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SysMIC Syllabus

SysMIC Syllabus

Module 1

M1.1 Introduction to MATLAB (10 hours) and Networks (20 hours)

  • Introduction to MATLAB

Assignment: Generating Spirograph patterns

  • Networks 1

Assignment: Food webs

Quizzes: Graphs and subgraphs, Degree and paths, Digraphs

  •  Networks 2

Assignment: Glycolysis simulation using SimBiology

Quizzes: Graph representation, Network structure and motifs, Algorithms

M1.2 Vectors and Matrices (10 hours)

Assignment: Modelling plasmid replication with Petri Nets

Quizzes: Vectors, Matrices, Matrix inverses and determinants

M1.3 Functions and Calculus (30 hours)

  • Functions and Calculus 1

Assignment: Bacterial growth, enzymatic reactions and gene expression 1

Quizzes: Numbers, accuracy and functions, Powers, exponential and logarithm, Differentiation and investigating functions, Functions in MATLAB

  •  Functions and Calculus 2

Assignment: Bacterial growth, enzymatic reactions and gene expression 2

Quizzes: Integration, Introduction to differential equations, Errors and accuracy, working with differential equations, Calculus in MATLAB

  •  Functions and Calculus 3

Assignment: Toggle switch and repressilator

Quizzes: Trigonometric functions, Calculus with trigonometric functions, Complex numbers, second order differential equations

M1.4 Model Building (10 hours)

Quizzes: First steps in Modelling, Building differential equation models

M1.5 Introduction to R (10 hours) and Probability and Statistics (20 hours)

  • Introduction to R

Assignment: Chicken weights

  • Probability and Statistics 1

Assignment: Measuring fluorescence

Quizzes: Descriptive statistics, Probability, Describing random variables, Common discrete probability distributions, Common continuous probability distributions

  • Probability and Statistics 2

Assignment: Cadmium toxicity microarray study

Quizzes: Central limit theorem, Confidence intervals, Hypothesis testing, Non-parametrics

M1.6 Mini Projects (10 hours)

Module 2

M2.1 Eigenvalues and Eigenvectors

  • Leslie matrix

Discrete time models

Exponential growth

  • Eigenvalus and eigenvectors in MATLAB
  • Example: Asymmetric bacterial growth
  • Multivariate normal distribution

Covariance matrix

  • Matrix diagonalisation

Principal component analysis

  • Example: Ovarian cancer data
  • Mathematical background: Eigenvalues and eigenvectors

M2.2 Functions of more than one Variable - Further Calculus

  • Example: Spatial concentration field
  • Functions of one variable (Revision)
  • Functions of two variables

Partial derivatives

  • The A C - B2 criterion

Classification of stationary points

M2.3 Systems of Differential Equations

  • Examples: The toggle switch (continued)

The repressilator (continued)

  • Taylor polynomials of one and two variables
  • First-order differential equations
  • Nonlinear differential equations
  • Classification of steady states

M2.4 Discrete Systems

  • Examples: Population growth (continued)

Agent-based models: Life

Modelling Ion channel gating

  • Discrete-time dynamical systems
  • Maps & orbits

Chaos

Universality

M2.5 Reaction-Diffusion Systems

  • Examples: Predator-prey model

FitzHugh-Naguma model

Fisher/ KPP model

Schnakenberg model

  • The READY online simulator
  • A stochastic process underlying diffusion
  • Random walks
  • The diffusion equation
  • Microscopic derivation of the diffusion equation

M2.6 Stochastic Systems

  • Examples: Markov chain for bacterial growth

Enzymatic reactions

Dimerisation

A bistable model

  • Sampling from random variables (Monte Carlo methods)
  • Random number generation
  • Properties of the exponential distribution
  • Continuous-time Markov chains
  • The Gillespie algorithm

 M2.7 Fitting Models

  • Parameter estimation for models

Optimisation approach

Bayesian approach

  • Regression models
  • Correlation

M2.8 Mini Projects (10 hours)

Module 3 - Research Project

M3.1 Writing a project plan including a mini-review (1 month)

  • Identify an area of interest and project focus
  • Use SysMIC materials and research literature
  • Find and meet Advisor(s) to help with theoretical aspects
  • Upload a mini-review (4-5 pages) with a project plan (1 page)

 M3.2 Modelling, data analyses and write a research report (3 months)

  • Perform proposed research project and modelling/ data analyses
  • Talk to Advisor(s) / on-line Tutors as you progress
  • Write the report in the style of a draft manuscript or journal template
  • Update your progress using an individual on-line course wiki/ blog

 M3.3 Attending a half-way seminar/ workshop

  • Prepare and deliver a short presentation or poster on your research project methods, results and analysis
  • Provide feedback and get help from other seminar/ workshop attendees
  • Complete your individual on-line course wiki/ blog

 M3.4 Writing an extended discussion and conclusion (1 month)

  • Using the feedback, expand the discussion section with future directions
  • (Optionally) Write a short future research proposal to develop the work
  • Submit the report with its extended discussion and conclusion

M3.5 Peer-reviewing of project reports (2 weeks)

  • Provide critical feedback on two project reports from others

M3.6 Correcting the report that has been peer-reviewed (2 weeks)