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Thermodynamic Self-organization as a Mechanism of
Hierarchical Structure Formation of Biological Matter
Georgi P. Gladyshev
N.N. Semenov Institute of Chemical Physics, RAS
117977 Moscow, up. Kosygina, 4. E-mail: academy@endeav.org
http://www.endeav.org/evolut
Abstract
In the past few years, it proved possible to build a noncontradictory
thermodynamic theory of biological evolution, the origin of life, and the
aging of living beings resting on a firm foundation of classical
thermodynamics.
The law of temporal hierarchies makes it possible to identify quasi-
closed systems in open biological systems and to use the approaches of
hierarchical quasi-equilibrium thermodynamics to establish the direction of
ontogenesis and the evolutionary processes. A short review of the
achievements of thermodynamics of biological evolution and aging are
presented. The application of the principle of stability of matter to the
structures of adjacent hierarchies constitutes additional proof that quasi-
equilibrium thermodynamics can be applied to the biological systems in the
real world.
This theory is corroborated by known fact and experimental
outcomes obtained during the study of living and synthetic systems using
the methods of macrothermodynamics and macrokinetics.
1
Key words: Biological evolution, aging, second law, law of
temporal hierarchies, macrokinetics, caloric restriction, differentiation of
cells
"One of the principal objects of theoretical research in any department of knowledge
is to find the point of view from which the subject appears in its greatest simplicity."
J. Willard Gibbs
“Yet science seems to have driven us to accept that we all merely small parts of a
world governed in full details (even if perhaps ultimately just probabilistically) by very
precise mathematical laws.”
Roger Penrose
1. Introduction
The title of this paper contains the terms “thermodynamic self-
organization” and “mechanism” of the process of biological matter structure formation.
The term “thermodynamics” is interpreted as it is in classical thermodynamics or
thermostatics. The reader may, therefore, gain an impression that the use of these
concepts in the title is incompatible, since thermodynamics does not provide
information on the mechanism of processes but only shows their direction and
determines the extent of a reaction.
The reference is, however, to the formation and functioning of hierarchical
structures of the biological world, which are studied in terms of different time scales
“separated” by signs of strong inequalities in conformity with the law of temporal
2
hierarchies [1. The existence of different time scales in the world of biological matter
prompts some conclusions on the interdependent processes under way in different
hierarchies. The mechanisms of these processes (mechanisms of thermodynamic
correlation between hierarchies) are connected with a macrokinetic description of
phenomena and manifest themselves through macrolevel thermodynamics, i.e.,
hierarchical thermodynamics or macrothermodynamics. The prefix macro– in the term
“macrothermodynamics” emphasizes that this branch of knowledge studies
heterogeneous (polyhierarchical) macrosystems. As regards the supramolecular living
objects, this means studying the systems in which autonomously existing molecules
cannot be identified. Another generally known example, which can be examined not
only at molecular but also at macrolevel, has to do with the discovery of the great
Gregor Mendel. In this case, we refer to the “transmission” of genetic information
recorded at molecular level to the level of organism, population, ecosystem, etc. This,
of course, makes it possible to examine the mechanisms of mutual influence of
thermodynamic self-organizing structures of different hierarchies. It should be noted
that the thermodynamics of systems and processes usually describes the behavior of
systems only at macroscopic level. In this context, the term “macrothermodynamics”
has no particular sense.
This paper deals, therefore, with the phenomenon of thermodynamic self-
organization (self-assembly) of biological structures whose formation can be described
in terms of thermodynamic systems close to the state of equilibrium [1 – 6]. Their
emergence and behavior is studied using the methods of equilibrium (quasi-
equilibrium) thermodynamics [3, 7 – 15]. As was established in the past few years, the
mathematical structure of these methods can be applied to the description of all
hierarchical levels of the living world.
This paper does not use concepts on dynamic self-organization (or simply
self-organization, to use I. Prigogine’s term [16]), which can be observed in systems in
a far from equilibrium state and described by kinetic functions, that is, functions whose
differentials are not total (Prigogine). Dynamic self-organization is not, as a rule,
3
observed in evolving organic systems, and if is, its role in the formation of biological
structures is minor.
I believe, as do some of my colleagues, that the findings presented in this
paper boost the ideas of G. Galileo, J.C. Maxwell, Charles Darwin, and other classics
based on the belief that there exist universal natural laws operating at all hierarchical
levels of matter [17]. The thermodynamic theory of biological evolution makes one
choose science vs. creationism. I am inclined to side with Penrose, who believed that
our world is totally governed “(even if perhaps ultimately just probabilistically) by very
precise mathematical laws” [17, p. 447].
There is already a large body of incontrovertible proof of the justice of
macrothermodynamic (or just thermodynamic) theory of biological evolution and the
aging of living beings. There are, however, problems awaiting solution. It is probably
necessary to identify and describe, in detail, the link between macrothermodynamics
and macrokinetics. This link may manifest itself in “the principle of stability of
substances” [1, 18] and other newly discovered laws of the structure and evolution of
biological systems. Work in this field, which is most probably “designed to change the
destiny of the coming generations” [19, 20], is obviously just beginning. Nevertheless,
there are already breakthroughs [1, 20] that deserve to be called fundamental. Special
mention should be made of the work of Jean-Marie Lehn, a classic of supramolecular
chemistry, which is obviously going to play an outstanding part in the advancement of
macrothermodynamic theory.
2. Classical Thermodynamics as the Guiding Principle of Cognition of
the World
Basing himself on universal laws of nature and using deduction, J.W. Gibbs built the
most precise physical theory [21]. This flawless phenomenological thermodynamic
theory, which is, in my view, superb, contributed a great deal to the outstanding
successes of the natural sciences and helped us gain awareness of the world around us.
4
The most important results were probably achieved by physical and chemical
disciplines in the identification of the “motive forces” of spontaneous processes
occurring in the world of chemical and supramolecular transformations.
Although the thermodynamic theory created by Gibbs and the other classics of
natural sciences rests on idealized equilibrium models, with good approximation it was,
and is still used in many natural sciences.
Subsequently, thermodynamic theory was advanced as it was, and still is applied to
systems and processes close to the state of equilibrium [22, 23]. The obtained outcomes
proved interesting and useful, but quite modest.
The mid-20th century produced ideas on the “thermodynamics” (“thermodynamic
kinetics”) of systems far from the state of equilibrium [16]. This trend has not yet
yielded any tangible practical results [24], founding itself on kinetic functions and
ignoring the use of functions of state. This route was chosen by modern synergetics,
which rests on nonlinear models [25]. The headway made in this study field is
sometimes of indisputable interest in terms of mathematical modeling of complex
processes. At the same time, its approaches make the physics, chemistry, and biology of
phenomena more remote and incomprehensible.
One should specially emphasize that the methods of statistical thermodynamics also
made a tremendous impact on scientific advances. However, productive use of these
methods is confined, in practice, to simple systems, when individual particles or
kinetically autonomous structures can be identified. It is no chance that Gibbs’s primary
purpose in creating statistical thermodynamics was to provide a foundation for
phenomenological thermodynamics.
So some researchers’ attempts to discard the classical methods of cognition have not
resulted in the expected great progress of science.
The classical methods used in natural sciences rest primarily on linear models. Their
application implies identifying a certain hierarchy of the examined structures (systems),
set time and energy scales, and the boundaries of the studied space.
5
Overvaluing the prospects of the new approaches and the absence of ideas on the
possibility of identifying “temporal hierarchical structures” in the biological world
resulted in a number of misunderstandings in biological sciences. For decades, it was
believed that methods of equilibrium (quasi-equilibrium) thermodynamics were not
rationally applicable to living systems, since the latter are open. It was also assumed,
erroneously, that for some unfathomable reason, they are moving spontaneously away
from equilibrium state, and that most processes in the living organisms should be
considered only in terms of the existence of dissipative structures in the biological
world.
There is also a well-known opinion that the living organisms are forever battling
with the second law of thermodynamics; this, some researchers maintain, “is a
wonderful mystery” [17]. However, to avoid misunderstandings, one should point out
right away that this assumption holds water only if interpreted adequately and with
some reservations. It is easy to show that it can be applied not only to living but also to
lifeless systems.
The energy-consuming chemical substances formed as a result of the effect of solar
energy (or other external energy sources) are, in the final analysis, transformed, by the
operation of the second law of thermodynamics into thermodynamically stable (in the
conditions of the Earth) compounds, CO2, N2, H2O, and others. Living systems, as it
were, obstruct the achievement of chemical equilibrium by forming higher hierarchical
structures, e.g., supramolecular structures, cells and organisms, as a result of the
spontaneous process of thermodynamic self-organization (self-assembly). This slackens
up the establishment of chemical equilibrium at all hierarchical levels and can be
explained in terms of the phenomenon of structural stabilization and the principle of
stability of matter.
The products of photosynthesis and the compounds formed as a result of their
transformation decompose, producing stable molecules mentioned above. However, life
does not stop due to the introduction into the cycle of matter of new portions of
products of photosynthesis and other non-spontaneous processes.
6
As was already noted, the battle against the second law can be observed not only in
living systems. Imagine that you are sitting in front of an open fire feeding it with
firewood, which burns up in conformity with the second law. If you continue to throw
in more logs, the fire does not die down. You can see that as several of the logs are
charred, they begin to burn more slowly due to the poor access of oxygen to the inner
layers of the wood. In this case, the role of the Sun is performed by firewood, and the
role of “inhibitor”, by the layers of carbon (charred wood) on the surface of the logs. As
regards living objects (tissue), the role of inhibitor is performed by structures at higher
hierarchical levels. One can give any number of examples of the battle against the
second law in inorganic nature, when a cycle of inorganic matter takes place. Such
cycles are often observed on the geological time scale. Obviously, “the struggle against
the second law” is typical of many simple and complex systems of any origin, living
organisms probably being the most complex ones. R.Penrose and other researchers’
conclusion regarding the battle against the second law of thermodynamics should be
treated as just an application of the Le Chatelier – Braun principle (the principle of least
constraint) to quasi-closed organic systems.
It also needs to be stressed that physicists and mathematicians, and, in their steps,
scientists specializing in other fields [11, 17, 24], frequently use the concept of entropy,
which does not fit the classical definition proposed by Clausius and Gibbs. This paper
deals with classical thermodynamics and macrothermodynamics (thermodynamics of
hierarchical systems), which use the functions of state with total differentials [21, 8-13].
After the author of this paper had formulated the law of temporal hierarchies (he was
first aware of its existence in 1976 – 1977 [26]), it became obvious that the methods
developed by J.L. Lagrange, J.W. Gibbs, and other classics can be applied to
dynamically open living systems. Hierarchical equilibrium (quasi-equilibrium)
thermodynamics or macrothermodynamics came into being, and it was shown that
linear models with good enough approximation can be used to describe evolutionary
processes and many transformations that occur at all hierarchical levels of living (as
well as non-living) matter.
7
Following the guiding principles of Lagrange, Gibbs, Clausius, and other classics
and basing oneself on one of the most powerful cognitive methods, the method of
mathematical deduction (to which, incidentally, Erwin Schrodinger [27] referred as not
just universal but also “frightening”), it proved possible, or so the author believes, to
build a precise enough physical (physicochemical) theory of biological evolution and
the aging of living beings [1, 5, 6, 12].
The law of temporal hierarchies (Gladyshev’s law) helped substantiate the idea that
an overwhelming majority of supramolecular and other processes (at least structure-
forming ones) in the biological world takes place in quasi-closed systems under
regimen close to the state of equilibrium [1]. Hence the conclusion that the relevant in
vivo and in vitro processes can with equal justice be studied in terms of chemical,
supramolecular, sociological, and, generally speaking, hierarchical thermodynamics.
Chemists, biologists, geologists, and others have for decades been using the methods
of equilibrium thermodynamics when examining various transformations in vitro.
The thermodynamic theory of biological evolution and the aging of living beings has
lifted all earlier restrictions connected with the “openness” of biological systems and
the alleged non-equilibrium of most processes in living systems. The theory is in line
with the experience gained by physics, chemistry, and biology, and in practical terms,
with the long experience of medicine, dietology, sociology, and other branches of
knowledge [1].
The model of the thermodynamic theory of biological evolution and aging implies
analyzing the changes of the Gibbs (Helmholtz) specific function in time “inside” each
temporal (structural) hierarchical level of living systems, as well as the interactions
between different-level structures. Such studies can be conducted with the help of
“macrokinetic description”.
A detailed substantiation of this theoretical model can be found in [1, 2] and a
number of other works [28-33] by the same author.
One often hears in the past years that to solve universal problems, “one should base
oneself totally on the ideas of Gladyshev, Galileo, and Maxwell” regarding the trend of
8
evolution “in strict conformity with the universal laws of Nature”. What is more, some
researchers believe that the Darwinian theory of biological evolution should be carried
further by “Gladyshev’s macrothermodynamics” – hierarchical thermodynamics of
quasi-closed systems, whose existence in real world has been proved irrefutably (cf.
Internet site: Evolution vs. Thermodynamics – EvC Forum. Search words in
www.yahoo.com: Gladyshev, Galileo and Maxwell, "Gladyshev`s
"macrothermodynamics", etc.).
3.The Thermodynamic Theory of Evolution and Development
The study of the processes that lead to the origin and development of living systems
in terms of hierarchical structures and identification of the law of temporal hierarchies
gives reason to assert that the direction of the processes of the development and
evolution of living beings can be ascertained on the basis of thermodynamic
(thermostatic) principles formulated by the classics of the natural sciences, R. Clausius,
J. Gibbs and others [1-14, 21] .
The formation of structural hierarchies in open natural biosystem within the
framework of the model of quasi-closed systems can be described in terms of
hierarchical thermodynamics (thermostatics).
In the course of the evolution of open natural systems, each higher hierarchical level
j is formed as a result of thermodynamic self-organization (self-assembly) of lower-
level, j-1, structures. This self-assembly occurs through the stabilization of level j.
The latter is connected with the fact that the Gibbs specific function of the formation of
structure j tends to a minimum.
The cycle – the relative matter circulation in nature can also be studied from the
stand of hierarchical thermodynamics [1, 34 ]. Fig. 1 presents the scheme of the change
of Gibbs function (Gibbs’ free energy of the formation of structures of the biological
world). Obviously, the motive force of the non-spontaneous processes of the cycle of
9
matter, first of all, is connected with the Sun. In terms of “dark” spontaneous processes,
the motive force of the self-assembly and evolution of biological structures at all
hierarchical levels is “thermodynamic forces.” In conformity with the principle of
energy differentiation (and the law of temporal hierarchies), the specific values of Gibbs
function of self-assembly (thermodynamic self-organization) at different hierarchical
levels differs significantly. Thus, there exist the series
… … , (1)
where and are the changes of the specific values of Gibbs function of
the formation of structural hierarchies j and j + 1 calculated for a unit of volume or
mass. In other words, the coordinate axes of the scheme presented in Fig. 1 are of
different scale in a significant degree.
Gibbs function of the formation of molecules and supramolecular structures as
complex systems often coincide, in the conditions of the Earth, with the Gibbs function
of the formation of the corresponding simple systems. In view of this, the asterisk in
G*i may be omitted.
10
Fig. 1. Scheme of the change of Gibbs function of the formation of complex
systems, G*i during the emergence and degradation of chemical (ch) and
supramolecular structures (im), as well as organisms (org), populations
(pop), communities (com), and ecosystems (eco).
The law of temporal hierarchies [1, 2, 5, 6, 12, 34] makes it possible to identify
quasi-closed thermodynamic systems (subsystems) in open biosystem. It is possible to
study their development (ontogenesis) and evolution (phylogenesis) by studying the
changes of the value of specific (per unit of volume or mass) Gibbs function of the
formation of the given higher hierarchical structure out of lower-level structures. Thus,
it was established that in ontogenesis (or phylogenesis), the specific Gibbs function of
11
the formation of supramolecular structures of an organism’s tissues, , tends to
minimum:
, (2)
where V is the volume of the system; m is the mass of the identified micro-volumes; x,
y, z are coordinates; symbol «--» means that value is specific; and symbol «»
emphasizes the heterogeneous character of the system. Let us note that equation (2)
implies taking account of all supramolecular interactions in all hierarchical bio-tissue
structures (intracellular, intercellular and others). This is fully justified because the
structural hierarchy does not always coincide with the temporal hierarchy. Thus, some
types of cells do not divide and, like organisms, age simultaneously with the organism.
However, any supramolecular hierarchy (j-1) has some higher hierarchy (j + x), so that
,
where and are the mean life times (life spans) of elementary structures of the
corresponding structural hierarchies in a living system, x = 0, 1, 2, …, etc.
The use of equality (2) means, in fact, that we apply the law of temporal
hierarchies as [1, 34]:
… … . (3)
Here, ( ) is the average life span of an organism’s molecules (chemical
compounds) that take part in metabolism. ( ) is the average life span of any
supramolecular structures of an organism’s tissues that are renewed in the process of its
growth and development. is the average life span of an organism in a population.
And is the population’s average life span. The series of strong i nequalities (3) does
not include the life span of cells (cell) and some other supramolecular structures.
However, this series of course tallies well with reality and reflects the existence of
12
temporal hierarchies in the living systems. The latter rigidly substantiates the possibility
of identifying quasi-closed systems (subsystems) in open biological systems.
The thermodynamic theory of biological evolution and the aging of living beings
accords with numerous facts and with mankind’s empirical experience [1 –12, 30 -35].
A graphic example (Fig. 2) of the accord between theory and observations is
connected with the well-known medical recommendation to include vegetable oil and
seafood (cold seas) into one’s diet.1 These products add “young chemical matter” to the
biotissues [1, 19], “building material” that corresponds to the composition of a young
organism. In thermodynamic terms (and in the light of known facts), this rejuvenates
the organism’s tissues. This is easy to see having analyzed the approximate equation —
an analogue of Gibbs-Helmholtz equation (Gibbs-Helmholtz-Gladyshev equation):
,
where is the specific Gibbs function (Gibbs specific free energy) of the
formation of the condensed phase of matter i, and are the change of specific
enthalpy and entropy during the solidification of natural fat (oil), is the melting or
freezing point, and T0 is the standard temperature (e.g., 37 C) at which the comparison
of values is done.
It follows from equation (4) that, at a certain approximation, there should be a
correlation between (calculated for the standard temperature) or the indicator of
the product’s anti-aging (gerontological) value, GPGi [5, 36], and the fats’ or oils’
congeal (pour or freezing, or melting) point [37-39]. Let me note that the GPGi
indicator is proportionate to value [40]. Indeed, such a correlation does exist. This
is confirmed by the known data presented in Fig. 2. We can see that as a rule, vegetable
1 This example may help the reader believe in the effectiveness of the thermodynamic theory when
ascertaining the direction of the evolution and development of the living organisms.
13
oils have a relatively low pour point and, consequently, higher values (as
compared to fats). According to the theory, they have heightened anti-aging value. It is
common knowledge that these oils are recommended for use as food during various
diseases and to prolong the duration of healthy life [41-42]. Needless to say, the
correlation presented in Fig. 2 can be specified by a strict evaluation of and the
GPGi indicator. The latter’s value, as well as a product’s congeal point Tcong ( ),
depend on the environment and the age of the plant or animal used as food [1]. To
emphasize this point, the data in Fig. 2 are presented as large circles. Let me note that
such calculations are easy to perform in relation to proteins and carbohydrates, as well
as the food additives and medicines.
A convincing argument in favor of the thermodynamic theory of aging is a well-
known phenomenon, namely, medical recommendations to reduce the caloric intake. In
will be in order here to quote prominent gerontologists [43] saying in the popular
scientific magazine: «Investigators have know for decades that caloric restriction
extends life and the
Fig. 2. Dependence of “anti-aging (gerontological) value” of edible oils and
fats, GPGi, on their congeal point, Tcong. GPGi and Tcong depend on the environment and
age of plants and animals. A ten-point GPGi scale is used. It is assumed that ten GPGi
points are given to the oil with a congeal point of -30C; no points are given to fat with
a pour point of 47C.
14
duration of good health in all species in which it has been studied, as long as the diet
includes enough nutrition for routine maintenance of the body. These findings suggest
that caloric restriction might have similar effects in humans». These researchers believe,
however, that there is no indicator, which would make it possible to objectively assess
the rate of aging in humans or other species. The thermodynamic theory of aging
introduces such an indicator or yardstick, which can help established the degree of
aging of tissues in living organisms. This yardstick is the GPGi index, which is
calculated by measuring value for various types of tissues. Then the less negative
value of , i.e. the higher the value of indicator GPGi, the younger the tissue is.
Reducing the caloric intake helps keep the value of index GPGi of human, animal, and
plant tissues higher (cf. the scheme of the changes of value in the process of aging
[1, 5, 26, 44, 45]). This reminds us yet again that nutrition significantly affects human
longevity in the state of health. There is reason to believe that gerontologically good
nutrition also has a favorable effect on overall longevity.
It is shown that the principle of stability of matter - the feedback principle is
applicable to all biological systems (their hierarchies) [1, 18]. The core of this principle
is as follows: during the formation (self-assembly) of the most stable structures at the
highest hierarchical level (j), for example, the supramolecular level, nature
spontaneously uses predominantly the least stable structures (accessible to the given
local segment of the biosystem), e.g., the molecular level (j-1). It has been
quantitatively proved that the principle works at the molecular and the supramolecular
levels of the biotissue. There are also facts confirming its applicability to the social
hierarchies. Thus, hierarchical thermodynamics of complex systems can help explain
the social management techniques developed over centuries, such as “divide and rule”
[1], etc.
Further on, this work uses multicellular living organisms to examine the general
scheme of the development of organisms, as well as the structures of the higher
15
hierarchies of biosystems (populations, communities, etc.) from the stand of equilibrium
(quasi-equilibrium) hierarchical thermodynamics of complex quasi-closed systems.
4.The melting point of the organisms’ supramolecular structures
As the author repeatedly stressed, the soundness of the thermodynamic theory of
evolution and aging is corroborated by numerous generally known facts relating to the
change of the ratio of high- and low-melting structures in an organism’s tissues as its
body temperature (the temperature of the habitat) changes. Nevertheless, many
gerontologists and other researchers disregard this fact.
It would be useful to draw the specialists’ attention to the models whose study makes
one believe in the prognostic value of the theory.
The simple two-state model is:
= , (5)
where N – is the native (associated) state of the supramolecular structure, and D is the
unfolded state.
In this simplest case, we can apply the obvious equation:
, (6)
where и - concentration of и structures - gas constant, - temperature.
There are other long known simplified models representing the melting of nucleic acids,
proteins, and their complexes. These models were previously used only in the study of
closed laboratory systems with variable composition (substances of the same type). No
one tried to apply these models to the evolution of open real systems.
After the law of temporal hierarchies (3) had been discovered, it became obvious
that many known models can, with good reason, be applied to those open biological
systems which can be treated as quasi-closed at certain time periods.
16
For example, the equilibrium transformation between double- and single-helix DNA
examined in old classical works [46, 47] can be presented as:
, (7)
where М is a small molecule, and are single helixes, and D is a double helix.
According to the limiting model, during the melting M molecules are
released or are bound.
The equilibrium or self-assembly constant for the process (7) can be presented as:
.
The dependence of lnK on the concentration of small molecules, ligands, can be
defined from equation:
. (8)
The dependence of on melting point ( ) of the supramolecular structures
participating in equilibrium (7) is defined by the well-known equation:
. (9)
Equation (9) is correct when the change of enthalpy of the reaction does not
depend on temperature. This is quite true of type (7) processes. But the use of this
equation for the cases of self-assembly of different-type substances requires
additionally taking into account that for the different substances can be notably
different.
If all variables except do not depend on T, it can be assumed that:
17
. (10)
Values and in equations (9) and (10) belong to the kinetically independent
(cooperative) unit that takes part in the processes of melting and coupling (self-
assembly).
The presented type (9) and (10) dependencies can also be used if the calculations are
made for a unit of mass (volume) of supramolecular structures. In other words, if a
researcher do not like to use some mean values of , constant of self-assembly, (
), he or she may use the values and others. This is convenient, since it is not
easy to measure the concentration of kinetically independent units. In addition, this
value is not constant for different microvolumes of supramolecular structures. As was
already noted, in supramolecular thermodynamics, values , , and others are
designated as , , , etc. It should be noted that the values of “ “ and
“RT” in equation (6) and others should be related to the same units (mole, cooperative
unit, kinetic independent unit, gram, grams in liter and so on).
It is important that an increase of the concentration of small molecules in the
environment of DNA structures (chromatin) causes a rise of , if these molecules tend
to bind with double and not single helixes. When small molecules tend to bind with
single helixes, a decrease of is observed. In principle, this conclusion is true of any
supramolecular structures that contain DNA, RNA, proteins, polysaccharides, and many
other molecules [46]. Some aspects of the interaction between genetic structures and
small molecules are discussed in a short paper dealing with gene and aging
thermodynamics [48].
The author [5] demonstrated the existence of dependence using the
solidification (congealing) of a number of fatty acids with different and values
18
as a example2. The high-melting supramolecular structures or substances have, as a rule,
high values of and ( )3.
I would like to give the long-known examples [39]. Butterfat has a of 28-36 oC and
the heat of fusion 81.6 J/g. Cottonseed oil has a from –1 oC to –6 oC and the heat of
fusion 86.0 J/g. Peanut oil has a of -3 oC and the heat of fusion 90.9 J/g. Fully
hardened cottonseed oil (Iodine value ca. 1) has a of 40 oC and the heat fusion 185.0
J/g.
These high-melting substances (structures) with decreasing temperature of an
organism’s tissues (the temperature of the environment) are freezed out and their role in
the processes of metabolism and structure formation is decreased.
This conclusion fully corresponds to the classical equilibrium thermodynamic theory
of solutions. Thus, for ideal solution of a solid in a physiological liquid, by using the
Gibbs-Helmholtz equation, one can obtain:
, (11)
were x is the solubility of the solid, p - pressure, sat is saturated solution, is the
heat of solution of a mole of a substance in a saturated solution (differential or partial
heat of solution). For ideal solutions the heat of solution is equal to the heat of fusion
of the solid: . In accordance with equation (11) one can see that the
temperature dependence of solubility of solid is determined first of all by its heat of
fusion .
To demonstrate the effect of the change of the ratio of the concentrations of low- and
high-melting supramolecular structures during temperature changes in an organism’s
tissues, let us consider Fig. 3. The example presented in it can help foster belief in the
2 The presented example was complex and non-informational for understanding. However, the
conclusions were true.
3 However, the common dependence between and does not exist.
19
correctness of the thermodynamic theory as applied to open (quasi-closed at certain
points) systems.
Although the scheme presented in Fig. 3 is simplified it, strictly speaking,
graphically demonstrates the following. As the organisms’ body temperature (both in
ontogenesis and phylogenesis) goes down, the relative amount of fatty acids, fats
(lipids) and other supramolecular structures with increased and in the tissues of
these organisms should decrease in a greater measure than the relative amount of low-
melting structures. And the other way around, the relational content of supramolecular
structures with decreased and should go up as the organism’s temperature does
down. This is in line with the Le Chatelier - Braun principle.
Fig. 3. Temperature dependence of solubility of two substances . Illustrative ideal
model .
1 – palmitic acid ( = 61.8 oC, = 50.7 cal/g );
2 – oleic acid ( = 13.4 oC, = 25.5 cal/g );
20
x – solubility; - heat of solution; for ideal solution =
As was already noted, natural fats and oils with low-melting points (slip points) are
accumulated in the tissues of organisms with decreasing body temperature (temperature
of the environment). The fats and oils with low-melting points contain non-saturated
acid residues basically4. That is why the concentration of non-saturated bonds in these
products (their Iodine values) is increased with decreasing the body temperature of
living beings.
As was already noted, this important conclusion prompted by the theory is in accord
with a vast number of known facts [1, 49, 50]. Many new research findings can be
found in Internet.
This is a proper place to give a long-known example of the variation in the structure
and composition of collagen. It has been established that the temperature of
denaturation (melting point) of collagen in homothermous animals is close to their body
temperature, and in poikilothermous animals, to the temperature ceiling of their habitat
(i.e., the animal’s highest body temperature). Fig. 4 shows the dependence of
denaturation temperature ( ) of the collagen molecule on body temperature
(homothermous animals) or the temperature ceiling of the environment
(poikilothermous animals) [49, 50]. The presented dependence is in line with
correlations (11) and, of course, the data in Fig. 3.
4
? As a whole, one should take into account that the melting point generally increases with increasing
proportion of long chain fatty acids or decreasing proportion of short chain or unsaturated fatty acids.
Besides, the latent heat of fusion increases with increasing chain length and increasing degree of
saturation [39].
21
Fig. 4. The relationship of the denaturation temperature ( ) of collagen molecules to
the body temperature (homothermous animals) or to the upper temperature limit of the
environment (poikilothermous animals): (1) pig, parasitic nemathelminthic worms -
Ascaris and Acanthocephala; (2) human, rat, cow; (3) snail; (4) tuna; (5) cod; (6) ice-
fish.
Decreasing body temperature or the temperature of the environment promotes the
accumulation of low-melting collagen structures in an organism’s tissues. Thus, the data
in Fig. 4 also constitute irrevocable proof of the correctness of the thermodynamic
theory of evolution and aging.
There are also examples of “adaptation” of nucleic acids, their complexes, and
chromatin to the body temperature of homothermous living beings or the temperature of
the environment of poikilothermous living beings (cf. [3]). Due to its relative stability,
this DNA adaptation is observed extremely slowly and is not obvious at certain points
of an organism’s life. The RNA structure should adapt relatively faster. Nevertheless, it
turns out that in the process of phylogenesis (evolution), the organisms’ DNA (RNA)
structure changes noticeably as the temperature of the environment (and other factors)
change. All this confirms the general proposition of our physical (physicochemical)
theory of evolution: evolutionary changes in the biological world (and in inorganic,
non-living nature) are determined by internal (the organisms’ genetics) and external
(parameters of the environment) factors. The relative contribution of these factors
depends on the selected time scale (as we observe some changes or others) and the
stability of the examined structures. This is a manifestation of the unity of general laws
of nature (the law of energy conservation, a private case of which is the first principle of
thermodynamics, the second principle of thermodynamics, and the law of temporal
hierarchies).
5.Genetic regulation of development
22
It is assumed, with good reason, that most multicellular plants and animals begin
their life cycle with one cell, a zygote (fertilized ovum). Multiple mitotic divisions lead
to the formation a complex highly differentiated organism. This process is called
growth and development, and involves differentiation. As a result of the latter, a cell
acquires a certain structure and, multiplying, produces other cells of the same type.
Various tissues (organs) are formed in a multicellular organism, and a complex
organism evolves. The origin of this phenomenon is not clear [51]. However, growth
and development are certainly linked to gene induction and repression. It is assumed
that differentiation manifests itself through complex interactions among the cell’s
nucleus, cytoplasm, and environment. Various stages of the differentiation mechanism
have been examined in literature. Naturally enough, there are many of them.
The phenomenon of differentiation has not, on the whole, been examined in terms of
thermodynamics. The thing is that there used to exist a ban of sorts on the use of
classical (equilibrium) thermodynamics for revealing the “motive forces” of
differentiation. It was connected mainly with the open character of the living
biosystems. It should be noted that at the same time, classical thermodynamics was (still
is) widely used in the study of closed “laboratory” biological systems” [46]. The rapid
headway of bioorganic physical chemistry and the other adjacent disciplines is
associated with this circumstance.
As was already noted, in the past few years it became possible to make a
substantiated study of open living systems with the help of thermodynamic
(thermostatic) quasi-closed models. The latter are analogues of the models of
chromatographic systems based on the use of methods of classical thermodynamics
[52].
It is indicative that the processes of growth and development can be examined in
terms of the change of the specific Gibbs function during cell differentiation, etc.
It is known that all cells in an organism contain the same genes. But only some of
them function during differentiation. This leads to the formation of different tissues.
23
6. Embryonic development
Embryonic development begins with fertilization and is made up of cleavage,
gastrulation, organogenesis, and the emergence of the functions of the organs’ tissues.
During cleavage, an equi-hereditory nuclei division takes place. But the division of the
cytoplasm, which differs depending on the part of the ovum, is not equal. These primary
distinctions in the cytoplasmic environment of the ovum are believed to determine the
early stages of the embryo’s differentiation. During gastrulation, the embryonic leaflets
are separated and an overall plan of the organism’s structure (a “holographic” blueprint)
is formed. Than during organogenesis the appearance of tissue germs and organ systems
in embryonic leaflets take place. Although the embryo’s cells receive the full
complement of genes during division, only some of these genes function in each type of
tissue.
After division, each cell finds itself in an “environment of its own,” which has
certain specific properties. The latter may be connected (directly or indirectly) with
water concentration in the system, the amount of carbon dioxide, oxygen, and other
components of the atmosphere, the presence of biologically active hormone molecules
and other metabolites, and with a number of other factors. The latter include
temperature, the intensity and spectrum of penetrating radiation, and the values of
electromagnetic gradients. It is assumed that these factors can affect differentiation
through the cytoplasm, which, in turn, affects genes. There is reason to assume that the
distinctions between these factors arise from the different position of cells in a living
heterogeneous system.
A simple analogy between the position of a cell in developing embryonic tissue and
the growth of a plant (e.g., tree) leaf would be in order here. The growing leaf orientates
itself in space guided by the maximum intensity of the solar energy flow. The amount
of the solar energy accumulated by the leaf is determined by both the direct access of
sunlight and the flow of dissipated light, which depends on the spatial position of the
24
leaf among its neighbors (other leaves). The latter perform the role of components of
the inner environment of the leaf in question. They are, if you will, the surrounding
“cells.” This analogy makes it easier to comprehend the phenomenon of the
differentiation and development of an embryo’s cells.
If we approach the issue from the stand of supramolecular thermodynamics, a
question would arise: are the seemingly minor changes in the biomass micro-volume
during embryonic development sufficient for affecting the thermodynamic direction of
differentiation and development? The answer is clear: quite sufficient. Numerous facts
described in manuals and monographs confirm this opinion. Thus, insignificant
temperature fluctuations can produce a noticeable change in the morphological structure
of tissue, because kinetically independent particles (along with low-molecular ones) are,
here, constituted by enormous supramolecular formations. Their rearrangement or
redistribution in the system is easy to see with a naked eye. It is clear that minor
temperature changes (around several tenth or hundredth of a degree) can significantly
affect the transformation of the gene structure. What is more, they can substantially
change the rate of synthesis of individual enzyme processes due to their high energy of
activation.
Insignificant fluctuations of PH and the concentration of various substances are also
known to affect the functioning of genes (chromatin). The differences in PH can be
determined by the location of dividing cells.
Having appeared “in a place of its own,” each new cell finds itself surrounded by
other cells in physiological (intercellular) liquid. The other (previously formed) cells
and the physiological environment are the habitat (thermostat in the physical sense of
this term) of the new cell. According to the parameters of the habitat, the cell’s genetic
apparatus is “transformed”: only certain genes go into action. Another division follows,
and the new cells receive a new command from its thermostat, etc.
Each cell (chromatin) micro-local volume (i) has “thermodynamics of its own”
determined by the trend of towards minimum. The local micro-volume must contain
a sufficient number of particles (low-molecular substances and kinetically independent
25
fragments of supramolecular structures) to make the laws of statistics and,
correspondingly, the second law of thermodynamics applicable.
Since thermodynamic laws operate in each local micro-volume, equation (2) is
applicable to any tissue macro-fragment.
7. Individual facts
Examples that confirm the possibility of regulating gene activity under changes in their
environment include the studies of chromatin transformation under the impact of
chemical agents and physicochemical factors [53, 54]. Even insignificant fluctuations of
chromatin’s environmental parameters result in its observable changes.
Heterochromatinization of chromosomes is observed in ontogenesis and is a fact that
determines an organism’s aging (development) [53, 54].
Convincing proof of the influence of the cell membranes’ structural component,
lipids, on gene transcription is provided by numerous experimental studies [55]. It has
been proved absolutely that lipids perform an important role not only in signal
transduction and intercellular transport, but also in gene transcription. Since living
organisms (their biotissues) quickly adapt to the character of fats and oils used as food
[56], it is clear that the character of nutrition affects the work of the genetic apparatus.
Such effect can, in principle, result not only in the transformation of the work of the
genetic apparatus but also gradually fix individual genetic characters. The latter accords
with the existence of feedback between the biostructures in different hierarchies [1, 18].
A well-known example is animals changing their coloring with a change of the
environment’s background coloring. Some rodents’ changing their fur color at
insignificant temperature changes (around 1C) have been described.
The optimal rate of the germination of seeds of some plants also frequently lies
within the 1C range of temperature fluctuations. A commonly known fact is the effect
of insignificant temperature changes upon the function of testes in animals and humans.
26
All this confirms the high sensitivity of genes to the changes in the parameters of their
intracellular environment and the environment of cells and organisms.
There is no doubt that all phases of the process of embryonic development are
governed by thermodynamics. Thus, the “mitoticspinalle” model viewed as a self-made
machine can be presented as a series of consecutive stages of structure formation. The
implementation of each of these stages can, without question, be regarded as a process
directed towards a decrease of in each local zone of the developing structure.
Unfortunately, many researchers continue to believe that “the biochemical and physical
principles that govern the assembly of this machine are still unclear. However,
accumulated discoveries indicate that chromosomes play a key role”[54]. It would, of
course, be interesting to examine the stages of the functioning of the self-made machine
using the DSC method and others.
There is reason to believe that the genome of embryonic stem cells retains
totipotency, the ability to choose an appropriate development program [57], which, in
my view, is determined by the functioning of genes through the “mechanism” of
thermodynamic demand. It has been established that there exist totipotency proteins that
help preserve the special structure (conformation) of chromatin. It is also believed that
the design of a future organism is written down in the totipotent cells in the language of
mRNA.
It is known that supramolecular structures are often formed without direct
participation of, for example, the structures of nucleic acids and proteins. Thus, the
“protein - RNA interactions are mediated by the specific recognition of widened major
groove and the tetraloop without any direct protein-base contacts and include a complex
network of highly ordered water molecules” [58]. This confirms yet again the need to
study the changes in the specific averaged values of thermodynamic potentials
(functions) within the framework of supramolecular thermodynamics. The latter’s
action should extend to all types of supramolecular structures interacting in a living
organism. Proof of this are the numerous proven facts studied by information biology
27
and medicine. A number of physically substantiated examples can be found, for
instance, in the monograph [59] and the work [60].
In my view, both the information theory and supramolecular thermodynamics
support the theory of Poitevin [61]. He believes that an organism is a sum of interacting
systems that exchange information in the course of rhythmic action. A special place is
allocated to electrical and chemical signals. The organism is treated as a generalized
information exchange system. In such a living system, the distinctions between the
brain and the other parts of the organism are disappeared (no “distinction between mind
and body”). This point of view corroborates the theory on the establishment of partial
chemical and supramolecular equilibrium in the organism and the helpfulness of
studying the summary variation of the chemical composition of both individual tissues
and the organism at large [1, 2, 62]. As the author wrote in his earlier works, such
variation is a consequence of the thermodynamic direction of the evolution of
supramolecular structures, as well as the higher hierarchical levels of the biological
world.
The environment also determines behavioral reactions at the level of organisms and
populations. Operating here, however, are not only physicochemical factors but also all
the parameters of the thermostats of complex thermodynamic systems. In human
societies, human behavior is also affected (apart from the known material factors) by
the parameters of Popper’s 3rd world [63].
Although my conclusions are general, they show that there are no principle
contradictions between known facts and the conclusions of supramolecular
thermodynamics on the trend of differentiation processes. It follows that this trend is
determined by “thermodynamic demand” for genes on the part of the environment
(structures of higher hierarchies), which stimulates (induces and represses) the genes’
directed functioning.
Thus, the overall potential program of cell differentiation is contained in genes.
However, this program is transformed (corrected) under the impact of the environment.
28
It is determined by the parameters of the environment (the medium) of the genes
themselves.
Thus, the thermodynamic model of cell differentiation and the behavior of
organisms, populations, and higher structures of the biological world does not, of
course, make it possible to draw conclusions regarding the mechanisms of processes.
But it can help identify their direction and degree of advancement of processes (the
extent of processes). Awareness of the thermodynamic (thermostatic) aspects of the
development of open biological systems can be useful for comprehending the
phenomenon of life within the framework of general laws of nature.
8. Macrothermodynamics and the functioning of the brain
The macrothermodynamic model is based on the segmentation (split-up) of
any living (and non-living) heterogeneous system in the set hierarchy into a sum of
quasi-closed macrovolumes (or identified masses), each of which has “local
thermodynamics” of its own. These macrovolumes interact. As a result of linear
superposition of many different alternative arrangements of attaching structures, the
values of the function of state are averaged, and this entitles one to talk about these
functions’ specific values. This idea of the possibility of averaging [1, 26] conforms to
R.Penrose’s hypothesis that, as the mechanism of cerebral links, the mechanism of the
growth of quasicrystals is connected with the “quantum linear superposition of many
different alternative arrangements of attaching atoms (by the quantum procedure U)”
[17, p. 437]. Refraining from a discussion of terminology and superposition
mechanisms, one can say that Nature seeks out a crystalline configuration or another
arrangement of configurations (conformations) of molecules (taking part in the
formation of the structure of the macrovolume) which matches the lowest level of
Gibbs function for the macrovolume under consideration. The problem of
minimization must be dealt with among a large number of atoms, molecules, or
molecular fragments with account of their co-operative effort. According to Penrose,
29
this effort must have a quantum-mechanic origin; the way this is done is by many
different combined arrangements of atoms being “tried” simultaneously in linear
superposition. This “trial” is perhaps a little like a quantum computer. Needless to say,
these combined arrangements are formed at atomic and supramolecular levels or, to use
a trendy word, at nano level. What is more, minimization of the Gibbs function takes
place with participation of atoms, molecules, and supramolecular formations located at
distances that far exceed the nanolevel (the n-level). This well-substantiated point of
view is in accord with the many outstanding works by J.-M.Lehn and his colleagues
[20], who laid down the foundations of supramolecular chemistry, a discipline of the
future.
The discussed model should not provoke opposition from physicochemists. It is in
accord with brain plasticity as interpreted by Penrose, who regards the brain as a
formation that resembles a computer which is continually changing, taking account of
the feedback that arises between the system proper and the environment. Also, using
physicochemical lingo, the existence of critical values, such as the level of
supersaturation, is assumed. Needless to say, to understand how the brain functions, one
has to take account of the feedback, since it is not enough to factor in only the
minimization of Gibbs function caused by the brain receiving signals from the external
environment. The emergence of thought, that is, conscious thinking, is connected “with
resolving out alternatives that were previously in linear superposition” [17, p. 438].
Penrose believes that “this is all concerned with the unknown physics (processes, not
laws. – G.G.) that governs the borderline between U and R and which … depends upon
a yet-to-be discovered theory of quantum gravity – CQG! According to Penrose the U
part of quantum mechanics has a completely deterministic character, the R “quantum-
jump” part is not deterministic, and it introduces a completely random element into the
time-evolution. I am convinced, however, that these physical processes, which are
apparently non-algorithmic, hold also be governed by the laws of
macrothermodynamics ! In terms of this discipline, the non-algorithmic elements can be
explained by the joint operation of the “inner thermodynamics” of the brain’s thinking
30
structures and the thermodynamics of the continually changing environment (whose
parameters vary around middle values, which does not preclude regarding the thinking
structures as quasi-closed). One may hope that macrothermodynamics “will bridge the
gap between the treatment of the issue in terms of physics and physical chemistry, on
the one hand, and structural and synthetic chemistry, on the other” [20].
The new publications and Internet materials known to the author are not at odds with
either the more general ideas formulated by R.Penrose and J.-M.Lehn or my
thermodynamic models [1, 29-33].
9.The formation of quasicrystals and the cluster structure of polymers
confirm the effectiveness of macrothermodynamics
A number of known facts indicate that it would be sensible to identify, in
heterogeneous systems, macrovolumes characterized by specific (averaged) values of
the Gibbs function of supramolecular interactions. It was noted in the previous section
that if quasicrystals are formed, such macrovolumes are large, and the averaging of
local equilibrium takes place not only at nanolevel but also on a larger scale. The
averaging values of the macrovolume functions of state for any large systems (e.g.,
populations) containing a large enough number of structures of the hierarchy under
consideration is also justified, since all the identified macrovolumes, as well as their
sums, can be treated as quasi-closed systems.
The first quasicrystals, crystals with a forbidden non-Fedorov symmetry group (with
fivefold symmetry – icosahedral symmetry) were discovered in 1984 [64]. These
quasicrystals were characterized by remote orientational order and the absence of
translation symmetry. Then it was established that there are quasicrystals with
metastable and with equilibrium structure. The latter appear as a result of slow cooling
of relevant crystallizing systems [65]. Crystals were obtained with eightfold, tenfold,
12-fold symmetry, also forbidden for Fedorov’s symmetry groups. The former models
of quasicrystals were build using Penrose’s tiling patterns.
31
The existence of remote local order (according to G. Kozlov, “short-range local
order”) of thermodynamic origin in amorphous polymers was proved by G. Kozlov et
al. [66].
It can be shown that the formation of cluster structure of polymers is consistent with
"Gladyshev's evolution theory of hierarchical systems [66]". Experimental verification
of the physicochemical theory of chemical system evolution was undertaken based on
the correlation between the Gibbs specific function of supramolecular (intermolecular)
interaction (the superscript "im" points out the intermolecular or, as in this case,
intersegmental nature of interaction) and the melting temperature of polymer
structure. The choice of these parameters has been substantiated in Refs [67].
As is well known, the Gibbs-Helmholtz equation is true for the processes taking
place in simple closed systems:
, (12)
where and are change of the Gibbs function and enthalpy, respectively, is
the temperature, p - the pressure.
If is assumed independent of T in a given temperature interval, the following
equation holds for the non-equilibrium phase transition, i.e. self-assembly of an
individual substance, at temperature :
, (13)
where is the change in the Gibbs function during crystallization (self-assembly)
of substance being studied from the overcooled state at , is the change
of enthalpy in the course of crystallization (solidification), and is the crystallization
entropy (the entropy change during phase transition).
It was suggested that Eqn (13) should also be used for open system in which
neither the composition nor is subject to significant alteration. Later studies
demonstrated the possibility of applying this equation to various chemical compounds
having melting temperatures 100 oC and undergoing condensation at a constant
32
temperature (25oC) [1, 2, 67, 68]. With a stricter approach, for these cases Eqn.
(13) should be written in the form:
, (14)
where the subscripts i = 1, 2,…, n refer to different substance. Equation (14), it was
Eqn. 4 before, is an analogue of Equation (13) in terms of form. In other respects, these
two equations are basically different in that the latter (Equation 13) contains a variable
characterizing the non-equilibrium transition of an individual substance in the
system at any temperature . The values of , , refer to this individual
substance and are assumed to be constants. On the whole, however, Eqn. (13) represents
a functional dependence . In Eqn. (14) the variable is related to non-
equilibrium transition of various compounds with different melting temperatures at
a constant (standard) temperature . In this case, Eqn. (14) represents the function
. Sometimes Eqn. (14) is define as Gibbs-Helmholtz-Gladyshev equation
[66].
The authors Ref [66] presented the figure with shows the dependence of on
for amorphous glassy, amorphous-crystalline, and cross-linked polymers.
As expected, decreases linearly with increasing (in fact, - glass transition
temperature). It is even more important that the straight line in author's figure, which
fairly well approximates the results of the study, is consistent with the findings of
papers [12, 67] presented as the plot of versus for quite different chemical
compounds, but with the coefficient 10:1 along the axis [66]. This is due to the
difference between the molar volumes of the segments (i.e. kinetically independent
fragments) and compounds used in Ref [69], which amounts to approximately one order
of magnitude. In principle, this allows one to compute the size of the segment, which is
unlike in different polymers.
The G.V.Kozlov's and V.U.Novikov's [66] data indicate that the cluster model
based on the assumption of local order in the amorphous state of polymers is in good
33
quantitative agreement with "a much more general macrothermodynamic hierarchic
model and occupies a relevant energy niche in the hierarchy of real word structures"
[66]. The plot of work [66] readily illustrates the tendency of structural evolution of a
physically aging polymer. With the trend in the polymer structure to equilibrium, Gim
tends to a minimum (i.e. sifts towards negative values). A concomitant
enhancement of local order is accompanied by a rise in [70]. Equally possible is
polymer "rejuvenation", i.e. a process thermodynamically opposite to that considered
above. In practice, it is realized through “pumping” mechanical or other energy into the
polymer [71] .
It may be concluded [66] that the dependencies Gim=f(T) for polymer
suprasegmental structure obtained in the framework of macrothermodynamic hierarchic
model are consistent, both qualitatively and quantitatively, with the analogous
correlation for a wide variety of chemical compounds reported in earlier studies [3, 69].
This confirms the reality of these structures in the amorphous polymer state. Equation
(13) and (14) are equally applicable to the description of thermodynamic behavior of
these structures and can be used for their quantitative simulation. If stricter calculations
are needed, corrections for variations of thermal capacity during phase transition can be
introduced [1-6].
The macrothermodynamic approach can, hopefully, indicate the direction of the
evolution of other artificial and natural quasi-closed systems, probably including the
ones of most interest to humans, biological systems.
Additional information can be found on the Internet: http://www.endeav.org/evolut
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