# INTRODUCTION TO MATHEMATICAL BIOLOGY - 2022/3

Module code: BMS3090

## Module Overview

This module aims at providing students with the problem-solving skills required to construct and solve simple mathematical models of biological systems. Dynamical modelling, in terms of ordinary differential equations, will be introduced, using population dynamics and molecular networks (metabolic reactions and gene regulation) as case studies. The students will be provided with the general techniques to analyse such models, and compute the solution numerically with the aid of a computer. Derivation of qualitative features, relating to steady states analysis, multistability, and oscillatory behaviours, will also be discussed. The module will also provide the students with the opportunity to develop poster presentation skills, and become acquainted with the relevant literature in mathematical/computational biology.

### Module provider

School of Biosciences

ROCCO Andrea (Biosciences)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 116

Lecture Hours: 24

Laboratory Hours: 10

Semester 1

## Prerequisites / Co-requisites

A knowledge of mathematics equivalent to A-level standard is strongly recommended (students without A-level mathematics (or equivalent) are advised to speak with the module co-ordinator before selecting the module).

## Module content

Indicative content includes:

1   Revision of Maths

2   Dynamical modelling of biological systems
Differential equations
How to solve differential equations with a computer

3   Population dynamics
Case study: Bacterial growth – Log and stationary phases
Case study: Antibiotic killing – Bacterial persistence

4   Differential equations for molecular networks – The Law of Mass Action
Case study: Michaelis-Menten kinetics – Hill functions
Case study: Gene expression models – Activators and repressors, cooperativity, ‘AND’ and ‘OR’ gates, Competitive activation

Multistability
Case study: A genetic model for bacterial persistence

6   Feedback loops – Genetic switches
Case study: Lac operon
Case study: Lambda phage
Case study: Quorum sensing

7   Oscillations
Case study: Glycolytic oscillations

8   Introduction to noise in molecular networks
Stochastic differential equations
How to solve stochastic differential equations with a computer
Case study: Stochastic gene expression

## Assessment pattern

Assessment type Unit of assessment Weighting
Oral exam or presentation Poster Presentation 40
Examination End of Semester Examination - 2 hours 60

## Alternative Assessment

If the poster requires re-assessment this may be by the submission of an electronic copy of a poster addressing an alternative biological question. If only the poster presentation session was missed this may be carried out in the form of a short, viva style assessment carried out by two members of academic staff.

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to recognise biological problems and to select and apply the most appropriate mathematical solutions in order to solve them.

Thus, the summative assessment for this module consists of:

·         Poster presentation (40%): each student will present their critical review of an individual paper or topic representing the mathematical solution to a biological question.  They will be expected to review the strategies undertaken, including their strengths and limitations.  Assessment will occur during a poster presentation session, in which students will defend and discuss their review with the module organiser and at least one other member of academic staff.  The poster will also be submitted electronically via SurreyLearn.

·         2 hour exam (60%): Questions will represent problem-solving exercises in which the students will demonstrate their ability to select and justify appropriate analysis methods.  Students will need to select 2 questions from a total of 3.

Formative assessment and feedback

Students will be able to obtain ongoing feedback during the practical sessions, which will provide opportunities to practice approaches discussed in lectures.  Further feedback and formative assessment will be available via the comprehensive series of tutorials timetabled within this module; these will give students an opportunity to discuss issues that arise during lectures and practicals, as well as to discuss their solutions to problems.

## Module aims

• Introduce students to the field of Mathematical Biology.
• To provide students with a theoretical understanding of dynamical systems modelling in Biology, in particular with respect to population dynamics and molecular networks modelling
• To provide students with a theoretical understanding of dynamical systems modelling in Biology, in particular with respect to identification of steady states, multistability, and oscillatory behaviours
• To provide students with a theoretical understanding of dynamical systems modelling in Biology, in particular with respect to model solving by computer simulations
• To provide students with a theoretical understanding of dynamical systems modelling in Biology, in particular with respect to analysis of a number of case studies

## Learning outcomes

 Attributes Developed 1 Construct simple models of population dynamics and molecular processes in terms of differential equations 2 Critically analyse these models, extracting dynamical features analytically 3 Solve the models by using direct computer simulations 4 Become acquainted with reading literature in mathematical/computational biology 5 Develop presentation skills by poster presentations

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to teach students the practical and problem solving skills required to tackle mathematically complex biological questions.  As such the teaching strategy places equal importance on lecture content and practical skills; for each topic covered in lectures there is an equivalent computer-based session. In addition to this students will have further learning opportunities afforded by the provision of self-study worksheets and “drop-in” tutorials at which they can discuss their progress.

The learning and teaching methods include:

• 24 h lectures
• 10 h computer-based practical sessions
• 116 hours of self-study

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.