Monday, October 25, 2010
Someone Rear-Ended Me Yesterday
So yesterday I was driving, minding my own business. It had just rained so the ground was wet. I went over a hill and the light at the bottom of the hill was yellow. So I slowed down and stopped. A few seconds later I hear a screech and feel my car jolt forward into the intersection. Some girl wasn't paying attention and didn't see me stop. So I get out of the car and look at the damage. My car, a 1997 Ford Taurus, didn't have hardly a scratch. She went under my bumper. She was driving a 2006 Chevy Cobalt. And her car was in bad shape. The radiator was busted, and her hood was quite crinkled. So we pulled off the road and called the cops. They came, filled out a police report, and we went on our way. I have Geico insurance, but not collision, so I will have to get my bumper repaired through her insurance. Oh well, wasn't my fault. Sucks for her though, but she had insurance, so she should be fine. Just a testament to Ford over Chevy.
Tuesday, October 12, 2010
Got a "B" on an Exam Today
So I graduated from Purdue University not too long ago with an engineering degree. I did very well, and have done well at work since then. I recently decided to get my Master's degree in my spare time, so that is what I do when I'm not designing new product lines and testing them out, or performing research. The thing I hate about getting my Master's is that I have to redo the things that I have already done years ago. One course I am taking is a math course, focusing on upper level differential equations. I took this same course at Purdue like four years ago, and got an A with no problems. But this course is different. It seems as if the professor likes math to be done his way, and not the traditional way. So we had our first exam and I got a "B". Not a big deal, but I usually do better. Solving proofs is not, as I see it, the duty of an engineer. Especially solving them without any reference material. I hate closed book exams. The way I see it, my job as an engineer is to apply these math concepts, and if I need to solve some equations, that is what I write Matlab and Excel programs for, or I can look them up in differential tables. Oh well, the school is paying me to get my Master's, so I don't really care too much. It is just something to do and gives me extra spending money on top of my work salary and patent income. So I got a B... I have the rest of the semester to turn it into an A. Or am I just being too picky?
Sunday, October 10, 2010
Numerical Symmetry on 10/10/10
So I thought this was worth sharing: Today I was driving my car and looked down at the odometer and it read 201102 miles. I then looked at the trip odometer and it read 555.5 miles. Pretty cool. If I wasn't on the highway I would have stopped to get my camera to take a pic, but by then it would have been too late. I later realized that today is 10/10/10. This kind of numerical symmetry rarely happens unplanned, but when it does it does it makes you glad you realized that it did.
Saturday, October 9, 2010
Spectrophotometry to Calculate Enzyme kinetics, based on Concentration, pH and Inhibitors
Here is another school paper that I wrote in 2006. I hope it is useful to someone out there, or at least furthers someone's knowledge on some basic chemistry regarding enzymes.
Abstract:
The goal of this study was to use spectrophotometry to assess the kinetics of the enzyme glucose oxidase, to analyze the effects of an inhibitor, and also to determine the optimal pH at which glucose oxidase acts. This was done by combining glucose oxidase with a glucose substrate under varying conditions, allowing the reaction to proceed while being read in a spectrophotometer, and using the data read over a time interval to draw conclusions about the varying conditions affecting the rate of reactions to product. Michaelis-Menten and Lineweaver-Burk plots were constructed based on the absorbance values determined from the spectrophotometer readings. The findings of this experiment show that the rate of reaction to products had a maximum velocity of -1.609*10-6M/sec, with a Km value of 0.1796. Other findings show that D-glucal is a competitive inhibitor, and that the optimal pH for glucose oxidase to perform is 6.
Introduction:
The purpose of this research endeavor was to determine the use of enzymes in biological systems, to use a spectrophotometer to assess the kinetics of the enzyme glucose oxidase, as well as to analyze the effects of an inhibitor, and also to determine the optimal pH at which glucose oxidase acts. Enzymes act to increase the speed of a chemical reaction without being changed or used up in the reaction that they catalyze (#1). This is done by lowering the activation energy of the reaction (#1). The Michaelis-Menten equation shows how initial reaction rate and substrate concentration are related. A Lineweaver-Burk plot can also be used to determine kinetics of a reaction, and is generally the reciprical of both sides of the Michaelis-Menten equation. Inhibition can be determined as well from Lineweaver-Burk plots. Competitive inhibition is when an inhibitor of a similar structure to the substrate binds to the active site and vies with the substrate for binding (#2). Non-competitive inhibition is when the inhibitor binds to a site other than the active site and changes the conformation of the active site to inactivate the enzyme (#2). By utilizing the enzyme glucose oxidase to catalyze a reaction, and analyzing that reaction over time through a spectrophotometer, substrate concentration and reaction rate may be determined. By plotting results of spectrophotometric readings, Km and Vmax values may be found. By performing another reaction with D-glucal used as an inhibitor, a supporting graph is used to find out if D-glucal is competitive or non-competitive. Varying the pH of the reaction can also show the optimal pH value that glucose oxidase performs.
Materials and Methods:
pH 7 buffer, glucose oxidase stock, and ABTS/HRP stock is added to wells of a 96-well plate, and water is added as a blank. A concentration gradient of glucose solution is added to the same wells and the samples are read in a spectrophotometer at a wavelength of 725nm every 10 seconds over the course of 3 minutes, and the results are recorded.
pH 7 buffer, glucose oxidase stock, and ABTS/HRP stock is added to wells of a 96-well plate, and water is added as a blank. A concentration gradient of glucose solution is mixed with D-glucal stock solution, and this solution is added to the wells. The samples are read in a spectrophotometer every 10 seconds over the course of 3 minutes and the results are recorded.
pH 4, 5, 6, and 7 buffer are added to wells of a 96-well plate, glucose oxidase stock and ABTS/HRP stock solution is added to these wells, and water is put in the plate as a blank. Glucose stock solution is added to the wells and the plate is immediately read in a spectrophotometer every 10 seconds over three minutes, with the results recorded.
Results:
See appendix for all absorbance values and relevant calculations. Using the absorbance values determined from the spectrophotographic readings, and using the extinction coefficient given in the lab of 19000/M/cm, and the pathlength of 1cm, the concentration of the product (D-gluconolactone) can be calculated. Taking the change in product concentration over a time interval yields a reaction velocity, and plotting this vs. the glucose concentration yields the plot below.
Figure 1.1: Michealis-Menten plot of initial reaction velocity vs. substrate concentration, showing the location of Vmax, Vmax/2, and Km values.
By taking the reciprocals of the reaction velocities determined above and plotting them against the reciprocal of the glucose concentration, a Lineweaver-Burk plot may be constructed. From this plot, using the equation of the best fit line, the x and y-intercepts may be calculated, and thus Km can be found by -1/(x-intercept), and Vmax¬ can be found by 1/(y-intercept). This plot is shown on the next page in Figure 2.1.
Figure 2.1: Lineweaver – Burk plot showing the relationship between reaction rate and glucose concentration.
Using the absorbance values determined from the second part of the lab, a Lineweaver-Burk plot may be constructed using the same principles as used on the previous graph. This plot is shown below along with the values from the previous figure, without an inhibitor. The relationship shown can help to determine whether D-glucal is a competitive or non-competitive inhibitor as well as it shows how the rate of reaction is affected by an inhibitor of the glucose oxidase reaction.
Figure 3.1: Lineweaver-Burk plot showing reaction with and without D-glucal, showing that D-glucal is a competitive inhibitor.
By using the absorbance values for varying pH from part three of the lab, as well as the extinction coefficient of 19000 M-1cm-1, the concentrations of the resulting product can be determined. Plotting these concentrations vs. the time taken for their formation yields the plot below. Based on this curve, it is possible to determine at exactly what pH value the enzyme glucose oxidase reacts optimally.
Figure 4.1: Concentration vs. time for varying pH values. The pH 5 line did not yield any change in concentration, possibly due to the accidental omission of glucose oxidase from the well.
Discussion and Conclusions
Plotting the reaction rate vs. glucose concentration as shown in Figure 1.1 gives a curve that follows Michaelis-Menten kinetics because it follows the standard curve for a Michaelis-Menten graph. The Lineweaver-Burk plot (Figure 2.1) was constructed by plotting 1/Vi vs. 1/[glucose]. Using the Lineweaver-Burk plot shows the K¬M value to be .1796, and the Vmax value to be -1.609*10-6. Having a negative value for Vmax is not accurate, and shows there was some experimental error in completing this part of the experiment.
Based on Figure 3.1, the Lineweaver Burk plot showing the reaction with the inhibitor and without the inhibitor, D-glucal is shown to be a competitive inhibitor, because it has a Vmax value that is close to that of the reaction without the inhibitor. The intersection of the two best fit lines occurs close to the y-axis, which is characteristic of competitive inhibition, and not close to the x-axis, which is characteristic of non-competitive inhibition. The results do not show the intersection of the two lines at the y-axis exactly due to the inaccurate absorbance values for the 0.05M glucose concentration data point on the inhibited graph. The absorbance value was lower than anticipated. Possible error in the preparation of the glucose solution, such as insufficient mixing of reactants, could have contributed to this problem. Still, competitive inhibitors do not affect Vmax, and thus D-glucal is a competitive inhibitor.
Based on Figure 4.1 of absorbance vs. time for the differing pH values, the optimal pH for glucose oxidase is pH 6. This is because the best fit line for pH 6 had the greatest value of slope of all the equations for the differing pH values, showing pH 6 to be the most favorable. The greater the slope of the best fit line, the faster the reaction rate. However, we cannot be certain about this value because pH 5 did not yield any absorbance values for our experiment. A possible explanation for the inaccuracy of pH 5 would be the accidental omission of glucose oxidase from the solution.
The enzyme glucose oxidase has many uses outside the laboratory. Commercial uses of glucose oxidase include the following: diabetes monitoring, biofuel cells, food and beverage additive, wine production, oral hygiene, and is also a commercial source of gluconic acid (#3).
Lineweaver-Burk utilizes reciprocals for both the x and y value data points. This distorts the results extrapolated from the plot, because the double reciprocal of the Lineweaver-Burk plot amplifies any experimental error, giving a high error for determining Km and Vmax (#4).
For this experiment, the reactants combine in a similar way to the Cell cycle and ELISA lab. This is because glucose oxidase is similar to the primary antibody used in previous labs. Because glucose oxidase is an enzyme for glucose, it binds to it and in that way it acts like a primary antibody in that it binds to the molecule of interest. Horseradish peroxidase is similar to the secondary antibody from previous labs in that it is bound to the primary antibody (glucose oxidase) and it acts as a bridge to the color changing substrate which in this case is ABTS.
Based on the Lineweaver-Burk plot of the data shown in Figure 8.1 in Appendix 3, the inhibition between the ACE inhibitor peptide and the biologically engineered ACE inhibitor is non-competitive. This data does not support the finding that the biologically engineered inhibitor and the naturally occurring inhibitor are equally capable of inhibiting ACE activity. The reason for this is the difference in the reaction velocities between the engineered and natural inhibitors. The engineered ACE inhibitor is found to be less effective than the natural inhibitor, because the engineered ACE inhibitor has a faster reaction velocity, and is closer to the control, which shows no inhibition.
Appendix 1
Table 1.1: Raw data from kinetic reads from the spectrophotometer for all three parts of the laboratory.
Appendix 2
From Lineweaver-Burk:
Vmax: y-int. = -621502
1/Vmax = -621502
Vmax = 1/-621502
Vmax = -1.609*10-6
KM: x-int. = 1/KM
x-int. = 5.5686152
5.5686152 = 1/KM
KM = 1/5.5686152 = .1796
Appendix 3
Figure 8.1: Lineweaver-Burk plot of initial reaction rates of engineered ACE Inhibitor and Natural ACE Inhibitor Peptide, showing the relationship to be non-competitive inhibition.
Appendix 4:
Sample calculation for changing absorbance into concentration for MM graphs:
Absorbance = ε*c*b
ε = extinction coefficient = 19000 M-1cm-1
b = pathlength = 1cm
c = concentration
Ex:
Kinetic read 2 (10 sec) of Part 1, 0.1M glucose concentration:
A = 1.476
c = A/ε/b
c = 1.476 / 19000 / 1
c = 7.768*10-5
Appendix 5:
Sample calculation for Vi for Part 1, 0.1M glucose concentration, over time interval between 10 seconds and 20 seconds, (same calculations also used in Part 2).
Ex:
Δt = change in time = 10 seconds
Concentration at 10 seconds: 7.768*10-5
Concentration at 20 seconds: 8.479*10-5
Difference = Conc20 - Conc10 = 7.105*10-6
Vi = Difference / Δt = 7.105*10-6 / 10 seconds = 7.105*10-7
1/Vi was used for Lineweaver Burk plots, while Vi itself was used for Michaelis-Menten plots
References
#1: “Enzyme Kinetics.” Basic Enzyme Reactions. Worthington-Biochem. 27 Oct 2006.
#2: “Competitive and Noncompetitive Inhibition.” MIT. 27 Oct 2006.
#3: “Glucose Oxidase and Biosensors.” From Biosensors to Food Preservative. InterPro. 27 Oct 2006.
#4: “A complete guide to nonlinear regression.” Displaying enzyme kinetic data on a Lineweaver- Burk plot . 1999. GraphPad Software. 27 Oct 2006.
Abstract:
The goal of this study was to use spectrophotometry to assess the kinetics of the enzyme glucose oxidase, to analyze the effects of an inhibitor, and also to determine the optimal pH at which glucose oxidase acts. This was done by combining glucose oxidase with a glucose substrate under varying conditions, allowing the reaction to proceed while being read in a spectrophotometer, and using the data read over a time interval to draw conclusions about the varying conditions affecting the rate of reactions to product. Michaelis-Menten and Lineweaver-Burk plots were constructed based on the absorbance values determined from the spectrophotometer readings. The findings of this experiment show that the rate of reaction to products had a maximum velocity of -1.609*10-6M/sec, with a Km value of 0.1796. Other findings show that D-glucal is a competitive inhibitor, and that the optimal pH for glucose oxidase to perform is 6.
Introduction:
The purpose of this research endeavor was to determine the use of enzymes in biological systems, to use a spectrophotometer to assess the kinetics of the enzyme glucose oxidase, as well as to analyze the effects of an inhibitor, and also to determine the optimal pH at which glucose oxidase acts. Enzymes act to increase the speed of a chemical reaction without being changed or used up in the reaction that they catalyze (#1). This is done by lowering the activation energy of the reaction (#1). The Michaelis-Menten equation shows how initial reaction rate and substrate concentration are related. A Lineweaver-Burk plot can also be used to determine kinetics of a reaction, and is generally the reciprical of both sides of the Michaelis-Menten equation. Inhibition can be determined as well from Lineweaver-Burk plots. Competitive inhibition is when an inhibitor of a similar structure to the substrate binds to the active site and vies with the substrate for binding (#2). Non-competitive inhibition is when the inhibitor binds to a site other than the active site and changes the conformation of the active site to inactivate the enzyme (#2). By utilizing the enzyme glucose oxidase to catalyze a reaction, and analyzing that reaction over time through a spectrophotometer, substrate concentration and reaction rate may be determined. By plotting results of spectrophotometric readings, Km and Vmax values may be found. By performing another reaction with D-glucal used as an inhibitor, a supporting graph is used to find out if D-glucal is competitive or non-competitive. Varying the pH of the reaction can also show the optimal pH value that glucose oxidase performs.
Materials and Methods:
pH 7 buffer, glucose oxidase stock, and ABTS/HRP stock is added to wells of a 96-well plate, and water is added as a blank. A concentration gradient of glucose solution is added to the same wells and the samples are read in a spectrophotometer at a wavelength of 725nm every 10 seconds over the course of 3 minutes, and the results are recorded.
pH 7 buffer, glucose oxidase stock, and ABTS/HRP stock is added to wells of a 96-well plate, and water is added as a blank. A concentration gradient of glucose solution is mixed with D-glucal stock solution, and this solution is added to the wells. The samples are read in a spectrophotometer every 10 seconds over the course of 3 minutes and the results are recorded.
pH 4, 5, 6, and 7 buffer are added to wells of a 96-well plate, glucose oxidase stock and ABTS/HRP stock solution is added to these wells, and water is put in the plate as a blank. Glucose stock solution is added to the wells and the plate is immediately read in a spectrophotometer every 10 seconds over three minutes, with the results recorded.
Results:
See appendix for all absorbance values and relevant calculations. Using the absorbance values determined from the spectrophotographic readings, and using the extinction coefficient given in the lab of 19000/M/cm, and the pathlength of 1cm, the concentration of the product (D-gluconolactone) can be calculated. Taking the change in product concentration over a time interval yields a reaction velocity, and plotting this vs. the glucose concentration yields the plot below.
Figure 1.1: Michealis-Menten plot of initial reaction velocity vs. substrate concentration, showing the location of Vmax, Vmax/2, and Km values.
By taking the reciprocals of the reaction velocities determined above and plotting them against the reciprocal of the glucose concentration, a Lineweaver-Burk plot may be constructed. From this plot, using the equation of the best fit line, the x and y-intercepts may be calculated, and thus Km can be found by -1/(x-intercept), and Vmax¬ can be found by 1/(y-intercept). This plot is shown on the next page in Figure 2.1.
Figure 2.1: Lineweaver – Burk plot showing the relationship between reaction rate and glucose concentration.
Using the absorbance values determined from the second part of the lab, a Lineweaver-Burk plot may be constructed using the same principles as used on the previous graph. This plot is shown below along with the values from the previous figure, without an inhibitor. The relationship shown can help to determine whether D-glucal is a competitive or non-competitive inhibitor as well as it shows how the rate of reaction is affected by an inhibitor of the glucose oxidase reaction.
Figure 3.1: Lineweaver-Burk plot showing reaction with and without D-glucal, showing that D-glucal is a competitive inhibitor.
By using the absorbance values for varying pH from part three of the lab, as well as the extinction coefficient of 19000 M-1cm-1, the concentrations of the resulting product can be determined. Plotting these concentrations vs. the time taken for their formation yields the plot below. Based on this curve, it is possible to determine at exactly what pH value the enzyme glucose oxidase reacts optimally.
Figure 4.1: Concentration vs. time for varying pH values. The pH 5 line did not yield any change in concentration, possibly due to the accidental omission of glucose oxidase from the well.
Discussion and Conclusions
Plotting the reaction rate vs. glucose concentration as shown in Figure 1.1 gives a curve that follows Michaelis-Menten kinetics because it follows the standard curve for a Michaelis-Menten graph. The Lineweaver-Burk plot (Figure 2.1) was constructed by plotting 1/Vi vs. 1/[glucose]. Using the Lineweaver-Burk plot shows the K¬M value to be .1796, and the Vmax value to be -1.609*10-6. Having a negative value for Vmax is not accurate, and shows there was some experimental error in completing this part of the experiment.
Based on Figure 3.1, the Lineweaver Burk plot showing the reaction with the inhibitor and without the inhibitor, D-glucal is shown to be a competitive inhibitor, because it has a Vmax value that is close to that of the reaction without the inhibitor. The intersection of the two best fit lines occurs close to the y-axis, which is characteristic of competitive inhibition, and not close to the x-axis, which is characteristic of non-competitive inhibition. The results do not show the intersection of the two lines at the y-axis exactly due to the inaccurate absorbance values for the 0.05M glucose concentration data point on the inhibited graph. The absorbance value was lower than anticipated. Possible error in the preparation of the glucose solution, such as insufficient mixing of reactants, could have contributed to this problem. Still, competitive inhibitors do not affect Vmax, and thus D-glucal is a competitive inhibitor.
Based on Figure 4.1 of absorbance vs. time for the differing pH values, the optimal pH for glucose oxidase is pH 6. This is because the best fit line for pH 6 had the greatest value of slope of all the equations for the differing pH values, showing pH 6 to be the most favorable. The greater the slope of the best fit line, the faster the reaction rate. However, we cannot be certain about this value because pH 5 did not yield any absorbance values for our experiment. A possible explanation for the inaccuracy of pH 5 would be the accidental omission of glucose oxidase from the solution.
The enzyme glucose oxidase has many uses outside the laboratory. Commercial uses of glucose oxidase include the following: diabetes monitoring, biofuel cells, food and beverage additive, wine production, oral hygiene, and is also a commercial source of gluconic acid (#3).
Lineweaver-Burk utilizes reciprocals for both the x and y value data points. This distorts the results extrapolated from the plot, because the double reciprocal of the Lineweaver-Burk plot amplifies any experimental error, giving a high error for determining Km and Vmax (#4).
For this experiment, the reactants combine in a similar way to the Cell cycle and ELISA lab. This is because glucose oxidase is similar to the primary antibody used in previous labs. Because glucose oxidase is an enzyme for glucose, it binds to it and in that way it acts like a primary antibody in that it binds to the molecule of interest. Horseradish peroxidase is similar to the secondary antibody from previous labs in that it is bound to the primary antibody (glucose oxidase) and it acts as a bridge to the color changing substrate which in this case is ABTS.
Based on the Lineweaver-Burk plot of the data shown in Figure 8.1 in Appendix 3, the inhibition between the ACE inhibitor peptide and the biologically engineered ACE inhibitor is non-competitive. This data does not support the finding that the biologically engineered inhibitor and the naturally occurring inhibitor are equally capable of inhibiting ACE activity. The reason for this is the difference in the reaction velocities between the engineered and natural inhibitors. The engineered ACE inhibitor is found to be less effective than the natural inhibitor, because the engineered ACE inhibitor has a faster reaction velocity, and is closer to the control, which shows no inhibition.
Appendix 1
Table 1.1: Raw data from kinetic reads from the spectrophotometer for all three parts of the laboratory.
Appendix 2
From Lineweaver-Burk:
Vmax: y-int. = -621502
1/Vmax = -621502
Vmax = 1/-621502
Vmax = -1.609*10-6
KM: x-int. = 1/KM
x-int. = 5.5686152
5.5686152 = 1/KM
KM = 1/5.5686152 = .1796
Appendix 3
Figure 8.1: Lineweaver-Burk plot of initial reaction rates of engineered ACE Inhibitor and Natural ACE Inhibitor Peptide, showing the relationship to be non-competitive inhibition.
Appendix 4:
Sample calculation for changing absorbance into concentration for MM graphs:
Absorbance = ε*c*b
ε = extinction coefficient = 19000 M-1cm-1
b = pathlength = 1cm
c = concentration
Ex:
Kinetic read 2 (10 sec) of Part 1, 0.1M glucose concentration:
A = 1.476
c = A/ε/b
c = 1.476 / 19000 / 1
c = 7.768*10-5
Appendix 5:
Sample calculation for Vi for Part 1, 0.1M glucose concentration, over time interval between 10 seconds and 20 seconds, (same calculations also used in Part 2).
Ex:
Δt = change in time = 10 seconds
Concentration at 10 seconds: 7.768*10-5
Concentration at 20 seconds: 8.479*10-5
Difference = Conc20 - Conc10 = 7.105*10-6
Vi = Difference / Δt = 7.105*10-6 / 10 seconds = 7.105*10-7
1/Vi was used for Lineweaver Burk plots, while Vi itself was used for Michaelis-Menten plots
References
#1: “Enzyme Kinetics.” Basic Enzyme Reactions. Worthington-Biochem. 27 Oct 2006
#2: “Competitive and Noncompetitive Inhibition.” MIT. 27 Oct 2006
#3: “Glucose Oxidase and Biosensors.” From Biosensors to Food Preservative. InterPro. 27 Oct 2006
#4: “A complete guide to nonlinear regression.” Displaying enzyme kinetic data on a Lineweaver- Burk plot . 1999. GraphPad Software. 27 Oct 2006
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