Quantitative Modeling in Biology

Recommended Prerequisites

Complementes of Mathematical Analysis, Computational Methods in Biology; Computational Methods in Biomedicine, Mathematical Analysis II.

Teaching Methods

Theoretical classes: Expositive lectoring with constant references to biological systems whose description fits the topics presented. It encourages the discussion of other topics relevant to the discipline and that are  target of active research in the community. 

Practical classes: Resolution of exercises, discussion and presentation by students of relevant articles. Students are encouraged to have a research frame of mind, and to work as a team to develop a theoretical and computational model that describes biological phenomena.

Learning Outcomes

Know the "state of the art" in Biological Modeling.

- To prepare the student for research in biological physics: foster the student's motivation for research and the ability to work as a team

- Prepare the student to analyze biological systems in a qualitative and quantitative way using computational and mathematical models.

Work Placement(s)

No

Syllabus

Noise in biological systems:

- Description of fluctuations in genetic regulatory networks

- Markov processes, master equation

- Stochastic processes, Langevin equation, applications 

Chemotaxis and cell movement:

- Flows with low Reynolds number

- Strategies used by cells to move

- Modeling of ameboid and mesenchymal movements

- Advection as opposed to diffusion, non-linear diffusion in the cell 

Modeling tumor growth

- Use of Cellular Potts models   

- Phase-field models in Biology 

Dynamics of living tissues:

- Non-linear elasticity: Cauchy and Green elastic materials. Hyperelasticity.

- Residual stresses in biological systems. Elasticity of the tissue in the presence of fibers.

- Viscoelastic materials: Microscopic models of viscoelasticity. Constitutive relations for viscoelastic materials. Dynamics of viscoelastic materials. Applications to biology.

Head Lecturer(s)

Rui Davide Martins Travasso

Assessment Methods

Assessment
Research work: 40.0%
Exam: 60.0%

Bibliography

R.W. Ogden, Nonlinear elastic deformations, Dover (1997)


R.G. Larson, The structure and rheology of complex fluids, Oxford University Press (1999)

M. Eisenbach et al, Chemotaxis, Imperial College Press (2004)


N.G. van Kampen, Stochastic processes in physics and chemistry, North-Holland (1981)

G Forgacs, Biological Physics of the Developing Embryo, Cambridge University Press (2005)

R Phillips et al, Physical Biology of the Cell, CRC Press (2012)

JD Murray, Mathematical Biology, Springer (2007)

Milo, Phillips, Cell Biology by the Numbers, Garland Science (2012)

Avner Friedman, Chiu-Yen Kao, Mathematical Modeling of Biological Processes (2014)