The hierarchical equilibrium thermodynamics of living systems in
This article is dedicated to several aspects of thermodynamic (thermostatic)
model of biological evolution and aging of living organisms. Work in this
sphere was begun in 1975 (Gladyshev, 1978). Since then many experimental
results have accumulated that confirm the author’s theory.
The current article is not a survey of achievements in the sphere of
biological evolutionary theory and the development of biological systems.
The author refers only to research, which has a direct bearing on his model.
References to works which discuss other models of evolution and development
of the bio-world (from the position of synergetics, information theory,
kinetics, non-equilibrium thermodynamics and so on) may be found in a series
of surveys such as that in the article of Dr. Brooks (D.R.Brooks, 2001).
1. Natural Phenomena Models
"Mathematics is the language of science". This well-known phrase is
tied to G. W. Gibbs, creator of the strictest precise physical theory.
Indeed, in every age, researchers have tried to describe natural phenomena
in the language of mathematics and to quantitatively characterize relationship
facts discovered. It is only possible to establish relationship facts within
the models, which are exact only by definition and correspond to reality
in some degree. Generally, models are created in order to describe the
processes observed in given scales of time, energy, space and chosen structural
hierarchies. Therefore, it is not mere chance that, in science, nuclear
transformations, chemical and supramolecular interactions, biological,
social and other phenomena are considered separately.
The division of science into separate disciplines is justified from
the position of mathematics being a language of science. Such a division
allows the use of idealized linear models and the comprehension of the
physical essence of phenomena.
When one fails to create linear models, non-linear models are require.
If we can not isolate a specific hierarchy of structures, scale of time,
scale of energy and scale of space, we can only investigate a system as
a complicated non-linear system.
From this point of view, any observed complex "mixed" phenomena require
a non-linear description. Hence, when a researcher does not intend to or
is unable to create linear models, he uses non-linear models, which, because
they are not generally amenable to precise solution, distance us from the
physical, chemical or biological details of these phenomena. This circumstance,
despite the non-linearity of our world was well understood by the classicists
of natural science who, in the first instance, tried to depend upon linear
models. In using non-linear models, we somehow approach the sphere of mathematical
modeling, i.e. we move to the area of synergetics if one connects its approaches
It should be noted that synergetics is often defined as a branch of
science, which studies the relationship facts of origin and development
of temporal and (or) space structures. However, the said structures and
their transformations can be conceived and described from the position
of either linear or non-linear models.
We can use linear models, for instance, to talk about thermodynamic
self-organization (G. Gladyshev) - self-assembly of various hierarchical
structures or about dynamic self-organization or simply self-organization
in I. Prigogine's terminology.
From the point of view of thermodynamics (thermostatics), thermodynamic
self-organization investigated via functions of state, i.e. functions with
full differentials. Dynamic self-organization is characterized by kinetic
functions and cannot be described in terms of classic (equilibrium) thermodynamics.
If we compare linear models of classical science with non-linear synergetical
models, the following is evident. Linear models make it possible to establish
details of any phenomena, for example to "reveal" their physics and easily
quantitatively "coordinate" these phenomena with the general laws of nature.
As stated above, non-linear models, as a rule, distance us from the details
of the phenomena and push us into mathematical modeling which may be inefficient
from the point of view of understanding phenomena in terms of general laws
of nature. However, in many cases, such an approach allows to resolve important
Science makes use of different approaches and models. This allows us
to recognize the world around us. So, it would hardly be reasonable, as
has become fashionable, to declare that synergetics is the "cutting-edge
of science" and to disregard the classic approaches. Classic scientific
methods have reached the highest summits and shown themselves to their
advantage over the ages. Modern synergetics, whilst undoubtedly an attractive
and important area of research, has to "cleanse itself" of the elements
of "superficial" mathematical modeling and reveal new, truly rational,
constructive models of world recognition. The best criterion of quality
of any theoretical model is the strength of its foresight and possibility
of appraisal of observed and predictable characteristics in the language
of computation, i.e. that of figures.
2. Open systems examined by methods of equilibrium thermodynamics
The second half of the 20th Century has been characterized
by a series of misunderstandings in the field of the natural sciences.
Many researchers, following fashionable tendencies, contended that it was
impossible, in principle, to apply methods of classical thermodynamics
(thermostatics) when studying open systems
and, above all, biological systems. Moreover, on the basis of this conviction,
conclusions were reached regarding the impossibility of applying the second
law of thermodynamics in its classic formulation in the explanation of
the origin and evolution of life (Prigogine 1980; Gladyshev 1997; Shu-Kun
Lin 1999: 101). The above-mentioned situation facilitated the development
of approaches exploiting methods of mathematical modeling, which, however,
had nothing in common with the physical essence of the phenomenon of life.
A lot of work appeared which brought about confusion in the use of terms,
for example, such as entropy. For instance, the classic entropy of R.Clausius-J.W.Gibbs, is
often identified with the informational entropy of C.Shannon, .
All this led to many articles in scientific journals containing unwieldy
mathematical expressions and, in principle, complicated unverifiable experimental
If one took a step back and looked at this unfolding situation, one
could come to the conclusion that science had changed into its own particular
version of a “strange attractor”.
However, luckily, this was not so!
The number of researchers understanding the mistakes inherent in the
above-mentioned fashionable tendencies relating to the natural sciences
was constantly growing. So, the editor-in-chief of the new scientific journal
“Entropy”, Dr. Shu-Kun Lin writes in the editorial (Shu-Kun Lin 1999: 1):
“....it is no surprise that an honest chemist (among other educated chemists,
biologists, etc.) will tell you that he has never found an application
of this entropy theory in chemistry (or in biology, physics, engineering....)”.
The author has in mind “Prigogine’s dissipative structure theory”. He also
comments: “I have a clear opinion regarding this entropy theory. Its main
problem is that it does not conform with the Second law of thermodynamics”.
To differing degrees, this point of view is shared by many researchers,
for example, the author of the present publication, Dr. K. Denbigh (Denbigh
1989) and others (Gladyshev 1997).
It is important to note that, in the general case of Dr. Ilya Prigogine’s
entropy, it is a kinetic function insofar as its differential is not total.
In any case, this entropy does not identify with the entropy of R.Clausius
and J.W.Gibbs (Gladyshev 1997; Denbigh 1989).
Moreover, in parallel to the birth of the “fast-ripening” fields of
research, scientific directions oriented towards the solid foundations
of classicism were developing. Such fields, undoubtedly, encompass many
divisions of physical chemistry, as, for example, that of chromatography
The chromatographic method is based on the separation (the partition)
of chemical substances. It is linked to the separation of the substance
being examined between two phases – stationary (immobile) and mobile. The
stationary phase in the chromatographic column is usually a sorbent with
a developed surface. The mobile phase – a stream of gas or liquid (fluid),
which filters (moves) through the layer of sorbent. A typical chromatographic
system consists of a column containing sorbent, and a liquid substance
or a solution (a mixture of different substances), flowing into the column
Let’s ask a naive question. Is the chromatographic column an open system
in itself? The answer is clear; it stands to reason that this is an open
If the sorbent in the column has certain catalytic activity qualities,
then such a column may sustain chemical reactions between components of
the solution (gas) entering the column. It is also possible that there
will be chemical interaction between the components of the mobile and stationary
phases. In this way, such a column may sustain chemical reactions, which
also have their place in living organisms (Fig. 2).
Any educated biologist, chemist or physicist will be well aware that
processes occurring in effective chromatographic columns, are with a good
approximation, in a state of thermodynamic equilibrium. In other words,
such chromatographic columns are quasi-equilibrium steady state systems.
Fig. 1. Liquid chromatography column in which chemical reactions do
not occur. In the column steady state is established.
It is possible to regard an organism’s tissues as systems containing
a multitude of micro-chromatographic columns. Moreover, the nature of both
the stationary and mobile phases of these columns differs substantially.
At the same time, the effectiveness of such natural micro-columns must
be extraordinarily high.
When moving in the stream of the mobile phase, the components of the
original mixture, and also the substances synthesized in the column, move
along the column at differing rates. These rates are in inverse proportion
to the distribution constant of
the substances undergoing chromatography. Components with a high affinity
to the stationary phase, whose distribution constant significance is high,
move along the column more slowly than components with a low affinity to
the stationary phase. The fastest mover along the column is the component
with the smallest rating.
If we investigate the action of the column using the length of the delay-time
or retention time (the length of time the substances in question remain
in the column) ,
then it is convenient to use the well known correlation
coefficient which changes evenly during the evolution of the composition
in the stationary phase, for example, the biosystem (in principle, each
micro-volume is characterized by its coefficient ),–
absolute temperature, -
specific (averaged by volume or mass) Gibbs function (the Gibbs free energy)
of formation of supramolecular (intermolecular) structures, appearing as
a result of interaction between particles found in the mobile and stationary
phases. The sign "-
" means that the specific value is considered and the sign "~" points
out the heterogeneous nature of the system.
If substances with a high affinity to the sorbent are injected into
the column or are synthesized in the column continuously, then they will
accumulate in the column. Such a column, according to its components, the
concentration of which increases in the column, may be regarded as partially
kinetic quasi-closed. This column, as a living system, is enlarged and
its volume and mass are increased (Fig. 2). If the substances accumulating
in the column are capable of reproducing themselves, then their concentration
in the system will grow rapidly, a process which will noticeably change
the chemical and supramolecular compositions of the substances, playing
a role in the stationary phase.
It is also possible to use chromatographic methods to separate organelles,
cells and other bio-structures. The chromatographic systems studied by
chemists are analogues of living systems (Fig. 1 and 2).
The application of classical thermodynamic methods in order to investigate
dynamic systems under consideration is entirely correct, independent of
whether they are stationary, quasi-stationary or non- stationary! Moreover,
it is obvious that the equilibrium separation of substances in the column
does not depend on the degree of non-equilibrium of the chemical transformations
in the column, if applicable (Gladyshev 1999a,b; Porter 1983; Tanford 1978).
Fig. 2. Living chromatographic column in which biochemical reactions
There is the steady state in the column. At times, which are much more
than the average lifetimes of cells, the column is a non-stationary system.
The column is enlarged and its mass and volume
are increased. Small arrows means that a system is enlarged.
As far as studying the dynamics (kinetics) of changes in a substance’s
nature in the biological “columns” is concerned, it is advisable to investigate
the changes during
ontogenesis, phylogenesis or evolution of supramolecular structures. It
is understood that such an approach gives no information regarding the
mechanism of the process. However, it does give information regarding the
extent (degree of advancement) of the processes, for example, such as that
of tissue aging in living organisms.
However, one must not forget that rational applications of the methods
of equilibrium thermodynamics in order to investigate the open systems
under consideration needs certain limiting conditions to be fulfilled.
One of the fundamental conditions is connected with the constancy (invariability)
of the concentration of components of the solution or gas entering the
This condition, as is obvious from the standpoint of the thermodynamic
theory of evolution and aging of living beings, needs the provision of
a thermostat (in the wider sense of this term, as used in physics) for
the open system (Gladyshev 1995, 1997; Sychev 1986). In fact, this thermostat
is the environment that surrounds this very system. This thermostat is
characterized by constancy (invariability) in all thermodynamic parameters.
These parameters are temperature, pressure, intensity of physical fields,
concentration of chemical substances, etc.
We note that in the thermostats of living systems, these parameters,
although they vary in adaptive zones, retain more or less constant values
for comparatively long periods of time (Gladyshev 1997, 1999a). This is
a consequence of the general law of Nature – the law of temporal hierarchies
in the biological world (Gladyshev 1978, 1995, section 4 below). Let’s
also direct the attention of the reader to the fact that with respect to
chromatographic separation of substances, even chemical laboratory conditions
can support the values of temperature, pressure and other parameters relating
to the environment surrounding the column with limited precision. It is
understood that this precision corresponds in part to the lesser variations
with respect to different parameters of the thermostat than is the case
with many real biological systems, which exist for any length of time.
All the same, in all such cases, we are dealing with one or another open
system model - models that are studied using the methods of equilibrium
thermodynamics (Fig. 1 and 2).
Why is it that many researchers paid no attention to existing, constructive
scientifically based approaches toward understanding the origin of life
and evolution of living beings from the standpoint of physical chemistry
and, in particular, supramolecular thermodynamics? This is a complex question.
In my view, above all, the answer is dependent upon the circumstance that
science has become a mass phenomenon and many researchers, orienting themselves
towards the “declared fashion”, hope to achieve a “fast” result. Additionally,
it may be suggested that the majority of physical chemists do not wish
to dissect the mistakes of others and prefer to carry out their own experiments,
guided by classical scientific foundations.
3. Chemical and intermolecular interaction in biological systems
It is generally known that living systems consist of molecules, particles
capable of independent existence, formed from two or more atoms. Atoms
in molecules interact by means of chemical bonds, the energy of which varies
within broad limits. For example, within the nitrogen molecule, the energy
of the bond between atoms approaches approximately 1000 kJ/mole, whereas
the bond between atoms of carbon in different biopolymers and biomolecules
would generally vary between 150-300 kJ/mole. In the conditions in which
living organisms exist, these bonds are quite stable insofar as their energy
(energy essential for their decomposition ) is high in comparison with
the energy of molecule movement, characterized by the value ,
Boltzmann's constant, –absolute
An organism, consisting of different organs and tissues, is a “complex
living polycrystal”, formed from a diversity of molecules. Molecules unite
in supramolecular formations, examples of which are the double helixes
of DNA, the structures of proteids, and also chromatin and others.
Intermolecular interaction between separate atoms belonging to different
molecules is comparatively weak. As a rule, the energy of their interaction
does not exceed around 20 kJ/mole, although in individual cases, it does
reach a magnitude in the order of 40 kJ/mole. Such bonds within biological
systems, which always contain water, may comparatively easily be decomposed
as a result of changes in a number of parameters of the system, such as
temperature, environmental PH, ionic strength of the solution, and
also upon changes in the composition of the surrounding environment.
Thus, in tissues and bio-structures of living beings (as in many inanimate
systems), chemical and intermolecular connections differ substantially.
This allows the independent study of processes not only connected with
the decomposition and appearance of new chemical bonds in systems, but
also of processes of transformation of supramolecular structures, formed
by intermolecular interactions. The first type of transformation should
be ascribed to chemical processes, and the second to supramolecular processes.
Therefore, it is essential to differentiate between the change (the variation)
in functions of states of systems, connected with both chemical and supramolecular
transformations. Such a division of functions of states of systems in respect
of the components is apparently generally accepted and agrees with our
experience in the natural sciences. It allows the study of the thermodynamic
behavior of supramolecular structures independent of chemical transformations
within the system.
4. The law of temporal hierarchies
A look at the world around us shows that the average lifetimes (life-spans)
of bio-molecules, supramolecular structures, cells in tissues; organisms;
populations form a number of strong inequalities. Thus, the lifetimes of
amino acids in tissues (from the moment they appear in the cell up to the
time of their participation in chemical transformations) are substantially
shorter than the lifetimes of protein macromolecules in cells. In turn,
the macromolecules exist in the bio-tissue cells for a short time in comparison
with the lifetimes of the cells themselves. The cells live for a significantly
shorter period than the lifetime of the organism, and the lifetime of the
organism is a lot shorter than the lifetime of the populations they create.
It is clear that the indicated conformity to natural laws lays down
the conditions for the possibility of the metabolism. This conformity to
natural laws cannot be deduced from any well-known principles (Gladyshev,
1997, 1999a, 1999b). From this, it follows, that the series
is a general law of nature. Here t – average lifetime
of “free” molecules-metabolites (m), supramolecular structures (im),
organells (organell), cells in the tissue (cel); organisms
(org); populations (pop); societies (soc).
It is easily shown that the existence of series (1) allows us to pick
out the summation of structures of one hierarchy as a subsystem and to
consider this subsystem as a quasi-closed system. It is understood that
in order to study such a system, it is possible to use the methods of equilibrium
hierarchical thermodynamics (Gladyshev, 1997). For example, insofar as
cells live for a far shorter time than organisms, one may consider that
the organisms’ (organ’s) medium practically does not change during the
lifetime of the cells. This medium fulfills the role of a thermostat for
the quasi-closed subsystem (system) of the organism – cells.
It is necessary to bear in mind that each species of living being (tissue,
types of cell, types of organell, etc.) is characterized by its lifetime
values of the elements of the different hierarchical structures. However,
for all lower level hierarchies of living systems, which are part of a
higher level hierarchy (population, organism, organ, cell, supramolecular
formation, and so on), series (1), sometimes known as Gladyshev’s law,
This law can be formulated in another way: “Any living system of
any hierarchical level in a normal state has a thermostat - a surrounding
medium which is characterized by slightly changing average values of thermodynamic
The main reason for this statement is connected with the phenomenon
of metabolism. Lower level hierarchical structures are often reproduced
in a medium of higher level hierarchical structures during the lifetime
of the latter. Thus, we have:
average lifetime of structures of lower hierarchical level, -
average lifetime of structures of higher hierarchical level.
The existence of low (1-2) allows us to use quasi-closed thermodynamic
models to investigate living systems.
5. Model of biological evolution at the molecular level
Under the influence of solar energy, substances which were thermodynamically
stable under the conditions of a young Earth were transformed (as, indeed,
they are transformed today) into various products of photosynthesis (Porter
1983). Then, as a result of spontaneous "dark reactions” in accordance
with the laws of chemical thermodynamics, these products are transformed
into different substances. The selection of the indicated substances is
“made” by kinetics in accordance with these very laws. According to the
laws of local supramolecular (im) thermodynamics of quasi-closed
systems, from the whole spectrum of chemical substances (thanks to the
tendency of the supramolecular components of Gibbs function, ,
biostructures towards the minimum), the more stable superstructures, which
accumulate in micro- and macro-volumes of systems, are selected (Gladyshev
1978, 1999a, 1999b). Individual macromolecules and superstructures become
reduplicated, owing to the possibility of matrix mechanisms.The first to
be selected are nucleic acids, the composition and structure of which (owing
to the action of thermodynamic factors) slowly adapt themselves to the
nature of the surrounding, including that of proteins, whose composition
is determined by DNA itself. This explains the existence of feedback between
the structure of proteins and DNA. In accordance with our model, such feedback
has its basis in thermodynamics.
Running parallel to the processes of synthesis, there occur processes
of degradation relating to the decay of chemical compounds. However, living
systems oppose this and try to maintain their state. This tendency also
has a thermodynamic character. Biosystems reproduce dying supramolecular
structures. Additionally, as has already been noted, thermodynamics facilitates
the selection of the more stable ones among them.
It is thermodynamically advantageous for macromolecular chains to tie
up with chains similar to themselves and surround themselves (at the expense
of supramolecular contacts) with renewed “young” substances of living organisms.
Evolution selects those thermodynamically preferable paths of processes,
which facilitate cell division and preservation of DNA. All this occurs
with a background of variations in the parameters of the thermostats (the
surrounding environment), which (on a par with other factors) ensures that
life is supported. Thermodynamic factors facilitate the stabilization of
all complex biological structures, resulting in the appearance of the higher
hierarchies of the bio-world.
6. On the equilibrium character of the formation of supramolecular
In accordance with the thermodynamic theory of biological evolution
and aging of organisms, the specific value of the Gibbs' (or Helmholtz's)
function in respect of the formation of supramolecular structures of tissues
tends to the minimum. Although the “action” of the principle of structural
stabilization slows down this tendency (Gladyshev 1997, 1999a, 1999b),
the death, nevertheless, of the particular biosystem is inevitable. The
question lies only in how long this system will have existed.
The aging processes of the tissues of a living organism from the standpoint
of the transformation of their supramolecular structure in localized zones
occurs in conditions close to equilibrium as, for example, in the case
of slightly non- equilibrium phase transitions of the first order of any
substance. Moreover, it makes no difference how far from equilibrium the
processes of chemical transformation in the organism may be. The supramolecular
evolution of an organism’s structure “directed by thermodynamic force”,
only uses a chemical substance to build supramolecular structures in the
organism’s tissues (Tanford 1978).
7. What is the Gerontological Value of Bio-active Substances and
The concept of the gerontological value (or anti-aging value) of products
with a biological origin from the view-point of supramolecular thermodynamics
was first introduced into the scientific field in this century, the 1900s.
The gerontological value of food, cosmetic, or other natural
product or substance is the quality of the product (substance), expressed
in GPG units (the value of ,
the Gibbs function of formation of supramolecular structure of the tested
the Gibbs function of formation of supramolecular structure of the standard),
characterizing its ability to support the youthfulness and healthiness
of the organism, to rejuvenate its tissues, and positively influence the
duration and quality of life.
It is advisable to use the GPG indicator to evaluate the comparative
gerontological qualities (values) of a concrete foodstuff, a foodstuff
from a given class of food stuff (oils, fats, animal and fish flesh) or
from different classes of foodstuff (the bio-mass of any marine or vegetable
substance) and so on.
It is convenient to use the GPG indicator 10-point or 30-point scale.
The higher the indicator, the higher the gerontological value of the product.
For example, wheat shoots have a GPG indicator close to 9 points, whilst
an aging biomass of wheat stalk scores around 1 point.
Longevity and the preservation of health and youth are assisted by the
utilization of foodstuffs in ones diet, which have a high GPG indication.
Moreover, elasticity of the skin, sexual potency, muscle strength, and
other characteristics determining the quality of the organisms vital functions
are substantially improved.
The GPG indicator is an additional characteristic of natural products
with a biological origin. It is not a substitute for other well-known food,
cosmetic and medical product and composition indicators (for example, calorie
content, the ecological purity of a product and others). However, as a
measure of its value, it is highly useful when drawing up rejuvenating
diets and other compositions used by a person in his everyday life.
It can be formulated of the following principle (Gladyshev 1997; Gladyshev
and Kurnakova 1998; Lepock 1998): "Diets including “evolutionary young”
animal and vegetable foods stimulate longevity and improve the quality
of human life. The degree of “evolutionary” youth of a food product is
determined by its chemical composition and supramolecular structure. The
chemical composition and supramolecular structure of a product depend,
in their turn, on its ontogenetic and phylogenetic ages. An important quantitative
measure of the “gerontological efficiency” of a food product is its the
Gibbs function of supramolecular structure formation, which characterizes
the thermodynamic stability of its supramolecular structure".
8. Thermodynamic theory within the framework of its application cannot
Thermodynamics does not examine the mechanisms of processes and phenomena
– in this lies its weakness. The strength of thermodynamic theory lies
in the fact that it allows the possibility of studying the extent of transformation
of structures in the systems themselves (their composition) during the
process of evolution. When determining the direction of evolution of biosystems
on a chemical and supramolecular level, the “surprisingly incomprehensible”
complexity of structure of chromatin, organelles, cells, and any other
biological objects has no significance – the model presented in our work
supports the action of the laws of thermodynamics in each local volume
of supramolecular structures and, in the final analysis, in any (according
to size) macro-volume biological mass.
The calculations performed are found to fully correspond with the theory
and all facts known to the author (Gladyshev, 1978, 1995, 1997, 1998, 1999a-h;
Lepock, 1998; Hancock, 1990; Engberts and Kevelam, 1996; Arrhenius and
Mojzsis, 1996; Cantor and Schimmel, 1997; Ivanova, 1999; Wolffe, 1999;
Rafikov, Budtov and Monakov, 1978).
General methods are essential in order to learn about the world. One
of these, I suggest, ought to be the method of macrothermodynamics (the
hierarchical thermodynamics of heterogeneous systems), applying to all
hierarchical levels of living matter.
The law of temporal hierarchies of the biological world allows us to
pick out of the biomass, quasi-closed thermodynamic systems with a given
hierarchy. The use of this law of Nature as applied to supramolecular structures
of organisms allows us the opportunity of using the methods of equilibrium
supramolecular thermodynamics in the examination of open living systems.
It has been shown that supramolecular thermodynamics is one of the “keys”,
which allows us to explain the origin of life and evolution of living beings.
The Second law of thermodynamics in its classic formulation is easy
to apply in order to make calculations, carried out through methods of
chemical, supramolecular and overall hierarchical thermodynamics.
The author of the paper proposes that the thermodynamic theory of evolution
and aging of organisms within the framework of application of the basic
understanding of thermodynamics will never be refuted. It can only be perfected
and made more precise.
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