Introduction to Enzyme kinetics Why study kinetics Kinetic information is useful for examining possible mechanisms for the reaction This is true for all types of reactions kinetic principles are used to understand both catalyzed and non catalyzed reactions For enzymes kinetic information is useful for understanding how metabolism is regulated and how it will occur under different conditions For enzymes kinetic information is useful for understanding pathological states Diseases and disorders often involve alterations in enzymes or enzyme activities Understanding the way that enzymes work is critical for understanding how drugs work because most drugs function by interacting with enzymes In addition the more you know about an enzymatic reaction the more information you will have for designing new drugs Finally essentially all of biochemistry is based on enzymes It is nearly impossible to understand biochemistry without understanding enzymes and it is impossible to understand enzymes without understanding the kinetic principles of the reactions they mediate Thermodynamic considerations and transition state theory Consider a simple system involving the conversion of one molecule S into another molecule P The molecules S and P have different energies Energy S P S G P Progress of Reaction For this system as for any other G RT ln Keq G is a measure of the relative energies of the two molecules and thus gives the direction for the reaction when the concentrations of the two molecules are equal For reactions involving multiple substrates and products G gives the direction in which the reaction will proceed under standard conditions i e when the concentration of all participating species is one molar except protons and water Copyright 2000 2011 Mark Brandt Ph D 11 protons and water are exceptions because G refers to pH 7 0 and includes the high concentration of water in the term as a constant Thermodynamics determines which direction is preferred however standard thermodynamics yields no information about the rate of the reaction Because the tools and concepts of thermodynamics are very powerful they were extended to allow an understanding of why reactions occur with different rates If a maximum energy state exists intermediate between S and P and if this state is assumed to be in equilibrium with S and P it is possible to apply the concepts of thermodynamics to the reaction process This transient high energy intermediate is usually called a transition state and will be abbreviated X the symbol is typically used to designate the transition state The extension of thermodynamics to consider rates of reaction is called transition state theory to emphasize the importance of this concept S X P The equilibrium constant for the process of S going to the transition state is Note that concentration of S is usually abbreviated as S This allows the calculation of the G for the transition state G RT ln Keq The G is the free energy difference between S and the transition state Note that there is also a separate G in this case a larger one between P and the transition state G is often referred to as the activation energy it is the energy that molecules of S must have in order to form molecules of P Transition state X Energy G S G P Progress of Reaction Copyright 2000 2011 Mark Brandt Ph D 12 The rate of a chemical reaction depends on the G for the reaction Using the principles of transition state theory J H van t Hoff and later Svante Arrhenius derived an equation for the reaction rate constant k Ae G RT In this the Arrhenius equation k is the rate constant for the reaction and A is the Arrhenius constant for the reaction The Arrhenius constant for a reaction is a measurable quantity Transition state theory predicts that A kBT h where kB is the Boltzmann constant 1 380649 x 10 23 J K T is absolute temperature and h is Planck s constant 6 6261 x 10 34 J sec for real reactions the measured value of A tends to vary from this theoretical value The Arrhenius equation states that if the G decreases the rate of the reaction will increase note that it also states that the rate of the reaction will increase with increasing temperature changing temperatures is rarely possible for biological processes but control of temperature can be important for in vitro experiments Based on transition state theory the rate of a reaction is dependent on the energy difference between the initial state and the highest energy transient state along the reaction pathway Assuming that this is true rate enhancements by enzymes must be mediated by a decrease in the energy of the highest energy transition state A decrease in the energy of the highest energy transition state can be accomplished in one of two main ways Some enzymes use one of these ways and some use both 1 The enzyme stabilizes the transition state The same transition state that would normally be present in the reaction pathway is also present in the enzymecatalyzed pathway but in the enzyme catalyzed pathway this state has a lower energy 2 The enzyme allows a different pathway for the process Without the enzyme the reaction might proceed by some pathway The enzyme allows a different series of reactions to occur that would otherwise be either of much higher energy or impossible In the enzyme catalyzed process the highest energy transition state which does not exist in the non catalyzed process has a lower energy than the energy of the transition state for the non catalyzed process Let us consider the first of these possibilities Consider a reaction in which S is converted to P either as a simple chemical reaction or as an enzyme catalyzed process Instead of merely stating S P for transition state theory we need to add an additional term kuncat S X P E S ES kcat EX EP E P In each case the reaction pathway passes through an identical transition state X in the uncatalyzed pathway this species is not bound to the enzyme but it is the Copyright 2000 2011 Mark Brandt Ph D 13 same species in both cases In each case in the scheme above the rate constant shown is the one for the slowest step in the forward direction reaction In the reaction diagram we can show the binding of the substrate and dissociation of the product from the enzyme explicitly Note that the ES complex is lower in energy than the free S which is why this complex forms spontaneously X Energy G uncat EX E S G cat E P ES G EP Progress of Reaction Using the principles of transition state theory we can derive an