Michaelis-Menten graph

When the rate of reaction is measured at fixed [E], but varying [S] and the results plotted, the Michaelis—Menten graph is obtained (below). This rectangular hyperbola indicates saturation of the enzyme with substrate. 

In zone a of Figure 2.5, the kinetics are first order with respect to [S], that is to say that the rate is limited by the availability (concentration) of substrate so if [S] doubles the rate of reaction doubles. In zone c however, we see zero order kinetics with respect to [S], that is the increasing substrate concentration no longer has an effect as the enzyme is saturated zone b is a transition zone. In practice it is difficult to demonstrate the plateau in zone c unless very high concentrations of substrate are used in the experiment. Figure 2.5 is the basis of the Michaelis-Menten graph (Figure 2.6) from which two important kinetic parameters can be approximated ... 

Avoid the temptation to overly annotate your graphs but do mark on any important points or regions, for example segments representing zero and first-order kinetics on the Michaelis-Menten graph. 

It may help to write the equation down first to remind yourself which functions go where. The simple point of this diagram is that it linearizes the Michaelis-Menten graph and so makes calculation of and Krn much easier as they can be found simply by noting the points where the line crosses the y and x axes, respectively, and then taking the inverse value. 

Figures 4.12, 4.14, and 4.17 are Lineweaver-Burk graphs of competitive, noncompetitive, and uncompetitive reversible inhibitors. Sketch three Michaelis-Menten graphs showing an enzyme with and without one of the three types of inhibitors. Clearly label the important parts of each graph. 

Figure 4.1 Typical Michaelis-Menten graph which shows the dependency of the reaction rate on the substrate concentration for = 1 (adapted...

Figure 4.2 Is the catalytic specificity an appropriate value for the comparison of different enzymes Michaelis-Menten graphs for different AT, -values with Fgat(t) = + 3 (the value of 3 was arbitrarily chosen) and thus...

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

It was found out that reaction of the hydrolysis of highlymetoxilated beet pectin (catalyzed by P. fellutanum pectinesterase) obeyed Michaelis—Menten equation only under low substrate concentrations (up to 1.2%), when graph of the dependence of reaction speed was hyperbolic in form. 

In case of two —stage enzymatic reactions, which did not obey Michaelis— Menten equ — ation reaction speed was at its maximum and then decreased.Graph of speed of substrate hyd —rolysis against In concentration acquired a shape of symmetric or asymmetric bell (Figure 4). 

Characteristically, within certain concentration limits, if a chemical is absorbed by passive diffusion, then the concentration of toxicant in the gut and the rate of absorption are linearly related. However, if absorption is mediated by active transport, the relationship between concentration and rate of absorption conforms to Michaelis-Menten kinetics and a Lineweaver-Burk plot (i.e., reciprocal of rate of absorption plotted against reciprocal of concentration), which graphs as a straight line. 

Enzyme kinetics Michaelis constant, symbol iCm maximum velocity of an enzyme catalysed reaction, Vm DC inhibitor constant, symbol X Michaelis-Menten equation and graph in the absence and the presence of inhibitors. Lineweaver-Burke and Eadie-Hofstee plots. 

Use the data in Table 2.2 to plot Michaelis-Menten, Lineweaver-Burke and Eadie-Hofstee graphs to determine Km and Vm DC values. Answers are given at the end of the chapter. 

Test your IT skills. Try creating Excel spreadsheets based on the Michaelis-Menten equation (Equation 2.9) and its variants (Equations 2.10 and 2.11). Insert into your spreadsheets your own values for JCm, Vmax, [S], [I] and A) and use Excel to plot Michaelis-Menten, Lineweaver-Burke and Eadie-Hofstee graphs. 

A Michaelis-Menten type graph for an allosteric enzyme shows not the usual hyperbolic shape as shown in Section 1.4, but a sigmoidal relationship between [S] and activity. 

The effect of the inhibitor has resulted in a loss of the cooperative effect normally seen in allosteric enzymes so the graph looks like a simple Michaelis-Menten plot. 

Fitting velocity data directly to a hyperbohc curve has several advantages over linear methods, transformed or otherwise. The major advantages are that no transformation of data is necessary, curves are fitted easily with currently available graphing software, and variations in behavior from a simple Michaelis-Menten one-substrate equation usually result in an equation which still describes a hyperbola, thus requiring no change in the analytical approach. 

The Lineweaver-Burk equation is a reciprocal form of the Michaelis-Menten equation. The same data graphed in this way yield a straight line as shown in Figure 1-8-6. The actual data are represented by the portion of the graph to the right of the y-axis, but the line is extrapolated into the Idt quadrant to determine its intercept with the x-axis. The intercept of the line with the x-axis gives the value of The intercept of the line with the y-axis gives the value of... 

Kinetic analysis of tyrosinase and calculation of constants will be described using graphical analysis by the Michaelis-Menten equation, Lineweaver-Burk equation, or the direct linear curve. Procedures for preparing these graphs are described below. Alternatively, students may use available computer software to graph data and calculate kinetic constants. Recommended enzyme kinetic computer software packages include Enzyme... 

The treatment of results will be described for L-dopa. The procedure for D-dopa is identical. Prepare a table of L-dopa concentration per assay (mmo-lar) vs. AA/mm. Convert all AA/mm units to p,moles/min as desenbed in part B. Prepare a Michaelis-Menten curve (jumoles/min vs. [S]) as in Figure E5.1 and a Lineweaver-Burk plot (1/p.mole/min vs 1/[S]) as in Figure E5.2. Alternatively, you may wish to use the direct linear plot. Estimate and V max from each graph. The intercept on the rate axis of the Lineweaver-Burk plot is equal to UVm3zr For example, if the line intersects the axis at 0.02, then Vmax = 1/0.02 or 50 panoles of product formed per minute. The line intersects the 1/[S] axis at a point equivalent to — /Ku. If the intersection point on the 1/[S] axis is —0.67, then AM = -1/ -0.067 = 15 p-molar. Repeat this procedure for the data obtained for D-dopa. Compare the KM and max va ues and explain any differences. 

There are exceptions to Michaelis-Menten behaviour. For example allosteric enzymes which instead of a hyperbolic curve in a Lversus [S] graph yield a sigmoidal plot (the behaviour is rather like non-catalytic allosteric proteins, such as haemoglobin, Section 2.5. This type of curve can indicate cooperative binding of the substrate to the enzyme. We have discussed cooperativity in Section 1.5 (see also Section 10.4.3). In addition, regulatory molecules can further alter the activity of allosteric enzymes. 

In addition to being easier to fit than the hyperbolic Michaelis-Menten equation, Lineweaver-Burk graphs clearly show differences between types of enzyme inhibitors. This will be discussed in Section 4.5. However, Lineweaver-Burk equations have their own distinct issues. Nonlinear data, possibly indicating cooperative multiunit enzymes or allosteric effects, often seem nearly linear when graphed according to a Lineweaver-Burk equation. Said another way, the Lineweaver-Burk equation forces nonlinear data into a linear relationship. Variations of the Lineweaver-Burk equation that are not double reciprocal relationships include the Eadie-Hofstee equation7 (V vs. V7[S]) (Equation 4.14) and the Hanes-Woolf equation8 ([S]/V vs. [S]) (Equation 4.15). Both are... 

Included in the following table are some data points from a hypothetical enzyme kinetics study. Using a spreadsheet program with graphing abilities (such as Excel), generate a Line-weaver-Burk plot of the data points in the table. Determine the best-fit line for the data along with Vnax, ATm, and r2 (the square of the correlation coefficient of the line). Does this enzyme follow Michaelis-Menten kinetics Why or why not ... 

As a complement to question 1, plot the binding data of thiomuscimol in Michaelis-Menten (response versus [L]) format. Try to create a Lineweaver-Burk plot (1/response versus 1/[L]) and perform a linear regression on the data. What is the problem you encounter while making this graph Do your best to graph the data. From the best-fit line of the Lineweaver-Burk plot, determine Kt) and Enva. How well does Ku in this graph match the Ku you determined in... 

Let us give some examples for the graphs of linear mechanisms. The simplest mechanism of an enzyme catalytic reaction is the Michaelis Menten scheme... 

Regulatory enzymes are usually identified by the deviation of their kinetics from Michaelis-Menten kinetics plots of velocity versus substrate concentration can be a sigmoidal curve or a modified hyperbola [Fig. 9-7(o)]. If these curves are plotted in the double-reciprocal (Lineweaver-Burk) form, nonlinear graphs are obtained [Fig. 9-7(6)]. 

The Hanes-Woolf equation is another transformation of the Michaelis-Menten equation that yields a linear graph of the appropriate transformed variables. The equation is ... 

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