Assessment 2 – Computer Assignment 1. It is desired to find the rate parameters of an enzymatic...

Question

Assessment 2 – Computer Assignment
1. It is desired to find the rate parameters of an enzymatic reaction which is assumed to follow Michaelis-
Menten (M-M) kinetics. There are no inhibitors present and the reaction is not inhibited by the product or
the substrate. The reaction rates at different substrate concentrations were obtained using initial-rate
experiments. These are given in Table 1.
Estimate the rate parameters using linear regression based on the three commonly used linearization of
the M-M rate equation. Also estimate the parameters using non-linear regression. Use Matlab for the
egression analysis. Analyse your results and discuss the uncertainties (e
ors) in the parameters
particularly in terms of the effect of the linearized form that was used to estimate them. Summarise your
conclusions from this analysis.
[S]
(x 10-4 mol/l)
v
(x 10-4 mol/l/s)
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
Note: You need to review regression analysis using Matlab. A pdf file containing instructions on how to use
Matlab for regression analysis is provided under Activity 2.2 in Learnline. You also require an understanding
of how to estimate uncertainty in a parameter using propagation of e
ors. A document describing this
technique is also available under Activity 2.2.
2. (Problem 3.13 Kargi and Schuler). The following data was obtained from enzymatic oxidation of phenol
y phenol oxidase at different phenol concentrations.
(a) Determine the type of inhibition mechanism for this reaction.
(b) Determine the Michaelis-Menten parameters and the dissociation constant KI for the inhibitor.
Note: Inhibition can be due to inhibitor present or due to substrate. Use non-linear regression as well as
one of the linearised equations. Choose the linearised equation based either on your observations in the
first problem.
[S] mg/l v (mg/l-h)
10 5.0
20 7.5
30 10.0
50 12.5
60 13.7
80 15.0
90 15.0
XXXXXXXXXX
130 9.5
140 7.5
150 5.7
Your submission should be in the form of a report for each of the problem. This report will consist of a
ief
summary including the aim of your work, description of the methodology used, results and analysis
followed by conclusions.

Assessment 2: Marking Scheme
Format, clarity and structure of report 15%
 Aims
 Procedure adopted
 Clarity of graphs, figures
 Format
Problem 1: 55%
Implementation: 10% (Linear regression – 5%; Non-linear regression: 5%)
 Description of linearization methods and non-linear regression
 Estimation of parameters
Results: 15%
 Graphs
 Tables
Analysis & Conclusions: 30%
 Comparison of different linear methods including e
or analysis of parameters (15%)
 Comparison of linear and nonlinear methods including e
or analysis of parameters (10%)
Problem 2: 30%
Implementation: 7%
 How will inhibition be identified using linear regression? Which type of plot will be used? (8%)
 How will the inhibition be identified using non-linear regression? (7%)
Results: 8%
 Graphs
 Tables
Analysis and Conclusions: 12%
 Discussion based on graphs to identify type of inhibition using linear regression (3%)
 Discussion based on graphs to identify type of inhibition using nonlinear regression (3%)
 Estimation of parameters (9%)

qfile_636888946413587825_125540_1.pdf qfile_636888946413587825_125540_2.pdf

Nihal · Accepted Answer

Summery 
This report consists of a solution of two questions who answer are explained well. Matlab is used as the main tool for regression analysis. Both Linear and nonlinear regression is done in the Matlab. The results are shown in the shape of tables and groups and analyzed in the later part of the report.
Problem 1:
Aim of work
The aim of this work is to understand the regression analysis. Especially linear and nonlinear analysis and with the help of Matlab.
Methodology used
Regression is a solid strategy for recognizing which factors have sway on a theme of premium. The way toward playing out a relapse enables you to unhesitatingly figure out which factors matter most, which elements can be disregarded, and how these elements impact one another.
· Linear Regression 
It is an essential and ordinarily utilized kind of prescient investigation. The general thought of relapse is to analyze two things: 
· does a lot of indicator factors work admirably in foreseeing a result (subordinate) variable? 
· Which factors, specifically, are huge indicators of the result variable, and how do they– shown by the extent and indication of the beta estimates– sway the result variable? 
These relapse gauges are utilized to clarify the connection between one ward variable and at least one free factors. Before endeavoring to fit a direct model to watched information, a modeler should initially decide if there is a connection between the factors of intrigue. This does not really suggest that one variable causes the other (for instance, higher SAT scores don't cause higher school grades), yet that there is some huge relationship between the two factors. A scatterplot can be a useful device in deciding the quality of the connection between two factors. In the event that there have all the earmarks of being no relationship between the proposed illustrative and subordinate factors (i.e., the scatterplot does not show any expanding or diminishing patterns), at that point fitting a straight relapse model to the information most likely won't give a valuable model. A significant numerical proportion of the relationship between two factors is the convection coefficient, which is an incentive between negative one and positive one demonstrating the quality of the relationship of the watched information for the two factors.
The equation of linear regression is:
Here x is independent variable and Y is dependent variable who is depended on the slope of this line b and a is intercept.
There are many types of Linear regression.
A. Straightforward and different Linear regression 
The least complex instance of a solitary scalar indicator variable x and a solitary scalar reaction variable y is known as basic direct relapse. The augmentation to different as well as vector-esteemed indicator factors (signified with a capital X) is known as numerous straight relapse, otherwise called multivariable direct relapse. About all certifiable relapse models include various indicators, and fundamental portrayals of straight relapse are regularly expressed as far as the numerous relapse display. Note, in any case, that in these cases the reaction variable y is as yet a scalar. Another term, multivariate direct relapse, alludes to situations where y is a vector, i.e., equivalent to general straight relapse.
B. Logistic Linear regression
It is a generally utilized factual model that, in its essential structure, utilizes a strategic capacity to display a parallel ward variable; a lot increasingly complex augmentations exist. In relapse investigation, calculated relapse (or logit relapse) is assessing the parameters of a strategic model; it is a type of binomial relapse. Numerically, a twofold calculated model has a reliant variable with two conceivable qualities, for example, pass/come up short, win/lose, alive/dead or solid/wiped out; these are spoken to by a pointer variable, where the two qualities are named zero and one. In the strategic model,

Assessment 2 – Computer Assignment 1. It is desired to find the rate parameters of an enzymatic reaction which is assumed to follow Michaelis- Menten (M-M) kinetics. There are no inhibitors present...

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