Ukrainian Polymer Journal, Vol. 1, No 1, 1992, pp. 55-62.
Oriented Hydrodynamic Flows in Rotational Medium and Asymmetry in Bioworld
Institute of Ecological and Biophysical Chemistry, Academy of Creative Endeavors.
(Received March 20, 1991; accepted May 23, 1991)
A model of arising of asymmetry in the bioworld is proposed. It is supposed that chemical evolution on Earth has started from the uniform distribution of enantomorphous forms of substances. It is postulated and substantiated the role of Earth rotation in the selection of asymmetry signs of living and inorganic macrostructures, which could lead to the selection of asymmetric substructures (i.e. microstructures forming macrostructures) including D- and L- forms of molecules. It was established that the evolution is described both by thermodynamic and kinetic factors and by the trajectory factor (symmetry or chirality) which should be accounted for in rotating coordinate systems. The Coriolis forces can support spiral biostructures to a different degree depending on the habitation area of organism.
It has been generally accepted that chemical evolution on Earth has started from “uniform distribution and that such distribution is a nonsteady-state equilibrium affected even by the most insignificant random action” .
Because the nature of the physical factor in the primary Earth environment, determining selection of the right and the left at molecular level, has not been identified yet, it has been often assumed that asymmetry is associated with chirality of the molecules which were the first to appear and later were “multiplied” due to the stereospecific autocatalysis mechanism .
A number of attempts has been made to correlate the chemical asymmetry origination on Earth to the asymmetric effect of physical factor combinations on the chemical reactions resulting in origination of asymmetric molecules, e.g. with an asymmetric carbon atom. However, all known mechanisms associated with Earth rotation or Moon motion, magnetic or electric field effects, directed periodic variations in Earth surface illumination, effects of natural polarized light, etc., due to negligible effect of the corresponding factors over chemical reaction course, can not unambigously explain the origin of chemical asymmetry in the bioworld. H.Weyl has consicely rendered this finding as “neither Earth rotation nor the combined effect of Earth and Sun magnetic fields can be of any use to this end” . Apparently, it is easy to show that significant influence of fields of physical origin on the stereospecific reactions output is possible in the fields with intensities greatly exceeding the intensity of natural fields under Earth conditions, whereas the Coriolis forces do not affect the course of simple natural chemical processes. The point is, that the natural fields effects are by several orders less as compared to the thermal factor determined by kT value. Thus, synthesis of single chirality molecules are easily observed either at presence of an asymmetric agent  or under extremal conditions, e.g. in cosmic space, where effect of field asymmetric combinations is rather large [4-6].
In the latter case, thermodynamics can significantly facilitate the formation of enantiomeric forms only, and the reasons for that can be easily explained using e.g. variation of the Gibbs function of a complex thermodynamic system:
where: is the Gibbs function of a simple system j and the second member which is a sum of generalized forces and coordinates products accounts for inputs of all corresponding types of work executed in the system (magnetic, electrical, mechanical, gravitational, etc.). It follows from equation  that role of physical forces in complex thermodynamic systems can produce a significant effect only within rather large structures, where kT magnitude, as compared to the acting physical forces is relatively small. If those forces are asymmetric, the forces combination can produce both the left and the right structure forms.
Of a special interest can be the thermodynamics in a rotating coordinate system. In such systems the Coriolis force effect can become noticeable, though the force executes no work and, hence, can not be included in the equation for an associated characteristic function, variation of which describes behavior of the object under investigation in a rotating coordinate system. However, the work executed by the coordinate system, for example, with a stationary rotation axis, can be evaluated using the evident relation dA=Mzdj , where: Mz is the sum of force moments relative to rotation axis z,j are rotation angle. It should be noted, that the work executed by the investigated system self-rotation is, naturally, included into the thermodynamic equations.
The intention of this article is to make analysis of the physically substantiated model explaining probable effect of Earth rotation on selection of the living macrostructures asymmetry sign, which, basically, can govern the selection of the corresponding asymmetric substructures, including the D andL type molecules.
1. The model
Let’s assume that selection of the left or the right can go on the level of formation of cells and biotissue of plants or Protozos, as well as of inorganic structures due to selection between the left and the right forms of large supermolecular structures or formations.
Let’s postulate also, that asymmetry in the bioworld can be caused by the existence of oriented hydrodynamic flows of matter in a rotating medium.
Prior to getting down to quantitative estimations, let’s show that such a model is close to reality. To explain the point, it should be noted, that we, actually, postulate the fact that D and L molecular form selection in the course of living matter evolution on Earth have been caused by thermodynamics (naturally, with kinetic contribution to the process), and on levels of structures of higher hierarchies. We can assume that certain chiral chemical composition of organisms was maintained under juvenile Earth conditions at one of the hemispheres due to mechanisms related, basically, to the planet rotation around its own axis. In other words, Earth rotation direction (combined with gradients of the chemical potential determining fluid flow direction in plants and Protozoa and related to solar radiation flux gradients and gravitation) determined the dominating selection of asymmetric forms of large-scale superstructures and cells and, subsequently, of macromolecules, L-amino acids, D-sugars as the building material for living organisms.
At present, asymmetry in the bioworld (though life has spread all over the planet) has, probably, been maintained in accordance with the choice made due to the existing matrix mechanisms of biosynthesis.
There is a considerable body of evidence that asymmetry of amino acids and sugars is easily passed down to the cell level. In fact, it has been known that only asymmetry can produce asymmetry. Asymmetry of amino acids and sugars generates asymmetry of macromolecules and macromolecular superstructures. Thus, it is apparent, that quarternary protein structure can contain no mirrow reflection planes or inversion axes . Some proteins form spiral quarternary structures where subunits are interlaced by twist symmetry, which is natural, because ribbons and spirals are formed precisely at the symmetric contacts of substructures. It is those widely known facts which enable us to state that asymmetry can pass from the molecular level along “the hierarchical structures chain” down to the cell level and further on. However, due to variation of permanently acting forces on Earth and to various kinds of random influences on different levels of biostructure organization, asymmetry can be hold only up to specific organization levels where it “diffuses”, probably, as a result of “physical racemization” when a new asymmetry type emerges simultaneously with the dominating asymmetry type. An example to that is the biostructure inversion phenomenon . In addition, there is the phenomenon of rising  capable to bring spiral macromolecular structures to inversion. The evidence of asymmetry transition from lower hierarchical levels to the higher ones makes it possible to postulate a reverse phenomenon determined by evolutional selection and seemingly related to transition of asymmetry from the higher structures to the lower ones.
This phenomenon can be the foundation of chirality selection on molecular level.
Let’s discuss now a probable effect of the Coriolis force on selection of one of supermolecular and cell structure types – L or D (L-D, D-L) in the area of plant growth (or even inorganic crystals and crystal conglomerates).
To begin with, let’s shortly discuss some particular aspects related to the specificity of fluid systems rotating as one whole .
When fluid motion is related to coordinate axes rotating together with fluid in stationary way, it is necessary to account for effect of the Coriolis forces and centrifugal inertia forces on the fluid. Centrifugal force per unit force is recorded as 1/2С(WЧ), and the force effect is taken as equivalent to additional pressure ( is the position vector). The motion equation has the following form:
where: U is particle velocity measured in coordinate system rotating with constant angular velocity,W ; r is fluid density; p is pressure. The Coriolis force changes direction of fluid particles executing, as it has been stressed earlier, no work, and is directed perpendicular to the rotation axis and velocity vector. This force tends to change direction of only one velocity vector component, U, in the plane normal to vector W (transversal plane).
Direction of this change is counterwise to rotation of the moving coordinate system. When particle movement is basically determined by the Coriolis force, the particle travels along the trajectory, projection of which onto the transversal plane is a circumference, and the time period of passing along this circumference is of order W -1. The Coriolis force tends to bring the particle back to its position in the transversal plane, and here the restoration effect depends on the relative magnitude of this force as compared to other forces acting on the fluid. By introduction of the characteristic velocity value relative to the rotating coordinate system, U, and the characteristic linear dimension along the length of which velocity U has no significant variations, L, we can write down the known relation – the Rossby number:
This relation is of the same magnitude order with the relation of members U×СU and 2WЧU in equation (2). The Rossby number characterizes the relative effect of the Coriolis forces. When U/LW>>1, the Coriolis forces insignificantly effect fluid (gas) flow; at U/LW <<1 the Coriolis forces inhibit any divergence of the flow line in the transversal plane. When, U/LW ~1 the motion in the transversal plane (y, z) is not combined with the motion parallel to the rotation axis, and flow is completely independent of the third coordinate (x). This finding by Proudman  can be formulated as a statement that “the slow” steady-state motions relative to the rotating coordinate axes should be two-dimensional.
Because we are basically interested in the spiral trajectories, of the most interest is the case whenU/LW is commensurable with 1 (or exceeds it). If this condition is maintained, the inertia forces associated with the forward body motion are comparable to the Coriolis forces. Here, due to the forced motion of fluid areas near the body, as it has been assumed, probably, axis – symmetric waves should appear and propagate .
Of a special interest is the problem of fluid motion in the thin layer on rotating ball, thus modelling the real events on the globe. The Earth angular velocity, W, is equal to 2p radians per 24 hours. Hence, it is clear that in the scales measured in meters (L) at the visually perceptible motion velocities the Rossby number, U/LW, greatly exceeds unity, and the Coriolis forces associated with Earth rotation produce no noticeable effect on the motions under laboratory conditions. It should be noted that at larger L scales measured in hundreds of kilometers (100 km or more) the latter phenomenon takes place in atmosphere and oceans, and accouting for the Coriolis forces becomes necessary. At rather low flow velocities, same as at the larger L values, accounting for the Coriolis forces is necessary as well.
Let’s assume, that motion of young cells formed near the central parent cell at the tip of the growing plant pedicel  can be considered as a directed steady-state flow of the “cell fluid” or, seimplier, the cell flow. Such a flow, though with a rather slow motion velocity, is practically free from blow-up caused by diffusion or Brownian movement. If to assume pedicel growth rate as approximately equal to flow velocity of the cells travelling along a curvilinear trajectory with radius L and velocity n, then relation of the inertia forces and the Coriolis forces is of order n/fL; where: f – the Coriolis parameter (at the middle latitudes in the Northern hemisphere f@ 1Ч 10-1s-1; q =45° C). Hence, at L=10-2cm andn=10-1cm/day, we get:
If the relative flow turbulence has the same sign as the Coriolis parameter f=2W (double angular velocity of the Foucault pendulum at latitude p/2 - q ; W =7.29Ч 10-5rad/s), then the Coriolis forces will have direction away from the vortex flow center (cyclone). It should be noted, that the relative vorticity is positive at the counter-clockwise circulation in the Northern hemisphere, and is negative at the clockwise circulation in the Southern hemisphere. In the central part of the cyclone the pressure is decreased, whereas in that of an anticyclone it is increased. Apparently, the growing sprout is a model of anticyclone, because motion of fluid and cells is directed away from the growth center.
At the anticyclonic type motion the Coriolis forces in a way “compress” the sprout. It should be noted here, that, regardless of the coordinate system rotation direction, nutrients and moisture are delivered to the sprout in accordance with the chemical potential gradient, and in the growth area (maximum photosensitivity area) they have direction in accordance with the quantum light flux and gravitational gradients.
Thus, counter-clockwise Earth rotation involutes anticyclonic structures clockwise in the Northern hemisphere and counter-clockwise in the Southern one. Hence, in the case of acceptance of our concept stipulating that the Coriolis force role at origination of asymmetry in the bioworld makes it necessary to assume that life has initially been conceived at one of the hemispheres. This conclusion holds true in the case we assume that plants and Protozoa form cyclonic structures.
If Earth had no rotation, formation of asymmetric structures could not be possible. If Earth had opposite rotation direction or life had conceived in the other hemisphere, the bioworld, probably, would be built, basically, of D-amino acids and L-sugars.
Apparently, it should take a rather long time period to establish correlation between structures of different hierarchies on Earth, and the established correlation is basically determined by the Rossby parameter, though at some corresponding organization levels the lunar motion and physical fields, probably, can also produce some effect.
The expounded theory is capable to explain quantitatively numerous facts associated with L and Dforms equilibrium on various levels of biotissue organization. The quantitative estimates are difficult to obtain due to difficulties in the identification of functioning living subsystems in organisms, parameters of which determine the significant contribution of the Coriolis forces to selection of the right or the left forms. In addition, it should be noted, that the problems related to the spiral movement of fluids in the fields of various nature including those of Coriolis have not yet been studied in detail neither theoretically nor experimentally [10,13,14]. It is important to stress once again that the Coriolis forces alone are unable to create spiral structures. However, as it has been shown, combination of those “forces” with directed flows causes origination of spiral structures. We should also remember that the Coriolis forces alone execute no work and only deflect trajectory of flow motion. The forces act as if “twisting” the coordinate system externally. So, introduction of “the Coriolis work” member into the thermodynamic equations for a rotating system is excluded.
Thus, at discussion of the biological evolution phenomenon from the standpoint of the listed considerations, it should be noted that the evolution is described both by thermodynamic and kinetic factors, as well as by the trajectory factor (symmetry or chirality) which should be accounted for in rotating coordinate systems .
The Coriolis forces can support spiral biostructures to a different degree depending on the habitation area of organisms. At the equator the origination of spiral structures with opposite signs is equally probable. This is another evidence of nonabsolute character of selection, e.g. of the right biostructures, and confirms the probability of “physical racemization”. In addition, because selection proceeds on the level of multiple generations, kinetics of the chiral structures selection process is complicated. One can get the impression that selection on the level of the “Coriolis structures” could, actually, take place at the early evolution stages. As to the later period, holding asymmetry on the chemical level is, basically, associated with the stereospecific catalysis mechanism, however, “under control” of selection at the higher organizational levels. In the case of the Earth rotation termination, stereocatalysis would, probably, maintain life for some time period only, measured, possibly, in hundreds of thousand or millions years.
If to accept the concept of slow motions of morphogenetic type existing at the initial stages of organism development (when the organism structure is installed), then, using criterion n/fL=1/ft, it is easy to show that qualitively the Coriolis factor can produce noticeable effect on any biostructures (where the indicated flows act), formed within a day or a longer period. Indeed, taking into account that L/t=n and f=10-4s-1, we get: n/fL=1/ft=l/10-4s-1Ч 105s» 0.1 at t=10 days n/fL» 10-2.
In this context many examples can be rendered. Thus, for some snails the shell formation time lasts dozens days or sometimes even several months – in this case n/fL can be of order 10-3. At formation of coiling plant spiral structures the n/fL criterion value is also below unity. This value approaches unity at the flows in capillaries of the growing moss parts, conifers and other plants. On the other hand, we have estimated n/fL criterion values for the DNA synthesis processes, transcription, translation, selfassembly of microtubes inside cell flugellum, sliding of microtubes in ocean, movement of pseudodiums in the direction of cell transposition, motion of fluid in timber capillaries, blood flow in animal organisms, and the criterion magnitudes, as have been expected, are of order 10-3-10-6.
Apparently, the Coriolis forces play the most significant role also at formation of xylem spiral vessel structures. This finding is confirmed by the existence of the right and the left spirals in various kinds of plants, etc. Certainly, many problems remain far from clear and are pending for the corresponding explanations. However, it is evident that the existence of flows along chemical gradient with similar direction for all types of Protozoa and Earth rotation could contribute to selection of the corresponding asymmetric biostructures at one of the juvenile Earth hemispheres.
1. Weyl, H., Symmetry; Princeton, New Jersey; Princeton University Press; 1952.
2. Calvin, M., Chemical Evolution, Oxford : Clarendon Press, 1969.
3. Izumi, Y., Tai, A., Stereo-Differentiating Reactions; The Nature of Asymmetric Reactions; New York, San Francisko, London; Kodansha Ltd., Tokyo, Academic Press, 1977.
4. Gladyshev, G.P., Moon and Planets, 19, 98,1978.
5. Gladyshev, G.P., Khasanov, M.M., J.Theor.Biol., 90, 191, (1982.)
6. Khasanov, M.M., Gladyshev, G.P.; Org. Life; 10, 247, (1980.)
7. Cantor, Ch.R., Schimmel,P.R., Biophysical Chemistry, in 3 volumes; San Francisco: W.H.Freeman & Co., 1980.
8. Saenger, W., Principles of Nucleic Acid Structure, New York, Tokyo, 1984.
9. Batchelor, O.K., F.R.S., Introduction to Fluid Dynamics, Cambridge: Cambridge University Press, 1970.
10. Greenspan, H.P., Theory of Rotating Fluids; Cambridge; Cambridge University Press, 1968.
11. Proudman, Proc. Roy. Soc., A92, 408, (1916.)
12. Woring, F., Phillips, 1.; Growth of Plants and Differentiating.
13. Loytsyansky, L.G., Mekhanika zhidkosti i gaza (Fluid and Gas Mechanics) Moscow; Nauka Publ., (6th edition).
14. Sedov, L.I., Mekhanika sploshnoy sredy (Continuous Medium Mechanics), volumes 1, 2; Moscow, Nauka Publ., 1983, 1984 (4th edition).
15. Gladyshev, G.P., Thermodynamics and Macrokynetics of Natural Hierarchical Processes, Moscow, Nauka Publ., 1988.