Mathematical modeling in cellular biology

Additional Info

  • ECTS credits: 3
  • Semester: 3
  • University: University of L'Aquila
  • Objectives:

     

    Provide the mathematical tools suitable for the numerical solution of cellular dynamics models and the development of algorithms in a structured programming language.
    At the end of the course, each learner should:
    - have a good knowledge and understanding of the most widespread cellular models in the literature;
    - be able to apply his knowledge to solve numerically, using a programming environment (Matlab), problems related to cellular dynamics;
    - demonstrate critical spirit in the model construction phase, understanding the coherence between underlying biological hypotheses and their mathematical translation in the model;
    - demonstrate ability in numerical reasoning, both in choosing the most suitable numerical methodology to solve the problem in question, based on its features, and in the details of the programming process;
    - demonstrate ability to read and understand other texts on related topics.

  • Topics:

     

    Basic models: Malthus exponential growth, Verhlust logistic growth, Volterra model, prey-predator model.
    Model of the growth of bacteria in the chemostat.
    Growth of a structured population.
    Study of the action of a drug.
    Outline of the mathematical procedure for the identification of reaction constants.
    In vitro model of the Ebola virus.
    Model of immunosenescence and cancer cell proliferation.
    CD4 + cell homeostasis model.
    Deterministic and stoachastic cellular models of HIV.
    Positivity preserving chemical Langevin equations.
    Partitioning of the RNA graph for the research of modularity.
    Non-negative matrix factorization applied to radiation-induced metabolic changes in human cancer cells.

  • Prerequisites:

     

    Mathematical analysis, linear algebra, numerical analysis, Matlab.

  • Books:

     

    - C. Molina-Paris and G. Lythe. Mathematical Models and Immune Cell Biology. Springer-Verlag New York (2011).
    - L. A. Segel. Mathematical Models in Molecular and Cellular Biology. Cambridge University Press (1984).
    -G.Monegato, Fondamenti di Calcolo Numerico (Seconda Edizione), Clut (1998).
    -A. Quarteroni, R. Sacco, F. Saleri, P. Gervasio, Matematica Numerica, Springer (2014).
    -Bini, M. Capovani e O. Menchi, Metodi Numerici per l'Algebra Lineare, Zanichelli (1988).
    -W. J. Palm III, Matlab 6 per l'Ingegneria e le Scienze. Mc Graw Hill. 2003.

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