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Today’s high-impact biological journals require scientific results that tightly combine experimental data with theoretical predictions or verifications. However, there is still a large gap between the experimental and the theoretical / computational communities in terms of common language as well as capabilities and limitations of modelling tools. The current course bridges this gap by presenting an overview of systems biology with emphasis on the necessity, uses and pitfalls of dynamical modelling in biology. It introduces the required language and philosophy for a smooth and fruitful collaboration between life scientists and theoreticians (i.e. mathematicians, physicists, computer scientists). The main goal of this course is not a detailed description of the modelling tools in systems biology, but a thorough overview of the terminology and applicability range of these methodologies. The time dedication throughout this course will be one third for theoretical introduction, and two thirds for modelling applications for very diverse biological systems. The modelling applications will employ NetLogo**, the free open-source modelling environment.
The participants will get acquainted with the fundamentals of algebra and differential equations; with the history, concepts and tools of theoretical biology with emphasis on dynamic systems; and with the modelling of noise and spatial features in biological systems. As a result, they will acquire the necessary skills to understand and interpret models and modelling results from scientific articles, and will take the first steps into building their own mathematical models.
** Wilensky, U. 1999. NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modelling, Northwestern University. Evanston, IL.
Dr. Andreea Munteanu
(Centre for Genomic Regulation, Spain).
Dr. Carlos Rodríguez-Caso
(Universitat Pompeu Fabra, Spain).
Dr. Soledad De Esteban-Trivigno
(Transmitting Science, Spain).
The participants should hold a degree in biological or (bio)medical disciplines, and be interested or involved in interdisciplinary research. All participants must bring their own personal laptop (Windows, Macintosh, Linux). Recent version (5.0.2 or later) of the free software NetLogo, a multi-agent programmable modelling environment, has to be installed on the participant’s laptop (http://ccl.northwestern.edu/netlogo/). This free software will be used for the practical sessions.
1st Day. Concepts: Which tools do we need?
The first day will introduce the main tools and concepts employed throughout the course, both for the theoretical and the practical sessions. From the theoretical perspective, we shall introduce the meaning of equations, variables and parameters, vectors, integration methods as well as the interpretation of probability measures. From the practical perspective, we shall present the NetLogo environment and its main commands.
2nd Day. Dynamic systems: What is a dynamical model?
The second day will present the theoretical-biology history with emphasis on dynamic systems modelling. Using ordinary differential equations, we shall define the main concepts and tools of dynamic systems, and subsequently apply them to well-established biological cases mainly from population dynamics.
3rd Day. Genetic networks: How do we model genetic interactions?
The third day will address gene-regulation models. We shall construct the mathematical models, assess assumptions, obtain results, review caveats and limitations. Among classical examples, we shall address the lambda phage, genetic competence, toggle switch and synthetic oscillators.
4th Day. Stochasticity and spatial systems: When and why should we model noise and space?
The fourth day will address two concepts: Noise and spatial systems. Firstly, we shall expand on the role of noise observed the previous day, and the most common modelling methods for studying stochastic systems. Secondly, we shall model spatial systems where noise, diffusion and compartmentalization are important, such as habitat fragmentation, animal coats and morphogenesis.
Brief overview of the course and other modelling tools.
- Bialek W, Botstein D (2004) Introductory science and mathematics education for 21st-century biologists. Science, 303 (5659): 788-790.
- Enver T, Pera M, Peterson C, Andrews PW (2009) Stem cell states, fates, and the rules of attraction. Cell Stem Cell, 4 (5): 387-397.
- Roth S (2011) Mathematics and biology: A Kantian view on the history of pattern formation theory. Dev Genes Evol, 221 (5-6): 255-279.
- Fawcett TW, Higginson AD (2012) Communicating theory effectively requires more explanation, not fewer equations. Proc. Natl. Acad. Sci. USA, 109 (45): E3058-E3059.
- Jaeger J, Irons D, Monk N (2012) The inheritance of process: A dynamical systems approach. J Exp Zool B Mol Dev Evol, 318 (8): 591-612.
- Mogilner A, Allard J, Wollman R (2012) Cell polarity: Quantitative modeling as a tool in cell biology. Science, 336 (6078): 175-179.
- Hefferon J (2011) Linear algebra, http://joshua.smcvt.edu/linearalgebra/.
- Ingalls B (2012) Mathematical modeling in systems biology: An introduction, http://www.math.uwaterloo.ca/~bingalls/MMSB/.
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