo~ ? ̙33,j 0 L|(  Ld L c $4   L  L 3 r ss49 f  L   H L 0ηo~ ? ̙33,k 0 T|(  Td T c $4   L  T 3 rP ss49 f  L   H T 0ηo~ ? ̙33,l 0 \|(  \d \ c $4   L  \ 3 r ss49 f  L   H \ 0ηo~ ? ̙33,m 0 d|(  dd d c $4    d 3 r ss49 f    H d 0ηo~ ? ̙33,n 0 l|(  ld l c $4    l 3 rH ss49 f    H l 0ηo~ ? ̙33,o 0 0t|(  td t c $4    t 3 r䵒 ss49 f    H t 0ηo~ ? ̙33,p 0 P||(  |d | c $4    | 3 r ss49 f    H | 0ηo~ ? ̙33,q 0 p|(  d  c $4     3 r$ ss49 f    H  0ηo~ ? ̙33,r 0 |(  d  c $4     3 rƒ ss49 f    H  0ηo~ ? ̙33s 0 T(  d  c $4     s * 49 f   >@  H  0ηo~ ? ̙33,t 0 |(  d  c $4     3 rҒ ss49 f    H  0ηo~ ? ̙33,u 0 0|(  d  c $4     3 r ss49 f    H  0ηo~ ? ̙33,v 0 P|(  d  c $4     3 r ss49 f    H  0ηo~ ? ̙33,w 0 p|(  d  c $4     3 r ss49 f    H  0ηo~ ? ̙33,x 0 |(  d  c $4     3 rΒ ss49 f    H  0ηo~ ? ̙33,y 0 |(  d  c $4     3 rϒ ss49 f    H  0ηo~ ? ̙33,z 0 |(  d  c $4     3 rlے ss49 f    H  0ηo~ ? ̙33xXoh\Ew%iDX ^HbhRh%^&_f˟k#R_kXE/(*XAgmY8+Ι}%W%Gmcnvoޜ-{aX❨ͻbTK \zRbf#wBBo"^~%_967q1wKLlS`@:+[߫u?AOb8Áw@^̹pʴ-Y箖9w"V7B> s4ߕ1d|@C}aVq<F(B==CѻGŒK8.S边#;=S')cvG?[Ȁ(.rd)w~R7 Pʙf~.|ܥ% a9X&La~t,%hrqRr&9 G~Gh<_ˡYS]jl hڶSƶ d財 м^w_y1#̟3Cu֔6ZAngߨoMsG\&U]?K5ժױS诬}+V ˪V6΂"s]iyXN=Aߛv%A_o؈~M۫^u!m۠R S1etuڽh%neBZ.CWӯlR~e6|S3z/5~}DD"_уnrrkF.ܫ XFkP Zl 3?b?#?/U?ވ$H?lv/raWCYob _ZOҳ9/.}-󯪕(kI5Q6>짺\ԺUt>Urxf!O,6VUk6 Unw-_O׍nծ ^=x꘰N'YV˙&"%$Pc5ǵȬpa؂^ru 6zy"3)ogiTs˝UOey߭~y`D5LܛEn]~"xXKTA?3wזmb A.^?V EA'g!|z^* ^"PΙnGwW-;g>93s>ۂ{K@΁ј7|,bԥ!2WXC:_ Pr*EYY8*Rտw67BĹw>NfTSª0 I8t,A: ? 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