Chemical KineticsChemical kinetics: the study of reaction rate, a quantity conditions affecting it,the molecular events during a chemical reaction (mechanism), andpresence of other components (catalysis).Factors affecting reaction rate: Concentrations of reactants Catalyst Temperature Surface area of solid reactants or catalyst 2
Elementary vs. overall reactionsReactions are the result of molecular collisions; & almost invariablydepend on the collision of no more than 2 molecular species at a time.Overall reactions, such as: 2 KAlSi3O8 + 2H + + 9H 2O Al2Si2O5 (OH)4 + 4H 4SiO4 + 2K +do not reveal the sequential, and possibly parallel, sets of molecularinteractions, i.e. elementary reactions, that are actually involved.
Example of fast reactions (only 1 elementary step): Ag + + Cl - AgCl(s) CO2,aq + OH - - HCO3Example of a two step reaction: O3 O2 + O O + O3 2 O2 _____________ Overall reaction: 2 O3 3 O2 Determining a rate law requires knowledge of the rate-limiting elementary reaction (usually only one). Allows accounting for the stoichiometry and the reaction order. If this is not possible (eg. for an overall reaction), rate laws are determined experimentally.
Reaction Rate DefinedReaction rate: changes in aconcentration of a product or a reactant per unit time. [ ] concentrationReaction rate = —— t change [ ] t t
Expressing reaction ratesFor a chemical reaction, there are many ways to express thereaction rate. The relationships among expressions depend onthe equation.Note the expression and reasons for their relations for thereaction 2 NO + O2 (g) = 2 NO2 (g) [O2] 1 [NO] 1 [NO2]Reaction rate = – ——— = – — ———— = — ——— t 2 t 2 t
Half time• the time for half of the reactant initially present to decompose, its half-time or half- life, t1/2,is a constant and hence independent of the initial concentration of the reactant.• For first order reaction :
Variation of Reaction rates and Order 2nd order, rate = k [A]2 rate First order, rate = k [A] k = rate, 0th order [A] [A] = ___?
Transition State TheoryApplies statistical mechanics to individual elementary reactions.Meaningless for overall reactions.Focuses on the activated complex, the molecular configurationpresent at the top of the energy barrier (actually a saddle point)between reactants and products in an elementary reaction.Assumes this complex is a true chemical species and assumes that theinitial reactants are always at equilibrium with the complex. Predicts that the rate is proportional to the number of activated complexes and to their rate of decomposition. Applies near equilibrium.
TST is somewhat similar to the idea that the rate is proportionalto the deviation from equilibrium (or the degree ofsupersaturation or undersaturation). n G QRate kdiss 1 exp G RT ln RT K eq kdiss G0 K eq expk precip RT Activated Complex: a hypothetical species believed to exist in an intermediate state (transition state) that lies between the reactants & the products. It is a temporary state where bonds are in the process of breaking & forming; it is a very unstable species with a high potential energy
• in the hypothetical reaction, A2 + B2 2AB A + B A…B A B : : A B A B A…B reactants activated products complex
• Let us consider the reaction of a hydrogen atom with diatomic hydrogen (H2) to yield a new H2 molecule and a different hydrogen atom
Initial Velocity (vo) and [S]• The concentration of substrate [S] present will greatly influence the rate of product formation, termed the velocity (v) of a reaction. Studying the effects of [S] on the velocity of a reaction is complicated by the reversibility of enzyme reactions, e.g. conversion of product back to substrate. To overcome this problem, the use of initial velocity (vo) measurements are used. At the start of a reaction, [S] is in large excess of [P], thus the initial velocity of the reaction will be dependent on substrate concentration
Initial Velocity (vo) and [S] (cont)• When initial velocity is plotted against [S], a hyperbolic curve results, where Vmax represents the maximum reaction velocity. At this point in the reaction, if [S] >> E, all available enzyme is "saturated" with bound substrate, meaning only the ES complex is present.
Substrate Saturation of an EnzymeA. Low [S] B. 50% [S] or Km C. High, saturating [S]
Steady State Assumption• The M-M equation was derived in part by making several assumptions. An important one was: the concentration of substrate must be much greater than the enzyme concentration. In the situation where [S] >> [E] and at initial velocity rates, it is assumed that the changes in the concentration of the intermediate ES complex are very small over time (vo). This condition is termed a steady-state rate, and is referred to as steady-state kinetics. Therefore, it follows that the rate of ES formation will be equal to the rate ES breakdown.
Michaelis-Menten Equation Derivation• Rate of ES formation = k1([ET] - [ES])[S] (where [ET] is total concentration of enzyme E and k-2 is considered neglible)• Rate of ES breakdown to product = k- 1[ES] + k2[ES]
Michaelis-Menten Equation Derivation (cont)• Thus for the steady state assumption:• k1([ET] - [ES])[S] = k-1[ES] + k2[ES]• This equation is the basis for the final Michaelis- Menten following algebraic rearrangement and substitution of Km and Vmax terms.
Meaning of Km• An important relationship that can be derived from the Michaelis-Menten equation is the following: If vo is set equal to 1/2 Vmax, then the relation Vmax /2 = Vmax[S]/Km + [S] can be simplied to Km + [S] = 2[S], or Km = [S]. This means that at one half of the maximal velocity, the substrate concentration at this velocity will be equal to the Km. This relationship has been shown experimentally to be valid for many enzymes much more complex in regards to the number of substrates and catalytic steps than the simple single substrate model used to derive it.
Meaning of Km (cont)• The significance of Km will change based on the different rate constants and which step is the slowest (also called the rate-limiting step). In the simplest assumption, the rate of ES breakdown to product (k2) is the rate- determining step of the reaction, so k-1 >> k2 and Km = k- 1/k1. This relation is also called a dissociation constant for the ES complex and can be used as a relative measure of the affinity of a substrate for an enzyme (identical to Kd). However if k2 >> k-1 or k2 and k-1 are similar, then Km remains more complex and cannot be used as a measure of substrate affinity.
Uses of Km• Experimentally, Km is a useful parameter for characterizing the number and/or types of substrates that a particular enzyme will utilize (an example will be discussed). It is also useful for comparing similar enzymes from different tissues or different organisms. Also, it is the Km of the rate-limiting enzyme in many of the biochemical metabolic pathways that determines the amount of product and overall regulation of a given pathway. Clinically, Km comparisons are useful for evaluating the effects mutations have on protein function for some inherited genetic diseases.
Meaning of Vmax• The values of Vmax will vary widely for different enzymes and can be used as an indicator of an enzymes catalytic efficiency. It does not find much clinical use.• There are some enzymes that have been shown to have the following reaction sequence:• In this situation, the formation of product is dependent on the breakdown of an enzyme-product complex, and is thus the rate- limiting step defined by k3.
Important Conclusions of Michaels - Menten Kinetics• when [S]= KM, the equation reduces to• when [S] >> KM, the equation reduces to• when [S] << KM, the equation reduces to
Derivation of kcat• A more general term has been defined, termed kcat, to describe enzymes in which there are multiple catalytic steps and possible multiple rate-limiting steps. The Michaelis-Menten equation can be substituted with kcat
Definition and Use of kcat• The constant, kcat (units of sec-1), is also called the turnover number because under saturating substrate conditions, it represents the number of substrate molecules converted to product in a given unit of time on a single enzyme molecule. In practice, kcat values (not Vmax) are most often used for comparing the catalytic efficiencies of related enzyme classes or among different mutant forms of an enzyme.
Lineweaver-Burk (double reciprocal plot)• If the reciprocal (1/X) of the Michaelis-Menten equation is done, after algebraic simplification the following equation results:• This relation is written in the format of the equation for a straight line, y = mx + b, where y = 1/vo, m (slope) = Km/Vmax, x = 1/[S] and the y-intercept, b = 1/Vmax. When this relation is plotted,the result is a straight line graph
Uses of double reciprocal plot• The x intercept value is equal to -1/Km. The biggest advantage to using the double reciprocal plot is a more accurate determination of Vmax, and hence Km. It is also useful in characterizing the effects of enzyme inhibitors and distinguishing between different enzyme mechanisms.