SPACE-TIME STRUCTURE OF A BIOLOGICAL CELL, PERANGON SYMMETRY TRANSFORMATIONS AND AN EXCHANGE FORCE THEORY OF BIOLOGICAL CELLULAR ADHESION AND BIO-QUANTUM MACHINES

ALBERT EINSTEIN CENTENARY SYMPOSIUM,

S. N. Bose Institute of Physical Sciences, Calcutta, March 1-3, 1979.

SPACE-TIME STRUCTURE OF A BIOLOGICAL CELL, PERANGON SYMMETRY TRANSFORMATIONS AND AN EXCHANGE FORCE THEORY OF BIOLOGICAL CELLULAR ADHESION AND BIO-QUANTUM MACHINES

K. L. Narayana, M. Inst. P. (Lond),

Shivaji University, Kolhapur-416004.

A B S T R A C T

The theory which adopt a quantized space-time structure for the biological cell has been developed following the two basic postulates viz., (1) The Bio-metric may comprehensibly be treated subject to an inherent symmetry law of the physical universe which treats it on par with other metrics of cosmos and is describable in terms of selective violations of this symmetry law. (2). Bio-physical phenomenon, in terms of the Bio-metric quanta, or manifestations of the same compete directly or indirectly with biological living processes. Further, PERNGON SYMMETRY transformations of the type g _ik à g_ik’(x’)  = e^ζΔ  σ^α  g_ik(σx) involving both the gauze and scale transformations are suggested for the non-invariance of the Lagrangian. Using ζ =-1 and α = 5/2 Bio-metric quanta of mass 0.667E-30gm and with a coupling constant g_p² = 5.31E-06 is derived (weak interactions).

                 By a perturbation theoretic approach, the number of PERANGONS  that would envelop on electron participating in a biological process has been estimated with the interaction Hamiltonian, H’= √ (8πG) g_μν F^μν where F^μν and g_μν  describe the electron and PERANGON fields, with g_p² =  (B l₀ √ (8πG))/ m

With l₀ with fundamental length, Ā Boltzmann factor, m mass of electron. Threshold velocity criteria for the emission and absorption of these PERANGONS by electron are discussed, with electron dressed in PERANGONS to be referred as the PERAON. 

                 An exchange interaction theory of the Bio-metric quanta between different cells separated by a bio-distance is proposed. Balance of force relations of the exchange and electro-static interactions of the cells has been next used to derive the nature of exchange interaction as of an exponential type with the cut-off of the range of the force as 5.38E-08cm. It has been reasoned out that like cells of specific adhesion are coadurated by consonance quanta, and ratio cinate the fact that the CANCEROUS cells do not spectacle the adhesion.

                 Next the theory has been applied to explain the Quantum Proton dislocation across electrical gradients and useful relations about the biological mass work relations with the maximal efficiency (such as ζ_nl = r(1-r) (n²- 1/ r²) / (n² -1); r mass compression ratio, n quantum state, ζ_nl  efficiency) have been derived. The performance of the Quantum Machine vis-à-vis the Carnot cycle of thermodynamics has been exemplified with configuration co-ordinate model diagrams.

EXTENDED ABSTRACT

                  A formulation in which the biological cell has been endowed with a quantized metrical binding force and a space-time structure has been presented. Violation of an innate relation of the bio-metric with general metric gravitational space-time continuum has been used to define PERANGON TRANSFORMATIONS and involved philosophical aspects have been enunciated. Relevance of the inherent symmetry and invariance properties of the bio-metric in the context and in the recto-realm of biophysical, microphysical phenomenon and the biological cell characteristics has been discussed.

                

                 Dressing of an electron by the PERANGON QUANTA of the biological cell is detailed deriving the value of the coupling constant of the binding force of cell adopting a perturbation theoretic procedure. An exchange force theory of the cellular adhesion is proposed obtaining the characteristic cut-off of the force of PERANGON propagators. Intuitive reasoning of the loss of specific adhesion cells has been suggested.

ALBERT EINSTEIN CENTENARY SYMPOSIUM,

S. N. Bose Institute of Physical Sciences, Calcutta, March 1-3, 1979.

SPACE-TIME STRUCTURE OF A BIOLOGICAL CELL, PERANGON SYMMETRY TRANSFORMATIONS AND AN EXCHANGE FORCE THEORY OF BIOLOGICAL CELLULAR ADHESION AND BIO-QUANTUM MACHINES

K. L. Narayana, M. Inst. P. (Lond),

Shivaji University, Kolhapur-416004.

                 Simplest unit of life is regarded as the cell and it is affable for a systematic study by Quantum biophysical methods, by virtue of of its remarkable identity of individualistic existence despite the variety and totipotency. 

               Gross physical features of cell and its structural aspects are known to a certain extent to a stage where at theoretical approaches are expected to lead the experimental studies towards a fruitful goal of understanding the ‘livingness’ as a physical phenomenon. The origin of the typical cell is highly speculated, any discussion of it falls outside the scope of the present work the following four general explanations are worth to ponder. [Duchesne 1977].

(A)                The contemporary living is due to a supernatural event which is beyond any comprehensive understanding either by physics or the chemistry. This early belief of human thought has been almost abandoned.

(B)                Life is coeternal with neither a beginning nor an end. It might have been planted on the earth accidentally or as a part of evolution cycle.

(C)                 Might have been created in a spontaneous and quick process out of purely non-living matter, the place of its birth and mode of migration not known.

(D)                Evolved terrestrially or globularly, at specific instants of conditioned environments, but as sequential and progressive reactions responsible for its synthesis. (Dethier et al 1975, Garay 1971).

              A function of the cell metabolism is to supply the energy required to maintain the ordered structure of the living automate against disordering effect of the environment. Cell from a thermodynamic view point may be taken as an open system with a steady state energy flow or a systematic increase of energy, so balanced and adjusted with external environment of other cells, at least over a period of time. The consequent thermodynamic decrease of entropy has been first commented up on by Schrodinger (1944) in terms of a negative entropy concept, contrary to the law of increasing entropy of the Cosmic Physical Universe.

               Quantum mechanical approach to study the different aspects of theoretical cell biology is not uncommon. Notable of these are those by Van Neumann (1951, 1966); Wigner E.P. (1961); Arbib (1977); McClare (1972, 1971); Huxley (1975); Fox(197 ); Prigogne (1972); Heisenberg (1971); Szent-Gyorgi (1972); Elsassser (1970); Wigner E.(1969); Bohr(1961). The standard theory of Einstein, elastic reservoir theories, pulse-wave propagation theories etc., has been applied to study the living organisms. More beneficial as one may expect are the approaches by Lowdin (1963); Watson and Crick (1965), Rashevesky (1972); and Szent-Gyorgi (1972), Godwin (1962) to discover what may perhaps be referred as the fundamentally valid principles of biological organization and which are applicable to explain the all levels of biological activity.

               In this paper, I report an entirely different approach to explain theoretically a feature of the physical functioning of a cell. Essentially it predicts the existence of a new biological QUANTUM and gives rise to an exchange force theory of cell adhesion.

               As a backdrop of the theory we note the following:

(A)                   Typical cells are endowed with well defined (average) physical properties, such as size, electrical charge, magnetism, surface area etc.

(B)                   Properties of any cell can at best be most conveniently studied in terms of specific molecular, ionic or particle physic-chemical behavior.

(C)                   Cells exhibit identical features and are adhesives with other cells of characteristic nature.

(D)                   They function as machines of Quantum mechanical nature with a high degree of efficiency and consequently are the Quantum sources of useful energy.

(E)                   Typical cell is an entity of materialistic existence subjected to certain laws (may be specific) of general Physical Universe, though  concomitantly performs the duties as living matter and continues however, to play a role as an integral part of the Universe.

               The theory I propose intends to present the biological Quantum as a competing and an alternative physical entity which participates in the bio-physical functioning of the cell, explicitly the exchange force theory of specific cell adhesion has been formulated. Philosophical principles underlying the formulation of this theory are two-fold. Firstly, I expect that the elementary unit of living system ‘the cell’ is a space-time continuum which may be comprehensively be treated, subjected to an inherent symmetry law of the Physical Universe such as the elementary particles or the neutron stars. Following the enunciated principle I state that the cell possesses what may be termed as “Bio-Metric” the third of its kind. The other two are those suggested by Einstein, the metric of the Astrophysics, and the one suggested by Dirac, the metric of particle physics. The second principle is these bio-fields manifestly can be thought to exist in Quantized Units and specific cells are capable of exchange of these. This principle leads one to think of bio-physical phenomenon where the bio-quantal processes might directly or indirectly compete with the biological living processes, which possibility makes this principle much more of potent in physical considerations than the first one stated earlier.

               Enunciation of universality postulates valid for the micro-physics is not a new thing, for instance the usual form of Quantum theory and its applicability to deal with Genetic Code system to realize the universally postulates, has been the subject of study and investigations by Rosen (1972). Again, I expect analogous but by a distinctly different way to that of Eddington’s fundamental theory of physical constants, that all bio-physical quantities, constant over a range, be determined by a set of qualitative geometric and Quantum principles, though they the quantities can be inferred from quantitative experimental measurement or alternatively by phenomenological theories (Whittaker 1952).

               As for the subject matter of this paper, in the first section presented is a, description of the known physical features of cell useful and relevant to the present work. Developed in the next section is the predicted existence of a Bio-metrical Quantum of the living Cell. Also how these clothe an electron to form a new particle PERAON, has been quantitatively worked out in this section. Next a cursory account of the present status of theoretical understanding of Cell adhesion is given and details of the exchange force theory of Cell adhesion proposed has been discussed.

SECTION I

                 They the Cells vary in size being less than one micron. They may be regarded as an entire living system, just as a plant or an animal, exhibiting essential Genetic characteristics. They may perform different duties each individual Cell representing an overdeveloped function of the totipotency of ell (Coult 1966). Protophy are capable of photosynthesis while Protozoa are not.

               Cell plays a vital role of the living organism by holding in its narrow space, dynamically interesting entities of cytoplasm and the nucleus. Smallest Cells are smaller than larger viruses. They vary in ‘effective size’ from 12E-04 cm of diameter to about 250Å. Typical values are around 1000Å to 3000Å for the size of a cell and bacterial cell volume is about 1E-13ml. Metazoa cell volume is about 1.7E-09 ml. The human cell surface area is about 160μ² with membrane thickness of 52Å.

                 The cell weighs around 2E-09gm, with the aqueous part of it accounting for about 85E+12 atoms of H, and 42E+12 atoms of O. The non-aqueous part of consists around 350E+09 molecules of which 1% accounts for protein substances.

               I mention a few of these pertaining to the Cell. The Cell net surface charge is negative and is about 4.8E-04esu. Mutual Cell separation distance is usually of the order of 150Å, with a close gap, the other possibility, of the order of 20Å to 50Å. The cell in size may be contrasted with pleura-pneumonia like organisms, which average about 0.1μ. Magnetic gram susceptibility (Barnothy 1969) for 13 individual yeast cells (6 to 10μ size) has been found by Gull et al. (1960) to average at value of -0.83E-06 emu/g, with about 15% variation. 

               Death of a Cell causes an increase in diamagnetism observed by Bauer and Raskin 1936 in Biological Cells, B. Coli and B. Proteus, also in Yeast cells. They hypothesized that a protoplasmic molecule in an excited state up on the death of a cell. (Kavi and Narayana1977) contrary arguments are given by Sugiura and Kogs (1964).

                 The dielectric constant of the medium of a cell is around 80, with electrical resistance large when water is entering the Cells and lower in value when water is leaving the cell. [Ambrose 1964, Pethica 1961]. The capacity of Egg Cell is about 0.63μF cm^-2 with resistivity of 3450 ohms cm². Plant cell “Nitella” resistance of membrane is about 10⁵ ohm cm² and falls up to 500 ohms  cm² while its capacity 0.9 μF cm^-2  may fall by 15% contrary to high electrical resistance of the Cell, the surface tension is very low (Harvey 1931).  A potential difference of -10mV can be developed or is usually found between the inside and outside the Cell, ‘Halicystig Ovalis’,  even in the absence of ionic concentration gradients while in other instances it may  vary from +10mV to around -500mV (Maxey 1977).

SECTION II

                 Rashevsky as early as 1939 approached the problem of form of any organism, whether it be the shape or design in general as the living organism exists, from the view point that cell is the seat of innumerable metabolic reactions. Substances diffuse from in and outside the Cell, while the Cell itself is subjected to, and also is the cause of different kinds of forces as a result of the cellular metabolism. Knowledge of these may lead to the principles of adequate design of organic matter of substances with as many as 10¹³ Cells. Nature of these forms is not yet known.

                 Confining my attention however, to the case of a single biological cell, for an understanding of it as an entity all in itself, I invoke ‘an innate’ symmetry principle of space-time continuum. I believe that the Cell enveloped by the membranes provides as a good example of optimization of space-time continuum. It is nouveau riche due to the quality of its individualistic and imperious existence with totipotency of replication, thus typifying itself as a space-time continuum. This continuum is describable by a peerless metric which here afterwards to be referred as the biometric of the cell. The difference between the force that the bio-metric otherwise implies and the forces of the cellular metabolism would then be in any form such as the vibrational, rotational, kinetic or rest-mass energy etc. of the molecules, ions and or of the typical particle involved in transport mechanism.

                  A principle of inherent symmetry of nature which is violated in a specific way and that which treats both the physical universe as observed by Radio Astronomy experiments  extended over the Hubble radius (10²⁷ cm) and the space-time universe existing enveloped within the biological cell, is enumerated. It guarantees that these two are governed by analogous (but intimately related) metrical and geometrical quantities. Of course, the principle is inadequate and suffers from the same conceptual understanding of how a metrical tensor describes at the same time the geometrical aspects and as well as serves the purpose as a propagator of the force field which are characteristic of the space-time continuum.

                   The principle of inherent symmetry is related and stems from the physical fact the biophysical phenomena of the living cell remain invariant. In that the Cell exist as an entity possesses the character of reproducibility with the capacity for totipotency etc. constitutes again as direct evidence of certain biophysical invariance (Williams 1969).

               One can correlate this with the displacements of space and time and the invariance of the physical phenomenon underlying the structural aspect of the living cell would then be a striking intuitive realization. 

                 In physics Weyl (1952) and Wigner (1963) were the first to probably emphasize the invariance and symmetry aspects of space-time displacements. Many aspects of the classical, Quantum and field theories find precise significance through the invariance of  action integrals. Formulation of the same for biological cell, in the present author’s opinion would lead to most fruitful and meaningful study of physical invariance character, under both the discrete and continues parameter groups and as well the conservative laws of biological system whatever be the complexity of these systems. Selection rules would then be an automatic outcome of these invariance and symmetry principles.

                The two essential different kinds of QUANTA namely that of the biological cell and that of the general physical universe, I presume to be related through the enunciated symmetry principle. A new Quantum Number ζ for these quanta which gives, rise to a non-unitary transformation and which is violated selectively. The violation naturally would be an orderly one and also definite. The dynamics can then also be inferred through these violations.

               Adopt the following transformation for x and g_ik which represent space-time and metrical components of a continuum.

(1)                   Xà X’= σ X

(2)                   g_ik à  g’_ik (x’)  = e^ζ  σ^α  g_ik(σx)

where Δ is a parameter different for different quanta and

(3)                   Δ  à Δ’ ≡ Δ   if  |ζ|  ≡   |ζ’|

Obviously the transformation is both a gauze and a scale transformation and is to be referred as the PERANGON TRANSFORMATION. The non-invariance of the integral Lagrangian over a space-time extension may be noted as from the relation given below:

(4)                     Là L’ = ∫ d4 x’ σ^-4  e^2ζΔ  { [ κ² g’_ik g’_ik – A   k² g’ g’ ] σ²

           +[ ∂ g’_ik /∂ x’_i    ∂ g’_ik /∂ x’_i    + B  ∂ g’_rk /∂ x’_r    ∂ g’_sk /∂ x’_s   

        + C. ∂ g’ /∂ x’_l    ∂ g’ /∂ x’_l      +  D.  ∂ g’_ik /∂ x’_i    ∂ g’ /∂ x’_k   ] } σ ^2α

Where A, B, C, D are constants. Since our interest is in the mass, we do not attempt to find these constants (Narayana 1979, 1977). The relation implies that  σ = e ^{- ζΔ}   then the PERANGON TRANSFORMATION would lead to the formula

(5)                     g’_ik( x’)  = σ  g_ik (σ x)

for the metric quantities of the two different space-time extensions. 

       How best the PERANGON symmetry be exploited? Can we not conjecture from this principle a possible relation of the mass of bio-quantum of a biological cell with that of the GRAVITON of the Universe? Two main difficulties arise one refers to the non-vanishing feature of the rest mass of GRAVITON and the other regarding an intuitive objection against the presumption of existence of such a kind of bio-quantum. I present the argument that approximate knowledge of the masses of such QUANTA, within the experimental limitations of ‘observability’ and determination of the same, hints at as stated previously justification for the inherent symmetry principle including the ‘biological entities’ as observable physical objects.

       The rest mass of GRAVITON is taken to be 2E-62gm. Existence of a bio-quantum of this kind may perhaps be also inferred from the role that it would play as the ‘cause’ of the specific adhesion character of biological cells. I expect that these QUANTA typify the Cells including those of CANCEROUS cells‼

       The rest mass of these QUANTA the PERANGONS, can be determined from this relation m_g= m_p e^2ζΔ σ where ζ=-1. Adopting the Hubble radius of the Universe as 10²⁷ cm and X equal to the radius of a typical biological Cell (3000Å) we obtain the ratio of  x’/x= e^-Δ = 2E-32.The rest mass of PERANGON QUANTA of the Cell then turns out to be ) 0.667E-30gm. The values of the quantities ζ=-1 and α=5/2 are unique set as they would lead to some linear scale PERANGON TRANSFORMATION for the rest mass as well the radius a feature not noted previously (Narayana et al 1976). These PERANGON propagators do indeed hold the biological cell to exist as an entity.

       Coupling constant of this new physical force of binding of the biological cell, mediated by the PERANGONS is estimated adopting the different procedures.

        First we adopt the prescription to derive the coupling constants as laid down by Narayana et al (1976). The method makes use of fundamental length concept and a value g²_p / (ћc) = 5.31E-06 in dimensionless units has been obtained. Noteworthy, this value lies between the values of gravitational and weak interaction coupling constants. Thus the present theory gives rise to a coupling constant as fundamental as the Newtonian coupling constant. An amulet feature is that the biological Cell might have originated as an outcome of some initial instant of COSMIC evolution.

PERANGON CLOUD

        The PERANGONS would dress the electron in motion. The number of these that actual accompany an electron may be estimated and that would turn out to be an alternate method of arriving at the value of the coupling constant of the PERANGON force. The composite particle, electron plus PERANGON here afterwards is to be refereed as the PERAON. The energy considerations of an electron would be different as it moves through the PERANGON CLOUD. For study of this aspect I adopt a perturbation theoretic approach. We treat the ground state of the electron unperturbed as the state in which no PERANGONS are associated with it. To a first order of approximation, the total number of PERANGONS that are associated with the electron is given by,

(6)                     = ∑_q  ||² / (E_k- E_k-q – ω_q) ²

where |k-q ; 1> is the perturbed state of the electron E_k= K ²/ (2m*), where  K and m* being the momentum and the effective mass of an electron. ω_q I the frequency and H’ the effective Hamiltonian of interaction given by

(7)                     H’= (8πG) ^½ g_μν    F^μν

   With F^μν = p_μ p_ν / m the mass of electron m , and p_{μ ,}  p_ν  are the  momenta. Here the  g_μν are

(8)                     g _μν(q) = 1/ (2π)^3/2 { e ^+iq.r   a⁺ _qλ     +   e ^–iq.r a_qλ  } e^qλ _μν / (2ω) ^½

a⁺ _qλ     and a_qλ being the creation and annihilation operators of the PERANGON QUANTA in the polarized state (q λ) and e^qλ _μν the polarization vector associated with  the (μν)/ћ component describing the PERANGON momentum q. Following my recent work (Narayana 1979) the g_μν describe the PERANGON of intrinsic spin 5/2 and obeys the Fermi-Bose statistics!.

But when in association with electron quantum statistical considerations would be different (Bicz’o et al. 1966).

The matrix element of the interaction is

(9)                     ||=

(8πG)^½/ m  . (1/ (2π)^3/2) [(- I ћ)² / (2ω)^½] < k-q ; 1| q_μ . q_ν  a⁺ _ik   e^ik _μν |k ; 0> 

wherein the first quantization differential operators – iћ∂/∂x_μ   and – iћ∂/∂x_ν   have been adopted for the interaction operators.

The expression for than may be taken to be,

(10)                = (8πG/ m²) {2/ (2π)³} (ћ⁴ / ω) ∫_o^∞  q³   d³q   m*²/ ( q + q_c )²

Using the relations   ω = V_s ρ ,  q_c  = 2 V_s m* and neglecting K in comparison with q, and ρ is the biological Cell medium density 1.089 gm cm^-3.(Morowitz 1968) presuming that the medium is isotropic and elastic.

Restricting the variation of q to a value q _p , we obtain

(11)              = (1/ π 2) ( m* 2/ (ћ ρ V_s) )  (8πG/ m²) with

Contribution of terms involving q _{p /}  q _c  as of order unity.

        Extensive investigations previously made by Narayana and Kavi (1977) on the magnetic field effects on biological materials, have led to the conclusion that the reduced mass of an electron, during the Kreb’s cycle of ATP synthesis, is about m* = 0.2261MeV.

Adopting this estimate we obtain   = 764, which value to be comparable with the equation (10) given above. The comparison leads to the determination of the PERANGON coupling constant.

       The value of V_s is estimated from the relation k_BT= ½ M* V_s where k_B is the Boltzmann constant and T is the absolute temperature of the Cell. V_s is found to be about 1.44E+07 cm/s.

       Boltzmann statistical situation for the equilibrium configuration of the biological Cell would give a factor e ^{– εi  / kB T} . The energy ε of the electron in which state it partakes the process of dressing by PERANGONS, is determined so as that a unique coupling constant of the PERANGONS exists. In other words it has been taken that

(12)              (√8πG / m) . e ^{– εi  / kB T} = g²_p / (ћc) = 5.9965E-10 erg. Where l_o is the fundamental length, 2.8E-13 cm. 

       The constraint of V_s value, i.e. the velocity of electron in PERANGON media, should equal to one from thermodynamic equilibrium conditions is of significance. It is related to the group velocity V_g by the relation   V_g= p _min/ m*   where p_min is the one denouement from the relation 2 ⃗k . ⃗q – q ² – q q_c . The relation is analogous to the Cherenkov radiation threshold relation, that the Cherenkov radiation is produced only when the electrons should travel in a medium faster than the phase velocity of the radiation in that medium (Fargo 1970). The velocity of PERANGON itself is very large compared with the V_s. The thermal velocity make it difficult to lower the value of V_s and therefore it corresponds to the threshold energy for the electron PERANGON interactions and or otherwise for the emission of PERANGONS.

SECTION 3

       Simple physical forces have been thought by various earlier researchers to account for the spacing between cells, while certain substances involving Calcium or protein or mucus’s or muco-polysaccharides, etc. may be responsible for specific adhesion. Evidence regarding the state of affairs whether aggregation precedes or it follows the first appearance of cells has been unclear and also ambiguous. The Cell separation is usually of the order of 100Å, and at other instances, termed usually as the close gap, is of the order 20Å - 50Å. 

       Models built on oil globules such as that of Van Den Temple (1958) are of certain success in describing the various aspects of the coalescence. Like cells tend to adhere to each other. A measure of specificity is attributed for the cells in view of the property of adhesion and the experimental finding that there is a loss of this property specific adhesion in cancerous cells. Contacts recognizable of the cells are of three types; 

(1).  Adhesion to a common matrix or appearance of aggregates within the common matrix.

(2). With no material contact at all and

(3) Direct protoplasmic linkages between the cells.

               The protoplasmic contacts are of predominance in cells and these plasmadesmata bridges extend to lengths of the order of 100Å. Mescona, a pioneer researcher of the new field of cell adhesion believes that there exists a family of chemical substances that are responsible for specific functions. These substances are such as those that bind cells, determine blood groups and which compose antibodies, influence the selective susceptibility of the cells and also equip the cells with means of mutual recognition and specific association. The theory of cell adhesion and selective adhesion, which postulates the existence of specific substances playing a role has been perhaps been supplemented by a second theory. The later theory asserts the existence of binding sites of cells of various tissues and the adhesion is guided by the quantitative difference in the number of binding sites. Further, this theory reasons out that the strongly adhering cells once coalesced build, firm bridges, these then tend to push away the weakly adhering cells out of the way as the bridges are built up larger in number. The aggressive or the clumps of the cells occur forcing away the weaker ones to go continually to the periphery of the cell.

               The nature of the adhesive forces has been much thought and a number of kinds of these have been suggested. They cannot however, be the simple attractive forces. Also the chemical bond attractive forces (with bond energy 30-50Kcal/ mole over 1.5Å) or the hydrogen bonds (over 2Å with 3-5 Kcal/mole) or the ion pairs or triplets – COO-Ca ⁺⁺ -COO ^– type of dispersion forces (1000 to 100Å or less) are not considered to be the eventual binding forces of the cells. They are presumed to be either forces due to fluctuation on surface of like or opposite sign, or simple electrostatic attraction between surfaces of like charge but unequal magnitude. Of course, forces of attraction due to image forces, surface tension or Debye forces of induction arising between permanent dipoles are also presumed. Induced dipolar attractive forces and Keeson orientation forces existing between permanent dipoles are also suggested. Cell membranes do exhibit interesting other properties such as resistance etc. (Harvey 1931, Kanno et al 1965, Cole et al 1939).

CONCLUSION

                 A new theory of cell adhesion is given herein. The theory is essentially based on the notion of exchange interaction of cells. The QUANTA of exchange interactions are the PERANGONS. The attractive exchange interaction is counter balanced by the repulsive character of electrostatic Coulomb interaction of cells. Previous theories have assumed that the repulsive forces are balanced by Van der Walls force of attraction which diminish by 1/r³ or 1/r⁴, r being the inter-cellular separation distance.

               If the distance r= 150Å is taken for the separation of cells then the electrostatic energy is given by, with Q as the charge,

(13)              F_e  =  K_c Q ²/ r  =  7.76E+04 eV where K_c  is the coulomb interaction constant. When instead a close gap of 35Å is adopted the energy of repulsion increases proportionately.

This balance of forces relation, between the electrostatic and the proposed PERANGON exchange interactions, is given by

(14)              K_c Q ² = ^γ’_cell  m²_cell where m cell is the mass of the cell and ^γ’_cell is the cell-cell PERANGON interaction constant. Using the values cited we get,

^γ’_cell = 5.76 E+07 n . m²/ kg².

               A comparison of this with g²_p / m² cell shows that, ^γ’_cell  is relatively large. This one realizes as a consequence that no cut-off momentum transfer features have been adopted while writing down the balance of force relation. The cut-off limits are set by the intercellular separation distances and which is in turn an experimentally observed quantity.

                 Incorporating an exponential type of diminishing cut-off function of the exchange force, we rewrite the balance of force relation which leads to

(15)                 γ’_cell = { e ^–γ  g²_p / m²_cell  }

where e ^–γ   must equal to 7.3E-13 to account for the adopted ‘true’ coupling constant value obtained by two other considerations.

                 It may be invoked that μ r= γ, with r as the cell gap, μ gives the reciprocal of cut-off range of the force. Thus, 1/r₀ = μ = 5.38E-08 cm for r= 150Å. Next the de Broglie relation yields the cut-off momentum transfer as

(16)                 p= ћ / r₀  = 1.96E-20 erg.s/cm

The quanta of exchange are presumed to be the same as the PERANGON i.e. the quanta of the space-time continuum binding force of the biological cell. Moreover, intuitively it may be reasoned out that ‘like cells’ of specific adhesion are coadunate by consonance quanta, and ratio cinate the fact that CANCEROUS cells do not spectacle the adhesion.

                     PERANGON mass value yields the velocity from the momentum p= ћ / r₀  , as of the order 2.94E+10 cm/s. This is almost close to the velocity of light and not a surprising thing as the propagators of the momentum are to move at a fast rate. 

                      Excitation estimates of the mass of the PERANGON propagator adopting the conjugate momentum-positional co-ordinates Heisenberg relation assuming a velocity of propagator almost the same as the velocity of light would lead to the value 13eV for ΔX=150Å. This is too low and indirectly justifies the present theory. Massive propagators, also essential in order that the Quantum mechanical recurrence time, are to be of extremely short duration.

           The details of the theory for the Quantum Proton translocation across the electrical gradient and useful work derivation with maximal efficiency has been carried out but would be the subject of another publication elsewhere.

ACKNOWLEDGMENT

             The author is deeply indebted to Late Prof. K. R. Rao, D.Sc.(Madras), D.Sc.(London) of Andhra University, Visakhapatnam for his extensive research endeavor in several disciplines of Science and Technology, guiding several students for their Doctoral Theses (1932-1972), that has imbibed the present author to investigate the biological processes underlying the existence of livingness in the Universe.

REFERENCES

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