The dynamic phase transitions regions of hydrogen are known to by rather different from the static ones. If Ni is a conductor for negatively charged protium or a meson built of light quarks then its coherence domain dynamics may be analagous to those in water. I found this article. Note the low effective mass (m

The resulting mesonic “zoo” will be compared with predictions from actual phenomenological ansatzes: e.g. potential models, the bag model, and QCD sum rules, and also more general approaches such as QCD lattice gauge theories.

*= 13.6 eV).*_{eff}
Cell Size and Shape by Quantum Models of Water Coherent Domains Dynamics

Preoteasa, EA

^{1,*}; Apostol, MV^{2,*}^{*}National Institute for Physics and Nuclear Engineering, RO-077125, Bucharest-Magurele, Romania

^{1 }Correspondence: eugen_preoteasa@yahoo.com

^{2 }Correspondence: apoma@theory.nipne.ro entary characteristics of cells (with a few exceptions, of typically 1-100 µm diameter) which place them between the microscopic, quantum world and the macroscopic, classical one. A quantum mechanical model based on Planck’s energy quantization rule and statistics for the electron and proton transfer in cell respiration and oxidative phosphorilation succeeded to explain the empirical allometric relationship connecting size to metabolism [1]. By a different approach, making use of the the low effective mass (m

*= 13.6 eV) of water coherence domains (CDs) from the QED theory [2, 3] we previously proposed the evaluation of cell size by models based on water CDs Bose-type condensation (supercoherence), on CD translation in a spherical well, and on an isotropic oscillator consisting of two interacting CDs [4]. Although the results matched to relatively small and medium-sized bacteria, our initial models showed limitations with respect to larger cells, and approximated the various shapes of cells only to a spherical one. Here we present new models aiming to deal with larger spherical cells and with disk-like and rod-like cells.*

_{eff}
Because the values of the maximum radius

*a*of a spherical cell estimated by the models of spherical well (1.02 µm) and of isotropic oscillator (0.99 µm) showed an excellent agreement, we looked after a combined model – an isotropic two CDs harmonic oscillator enclosed in a spherical box with impenetrable walls, larger than that required only to accommodate the oscillator. The centre of mass of the oscillator of mass 2*m*performs an independent translation, while the oscillator vibrates as a reduced mass m_{eff}*/2. In a perturbational treatment, the unperturbed energy levels of translation in the box are shifted by the harmonic potential which acts as a small perturbation. Assuming that the difference between the perturbed first two levels exceeds thermal energy, a maximum radius*_{eff}*a*of the spherical cell of 3.21 ?m at 310 K is obtained (volume 138.6 ?m^{3}). The predicted size matches to larger prokaryotes like*Myxobacteria*(0.5 – 20 ?m3),*Bacillus megaterium*(7 – 38 ?m^{3}) and*Sphaerotilus natans*(6 – 240 ?m^{3}), and also to the smallest eukaryotic cells like yeast,*S. cerevisiae*(14 – 34 ?m^{3}), unicellular*fungi*and*algae*(20 – 50 ?m^{3}), and the*erythrocyte*(85 ?m^{3}). The disk-like and rod-like cells have in common the axial symmetry, and both can be approached by the model of a cylindrical potential box with impenetrable walls. Along the axis the problem reduces to a linear gap with infinite walls and length*a*, of energy levels E_{n}. Around the axis, we were interested only by the radial part of the solution, given by Bessel functions J*(r), with energy eigenvalues E*_{l}_{lm}. The total energy is E_{nlm}= E_{n}+ E_{lm}with no immediate restriction to the values of*l*,*m*with respect to*n*. Because*J*(?_{l}*r*) = 0, the maximum radius_{o}*r*is related to the roots_{o}*x*_{lm}of*J*(?_{l}*r*). In the case of the disk-like cell, we chose |110> (*n*= 1) as the ground state, and admit that the transition |110> --> |221> to a higher (*n*= 2) level is “biologically forbidden,” or thermally unfavourable (E_{221}– E_{110}? 3/2 k_{B}T). Using the*x*_{10}and*x*_{21}roots, we obtain for a thickness*a*= 1.15 µm, a radius*r*? 3.8 µm, while a_{o}*human erythrocyte*is 2 µm thick and has a 3.75 µm radius. For the rod-like cell, we postulate that biologically relevant transitions leave unchanged the axial translation energy E_{n}, ?*n*= 0. For*n*= 1, a thermally unfavourable, biologically forbidden transition |1*lm*> <--> |1*l*’*m*’> allows estimation of radius*r*. Choosing |102> ground state, and |102> --> |121> as a “life-forbidden” transition, and using_{o}*x*_{02}and*x*_{21}roots, a radius*r*< 0.28 µm is obtained for a length_{o}*a*= 1,02 µm. The dimensions*r*and_{o}*a*are roughly confirmed for typical and relatively small bacilli. The ratio 2*r*/_{o}*a*= 0.54 of the cell shape fits very well, e.g.:*Brucella melitensis*(0.5-0.8),*Francisella tularensis*(0.3-0.7),*Yersinia pestis*(~ 0.5),*E. coli*(0.25-0.4). Comparable results are obtained with other couples of states, classified by an empirical “selection rule” for “biologically forbidden” transitions ?(*l*+*m*) = 0, ±1.
The results suggest that the dynamics of water CDs in the in the cell, which represent bound quantum systems, are an essential factor in determining the cellular size and shape. It is plausible that evolution selected the size and shape of cells such as to fit the form of potentials and of the CDs’ wavefunctions. However, one can hope that quantum mechanics contains a vast conceptual provision, which could be applied in further water CD models to account for other ultrastructural features of cells.

References

1. Demetrius, L, (2003).

*Physica A*322: 477.
2. Preparata, G, (1995). QED coherence in matter,

*World Scientific*, Singapore-New Jersey.
3. Del Giudice, E, et al., (1986).

*Nucl. Phys.*B275: 185; (1988)*Phys. Rev. Lett.*61: 1085.
1. Preoteasa, EA; Apostol, MV, (2008). arXiv 0812.0275v2

*Phys Bio Phys*.
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doi:10.1016/0370-1573(88)90062-2 | How to Cite or Link Using DOI | |

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**Spectroscopy of mesons containing light quarks (u, d, s) or gluons**

Available online 23 September 2002.

### Abstract

This paper gives an overview of the increase of experimental knowledge of mesons which are built by light quarks. This naturally includes also those mesonic states containing gluons and those with an exotic internal quark structure such as qq̄-qq̄.The resulting mesonic “zoo” will be compared with predictions from actual phenomenological ansatzes: e.g. potential models, the bag model, and QCD sum rules, and also more general approaches such as QCD lattice gauge theories.

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