Two basic types of experiments BATCH VS. SEQUENTI AL DESIGN OF ANY RESEARCH PROJECT Optimal Experiment Design design = choice of screening BATCH DESIGN OF EXPERIMENTS concentrations for Dose-Response Screening of Enzyme Inhibitors 1. decide beforehand on the design of a com plete series of experim ents 2. perform all experiments in the series w ithout analyzing interim results Petr Kuzmic , Ph.D. 3. analyze entire batch of accumulated data BioKin, Ltd. W ATERTOW N, MASSACHUSETTS, U.S.A. 4. issue final report SEQUENTI AL DESIGN OF EXPERIMENTS PROBLEM 1. decide on the design of only one (or a small number of) experim ent (s) • Most assays in a typical screening program are not informative 2. perform one experiment SOLUTI ON 3. analyze interim results; did we accumulate enough experiments? • Abandon "batch design" of dose-response experiments • Use "sequential design" based on D-Optimal Design Theory 4. if not, go back to step 1 , otherwise ... 5. issue final report • Save 50% of screening time, labor, and material resources Optimal Design for Screening 2 Analogy with clinical trials What is wrong with this dose-response curve? ADAPTI VE CLI NI CAL TRI ALS ( ACT) : ADJUST THE EXPERIMENT DESIGN AS TIME GOES ON THE "RESPONSE" IS INDEPENDENT OF "DOSE": NOTHING LEARNED FROM MOST DATA POINTS Borfitz, D.: "Adaptive Designs in the Real World" BioIT World , June 2008 "control" data point: [Inhibitor] = 0 • assortment of statistical approaches including this point alone “early stopping” and “dose-finding” would suffice to conclude: • interim data analysis "no activity" • reducing development timelines and costs by residual utilizing actionable information sooner enzyme to make sure, activity let's use two points • experts : Donald Berry , chairman of the Department of Biostatistics not just one University of Texas MD Anderson Cancer Center • software vendors : Cytel, Tessela • industry pioneers : W yeth 1997 “Learn and Confirm” model of drug development log 10 [Inhibitor] "slow but sure restyling of the research enterprise" Optimal Design for Screening 3 Optimal Design for Screening 4 What is wrong with this dose-response curve? Why worry about doing useless experiments? THE SAME STORY: MOST DATA POINTS ARE USELESS IN CASE THE REASONS ARE NOT OBVIOUS: Academia: • time "control" data point: [Inhibitor] = 0 Publish your paper on time for grant renewal. • money Spend less on chemicals, hire a post-doc. • fame Invent a drug, get the Nobel Prize. these points residual would suffice enzyme activity Industry: • time Beat "the competition" to market. these points Spend less on chemicals, hire a post-doc. • money are useless • security Invent a drug, avoid closure of Corporate R&D. log 10 [Inhibitor] Optimal Design for Screening 5 Optimal Design for Screening 6 1
On a more serious note... Theoretical foundations: The inhibition constant THERE ARE VERY GOOD REASONS TO GET SCREENING PROJECTS DONE AS QUICKLY AS POSSIBLE DO NOT USE I C 5 0 . THE INHIBITION CONSTANT IS MORE INFORMATIVE Kuzmi č et al. (2003) Anal. Biochem. 3 19 , 272–279 E + I E • I K i = [E] eq [I] eq /[E.I] eq K i ... equilibrium constant � "Morrison equation" slope 1 Leishmania major Photo: E. Dráberová Academy of Sciences of the Czech Republic Four-parameter logistic equation slope 2 "Hill slope" no clear physical meaning ! Optimal Design for Screening 7 Optimal Design for Screening 8 Theoretical foundations: The "single-point" method Theoretical foundations: Optimal Design Theory AN APPROXI MATE VALUE OF THE INHIBITION CONSTANT FROM A SI NGLE DATA POINT NOT ALL POSSIBLE EXPERIMENTS ARE EQUALLY INFORMATIVE Kuzmi č et al. (2000) Anal. Biochem. 2 81 , 62–67 BOOKS: • Fedorov (1972) "Theory of Optimal Experiments" Relative rate "control" 100 V 0 • Atkinson & Donev (1992) "Optimum Experimental Designs" V r = V/V 0 K i = 12 nM 80 enzyme activity, % EDI TED BOOKS: 60 K i = 9 nM Single-point formula: • Endrényi (Ed.) (1981) "Kinetic Data Analysis: Design and Analysis K i = 11 nM of Enzyme and Pharmacokinetic Experiments" 40 K i = 8 nM − − I E V [ ] [ ]( 1 ) = • Atkinson et al. (Eds.) (2000) "Optimum Design 2000" K r V i − 1 / V 1 r 20 [I] JOURNAL ARTI CLES: 0 • Thousands of articles in many journals. 0.00 0.02 0.04 0.06 0.08 0.10 [Inhibitor], µM • Several articles deal with experiments in enzym ology / pharm acology . Optimal Design for Screening 9 Optimal Design for Screening 10 Optimal design of ligand-binding experiments Optimal design of enzyme inhibition experiments SIMPLE LIGAND BINDING AND HYPERBOLIC SATURATION CURVES THIS TREATMENT APPLIES BOTH TO "TIGHT BINDING" AND "CLASSICAL" INHIBITORS dissociation dissociation constant constant Endrényi & Chang (1981) J. Theor. Biol. 9 0 , 241-263 Kuzmi č (2008) manuscript in preparation SUMMARY: SUMMARY: K d K i • Protein (P) binding with ligand (L) P + L • Enzyme (E) binding with inhibitor (I) E + I P • L E • I • Vary total ligand concentration [ L ] • Vary total inhibitor concentration [ I ] Observe bound ligand concentration [ L B ] Observe residual enzyme activity, proportional to [E] free • Fit data to nonlinear model: • Fit data to nonlinear model: ⎛ ⎞ 1 ( ) = − − + − − + ⎛ ( ) ⎞ ⎜ 2 ⎟ 1 V V [ E ] [ I ] K [ E ] [ I ] K 4 K [ E ] "Morrison Equation" = ⎜ + + + + + − ⎟ 2 ⎝ ⎠ [ L ] [ L ] K [ P ] [ L ] K [ P ] 4 [ P ][ L ] 0 i i i ⎝ ⎠ 2 [ E ] B d d 2 TW O OPTIMAL LIGAND CONCENTRATIONS (we need at least tw o data points) : TW O OPTIMAL INHIBITOR CONCENTRATIONS (we need at least tw o data points) : = 1 = maximum feasible [Ligand] control experiment (zero inhibitor) [ L ] [ L ] [ I ] 0 1 max ( ) ⎛ ( ) ⎞ ( ) + − − ⎜ + + − − − ⎟ + 2 K [ P ] [ L ] [ L ] K [ P ] 4 [ P ][ L ] K [ P ] K [ P ] = i + ⎝ ⎠ d 1 1 d 1 d d [ I ] K [ E ] = + 2 [ L ] ( K [ P ]) ( ) ⎛ ( ) ⎞ ( ) 2 d − + + + + − − − − ⎜ 2 ⎟ K [ P ] [ L ] [ L ] K [ P ] 4 [ P ][ L ] K [ P ] K [ P ] ⎝ ⎠ d 1 1 d 1 d d Optimal Design for Screening 11 Optimal Design for Screening 12 2
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