Journal of Modern Physics, 2011, 2, 354-369
doi:10.4236/jmp.2011.25044 Published Online May 2011 (http://www.SciRP.org/journal/jmp)
Homeostatic Determinate Systems and Thermodynamics of
Selforganization and Evolution of Material World
Lev E. Panin
Scientific Research Institute of Biochemistry, Siberian Branch of RAMS, Novosibirsk, Russia
Received January 31, 2011; revised March 3, 2011; accepted March 7, 2011
Abstract
The paper considers new approaches to system analysis of natural phenomena in physics, chemistry and bi-
ology. It lays the foundation of the homeostatic determinate systems theory that allows revealing the mecha-
nism by which the basic principle of natural science, determinism, is being realized. Evolution of the mate-
rial world is represented as inevitable and continuous growth of orderliness (negentropy) based on transition
from one type of determinate systems to another. Increasing negentropy is shown to be closely associated
with continuous accumulation of information, which determines the natural diversity in physics, chemistry
and biology.
Keywords: Homeostatic Determinate System, Thermodynamics, Evolution
1. Introduction
The emergence of modern material world in its devel-
oped form is still an unsolved physical problem.
To emphasize the connection of physical laws of the
evolving Universe with the emergence of Homo sapi ens,
the anthropic principle has been formulated. It reads thus:
“We see the Universe as it is, because if it were different,
we would not be here and we could not observe it” [1].
The anthropic principle has weak and strong versions.
According to the weak anthropic principle, rational be-
ings may appear only in some regions of the giant ex-
panding Universe, which have space and time constraints.
If the Big Bang occurred tens billion years ago, it means
that this time was required for our galaxy to emerge and
then for intelligent life to come into existence. The strong
anthropic principle states that there are millions of dif-
ferent regions of the Universe or even the Universes,
whose physical laws or initial conditions prevent the
emergence of complex biological objects and intelligent
life. However, in some regions of the Universe or in dif-
ferent Universes there formed such a set of physical laws
that could lead to the appearance of rational beings. At
least, our existence allows us to think so. “We see the
Universe as we see it because we exis t” [1]. To strengthen
the anthropic principle, it should be noted that this proc-
ess was determinate and inevitable rather than stochastic.
However, it is necessary also to reveal the initial condi-
tions and the mechanism that allowed the Universe to
turn from its emergence to progressive evolution result-
ing in the origin of intelligent life.
The development of material world toward complexity
and increasing natural diversity violates the second law
of thermodynamics and makes it necessary to investigate
nonequilibrium processes that may give rise to orderly-
ness. Now these problems are considered by synergetics.
In this connection, H. Haken wrote: “In physics there is a
notion of “concerted effects”; however, it is applied
mainly to the systems in thermal eq uilibrium. I felt that I
should introduce a term for consistency in the systems
far from thermal equilibrium… I wished to emphasize
the need for a new discipline that will describe these
processes… Thus, synergetics can be considered as a
science dealing with the phenomenon of self-organiza-
tion” [2].
Among classical and well studied examples of self-
organization in nonequilibrium systems are the Benard
instability, Belousov-Zhabotinsky reaction, coherent ra-
diation of atoms in lasers, various chemical waves, etc.
[3]. All these phenomena belong to dissipative structures,
which “are an amazing example demonstrating how non-
equilibrium may be a source of order” [4 ].
Thus, now the self-organization processes are consid-
ered as a genesis of new structures and new behavioral
patterns in the far-from-equilibrium open systems [5].
Probably, this is true if self-organization is considered

L. E. PANIN355
only within the concept of dissipative structures. How-
ever, self-organization of matter in the course of its pro-
gressive and stable evolution is a much more compli-
cated process. We should understand how the nature
came from absolute chaos and maximum entropy to the
processes of sustainable self-organization.
2. System Analysis of Self-Organization
Mechanisms in Material World,
Homeostatic Determinate Systems in
Physics and Chemistry
Let us consider the simplest example of matter (atoms
and molecules) self-organization. This is the formation
of hydrogen molecules from hydrogen atoms.
If an atom has unpaired electron in its outermost elec-
tron level (shell) and such atoms approach each other,
their electron waves overlap to form a new wave, which
unites two atoms. Thus the covalent bond forms. Each
hydrogen atom has one s-electron. When such atoms are
approaching each other, an electron pair forms; this gen-
erates a single standing wave that combines two hydro-
gen atoms into a molecule. The formation of a covalent
bond is advantageous in energy terms. Thus, collective-
zation of electrons in a hydrogen molecule (H2) increases
their potential energy by 1.5 eV and decreases the kinetic
energy by 7.5 eV. Full energy of the interference of two
waves becomes 6 eV lower. The deformation of electron
clouds makes energy transformations more complicated
(Table 1).
On e ma y s e e f r om Table 1 that the overall energy gain
amounts to 4 eV; however, strength of the chemical bond
between hydrogen atoms depends primarily on releasing
7.5 eV at interference of two waves. Strength of a cova-
lent bond in the hydrogen molecule is 104 kcal/mol.
The formation of hydrogen molecule from two atoms
is thermodynamically advantageous. Total energy of
such system is lower by 4.0 eV. A new stable structure
with new properties has formed. This is the process of
self-organization. The work related with synthesis of H2
molecule was performed due to energy supplied from the
Table 1. Energy transformations at the interaction of two
hydrogen atoms, eV.
Components of ele ctron energy
of H2 molecule
Energy Energy of
interference
Energy of
modification,
etc.
Full energy
Kinetic –7.5 +11.5 +4.0
Potential +1.5 –9.5 –8.0
Full –6.0 +2.0 –4.0
environment. Such system has a higher orderliness
(negentropy).
Changes in the amount of information caused by ap-
pearance of the new system (structure) can be calculated
quite easily.
In atomic hydrogen, the probability that electron oc-
cupies one of allowed energ y levels is rather high. A mi-
nimum of information is connected with such electrons.
When each pair of electrons forms a new hybrid wave,
this abruptly decreases the number of degrees of freedom,
and their behavior becomes determinate. In a new wave,
each electron may stay only in one of two allowed states,
which differ in their spin (+ 12 or –12). According to
Shannon’s equation ,
log
ii
H
pp

the amount of information connected with such electron
increases and depends on th e quantity 1/2 × log 1/2. For
each pair of electrons this will be equal to log 1/2. Multi-
plying this quantity with the number of hydrogen mole-
cules in the given gas volume gives the total amount of
information connected with electrons. This value corre-
sponds to an increase of negentropy upon transition from
atomic to molecular hydrogen.
Note that the process moves towards increasing ne-
gentropy and may proceed under the natural conditions.
This is how the time’s arrow forms, moving towards
decreasing entropy in the nature, i.e., from chaos to mat-
ter self-organization due to delivery of energy from the
environment. In biological objects, the source of external
energy for various biosynthetic reactions is the oxidation
processes related with decomposition of rather complex
organic compounds (carbohydrates, lipids, and partially
proteins). This is why E. Schrodinger believed that we
are fed with negative entropy, thus being “the organiza-
tion sustained by derivation of orderliness from the en-
vironment” [6].
The formation of hydrogen molecules from hydrogen
atoms proceeds as a determinate process. The structure
of hydrogen atom is very simple: a proton with an elec-
tron revolving around it. In the atomic state, hydrogen is
a gas with a high level of entropy (low level of negen-
tropy). Its atoms, colliding with each other, excite elec-
trons, thus making them to occupy different energy lev-
els and sublevels. Such electrons have a large number of
degrees of freedom. However, the most probable is the
state when electron occupies the lowest energy level (1s).
For such a gas, temperature elevation serves as a specific
signal interacting with the memory elements (electro-
magnetic forces). As kinetic energy of the gas molecules
increases to a certain value, atoms having electrons at the
1s-level will interact with each other to form hydrogen
molecules. Therewith, electrons form a new hybri d wave.

L. E. PANIN 356
However, more than one decision can be implemented
at the formation of hybrid waves. According to the first
decision (and action program), both electrons form a
“convenient” wave; at that, they belong simultaneously
to both hydrogen atoms. The second decision (and action
program) implies the formation of “inconvenient” wave.
In this case, a crest and a trough of the hybrid wave are
separated by the rest zone (Figure 1). Such wave is th er-
modynamically unstable. It is destroyed, and then a deci-
sion is made to form a “convenient” wave.
It seems reasonable to describe such mechanisms of
the material world self-organization using the concept of
homeostatic determinate systems [3].
The concept of homeostatic determinate systems is
fundamental for synergetics. It provides deep insight into
physical meaning and genesis of the hierarchy of insta-
bilities in self-organizing homeostatic systems, into the
nature of interrelations between instabilities and order
parameters [3,7].
Under homeostatic determinate systems we understand
such systems where the eventual (actual) result of an
action is predicted (determined) via the interaction of
signals specific for the given system with its memory
elements. Structurally such systems include determinate
synthesis, choice of an adequate action program, its out-
come, and feedback closed on results-of-action acceptor
(Figure 2).
The most complex element of any homeostatic deter-
minate system is the determinate synthesis. Here the
dominant motivation, conditional (environmental) and
causal (triggering) afferentation interact with the mem-
ory elements of the system. This results in decision
making and choosing a termodinamic determined action
program. Information on the achieved result goes to re-
sults-of-action acceptor (feedback), where the anticipated
and actual results are compared. If the goal is not reached,
i.e., the actual result does not fit the anticipated one, ho-
meostatic determinate systems switch over to another
programs due to changes in the decision made.
This mechanism of the material world self-organiza-
tion radically differs from self-organization in dissipativ e
Figure 1. Programs used for the formation of covalent
bonds in hydrogen molecules.
Figure 2. A schematic diagram of homeostatic determinate
system: DMT – dominant motivation: system in a condition
of thermodynamic balance; ME – memory elements: metal,
covalent and hydrogen bonds, electrostatic and hydrophobic
interactions; a – trigger signaling: specific signals able to
interact with ME (mechanical load, tem- perature, pressure,
electric discharges, etc.; b1 and b2 – circumstantial signaling:
additional signaling accompanying the main one, for
example, an excited environment; DM – decision making:
transition of crystal to a new level of systemic organization;
AP – action program: formation of new bonds, which
change negenthropy (information) or enthropy; ARA –
actual results of action: emergence of a new system in one
of energetically allowed state; PRA – predicted result of
action: emergence of a new system in the energetically
stable state; DS – determinate synthesis, decision-making
process; c and d – straight line and feedback.
nonequilibrium systems, where dissipative structures
emerge due to reinforcement of the corresponding fluc-
tuations. The appearance of such structures was called by
I. Prigogine as “orderliness through fluctuations” [4].
Such mechanism of self-organization is abundant in the
nature, but it cannot und erlie the p rogressiv e ev olutio n of
material world, which is a stable and irreversible pro cess.
The nature has chosen the way of self-organization via
the formation of homeostatic determinate systems.
In physical determinate systems, the system-forming
factors are represented by four types of interaction:
– strong, or nuclear interaction (force) acts only be-
tween hadrons that form the atom nucleus (proton, neu-
tron), and does not depend on electric charge of the in-
teracting particles;

L. E. PANIN357
– weak interaction (force) acts between leptons (elec-
tron), between hadrons, between leptons and hadrons, and
does not depend on the charge of interacting particles;
– electromagnetic interaction (force) acts between elec-
trically charged p articles. With unlike ch arges it shows up
as attraction; with like charges, as repulsion;
– gravitational interaction (force) acts between all the
particles without exception and shows up as attraction.
Since elementary particles have small masses, the role of
gravitationa l interaction between them is negligible.
Due to the four type interactions, atoms of all chemi-
cal elements exist as systems, which are so stable under
natural conditions that we can inv estigate their properties
and use them. It can be stated that each chemical element
(atom) is a unique determinate system with unique prop-
erties.
The forces serve as memory elements in these systems
and determine their stability.
Strong interaction exists between quarks that form
protons and neutrons. It is performed via the exchange of
gluons (G0). Weak interaction is performed with W± and
Z0 bosons. They play an essential role in th e formation of
nuclei. Weak proton-electron interaction may be accom-
panied by the exchange of vector boson W+ or by the
exchange of neutral Z0 boson. Electromagnetic interact-
tion is accompanied by the exchange of photons (  ).
Gravitational interactions result from the exchange of
gravitons. This force manifests itself at the interaction of
large mass.
The exchange statuses form feedforwards and feed-
backs in the functional pairs. The main constituting ele-
ments of atoms are presented in Tables 2 and 3. Some of
them have a complicated structure.
Table 2. Elementary particles constituting the atoms.
Type of interaction
Particle Charge Weight*
Strong Electro-
magnetic Weak Stability
Proton + 1 1 + + + High
Neutron 0 1 + + + Low
Electron –1 1/1800 – + + High
Photon 0 0 – + – High
Neutrino 0 0? – – + High
Charged
pi-meson 1 1/7 + + + τ = 10–8 s
Neutral
pi-meson 0 1/7 + + + Τ = 10–16 s
* - in units of proton weight.
Table 3. Structure of protons and ne utr o ns.
Particle Quarks
Neutron n0 U+2/3 d–1/3 d
–1/3
Proton p+1 d–1/3 U+2/3 U
+2/3
The proton sounding with a high-energy neutrino beam
rev e al s a very complicated pattern. Proton no longer look s
as a simple combination of some quarks and gluons. A
high activity is observed inside the proton, caused by its
interaction with vacuum. It turns out that proton com-
prises a large number of quarks, antiquarks and gluons.
Three “v alence” quar ks are hardly dis tinguished, slig htly
contributing to the mass o f proton (se e Figure 3).
Three “valence” quarks are hardly discernible among
numerous gluons and quark-antiquark pairs (from Per-
kins [8]).
Atom as a system possesses all the features of deter-
minate systems:
1) Memory elements (four type forces) that are in-
volved in the interaction with external signals spe-
cific for the atom;
2) Decision making that chooses a certain action pro-
gram under disturbance;
3) Action program that ch anges the nature of interact-
tion between the structure-forming particles;
4) Result of action – the atom acquires new properties.
To provide stability of the system, feedback shou ld be
introduced. The feedback will close between the actual
and predicted results of action (PRA), which are the sta-
ble state of the exchange pairs implementing the four
types of interaction. The interaction energy in the pairs
should be minimal. In determinate systems they function
as the results-of-action acceptor.
If stable interaction is not observed in the exchange pairs,
the action program is corrected. Therewith, spontaneous
transitions may occur in the pairs; however, they may
occur also with virtual pairs, i.e., the particles-anti-parti-
Figure 3. Proton observed with the radiation providing
resolution on ca. 0.01 fm (10–15 cm).

L. E. PANIN 358
cles borrowed from vacuum. It became possible to op-
pose the principle of determinism against the relativistic
principle underlying the be ha vi o r of elementary parti cl e s.
Functional pairs in atoms serve as the results-of-action
acceptors; therewith, the formation of a stable state is
determined by the interaction of atom with the environ-
ment (vacuum) involving the virtual particles. Hence it
follows that the environment (physical vacuum) is most
essential for stable existence of any atoms and related
quantum transformations. Atoms, similar to living ob-
jects, are the open systems, which continuously exchange
mass, energy and information with the environment, i.e.,
with the quantum vacuu m.
The concept of determinate systems is a new instru-
ment for the analysis of functional states of atoms and a
new conceptual apparatus (language) for their descrip-
tion. They make it possible to consider statistical (sto-
chastic) processes in quantum physics as determinate, i.e.,
as the processes based on specific causal connections and
quite predictable results.
Einstein wrote: “I still believe in a possibility of con-
structing such model of reality, i.e., the theory that ex-
presses the objects themselves, but not only the prob-
abilities of their behavior” [9].
The formation of all atoms of the periodic table of
elements is considered in special literature [1 0]. Elemen-
tary particles and primary atoms present in the environ-
ment served as a construction material for the process.
Thus, the presence of hydrogen and its isotopes (deute-
rium and tritium) enabled synthesis of helium atoms in
the hot Universe:
23 4
11 20
H+HHe+n17.6 MeV.
These processes take place in stars. In our Solar sys-
tem they play a unique role. This reaction, releasing a
tremendous amount of heat, provided energy for evolu-
tion of material world on the Earth and origin of life,
which is related with increasing chemical diversity.
The appearance of unique properties of the chemical
elements due to increase in their weight and complica-
tion of their structural organization can be illustrated by
example of carbon and oxygen.
Carbon has two electrons at the first energy level and
four electrons at the second level, two of them occupying
s-sublevel and the other two, p-sublevel. This element is
very essential for all biological objects. Oxidizing, car-
bon acquires the valence +4, reducing, –4. This feature
allows carbon atoms to interact with each other and form
long aliphatic chains. Hydrocarbons are the most abun-
dant among them. When interacting with metals, carbon
is electronegative, with nonmetals it is electropositive.
The most part of carbon in the earth crust is fixed as the
limestone, CaCO3, and dolomite, МgCa(CO3)2. Coal, oil
and gas are also the carbon-containing compounds.
Pure carbon forms such dissimilar crystals as graphite
and diamond. The difference depends on the type of
carbon packing in the crystals. In graphite, carbon forms
an ordered plane structure. Plane crystals weakly interact
with each other and readily desquamate. In diamond
crystals, carbon forms three-dimensional structures, with
strong forces of intermolecular in teraction operating here.
Such packing allows diamond of any size to be consid-
ered as a single molecule. Carbon-based chemical com-
pounds make the foundation for all biological objects.
Oxygen is a gas, its atom is composed of eight neu-
trons, eight protons and eight electrons; the atomic
weight is 15.994. It has three isotopes (16O, 17O and 18O).
Oxygen may form compounds (oxides) with each of
chemical elements, including inert gases. It is the only
gas that exhibits paramagnetic properties. Its involve-
ment in the oxidation processes (combustion) is an im-
portant source of heat. In biological objects, oxygen sus-
tains the processes of slow oxidation of organic sub-
stances, supplying us with a necessary amount of energy.
These properties of oxygen are also vital for the devel-
oped form of life existing on the Earth.
Thus, formation of new physical determinate systems
(atoms) proceeded until the emergence of unstable ra-
dioactive elements. Beyond the 104th element of periodic
table of chemical elements, all atoms were very unstable.
Evolution of material world in this direction became im-
possible.
Further increase in natural diversity should be related
with another homeostatic determinate system. Here, the
memory elements were represented by new forces: co-
valent and hydrogen bonds, hydrophobic and electro-
static interactions. This was a fundamental change in the
evolution of material world. It was related with the activ e
formation of chemical determinate syste ms. Not only the
memory elements of these systems have changed, but
also their action program. The ability of electrons to
form different hybrid waves (action program) became of
crucial importance.
Example 1. A carbon atoms has four unpaired elec-
trons in its outermost electron shell, which form four
lobe waves (Figure 4(a)). Each of the waves may inter-
act, for example, with the sphere wave of hydrogen atom.
There are four hybrid lobe waves formed by four pairs of
electrons, which are typical of the methane (СН4) mole-
cules. Spatially such molecule is a tetrahedron.
Example 2. The formation of ethylene. In this mole-
cule, two carbon atoms are coupled with a double bond,
the remaining free bonds being saturated with hydrogen
atoms. This occurs as follows. Each carbon atom uses
two octuple waves and one sphere wave to form three
lobe waves arranged in the molecule plane. Both carbon

L. E. PANIN359
atoms form an internal stable hybrid wave from two lobe
waves. In such a way the first pair of electrons is used.
The second pair of electrons in a double bond forms the
external wave at interference of two octuple waves. In
the process, two wave crests merge at the top, and two
wave troughs merge at the bottom, or vice versa. The
external wave covers carbon atoms like a jacket (Figure
4(b)). Double bond has a high strength, so the distance
between carbon atoms here is shorter as compared to a
single bond. Double bond makes the molecule more rigid,
however, enhancing its reactivity. The molecule can sac-
rifice one of these bonds to interact with other atoms or
chemical groups, still retaining its atoms bound.
Example 3. In the H2O molecule, bonding involves
two unpaired p-electrons of the oxygen atom. Their or-
bitals make an angle of 90. Each of the orbitals overlaps
s-orbital of the hydrogen atom to form a covalent σ-bond.
The structure of water molecule is presented in Figure 5.
However, in water molecules an angle made by
р-orbitals of the oxygen atom is 104.5, which is 15
greater than that displayed in Figure 5. This occurs be-
cause the O–H bonds are not merely covalent. Their
electron density is shifted towards oxygen. The latter
acquires a surplus negative charge, and hydrogen atom
acquires a positive one, which causes mutual repulsion of
the orbitals and increases the angle. There is also an ac-
tion of some other factors. Overall, the H2O molecule is
a dipole having a positive charge on the one end and a
negative charge on the other.
A hydrogen bond can form between H2O molecules if
(a)
(b)
Figure 4. Two different programs used for the formation of
covalent bonds in two different chemical compounds: a –
formation of methane molecule: each of four hydrogen at-
oms donates its electron to form pairs with four electrons of
carbon residing in the lobe waves; b – formation of ethyl-
ene molecules; 1 – top view of the plane where atoms are
located, 2 – double bond waves (side view).
Figure 5. Bond formation in H2O molecule with participa-
tion of 2p-orbitals of the oxygen atom.
1s-orbital of the hydrogen atom is unoccupied. As we
have seen, this condition is partially satisfied in H2O
molecules. When approaching the second H2O molecule,
its negative pole further shifts the electron cloud towards
its “own” oxygen. The probability that the undivided
electron pair of another H2O molecule with reside at the
hydrogen atom is not high, although some exchange in-
teraction is allowable. This makes a contribution to the
hydrogen bond energy. The second (probably more sig-
nificant) contribution is made by electrostatic interaction
between hydrogen atoms (protons) and negatively charged
oxygen atoms of other molecules.
Water plays a unique role in living objects. In human,
it constitutes 70% of the body weight. All biochemical
reactions take place in a water medium.
Thus, chemical determinate systems gave rise to natu-
ral diversity in inorganic, organic and bioorganic chem-
istry, and resulted in the formation of liquid and many
solid crystals. This created prerequisites for origin of life
on the Earth.
From a physical standpoint, the evolution of material
word is based on increasing negentropy, i.e., the degree
of orderliness. E. Schrodinger defined it as

lg 1Sk D
where –S is the negative entropy, or negentropy; k is the
Boltzmann’s constant equal to 3.2983 × 10–24 cal/deg; D
is the quantitative measure of disorderliness of atoms in
the system,


lg1 D is the negative logarithm of D, and
1/D is the measure of orderliness.
However, of prime importance for us is that increasing
negentropy is always supported by increasing amount of
structural information. This can be expressed by the fol-
lowing equation:


lg 1log
ii
Sk Dpp 


L. E. PANIN 360
where pi is the probability of individual events in the
system. Thus, the informational component in this equa-
tion determines an increase of negentropy in the system
and is related with acquisition of new properties.
Developing the concept about a correspondence be-
tween negentropy and structural information, we can pre-
sent the following equality:

lg 1log
ii
Sk Dpp

Hence,
 
lg 1log
ii
Dpp
k
, and

log
110
ii
p
pk
D , then
 log
10 ii
p
pk
D  or
 log
110 ii
p
pk

If in the Helmholtz equation for free energy entropy is
replaced by D, this gives the following expression:
log
10 ii
p
pk
T
FU  
Thus, F can be considered as a function of the amount
of structural information in a system. This equation is
essential for understanding the evolution processes.
New chemical structures (compounds) based on chemi-
cal determinate systems are still emerging in the nature.
Now it is related with human activity aimed at the syn-
thesis of various novel compounds that were earlier ab-
sent. However, the nature made an important step toward
synthesis of high-polymer bioorganic compounds, such
as proteins, nucleic acids, complex carbohydrates and
lipids. Many of sporadically synthesized proteins could
have unique enzymatic properties, thus making the syn-
thesis processes more specific. After creation of this ma-
terial possessing versatile chemical properties, the nature
could move to the next step in systemic organization of
material world, which led to a multiform world of living
systems. This was another level of self-organization
based on homeostatic determinate systems and using new
memory elements and new action programs.
3. Formation of Homeostatic Determinate
Systems in the Living Nature
The appearance of developed forms of life on the Earth
was preceded by a long period of prebiological chemical
evolution. Active self-organization and self-assembly of
the structures with different complexity took place; this
was accompanied by the mechanism of natural selection.
The indicated processes occurred mainly in the “primary
water bouillon”. In terms of synergetics, these events
were considered in detail by Haken [2], Prigogine [11],
Eigen [12] and other authors.
To form a new type of homeostatic determinate sys-
tems able to provide further evolution of life on the Earth,
another memory element was necessary for the creation
of new determinate systems with new action programs.
Such elements underlying the new memory mechanisms
were found. Now they are called the genetic memory.
DNA molecules appeared quite suitable for this pur-
pose. They are the double helices composed of desoxy-
ribose, residues of phosphoric acid, and four types of
nitrous bases – adenine, guanine, cytosine and thymine.
Desoxyribose molecules, bound through phosp horic acid,
form long polymeric chains. In DNA molecules, two
such polymeric chains are connected to each other via
nitrous bases attached to the first carbon atom of desoxy-
ribose. Nitrous bases form the complementary pairs: ade-
nine – thymine and guanine – cytosine.
They can be used to encode more than 20 features.
These features are amino acids, which constitute any pro-
teins. By the coding theorem, if an event can be pre-
sented on the average as n-binary digits, it can be sym-
bolized also by any other events that admit encoding
with n-binary digits, i.e.
vv xx
Sn Sn,
where Sx denotes the numbers of real events;
Sy is the numbers of symbolic events;
nx and ny are the average number of digits, respective ly,
for one real and one symbolic event.
Let x stand for amino acids, and y for nucleotides.
Then,
nx = log20
2 = 4.322,
Sx = 1 (1 amino acid),
ny = log4
2 = 2,
14.3222.161
2
y
S

,
which means that a minimum amount of nucleotides
needed to symbolize any amino acid is 2.161, i.e., more
than two and less than three. Encoding amino acids by
nucleotide triplets, we obtain possible combinations of 4
elements taken 3 at a time, so that each combination un-
ambiguously defines each event. Evidently, there are 20
combinations:
ABA BCA ADC BDD
ABB BCB ADD CDA
ACA BCC BDA CDB
ACB ADA BDB CDC
ACC ADB BDC CDD
As follows from the above reasoning, from the mathe-
matical standpoint it is not impossible to encode the en-
tire multiform sequence of protein amino acids using
four nitrous bases.
Four types of nitrous bases gave rise to a triplet code.
Each triplet of nitrous bases corresponds to one of the

L. E. PANIN361
known 20 amino acids.
Thus, in the entire diversity of different macromole-
cules, DNA proved to be most appropriate for the forma-
tion of the next type of memory called the genetic mem-
ory. It is essential that DNA can split into two comple-
mentary chains and copy itself with the aid of DNA-
polymerase. It means that genetic information is com-
pletely retained at cell division and transferred from cell
to cell, i.e., hereditarily. In a cell, three types of RNA
(messenger, transfer and ribosomal) convey the genetic
information written in DNA to different intracellular
proteins, thus determining their specific structural and
functional properties. This un ique mechanism transforms
genetic sign into phenotypic. In this mechanism an im-
portant role belongs to comple mentarity of nitrous bases,
their ability to form the complementary pairs: adenine –
thymine and guanine – cytosine .
In the cell nucleus, DNA and histone proteins form a
close-packed structure – chromatin. Upon cell division,
histones are destroyed via hydrolysis and DNA is depro-
teinized. Free DNA is copied. This is followed by syn-
thesis of histones, and two daughter DNA are packed
again to form chromatin. All these events take place due
to self-assembly.
Thus, self-assembly may occur between two type po-
lymers: nucleic acids and proteins. This is exemplified
by disassembly and self-assembly of tobacco mosa ic virus
(TMV) under laboratory conditions. RNA isolated from
TMV and viral proteins spontaneously form the intact
particles of a high virulence.
A particle of bacteriophage T4 has a complicated struc-
ture. It includes a head consisting of proteins, which has
a shape of elongate icosahedron. The head is attached to
a tail surrounded with a retractive cover. The latter is
connected with a basal plate having six protein fibers.
DNA resides in the head. This particle can be completely
disassembled and assembled in a tube. A similar self-
assembly occurs in a bacterial cell, where comes only the
bacteriophage DNA containing the information about all
its components. Copies of DNA and viral proteins are
produced in a cell, this is followed by self-assembly of
the virus particles, which then leav e a cell, thus destruct-
ting it. Here, genetic information about the structure of
viral macromolecules is supplemented with the structural
information obtained due to self-assembly of particles,
where other memory elements represented by chemical
forces manifest themselves. This is how the nature inter-
relates evolutionary recent mechanisms of matter self-
organization with evolutionary earlier mechanisms.
Certainly, biological objects with various complexity
of their system organization are based on a large data
base related with the formation and operation of physical
and chemical determinate systems – this is a wide set of
biological elements entering the structure of many en-
zymes, hormones, vitamins, where their known physic-
cal-chemical properties are used. In particular, iron is
known to contribute to binding and transfer of oxygen by
erythrocyte hemoglobin. Copper performs essential func-
tions in the chain of electron transfer in mitochondria.
Iodine is a necessary component of thyroid hormones.
Cobalt enters the structure of vitamin B12. Calcium in
phosphates forms the structure of bone tissue. Na+ and
K+ define the electric potential of cell membranes. Elec-
trolytes (Na+, K+, Ca2+ and Mg2+ salts) determine os-
motic blood pressure. Examples of the chemical ele-
ments involvement in complex biological systems are
quite numerous.
Genetic memory underlay the formation of biological
determinate systems of various complexity: morphofunc-
tional determinate systems (cells, locomotor apparatus,
vascular and nervous systems, etc.); homeostatic deter-
minate systems (energy, water-salt, temperature homeo-
stasis and many other systems responsible for constancy
of internal medium of the organism).
Here we consider the principles of self-organization of
energy homeostasis as a determinate system at the mo-
lecular level. ATP is consumed in different parts of the
organism: for secretion of various substances, for mem-
brane transport, biosynthesis, regeneration, physical work,
heat generation, etc. In this connection, a certain deter-
minate system should be active in th e organism to restore
the ATP content in a cell and integrally in the entire or-
ganism. This function is performed by energy homeo-
stasis. Its structural-functional organization is shown in
Figure 6.
This system has several levels of organization: cell
level, organ level, and integral organism level. Result of
its action is the ATP concen tration in any cell of the bio-
logical system. ATP serves as the system-forming factor
(factor of homeostasis). A similar notion is the degree of
energization of adenylic nucleotides, or the energy
charge. The bulk of ATP in a cell forms due to phos-
phorylation in the oxidation chain localized in mito-
chondria; and a minor part, due to substrate phosphoryla-
tion. The latter route is essential only at the oxygen defi-
ciency. The oxidation processes in mitochondria are pre-
ceded by difficult transformations of energy substrates in
the corresponding metabolic routes. For carbohydrates
this is glycolysis (glycogenolysis). For fats, β-oxidation
of fatty acids. A decay of one molecule of glucose yield-
ing lactate reduces two molecules of NAD. One cycle of
β-oxidation reduces respectively a molecule of NAD and
FAD. Starting from acetyl-CoA, which forms both from
carbohydrates and fats, the oxidation takes a common
route: via the Krebs cycle and the oxidation chain of mi-
tochondria. The reduction of three NAD molecules

L. E. PANIN 362
Figure 6. Energy homeostasis as a determinate system. DMT
– dominant motivation: initial hormonal background of the
organism (concentration of catecholamines, glucocorticoids,
insulin, glucagon, etc.); ME – memory elements: gene pool
of the target organs, four types of nitrous bases (adenine,
thymine, guanine, cytosine); a – trigger signaling: stress
(production of hormones able to interact with ME); b1 and
b2 – circumstantial signaling (conditioning factors): nutri-
tion pattern, changes in the emotional sphere, changes in
the gene pool (mutations), action of pharmacological pre-
parations and biologically active substances; DM – decision
making: switching over the energy metabolism from car-
bohydrate type to the lipid one; AP – action program: en-
ergy metabolism of the organism; ARA – actual results of
action: ATP concentration in cells; PRA – predicted result
of action: the concentration ratios of substances in a cell
directly affecting the ATP formation (ATP/ADP+Pn,
NAD/NAD·H+, FAD/FAD·H+); DS – determinate synthesis;
c and d – straight line and feedback.
and one FAD molecule corresponds to each cycle. We do
not present the complete balance equations here. The
oxidation of NADH+ and FAD·H+ occurs with the par-
ticipation of oxidation chain in mitochondria. Overall,
these processes can be considered as a general program
of ATP regeneration in a cell. The mechanism of ATP
formation requires a continuous delivery of ADP and Pn.
Their pool in a cell is restored again at ATP decay.
Thus, a change in the con centration ratio of ATP/ADP
+Pn serves as the first results-of-action acceptor in a cell.
It determines the notion of phosphate potential (PP), or
the Klingenberg potential. At rest, high energization of
mitochondria and decreased content of ADP and Pn in-
hibit the process of oxidative phosphorylation. On the
contrary, in operative condition an increased content of
ADP and Pn enhances it. Rate ratio of these processes is
such that PP always tends to a certain constant value.
The second essential results-of-action acceptor in en-
ergy homeostasis is a change in the concentration ratios
of NAD/NAD·H+ and FAD/FAD·H+ or, more precisely,
in redox potential of th e system. It is closely related with
the value of phosphate potential. Its decrease at intense
decay of ATP accelerates the oxidation processes in mi-
tochondria. However, an increase in the concentration of
NAD and FAD changes redox potential of the whole
system and creates prerequisites for the activation of cell
energy metabolism. At increasing phosphate potential,
the situation is inversed. Thus, the concentration ratios of
ATP/ADP+Pn+, NAD/NAD·H+ and FAD/FAD·H+, serv-
ing as the results-of-action acceptor, are the essential
units of intracellular regulation of energy metabolism.
The action program is connected with the results-of-ac-
tion acceptor via redox potential of the system (cell).
However, it is not indifferent to the entire organism
which substrates in which tissues (organs) are to be oxi-
dized under functional stress. Under acute short-term
stress the oxidation of carbohydrates predominates in
various tissues. Under chronic long-term stress two pro-
grams are formed: some tissues (organs), such as brain
and erythrocytes, proceed w ith the oxidation of carbohy-
drates, i.e. implement the first program; other tissues,
such as muscles and heart, switch over to the oxidation
of fatty acids, i.e., implement the second program. Tak-
ing into account that muscular tissue constitutes more
than a half of the body weight, one may say that the en-
tire organism shifts its energy metabolism from carbo-
hydrate type to the lipid one. This is confirmed by in-
creasing blood content of lipids, decreasing respiratory
coefficient, and changes in other parameters. Examples
of such states include starvation, adaptation to cold, pro-
longed and quite intensive physical work. It is very im-
portant that even the brain can be shifted to the oxidation
of lipids (ketone bodies). This is connected with the or-
ganization of energy homeostasis at the organ level.
Decision making concerning the use of some or other
genetic program is based on determinate synthesis. Re-
call, it includes dominant motivation, conditional signal-
ing, causal signaling, and memory. In this case, dominant
motivation is determined by a change in the hormonal
background. At acute func tional tension of the organism,
mainly the urgent adaptation mechanisms operate. They
are related chiefly with an increased production of cate-
cholamines. Rapid mobilization of a carbohydrate re-
serve (due to glycogen decay in liver and muscles under
the action of phosphorylase) increases the blood content
of glucose. In this phase, commonly the insulin content

L. E. PANIN363
also increases. Favorable conditions for enhanced car-
bohydrate metabolism are established, which is the pro-
gram number one.
A carbohydrate r eserve in th e organism is not large, so
under prolonged stress the second genetic program is
formed, leading to the oxidation of fats. This occurs due
to changes in the dominant motivation caused by an in-
creased blood content of glucocorticoids (cortisol) and a
decreased content of insulin.
Along with the urgent mechanisms, the mechanisms of
long-term adaptation also come into action (with a cer-
tain time shift). In fatty tissue, the fat-mobilizing effect is
enhanced. In liver, glycolysis is inhibited and glyconeo-
genesis is intensified. In the process, essential are not
only such urgent mechanisms as allosteric regulation, but
also the induction of enzyme synthesis or, on the con-
trary, its suppression. The first mechanism is related, for
example, to glyconeogenesis enzymes; and the second
one, to the key enzymes of glycolysis. In liver, synthesis
of VLDL is enhanced. In this case, decision making is
affected by the information extracted from the memory
element s (a ge ne po ol).
This forms the structural trace of adaptatio n. Thus, de-
cision making reflects the extent of adaptive changes,
their quantitative rather than only qualitative aspect.
Biologically active substances that come into the or-
ganism with foodstuffs of vegetable or zoogenic origin
and with folk-medicine preparations may play an impor-
tant role in conditional signaling. Well known is the group
of vegetal adaptogens: ginseng, e leutherococcu s, rhodazine,
leuzea, etc. These preparations have a broad spectrum of
action, including also the energy metabolism; they fa-
cilitate mobilization of carbohydrates, free fatty acids,
etc., exert gonadotropic effect, and improve non-specific
resistance of the organism. Such pharmacological prepa-
rations as phenamine sharply enhance energy metabo-
lism of the organism. All these substances act at the level
of determinate synthesis, changing the mechanisms of
both urgent and chronic adaptation.
Any extreme irritant (stress) can play a role of causal
signalization for energy homeostasis. Its action forms a
certain dominant motivation.
Cessation of an extreme irritant also serves as a signal
for biological system. Homeostasis as a system persists,
but moves to a n ew level of activ ity. Blood content of cate-
cholamines and glucocorticoids decreases and content of
insulin increases. Dominant motivation is altered; a dif-
ferent decision is made for initiating another (former)
genetic program. However, the action of extreme irritant
has left a structural trace. Due to induction, synthesis of
many enzymes has changed. Immediate return to the ini-
tial state is impossible. Organism needs a time to “erase”
this structural trace using the lysosomal enzymes. If the
action of extreme irritant is repeated, the structural trace
of adaptation will be more pronounced. Thus, decision
making in homeostatic determinant systems does not
proceed as a heuristic search, it is genetically determined
and evolutionary reinforced by natural selection. Teleno-
my in homeostatic systems has an evolutionary solution.
Switching over the energy metabolism from carbohy-
drate type to the lipid one is characterized not only by
quantitative changes in the oxidation ratio of carbohy-
drate and lipid substrates, but also by qualitative shifts.
This relates primarily to rearrangement of respiratory
chain in mitochondria, where peroxide oxidation of fatty
acids and other substrates conjugated to phosphorylation
becomes essential now.
All the features of energy metabolism in individual
tissues (organs) are strictly coordinated at the level of
whole organism. The same objective – formation of a
necessary ATP amount – is attained differently in dif-
ferent tissues. Energy homeostasis works as a complex
co-operative system. Such a cooperative mechanism pro-
vides the optimal conditions for enhancing the fat-mobi-
lizing effect and FFA transport to muscles. When the
organism is stressed, liver supplies nerve tissue and ery-
throcytes with carbohydrates due to activation of gly-
coneogenesis, and simultaneously delivers lipids to mus-
cles due to activation of VLDL synthesis; thus, it oper-
ates according to programs number one and two.
At the level of entire organism other integrative me-
chanisms operate, different from those working in a cell.
A particularly large number of feedforwards and feed-
backs are functioning in the sphere of neuroendocrine
regulation. Of basic importance are the endocrine-meta-
bolic interrelations. Our works revealed that glucocorti-
coids increase the blood content of VLDL as well as the
synthesis of apoproteins. In their turn, by the negative
feedback mechanism, VLDL inhibit steroidogenesis in
adrenal glands and decrease the production of glucocor-
ticoids. VLDL are the main transport form of endogenic
fat in the organism. As a transport form of the lipid na-
ture energy substrates, VLDL are partially destructed in
peripheral tissues under the action of lipoprotein lipase to
form lipoproteins of a higher density, including HDL.
The latter ones, being a supplier of the substrate (choles-
terol) for steroid hormones, enhance steroidogenesis in
adrenal glands. Such is the case with rats. In cattle, LDL
serve as a source of cholesterol for steroidogenesis. Thus,
changes in blood lipoprotein spectrum are the results-
of-action acceptor at the level of entire organism. Note,
this is an essential but not sole example of feedback at
the level of intrasystem and the more so of intersystem
relations. In such a manner the energy homeostasis is
operating, which we commonly call the energy metabo-
lism.

L. E. PANIN 364
The ATP concentration in a cell is maintained due to
free energy (G) of chemical compounds, which are con-
tinuously oxidized during the operation of energy ho-
meostasis.
Under prolonged functional stress, when carbohydrate
and even lipid reserves become insufficient, the organ-
ism starts to consume its own proteins for energy pro-
duction. The proteins are first hydrolyzed to amino acids,
which are transformed into carbohydrates due to en-
hanced glyconeogenesis and then are oxidized into CO2
and H2O to yield ATP and a corresponding amount of
heat. Thus, under stress the entropy of a biological system
increases. There is a constant threat of equ ilibration with
the environment. All homeostatic systems of the organ-
ism, including the energy homeostasis, work to counter-
act this treat.
Biological objects as hierarchical self-organized sys-
tems are tremendously more complicated than the objects
of inanimate nature. However, their behavior under the
action of external factors on the organism is fundamen-
tally the same. For instance, in homoiothermal animals,
constancy of the body temperature (36.7˚C) is maintained
by temperature homeostasis. When the organism is ex-
posed to low temperatures, its operation is rearranged.
Under such conditions, fatty acids are oxidized intensely
with a lower efficiency. A major part of energy is dissi-
pated as heat. This decreases the weighted average body
temperature. The system is rearranged in compliance
with another genetic program (memory elements). The
system goes to a new level of homeostasis; efficiency of
the useful physical work decreases. As the ambient tem-
perature is further lowered, a decrease in efficiency of
the oxidation processes becomes more pronounced, and
energy dissipation increases (the next level of homeosta-
sis). Then the time comes when temperature homeostasis
fails to perform its functions. This leads to progressive de-
crease in the body temperature. The organism is freezi ng.
Homeostasis maintaining the constancy of arterial
pressure (AP) operates in a similar manner. In the norm,
a r atio of ma ximu m an d mi ni mum A P is 120 /80 mm Hg .
Meanwhile, stress triggers the release of adrenaline into
the blood, thus raising the arterial pressure. The system
moves to a new level of homeostasis. Then everything
re t urns to the i nit ia l lev el. A pe rmanent hyper tensi on may
occur in response to a prolonged increase of different
pressure factors in the blood. The top values (levels of
homeostasis) may vary depending on the organism. A
human feels discomfort (headache, quick pulse). Life can
be quite long at such level of homeostasis, until blood
stroke or infarction comes. A decrease in osmotic or on-
cotic blood will lower AP. This leads to hypotension
(another level of homeostasis). This is also not good,
resulting in insufficient supply of oxygen and glucose to
the organs (first of all, brain); lethal outcome cannot be
excluded in a critical condition. Other homeostatic sys-
tems of the organism obey the same principle of opera-
tion. When the organism is exposed to external factors,
homeostatic systems behave as dissipative ones, because
additional energy is required to maintain homeostasis
under extreme conditions.
The formation of homeostatic determinate systems in
living objects is related with the appearance of internal
medium of complex multicellular organisms. However,
such organisms can perform various behavioral acts only
if a new type of homeostatic determinate systems is pre-
sent. These are the neurodynamic systems.
Memory elements in such systems are represented by
nerve cells of cerebral cortex, which acquire information
from both extero- and interoreceptors. Five senses cor-
respond to exteroreceptors: vision, hearing, touch, smell
and taste. Vision acquires information as electromagnetic
modes. Hearing perceives it as acoustic vibrations. Touch
senses tactile signals (sensations). Among them are also
the temperature sensations. Smell and taste provide the
organism with information in the form of chemical sig-
nals. The entire information comes to appropriate nerve
centers called the analyzers. There are visual, auditory
and tactile analyzers; smell and taste probably have a
common analyzer. Information coming from internal
receptors of the organism (interoreceptors) has no addi-
tional specificity and is perceived by the same analyzers.
These are mainly chemical signals. Information con-
veyed to cerebral cortex is processed chiefly in vertical -
neuron chains that are perpendicular to the cortex surface.
Thus, we have four types of central analyzers and the
corresponding four types of neurons. The conceptions of
external world and its changes are formed in central
analyzers. Numerous interneuron contacts determine the
connections of these parts of cerebral cortex with its lo-
comotor parts, subcortical structures, limbic system, ve-
getative nervous system, etc.
Nervous activity is based on unconditioned and cond i-
tioned reflexes [13,14]. Conditioned reflexes are the at-
tribute of high nervous activity. Neuromuscular appara-
tus intended for actualization of unconditioned reflexes
should be referred to morphofunctional systems; and
complex behavioral reactions of the organism based on
numerous conditioned reflexes, to neurodynamic or psy-
chophysiological determinate systems. Decision making
and action program in such systems may be quite com-
plicated. For example, a complex neurodynamic deter-
minate system forms when a pilot strives to land a plane
precisely on the runway (Figure 7). The goal-forming
factor here is the necessity of pushing down the plane
and superposing it with the runway. Landing conditions,
which play a role of conditioning factor, may be very

L. E. PANIN365
unfavorable: poor visibility, a strong crosswind, severe
icing, etc. Using his knowledge of the plane control sys-
tem and having an appropriate experience, the pilot co-
ordinates his actions taking into account the aircraft posi-
tion relative to the runway at each particular moment.
Results-of-action acceptor here is the anticipated result –
superposition of the plane and the runway, although ac-
tual result of action may differ significantly from it. In
such cases, pilot has to change the action program with the
aid of a different decision making. When the task is ac-
complished, this neurodynamic determinate system ceases
to be. However, in the period when the system exercised
its functions, a large number of neurochemical connec-
tions operated to change the state of vegetative nervous,
cardiovascular, respiratory, digestive, egestive and other
systems of the organism. These mechanisms are thor-
oughly considered in the monograph by L. E. Panin [3].
The similarity of self-organization mechanisms in the
living and inanimate nature is often accompanied by
similar regularities of their behavior in the fields of ex-
ternal action. This refers to behavior of biological mem-
branes as liquid crystals and behavior of solid crystals.
4. Structural Transitions in Biological
Membranes and Solid Crystals in Terms
of Physical Mesomechanics and
Thermodynamics
Liquid and solid crystals are homeostatic determinate
systems [3].
“Classic al th er mod yna mic s le ads to the n otio n of sys tem
in equilibrium, such as, e.g., crystal” [4]. In so lid crystals
residing in the fields of weak external action, the state of
homeostasis is determined by the nature of interatomic
interactions. This is the metallic bonding, which has a
quantum-mechanical nature. It is responsible for the high
shear strength of crystals. According to the literature [15,
Figure 7. Landing in difficult conditions.
16], solid crystal in the fields of strong external action
behaves as an open thermodynamically nonequilibrium
system. “Pumping” of external energy results in a local
loss of shear strength, which is accompanied by local
structural-phase transformations in the crystal lattice.
The possibility of such transformations is determined by
electron energy spectrum of the crystal. This is con-
firmed by a relationship between packing-defect energy
() of the crystal and its electronic structure, i.e., me mo r y
elements of the crystal [3,17]. In solid crystals, which are
a structurally inhomogeneous medium, structural-phase
transitions occur mainly on the external surface and at
the internal interfaces. This is the place where a chess-
board distribution of stresses and deformations is formed:
the cells under compressive normal stress alternate
chequerwise with the cells under tensile normal stress [1 8 ] .
Tangential stresses also have a chessboard distribution,
which is spatially displaced in phase by π2. This can
explain the physical nature of plastic flow localization at
different scale-structural levels under differen t cond ition s
of loading. The excess molar volume and virtual nodes
of a higher energy structure in the interstitial space that
are present in the zones of tensile stress allow the occur-
rence of local structural transformations caused by non-
equilibrium state in this zone.
A similar situation is observed for biological mem-
branes under the action of various external factors (metal
oxide nanoparticles, stress hormones). In biological mem-
branes considered as liquid crystals, the system-forming
bonds are represented by low-energy forces: covalent
and hydrogen bonds, hydrophob ic and weak electro static
interactions. They serve as the memory elements and
determine also a low shear strength of biological mem-
branes and such notion as membrane “liquidness”. It can
be stated that homeostatic mechanisms of physical and
biological systems in dissipative state are universal.
Destruction of solid and liquid crystals increases the
molar volume.
A dependence of the Gibbs thermodynamic potential
F() on the molar volume  taking into account local
zones of different scale stress concentrators is described
by the equation:


i
i
F
UTSpC

  
,
where 
i – chemical potential, Ci – concentration
(Figure 8, [15]) .
At critical values of molar volume


1, 2,,6
i
 ,
the thermodynamic potential F(  ) has local minima.
They reflect local nonequilibrium potentials in the zones
of different scale hydrostatic tension. Critical values of

I correspond to different levels of homeostasis in a de-
formable solid:

0 is an equilibrium crystal; the in itial level of homeo-

L. E. PANIN 366
stasis;

1 are the zones of stress microconcentrators where
dislocation cores are generated; the next level of homeo-
stasis;

2,

3 are the zones of stress meso- and macroconcen-
trators where local structural-phase transitions with the
formation of meso- and macrostripes of local plastic de-
formation take place; the next levels of homeostasis;

4 corresponds to intersection of curve F(
 ) with the
abscissa. At a further increase of the local molar volume,
changes of the Gibbs thermodynamic potential proceed
under the conditions of F(
 )  0, and the system be-
comes unstable. Various forms of material failure appear;
solid crystal starts to behave as a liquid one.
  
6 – the existence of two phases is possible: at
 =

5 – the vacancy phase atom, at
  6 – different ther-
modynamic levels of the crystal lattice in a deformable
solid, different levels of its homeostasis.
Thus, plastic deformation of solid and liquid hetero-
crystals in the fields of external action is a multilevel
process of their destruction, with the corresponding levels
of crystal lattice self-organization and levels of its ho-
meostasis, i.e., the destruction via different phases of
strengthening (self-organization). This decreases the order-
liness and amount of struct ural informati on in the system .
Here we see the universal nature of homeostasis of
biological and physical systems in dissipative state.
Dependence of Gibbs thermodynamic potential on the
molar volume  and changes in the structural informa-
tion I), taking into account local zones of stress concen-
trators is determined by the expression:
F
(  )
0

0

1

2

3

–1

4 
6

5

Figure 8. The dependence of the Gibbs thermodynamic
potential F(  ) from the molar volume  in the light of local
zones of stress concentrators of different scales [15].




log
,10
ii
ppk
FIUTp C
ii


 


These quantitative interrelations underlie transition of
the system to a new structural level of homeostasis.
The above changes can be adequately described in
terms of determinate systems theory. Shock wave is the
external signal specific to polycrystal (a multiscale struc-
tured medium). When a shock wave is passing through
the sample, it interacts with the memory elements of the
system (polycrystal). The memory elements are repre-
sented by different type connections stabilizing the struc-
ture in time (the initial level of homeostasis). In metals
and alloys, these may be different manifestations of elec-
trostatic interactions (ionic forces, metallic bonding, and
Van der Waals forces). They are distributed nonuni-
formly over the volume of a deformed solid and vary in
the energy level. Energy of these forces depends on the
packing closeness of metal atoms or molecules in some
alloys (intermetallides), the presence of defects (porosity)
and impurities, and environmental influence (the action
of temperature, magnetic field, etc.). In determinate sys-
tems theory, the latter is considered as the effect of con-
ditioning factors that forms a background for the opera-
tion of system -specific external signals.
As a result of this interaction, a complex multilevel
hierarchical system (crystalline structure) decides to choose
some or other action program to be implemented. This
may be the generation and development of rotational
strain modes leading to rotational failure of the material
(the first action program), or predominant generation of
translational modes of deformation and appearance of
shear bands leading to the formation of micro- and
macroсracks (the second action program), or some other
programs may be implemented.
In the process, the eventu al result of action is attained,
and a system (metal sample or construction material)
moves to a new level of homeostasis. If the action of
system-specific external signal persists, a new decision is
made, and the system goes to the next level of homeosta-
sis. This proceeds until the system (sample or construc-
tion) is completely destroyed. Such a mechanism was
presented earlier as the structural levels of deformation
of solids [19], and later as physical mesomechanics of
deformable solids [20,21].
Results-of-action acceptor in metals and alloys or in
deformable solids is represented by the atoms of a crystal
lattice or by various mesostructures on which the action
of new forces or their combination is closed. They stabi-
lize the entire system in a new functional state at a dif-
ferent level of homeostasis (Figu re 2).
These notions of determinate systems and their transi-
tion to a new level of homeostasis agree well with the
modern ideas concerning the deformation mechanism of

L. E. PANIN367
solids [22]. Structural levels of deformation refer to
mesoscale levels and differ quailtatively from the sin-
gle-level approach employed by continuum mechanics
and disl oca tion t heor y. Th e nov el approach revealed gen-
eral regularities of the behavior of deformable solids at
mesolevel and made it possible to use the synergy prin-
ciple for explanation of self-consistent plastic flow at
different mesoscale levels. This resulted in the develop-
ment of multilevel mechanics of deformable solids,
which was called the “physical mesomechanics” [21].
However, here we encounter the same problem as that
indicated by W. Heisenberg in quantum physics [23].
The mathematical apparatus used to describe plastic de-
formation of solids is adequ ate for the process mechanics,
whereas the language describing the physical phenomena
is not adequate. The application of conceptual apparatus
of determinate systems theory allows us to overcome this
disagreement.
However, in biological membranes as liquid crystals,
destruction is related with structural transitions and is
generally accompanied by increasing structural orderly-
ness (the order  order transition). Earlier [24], it was
shown that the actio n of steroid hormon es on erythrocyte
membranes disturbs the mechanisms of self-organization
that operate in the cells in normal functional condition.
The active CO, NH and OH groups of stress hormones
interact with CO and NH groups both of proteins and
phospholipids in biological membranes. This leads to the
formation of complex protein-lipid clusters, where “com-
pressive” hydrophobic interactions are reinforced. Mole-
cularly bound water is displaced to adjacent regions. Here,
hydrostatic forces increase the “tensile” tangential stresses.
Mobile nanostructural boundaries are formed, along
which the biological membranes are destructed. This re-
sults in the formation of numerous pores and mesostrips
of plastic deformation. In terms of physical mesome-
chanics, these transformations resemble those developing
in solid crystals in the fields of external action (Figure 9 ).
However, in biological membranes such self-organiza-
tion may be related even with increasing order and de-
creasing entropy, but th is is incompatible with cond itions
that determine cell viability. Structural transitions cover
the membrane-bound enzymes, transmembrane carriers
and hormone receptors. It is reasonable to say that cell
membranes go to a new level of homeostasis (self-or-
ganization) which is incompatible with life. The nature
of life implies dynamics. The cell dies. Here, one can tell
about thermodynamic features related with changes in
the structure and function (properties) of solid crystals
and biological membranes in the fields of external action.
Various structural transitions (phase transitions, nano-
structural, etc.) strongly contribute to the functional ac-
tivity of a cell. These are the transitions like smectic A
(a)
(b)
Figure 9. a – Atomic force microscopy. The surface of rat
erythrocytes after adsorption of cortisol. Concentration of
the hormone is 10–6 M. Deep meso-bands with bifurcation
are seen; b – Formation of micropore chains along local-
ized-deformation shear-bands. Plate of high-pure alumi-
num 180 nm thick glued on flat specimen of commercial Al.
Alternative bending, Т = 293 K; cycle number N = 17.55 ×
106 [15].
 smectic C, smectic  cholesteric, and nematic 
isotropic state; in proteins, the transitions tangle  -
structure and tangle   -helix. They all affect the vital
characteristics of a cell. I. Prigogine believed th at there is
“a wonderful analogy between instability of nonequilib-
rium origin and phase transitions” [4]. This problem is of
great interest and deserves special examination.
5. Conclusion
Determinate systems represent a general principle of
matter self-organization in the nature, from atom to hu-
man (Homo sapiens). Using the wave properties of ele-
mentary particles (first of all electrons), four quantum
numbers characterizing their state, and Pauli exclusion

L. E. PANIN 368
log
ii
principle, the nature created a remarkable diversity of
physical and chemical phenomena. The first step towards
increasing diversity was the formation of atoms and then
the chemical elements. Today we know a little more than
100 chemical elements. Hydrogen is the first and most
simple of them. Fermium takes the hundredth place. It is
followed by mendelevium, nobelium, lawrencium, and
some other not very stable elements. This exhausts the na-
tural diversity associated with the structure of atoms. D. I.
Mendeleev was the first to perceive that properties of the
elements are in a periodical dependence on the charge of
their atomic nuclei. In the present-day periodic table of
chemical elements, atomic number, atomic weight, nu-
clear charge and physic-chemical properties are closely
interrelated. However, the latter ones depend to a con-
siderable extent on the changes in wave characteristics of
the elementary particles constituting these atoms.
Eventually, everything is reduced to the quantum me-
chanical phenomena in atoms as complex homeostatic
determinate systems connected with the outer world, i.e.,
physical vacuum. In these systems, memory elements are
represented by four types of interaction: strong, electro-
magnetic, weak and gravitational. The action of these
forces determines the nature of quantum interactions in
any atom and hence its physic-chemical properties. The
presence of unpaired valence electrons in the outermost
energy levels increases the chemical diversity. The varia-
tion of electron wave proper ties has a tremendous poten-
tial. Electrons may form spherical waves, octuple waves,
lobe waves, etc.; they may occupy different energy levels.
At synthesis of chemical compounds, electrons generate
various hybrid waves. Here the nature widely uses the
chemical bonds. However, along with chemical bonds,
other forces also contribute into chemical diversity. These
are the ionic and hydrophobic interactions as well as hy-
drogen bonds.
The four type forces play a role of memory elements
in chemical determinate systems. Transition to this level
of systemic organization of material world led to a sharp
amplification of natural diversity, which is now investi-
gated by inorganic, organic and bioorganic chemistry.
This type of systems includes also a multifarious world of
solid and liquid crystals, which are considered by physics,
geochemistry and biology.
In this case, an increase of negentropy in the course of
evolution has the same meaning as accumulation of in-
formation, and is determined by Shanon equation:
H
pp 

In open systems, increasing negentropy due to energy
supply from the environment, always increases the
probabilities of individual events determining the prob-
ability of a state of the entire system. This leads to ap-
pearance of thermodynamically stable systems and de-
termines the time’s arrow moving toward decreasing
entropy.
When biological determinate systems are formed, an
increase in negentropy, structural information and natural
diversity is based on the coding principles. They underlie
the operation of genetic mechanisms in each vegetal or
animal cell. In such systems, memory elements are rep-
resented by four types of nitrous bases: adenine, thymine,
guanine and cytosine. This produced a large set of pro-
teins with different properties: structural proteins, con-
tractile proteins, enzymes, carriers, hormone receptors, etc.
A tremendous variety of life forms on the Earth is based
on these processes.
However, the appearance of intuitive and conscious
forms of behavior in the objects of living nature became
possible only after the genesis of central and peripheral
nervous systems. They formed a basis for unconditioned
and conditioned reflexes as well as developed neuron net-
works. The latter served as a substrate for higher nervous
activity, including complex human behavior, conscious-
ness, thinking and memory. Complicated forms of self-
organization in material world evolutionarily derived from
the earlier forms.
Therefore, self-organization of material world devel-
oped toward increasing the orderliness (negentropy),
structural information and natural diversity due to free
energy of the environment via the formation of homeo-
static determinate systems and hierarchy of their interact-
tion.
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