bk_ch3_10_30_06_54pp

bk_ch3_10_30_06_54pp - Biological Kinetics K. Dane Wittrup...

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Biological Kinetics K. Dane Wittrup & Bruce Tidor October 30, 2006
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Contents 3 Binding Equilibria and Kinetics 1 3.1 Equilibrium monovalent binding . .......................... 1 3.1.1 Monovalent binding isotherm . ....................... 1 3.1.2 Graphical representations. 4 3.2 Binding rate expression. ............................... 5 3.3 Multivalent binding. ................................. 1 0 3.3.1 Independent sites — statistical mechanics. ................. 1 0 3.3.2 Cooperativity. ................................ 1 4 3.3.3 Avidity and effective concentration . .................... 1 6 Case Study 3-1 “The afFnity-enhancing roles of flexible linkers in two-domain DNA-binding proteins.” H.-X. Zhou. Biochemistry 40 : 15069–15073 (2001) 22 3.3.4 Equilibrium bivalent binding at cell surfaces. ................ 2 8 Case Study 3-2 “T-Cell Activation by Soluble MHC Oligomers Can Be De- scribed by a Two-Parameter Binding Model.” J. D. Stone, J. R. Cochran, and L. J. Stern Biophysical Journal 81 : 2547–2557 (2001). ........ 3 4 3.4 Measuring fast reaction rates . ............................ 3 6 3.4.1 Relaxation (perturbation, temperature jump). 3 7 3.4.2 Double jump experiments to detect hidden rate processes. ......... 3 8 3.5 Nucleic acid hybridization . ............................. 3 9 3.5.1 T m prediction . 3 9 3.5.2 Hybridization kinetics . ........................... 4 2 Case Study 3-3 “Use of hybridization kinetics for differentiating speciFc from non-speciFc binding to oligonucleotide microarrays.” H. Dai, M. Meyer, S. Stepaniants, M. Ziman, and R. Toughton. Nucleic Acids Research 30 : e86(2002) .................................. 4 4
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ii CONTENTS
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Chapter 3 Binding Equilibria and Kinetics “If a man’s wit be wandering, let him study the mathematics.” Francis Bacon In this chapter we will develop the basic mathematical relationships that describe the rates of the biomolecular interactions underpinning biological function. We Frst consider monovalent protein– ligand interactions, then the effects of multivalent interactions and energetic communication be- tween binding sites, and, Fnally, nucleic acid hybridization. 3.1 Equilibrium monovalent protein–ligand binding can be described with an equilibrium constant K d 3.1.1 Monovalent binding isotherm ±or given initial concentrations of protein and ligand, what fraction of the molecules are bound in complex at equilibrium? The simplest case to consider is that in which a single protein binds a single ligand to form a complex (±igure 3.1). where P = protein, L = ligand, C = complex, with the + k on k off LP C Figure 3.1. One molecule of ligand L binds to one molecule of protein P , to form one molecular complex C .
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2 CHAPTER 3. BINDING EQUILIBRIA AND KINETICS equilibrium dissociation constant K d defned as Follows: K d [ P ] eq [ L ] eq [ C ] eq (3.1) where the square brackets and subscript [] eq indicates a concentration at equilibrium, and the subscript “eq” will generally be dropped For convenience in situations where equilibrium conditions are clearly under consideration. The equilibrium dissociation constant K d is experimentally determined by taking measurements oF [ C ] as a Function oF the initial concentrations [ P ] o and [ L ] o . Such an experiment is called a titration , and the resulting curve oF [ C ] versus [ L ] o is reFerred to as a binding isotherm (because the experiment is generally perFormed isothermally.) The usual experimental strategy is to add increasing amounts oF ligand [ L ] o
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This note was uploaded on 07/19/2010 for the course BME 3604 taught by Professor Lt during the Spring '10 term at University of Florida.

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bk_ch3_10_30_06_54pp - Biological Kinetics K. Dane Wittrup...

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