Physics of Living Systems 1100-FUZ
Biological systems are among the most complex systems found in nature. Their complexity often makes mathematical modeling difficult, leading to a reliance on statistical methods or simplified descriptions. However, appropriately chosen even simple models can help identify key mechanisms, analyze system dynamics, and formulate and test hypotheses about biological processes.
The aim of the course is to demonstrate that the description of living systems can and should draw on methods developed in mathematics, physics, systems theory, and computer science. Particular emphasis is placed on moving beyond linear thinking about processes occurring in living organisms and on exploring ways to describe their non-trivial behavior. This approach is increasingly important in modern biology and medicine, where a systems-level understanding of the mechanisms underlying biological processes plays an ever-growing role.
Course format and assessment
The course combines lectures with workshop-based activities. An important part of the classes consists of scientific discussion, formulating questions, proposing and analyzing hypotheses, and jointly exploring ways to solve problems. The course also includes several experiments in which students may participate.
Each student is asked to select a topic or problem related to the course, research it, and present their findings. The presentation forms the basis for completing the course.
Course Content
1. Introduction
Challenges in modeling biological systems. Applications of methods and concepts developed in systems analysis, nonlinear dynamics, synergetics, nonequilibrium thermodynamics, catastrophe theory, and information theory.
2. Thermodynamics of Living Systems
Living organisms as open, nonequilibrium systems. Homeostasis and approaches to its description. Entropy production and equations of life. Prigogine’s theorem. Thermodynamic principles applied to living organisms. Models of hibernation in Arctic ground squirrels.
3. Kinetics of Biological Processes
Fundamentals of chemical kinetics and phase-plane analysis. The Lotka–Volterra model and the Belousov–Zhabotinsky reaction. Oscillations in biological processes, including glycolytic oscillations. Pharmacokinetics. A model of blood coagulation.
4. Nonlinearity and Self-Organization
The Michaelis–Menten model as a source of nonlinearity in biological processes. Models of hormonal regulation. Morphogenesis: the development of five digits. Turing structures: pattern formation in animals, including striped patterns in spotted animals.
5. Electrical Processes in Living Organisms
Electrical conduction in tissues. The physics of membrane potential generation. The Hodgkin–Huxley model. Bioimpedance and its medical applications (experiment). Electrical activity of the heart and ECG.
6. Information Transfer and Coding in Living Organisms
Information transfer in living organisms. Information coding in the nervous system. Artificial neuron models and neural networks. Elements of information theory in the analysis of biological data, including genetic sequences.
Main fields of studies for MISMaP
biology
computer science
mathematics
biotechnology
chemistry
physics
Course coordinators
Type of course
elective courses
supplementary
optional courses
Mode
Prerequisites (description)
Learning outcomes
Understanding the specific features of describing living systems. Understanding the principles of model construction, parameter selection, model dimensionality, assessment of model adequacy, etc. Knowledge of methods useful for analyzing complex systems, including biological system
Assessment criteria
The assessment reflects engagement during the classes, completion of a self-selected assignment, and its presentation.
Bibliography
1. Kubisz L. "Biofizyka". Warszawa: PZWL, 2024.
2. Tadeusiewicz R., Jaworek J., Kańtoch E. et al. "Wprowadzenie do modelowania systemów biologicznych oraz ich symulacji w środowisku MATLAB". Lublin: Instytut Informatyki UMCS, 2012.
3. Orlik M. "Reakcje oscylacyjne: porządek i chaos". Warszawa: WNT, 1996.
4. Jaroszyk F. (red.). "Biofizyka. Podręcznik dla studentów". Warszawa: PZWL, 2008.
5. Molski A. "Wprowadzenie do kinetyki chemicznej". Warszawa: WNT, 2001.
6. Heimburg T. "Linear nonequilibrium thermodynamics of reversible periodic processes and chemical oscillations". Physical Chemistry Chemical Physics, 2017, 19(26), 17331. DOI: 10.1039/C7CP02189E.
7. Prigogine I. "Time, Structure and Fluctuations". Nobel Lecture, 1977.
8. Petitjean H., Finck S., Schmoll P. et al. "The Concept of Homeodynamics in Systems Theory". Complexities, 2025, 1, 6.
9. Davies K. J. A. "Adaptive Homeostasis". Molecular Aspects of Medicine, 2016, 49, 1. DOI: 10.1016/j.mam.2016.04.007.
10. FitzGerald C. E., Engedal A. J., Mangan N. M. "Discovering a low-dimensional temperature control architecture across animals", 2024.
11. The Faculty and Staff of the Centre for Nonlinear Dynamics in Physiology and Medicine. "Nonlinear Dynamics in Biology and Medicine". Lecture Notes of the Montreal ’96 Summer School. Montreal: McGill University, 1996.
12. Suffczyński P. "Sygnały bioelektryczne". Materiały dydaktyczne dla studentów.
13. Tuszynski J., Kurzynski M. "Introduction to Molecular Biophysics". Boca Raton: CRC Press, 2003.
14. Watson H. "Biological membranes". Essays in Biochemistry, 2015, 59, 43. DOI: 10.1042/BSE0590043.
15. Lodish H., Berk A., Matsudaira P. et al. "Molecular Cell Biology". New York: W. H. Freeman, 2007.
16. Jaroszyk F. "Biofizyka". Warszawa: PZWL, 2011.
17. Leyko W. "Zarys biofizyki". Warszawa: PWN, 1973.
18. Pilawski A. "Podstawy biofizyki". Warszawa: PZWL, 1977.
19. Glaser R. "Wstęp do biofizyki". Warszawa: PZWL, 1974.
20. Żurada J., Barski M., Jędruch M. "Sztuczne sieci neuronowe: podstawy teorii i zastosowania". Warszawa: PWN, 1996.
21. Schneider T. D. "A brief review of molecular information theory". Nano Communication Networks, 2010, 1(3), 173–180.
22. Lu Y. R., Tian X., Sinclair D. A. "The Information Theory of Aging". Nature Aging, 2023, 3(12), 1486.
23. Yockey H. P. "Information Theory, Evolution, and the Origin of Life". Cambridge University Press, 2005.
24. Cotterill R. "Biophysics: An Introduction". Chichester: John Wiley & Sons, 2002.