### ENGG1811–Assignment 2: Biofuel Production – Simulation and Design

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Learning Objectives:

1. Applying programming to solve a simple engineering design problem

2. Writing a python program to simulate an engineering system

3. Applying a number of python features, which include array, vectorisation, built-in

functions and others

4. Applying good software engineering practices, which includes proper documentation,

program style.

Aaron Quigley, October, 2020

Deliverables: Submit by 17:00 on Friday of Week-10.

Late Penalty: Late submissions will be penalised at the rate of 10% per day (including

weekends). The penalty applies to the maximum available mark. For example, if you

submit 2 days late, maximum available marks is 80% of the assignment marks.

Submissions will not be accepted after 9am Wednesday of Week-11.

To Submit this assignment, go to the Submission page and click the link named

“Make Submission”.

GENERAL RULES

1. This assignment is weighted at 20%

2. You are reminded that work submitted for assessment must be your own. It’s OK

to discuss approaches to solutions with other students, and to get general help

from tutors or others, but you must write the python code yourself. Increasingly

sophisticated software is used to identify submissions that are unreasonably

similar, and marks will be reduced or removed in such cases.

3. The Student Code of Conduct sets out what the University expects from students

as members of the UNSW community. As well as the learning, teaching and

research environment, the University aims to provide an environment that enables

students to achieve their full potential and to provide an experience consistent

with the University’s values and guiding principles. A condition of enrolment is that

students inform themselves of the University’s rules and policies affecting them, &

conduct themselves accordingly. (see the course outline page with links).

4. You should also read the following page which describes your rights and

responsibilities in the CSE context: Essential Advice for CSE Students

Essential

The University views plagiarism very seriously. UNSW and CSE treat plagiarism as

academic misconduct, which means that it carries penalties as severe as being

excluded from further study at UNSW. [see: UNSW Plagiarism Procedure]

Resources Provided to you

There are a number of python files that you need to do this assignment. These files are

in assign2.zip. We introduce these supplied files, see the section on Supplied Files.

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Introduction

In these days, with the worlds attention turned to viruses, infection and disease

transmission some people think that bacteria are harmful. In reality there are many

different types of bacteria in this world. Some bacteria are harmful to humans but some

bacteria help us (e.g. curdling milk) or in our bodies (e.g. our digestion) help us to live.

Have you ever considered the possibility that bacteria can also be “factory workers”?

Engineers and scientists are working on using bacteria to produce certain chemicals and

materials. An example is to use bacteria to produce fuel for us. In engineering, we often

want to optimise the process, so we may want to make the bacteria to produce as much

fuel as possible in a given time. However, there are often constraints in nature. The truth is

that fuel is toxic to bacteria, so we need to find a way for the bacteria to make a lot of fuel

but at the same time keep them alive! This biofuel production process is the theme of this

assignment.

The aim of this assignment is to give you an opportunity to work on a small-scale

engineering design problem in python. The engineering system that you will be working on

is biofuel production. Your goal is to determine the design parameters so that the bacteria

can produce as much fuel as possible while respecting a couple of constraints. You will

use simulation as part of the design process.

For this assignment, given the marks allocated, you need to work alone.

Assignment overview

This assignment is design to imitate engineering design. You will see the following

elements:

1. (Simulation) Simulation of a biofuel production system with different design

parameters.

2. (Design) Evaluate the performance of the systems that you have simulated.

As noted on page 1, there are a number of files provided to get you started please see the

section on Supplied Files below for more details.

We will first give an introduction to biofuel production. This introduction is meant to give

you some intuition on the design problem. After that we will tell you what you need to do

for the assignment.

Biofuel production process

We will give you a basic mental picture that you can use to visualise biofuel production. A

pictorial representation of a bacterium is in Figure 1. A bacterium is a single-cell organism.

It has a cell membrane, which you can think about as the “skin” of a bacterium. By using

bioengineering, we can get the bacteria to produce fuel for us. This production will take

place within the bacteria, i.e. inside the cell membrane of the bacteria.

Now that you know that fuel is produced inside the membrane of bacteria, the next thing

you need to know is that having the fuel staying inside the bacteria is neither good for us

nor the bacteria. It is not good for us because we cannot collect the fuel. It is not good for

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

the bacteria because it is toxic to them. This means we need a way to get the fuel from the

inside of the membrane to the outside. A good news is that bacteria can make efflux

pumps on the membrane to push the fuel from the inside of the membrane to the outside.

With these efflux pumps, we can reduce the amount of fuel in the bacteria (i.e. toxicity

level) and collect the fuel, solving the problem that we talked about in the last paragraph,

but there is one catch. Efflux pumps, though useful, can be a burden to the bacteria. This

means that a bacterium should not have too many efflux pumps. A clever way is to get the

bacteria to make efflux pumps on demand. If a bacterium senses that there is a lot of fuel

inside its membrane, it should make more efflux pumps to expel the fuel; and vice versa.

With the help of bioengineering, it is possible to have biosensors in bacteria to sense the

amount of fuel in the bacteria.

The above mental picture should give you the intuition you need for the biofuel production

process. In order to do engineering design, we need a mathematical model which we will

discuss next.

“One mechanism for dealing with toxicity is to export the fuel molecules using efflux

pumps. These pumps are protein complexes in the cell membrane that recognize toxic

substrates and expel them. Once a toxin is sensed, a channel in the membrane opens in

an iris-like fashion and the toxin is pushed out using the electrochemical gradient across

the cell membrane.” From, Dunlop, Mary J., Jay D. Keasling, and Aindrila Mukhopadhyay.

“A model for improving microbial biofuel production using a synthetic feedback loop.”

Systems and synthetic biology 4.2 (2010): 95-104.

Aaron Quigley, October, 2020

Figure 1: (a) Biofuel production using microbes (e.g. bacteria) to convert sugar into fuel.

(b) Efflux pumps can be used to export biofuel out of the cell (adapted from Dunlop 2010)

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

A mathematical model for the biofuel production process

From the biofuel production description that we have discussed above, you know that we

are interested in a few quantities: the amount of biofuel inside the bacteria because this is

related to the toxicity level; and, the amount of biofuel outside the bacteria because this is

the amount that we can collect. We would like to have a mathematical model which tells us

how these two quantities vary over time. The mathematical model can tell us how the

following five quantities vary over time:

• The amount of bacteria in the colony denoted by the mathematical symbol n. Note

that we scale the amount by the maximum possible of bacteria so n is a number in

the interval [0,1].

• The biosensor output denoted by R which is a non-negative real number.

• The amount of efflux pumps, denoted by p, which is a non-negative real number.

• The amount of biofuel in the interior of the bacteria, denoted by bi, which is a nonnegative

real number. We also call this internal biofuel.

• The amount of biofuel in the exterior of the bacteria, denoted by be, which is a nonnegative

real number. We also call this external biofuel.

You will use simulation to determine these five quantities.

There are two design parameters which we will vary, they are:

• The biofuel production rate αb. (python variable name alpha_b)

• The efflux pump production rate αp. (python variable name alpha_p)

We have placed the mathematical model for the biofuel in the appendix 1. We believe it is

best for you to understand what you need to do for this assignment first before exploring

the mathematical model. You should be able to understand what you need to do for the

assignment without going into the mathematical model at this stage.

The mathematical model (in Appendix 1) for biofuel production is based on Reference [1].

Overview of tasks

We have divided the work into a number of tasks.

• Task 1 and Task 2: are on simulation

• Task 3: is on engineering design

Task 1: Simulate the biofuel production system with a python function

The aim of this task is to write a python function sim_biofuel (which should be in a file

with name sim_biofuel.py) to simulate the biofuel production process. You can find a

template for this function in sim_biofuel_template.py (in assign2.zip). You should

rename it as sim_biofuel.py before you start. The declaration of the function

sim_biofuel is:

def sim_biofuel(data_set_to_use, time_array, init_bacteria_amount, alpha_b, alpha_p) :

The above function returns five arrays. All these five arrays should have the same length

as the input array arrayTime. These five arrays contain the following simulation outputs

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ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

in this order of expected function output:

• bacteria_amount_array for the amount of bacteria n

• sensor_array for the biosensor output denoted by R

• pump_array for the amount of efflux pumps p

• biofuel_int_array for the amount of biofuel in the interior of the bacteria bi,

• biofuel_ext_array for the amount of biofuel in the exterior of the bacteria be,

The inputs are:

• data_set_to_use is an integer indicating data set to use containing constants

you need for simulation.

• time_array is a array of time instances that you need for simulation.

• init_bacteria_amount is a scalar for the initial amount of bacteria in the

colony.

• alpha_b is a scalar for the design parameter for biofuel production rate αb

• alpha_p is a scalar for the design parameter efflux pump production rate αp

The implementation of sim_biofuel requires the mathematical model for the biofuel

production process. (The model is in Appendix 1 and the suggestion is that you read the

model later.)

Hint: You can use the python simulation program para_ODE_ext_lib.py and

para_speed_height_by_ODE.py (code from Week 7’s lecture) or the material from “Lab

08: Simulation and its applications” as a starting point to develop the function sim_biofuel.

The only non-zero initial condition is the amount of bacteria. This is defined by the

constant INITIAL_BACTERIA_AMOUNT, which is specified in the simulation data set. The

python files provided for testing load this constant in for you, so you can assume this

constant is available and use it. You can assume the initial conditions for R, p, bi and be

are zero.

The array time_array is a uniformly spaced array of time instances. The start and end

times, as well as time increments, are specified in the simulation data set. The python files

provided for testing your function load these constants in for you, as well as define the

array time_array. So, you can assume the time array is available and use it.

When you call the function sim_biofuel, the only inputs that you need to adjust are the

values of alpha_b and alpha_p.

For example, if you want to do simulation with αb = 0.1 and αp = 0.6, you should use:

def sim_biofuel(data_set_to_use, time_array, INITIAL_BACTERIA_AMOUNT, 0.1, 0.6) :

Note that you can leave the first three inputs (shown in red) as they are shown in the

above line. You may want to read through the file test_1.py to give you an example on

how to call the function.

You can use the python program test_1.py (in assign2.zip) to test your sim_biofuel.

The program test_1.py first reads in the constants and parameters for the selected

data set. It then creates an equally spaced array time_array. The program then calls the

function sim_biofuel to compute the five outputs of the simulation, and compares them

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ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

to the reference values. If you see the error is small, i.e. less than 10-6, then your

sim_biofuel should be working correctly.

Note that we have provided two different sets of system and simulation parameters. You

can choose between them by assigning the variable data_set_to_use to either 1 or 2.

You can find this variable near the beginning of the file. For each system parameter set,

you can use three different pairs of design parameters in test_1 to test your

data_set_to_use. The selection is done by setting the variable test_index to 1, 2 or

3.

You can test this function by using the script test_1. If you adjust the value of the

variable test_index, you can choose between 3 different set of design parameters.

Task 2: Generate the design objective and constraints for many pairs of (alpha_b,

alpha_p)

We have mentioned earlier that biofuel is toxic to the bacteria. It would be desirable if we

can choose our design parameters αb and αp to limit the maximum amount of biofuel

inside the bacteria. This is one design constraint that we want to impose. For our design,

we would like to find design parameters which limit the maximum amount of internal

biofuel. We want to do this quantitatively. Let us assume that you have done the simulation

and have the amount of internal fuel stored in the array biofuel_int_array. The

maximum amount of internal biofuel is then the maximum value in the array for

biofuel_int_array.

You have seen that different values of αb and αp can lead to different behaviour of internal

biofuel level. In the same way, different values αb and αp can lead to different amount of

fuel that we can collect. Our design objective is to collect as much fuel as possible at the

end of the production process. We can measure this design objective quantitatively by

using the value of the last element of the array biofuel_ext_array, which represents

the amount of external biofuel at the end time of the simulation.

In this task, you will use many different pairs of (alpha_b, alpha_p) for simulation. For

each pair of (alpha_b, alpha_p), you will simulate the biofuel production and use the

output of the simulation to determine: (1) The amount of biofuel you can collect and (2)

The maximum amount of internal biofuel.

The steps for this task are:

1. Create an array of alpha_p_array of equally spaced αp values. The first value is

ALPHA_P_LOWER and the last value is ALPHA_P_UPPER with an increment of

ALPHA_P_STEP. These three constants are specified in a parameter set that the

program test_2.py reads in. You can use them directly. Hint: Note that the

program test_2.py has a line which creates an equally spaced array

time_array. You can similarly create an array equally spaced alpha_p_array

using the above three values (lower, upper and step values).

2. Create two zero arrays whose number of rows is the number of elements

in alpha_b_array and the number of columns is the number of elements in

alpha_p_array. You should call these two arrays max_internal_biofuel

and final_external_biofuel.

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

3. Perform simulations for all possible pairs of (alpha_b, alpha_p) where

alpha_b comes from the elements in alpha_b_array and alpha_p comes from

the elements of alpha_p_array. For each pair of (alpha_b, alpha_p), we

need to do the following:

◦ The (i,j) element of the array max_internal_biofuel, i.e.

max_internal_biofuel(i,j), should be assigned the maximum amount

of internal biofuel when alpha_b_array(i) and alpha_p_array(j)

are used. For example,

◦ The (i,j) element of the array final_external_biofuel, i.e.

final_external_biofuel(i,j), should be assigned the amount of

biofuel that can be collected when alpha_b_array(i) and

alpha_p_array(j) are used. This array final_external_biofuel

will be similar to the above example for max_internal_biofuel.

Hint: please read the examples in the file numpy_2d_examples.py

In this part you need to implement the following function:

def generate(data_set_to_use, time_array, INITIAL_BACTERIA_AMOUNT, alpha_b_array,

ALPHA_P_LOWER, ALPHA_P_UPPER, ALPHA_P_STEP) :

Input (7 values):

• data_set_to_use, time_array,

INITIAL_BACTERIA_AMOUNT, alpha_b_array,

ALPHA_P_LOWER, ALPHA_P_UPPER, ALPHA_P_STEP

Output (4 values):

• alpha_b_array, alpha_p_array,

max_internal_biofuel, final_external_biofuel

You can use the file test_2.py to check whether you have calculated the two arrays

max_internal_biofuel and final_external_biofuel correctly.

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Task 3: Engineering design

The engineering design problem is to choose good design parameters to meet our design

requirements. In our case, a design has two design parameters alpha_b and

alpha_p. In Task 2, you have associated each design, or each pair of (alpha_b,

alpha_p), with two quantitative measures:

• Amount of biofuel that can be collected

• Maximum amount of internal biofuel

We want to choose the best pair of (alpha_b, alpha_p) based on these two

quantitative measures. We know that large amount of internal biofuel is undesirable. What

we want to do is to impose an upper limit on maximum amount of internal biofuel. We

introduce the following threshold:

• THRESHOLD_MAX_INTERNAL_FUEL is a threshold on the maximum amount of

internal biofuel

The above constant is specified in a parameter set that the program test_3.py reads in.

We say that a design is acceptable if

• Maximum amount of internal biofuel is less than or equal to

THRESHOLD_MAX_INTERNAL_FUEL,

Out of all the designs that are acceptable, we will choose the design that allows us to

collect the largest amount of biofuel. We will call this design the best design.

For comparison purpose, we will also determine a poor design which we define as the

design that maximises the amount of biofuel that can be collected, without considering the

above constraint.

Once you have obtained the best design and the poor design, you need to return these

four values from the following function you need to implement for his part.

A requirement for Task 3 is that you should complete this task without using any loops.

You can only get full marks if your solution does not use loops. If your solution requires

loops, then you can only get a reduced mark.

Hint: You can easily implement this function WITHOUT using a loop structure. Please read

(or re-read!) lecture notes and labs on numpy, and also the related code examples. In

particular, look for numpy functions that may help you to solve problems related to Task-3.

In this part, you need to implement the following function:

def design( THRESHOLD_MAX_INTERNAL_FUEL,

alpha_b_array, alpha_p_array,

max_internal_biofuel, final_external_biofuel) :

Output (return values):

• best_alpha_b, best_alpha_p, poor_alpha_b, poor_alpha_p

You should be able to determine whether your answers are correct by manually checking

on the elements of the arrays. You can do that. The arrays are big so you may want to

come out with some smaller arrays yourselves to test your work. We strongly encourage

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

you to do that because it is always good to try to check your own work. When you go out

to work, you will need to check your own work. We have also placed the answers here

but we encourage you to check your own work before looking at them.

Remark: We have used exhaustive search here to determine the design parameters. This

is certainly not the most efficient algorithm but you will learn better optimization methods in

later years.

Style

You should make sure that all your files are properly documented with appropriate

comments. Variables that you use should have well chosen names and their meaning

explained. Appropriate style should be used.

Supplied Files

The supplied files are (in assign2.zip):

• The file sim_biofuel_template.py is for Task 1. You should rename it as

sim_biofuel.py

• The file generate_template.py is for Task 2. You should rename it as

generate.py

• The file design_template.py is for Task 3. You should rename it as design.py

• We have two sets of parameters. You can choose between the two sets of

parameters by using the variables data_set_to_use. Each set of parameters is

made up of constants in two files:

1. System parameters which are the constants you need for the mathematical

model in biofuel_system_parameter_sets.py.

2. Simulation and design parameters in

biofuel_simulation_design_parameter_sets.py.

• Files for testing

1. test_1 for testing Tasks 1.

2. test_2 for testing Tasks 2.

3. test_3 for testing Tasks 3.

4. These files require support files, which are set1_check.pickle and

set2_check.pickle files.

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Getting Started

1. Download the zip file assign2.zip, and unzip it

2. Rename/move the directory (folder) you just created named ‘assign2’ to ‘ass2’. The

name is different to avoid possibly overwriting your work if you were to download

the ‘assign2.zip’ file again later.

3. First browse through all the files provided, and importantly read comments in the

files.

4. Do not try to implement too much at once, just one function at a time and test that it

is working before moving on.

5. Start implementing the first function, properly test it using the given testing file, and

once you are happy, move on to the the second function, and so on.

6. Please do not use ‘print’ or ‘input’ statements. We won’t be able to assess your

program properly if you do. Remember, all the required values are part of the

parameters, and your function needs to return the required answer. Do not ‘print’

your answers.

Testing

Test your functions thoroughly before submission. You can use the provided python

programs to test your functions.

Please note that the tests provided in these files cover only basic scenarios (cases), you

need to think about other possible cases, modify the files accordingly and test your

functions.

Submission

A complete submission should contain the following three files (as described above):

1. sim_biofuel.py

2. generate.py

3. design.py

The submission system will accept the above three filenames. You must not submit any

other files.

To Submit this assignment, go to the Submission page and click the tab named “Make

Submission”.

Assessment Criteria

We will test your program thoroughly and objectively. This assignment will be marked out

of 20 where 18 marks are for correctness and 2 marks are for style.

Correctness

The 18 marks for correctness are awarded according to these criteria.

Criteria Nominal marks

Task 1 (Function sim_biofuel) 6

Task 2 (Correct max_internal_biofuel and

final_external_biofuel) 6

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Style

Two (2) marks are awarded by your tutor for style and complexity of your solution. The

style assessment includes the following, in no particular order:

• Use of meaningful variable names where applicable

• Use of sensible comments to explain what you’re doing

• Use of docstring for documentation to identify purpose, author, date, data dictionary,

parameters, return value(s) and program description at the top of the file

Assignment Originality

You are reminded that work submitted for assessment must be your own. It’s OK to

discuss approaches to solutions with other students, and to get help from tutors and

consultants, but you must write the python code yourself. Sophisticated software is used to

identify submissions that are unreasonably similar, and marks will be reduced or removed

in such cases.

Further Information

• Use the forum to ask general questions about the assignment, but take specific

ones to Help Sessions.

• You can ask your tutor during your lab time any queries you may have regarding

this assignment.

• Keep an eye on the class webpage notice board for updates and responses.

Task 3 (Correct values of alpha_b and

alpha_p for the two designs). Reduced

maximum: 1.5

6

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Appendix 1

Mathematical model for biofuel

The model consists of five ordinary differential equations:

Some helpful intuition for some of these equations at the end of the

appendix.

Note that for the purpose of simulation, there are three groups of

quantities:

1. Time dependent variables: n(t), p(t), R(t), bi(t) and be(t). These are

quantities that you want to use simulation to obtain.

2. Two design parameters: αb (python variable: alphaB) and αp

(python variable: alphaP). You will use different values of these two

parameters in simulation to see how they change the amount of fuel

produced internally and externally. Note that alphaB and alphaP

are two inputs to the simulation function that you need to write.

3. The rest of the parameters (αn, δn etc.) are constants. A mapping

between the mathematical symbols and their python constant names

is below. You will need to make use of these constants in your python

simulation code. Essentially, you replace the mathematical symbol

by its corresponding python name in your simulation code.

Aaron Quigley, October, 2020

ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

The next step is to apply Euler’s forward method to the ordinary

differential equations, which result in the following equations you need for

simulation.

Mapping between symbol names and python constant

names

The python constant names are in upper case. For most symbols, the first

part is the name of the Greek alphabet, followed by an underscore and then

the subscript. The values of these constants are defined in files with the

name that contains the words “biofuelSystemParameterSet”.

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ENGG1811 20T3 Assignment 2: Biofuel Production – Simulation and Design

Meaning behind the equations

Right-hand side (RHS) of (1) describes the rate of change in the amount of

bacteria. The first term is the logistic growth function taking into account

the limitation of resources. You can learn more on logistic growth from

this Wikipedia page (https://en.wikipedia.org/wiki/Logistic_function ). The

second term is the death rate of bacteria due to biofuel. The third term is

the death rate due to efflux pumps.

RHS of (3) is the rate of change in the number of efflux pumps. The first

term is a base production rate. The second term describes how biofuel in

the bacteria affects the production rate. Essentially, the more the biofuel

inside the bacteria, the higher the production rate. The last term is the

pump degradation rate.

RHS of (4) is the rate of production of biofuel in the interior of bacteria.

The first term says the production rate is proportional to the amount of

bacteria. The second term is the rate at which biofuel is pumped out of the

bacteria by efflux pumps.

RHS of (5) is the rate at which biofuel is pumped into the exterior.

Aaron Quigley, October, 2020