Fundamental constants of chemistry and biology

The achievements of natural sciences in recent decades are so ambitious that the very attempt to understand them today has become a difficult cognitive problem. Increasing differentiation is an obvious fact of modern science, which has put on the agenda the problem of finding and developing common fundamental principles of scientific knowledge. Solving such a problem is by no means a trivial task. The search for a single foundation of natural science has long ceased to be the domain of philosophers alone. Today, scientists from various fields of knowledge are involved in its resolution: physicists, chemists, biologists, mathematicians, etc. The main emphasis in the search for generalizing ideas can be placed on the meaning of symmetry and the role of fundamental world constants. The extension of this "physical ideology" to chemistry and biology is not only important from a methodological point of view, but also, more importantly, makes it possible to more clearly identify the relationship of these sciences. In addition, it makes it possible in some cases to say multa paucis — there is a lot in it.
    The problem of fundamental constants thus acquires global, worldview related significance from a conceptual perspective. Leaving aside for the purposes of this article the discussion of the important role played in the formation of our Universe by a number of fundamental physical constants—such as the constants of gravitational, electromagnetic, weak, and strong interactions—we will focus on just three constants: Avogadro’s, Boltzmann’s, and Planck’s. These physical constants form the fundamental chemical and biological constants [1].
In 1811, Avogadro introduced a new concept — molecules as compounds of atoms. Avogadro's hypothesis essentially consolidated the idea of the discrete structure of matter in science (although the official recognition of the hypothesis itself took place only at the First International Congress of Chemists in 1860, four years after the author's death), and the number N(A) = 6.0227 • 10^23 mol^-1 (in the future, it is important for us to The value of this quantity, rather than its dimension (mol^-1), was calculated for the first time by Loshmidt in 1865. It is important that in the 19th century a new macroscopic concept arose — the amount of matter, and in the 20th century it became clear that the Avogadro number determines a sufficient condition for macrostance. We do not know the necessary condition. For some objects, it may be a million structural elements, while for others it may be only a thousand, but we definitely know that no matter what we take in the amount of N(A), it is always a macro object.
The second constant we need accompanies all the characteristics and phenomena of microworld physics and owes its “origin” to Planck. It all began with his report on February 14, 1900, on the emissive power of a black body, where the constant h = 1.05;;;10;;;;J;·;s was introduced for the first time. What is the meaning of this fundamental quantity? The thing is that in classical physics, quantities such as momentum p, energy, and action (there is also such a quantity; its dimension is energy ; time) can take on any arbitrarily small values. However, as soon as we “enter the microworld,” i.e., we become interested in phenomena and objects with dimensions < 10^-7 cm, the situation changes fundamentally. Thus, the action can no longer differ from zero by an arbitrarily small amount. The first, smallest value of it turns out to be equal to the value of this particular Planck constant h . The next largest value will be 2 h, then 3 h, and so on. Other physical quantities, such as spin, etc., find themselves in a similar situation. Thus, not only matter is discrete, but also a number of physical characteristics that describe it. Furthermore, in the microcosm, it is not the deterministic picture of describing objects that becomes fundamental, but the probabilistic one. The immediate consequence of this is that when describing phenomena in the microcosm, particles do not have a concept of trajectory in the usual macroscopic sense. This is essentially the uncertainty principle formulated by W. Heisenberg in 1927. The presence of an electron’s spin (which is also determined by h) leads to the Pauli exclusion principle. The Pauli exclusion principle determines the specific patterns in how electrons fill quantum states in an atom, and it is precisely this that accounts for the nature of the periodicity in the changes in the properties of elements in D. I. Mendeleev’s periodic table.
We now move on to the third stated constant — the Boltzmann constant k. The second law of thermodynamics, unlike the first, is not a universal law of nature; it is valid only in relation to isolated thermodynamic systems. Nevertheless, the second law occupies a unique place among other fundamental laws. The fact is that the second law speaks of the irreversibility and unidirectionality of processes in an isolated system, and thereby determines the difference between future processes and past ones, and highlights the direction of time (the arrow of time). As is well known, the measure of irreversibility is entropy. Boltzmann first provided a probabilistic interpretation of entropy in 1877, using the idea of determining the most probable state of a system from a thermodynamic point of view. The transition of a system from a non;equilibrium state to an equilibrium state is accompanied by an increase in entropy and the statistical weight G [2]. The relationship between the statistical weight G (a characteristic of the microcosm) and entropy S (a characteristic of the macrocosm) is defined by the formula:
S = k ln G                (1)
Here, the so;called Boltzmann constant k = 1.38;;;10;;;;J/K (joule per kelvin) first appears. Despite the fact that the constant k does not determine elementary physical processes and is not included in the basic principles of dynamics, the following circumstance is important: the Boltzmann constant establishes a connection between microscopic dynamic phenomena and the macroscopic characteristics of the state of a large (on the order of Avogadro’s number) collection of particles. Strictly speaking, this constant was first introduced by Planck, just like formula (1). Nevertheless, the constant k is named after Boltzmann “for a quite understandable reason” (in Planck’s own words). And the reason for this is that Boltzmann not only established for the first time the proportionality between S and ln G, but also showed that in the final state with maximum entropy, in the so;called attractor, the probability distribution of particles W(v) over velocities v follows the Maxwell distribution:
 W(v) ~ exp(-m^2 / 2kT)                (2),
 where m is the mass of the particles, T is the temperature.
It is evident that in the state of the attractor — the global asymptotic equilibrium in which the system ultimately finds itself — the probability W(v=0) of encountering a particle with zero velocity is maximum and equal to one, but this is a non;zero probability of encountering particles with velocities, and therefore with energies, not equal to zero. In what follows, this circumstance will be used by us in the qualitative justification of one of the axioms of biology. Thus, the state of maximum entropy is not a static state, but rather a somewhat dynamic state of chaos. Using the meaning of the physical constants mentioned above, let us proceed to the definition of chemical and biological constants [1].

Conceptual systems of chemistry. Chemical constant.

Based on a historical and methodological analysis of the development of chemistry, V. I. Kuznetsov established that there are certain patterns in this development. According to Kuznetsov [4], the entire history of chemistry is a process of development and the emergence of new conceptual systems. These systems represent a set of laws, theories, and views that characterize the level of knowledge about a chemical phenomenon. From the emergence of scientific chemistry, from the time when the atomic;molecular concept appeared, to the present day, four conceptual systems are clearly discernible.
1. The doctrine of the composition of matter (17th–18th centuries).
2. The doctrine of the structure of matter (1960s).
3.   The doctrine of chemical reactions (late 19th century).
4. The doctrine of chemical evolution (1960s–1970s). At the first stage, the central problem was solving the issue of the relationship between composition and properties; researchers sought to explain the properties of chemical compounds by their elemental composition.
Subsequently, knowledge about the structure of matter was required. In solving this problem, it was possible not only to explain the properties of various chemical compounds but also to open the way to the synthesis of new substances. From this point on, a new concept emerges — reactivity, which already required taking kinetic factors into account. The transition to kinetic theories is associated with the introduction of the concept of organization, which, in a certain sense, is analogous to the concept of structure and is also an attribute, albeit of a more complex kinetic chemical system. Further, the logical completion of the scheme leads to the description of systems of an even higher level of organization, such as, for example, self;organizing catalytic systems. Recently, a new concept of behavior has emerged, which expresses something different compared to the concepts of properties and reactivity. This concept is associated with the problems of chemistry that underlie the fourth conceptual system. Here, the problem of the behavior of complex pre;biological systems and the level of their organization is studied. The final stage, which lies on the border between chemistry and biology, is the biology of artificial living systems. At this stage, it is possible to create in the 21st century a scientific, theoretical, and experimental foundation for elucidating new biological patterns and building theoretical biology. A consistent chemical theory should explain and predict the dependence of reactivity on the structure of the unchanging molecular fragments of the reaction. The quantum;mechanical explanation of reactivity is based on the theory of the activated complex [9], hereinafter abbreviated as AC.The AC theory is the simplest and historically first version of the statistical theory of chemical reactions;it was developed in the 1930s by E. Wigner, M. Polanyi, H. Eyring, M. Evans.This theory is based on three assumptions, or three axioms [4].
1. The transition of a chemical system from the initial state to the final state is associated with the formation of an activated complex (AC), or a transition state.
2. There is a thermodynamic equilibrium between the reactants of a chemical reaction and the AC.
3. The rate of a chemical reaction is identified with the lifetime of the AC. All three assumptions cannot be rigorously justified within the framework of chemistry; they should be considered axioms of chemistry.
Taking into account knowledge of the fundamental physical constants of Planck and Boltzmann, one can immediately and qualitatively (without using a rigorous theory) estimate the lifetime of the AC. Indeed, since the elementary act of a chemical reaction occurs at the microlevel, its description must necessarily include Planck’s constant h, which has the dimension of energy ; time. The result of a chemical reaction is recorded at the macrolevel, so there must be a connection between the “micro” and the “macro,” which means that the description must include the Boltzmann constant k, which has the dimension of {energy/temperature}. It is known that the chemical reaction accelerates with increasing temperature. Hence, the shorter the battery life, the higher the temperature. Comparing the units of measurement of the constants h, k and temperature T, we obtain the only possible relationship with the dimension of time:
t(AC)=h /kT                (3).

At temperatures typical for chemical reactions, t(AC) ~10^-13 c, therefore, it has not yet been possible to observe the activated complex. If this becomes possible, then axiom 1 will no longer be necessary, and its statement will become a proven fact. As can be seen from (3), the lifetime of the AK does not depend on the reactants involved in the reaction or the final reaction products, i.e., for any reaction, the value of t(AK) does not change. Therefore, the LIFETIME OF THE AK — t(AC) — is a FUNDAMENTAL CHEMICAL CONSTANT.

Axioms of biology. Biological constants.

The main task of biology as a science is to understand all phenomena of living nature based on scientific laws, taking into account the fact that the properties of an organism as a whole differ from the properties of its individual parts. We cannot yet provide a strict definition of life and cannot say exactly how and when it arose. The most that is currently possible is to list and describe the characteristics that distinguish it from non;living nature and to put forward scientific hypotheses about its origin and evolution. Along with the well;known characteristics of life [5], which do not require any comments, there are other, no less important ones. Let us provide one example, which we call the “zero axiom of biology.” Zero — because at one time B. M. Mednikov proposed a biological axiomatics consisting of four axioms [5]. Following B. M. Mednikov, we will present these axioms later, after the zero axiom.
In 1847, Pasteur made a fundamental discovery that for a long time defied explanation and was only properly appreciated in recent years. Pasteur discovered that in living organisms, amino acids and sugars are optically active. Moreover, in the course of further research, Pasteur made an exceptionally important conclusion: the molecular basis of life is not only chiral but also asymmetric [6]. When these biochemical compounds are artificially synthesized, optically inactive mixtures are formed (they contain an equal number of left; and right;rotating molecules), which is the most advantageous state from a thermodynamic point of view. Therefore, Pasteur’s discovery is not only one of the important features that distinguish living from non;living matter, but also requires an explanation of the aforementioned asymmetry. In other words, any scientific hypothesis attempting to explain the origin of life must also include an explanation of the conditions under which a chirally asymmetric system — a system with broken mirror symmetry — emerged from an initially symmetrical system. There are two fundamentally different approaches to explaining the chiral asymmetry of the bioorganic world. Various aspects of the violation of mirror symmetry in the bioorganic world are examined by V. A. Avetisov and V. I. Goldansky in [7, 8]: 1) Chiral asymmetry is a consequence of the evolution of structures and functions at the chemical level of complexity; 2) a consequence of the evolution of structures and functions at the biological level of complexity.
One possible explanation for the first hypothesis was previously proposed by L. L. Morozov [9, 10]. His conclusion is briefly as follows. The formation of a system with broken (reduced) symmetry occurs as a result of self;organization [11]: away from the state of thermodynamic equilibrium, the symmetry of the macroscopic state of the system may be spontaneously broken when the bifurcation point is crossed. Thus, according to Morozov, the emergence of life should be viewed as a “favorable” catastrophe that occurred at a bifurcation point. For us, it is not important which of the two hypotheses (chemical or biological) actually occurs. The following is important: in both the first and second cases, the explanation of life must move into the realm of condensed matter physics and cooperative phenomena (and inevitably depend on the Boltzmann and Planck constants). Furthermore, self;replication at the molecular level of chirally pure systems, being a problem for physical theory, becomes yet another characteristic of living systems. The most brilliant idea regarding the origin of life belongs to our outstanding scientist D.S. Chernavsky [12].
Let us now formulate this “ZERO” axiom in the following form.
AXIOM 0. THE NATURAL ORIGIN OF LIFE IS CONNECTED WITH THE APPEARANCE OF CHIRAL ASYMMETRY OF ITS MAIN CARRIERS (informational and functional).
In this formulation, the axiom statement is functional, i.e. it does not depend on which media life is based on (it may not be earthly life). It is important that if life arose in the process of self-organization, then a chiral asymmetry necessarily arises. With an artificial occurrence, this may not be the case. Let us now turn to quoting the rest of the axioms of biology according to Mednikov [5], of which, however, we will only need the last two directly!
Axiom 1. All living organisms must be a unity of phenotype and genotype (the program for building the phenotype), passed down from generation to generation.
Axiom 2. “Hereditary” molecules are synthesized via a template mechanism. The gene of the previous generation is used as the template on which the gene of the future generation is built.
To induce a single mutation — a hereditary change in the genetic program — it is necessary to supply DNA with a minimum energy E(min) ~ 2.5–3 eV. The average energy of thermal motion of the molecules surrounding DNA at temperatures typical for a living organism is approximately 0.025 eV, i.e., at physiological temperatures, DNA turns out to be sufficiently stable. However, the speeds of molecules in chaotic motion are not the same even in a state of thermodynamic equilibrium. There is a certain spread in their values, similar to the Maxwell distribution (2) for an ideal system. Regardless of what this distribution is, its dispersion depends on the Boltzmann constant. Consequently, there are always molecules with speeds whose energy is sufficient to disrupt the structure of a gene and cause a mutation. Such changes in genetic programs are random, unpredictable, and not directed. Therefore, these mutations can only accidentally turn out to be adaptive or adaptive.
Naturally, temperature is not the dominant factor in the process of mutagenesis.
The effect of hard radiation quanta (ultraviolet radiation, X;rays, gamma quanta), fast elementary particles, and molecules of substances capable of reacting with DNA (chemical mutagens) is much more significant. If a mutation is caused by a quantum or a particle, the Heisenberg uncertainty principle begins to manifest itself, i.e., the quantum nature of the interaction between particles or radiation and the information carrier becomes evident. In this case, the so;called effective exchange radius (the size of the region to which energy must be brought for a gene mutation to occur), first measured by N. V. Timofeev;Resovsky and K. Zimmermann, is important — R(eff) ~10;; cm.
The dimensions of the region are known (this is the microworld), so the momentum is known only with an uncertainty on the order of the constant h; consequently, the mutagenesis process in this case is also probabilistic. A similar probabilistic picture arises when considering other mutagens, since the description of interaction processes in the microworld is probabilistic. Summarizing these qualitative considerations, Mednikov formulates the following principle as an axiom.
Axiom 3. In the process of transmission from generation to generation, genetic programs change randomly and non;directionally as a result of many factors, and only by chance do these changes turn out to be adaptive.
Thus, this axiom is based on the most important principles of statistical physics and the Heisenberg uncertainty principle. It turns out that the third axiom directly depends on the physical principles and constants of Boltzmann and Planck. The following is important for us. The existence of this axiom is due to the presence of two characteristic parameters, E(min) and R(eff), which are essentially FUNDAMENTAL BIOLOGICAL CONSTANTS.
Here, it is important to understand that these parameters are fundamental constants, but not numerical (as in physics), but semantic. In other words, for random and undirected changes in genetic programs, it is not their numerical value that matters (for life forms not based on DNA, but on some other information carrier, the numerical values of these constants are likely to be different), but the semantic one: E(min) — the minimum energy required for a mutation to occur, and R(eff) — the effective distance required for a mutation to occur.
The fourth axiom owes its origin to the outstanding geneticist N.V. Timofeev;Resovsky and is known as the principle of amplification. It is easiest to understand this principle using the example provided by V.A. Ratner in [5]. Let there be a fertilized egg cell — a carrier of a gene mutation that encodes a functional carrier essential for life: an enzyme without which a living organism cannot survive. In the process of the organism’s growth and development, the egg cell has transformed into 10^15 cells, and the genes have multiplied accordingly. Each gene produces 100 molecules of m;RNA, on each of which 100 molecules of an enzyme are synthesized. Each enzyme molecule carries out 10^4 acts of its (important for the organism’s life) reaction. As a result, we have 10^15;;;10^2;;;10^2;;;10^4;~;10^23, i.e., a number comparable to Avogadro’s number, which means we have already reached the macrolevel. This is how much the results of a single quantum leap, a single mutation at the microlevel, have been amplified. At the macrolevel, natural selection is already at work. What is important is that it is not the genetic programs that are subject to selection, but the phenotype, in which each change is amplified by a factor of 10^23. Accordingly, the principle of amplification can be formulated as follows.
Axiom 4. Random changes in genetic programs (microlevel) during the formation of the phenotype (macrolevel) are repeatedly amplified and subjected to selection by environmental conditions.
 Thus, the fundamental physical constants of Avogadro, Boltzmann, and Planck form not only chemical (in the theory of the activated complex) and biological axioms, but also unique characteristics that should be considered as fundamental chemical and biological constants.
The article is based on the author’s lectures at the plenary sessions of the Soros Teachers’ Conference, which he delivered in 1998 — “Self;organization and restructuring (a special case of catastrophe theory) at the physical, chemical, biological, and social levels” — and in 1999 — “The influence of fundamental physical constants on chemical and biological processes”.
The author is grateful to Professor G. V. Lisichkin for stimulating this work.

Literature
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  Russian text. © Copyright: Yuri Khapachev, 2026
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