Courses

Last Updated:
10/03/2019 - 15:02

IAM560 - Stochastic Aspects of Dynamics

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Derya Altıntan
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Mathematical modelling of stochastic reaction systems. Deterministic approach: ODE models, Reaction Rate Equations. Stochastic Models: Chemical Master Equation, Chapman-Kolmogorov Equations, Gillespie Algorithms, Explicit Solution Formulas, Hybrid Methods, Tau-Leaping method. Lotka-Volterra Models, Michaelis-Menten Models.

Course Objectives

This course covers mathematical methods used for modelling biochemical reaction systems. It explains the general properties of these models and gives the theoretical background of these models which are based on Ordinary Differential Equations and Markov Chains. Objectivess of this course are:

• to understand the basics of modelling reaction systems
• to construct the traditional deterministic equations to model any biochemical reaction systems and solve these equations
• to understand the stochastic modelling approach
• to construct Chemical Master Equation for any given reaction systems
• to understand the relation between deterministic and stochastic modelling approach
• to learn how to simulate reaction systems via MATLAB

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

• understand deterministic and stochastic modelling approaches
• construct ODE systems and CME systems to model any given biochemical process
• simulate biochemical reaction systems
• understand the main differences between different modelling approaches and simulation strategies

Tentative (Weekly) Outline

1. Representation of biochemical reactions
2. Classical continuous deterministic models
3. Basics of probability
4. Probability distributions
5. Stochastic Processes
6. Molecular approach to kinetics, Mass Action Kinetics, Markov Processes
7. Discrete Time Markov Chains, Continuous Time Markov Chains
8. Chapman-Kolmogorov (forward) Equation, Rate Constant Conservation, Chemical Master Equation
9. Gillespie Algorithm (Direct Method)
10. Gillespie Algorithm (First Reaction Method)
11. Case Studies- Michaelis Menten Kinetics, Lotka-Volterra Systems
12. Explicit Solution Formulas
13. Exact-Approximate Solution Strategies
14. Hybrid Methods

Course Textbook(s)

• D. J. Wilkinson, Stochastic modelling for systems biology. Boca Raton, FL: Taylor & Francis. 2006.
• EJ. R. Norris, Markov Chains, Cambridge University Press, 1997