Advanced Modelling for Life Sciences

Life science systems across all scales (such as subcellular, tissue level, organism level, ecological populations) vary over time and space and include various aspects of randomness. Examples are plentiful, from the robust performance of intracellular genetic pathways to the growth of crops, the spreading of viral infections and cancerous cells, movement of animals, and flow of compounds in bioreactors or in the atmosphere.

Modern life sciences require the development and use of mathematical models. Models are ubiquitously used for applications like the description of life science systems and the prediction of how these systems develop over time and space.

For different problems and depending on the available data or the research question, different types of mathematical models are required. In this course we focus on different modelling frameworks and how to choose a particular modelling framework given a certain situation. The modelling frameworks that are discussed in this course are:

• ordinary differential equations (ODEs). This is the common choice when we want to model time-dependent systems in the absence of (relevant) spatial variations and noise or relevant biological variability.;
• partial differential equations (PDEs). This is a typical framework for when spatial changes in time-dependent systems become relevant;
• stochastic differential equations (SDEs) and Gillespie algorithms are useful frameworks for when random effects and noise in time-dependent systems cannot reasonably be ignored and should be explicitly included;
• hybrid models that combine differential equation-based modelling with machine learning/neural network-based methods for the description of time-dependent systems. These are useful when available data is relatively sparse and prior knowledge of a system can be encoded in the model to improve model performance.

This course will show students how to choose the most applicable methodology and investigate life science problems with their models.

To do this, the course is divided into 4 sub-modules beginning with (I) a review of key concepts in ODE and PDE modelling before discussing how these theoretical frameworks can be extended to (II) SDEs and (III) hybrid models, and finishing with (IV) an open research problem where one needs to decide which methods to use for dealing with a specific application of their interest and justify their choice of methods. In modules (I) to (III), lectures will be given covering guidelines and key theoretical steps needed to construct, analyse and interpret such models, with practicals being used to practice these skills for exemplar systems and research questions. At the end of each module, students will complete an assessed assignment on the material introduced in the module. In ...

• Explain theory and usage of guidelines of advanced modelling methods

• Apply modern computational approaches for implementing and tackling modelling problems

• Generate new hypotheses from mathematical models

• Effectively set up, perform, and communicate (in different forms) methods and results of modelling research

• Implement good poster design practices

• Justify choices of modelling approaches to address questions in the life sciences

• ? (50%) Self-study assignments will be provided at the end of study weeks to assess students understanding of the week’s material. These will be open questions mixing analytical and computational methods. A minimum grade 5.5 is required for each assignment to bale to participate to oral test. The assignment can be resubmitted during resit periods.
• ? (40%) Description = Students will use the skills taught in the course to model and analyse an example biological system. Students are provided with background information, instructions, and the grading rubric. The project takes place in the last of the course. The student will produce a poster detailing project’s methodology and results. Students provide a 5 minute presentation describing their project for others in the class, with 5-10 minutes allowed for questions from the audience. The project can be redone during resit periods.
• ? (10%) The poster defence will be assessed by other students (peer grading). Instruction and evaluation rubrics will be provided.
• ? (%) Oral exam where students are assessed on what they have been taught in the course and what they have done in their project research. Need >5.5 over the 3 assignments to take part Students are provided with closed book preparation time to consider answers before the oral exam begins and they must explain to the examiners how they came to their answers. Grading follows a pre-defined rubric held by the examiners. The oral exam can be retaken during resit periods.

Students are advised to have taken at least one of the following courses: SSB30806 Modelling in Systems Biology, MAT23306 Multivariate Mathematics Applied, or BCT30806 Physical Modelling. Other relevant modelling courses include: SSB32806 Introduction to Systems & Synthetic Biology, EZO23306 Modelling Biological Systems, or BCT20306 Modelling Dynamic Systems. Courses that cover intermediate statistics such as SSB30306 Molecular Systems Biology or MAT34806 Bayesian Data Analysis are also useful but not required to follow the course.

• All material will be made available to students during the course and via the course Brightspace page. The principal scripting language used during the course are Python\\Matlab. Programming skills are desired.