Biosolitons - One Secret of Living Matter.

The Bases of Solitonic Biology

S.V. Petoukhov

Department of Biomechanics,
Mechanical Engineering Research Institute,
Russian Academy of Sciences.
1999, Moscow,
GP Kimrskaia Typographia
(in Russian).

The book contains 288 pages, 51 drawings, 219 bibliographic sources cited.

State registration in «Russian Book Chamber»: No. 38213 on October,6, 1999.


The book represents the opportunities opened up by a solitonic approach to supramolecular biology and its phenomena of macroscopic structural self-organization and functions. These phenomena are connected traditionally with biological symmetries, which are a classical theme of theoretical biology, biomathematics, biophysics, etc. A physical concept of solitons concerns symmetries principles and features of physical domains with its symmetrical characters (like as magnetic domains, ferroelastic domains, etc.). In particularly, as well-known, solitonic equations have an infinite number of laws of conservation and associated symmetries.

The results of original research conducted by the author on a wide range of biological phenomena are described from the standpoint of solitons. The existence of soliton-like supramolecular processes in locomotor and other manifestations of dynamic biomorphology on a wide variety of branches and levels of biological evolution is demonstrated citing specific examples. Biosolitons are understood here primarily as characteristic single-hump (single-pole) local deformations which ate distributed along an organism, preserving their form and velocity.

The soliton is a type of energy well-known to physics which is found in physical environments in the form of stable, self-localising bundles of energy. In special conditions, solitons are capable of interaction with one another in a way similar to charged particles, of multiplying and perishing, of forming groups of pulsating and other non-trivial dynamics, and of overcoming the tendency towards disorder in solitonic environments. These remarkable bundles of energy have long been observed in plasma, liquid and solid crystals, magnetic and other domain structures having moving domain walls in the form of solitons, as well as classical liquids, non-linear lattices, etc. However, solitons have not yet been observed, nor their possible existence studied, in living substances at the macroscopic level. Nor have the key significance of solitons for the understanding of living organisms, their physiology, co-operative behaviour of many parts of the organism, etc. yet been covered in the pertinent literature. The book before you is dedicated to the authorís discovery of solitons in living substances at the supramolecular level, their systematic study, and the confirmation of the key significance of biosolitons in the physiology of organisms.

The concept of the soliton, which is now a key concepts of non-linear dynamics, has only in the last decade became a hot topic of discussion in contemporary theoretical physics as a result of work by mathematicians and specialists in mathematical physics. Solitons, often referred to as wave atoms, possess the characteristics of both waves and particles simultaneously, but are neither of the two; in actuality they are a new subject for scientific research.

Solitons have been observed as conditions of special non-linear environments, or systems, and differ in a principal way from classical linear waves, the theory of which was used in the past for the interpretation of wave-like natural processes. In particular, solitons are often frequently found in the form of self-localised bundles of energy having the typical form of a single-hump wave, which, while moving, preserves both its form and velocity without dissipation of energy. Scientists who earlier investigated natural phenomena related to solitons could not understand or explain these phenomena employing the classical theory of linear waves in currency at the time. In our opinion, the solitonic nature of many biological phenomena in the past prevented scientists from gaining an understanding of many aspects of living matter.

The amazing ability of biological organisms to self-develop and engage in active motion has been a subject of great interest to humankind from ancient times. This ability is connected with the biological use of energy which enters living matter and participates in ordering processes and transformation, similar to the growth of a small seed into a great tree. One of the unique characteristics of living organisms is the presence of forms of constant motion, or "charges of motion" in them. The well-known expression, "life means motion" comes to mind. For example, it is always possible to distinguish living cells from dead ones in that living cells are constantly moving and changing their forms.

In the book before you, the author discusses the observed phenomenon that many supramolecular biological motions, including locomotions, have the form of stable single-hump waves which spread out along a body, preserving their form and velocity with no observable heating of the surrounding medium. There are biological examples of such single-hump waves which move in opposite directions passing undisturbed through one another like classical solitons. The author proposes that solitons be used as a model of such supramolecular biological motion as has been observed on most of the various branches and levels of biological evolution in a great range of sizes of different organisms.

The àuthor has followed the example of J.Russel, who first discovered solitons and who observed this unusual single-hump wave on the surface of the water in a canal. The author has made similar morphological observations of macrobiological motion. As a result he has to his surprise found numerous biological examples of such single-hump waves and has interpreted them as solitons. He refers to phenomena of the solitonic type in living matter as biosolitons. These initial results have allowed him to proceed with a systematic study of the manifestations and the important role of biosolitons in biological bodies and processes. This study has led to the foundation of a new area of scientific study referred to as "solitonic biology". One of the most significant aspects of this area of study is the subconcept of biological domains with biosolitonic domain walls. This subconcept represents a domain self-organization of living matter in the framework of which many biosolitons become connected with the mechanisms of the formation of biodomains and domain walls moving in the form of solitons (similar to the theory and processes, well-known to physics, of self-organization of domain structures in non-biological condensed media, namely magnetic, polyphase alloys, superconductors, etc.). Correspondingly, an organism can be viewed as a multilevel, polydomain structure or a supernetwork of biosolitonic domain walls. The notion of soliton is the key to unlocking a chain of interconnected biological riddles.

According to the concept of biosolitons presented herein, living matter serves as a special solitonic environment. This environment generates, when supplied with sufficient energy, multilevel colonies of biosolitons. Biosolitons reveal their ability to engage in specific interaction and behaviour in these colonies, which includes attraction and repulsion, the creation of new biosolitons, the formation of stable connected groups having non-trivial space-time behaviour, etc. In addition, biosolitonic colonies have demonstrated the ability to create and support within their systems a special high order in counterweight to the tendency to disorder ("thermal death"), observed in thermodynamics (see paragraph 6.4). One of the main problems of biology is the maintenance of the spatial configuration of a body under constant renewal of its substratum. This biological property also finds a useful analogy in the properties of solitons as a moving, stable energy formation which maintains its form in conditions of constant renewal of its composition (see paragraph 5.2).

According to this biosolitonic concept of the specific energy nature of the organisation of systems in biological bodies, biosolitons act as a universal type of collective behaviour of living matter and active participants in biological self-organisation and vital activity. Their energy colonies promote, in particular, an enlarging of the biosolitonic environment in the course of transformation of food and energy coming from outside into new masses of living matter. It is important that the solitonic environment traps incoming stimulatory energy which is transformed into a non-dissipative solitonic type of physical energy which is made use of in the organism in harmony with the chemical types of energy found in that organism (see paragraph 6.2).

According to the concept described herein, the biological morphology and physiology of organisms is defined, to a great degree, by the morphology and activity of biosolitonic groups which are self-localising, interacting, non-dissipative energy formations having special forms. The specific soliton type of physical energy turns out to be essential for living matter on a wide variety of different levels of organisation and evolution. In our opinion, life is a form of existence of soliton energy.

The author asserts that solitons are of additional fundamental significance to the understanding of cooperative forms of behavior and self-organization of living matter which manifests itself as a polyphase solution of bio-polymers having a plethora of non-linear lattices in the form of polymeric nets, cytoskeletons, etc. The physiology of organisms is closely related to cooperative processes of phase changes and the movement of fronts of phase reconstructions, including those of non-linear lattices, etc., in which the participation of soliton-like processes is a natural one. Thus the possibility of making use of the concept of solitons as a basis for the modeling of a wide variety of biological processes finds a concrete scientific foundation. The authorís having revealed the simplest types of soliton-like processes in macrobiological systems points to the solitonic character of living matter. This opens up the possibility of further biological research into further types of mathematical solitons, namely breathers, wobblers, pulsons, clusters, etc., the mathematical existence of which had been posited by mathematicians in the analysis of solitonic equations and only then discovered by physicists in physical nature.

The book before you is intended to be of interest to a wide variety of readers, but primarily those interested in problems of theoretical and mathematical biology with its phenomena of biological symmetries or in new applications of the theory of solitons. It includes much overview material to acquaint the reader with the theory of solitons and its known physical applications.


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Chapter 1. History and particularities of solitons

Chapter 2. Locomotion and biosolitons

2.1. Biosolitons in locomotions of a snail and worm-like organisms

2.2. Biosolitons in locomotions of millipedes

2.3. Biosolitons in locomotions of snakes and fish

2.4. Biosolitons in locomotions of non-muscle motor systems

2.5. Conformations of biological bodies

Chapter 3. Solitons in crystals

3.1. Frenkel-Kontorova solitons

3.2. Magnetic and other solitons similar to dislocations

3.3. Soliton sine-Gordon equation

Chapter 4. Biological domains and biosoliton domain walls

4.1. Biological domains

4.2. Analogies between biodomains and springy domains of heterophases alloys

4.3. Biogenesis crystals

4.4. Colonial organisms

Chapter 5. Growth transformations and morphogenesis

5.1. Growth transformations

5.2. Morphogenesis

5.3. Cell division

5.4. The problem of morphological parallelisms, Vavilovís law of homological ranges and the holistic
       biological approach

5.5. One and two dimensions in biological bodies

Chapter 6. Life as a form of existence of solitonic energy

6.1. On the creation of order in living matter and biological evolution

6.2. Physical and chemical accumulators of energy

6.3. Self-organisation, self- reproduction and hereditary information

6.4. On co-operative particularities of the behaviour of living matter

6.5. Left-right dissymmetry in living matter

6.6. Soliton environments as a new model of biological environments

Chapter 7. Sensory-motor systems and highest physiological functions

7.1. Receptor cells and biosolitons

7.2. Receptor systems

7.3. Muscles

7.4. Neurons

7.5. Motor co-ordination and psycho-physics

Chapter 8. Biosolitons in different modelling tasks

8.1. On the bases of modelling of locomotion

8.2. Medicine and biosolitons

8.3. An energy approach to love, beauty and art

8.4. On biosolitons and remote influences

Chapter 9. On molecular Davydov solitons


About the author