BC351 Protein Function Basic Enzyme Kinetics Lecture 6 Terms Kinetics Rate constant Saturating Conditions kcat Km Principles 1 The purpose of studying enzyme kinetics 2 Introduce you to the language of enzyme kinetics 3 Develop a molecular understanding of an enzymatic reaction a To do so we will be looking at lots of graphs and basic equations describing the data within the graphs I Introduction a Why do a Kinetic study i Definition of kinetics 1 ii There are several reasons 1 To characterize the enzyme a From a research standpoint this is basically answering the question What does the enzyme do if it is working properly iii To understand the mechanism of the enzyme 1 This can lead to fascinating discoveries in a Drug design b Biomedical engineering LN06 1 II General kinetics pg 188 a The primary question of kinetics is i What is the rate of the production of X dependent upon ii Let s start with a very simple reaction A X d X Rate or Velocity v0 k1 A dt 1 But what is this rate dependent upon a Two things i The concentration of the reactants d X dt A ii The rate constant k 1 Definition of the rate constant a A k1 X k1 k BT G RT e h 2 Large vs small 2 So a d X dt k1 A LN06 2 III Enzyme kinetics pgs 194 197 a The question is i What is the rate of an enzymatic reaction dependent upon ii Compare a simple chemical reaction on left and the simplest enzymatic reaction on right A k1 k1 X Efree S k 1 d X dt k2 E S Efree P k 2 d P dt A S iii Notice for the enzymatic graph you get to possibilities 1 Hyperbolic curve 2 Sigmoidal curve 3 Either way there is not a linear relationship b w S and rate but there is some dependency LN06 3 iv The Michaelis Menten equation 1 To really understand this equation and all the parameters it is instructive to go through its derivation However we won t be doing that and if you want more detail look at pages 194 197 of your book d P Vmax S v0 dt Km S kcat E T S Km S v It the rate of the production of P is dependent upon 1 Vmax a Vmax kcat E T b Dependent upon kcat and E T 2 S 3 Km IV E How does each kinetic variable affect the rate pgs 197 199 a Marble transfer reaction S 1 GRAB ES 2 UP 3 OVER 4 DROP LN06 ES 4 EP E P b E T i The more enzymes the greater the rate of production V max k cat E T v0 E T c S i This quantity is related to an enzymes to find time ii At low S E S 1 GRAB ES 2 UP ES 3 OVER EP 4 DROP E P 1 Increases in S will have a linear effect on rate 2 Why Because each time the S goes up the enzyme s to find time goes down LN06 5 iii At saturating conditions 1 Definition of saturating conditions a E S 1 GRAB ES 2 UP ES 3 OVER EP 4 DROP E P 2 At these S additional substrate will not increase the enzymes to find time and thus no increase in the rate will be observed a This describes the hyperbolic behavior of the curve LN06 6 d kcat AKA Turnover number i Enzymes to convert time at saturating conditions ii Definition of kcat 1 iii Larger turnover numbers mean faster rates and larger Vmax E S 1 GRAB ES 2 UP ES 3 OVER EP 4 DROP E P iv Comparison of two different reactions E S 1 GRAB ES 2 UP ES 3 OVER 4 DROP v Comparison EP E ofP two different enzymes 1 This is a good way to measure catalytic efficiency at saturating conditions LN06 7 e Km i How much substrate is needed ii Definition of Km 1 iii This value determine how steep or shallow the curve is f Measuring true catalytic efficiency i At High S unlimited 1 kcat ii At Low S more biologically relevant and this is what is used 1 kcat Km E S 1 GRAB ES 2 UP ES 3 OVER EP 4 DROP E P LN06 8 V Enzymology in practice a Human sulfite oxidase deficiency i Human sulfite oxidase deficiency is a horrible genetic disease resulting in debilitating neurological disorders that manifest shortly after birth 1 Symptoms include a Seizures mental retardation dislocation of the ocular lenses b The disease often leads to death ii Sulfite oxidase 1 This is the terminal enzyme of the sulfur containing amino acid degradation pathway a This is a complicated but important pathway and we will not be going over it in class iii The disease is the result of a mutation in the sulfite oxidase active site changing Arg 160 to Gln R160Q iv When 1st discovered researchers did a kinetic study on this and the native wildtype enzyme and found the following Enzyme Km uM kcat s 1 kcat Km M 1 s 1 Wild type 17 18 1 1 x 106 R160Q 1900 3 1 6 x 103 Garrett R M Johnson J L Graf T N Feigenbaum A Rajagopalan K V 1998 PNAS 95 6394 9398 LN06 9