Louis Michaelis and Maude Menten's theory (1913) Applies to Enzymes - Carriers - proteins Related terms - Dose dependent kinetics - Saturation Kinetics
- Capacity limited kinetics Saturation Kinetics/ Capacity limited kinetics Assumptions 1. It assumes the formation of an enzymesubstrate complex 2.
It assumes that the ES complex is in rapid equilibrium with free enzyme 3. Breakdown of ES to form products is assumed to be slower than 1) formation of ES and 2) breakdown of ES to re-form E and S Derivation
For the reaction E+S ES P+E k-2 the reverse reaction can be neglected at the beginning (initial rate with [P]=0)
1) The rate of formation of the product v = k2[ES], 2)[Enzyme]total = [E]t = [E] + [ES] 3) At steady state: d[ES]/dt = 0 4) KM = (k-1 + k2)/k1 The rate of formation of ES is given as Assume steady state:
d[ES]/dt = 0 0 k1 [ E ][ S ] k 1 [ ES ] k 2 [ ES ] So: k1[E][S] = k-1[ES] + k2[ES] Rearranging we get [ES] = (k1/(k-1 + k2))[E][S]
The rate of formation of the product is given as [ ET ][ S ] [ ES ] (Km S ) the maximum rate is given as hence The Michaelis Mentens Equation
At [S] Km, Vo is proportional to [S] At [S] Km, Vo = Vmax 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 Understanding Km The "kinetic activator constant" K is a constant m K is a constant derived from rate
m constants K is, under true Michaelis-Menten m conditions, an estimate of the dissociation constant of E from S Small K means tight binding; high K m m means weak binding
Understanding Vmax The theoretical maximal velocity V max is a constant V max is the theoretical maximal rate of the reaction - but it is NEVER achieved in reality To reach V max would require that ALL enzyme molecules are tightly bound with substrate V
max is asymptotically approached as substrate is increased The dual nature of the Michaelis-Menten equation Combination of 0-order and 1st-order kinetics When S is low, the equation for rate is 1st order in S When S is high, the equation for rate is 0-order in S
The Michaelis-Menten equation describes a rectangular hyperbolic dependence of v on S a)Invitro determination Lineweaver Burk Double Reciprocal Plots It is difficult to determine Vmax experimentally
The equation for a hyperbola can be transformed into the equation for a straight line by taking the reciprocal of each side Vmax C v Km C 1 Km C
v Vmax C Km 1 1 v Vmax C Vmax The formula for a straight line is y = mx + b
A plot of 1/V versus 1/[S] will give a straight line with slope of KM/Vmax and y intercept of 1/Vmax Such a plot is known as a Lineweaver-Burk double reciprocal plot
Lineweaver-Burk plot (doublereciprocal) 29 HanesWoolf plot invert and multiply by [S]: Rearrange
b. In Vivo Determination Vmax Vmax Css v K m C ss If K 0 input rate Vmax C ss K0 K m C ss
Km K0 K 0 ( K m C ss ) Vmax Css K 0 K m K 0Css Vmax C ss K 0Css (Vmax Css ) K 0 K m K 0 Vmax K0
K m Css K0/Css JB is an 18 year male receiving phenytoin for prophylaxis of post-traumatic head injury seizures. The following steady state concentrations were obtained at the indicated doses: Dose (mg/d) Css (mg/L) 100
3.7 300 47 From this data, determine this patients Km and Vmax for phenytoin. JB is an 18 year male receiving phenytoin for prophylaxis of post-traumatic head injury seizures. The following steady state concentrations were obtained at the indicated doses: Dose (mg/d) Css (mg/L)
K0 (mg/d) Km = 9.7 mg/L K0/Css (L/d) 2/6/20 34 Significance of Km Km is a constant Small Km means tight binding; high Km means weak
binding Useful to compare Km for different substrates for one enzyme Hexokinase : D-fructose 1.5 mM D-glucose 0.15 mM Useful to compare Km for a common substrate used by several enzymes Hexokinase: D-glucose 0.15 mM Glucokinase: D-glucose 20 mM
Other applications 1)The Catalytic Efficiency kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate. kcat/Km is an apparent second-order rate constant which measures how the enzyme performs when S is low 2) Competitive inhibitor
Vmax unaltered, Km increased 39 3) Noncompetitive inhibitor Km unaltered, Vmax decreased 40
References Leon Shargel, A Text book of Applied Bio pharmaceutics and pharmacokinetics,5th edition Milo Gibaldi , Donald Perrier, Pharmacokinetics,2nd edition V.Venkateshwarlu, Biopharmaceutics and pharmacokinetics,(2004) Garret & Grisham , Biochemistry, 2nd edition http://en.wikipedia.org/wiki/Michaelis-Menten_kinetics German biochemist and physician
Let's look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient...
If this is an ongoing problem, your phone/device will automatically be sent to the office for parent/guardian pick-up and a MAJOR referral issued! ... The more you can practice with this type of lock, the easier opening your locker at...
Do Now: What is a bibliography vs works cited? According to the MLA manual: Works Cited is sometimes referred to as References. ...In Works Cited you only list items you have actually referred to and cited in your paper.A Bibliography...
Your Questions Answered. Act I FYI, the full title of the play is… The Most Excellent and Lamentable Tragedy of Romeo and Juliet *In Romeo and Juliet the tragic heroes are responsible for their falls to a certain extent, but...
Un resorte elástico Ley de Hooke Esfuerzo y deformación Tipos de esfuerzo Resumen de definiciones Esfuerzo y deformación longitudinales Ejemplo 1. Un alambre de acero de 10 m de largo y 2 mm de diámetro se une al techo y...
Define flexibility, muscular strength, and muscular endurance. Describe the benefits of improving and maintaining flexibility, muscular strength, and muscular endurance. ... Describe the SPORT and FITT principles . Discuss how training principles can improve cardiovascular fitness.
detoxify soluble toxic ions to insoluble and other less toxic forms. What is Bioprocessing???? } Chemical detoxification methods Bacteria currently being used LHVE - species of interest. characteristics include: gram positive, rod shaped bacteria forms spores. gelatinase activity.
Ready to download the document? Go ahead and hit continue!