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S 4 TK y y r    x*a00aa 4 TV y y r3    z*a00aaH 4 0ηo~ ? ̙3380___PPT10.pU( xp\(  \ \ N(: ]e]e    :  V* AAA \ N: ]e]e %   :  X* AAA \ T$: ]e]e   :  V* AAA \ T<: ]e]e %  :  X* AAAH \ 0ηo~ ? ̙3380___PPT10.CP) 0 0H(     6   = Determination of Binding Affinities and Molecular MechanismsL>$3333XB  0D  <\    0Petr Kuzmi  BioKin, Ltd.>    XB  0D0  <8  @  PPart 1: Theory&  C \A0BS_bannerThe Biochemical Society c   <T 0  a!Training Day May 2, 2014 (London)$" H  0޽h ? ̙33y___PPT10Y+D=' D = @B +Z  0 U M pF  (   x  c $ ``   XB  0D` 0 <"`  Nchoose experimental method 3 < "`P  Ichoose concentrations 5 <4 "``   @ collect data   6 Bؘ 8c"`  G data analysisdB 7 <DԔ0dB 8 <DԔ dB 9 <DԔPpl @`0  A @`0 ,$D 0lB ; <DԔ@@0 ZB <  s *DԔ``0 ZB = B s *DԔ@0 `0  >  < @  \&preliminary vs. refinement experiments''l 0  B 0 ,$D 0lB ? B <DԔ  @  < "`0   Bpublish reportl 0  E  0,$D 0 C  <Ħ "`0   Gbinding constants  D  <P "`0  Imolecular mechanism  F <袎   /THE FOCUS OF THIS TRAINING DAY IS DATA ANALYSIS>0" 3  33H  0޽h ? ̙33___PPT10+EOKDi' D = @B D$' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*A %(D' =-o6Bdissolve*<3<*A D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*B %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*E %(+  0  T (  T x T c $ ``   XB T 0D` T < T( \Algebraic fitting models( LB T c $DP P  T < L   \Numerical fitting models( RB T s *DԔ T <Ǝ   ausingle algebraic equations systems of simultaneous equations may not exist for some mechanisms always exist for any mechanism must be derived by hand derived automatically by the computer special experimental conditions applicable to any set of conditions many software packages highly specialized software SigmaPlot, GraphPad, Origin, ... DynaFit, BioEQSv&|       oRB T s *DԔ   T <d׎   ,ADVANTAGES OF THE GENERAL NUMERICAL APPROACHN- 3  3  33H T 0޽h ? ̙33y___PPT10Y+D=' D = @B +  0    X - (  X x X c $$ ``   XB X 0D`  X <  EONLY A QUICK GLANCE DURING THIS IS A TRAINING DAY, NOT A THEORY CLASSNF% 3 3 33  X < d J REFERENCES$    X < JD<4___PPT9 T\Kuzmic, P. (1996) Anal. Biochem. 237, 260-273 Kuzmic, P. (2009) Meth. Enzymol. 467, 247-280 ] >! @`l    X   ,$D 0  X  <P)  1 QCITATION ANALYSIS$t X  <(- J  ~ Cited in approximately 850 journal articles since 1998 Journals most frequently citing DynaFit: Biochemistry, J. Biol. Chem.fG [l t   X t  ,$D  0 X  < 7 t H  ]WHAT CAN DYNAFIT DO FOR YOU& X  <`<    B Derive mathematical models for data fitting, fully automatically.4C(H X 0޽h ? ̙33___PPT10+P(Dg' = @B D"' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*X %(D' =-o6Bdissolve*<3<*X Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*X D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*X +  0 {s d  (  d x d c $ ``   XB d 0D` d <Ԓ  FTHIS PROBLEM CAN BE HANDLED ALGEBRAICALLY, ALTHOUGH IT IS A STRETCH...LG  3 36 33X  d 0A?pgl  d 6AjJ?"`pb <  d 0A?"` c p ,$D 0 d 0A?"` CQ,$D 0l   d   ,$D 0n d  0A?"`  d  <蛣  G X  SAlgebraic data-fitting model:H d 0޽h ? ̙33  ___PPT10 +)LD ' D = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*d %(D' =-o6Bdissolve*<3<*d D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*d %(D' =-o6Bdissolve*<3<*d D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*d %(D' =-o6Bdissolve*<3<*d +9  0 |t  h (  h x h c $ ``   XB h 0D` h <  FTHIS PROBLEM CAN BE HANDLED ALGEBRAICALLY, ALTHOUGH IT IS A STRETCH...LG  3 36 33X h 0A?pgl h 6AjJ?"`pb < l  k   h  k ,$D 0  h  BL  X  QDynaFit data-fitting model:A  h  B乣 jJ"` k  _[mechanism] P + A <==> PA : Ka dissociation P + B <==> PB : Kb dissociation``DZ h <  [0T,$ 0 where the requisite mathematics is  somehow handled by the computerEEH h 0޽h ? ̙33e]___PPT10=+0D' D = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* h %(D' =-o6Bdissolve*<3<* h D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h %(D' =-o6Bdissolve*<3<*h +8+0+h 0 +   0  l A(  l x l c $̣ ``   XB l 0D` l <ȣ  @THIS PROBLEM CANNOT BE HANDLED ALGEBRAICALLY, EVEN IN PRINCIPLE!LA  3 3- 33f  l 0A?"`YX  l 0A?@ l D l D,$D  0`B l B 0D` l  B<ԣ `D uglycosylase (two sites)(    &l   l  ,$D  0f l  6A ?p x`B l B 0Dp `  l  Bۣ `   Zcompetitor (two sites)(  6 l <` "`d8,$D  0 <There can be no algebraic fitting model for this experiment!0= H l 0޽h ? ̙33___PPT10+`gDu' ޣ = @B D0' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*l D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*l Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*l D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*l D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*l D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*l +8+0+l 0 +  0 s k p  (  p x p c $ ``   XB p 0D` p <(  @THIS PROBLEM CANNOT BE HANDLED ALGEBRAICALLY, EVEN IN PRINCIPLE!LA  3 3- 33X p 0A?`^  p 6A ?x6 Sl |  p | ,$D 0 p  < |  P  QDynaFit data-fitting model:  p  <   [mechanism] DNA + Gly <==> DNA.Gly : Kd1 dissoc DNA.Gly + Gly <==> Gly.DNA.Gly : Kd2 dissoc DNA + Comp <==> DNA.Comp : Kd1* dissoc DNA.Comp + Comp <==> Comp.DNA.Comp : Kd2* dissoc#!"   LB p c $D p < d$ m Glycosylase,   LB p c $DLL p <  R Competitor, LB p @ c $DLB p c $Dp p <\ dm8 ;DNAH p 0޽h ? ̙335-___PPT10 +D' D = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*p %(D' =-o6Bdissolve*<3<*p +   0 0  t (  t x t c $$ ``    XB t 0D`  t <T& = FMINIMUM AMOUNT OF THEORY NEEDED FOR CONSTRUCTING MECHANISMS IN DYNAFIT>G 3? 33   t <-    l Statistical factors Thermodynamic box Intensive physical quantities Rapid equilibrium enzyme kineticsmm  t <<2 9{ @,$ 0 :F0H t 0޽h ? ̙33___PPT10+ ND' 5 = @B DD' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* t %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* t D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* t +8+0+ t 0 +  0   (   x  c $= ``    XB  0D`<  <>   P = PROTEIN,  L = LIGAND. OTHER SYMBOLS WOULD WORK EQUALLY WELL*FE 33<  <D p Z .[mechanism] P + L <==> P.L : Kd dissoc@/>  <M  @   [_[mechanism] P + L <==> P.L : Kd1 dissoc P.L + L <==> P.L2 : Kd2 dissoc` P  <Y X d s'Single-site binding: one complex formed0(  <@ $ j  r&Two-site binding: two complexes formed0'RB  s *DԔH  0޽h ? ̙33y___PPT10Y+D=' D = @B +  0  y @  x  (  x x x c $g ``    XB x 0D` x <i  7 [mechanism] P + L <==> P.L : Kd1 dissoc P.L + L <==> P.L2 : Kd2 dissoc [constants] Kd1 = 12.34 ? ; optimized parameter Kd2 = 4 * Kd1 ; statistical factorvv#Pa< x <v 5 2Two non-interacting sites: one adjustable Kd value`3 *Nz 0   x  0  ,$D  0ZB x  s *DԔ0 0   x  <  p 9  [mechanism] P + L <==> P.L : Kd1 dissoc P.L + L <==> P.L2 : Kd2 dissoc [constants] Kd1 = 12.34 ? ; optimized parameter Kd2 = 56.78 ? ; optimized parameterdv#PbN  x  <,  d  0Two cooperative sites: two adjustable Kd values l1  & B  x <| q VALUES  12.34 AND  56.78 STAND FOR ANY SUITABLY CHOSEN NUMERICAL VALUE*IH 33H x 0޽h ? ̙33___PPT10+(z3D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*x D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*x +S  0 P | (  | x | c $H ``    XB | 0D`X | 0A ?0  | < u bFOR IDENTICAL NON-INTERACTING SITES, P P.L IS TWICE AS LIKELY TO OCCUR AS P.L L.P.LRX' 3  3 3 3>) ^ | 6%%Gz   |   ,$D  0 |  <8  U ORate constants:$   |  2A  ?jJ?#" `?  `  |  0 z P  |  P,$D 0`B  | B 0DPp``B  |  0Dp & |  <  (o ftwo possibilities for the first  marble to fall in04" ` |  00  6z   |   ,$D 0`B |  0D  TB | c $D0  TB | c $D0 p $ |  <  +  done possibility for the second  marble to fall in03 # ` |  00  ^ | 6%%^ | 6%%z p`  |  p` ,$D 0x |  S A  ??#" `?p x |  S A  ??#" `?0 `  H | 0޽h ? ̙33 ___PPT10+UT)yD' = @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<*| 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<*| 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 $ ``    XB  0D`X  0A ?0   < u bFOR IDENTICAL NON-INTERACTING SITES, L.P.L P.L IS TWICE AS LIKELY TO OCCUR AS P.L PRX+ 3  3 3  3>% ^  6%%z ^   ^,$D 0,   <  (^o lone possibility for the remaining  marble to fall out07 ' `   00  |T 0 p   # p `B   0D  TB  c $D0  TB  c $D0 p z      ,$D 0`B  0D ` `B  0D 2   <0  +  Xtwo possibilities for a  marble to fall outJ-   `   00  ^  6%%^  6%%^  6%%^  6%%z      ,$D 0x   S A ??#" `? x   S A ??#" `?   ^  6%%Gz      ,$D  0   <(  U ORate constants:$ `   0    2A ?jJ?#" `?  H  0޽h ? ̙33 ___PPT10+& D' = @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<* 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<* 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 p )* -(   x  c $d ``    XB  0D`X  0A ?0@ l ^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%XB  0D|``lXB  0D|lXB  0D `` XB  0D  z kQ   kQ,$D 0x   S A ??#" `? |Q x   S A  ??#" `?k z h    h ,$D 0x   S A  ??#" `? h   x   S A   ??#" `?(   ^  6   S A  ??#" `?p 8  $D 0^  6   S A  ??#" `?|p  8  $D 0  <"  4NFOR TWO IDENTICAL NON-INTERACTING SITES, Kd(2) IS FOUR TIMES LARGER THAN Kd(1)O* 3 3 3 3  3 3 3 3 3 3 3^  6%%^  6%%/z      ,$D 0x   S A  ??#" `?p  x   S A ??#" `?p_tE  n2   0"`  t   6jJ"`  !  <"  x ?recall:^ " 6^ # 6 $  S A ??#" `? 08 $D 0z   %   ,$D 0x &  S A ??#" `?  ` '  0P @t (  6jJ"` 2 ) 6jJ"` b@,$D  0H  0޽h ? ̙33___PPT10`+PWDD' D = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*% %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*) %(D' =-o6Bdissolve*<3<*) +  0   0 F (   x  c $8"" ``  "  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6^  6%%^  6%%^ " 6^ # 6b * <-" P For two identical, non-interacting sites, Kd(2) is always four times larger than Kd(1). For two cooperative sites, both Kd(2) and Kd(1) can attain any arbitrary values.0             f , 0A ?"`@l ` |P /  `|P,$D  0 -  <L?" ` |  v*DYNAFIT NOTATION FOR NON-INTERACTING SITES0+ .  <D" ` P [mechanism] P + L <==> P.L : Kd1 dissoc P.L + L <==> P.L2 : Kd2 dissoc [constants] Kd1 = ... ? ; any appropriate value Kd2 = 4 * Kd1 ; statistical factorvv'Pc 0 <Q"  3HOW TO REPRESENT (LACK OF) COOPERATIVITY IN DYNAFIT>4, 3 33H  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 LD %C (   x  c $|\" ``  "  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6 ' B1 @ TBisswanger, H. (2008) Enzyme Kinetics, 2nd Ed., Wiley-VCH, Tuebingen, p. 14, Eq. (2)^U+H ,   ( < v Z(NON-INTERACTING, IDENTICAL BINDING SITES))^ + 6| *  s ,A fjJ?#" `?[  , <d> pv n = number of binding sites i = ith binding step Kd = microscopic dissociation constant Kd(i) = macroscopic Kd in ith binding step      b"%^ 0 6^ 2 6^ 4 6^ 6 6<l g  8 g ,$D 0 -  <TU Z  dEXAMPLE: n = 4: r /  C A ?#" `? e  r 1  C A ?#" `? g  r 3  C A  ?#" `? g  r 5  C A# ?#" `?@ g  dl p   =  p ,$D 0t2 9  6jJ"`p 0 t2 :  6jJ"`h ( t2 ;  6jJ"`` t2 <  6jJ"`  rz p   >   x ,$D 0t2 ?  6jJ"`p 0 t2 @  6jJ"`h ( t2 A  6jJ"`` t2 B  6jJ"`   C < U  X ,$ 0 V1 : 2.66667 : 6 : 16H  0޽h ? ̙33. & ___PPT10 +rXD ' D = @B Dm ' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*8 %(D' =-o6Bdissolve*<3<*8 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<*C %(+8+0+C 0 +  0    ( | (   x  c $ ``   XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6  B\ @  Qdistributed example file: ./courses/BSTD-2014/ThT_22AG/noninteracting.txt Gabelica et al. (2013) Biochemistry 2013, 52, 5620-5628, Figure 3D3  K;^  6^  6^  6^  6^  6 & 6( B  [mechanism] DNA + Lig <==> DNA.Lig : Kd1 dissoc DNA.Lig + Lig <==> DNA.Lig.2 : Kd2 dissoc DNA.Lig.2 + Lig <==> DNA.Lig.3 : Kd3 dissoc DNA.Lig.3 + Lig <==> DNA.Lig.4 : Kd4 dissoc [constants] Kd1 = 40 ? ; = 1/4 Kd , Kd ... microscopic Kd2 = 2.66667 * Kd1 ; = 2/3 Kd Kd3 = 6 * Kd1 ; = 3/2 Kd Kd4 = 16 * Kd1 ; = 4 Kd   3%$   23$$ ' <iD  7ASSUME FOUR IDENTICAL, NON-INTERACTING DNA/Ligand SITES28l ( 6jJ"` P8 H  0޽h ? ̙33y___PPT10Y+D=' D = @B +O  0 vn  (   x  c $ć" ``  "  XB  0D`   <p" = FMINIMUM AMOUNT OF THEORY NEEDED FOR CONSTRUCTING MECHANISMS IN DYNAFIT>G 3? 33,  <"    l Statistical factors Thermodynamic box Intensive physical quantities Rapid equilibrium enzyme kinetics8mC  <" P{ W  :F0H  0޽h ? ̙33y___PPT10Y+D=' D = @B +  0   = 1(   x  c $L" ``  "  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6^  6%%^  6%%^ " 6^ # 6@ + <" 08 Example: enzyme  E simultaneously binding two co-substrates  A and  B $KC , <p"   3EXB - 0DPNXB . @ 0D.~  / <l" `m Z aEA( 2 <p" p k j  aEB(XB 3 0D .p XB 4 0D N 1l  r  < P  ,$D 0`B 5 0D@ P `B 6 B 0Dp `B 7  0Dp  0 `B 8 0D  `  9  <"  ` cZ  EABF`B :  0D   ;  <" ` r4  <products 2 = <" "`N ,$D 0 Qthermodynamic box$ H  0޽h ? ̙33___PPT10+oMMD:' D = @B D' = @BA?%,( < +O%,( < +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<*= %(+8+0+= 0 +&  0  '. (   x  c $" ``  "  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6^  6%%^  6%%^  6^  6  <" pj 3EXB  0D- 0XB  @ 0D@ ]   <"  L  aEA(  <"  J  aEB(XB  0D  XB  0D- 0 ^B  6D  ^B  @ 6D M 0 ^B  6D } `^B  6D    B"   EABF1 ! <" l@,$ 0 Kd(A)V   1 " <" 8 ,$ 0 Kd(B)V   F # <$+ l @,$ 0 Kd(AB)j   F $ <+   ,$ 0 Kd(BA)j   ^ ) 6:l    +   ,$D  0 %  <+  D U  Nclockwise around the cycle: x (  S A 0??#" `? f  0t2 *  6jJ"` 0 ^ - 6%%p ,  S A 1??#" `? a  1 . <+    V$upper branch must meet lower branch:%%H  0޽h ? ̙33ph___PPT10H+M@DL'  + = @B D' = @BA?%,( < +O%,( < +D ' =%(Dp ' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*! %(D' =-o6Bdissolve*<3<*! D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*" %(D' =-o6Bdissolve*<3<*" D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-o6Bdissolve*<3<*$ D@' =A@BB BB0B%(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<*+ ++0+! 0 ++0+" 0 ++0+# 0 ++0+$ 0 +8  0 3+ 4 (   x  c $0*+ ``  +  XB  0D`  <++  5HOW TO REPRESENT CYCLIC BINDING MECHANISMS IN DYNAFIT>6. 3 33  <2+ 60 3EXB  0DXB  @ 0D V  <(0+  aEA(  < <+    aEB(XB  0DFPXB  0Dvp^B " 6DF^B # @ 6D^B $ 6D@&^B % 6D`V & BPB+ Vp P EABFl l  . l ,$D 0 *  <dI+ l@ Kd(A)V    +  <TP+ -  Kd(B)V    ,  <W+ l @ Kd(AB)j    -  <$`+   Kd(BA)j   ' / <h+  mb ,$ 0 ;There are four equivalent ways to represent this mechanism.0< u 0 BXn+ >"`0@ m,$D  0 }[mechanism] E + A <==> E.A : KdA dissoc E + B <==> E.B : KdB dissoc E.A + B <==> E.A.B : KdAB dissocd~#% u 1 B}+ >"`@ m,,$D  0 }[mechanism] E + A <==> E.A : KdA dissoc E + B <==> E.B : KdB dissoc E.B + A <==> E.A.B : KdBA dissocd~#%  2 B+ >"`p@ m ,$D  0 }[mechanism] E + A <==> E.A : KdA dissoc E.A + B <==> E.A.B : KdAB dissoc E.A.B <==> E.B + A : KdBA dissocd~%  3 Bȝ+ >"` @ l ,$D  0 ~[mechanism] E + B <==> E.B : KdB dissoc E.B + A <==> E.A.B : KdBA dissoc E.A.B <==> E.A + B : KdAB dissocd%   4 <(+ 4j,$  0 vBNumber of binding steps must match the number of unique complexes.CCH  0޽h ? ̙33]U___PPT105+2D' + = @B D' = @BA?%,( < +O%,( < +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<*/ %(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0 %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0 D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0 D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1 %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*1 D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*1 D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2 %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*2 D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*2 D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3 %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*3 D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*3 D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4 %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4 D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4 +P+0+/ 0 ++0+0 0 ++0+1 0 ++0+2 0 ++0+3 0 ++0+4 0 +f  0 @ 2 (   x  c $4+ ``  +  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6^  6%%^  6%%^  6^  6^  6l   +  ,$D  0x &  S A 3??#" `?a  3 '  <+  -  U#left branch must meet right branch:$$X ( 0A?v h f ) 0A?"`" * B8+ `  v"PLoS Pathog 10(2): e1003907 (2014)## "l 0P  0 P0 ,$D 0 %  <+  P$ |&2.56 1.55 = 3.97 : t -  6jJ"`00 l    1   ,$D 0 .  <+   t  |&7.57 0.52 = 3.93 : t /  6jJ"`  2 <+  ,$ 0 60H  0޽h ? ̙33___PPT10 + nD ' + = @B DV ' = @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<*0 %(D' =-o6Bdissolve*<3<*0 D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*1 %(D' =-o6Bdissolve*<3<*1 DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2 %(+8+0+2 0 +/  0 VN  (   x  c $T+ ``  +  XB  0D`   <+ = FMINIMUM AMOUNT OF THEORY NEEDED FOR CONSTRUCTING MECHANISMS IN DYNAFIT>G 3? 33   <D3    l Statistical factors Thermodynamic box Intensive physical quantities Rapid equilibrium enzyme kineticsmm  <83 {   :F0H  0޽h ? ̙33y___PPT10Y+D=' D = @B +   0   P  Z (   x  c $$3 ``  3  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6^  6%%^  6%%^  6^  6RB  s *DԔ  RB  s *DԔ    <3  A Extensive   <3   A Intensive RB  s *D100  <p3 t  j(Signal is proportional to concentrations&)  <3  { j(Signal is proportional to mole fractions&)A  <"3   ofluorescence intensity NMR peak area UV/Vis absorbance HPLC peak area radioactive counts optical rotation ... pp,4  <t(3   =fluorescence polarization (anisotropy) NMR chemical shift ...>>'H  0޽h ? ̙33y___PPT10Y+D=' D = @B +5   0 \ T `   (   x  c $23 ``  3  XB  0D`^  6%%^  6%%^  6%%^  6%%^  6%%^  6%%^  6^  6^  6%%^  6%%^  6^  6  <083 /  /HOW TO REPRESENT INTENSIVE VARIABLES IN DYNAFIT>0( 3 33  B\,3 jJ"` s[responses] intensive ...8  D  <D3 #` Use the DynaFit keyword  intensive in the [responses] section of the input script:TTf  0A?"`@   <,:3 0} <Example: Protein-protein binding constants determined by NMR$=69H  <M3 *d .Kuzmic, P. (2009) Meth. Enzymol. 467, 247-280 ^/ ,H  0޽h ? ̙33y___PPT10Y+D=' D = @B +/  0 VNp  (   x  c $ ^3 ``  3  XB  0D`   <_3 = FMINIMUM AMOUNT OF THEORY NEEDED FOR CONSTRUCTING MECHANISMS IN DYNAFIT>G 3? 33   <+B#style.visibility<*# %(D' =-o6Bdissolve*<3<*# 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?\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   p(   x  c $3 ``  3  XB  0D`^  6^  6^  6  <3 ` D<4___PPT9 Compute the composition at equilibrium. Look up all enzyme-substrate complexes that do form products. Multiply their concentrations by an appropriate proportionality constant: constant = molar instrumental response of the product relevant kcat Compute the sum total of all such terms. The result is the initial rate under the rapid equilibrium approximation.'K ?  z @`RB  s *D8c  H  0޽h ? ̙33y___PPT10Y+D=' D = @B +  0     g (   x  c $L3 ``  3  XB  0D`^  6^  6^  6  <X3  JTWO EQUIVALENT WAYS TO REPRESENT RAPID-EQUILIBRIUM ENZYME KINETICS DYNAFIT>KC 3 33Z  <3 & pSee  DynaFit Scripting Manual on http://www.biokin.com/@9)  <,3 @ %  ` METHOD 1: initial rate formalism$!  B3 jJ"`0   :[task] data = rates approximation = rapid-equilibrium [mechanism] E + S <==> E.S : Ks dissoc E.S ---> E + P : kcat [constants] Ks = ... kcat = 3 [responses] P = 4 ...#2bW   l l @  @l ,$D  0   B3 jJ"`l 0 .*[task] data = equilibria [mechanism] E + S <==> E.S : Ks dissoc [constants] Ks = ... [responses] E.S = 12 ; = 3 4 ... \ >8 ,   <3 p @ _METHOD 2: equilibrium formalism$ H  0޽h ? ̙33___PPT10+$D|' = @B D7' = @BA?%,( < +O%,( < +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<* +o   0    & (   x  c $ ``   XB  0D`  <б `_ V Statistical factors Independent binding sites: Kds are linked via statistical factors. Cooperative binding sites: Kds can attain arbitrary values. Thermodynamic boxes The  leave one out rule: thermodynamic cycles must remain open. It does not matter which edge of the box is left out. Intensive physical quantities Use intensive keyword for NMR chemical shift or fluorescence polarization. Omit this keyword for fluorescence intensity, UV/Vis absorbance, etc. Rapid equilibrium enzyme kinetics All rapid equilibrium enzyme kinetics can be expressed as  binding equilibria . Turnover numbers ( kcat values) become  responses in the binding model.  (   f  / & #P 3P4C3H  0޽h ? ̙33y___PPT10Y+D=' D = @B + 0 @ 3( @Y@  X  C 4     S xa 49 f   5 @ H  0ηo~ ? ̙33^ 0   n(   X  C 4   :   S (: 49 f  :  p The study of biomolecular binding equilibria has many aspects, enumerated on this diagram. Importantly the subject of this Biochemical Society  Training Day is solely how to analyze available experimental data  once the experimental data already exist. Unfortunately, in the limited time available in a one-day workshop, we will not be able to discuss how to chose the most appropriate experimental technique for any given research problem. However, in the afternoon  hands on session we will address at least briefly how to make an reasonable choice of concentrations for a binding study given the presumed range of binding affinities. J #    H  0ηo~ ? ̙3380___PPT10.YP:zF  0    V (   X  C 4   :    S \U: 49 f`  : H@___PPT9"  Almost all report in the biochemical literature, focusing on the study of binding equilibria, make use of the traditional algebraic fitting equations ( binding isotherms ). There are two major disadvantages to that approach: An algebraic  binding isotherm may not exist for many practically useful binding mechanisms, because those mechanisms are too complex. Traditional binding equations often require special experimental conditions, such that certain components (for example the ligand) must be present in very large excess over other components (for example the receptor protein). See for example ref. [1] for a long list of such restrictions. A completely different approach, used in a relatively small number of research papers to date, uses the numerical models, which are applicable to any mechanism regardless of complexity; do not require any special set of conditions; and can be derived automatically by the computer. DynaFit is a software package which enables this. REFERENCES [1] J.A. Goodrich & J.F. Kugel (2007) Binding and Kinetics for Molecular Biologists, Cold Spring Harbor Laboratory Press" " z  N    ' @   - & > [H  0ηo~ ? ̙3380___PPT10.YcD  0    T (   X  C 4   :    S |b: 49 f  :  V DynaFit is one of only two software packages I am aware of (the second one is BioEQS [1-3]) that can be used to study binding equilibria under the following conditions: 1. No restrictions are placed on the complexity of the binding mechanism. 2. No restrictions are placed on the experimental conditions (in particular, it is not required that any component be in large excess) DynaFit has been used successfully in dozens of published equilibrium binding studies. Those studies would not be possible to conduct otherwise, or else the authors would have to design an equivalent software package from scratch. REFERENCES 1. Royer, C. A., Smith, W. R. and Beechem, J.M.  Analysis of Binding in Macromolecular Complexes: A Generalized Numerical Approach , Analytical Biochemistry 192, 287 (1991). 2. Royer, C. A. and Beechem, J.M.  Numerical Analysis of Binding Data: Advantages, Practical Aspects and Implications , Methods in Enzymology, 210, 481 (1992). 3. Royer, C. A.  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