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Model selection results33tT/Fixed or optimized [RNA]? Confidence intervals00XConfidence intervals: Results^PExperiment #2: RRE / Neomycin  raw data))_LExperiment #2: RRE / Neomycin  script''`NExperiment #2: RRE / Neomycin  results((aExperiment #1 & #2: Summaryb$The main question remains unanswered%%c)Simultaneous vs. exclusive: stoichiometry**d,Simultaneous vs. exclusive: DynaFit notation--e Two new concepts to consider ...!!f)From stoichiometry to molecular mechanism**g&Thermodynamic box: A very general idea''h#Thermodynamic box: DynaFit notation$$iIndependent / interacting sites  j#Independent sites: DynaFit notation$$k,Simultaneous vs. exclusive: DynaFit notation--l$Automatic model selection in DynaFit%%mLModel selection: round 1  fixed [RNA]''nTModel selection: round 2  optimized [RNA]++o(Mechanism for HIV-1 RRE / Neomycin / Rev))p(Mechanism for HIV-1 RRE / Neomycin / Rev))qSummary and conclusions/~!"AHKLNVXZ\^`befhjx   0` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> <4(    6ܪ  P   T Click to edit Master title style! !  0ȭ     RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0  ``   X*  0P  `    l*(    0  `    `* 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(  \ \ NԢ]e]e    p* AAA \ Nע]e]e %   r* AAA  \ T]e]e    p* AAA \ T]e]e %   r* AAAH \ 0ηo~ ? ̙3380___PPT10.|  0 @ (   X  0A?`m,  60  p \Binding and Kinetics for Experimental Biologists Lecture 4 Equilibrium Binding: Case StudyN]0     <5 /  (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=' F= @B +  0L0 2P ~(  P r P S p `   XB P 0D`X P 0A?`m  2P T0 ?` Z2  xTopics: - generalized numerical model for equilibrium binding data - PREVIEW: model discrimination analysis (Akaike Information Criterion, AIC) - representing equilibrium binding mechanisms in DynaFit: the  thermodynamic box ; exclusive vs. non-exclusive binding; interacting vs. non-interacting binding sites. Example: HIV-1 Rev responsible element (RRE) RNA sequence interacting with (a) a model peptide representing the Rev protein (b) Neomycin B as a potential Rev competitor Goal: determine molecular mechanism   Rev and  Neo mutually exclusive?=3>  t  x 3  E ,o @`H P 0޽h ? ̙33y___PPT10Y+D=' F= @B +  0L0 %    (   x  c $x `   XB  0D`X  0A?`m  < BUNIFORM USER INTERFACE: SYMBOLIC DESCRIPTION OF REACTION MECHANISM*CB 33~  H A ?"``\ H   T  8c?"`P   T  8c?"`` p l  T?"`o ` ,$D  0 species names are arbitrary: P, D works as well as Prot, DNA equilibrium constant names are also arbitrary (K1, Kd1, Keq.1, ...) any number of steps in mechanism any mechanism    1          *  3 @`#l  @ p  @ p,$D 02   N ?"`@ @    TH  ?  p ?DynaFit automatically derives the underlying mathematical model,@393H  0޽h ? ̙33{s___PPT10S+D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B+checkerboard(across)*<3<* +8+0+ 0 +'   0L0 6 . `,  (   x  c $`   XB  0D`X  0A?`mB  <%  UNDER THE HOOD : A SYSTEM OF SIMULTANEOUS NONLINEAR ALGEBRAIC EQUATIONS*IH 33 * T ?d  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 + Tl- ?4   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 , T7 ?Pe 6DynaFit uses a modification of algorithm  EQS by W.R. Smith (1990) MATHEMATICAL DETAILS:@]3 *0H  0޽h ? ̙33y___PPT10Y+D=' F= @B +<  0L0 KCp   (   x  c $`0   XB  0D`X  0A?`m  <, <Rev REGULATES THE TRANSCRIPTION OF HIV-1 REGULATORY PROTEINS*=< 33~  H A ?"`0pp@  T ?a}  Cullen (1991) FASEB J. 5, 2361-8^!        T ?`   ~&234 nucleotide RRE RNA target sequence''   N ?"`P0   T ? ]  +Rev trans-activator protein binds near here>,33#3H  0޽h ? ̙33y___PPT10Y+D=' F= @B +  0L0   3 8 (   x  c $q`0   XB  0D`X  0A?`m(  <s  PNEOMYCIN BINDS TO Rev RESPONSIBLE ELEMENT. COULD IT DISRUPT THE BINDING OF Rev?PQ 3- 3 33Rl  ~ d  " @ N ,$D  0   Zpz ? ~ d  jSuc-TRQARRNRRRRWRERQRAAAAK   TD ?  }  FRev model peptide: X  0A?0 /    `l >?"`0n} 2Lacourciere et al. (2000) Biochemistry 39, 5630-413          2 tl P 0  '   ,$D  0   N A ?"`P 0  ~B   N DV? 2    `  ?"`h@ 7*   N ?P TZ  sfluorescent probe on U72 >   l  ` @  3  ` @ ,$D 0B .  T D? ` PB /   ` D? 00 B 0 B  ` D?  B 2 B  ` D? 0 @ H  0޽h ? ̙33X P ___PPT100 + MD ' F= @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<*' D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*3 %(+  0L0   (   x  c $`0   XB  0D`X  0A?`m&  T ?P D<4___PPT9 VExperiment #1: Observe the binding of RRE to Rev Experiment #2: Observe the binding of RRE to Neomycin Experiment #3: Observe the binding of RRE to Rev + Neomycin Compare the observations with two alternate mechanisms: a. Neomycin competes with Rev peptide ... b. Neomycin does not compete with Rev peptide ... ... for binding to the fluorescently labeled RNA fragment Conclude which of the two models is more likely to be true,&3)(3>>&04  @`H  0޽h ? ̙33y___PPT10Y+D=' F= @B +%  0 G?1h (  h x h c $P$ `   XB h 0D`X h 0A?`m h <&   2EVERY DYNAFIT SCRIPT HAS TO CONTAIN THESE SECTIONS<3* 3 33 h TG  ?@  [task] task = fit data = equilibria [mechanism] [constants] [concentrations] [responses] [data] variable ... set ... [output] directory ... [set:...] [end]   @!  : l   1h  ,$D 0  #h  T  ?0 c   =where to find the experimental data (not the data themselves)&>  31  $h  T4  ?0 @ tBmolar response coefficients (e.g., UV/Vis extinction coefficients)CC  %h  T  ?0 % 7concentrations of reactants applicable to all data sets88*  3  3xB &h B H D?0 xB 'h B H D?0 xB (h B H D? 0  )h  Tx  ?0   u3which component is varied in the binding experiment&43  3xB *h B H D?2 0 2  +h  T(/  ?0   Sexperimental data& 3 xB ,h B H D?D 0 D   -h  Td4  ?0  ~,numerical estimates of equilibrium constants6- 3  3xB .h B H D?{0 { /h  T:  ?0 @ v$definitions of equilibrium constants6%  3  3xB 0h B H D?x0 xH h 0޽h ? ̙33~___PPT10^+^BDB' F= @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*1h %(+  0 Y Q P   (   x  c $+ `   XB  0D`X  0A?`m  <- >  RNOTHING SPECIAL  JUST SIMPLE 1:1 BINDING**) 33  TY  ? =[mechanism] R72 + Rev <===> R72.Rev : K dissoc>>7z p0    .,$D  0   H A ?"`0   T  ?p  71:1l  h   @ h ,$D  0   H A ?"` h    Th  ?P` 4  71:1   `Ž  >?"`0n} 2Lacourciere et al. (2000) Biochemistry 39, 5630-413          2 H  0޽h ? ̙33___PPT10+dD' F= @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<* +-!  0  # ~(   x  c $8 `   XB  0D`X  0A?`mD  < g LOOK FOR  HALF-MAXIMUM CONCENTRATION TO ESTIMATE DISSOCIATION CONSTANTS *JI 33X  T`  ? V[mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = ...@W>37  N A ?"`@ 5pB  @ H D?P 0Ql  `   `  ,$D 0xB   H D? ``xB   H D?     Tg  ?` P  Ihalf-maximum effect 3l        ,$D 0~B  B N D>? -    T@m  ?   =0.02 M3  Tk ?"`0p,$D 0 <0.023T  TL ?"`; 3 ,$D  0 @dissociation constants have the same dimension as concentrations2A   ! l ! T ?"` #  ,$D  0 >units must be the same as those used in the experimental data!L?     2 " T  |?"` p ,$D 0 #  `  >?"`0n} 2Lacourciere et al. (2000) Biochemistry 39, 5630-413          2 H  0޽h ? ̙33___PPT10+D' F= @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<* %(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' =-m6Bbox(in)*<3<* D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*! %(D' =-m6Bbox(in)*<3<*! D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*" %(++0+ 0 ++0+ 0 ++0+! 0 +  0 %     (   x  c $ `   XB  0D`X  0A?`mB  <  LLIST ONLY CONSTANT (NOT VARIABLE) CONCENTRATIONS IDENTICAL IN ALL DATA SETS nM  3 3 3  3 33h  T4  ?  x[mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = 0.02 [concentrations] R72 = 0.03.yY 7<v  Z<  ? 0 2Lacourciere et al. (2000) Biochemistry 39, 5630-413          2   N:  ?"`0 P  a [R72] = 30 nM  l  TxM ?"`  0 ,$D  0 >units must be the same as those used in the experimental data!L?     l  @p   > ,$D  0   H A ?"` @p2   T  8c?"` bH  0޽h ? ̙33aY___PPT109+ZkD' F= @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<* +8+0+ 0 +   0   @b(   x  c $| `   XB  0D`X  0A?`mp  <~  zLIST ALL MOLECULAR SPECIES  VISIBLE IN THE GIVEN EXPERIMENTSn> 3 3 3  3 33  T  ?  n[mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = 0.02 [concentrations] R72 = 0.03 [responses] R72 = ... R72.Rev = ...t337lv  Z0  ? 0 2Lacourciere et al. (2000) Biochemistry 39, 5630-413          2   N A ?"` `5l 0   0  ,$D 0~B   N D|?    TX ?"`0  0.03 M R72 signal = 1.0N3   TX  ?0$ ,$  0 F how much experimental signal is associated with one concentration unit of each visible species? ^g     |l  P   P  ,$D 0!   ZP ?"`0  1.0 / 0.03 = 33.3P   Tȳ ?"` P   =33.3 3.l     ,$D 0B   T D|? ` `&   Z ?"`  0.03 M R72.Rev signal ~ 2.0N3 l     ,$D 0'   Z ?"`  2.0 / 0.03 = 66.6P    Z ?"`    =66.6 3H  0޽h ? ̙33h ` ___PPT10@ +\D ' F= @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<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<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+ 0 +  0    9 (   x  c $ `   XB  0D`X  0A?`m  T  ?"` v[mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = 0.02 [concentrations] R72 = 0.03 [responses] R72 = 33.3 R72.Rev = 66.6 [data] variable ... set ... d3 37  T' ?"`  ,$D 0 ;Rev3~  H A ?"` v   T+ ?"` L @,$D 0 @R72--Rev ~  T/ ?"` @B,$D  0 [set:R72--Rev] Figure 2B in Lacourciere et al. (2000) Rev,uM F370* 0.0000 1 0.0020 1.0803 0.0040 1.1005 0.0080 1.1749 0.0213 1.3921 0.0347 1.5824 0.0480 1.7166 0.0680 1.7993 0.0880 1.9123 0.1080 1.9317 0.1480 1.9436 0.2147 1.9781 0.2813 1.9298 r4, l 0 @  0 @,$D 02   N  ?"`0    T<  ?@*@ Na  comment   a  T\@ ?"`p  ,$D  0 9raw data courtesy of Jim Stivers Johns Hopkins University$:!  3  <hG  KEXPERIMENTAL DATA CAN BE EMBEDDED IN THE SCRIPT OR RESIDE IN SEPARATE FILES`L 3 3 3 33H  0޽h ? ̙33___PPT10+*ED ' F= @B D{ ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(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' =-m6Bbox(in)*<3<* D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 +  0      (   x  c $Pb `   XB  0D`X  0A?`m  <4d 2  VWHAT ARE THE  UNKNOWNS IN THIS EXPERIMENT?*,+ 33  Ti  ?"` 3[mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = 0.02 [concentrations] R72 = 0.03 [responses] R72 = 33.3 R72.Rev = 66.6 [data] variable Rev set R72--Rev 7  Tp  ?,$ 0 7?33l I _  I _,$D 0   N A ?"`  _@ I    I  B   Z D8c?p      Tu  ?I 0 $  7?3l I   I ,$D 0B   Z D8c?p     T0z  ?I 0  7?l  Z    Z ,$D  0   T} ?"` Z  it s not a given that the best-fit curve must go through the [0,1] data point!XO)      xB  B H D?  H  0޽h ? ̙33, $ ___PPT10 +:;D ' F= @B Dk ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(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<* %(+8+0+ 0 +  0 800   (   x  c $ `   XB  0D`X  0A?`m   < [ GALWAYS USE THIS FEATURE TO ASSESS THE QUALITY OF YOUR INITIAL ESTIMATE!<H  3= 33p  H A ?`   T  8c?"`\0  N ?"`p 0   H A  ?p*,$D  0l 0     0 ,$D  0Z   T  ?0   Kd = rR72 = rR72.Rev =   TĢ  ?   0.02d 33.3d 66.6dd   H  0޽h ? ̙33___PPT10+#ߒID' F= @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<* +  0 f^P   (   x  c $ `   XB  0D`X  0A?`m  N ?"`P` p   H A  ?`   T  8c?"`R   H A  ?R,$D  0 z 0      0 ,$D  0Z   T  ?0   Kd = rR72 = rR72.Rev =   T8  ?   0.013d 33.4d 67.8dd   *  <P c DRUN THE SCRIPT ONLY WHEN THE INITIAL ESTIMATE LOOKS REASONABLY GOOD!^E 3 3! 3 3 3H  0޽h ? ̙33___PPT10+43uD' F= @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<* +\   0 p   G(   x  c $h `   XB  0D`X  0A?`m   T  ?t ADynaFit output:p  H A  ?`2  T  |?"`c "    T  ?b  jSpecial situation: the Kd is lower than the (fixed) RNA concentration! [R72] = 0.030 M Kd = 0.013 Mk 0 3,C l  ``   ``,$D 0   H G+fH1^?"` F`  t@ Where have I seen this before? !!`   0A?& ``H  0޽h ?  ̙335-___PPT10 +WD' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +   0    (   x  c $t `   XB  0D`X  0A?`mp   H A  ?0 .p  H A ?P   T  V?"` R  T  V?"`|`<  T  V?"`{ ;k  6$@  "` ` ,$D  0 1... then it must be optimized, along with the Kd!T2  .H  0޽h ? ̙33xp___PPT10P+|`D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* +8+0+ 0 +N  0 + #   (   x  c $@K `   XB  0D`X  0A?`m  < 1  ^ADD ONE MORE  UNKNOWN AND SEE WHAT HAPPENS ...*0/ 33  Tl  ?"` 3[mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = 0.02 [concentrations] R72 = 0.03 [responses] R72 = 33.3 R72.Rev = 66.6 [data] variable Rev set R72--Rev 78 0   0    TH  ? 7?3   T  ?I 0 @  7?3   T  ?I 0  7?36F P 0    p 0U   H A ?"`P 0  xB   H DV? 2   Z  ?"`h@ 7*   H|  ?P TZ  sfluorescent probe on U72 >   pB  H D?P   Tp ?"`HiD ,$D 0 9?$3H  0޽h ? ̙33___PPT10+YDO' F= @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+ 0 ++  0 4)(  4x 4 c $l `    XB 4 0D`X 4 0A?`m  4 <x   ,AKAIKE INFORMATION CRITERION IS INCONCLUSIVE<- 3 33'~ 4 H A ?"`0 ] ~ 4 H A ?"`#p P m 4 T  ?0  )K = (12.6 2.1) nM [RNA] = 30 nM, fixedp*      , K  4 T  ? . 'K = (5.5 2.0) nM [RNA] = (47 5) nMP(    ,p  4 H A ?  fz t   4 t ,$D 0  4 T  8c?"`N Ft   4 Ft xB 4 H D?  4 T<  ?Ft !  d.sum of squares did decrease by a factor of two// 3z '= 4 '=,$D 0 4 T  8c?"`g0xB 4 H D?0 4 T  ?"`'= ~6however the number of adjustable parameters increased!,7 30 3z  2 4  2,$D 0 4 T  8c?"`  xB 4 H D? ,` , 4 T#  ?V 2q k#this number must be larger than ~10,$  z  P0 4  P0,$D 0 4 T  8c?"`  0xB 4 H D? ` N 4 Z)  ?W P0 R Akaike weight must be larger than ~0.95,*  #H 4 0޽h ? ̙33: 2 ___PPT10 +NHD ' F= @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(+2  0 b Z  X  (  X x X c $L `  L  XB X 0D`X X 0A?`m X <=p  THE  PLUS OR MINUS STANDARD ERRORS ARE ALMOST ALWAYS WRONG (TOO SMALL)nH 3 3 3  3  33  X N `p  ?"` :[task] task = fit data = equilibria [mechanism] R72 + Rev <===> R72.Rev : K dissoc [constants] K = 0.02 ?? [concentrations] R72 = 0.03 ?? [responses] R72 = 33.3 ? R72.Rev = 66.6 ? ...  X T$p ?"` *  8??3  X Tlp ?"`R  8??3|  X ZOp ?"`   ,$D  0  PROFILE-T METHOD Watts, D. G. (1994) "Parameter estimation from nonlinear models Methods Enzymol. 240, 24-36. Bates, D. M., and Watts, D. G. (1988) Nonlinear Regression Analysis and its Applications Wiley, New York, pp. 127-130 3 A    1 3  ]H X 0޽h ? ̙33xp___PPT10P+V!D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* X %(D' =-m6Bbox(in)*<3<* X +8+0+ X 0 +>  0 <40   (   x  c $8l  5THE NOMINAL [RNA] CONCENTRATION IS PROBABLY INCORRECTL6# 3 3  33p  H A ? @.   TFl  ? A=  Kd, nM [R72], nM2 6  TTl  ? N   J5.5 47.4&   ZIl  ? N   ,2.2 11.2 34.6 57.2H33  T l  ? n  ; parameter    Tl  ?  >  @best-fit value   TDl  ? >  Aformal error,    Tl  ?  S   I2.0 4.8&  TXl  ? >  Kconfidence interval (95%)   T,ol ?"`@  ,$D 0 Q... nominal: 30.0$   Ttsl  ?D CDynaFit output:   Tzl ?"` @,$D 0 ]reasonable suspicion: actual RNA concentration might be higher by ~60% than the nominal valuer^        H  0޽h ? ̙33___PPT10+9D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +p+0+ 0 ++0+ 0 +   0  -<T(  <x < c $l `  l  XB < 0D`X < 0A?`m < <@l H  ,FIXED RRE-72AP CONCENTRATION: [R72] = 0.1 Mb- 3 3  334 < # A`   l t `  <t ` ,$D 0xB < H D?   < T4l  ?t `   Kd ~ 0.3 MB  3 3  3 3l @  P  <@ P ,$D 0@ @  P  <@  P xB < H D?p  xB < H D?@ P P xB < H D?@   < T|l  ? 8] [half-maximum effect,  3 3l  `   <` ,$D 0xB < H D?@ ` @  < T( l  ?  ionly R72 (0.1 M)<    "l T t !<Tq t,$D 0xB <B H D?  & < T܎l  ?Tt "molar response of R72 1.0/0.1 = 10\#      z  `  $< ` ,$D 0xB %< H D?@ ` @  &< T`Ul  ?  monly R72.Neo (0.1 M)<   6z T t *<  p ,$D 0xB +<B H D?  , ,< Tl  ?Tt (molar response of R72.Neo 0.85/0.1 = 8.5\)       -< T#l  ?0 DINITIAL ESTIMATES:H < 0޽h ? ̙33___PPT10+Dn' F= @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<**<%(+   0 ld@ D(  Dx D c $Tl `  l  XB D 0D`X D 0A?`m D <40l   u/USING INITIAL ESTIMATES ESTIMATED FROM RAW DATA*0/ 334 D N\*l  ?"` [task] task = fit data = equilibria [mechanism] R72 + Neo <===> R72.Neo : K dissoc [constants] K = 0.3 ?? [concentrations] R72 = 0.1 ; fixed! [responses] R72 = 10 ? R72.Neo = 8.5 ? ...3E3 3_l V @@  DV @@,$D  0x  D H A ? @@  D N ?"` p P   D T_l  ?V   C File .. Try  H D 0޽h ? ̙333+___PPT10 +'A+D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =-m6Bbox(in)*<3<* D+   0 C ; `L (  Lx L c $hl `  l  XB L 0D`X L 0A?`m L <38  q+USING INITIAL ESTIMATES FROM PREVIOUS SLIDE*,+ 33p  L H A ?0P p  L H A ? @`  L T8 ?, J  nKd, M2  L T8 ? [  F0.29& L Z$8 ?^  X0.15 0.56&  L T8 ?* {  ; parameter   L T8 ?* J @best-fit value  L T8 ?*J Aformal error,   L T8 ?`  F0.07& L T\8 ?*J Kconfidence interval (95%)  L TP8 ? E  CDynaFit output: H L 0޽h ? ̙33y___PPT10Y+D=' F= @B +  0    T (  Tx T c $T8`  8 XB T 0D`X T 0A?`m T <n8_  'ONLY BINARY INTERACTIONS STUDIED SO FARL( 3 3 33,F  ~ d  T @ N  T Zs8 ? ~ d  jSuc-TRQARRNRRRRWRERQRAAAAK T T8 ?  }  FRev model peptide: X T 0A?0 / 6F P 0  T `  T H A ?"`P 0  xB T H DV? 2 T Z`8 ?"`h@ 7* T H 8 ?P TZ  sfluorescent probe on U72 >   F  ` @  T  ` @ B T T D? ` PB T  ` D? 00 B TB  ` D?  B TB  ` D? 0 @ E T T8 ?@ h  Kd = 290 nMn 33333 3$F  T T8 ?l @ @   Kd = 6 nMn 33333 3$H T 0޽h ? ̙33y___PPT10Y+D=' F= @B +  0    \y (  \x \ c $&8`  8 XB \ 0D`X \ 0A?`m# \ T(8 ?p ?Could Neomycin prevent the Rev peptide from binding to the RNA?D@ l p0 \0p,$D 0 \ T8 ?p0 Ain other words: ; \ T18 ?p  =Is the binding of Rev and Neomycin simultaneous or exclusive?V>#  "l  q \ q,$D 0 \ T$8 ? 0q Enon-competitive 3 \ T8 ?p A competitive  3Q \ T8 ?P p$ ,$ 0 AAnd how do we translate these ideas into stoichiometric notation?<B)333l P 0    \0 P  ,$D 0rB \ B D?P @ @  \ T98 ?0   =DynaFit H \ 0޽h ? ̙33  ___PPT10 +b7Da ' F= @B D ' = @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<*\DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \+8+0+\0 +  0 dF(  dx d c $I8`  8 XB d 0D`X d 0A?`m  d <M8 5IT DEPENDS ON HOW MANY DIFFERENT COMPLEXES ARE FORMEDL6 3 3  33 d TT8 ?T0Y < EXCLUSIVE:  d T,Y8 ? Neo + RRE + Rev63 @ d TH_8 ? @ "NeoRRE + RRERevR3 $pB d H D?8  pB d@ H D?8   d T$h8 ?d E$  ? SIMULTANEOUS: d Tl8 ?,   Neo + RRE + Rev63  d TQ8 ?, 1  >>NeoRRE + RRERev + NeoRRERev 3 36 pB d H D? 8  pB d@ H D? 8   d T  >?"` 00 J d Td^?"`IC ,$D 0 ( not necessarily different binding sites@)6 d T``?"`` l ,$D 0 p" always at different binding sites2#!H d 0޽h ? ̙33___PPT10+=ZD' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-o6Bdissolve*<3<*dD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-o6Bdissolve*<3<*d+p+0+d0 ++0+d0 +u  0    lx (  lx l c $x`   XB l 0D`X l 0A?`m l <dz |6HOW MANY DIFFERENT COMPLEXES IS NOT THE ONLY QUESTION*76 33 l T,?"`# ^[mechanism] ; exclusive RRE + Rev <===> RRE.Rev : Kr dissoc Neo + RRE <===> Neo.RRE : Kn dissoc .n!   l T?"`v<  9[mechanism] ; simultaneous RRE + Rev <===> RRE.Rev : Kr dissoc Neo + RRE <===> Neo.RRE : Kn dissoc ??? + ??? <===> Neo.RRE.Rev : ?? dissoc m333 $    El  P  l| P ` ,$D 0xB l H D?  xB l H D?  xB l H D?P P rB l B D? P  l T8 ?  Cwhat goes here?H l 0޽h ? ̙335-___PPT10 +D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*l+H  0 ogt(  tx t c $`   XB t 0D`X t 0A?`m t <  q+... BEFORE WE CAN FINISH OUR DYNAFIT SCRIPT*,+ 33 t T ?P` D<4___PPT9 n thermodynamic box independent vs. interacting sites28" @`H t 0޽h ? ̙33y___PPT10Y+D=' F= @B +4>  0 33 CG|g3(  |x | c $,`   XB | 0D`X | 0A?`mZ | 0. LONLY BIMOLECULAR INTERACTIONS ARE REALISTIC: THREE MOLECULES NEVER COLLIDE !M 3  3 3 3  3 3  33: | T( ?\h0 A + B + C  3pB | H D?@ pB  |@ H D?@   | Td< ?\` 0 (AB + BC + ABC 336  | TU ?0 Joverall stoichiometry:  | TF ?<  Rpossible molecular mechanisms: | N  ?"`, | l  ]  D| ] ,$D  0  | Th< ?86  jB FxB | H D?xB |B H D? | T= ? 8  ABJ3xB | H D?xB |B H D? | ZtE ?0o F+A(3 | Z(L ?; F+C(6 | TM ?8   ABC h3 | T ? 7\  jB FxB | H D?  xB |B H D?   | T8! ?! \  BCJ | ZN ?1 k  F+C( | N  ?"`  -| T@, ?d  ]  @ sequential I   l 0 ]  E|0 ] ,$D  0 | Tp2 ?t 8  jB FxB | H D? `xB  |B H D? ` !| T$ ?8  ABJ3xB "| H D?p P xB #|B H D?p P  $| Z2 ?  F+A(3 %| Z ?   F+A(36 &| T ?G J\   ABC h3 '| T. ?u \  jB FxB (| H D? a xB )|B H D?  a  *| TpѠ ? \  BCJ +| ZŠ ?   F+C( ,| N  ?"`0 `  .| TP٠ ? ]  A sequential II l    F| ,$D  0 /| T ?d \  jB FxB 0| H D?p P xB 1|B H D?p P   2| TX ? \  ABJ3xB 3| H D?` 1@1xB 4|B H D?` a@a 5| Z ?  F+A(3 6| Z ?q \ 0 F+A(36 7| Tp ?7 :  ABC h3 8| T ?e  jB FxB 9| H D?q1Q 1xB :|B H D?qaQ a ;| T$ ?   BCJ <| Z ?\ 0 F+C( =| N  ?"`  P  >| T$ ? :random xB ?| H D?i I xB @|B H D?i  I  A| ZЭ ?z   F+C(6 B| Tl ?@ Cd   ABC h3H | 0޽h ? ̙33  ___PPT10 + 6D ' F= @B D| ' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D|%(D' =-m6Bbox(in)*<3<*D|D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*E|%(D' =-m6Bbox(in)*<3<*E|D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*F|%(D' =-m6Bbox(in)*<3<*F|+$  0 XP@[(  x  c $(Ҡ`   XB  0D`X  0A?`m  0T ENO MATTER WHICH PATH WE TAKE, THE FREE-ENERGY CHANGE MUST BE THE SAMENF" 3 3 33 0 Z[ ?" jB F 3 Ze ?@ ABJ34 8 Zdi ?ps   ABC h3 < Zlʒ ? @T  BCJpB D H D?0pB E@ H D?@DpB K H D? pB L@ H D?@ pB M H D?`pB N H D?ppB O H D?@ pB P H D?@`  Q TВ ? FKA(  R HՒ ?  oKCA6   S Tڒ ?0   FKC(  T H|= ?0    oKAC6  f U TTC ?` N  Fall  K s are dissociation constants^$   V TJ?"`v  X.KCA KA = KAC KC  $ ! W THL ?v  %dissociation from ABC: first C then A\& ! X Tp` ?0 %dissociation from ABC: first A then C\& q Y T$\?"`p 0 + ,$D 0 EOnly three of four equilibrium constants can have an arbitrary value.JF  #    Z T#?"` 0 @ ,$D 0 2Any one of the K s is a priori defined in terms of the remaining three.fH      ! 6l [ T,+?"` 0 [ ,$D 0 LIt does not matter which K we select to be dependent on the remaining three.>M   3 H  0޽h ? ̙33  ___PPT10 +չD ' F= @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Y%(D' =-o6Bdissolve*<3<*YD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Z%(D' =-o6Bdissolve*<3<*ZD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*[%(D' =-o6Bdissolve*<3<*[++0+Y0 ++0+Z0 ++0+[0 +!  0 `"(  x  c $`   XB  0D`X  0A?`mh  0 THERE ARE MULTIPLE EQUIVALENT WAYS TO SPECIFY THE  RANDOM MECHANISM IN DYNAFITNP3 3 3 33  T ?" jB F   T,Ē ?@ ABJ3.  T| ?ps   ABC h3   T,3 ? @T  BCJpB   H D?0pB  @ H D?@DpB   H D? pB  @ H D?@ pB  H D?`pB  H D?ppB  H D?@ pB  H D?@`   T  ? FKA(   H ?  oKCA6    T\x ?0   FKC(   Hh} ?0    oKAC6  f  Th ?` N  Fall  K s are dissociation constants^$  #  T ?"`hp  k[mechanism] A + B <==> AB : Kc diss B + C <==> BC : Kc diss AB + C <==> ABC : Kca dissl 3t"  T| ?"`p T  k[mechanism] A + B <==> AB : Ka diss B + C <==> BC : Kc diss A + BC <==> ABC : Kac dissl 3b'  T ?P6  Eor, equivalently: o   T?"` q 0 ,$D 0 CThere must be only three steps (any three) in the DynaFit notation!JD ! ! T춈 ?@ P @ for example:  H " T<?"` p .,$D 0 @How many other ways exist to specify this mechanism in DynaFit ?&A . H  0޽h ? ̙33___PPT10+EWD' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-o6Bdissolve*<3<*"+p+0+ 0 ++0+"0 +(  0 OG(  x  c $`   XB  0D`X  0A?`m6  00 WHETHER OR NOT PAIRS OF EQUILIBRIUM CONSTANTS IN THE  BOX ARE THE SAME,HG 33  T ?" jB F   T  ?@ ABJ3.  Tț ?ps   ABC h3   TLj ? @T  BCJpB   H D?0pB  @ H D?@DpB   H D? pB  @ H D?@ pB  H D?`pB  H D?ppB  H D?@ pB  H D?@`   Td ? FKA(   H U ?  oKCA6    T ψ ?0   FKC(   H$H ?0    oKAC6  f  TK ?` N  Fall  K s are dissociation constants^$    HY?"`P0 ` U'independent sites: KCA = KC KAC = KA(         ,:  H?"`p0 `6  Ninteracting sites: KCA KC KAC KA(         ,H  0޽h ? ̙33y___PPT10Y+D=' F= @B +  0 U(  x  c $0d `   XB  0D`X  0A?`m  0 AB : KA diss B + C <==> BC : Kc diss AB + C <==> ABC : Kc dissl 3b'  TȲ  ?"`p T  mk[mechanism] A + B <==> AB : Ka diss B + C <==> BC : Kc diss A + BC <==> ABC : Ka dissl 3P'  T<  ?P6  Eor, equivalently:   T  ?@ P @ for example:  ;  T ?"` q  ,$D 0 u)Only two distinct dissociation constants.0*"H  0޽h ? ̙33zr___PPT10R+p9D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+0 +i   0    (  x  c $@ `   XB  0D`X  0A?`m  <  :FINALLY WE KNOW ENOUGH THEORY TO FINISH THE DYNAFIT SCRIPT*;: 33  Z  V?"`1 ^[mechanism] ; exclusive RRE + Rev <===> RRE.Rev : Kr dissoc Neo + RRE <===> Neo.RRE : Kn dissoc .n!    Z$  V?"`J  8[mechanism] ; simultaneous, non-interacting RRE + Rev <===> RRE.Rev : Kr dissoc Neo + RRE <===> Neo.RRE : Kn dissoc Neo.RRE + Rev <===> Neo.RRE.Rev : Kr dissoc 3m*3 5      Z@`  V?"` L F[mechanism] ; simultaneous, interacting RRE + Rev <===> RRE.Rev : Kr dissoc Neo + RRE <===> Neo.RRE : Kn dissoc Neo.RRE + Rev <===> Neo.RRE.Rev : Krn dissoc  m* 1   H  0޽h ? ̙33y___PPT10Y+D=' F= @B +   0 x (  x  c $dk `   XB  0D`X  0A?`mx  Npm  ?`P  [task] task = fit data = equilibria model = exclusive ? ... ... [task] task = fit data = equilibria model = interacting ? ... ... [task] task = fit data = equilibria model = non-interacting ? ... ...3(3 3(3 3(3pB  H D8c?` pB  H D8c?`` `   H A ?^` ,$D  0z     ~> ,$D 0   H A ?"` rB   B D? rB   B D?pB  H D8c? ` H  0޽h ? ̙332*___PPT10 +?D' F= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-m6Bbox(in)*<3<* D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* +  0 (  x  c $H `   XB  0D`X  0A?`m  <T q  |$NEITHER MODEL FITS VERY WELL AT ALL!<%  3 33l |@ |@,$D  0  BA8c?"6@`NNN?N|;   N` 8c?"0@NNN?Nl @ ; exclusive   BA8c?"6@`NNN?N|;   BA8c?"6@`NNN?N|;   N8 8c?"0@NNN?N0 l } @ Anon-interacting  N 8c?"0@NNN?Nl @ = interacting   N̚ 8c?"0@NNN?Np A experiment #3   N( 8c?"0@NNN?N  Blabeled [RNA]:  N 8c?"0@NNN?N;  ? Neomycin B:    N৘ 8c?"0@NNN?N< l @ Rev peptide:    N< 8c?"0@NNN?N z h100 nM, constant3   N( 8c?"0@NNN?N  d990 nM, constant .  N 8c?"0@NNN?N p x$0  655 nM, varied B  TT 8c?"6@`NNN?Nt,$D 0 L[RNA] is under suspicion   Z| ?"6@`NNN?Np0,$D  0 TAll equilibrium constants were fixed at values determined in binary binding studies.JU     H  0޽h ? ̙33  ___PPT10i +z~uD ' F= @B D ' = @BA?%,( < +O%,( < +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<*D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*+p+0+0 ++0+0 +.+  0  %O(  x  c $Ҙ `   XB  0D`X  0A?`m  <|Ԙ   f GOODNESS-OF-FIT IS MUCH IMPROVED*!  33  Tژ 8c?"0@NNN?Nl @ ; exclusive    Tޘ 8c?"0@NNN?Nl 0 } @ Anon-interacting   Th 8c?"0@NNN?Nl @ = interacting    N 8c?"0@NNN?Np A experiment #3   N 8c?"0@NNN?N  Blabeled [RNA]:  N 8c?"0@NNN?N;  ? Neomycin B:    Nh 8c?"0@NNN?N< l @ Rev peptide:  ^  N 8c?"0@NNN?N  178 nM, optimized in the fitN33    N 8c?"0@NNN?N  d990 nM, constant .  N 8c?"0@NNN?N p x$0  655 nM, varied   BA8c?"6@`NNN?NP   BA8c?"6@`NNN?NP   BA 8c?"6@`NNN?NP @l `# ;  # `; ,$D 0<  Nl 8c?"0@NNN?N`#   ~ SSQr = 3.094<     <  NQ 8c?"0@NNN?N #   ~ SSQr = 1.002<     <  NU 8c?"0@NNN?N# ;  ~ SSQr = 1.000<     cz `# 8    `8 ,$D 0=  N4Z 8c?"0@NNN?N`#    wAIC = 0.000<    O   N_ 8c?"0@NNN?N #    wAIC = 0.948N     = ! Nf 8c?"0@NNN?N# 8   wAIC = 0.052<    7 " Tl 8c?"6@`NNN?Nl 0 } @,$D  0 Anon-interacting $ BA!8c?"0@NNN?NU> {,$D 0` % Hp 8c?"6@`NNN?N@ ,$D 0 v& actual [RNA] 78% higher than nominal?4'(2H  0޽h ? ̙33 ___PPT10+#DW' F= @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<*%(D' =%(D' =%(D>' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-m6Bbox(in)*<3<*"D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-o6Bdissolve*<3<*$D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =-o6Bdissolve*<3<*%+p+0+"0 ++0+%0 +q  0 @1((  x  c $~ `   XB  0D`X  0A?`m  T  ?  RRE F   Tp  ?  RevRREL 3: ! T  ?  RevRRENeo h 3  " T  ?,  RRENeoL pB # H D?; pB $@ H D?O pB % H D? pB &@ H D? pB ' H D? <pB ( H D? { lpB ) H D?K pB * H D? k = + T  ?[4   Kd = 5 nMh 3333$ , H  ?  t290 nM0 / T  ?    r5 nM03333 0 HL  ?   t290 nM0# 1 <D  =NON-EXCLUSIVE BINDING TO TWO DISTINCT, NON-INTERACTING SITES^>  3 3 3 33H  0޽h ? ̙33y___PPT10Y+D=' F= @B +j  0 `/!(  x  c $d `   XB  0D`X  0A?`m  <4  CSTRUCTURAL IMPLICATIONS OF THE BINDING DATA: SEPARATE BINDING SITES<D- 3 33,F  ~ d   0 >   Z,  ? ~ d  jSuc-TRQARRNRRRRWRERQRAAAAK  T  ?  }  FRev model peptide: X  0A? p  6F P 0   0   H A ?"`P 0  xB  H DV? 2  Z  ?"`h@ 7*  H  ?P TZ  sfluorescent probe on U72 >   B $ TD?"0@NNN?N pB '@ TD?"0@NNN?N7 i72 ( T3o?"6@`NNN?N ) T0 ?"0@NNN?Nd L Neo site  2 * T3o?"6@`NNN?N  + T ?"0@NNN?N L Rev site  B , TD?"0@NNN?N) p) B -@ TD?"0@NNN?N` i`  . T|  ?@ y   Kd = 5 nMF   $ / Hx  ? `  Kd = 290 nMF    $H  0޽h ? ̙33y___PPT10Y+D=' F= @B +   0   R (  x  c $ `   XB  0D`X  0A?`m  TD  ?IVD<4___PPT9 $Equilibrium binding data are easily handled by numerical models. Arbitrary conditions (no  excess of A over B ); arbitrarily complex mechanisms. Certain restrictions exist on representing reaction mechanisms. The  thermodynamic box rule must always be obeyed. Exclusive vs. non-exclusive binding is expressed simply as a different number of complexes present in the overall mechanism. Interacting vs. non-interacting sites are expressed simply by assigning identical vs. unique values to equilibrium constants. Incorrectly specified concentrations have a large impact on best-fit values of equilibrium constants and on model selection. BUT THERE IS SOME RELIEF: when the binding is  tight , actual concentrations can be inferred from the data; when the binding is  loose , systematic concentration errors do not matter (much). DynaFit is not a  silver bullet : You must still use your brain a lot.A$    #    5    "    =,  R % f 23 @`H  0޽h ? ̙33y___PPT10Y+D=' F= @B +  0 T p(  T ^ T S 4    T # l ss49 f     H T 0ηo~ ? ̙33+ 0 P T(   d  c $4     s * 49 f   >@  H  0ηo~ ? ̙33,, 0 p |(   d  c $4      3 r ss49 f     H  0ηo~ ? ̙33: 0  l T(  l d l c $4     l s * 49 f    >@  H l 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 r\ ss49 f     H  0ηo~ ? ̙33,? 0   |(   d  c $4      3 r ss49 f     H  0ηo~ ? ̙33C 0 `  T(   d  c $4      s *l 49 f    >@  H  0ηo~ ? ̙33D 0   T(   d  c $4      s *L 49 f    >@  H  0ηo~ ? ̙33E 0   T(   d  c $4      s *$ 49 f    >@  H  0ηo~ ? ̙33F 0   T(   d  c $4      s * 49 f    >@  H  0ηo~ ? ̙33G 0   T(   d  c $4      s * 49 f    >@  H  0ηo~ ? ̙33H 0   T(   d  c $4      s *t 49 f    >@  H  0ηo~ ? ̙33I 0 @  T(   d  c $4      s *L 49 f    >@  H  0ηo~ ? ̙33J 0 `  T(   d  c $4      s *$ 49 f    >@  H  0ηo~ ? ̙33K 0   T(   d  c $4     s *4 49 f   >@  H  0ηo~ ? ̙33L 0   T(   d  c $4     s *@ 49 f   >@  H  0ηo~ ? ̙33M 0  $ T(  $ d $ c $4    $ s *M 49 f   >@  H $ 0ηo~ ? ̙33T 0  \ T(  \ d \ c $4    \ s *Z 49 f   >@  H \ 0ηo~ ? ̙33X 0 @  T(   d  c $4     s *Xg 49 f   >@  H  0ηo~ ? ̙33] 0 8T(  8d 8 c $4    8 s *0t 49 f   >@  H 8 0ηo~ ? ̙33^ 0 0@T(  @d @ c $4    @ s * 49 f   >@  H @ 0ηo~ ? ̙33_ 0 PHT(  Hd H c $4    H s * 49 f   >@  H H 0ηo~ ? ̙33` 0 pPT(  Pd P c $4    P s *l 49 f   >@  H P 0ηo~ ? ̙33a 0 XT(  Xd X c $4    X s *D 49 f   >@  H X 0ηo~ ? ̙33b 0 `T(  `d ` c $4    ` s * 49 f   >@  H ` 0ηo~ ? ̙33c 0 hT(  hd h c $4    h s * 49 f   >@  H h 0ηo~ ? ̙33d 0 pT(  pd p c $4    p s * 49 f   >@  H p 0ηo~ ? ̙33e 0 xT(  xd x c $4    x s *X 49 f   >@  H x 0ηo~ ? ̙33f 0 0T(  d  c $4     s *0 49 f   >@  H  0ηo~ ? ̙33g 0 PT(  d  c $4     s * 49 f   >@  H  0ηo~ ? ̙33h 0 pT(  d  c $4     s *l 49 f   >@  H  0ηo~ ? ̙33i 0 T(  d  c $4   l   s *l 49 f  l  >@  H  0ηo~ ? ̙33j 0 T(  d  c $4     s *xl 49 f  l  >@  H  0ηo~ ? ̙33k 0 T(  d  c $4   8  s *X849 f  8 >@  H  0ηo~ ? ̙33l 0 T(  d  c $4   8  s *849 f  8 >@  H  0ηo~ ? ̙33m 0 T(  d  c $4   8  s *849 f  8 >@  H  0ηo~ ? ̙33n 0 0T(  d  c $4   8  s *849 f  8 >@  H  0ηo~ ? ̙33o 0 PT(  d  c $4     s *L49 f   >@  H  0ηo~ ? ̙33p 0 pT(  d  c $4     s *$49 f   >@  H  0ηo~ ? ̙33q 0 T(  d  c $4      s *@49 f    >@  H  0ηo~ ? ̙33r]Wg`g} sa@l΍@ пGAɸ =|qU`8Un}txx) 5EAMY$e0?q}Vm/}  M [*7BRp ӛL%1 +="1Oh+'0T hp  Algebraic Model..508Microsoft PowerPoint@Fس@E1(@s}*@SlaGSg  )'    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www``4'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___www¼rrIrrrrrnnrrݼݻݵݻݵݻݼݼϋϋϋϋϋϋϋݻݻ⵴eeeeefeeeeeelrlmݮݻzztztzRztellefme↮euݼeffll݋eݼtݮfelemfeݦelQreeݒfeel⼋QX݋݋ݼelleeemeeePmeeeݒüfllf݋lXlRzݼ⼼elmlmfe⦋ePJeݼztݼ⼋slRJzݼyyKttü eeeeeeeeeeeeefeeeeeeeeeeeeeeeeee_eeeee_eefeeef_eefeeef_eef_eef_eef_eef_eef_eef_eef_eef_eef_eef_eef_eef_eef_e_e_eeeeeeeeeee_e_e_e___e___ee________e_e_e_e_e_e_eeee_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e___e_eeeeeeeeeee_e__e__e_e_e__e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e_e?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)PicturesKCurrent UserSummaryInformation(TPowerPoint Document(#DocumentSummaryInformation8