dimensional information structure of living cell fate
D. Štys, J. Urban, T. Náhlík, J. Vaněk, T. Levitner, P. Císař
Institute of Physical Biology, University of South Bohemia, Zámek 136, 373 33 Nové Hrady, Czech Republic
Keywords: Information entropy, intracellular structure, multifractal space, information dimension, cell state attributes
Living cell is best examined by time-resolved optical microscopy. The holy grale of the approach is fast capture of inasmost complete three-dimensional information about the cell with spatial resolution sufficient to capture all relevant objects, spectral resolution which enables to characterize their chemical composition and time resolution sufficient to capture all relevant events. In the previous sentence there are numerous vaguely defined terms which may only be defined only with respect to the appropriate model of the cell structure (equivalent of the state space in mechanics) and cell dynamics (moment components of the phase space).
In ideal case we should be able to follow the trajectory of the cell in the multidimensional chemico-mechanical phase space in continuous time. In any real case, we have only real capture of a slice of a mechanical space at a time instant and have no realistic control over the identity of element of the chemical space – equivalent of component in thermodynamic terminology. Cells are dynamic systems exhibiting asymptotic stability. Such behaviour is expected by non-linear dynamic systems where in the state space on obtains regions of asymptotic stability which are populated with significantly higher probability than rest of the state space . These are the objects which we observe at our given timescale.
This natural premise, plus generalised stochastic systems theory  which brings the observation into the reality of the measurement, forms the theoretical basis and the framework for analysis of the observation, the elements of the model of cell monolayer. In relation to them we may analyse the information content of the measurement . Thus, we expect to observe individual dynamic objects characterised by structural similarity, characteristic coloration (i.e. colours, their heterogeneity, dynamics) and oscillations between several observable states.
The information channel – the microscope – is characterised by the point-spread function, a recipe by which a microscopic object is depicted at the destination – camera screen. The point spread function may be completely understood only for objects of known structure sufficiently separated from each other. This condition is never satisfied in living cell microscopy. The microscopy image, nevertheless, carries nearly complete information about the multidimensional mechanico-chemical state space and may be extended to approximation of the phase space.
In this paper we report (I) mathematical description of the observable state space in cell microscopy, (II) partial description of the information content of the optical microscopy mesurement, (III) observation of certain elements of the model of cell monolayer.
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This work was partly supported by the Ministry of Education, Youth and Sports of the Czech Republic under the grant MSM 6007665808 and grant HCTFOOD A/CZ0046/1/0008 of EEA funds.