

Liudmila B. Boldyreva
Correspondence: Liudmila B. Boldyreva boldyrev-m@yandex.ru
Author AffiliationsAssociate Professor, The State University of Management, Moscow, Russia.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
As follows from the current studies, the therapeutic effect of nanoparticles on the cells of a biological organism is not determined in some cases by the electric or magnetic forces. The paper aims at showing that there is a physical process that might account for the features of the non-electromagnetic effects of nanoparticles on biological systems. An analysis is given of some features of the effects (non-electrostatic) of metal nanoparticles on biological systems, namely: the non-monotonic size-effect dependence, the dependence on nanoparticle form, the adhesion of certain metal nanoparticles to specific cells. It is shown that these features of the effects of nanoparticles on biological systems are analogous to the features of the interaction of spin structures in superfluid 3Не-В by spin supercurrents. This approach allows one to improve the efficacy of therapeutic applications of nanoparticles, in particular, they make it possible to determine which metal would exert maximum effect on a definite biological system.
Keywords: Nanobiology, nanomedicine, metal nanoparticles, spin supercurrent, model of superfluid physical vacuum
The main applications of metal nanoparticles (NPs) in medicine are the targeted drug deliver, treatment, diagnosis, monitoring, and control of diseases. In this paper the following features of metal NPs effects on biological systems in the drug deliver and treatment of diseases are considered.
Figure 1 : The type of dependence of
normalized toxicity rate T / T ' ( T = T ' at d = 9nm
) on the nanoparticle size d.
It is important to establish the mechanism of action of NPs, at least metal NPs, on biological systems. In spite of the extensive studies undertaken recently, it seems that many points here still remain unclear. Meanwhile, without distinct understanding of the processes underlying the biological effects of metal NPs one can hardly hope to give wellfounded recommendations for the safe application of metal NPs in medicine [1].
It is shown in this work that the above-mentioned features are like those of the interaction of spin structures in superfluid 3Не-В through spin supercurrents. The author argues that the coincidence of the features of non-electrostatic effects of NPs on biological systems and the properties of the spin supercurrents emerging between the spin structures in superfluid 3Не-В is not accidental and can be explained on the basis of modern physical concepts.
Some properties of spin supercurrents in superfluid
3Не-В
Definition of spin supercurrents. In superfluid 3Не-В there may
exist spin structures where coherent precession of spins of 3Не
atoms takes place. Such a structure is called a homogeneously
precessing domain (HPD) [21-24]. An HPD is characterized by
spin S, precession angle (phase) α , nutation angle β , and
precession frequency ω (Figure 2).
Figure 2 : The diagram of precession
of spin S with frequency ω; α is the
precession angle (phase), β is the
nutation angle.
The precession and nutation angles determine the spin part of the order parameters for superfluid 3Не-В, and there are processes that tend to make equal the respective angles throughout the whole volume of the superfluid. Such processes in superfluid 3Не-В are spin supercurrents. In the case where the precession frequencies are aligned with axis z, the spin supercurrent component in the direction of axis z, Jz , is determined as:
(1)
where b1 and b2 are proportionality factors depending on β and the properties of the medium. In a HPD its energy U is related to the frequency ω of precession as:
The phase slippage. In superfluid 3Не-В such a phenomenon as phase slippage exists. At a definite difference in precession angles, Δαc, determined by the properties of the superfluid medium, a precession phase slippage (drop) by the value of 2π n (n=1,2...) takes place. The critical spin supercurrent Jc corresponds to the value Δαc. Figure 3 shows an example of the normalized spin supercurrent Jz / Jc between two spin structures as a function of Δω.t , where Δω is the difference between the precession frequencies in the structures, t is time. In the example Δω.t is greater than Δαc and Δω does not depend on t. The line a-b corresponds to the change in the supercurrent in the process of phase slippage and the phase slippage occurs at Δαc>2π. In the course of phase slippage the spin supercurrent value changes from Jc to g Jc ; proportionality factor g is a function of b1 and the phase slippage value.
Figure 3 : Normalized spin supercurrent
Jz / Jc against Δω.t, provided the latter may exceed
Δαc and Δω does not depend on time t. The line
a-b corresponds to the phase slippage: Δαc>2π ; g
is a proportionality factor.
Dependence of spin supercurrent on the configuration of spin structures. The spin supercurrents between HPDs depend on the mutual position of the latter in space. Let us consider two versions of configuration of a sequence of HPDs (HPD1,..., HPDp,..., HPDq,..., HPDr) having respective precession frequencies ω1,...,ωp,..., ωq,...,ωr. In the first version all precession frequencies are aligned with axis Z (Figure 4a) and due to action of spin supercurrents the respective characteristics of the above HPDs may be made equal. If so, under the equation (1) the spin supercurrent ( Jp-q ) between arbitrary HPDp and HPDq may become zero, i.e.
Figure 4 : Two versions of configuration of a sequence of HPDs (HPD1,...,
HPDp,..., HPDq,..., HPDr) having respective precession frequencies ω1,..., ωp,..., ωq,..., ωr, aligned with the tangent to Z: (a)
the linear configuration, (b) the circle configuration; ( Jp-q )a and ( Jp-q )b are spin supercurrents.
In the second version the sequence of HPDs makes up a ring, thus the straight line coincident with the axis Z will become a circumference, see Figure 4b. If the precession frequencies of the HPDs in question, ω1,...,ωp,..., ωq,..., ωr, are tangential to the circumference, that is, the precession frequencies are not aligned, then the equalization of the respective angles of precession and nutation angles of any two HPDs cannot take place, and, according to equation (1), the spin supercurrent between any two HPDs will never be zero. Thus for the spin supercurrent ( Jp-q )b between arbitrary HPDp and HPDq the following holds:
So the space between the HPDs that form a ring will be "filled" with spin supercurrents. (The non-zero spin supercurrents will be present even if a curved chain of HPDs is open, that is, does not make a ring.) Thus the configuration of the spin structures between which spin supercurrents arise will affect the magnitude of the supercurrents.
The efficacy of spin supercurrent. Generally, determination of time dependency of the magnitude of the spin supercurrent between two HPD is a difficult problem, because the speed of transmission of information of the existence of order parameter gradient is, in theory, infinite, and the speed of the spin supercurrent is finite. Besides, a possibility of phase slippage should be taken into account.
The respective precession and nutation angles of the interacting HPDs will become equal, provided the distance X between them and the difference between their precession frequencies, Δω , satisfy the following conditions: X →0 and
An increase in the number of interacting HPDs may result in a decrease of efficacy of the interaction caused by spin supercurrents. Let us consider the case where one HPD (HPD0) interacts with several HPDs (HPD1,..., HPDw ). If the precession frequencies of all HPDs are aligned, then according to (1) the total spin supercurrent Jsum beetween HPD0 and HPD1,.., HPDi ,.., HPDw may be defined as
where ji is spin supercurrent between HPD0 and HPDi , ji , under (1), is determined as:
(7)
where Δαi and Δβi are the respective differences in
precession and nutation angles between the HPD0 and HPDi .
Using Eq. (7) in (6), we obtain:
.
If all the values and signs of Δαi and Δβ are respectively equiprobable and w → ∞ , then
The force interaction between spin structures. In superfluid 3Не-В the motion of 3He atoms constituting a Cooper pair relative to each other corresponds to the р-wave state. In this state, attractive forces act between like-charged particles with the spins oriented in the same direction. Under the definition expressed by equation (1), the spin supercurrent emerging between two spin structures "tends" to make equal the respective characteristics of the structures. If such equalization takes place, the following equalities hold:
(9)
where Δα, Δβ, Δω are the difference between the respective
precession angles, nutation angles, and precession frequencies
of the interacting spin structures. Under these equalities, the
spins of spin structures will be aligned and attraction forces
F may arise between the spin structures
(Figure 5).
Figure 5 : Attraction forces F between two spin
structures whose spins S are aligned.
Matching of the features of effects of metal nanoparticles on biological systems and the properties of spin supercurrents in superfluid 3Не-В
According to quantum field theory, quantum entities (that is, the entities whose state is described by a wave function: electrons, neutrons, protons, etc.) create pairs of virtual particles in the physical vacuum. The virtual particles have spin which is the same as for the real particles. Hence it follows that (1) spin correlations can take place; (2) the virtual particle spin has no definite direction, and by the magnitude of spin the magnitude of its projection onto a preferential direction is meant; this can be interpreted as a precession of the spin about the preferential direction and allows one to introduce the frequency of the precession, the angle of precession, angle of nutation and energy, Us which is determined by precession frequency ωs and spin Ss as
Consequently, nanoparticles and biological systems as consisting of quantum entities may produce spin structures in the physical vacuum, and spin correlations may take place between them.
The spin correlations are responsible for the first feature of the effects of metal nanoparticles on biological systems (see Introduction): the possibility of action of nanoparticles on biological systems by non-electric forces.
In this section it will be shown that under the assumption that the properties of the spin correlations are analogous to those of spin supercurrents in superfluid 3Не-В, the features of effects of NPs on BS mentioned in Introduction can be explained on the basis of the properties of spin supercurrents between spin structures in superfluid 3Не-В.
Thus the second feature of the effects of metal nanoparticles on BS (see Introduction), i.e. the non-monotonic "size-effect" dependence is a result of the phase slippage effect taking place in the spin structures produced by the nanoparticles and BS in the physical vacuum.
Thus the third feature of the effects of metal nanoparticles on BS (see Introduction), namely, the dependence of efficacy of nanoparticles' action on the form of the nanoparticles is due to the dependence of spin supercurrent on the configuration of the spin structures between which the spin supercurrent emerges.
Equalities (9) hold most strictly for those NPs that are contained already in the BS and, consequently, determine the range of spin precession frequencies for the spin structure produced by BS. In this case the precession frequencies of the spin structures produced by the NPs and BS satisfy the condition (5) and the spin supercurrent between the structures causes the maximum equalization of their respective characteristics. Condition (5) can be satisfied by means of forced changing of the precession frequencies of the spin structures produced by BS (for example, this may be done by heating the BS [7,8]).
Thus the forth feature of the effects of metal nanoparticles on BS (see Introduction), i.e. the possibility of adhesion of nanoparticles of certain metals to specific cells of the biological system, in particular to those which contain already the same metal, is due to the fact that between the spin structures with the respective equal precession frequencies, nutation angles and precession angles there exist attraction forces.
Note. Attractive forces between spin structures may arise if the precession frequencies are oriented in the same direction (in the equalities (9) Δω is a vector). This condition imposes certain requirements on the configuration of interacting spin structures and, respectively, the configuration of the bodies producing the spin structures. So we may suppose that 3D nanoparticles would adhere to 3D cells of the BS, because such NPs and biological system cells may produce spin structures with similar orientation of spins in the physical vacuum. This may account for the experimental fact that 3D nanoparticles can penetrate to a DNA molecule, having a spiral shape, deform and even unwind the spiral. Examples of such NPs are fullerenes (computer simulation has shown that fullerenes, namely, spherical C60 molecules, are potentially dangerous to DNA molecules [25]) and dendrimers (dendrimers of the 3D and higher generations have the form close to a sphere) [26].
This property of spin supercurrents may underlie the fifth feature of the effects of metal nanoparticles on BS (see Introduction): the independence of the action of nanoparticles on biological systems on the existence of nanoparticle's protective shell.
The pair of virtual particles produced by a photon in the physical vacuum is converted into real particles (a pair of electron and positron or a pair of proton and antiproton), if the energy of the photon equals the total energy of the pair of real particles produced [27]. This means that the energy of a pair of virtual particles, that is, the energy of the spin structure produced by the photon in the physical vacuum ( US )ph is equal to the energy of photon, Uph :
For the total spin of the pair of virtual particles produced by the photon (SS )ph , we have:
Taking Eq. (10) into account and comparing the well-known
relation between energy Uph and photon frequency ωph ,
, with Eqs. (11)-(11), we obtain that the precession
frequency in the spin structure produced by a photon in the
physical vacuum ( ωS )ph is equal to the photon frequency:
For the total spin of the pair of virtual particles produced by the photon, (SS )ph , we have:
Thus according to (13), the effect on a biological system by a NP whose spin structure has precession frequency ω is analogous to the effect on the BS by a photon with frequency ω .
It agrees with Paracelsus' views on treatment of diseases [28]. The outstanding medieval physician and philosopher thought that light emitted by celestial bodies can cure certain diseases: for example, the disease whose symptoms are like those of anaemia should be cured by radiation of Mars. Note that in the modern medicine anaemia is treated by iron-containing preparations; and Mars is characterized by the presence of iron oxide on its surface, which accounts for the color of the planet: "red planet".
Note. It is possible for NPs to affect a BS indirectly, through an intermediary which has acquired the properties of the NPs as a result of the preceding interaction with the latter. That is, if there is an object or medium (for example, water) and the precession frequency of its spin structure becomes equal to that of the spin structure of the NPs as a result of interaction between the spin structures, then the object or medium acquires a capacity to produce the same effect on the BS as the NPs.
( US )q is the energy of the spin structure produced by the quantum entity in the physical vacuum. According to quantum theory, electric interactions of electrically charged real particles are effected by virtual photons. This means that at least for spin (SS )q of the spin structure (virtual photon) produced by the electrically charged particle in the physical vacuum the following holds:
Taking Eq. (10) into account and comparing the well-known
relation between energy of quantum entity and frequency of
its Schroedinger wave function, ωSh , i.e.
, with
Eqs. (14)-(15), we obtain that the precession frequency in the
spin structure produced by a quantum entity in the physical
vacuum ( ωS )q is equal to the frequency of quantum entity's
Schroedinger wave function:
Thus taking into account Eq (16), one can draw the following conclusion: for the action of nanoparticles on a biological system to be effective it is necessary that the frequency of the Shroedinger wave function of quantum entities constituting the nanoparticles were of the same order of magnitude as the frequency of the Schroedinger wave function of quantum entities constituting the biological system. According to the definition of the frequency of the Schroedinger wave function, the equality of the frequencies of the Schroedinger wave functions for quantum entities means that their energies are equal.
Note. The determining of the NP's size (in terms of the number of quantum entities; in Eqs. (6)-(8) this number is denoted as w) at which the spin supercurrent ceases to be the factor that governs the effects of the NPs on the biological system is an involved problem in the general case, because it is necessary to know the magnitude of the spin supercurrent and the characteristics of spin structures produced by the NPs and the biological system in the physical vacuum. Let us consider the specific case: the toxic effect of silver 9nm NPs on a biological system in experiments with E.coli, see Figure 1. Taking that NPs are spheres and that the silver atom diameter is about 0.144nm, with the atom itself containing 155 quantum entities (protons, neutrons and electrons), we obtain that a silver 9nm nanoparticle contains approximately 38.106 quantum entities. (We assume for simplicity sake that the spin structures produced in the physical vacuum by protons, neutrons and electrons of the silver atom have the same characteristics.) Since with this number of quantum entities the effect of silver NPs on the biological system, caused by spin supercurrents, is highly pronounced, the value of w must be greater than 38.106.
It has been shown that some features of non-electric and non-magnetic effects of metal nanoparticles on biological systems are analogous to those of spin supercurrents between spin structures in superfluid 3Не-В.
The results obtained in this work can be used as a basis for improving therapeutic applications of nanoparticles, in particular, they make it possible to determine which metal would exert maximum effect on a definite biological system.
NP: NanoParticle
BS: Biological System
HPD: Homogeneously Precessing Domain
The author declares that she has no competing interests.
Liudmila B. Boldyreva is grateful to Mikhail Boldyrev, EE, for his continuous support and assistance in translating the article from Russian into English.
EIC: Mallikarjuna Nadagouda, US Environmental Protection
Agency, USA.
Received: 25-Apr-2014 Final Revised: 16-May-2014
Accepted: 22-May-2014 Published: 11-Jun-2014
Boldyreva LB. The physical aspect of the effects of metal nanoparticles on biological systems. Spin supercurrents. Nanomater Nanosci. 2014; 2:1. http://dx.doi.org/10.7243/2053-0927-2-1
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