Python代写｜Data Science Assignment 1

本次代写是一个Python数据科学的assignment

Read the following paper
https://www.biorxiv.org/content/10.1101/2021.07.08.451443v1.abstract and write a report
limited to 3 pages, including citations, figures etc. Reports beyond 3 pages will be rejected
automatically.

Implement a simpler version of the method using the MNIST data set for regression on digit
0 and digit 7. Each bag consists of 100 images with a fraction x of digit 0 and 1-x of digit 7.

Then train neural network on regression using the neural network architecture specified in
the given paper.

Report and code is graded based on:

1. Clarity
2. Show of understanding in the biological and cancer domain knowledge
3. Show of understanding in the machine learning technology
4. Generate results on the MNIST toy data set – graphs and plots to show that your
code is working
5. Put a version of your source code in github, code is graded based on:
a. Good code design
b. Good coding habits
c. Correctness

Enzymes are catalysts that help convert molecules that we will call substrates into other
molecules that we will products. They themselves are not changed by the reaction. Within
cells, enzymes are typically proteins. They can speed up biological reactions, sometimes by
up to millions of times. They are also regulated by a very complex set of positive and
negative feedback systems. Computational biologists are painstakingly mapping out this
complex set of reactions. In this problem, we will model and simulate a simplified enzyme
reaction.

An enzyme E converts the substrate S into the product P through a two-step process. First,
E forms a complex with S to form an intermediate species ES in a reversible manner at the
forward rate k1 and reverse rate k2. The intermediate ES then breaks down into the product
P at a rate k3, thereby releasing E. Schematically, we write

8.1. Using the law of mass action, write down four equations for the rate of changes of the
four species, E, S, ES, and P.

8.2. Write a code to numerically solve these four equations using the fourth-order Runge
Kutta method. For this exercise, assume that the initial concentration of E is 1 µM, the initial
concentration of S is 10 µM, and the initial concentrations of ES and P are both 0. The rate
constants are: k1=100/µM/min, k2=600/min, k3=150/min.

8.3. We define the velocity, V, of the enzymatic reaction to be the rate of change of the
product P. Plot the velocity V as a function of the concentration of the substrate S. You
should find that, when the concentrations of S are small, the velocity V increases
approximately linearly. At large concentrations of S, however, the velocity V saturates to a
maximum value, Vm. Find this value Vm from your plot.