A semi-classical approach of the relationship between simple cells' size and their living temperature limits based on number fluctuations of water coherence domains

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A semi-classical approach of the relationship between simple cells' size and their living temperature limits based on number fluctuations of water coherence domains
  A semi-classical approach of the relationship between simple cells' size and their livingtemperature limits based on number fluctuations of water coherence domains This article has been downloaded from IOPscience. Please scroll down to see the full text article.2011 J. Phys.: Conf. Ser. 329 012002(http://iopscience.iop.org/1742-6596/329/1/012002)Download details:IP Address: article was downloaded on 15/12/2011 at 10:55Please note that terms and conditions apply.View the table of contents for this issue, or go to the  journal homepage for more HomeSearchCollectionsJournalsAboutContact usMy IOPscience  A semi-classical approach of the relationship between simple cells’ size and their living temperature limits based on number fluctuations of water coherence domains E A Preoteasa 1,3  and C Negoita 2   1  Department of Life and Environment Physics, Horia Hulubei National Institute of Physics and Nuclear Engineering, P.O. Box MG-6, 077125 Bucharest-Magurele, Romania   2  Laboratory of Microbiology and Immunology, Faculty of Veterinary Medicine, 105 Spl. Independentei, 050097 Bucharest 5, Romania 1 E-mail: eugenpreoteasa@gmail.com Abstract . Starting from the concepts of the quantum electrodynamics (QED) theory of coherence domains (CD) in water we propose a model aimed to evaluate the relationship  between the size and the living temperature limits for simple, small cells. Cells are described as spherical potential wells with impenetrable walls, with CDs moving inside. The radius of the spherical potential well was estimated for physiological temperatures and the results match to  bacteria and yeasts cells ’ size . As a CD in the spherical cell exerts a force upon the membrane, a ‘gas’ formed by CDs bears a pressure  on the walls. A classical statistical stability condition relates this pressure to cell volume and to the relative fluctuations   of the CD number, allowing the evaluation of an upper temperature limit as a function of cellular volume. Assuming further that the CDs in the living cell form together a coherent state, the number-phase incertitude relationship (Heisenberg limit) applies. The maximum coherence between CDs is found in the ground state, a picture consistent also to Fr  ö hlich ’s postulate . For a given phase dispersion, a lower temperature limit as a function of the cell volume is found. Although we neglected the rod-like shape of certain bacteria and the presence of nucleus in yeasts, the biological data of volume and optimal living temperature intervals fit well to our model’s predictions. Moreover the larger the cell volume, the higher are the number of CDs and   the coherence of their system. In addition we suggest a new classification criterion for small cells  based on model’s  parameters, which show discontinuities between Gram negative and positive microorganisms as well as between prokaryotes and the smallest eukaryotes. 3  To whom any correspondence should be addressed.   1  1. The problem of the cell size. An unexplained simple biological fact Dimensions represent perhaps the most elementary characteristic of the living cells. They are apparently macroscopic objects, with typical sizes of 1  –   100  m [1]. Smaller biological objects like viruses, proteins or nucleic acids are not actually living objects. Cells are far larger than objects of the microscopic, quantum world such as atoms and molecules, and also larger than nanoparticles, which define the mesoscopic scale (Figure 1). The dimension of the cells is basically an empirical fact from the standpoint of traditional biology. Molecular biology sensibly postulates that a lower size limit is explained by a minimum number of 5.10 2  –   5.10 3  different enzymes, while an upper size should be limited by the efficiency of metabolism,  by the surface to volume ratio and by the dimensions of vacuoles. But this approach, though significant, is also based indirectly on certain empirical facts and therefore only displaces the problem, failing at least in part to look at the cell size as a basic feature of relevance for the phenomenon of life. 2. Physical views on the cell size and the quantum biological approach From the physical point of view, cell size is not a parameter reducible to the empirical data of molecular and cell biology, which in the large frame of Nature appear elementary, particular and casual, but instead it should be an essential feature of the living matter related to a specific kind of dynamics. Schrödinger [2] pointed out that in a living organism molecules must cooperate, and this condition requires a volume large enough to ensure the cooperation of a sufficient number of molecules against thermal agitation. Along this line the dissipative structures theory [3] is looking up to the cell as a giant density fluctuation and shows that its dimensions must exceed the Brownian diffusion which takes place during the lifetime of the cell. These two views look at the cell as a whole, without taking into account the molecular details inside the cell. The same perspective is assumed by quantum biology, which proposes to understand the characteristics of the cell and multicellular organisms based on their integrative features, such as the emergence of self-organization and hierarchies of collective order above the molecular level (e.g., [4]). This approach tries to answer whether quantum mechanics plays a non-trivial role in understanding life or not, beyond the quantum chemistry calculations of molecular structure and properties. An answer based on quantum mechanics to the cell size problem was given in a model proposed by Figure 1 . Size scale of biological objects.   2  Demetrius [5], which connects size to metabolism, probably the most essential feature of life [6]. The model proved itself capable to derive the empirical allometric relationship, P =  W  , where W is the weight of a cell or organism and P the metabolic rate, and   < 1 is an dimensionless scaling exponent which depends on the metabolic efficiency. The model applies Planck’s energy quantization rule and statistics for the electron and proton transfer taking place in the coupled cell respiration and oxidative  phosphorylation according to the chemiosmotic theory. However, the dependence of the cell size on metabolism in the quantum model of Demetrius leaves unanswered the question of the nature of metabolic rate (which may be interpreted as an observable of physical srcin specific to the uniquely complex system which is the living cell or, alternately, a primary fact of the biological realm). Another valuable physical approach of the cell size and geometry problem has been proposed recently ([7] , to be published in this volume). These authors studied the oscillations of microtubules’ network in the dividing and non-dividing eukaryotic cell. The tubulin heterodimer was approximated as an elementary electric dipole performing coherent or quasi-coherent electromechanical longitudinal oscillations with low damping in the surrounding organized water. The size and shape of the cell was related to the electric field calculated around the oscillating microtubule network. We do not intend to search here an answer to the question of the nature of metabolic rate, a challenge which is neither simple nor obvious. Rather, we propose here a new quantum model for the evaluation of cell size without any hypothesis on metabolism, along a line of attack related to our  previous studies [8]. And while the microtubules continue to stimulate quantum mechanical models [9-11], our study is focused on the ubiquitous component of living cells, either prokaryotic or eukaryotic: water. 3. The QED theory of coherent domains of water The philosophy of our approach finds support in a definition of life given by Del Giudice: “ the  protagonists of the biological process … [ are] mesoscopic collectives characterized by millions of molecules acting in unison in wide regions of the space for long intervals ”  [12]. This view is in agreement to the theory of long-range coherence of dipole oscillations developed by Fröhlich [13-16] which helps understanding certain fundamental integrative features of living organisms. The very long-range character of this theory overcomes the fragmentary picture of molecular biology which admits information to be carried only by chemical messengers involved in short-range specific interactions and moving only at random. An active role for water in these long-range correlations within the cell, as opposed to its mere function of a cellular environment, is sustained by models of water collective dynamics based on H 2 O molecule ’s  electrical properties. Moreover this role is related to inhomogeneous structures formed in water by self-organizing phenomena; we also proposed a model of ionic plasma oscillations accounting for density oscillations in liquid water [17]. As characterized by Ben- Jacob, water is „an ac tive substance saturated with life- giving properties“  [18], in accordance to the quantum electrodynamics (QED) theory of coherence domains (CD) of water, described as clusters of electrical dipoles self-organized to oscillate in-phase with each other [19-24]. We note in this connection that quantum coherence is a theoretical concept describing a general  property of living and non-living matter [24]. Most important, quantum coherence has been already demonstrated experimentally in plant photosynthesis, where light absorbing molecules capture and transfer energy according to quantum-mechanical laws at temperatures up to 180 K [25], and in a model system represented by a wet conjugated polymer where coherent intrachain energy migration takes place at room temperature [26]. Recent results obtained on the cryptophytae  marine algae by 25   3  fs laser pulse irradiation and photoecho spectroscopy demonstrated that there exist long-lasting oscillations exciting a coherent superposition of antenna's molecules vibrational-electronic eigenstates, with correlations across 5 nm long distances among dihydrobiliverdin pigments ‘ entangled ’  together  by quantum coherence, even at 294 K [27].  In vitro  studies on various water-containing systems evidenced experimentally a good number of phenomena consistent to the QED theory of CDs. These include among others the water bridge formed in ~15 kV static electric field [28], the long-lasting  perturbations induced by weak extremely low frequency electromagnetic fields in solutions of glutamic acid [29], the ion cyclotron resonance (ICR) phenomenon in biological and biochemical systems [30, 31] and the sharp changes in conductivity for amino acids solutions exposed to ICR magnetic fields tuned to the q/m  ratio of amino acid [32], the gel-state water extending up to ~1-10    m at interfaces [33], and the phenomenon of autothixotropy evidencing the formation of fragile but trully macroscopic (~cm) structures in water by an ‚ephemeric polymerisation’ [34]. A low effective mass (excitation energy) of the water CDs was evaluated to about 12.1-13.6 eV, much lower than e.g.  the electron mass [21, 24]. Accordingly, their wave-like properties are strongly enhanced because their de Broglie wavelength   = h/mv  will be much longer and comparable to the cell size. These properties together with the boson nature of the CDs, as well as with the capacity of CDs to interact with oscillating dipoles up to a few  m apart through the attractive r  -3   Fröhlich  potential [35] endowed with resonant character of Askaryan forces ’  type [36] sustain the view of a “supercoherence” state, a coherence spanning all the CDs throughout the cell water. Thus a supercoherent network of water CDs in the cell is postulated to play the role of command and control for the huge number of molecular interactions which take place at the right time and place through the life cycle of the cell. Long-range forces may provide an explanation for rouleaux formation [37] and anomalous light diffusion [38] of erythrocytes, dielectrophoresis of small dielectric particles by cells [39], and variations of the optical spectra of a nutrient in suspensions of yeast cells as a function of cell density [40]. A certain type of supercoherent state, or a Fröhlich  condensate, has been unambiguously evidenced in living cells by a 8.085- MHz resonance by Pokorny’s group [ 41, 42], who identified microtubules’ network oscillations as a possible candidate . 4. Previous models and scope of the present study Taking as a starting point the concept of water CD elaborated in the (relativistic) QED theory of the Milano group, we previously proposed a few different but related models explaining the size of the cell in the frame of non-relativistic quantum mechanics [8, 43]. To this purpose we postulated that the cell membrane is an impenetrable or semi-penetrable wall for the CDs and the shape and size of the cell selected during evolution are such as to represent a potential well or a resonant cavity imposing to the supercoherent CD system a specific type of dynamics, which is consistent to an integrated and unitary informational control of the molecular dynamics inside the living cell. With this heuristic approach and taking advantage of the low effective mass of CDs ( m eff      13.6 eV   2.4 × 10 -35  kg) we evaluated the lower and higher cell size limits of spherical cells by models based on Bose-like condensation, on CD translation in a spherical well, and on an oscillator consisting of two interacting CDs [8, 43]. In our potential wells and harmonic oscillator models we assumed, for the sake of cell stability, the second energy level to be thermally inaccessible from the first (ground) level, where the system remains during cell life. The results matched well the size and shape of bacteria, yeast and erythrocytes, and explained also why the D 2 O toxicity is higher for eukaryotes. For instance in a model   4
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