Physical and mathematical challenges in molecular and cell biology – users point of view
D. Štys 1, 2, 3, Š. Papáček 1
1Institute of Physical Biology, University of South Bohemia
2 Institute of Systems Biology and Ecology CAS, Zámek 136, 373 33 Nové Hrady, Czech Republic
3Institute of Microbiology CAS, 379 81 Třeboň, Czech Republic.
Keywords: Maxwell´s demon, Brownian motor, intracellular noise, macromolecular crowding, small-system thermodynamics
In the paper will be discussed the origins of physical differences between the test-tube biochemistry and “living cell as test tube” and the subsequent necessities of new kind of mathematics . It will be discussed:
(1) Ratchets in protein-based systems (namely information ratchets) [2, 3], the principle that allows the protein to act as Maxwell´s demon. Machines based on this principle, seemingly being the perpetuum mobile of second kind, are widespread in the world of proteins.
(2) Stochastic resonance, the non-trivial principle that may lead to synchronised switching of noisy systems invoked only by low level trigger signal [3, 4] and acting generally as one of the switching mechanism of Brownian motors.
(3) The role of intracellular noise in systems of low number of particles that leads to the differences in reaction rates and courses  and may cause the bifurcations, oscillations and other types of complex behaviour , i.e. the cases not predicted by classical chemical kinetics or Langevin equation .
(4) Macromolecular crowding caused by high concentrations of large molecules in the cell (5-30% volume occupancy). This principle, exemplified by two extreme cases of crowding (influence of macromolecules) and confinement (trapping of large particles in small compartments) , leads to large deviation from ideal behaviour in protein-protein reactions and may be the leading principle in chaperone function .
(5) Effects of nanoscales, referred in protein word as non-equilibrium thermodynamics of small systems [10, 11]. At these scales the state of the system is not described by quantities such as temperature, pressure or chemical potential, therefore we have to define the so-called control parameters . In effects, we may observe work fluctuations, transient violations of the second law of thermodynamics and free-energy recovery which are the elements leading to miraculous efficiency of proteins as molecular nanomachines.
Popular reviews summarizing the above mentioned principles may be found in [13, 14, 15 and 16].
We set aside the questions of modularity, evolution and population dynamics although they are not fully separable from questions discussed in this paper. Interested learners are invited to courses of Physical Biology organized annually as a part of the lifelong education by the Institute of Physical Biology, University of South Bohemia.