The Cell Membrane Modeled as an RC Circuit

Cilj ovog rada je dati kvalitativan i kvantitativan opis električnih svojstava stanične membrane prikazane modelom RC električnog strujnog kruga. Pomoću modela RC kruga moguće je dati fizikalno-matematički opis prijenosa informacija u stanicama. Primjenom ovog modela, na primjeru stanične membrane aksona živčane stanice, propagacija električnog impulsa odgovornog za prijenos informacija u biološkim procesima prikazana je diferencijalnom jednadžbom drugog reda. Numerička rješenja ove jednadžbe prikazana su kao digitalni impulsi. Predstavljeni prikaz propagacije signala razradili su Hodgkin i Huxley 1952. godine te se njihov rad smatra jednim od najvećih postignuća biofizike 20. stoljeća. Nešto suvremeniju analizu ponudio je Rob Phillips, čija je knjiga Physical biology of the cell temeljno polazište ovoga rada. Kako promatrani problem zalazi u više znanstvenih polja, konzultirana je i različita stručna literatura iz fizike, biologije, kemije i neuroznanosti.The goal of this thesis is to give a qualitative and quantitative description of the electrical properties of the cell membrane described by the model of RC electrical circuit. Using this model, it is possible to give a physical and mathematical description of information transfer in cells. Applying this model to the cell membrane of the nerve cell axon results in the second-order differential equation that represents the propagation of the electrical impulse responsible for information transfer. The numerical solutions of this equation are digitals impulses. This model of a signal propagation was derived by Hodgkin and Huxley in 1952. Their work is considered to be one of the greatest achievements of 20th century biophysics. A more modern approach can be found in the book Physical biology of the cell written by Rob Phillips which was the fundamental starting point of this thesis. Since this model contains the elements of different scientific fields, various professional literature from physics, biology, chemistry and neuroscience was consulted