Three
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

stys@jcu.cz

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 [1]. These are the objects which we observe at our
given timescale.

This
natural premise, plus generalised stochastic systems theory [2] 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 [3]. 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.

References

1.
P.
Cvitanovi´c, R. Artuso, R. Mainieri, G. Tanner and G. Vattay, *Chaos:
Classical and Quantum *(Niels Bohr Institute, Copenhagen 2009); ChaosBook.org/version13.

2.
Žampa,P. and Arnošt,R. (2004)
Alternative approach to continuous-time stochastic systems definition. In *Proceedings
of the 4th WSEAS Conference*. Wisconsin.

3.
Štys D., Urban J., Vaněk J. and
Císař P., Analysis of biological time-lapse microscopic experiment from the
point of view of the information theory, Micron 2010 in press

Acknowledgements.

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.