Biological systems state variable
identification using joint analysis of biological and technical hypothesis in
the time-lapse tissue culture development experiment
Pautsina A., Urban J., Stys D., Vanek J., Cisar P., Nahlik T., Lapitski A.
The time-lapse microscopy experiment is the best representation of biological cell dynamics. Cell fate is best described by the chaotic attractor and that the observable cell states represent individual basins of attraction. It is, however, not quite clear in which relation the experimentally observable macroscopic parameters are to the state variables of the attractor space. In other words it may be said that the experiment cuts the state space by a fraction of space, possibly, of lower dimension and of unknown shape with respect to system coordinates.
The only realistic approach towards objective analysis of the experiment is to determine evolution in time of information fluxes defined by the experiment. Here we present two essential representations of the system: (1) representation of information content of each timestep portrait-image in values of information entropy (this we assume to be in relation to dynamic biological system state in time of measurement) and (2) map of information content fluxes which we assume to be in relation to image of local Lyapunov exponents or eigenvalues of Jacobian matrix in actual point in state space. Such detailed analysis is extremely computationally intensive, however, it might be of high value for rapid diagnostics in medicine, biotechnology and any other discipline utilizing cell biology results.