Energy and negentropy in enzymic catalysis

Information-energy equivalence and the emergence of self-replicating biological systems

Biological processes are characterized by a decrease in entropy in apparent violation of the second law of thermodynamics. Information stored in genomes help to solve this paradox when interpreted under the relationship between information and energy stated by Brillouin in the 1950's. However, the origins of living forms from inanimate matter which have no information storage device remains an open question. In this paper, a theoretical approach is developed on this issue. The replication of a simple entity with a binary genome is assumed to require an information-equivalent energy in addition to the standard activation energy. It is found that, in some conditions, a decrease in entropy can be accomplished together with a decrease in Gibbs free energy. An equation of the total energy for the replication of this entity is derived. Three factors are predicted to lower this energy: a small number of states of the coding sequence, a lower temperature, and a high ratio of the reaction on diffusion coefficients. These factors may have favoured the emergence of evolutionary demons-information storage devices that are able to decrease entropy. It is evaluated that some short, single-stranded RNA sequences made only of G and of C may conform to this model. The consequences of this model and its predictions on the origins of life on Earth and on other planets are discussed.

Molecular mechanisms of encoding and decoding information in cell computing

The process of computing may be defined simply as the goal-directed selection process (GDSP) that selects m out of n possible choices to achieve some desired goals, thereby generating or utilizing the amount of Shannon information, I, that can be approximated as I = - log₂ (m/n) bits. There are at least 3 distinct kinds of the physicochemical systems that can execute GDSP; (i) enzymes (i.e., microscopic or molecular computers), (ii) living cells (as mesoscopic computers), and (iii) brains (as macroscopic computers). In order to help define the principles and mechanisms underlying cell computing, it was thought necessary to compare cell computers with molecular computers (e.g., enzymes) on the one hand and with the macroscopic computers (e.g., Turing machine) on the other. It was concluded that all these different kinds of computers are ultimately driven by the information-energy particle called gnergons, consistent with the Gnergy Principle of Organization formulated by the present auditor in 2018. Also, it was concluded that to delineate how cells compute supported by enzymes necessitated treating enzymes not only as particles but also as standing waves, thus leading to the postulate of the wave-particle duality of enzymes formulated in this paper for the first time, in analogy to the wave-particle duality of light formulated in physics about 100 years ago.

Role of constraint in catalysis and high-affinity binding by proteins

Using a model for catalysis of a dynamic equilibrium, the role of constraint in catalysis is quantified. The intrinsic rigidity of proteins is shown to be insufficient to constrain the activated complexes of enzymes, irrespective of the mechanism. However, when minimization of the surface excess free energy of water surrounding a protein is considered, model proteins can be designed with regions of sufficient rigidity. Structures can be designed to focus surface tension or hydrophobic attraction as compressive stress. A monomeric structure has a limited ability to concentrate compressive stress and constrain activated complexes. Oligomeric or multidomain proteins, with domains surrounding a rigid core, have unlimited ability to concentrate stress, provided there are at least four domains. Under some circumstances, four is the optimum number, which could explain the frequency of tetrameric enzymes in nature. The minimum compressive stress in oligomers increases with the square of the radius. For tetramers of similar size to natural enzymes, this stress agrees reasonably well with that needed to constrain the activated complex. A similar principle applies to high affinity binding proteins. The models explain the trigonal pyramidal shape of fibroblast growth factor and provide a basis for interpretation of protein crystal structures.

Free energy and information contents of conformons in proteins and DNA

Sequence-specific conformational strains (SSCS) of biopolymers that carry free energy and genetic information have been called conformons, a term coined independently by two groups over two and a half decades ago [Green, D.E., Ji, S., 1972. The electromechanochemical model of mitochondrial structure and function. In: Schultz, J., Cameron, B.F. (Eds.), Molecular Basis of Electron Transport. Academic Press, New York, pp. 1-44; Volkenstein, M.V., 1972. The Conformon. J. Theor. Biol. 34, 193-195]. Conformons provide the molecular mechanisms necessary and sufficient to account for all biological processes in the living cell on the molecular level in principle--including the origin of life, enzymic catalysis, control of gene expression, oxidative phosphorylation, active transport, and muscle contraction. A clear example of SSCS is provided by SIDD (strain-induced duplex destabilization) in DNA recently reported by Benham [Benham, C.J., 1996a. Duplex destabilization in superhelical DNA is predicted to occur at specific transcriptional regulatory regions. J. Mol. Biol. 255, 425-434; Benham, C.J., 1996b. Computation of DNA structural variability--a new predictor of DNA regulatory regions. CABIOS 12(5), 375-381]. Experimental as well as theoretical evidence indicates that conformons in proteins carry 8-16 kcal/mol of free energy and 40-200 bits of information, while those in DNA contain 500-2500 kcal/mol of free energy and 200-600 bits of information. The similarities and differences between conformons and solitons have been analyzed on the basis of the generalized Franck-Condon principle [Ji, S., 1974a. A general theory of ATP synthesis and utilization. Ann. N.Y. Acad. Sci. 227, 211-226; Ji, S., 1974b. Energy and negentropy in enzymic catalysis. Ann. N.Y. Acad. Sci. 227, 419-437]. To illustrate a practical application, the conformon theory was applied to the molecular-clamp model of DNA gyrase proposed by Berger and Wang [Berger, J.M., Wang, J.C., 1996. Recent developments in DNA topoisomerases II structure and mechanism. Curr. Opin. Struct. Biol. 6(1), 84-90], leading to the proposal of an eight-step molecular mechanism for the action of the enzyme. Finally, a set of experimentally testable predictions has been formulated on the basis of the conformon theory.

Isomorphism between cell and human languages: molecular biological, bioinformatic and linguistic implications

The concept of cell language has been defined in molecular terms. The molecule-based cell language is shown to be isomorphic with the sound- and visual signal-based human language with respect to ten out of the 13 design features of human language characterized by Hockett. Biocybernetics, a general molecular theory of living systems developed over the past two and a half decades, is found to provide a physical theory underlying the phenomenon of cell language. The concept of cell language integrates bioenergetics and bioinformatics on the one hand and reductionistic and holistic experimental data on the other to account for living processes on the molecular level. The isomorphism between cell and human languages suggests that the DNA of higher eucaryotes contains two classes of genes--structural genes corresponding to the lexicon and 'spatiotemporal genes' corresponding to the grammar of cell language. The former is located in coding regions of DNA and the latter is predicted to reside primarily in noncoding regions. The grammar of cell language is identified with the mapping of the nucleotide sequences of DNA onto its 4-dimensional folding patterns that control the spatiotemporal evolution of gene expression. Such a mapping has been referred to as the second genetic code, in contrast to the first genetic code which maps nucleotide triplets onto amino acids. The cell language theory introduces into biology the linguistic principle of 'rule-governed creativity,' leading to the formulation of the concept of 'rule-governed creative molecules' or 'creations.' This concept sheds new light on molecular biology, bioinformatics, protein folding, and developmental biology. In addition, the cell language theory suggests that human language is ultimately founded on cell language.

A general theory of chemical cytotoxicity based on a molecular model of the living cell, the Bhopalator

To define the molecular processes underlying toxicological manifestations experimentally measured on the cellular level, it is essential to have available a molecular model of the living cell itself. The Bhopalator is a molecular model of the living cell formulated by integrating the three major branches of biology within a coherent theoretical framework - the Watson-Crick molecular genetics, the conformon theory of enzymic catalysis, and the theory of dissipative structures developed by I. Prigogine. According to this model, the living cell is a self-moving, self-thinking and self-reproducing machine (automaton) that receives information and energy from its environment, processes them according to the genetic programs stored in DNA, and generates output signals to environment in order to realize teleonomically designed functions. The Bhopalator suggests a set of general statements useful in toxicological research, and these statements have been utilized to provide possible answers to several fundamental questions raised by recent experimental findings on chemically-induced cell injury and death.

The bhopalator: a molecular model of the living cell based on the concepts of conformons and dissipative structures

A molecular model of the living cell has been formulated based on a new theory of enzymic catalysis which takes into account the complementary roles of free energy and genetic information. The elementary units of free energy and genetic information that are necessary and sufficient for effectuating molecular mechanisms responsible for the life of the cell are called conformons. Conformons are visualized as a collection of a small number of catalytic residues of enzymes or segments of nucleic acids that are arranged in space and time with appropriate force vectors so as to cause chemical transformations or physical changes of a substrate or a bound ligand. So defined, conformons provide a plausible molecular means to link the genetic information stored in DNA and its ultimate expression, namely networks of coupled intracellular biochemical reactions and physical processes maintained by a continuous dissipation of free energy--dissipative structures of Prigogine. The proposed model of the living cell appears to possess the potential for bridging the gap between molecular biology and the biology of multicellular systems.

The biological functions of low-frequency vibrations (phonons) 5. A phenomenological theory

Low-frequency internal motions of a biomacromolecule are thought to possess significant biological function from the dynamic point of view. In this paper, a general phenomenological theory is established by which it is clearly verified that low-frequency resonance plays a central role in the energy transmission required during the cooperative interaction between subunits in a protein oligomer. According to the present theory, it is found that the energy transmission between a pair of diagonal subunits in a protein oligomer with a polygon arrangement is the most efficient, so as to in a sense further predict that after a ligand is bound to a subunit by random collision, its diagonal subunit in the same protein oligomer will possess the greatest probability of binding with the next ligand. Furthermore, based on the concept of the 'resonance-controlled trigger' derived from the phenomenological theory, it is feasible to estimate the lower time limit of allosteric transition from one subunit to the other. Such a time limit depends on the dominant low-frequency mode of each subunit, the ratio of the coupling force constant to the corresponding inherent force constant, as well as the geometrical arrangement of subunits in a protein oligomer. So far none of the allosteric transitions observed in proteins has exceeded the time limit as defined here, indicating a logical consistency between our theory and the experiments.

The biological functions of low-frequency vibrations (phonons). 4. Resonance effects and allosteric transition

Based on the internal structure of oligoprotein as well as the basic physical characteristics+ of vibrations, it is deduced that the low-frequency vibrations possess some exceptional functions in transmitting biological information at the molecular level. In particular, according to the viewpoint of energy exchange and intramolecular displacement, it is demonstrated that the low-frequency resonance plays a very significant role during the dynamic process of allosterism of an oligomeric protein molecule. Furthermore, the cooperative reaction between hemoglobins and ligands is taken as an example, through which it is seen that some observed phenomena, whose dynamic principle has thus far been unclear, can be explicitly interpreted in terms of the concept of low-frequency resonance.

Low-frequency vibrations of DNA molecules

A model for calculating the low-frequency modes in DNA molecules is presented. The present model is associated with the 'breathing' of a DNA molecule as well as its complementary hydrogen bonds. The calculated results show excellent agreement with the observed low-frequency wavenumber (30 cm-1). Consequently, such an internal motion as reflected in the proposed model might be the origin of the observed low-frequency vibration in DNA molecules. This is helpful for investigating the relevant biological functions, which so far have been discussed by many scientists.

Biological functions of low-frequency vibrations (phonons). III. Helical structures and microenvironment

Low-frequency vibrations in biomacromolecules possess significant biological functions. In this paper, the alpha-helix element is compared with a mass-distributed spring. Based on this, a set of intuitive and easily handled equations are derived for predicting the fundamental frequencies of helical structures in protein molecules. As shown in the equations, the fundamental frequency depends not only on the constituents of a helix itself but also on its microenvironment. The calculated results agree with the observations. The calculations also demonstrate that the low-frequency vibrations with wave number of approximately 30 cm-1 do not necessarily arise from motions that involve either all or very large portions of the protein molecule as previously thought; a piece of helix containing more than 10 residues and surrounded by a proper microenvironment can also generate such low-frequency motions. Furthermore , we illustrate that the low-frequency motions are closely related to the native state of a protein molecule. Upon denaturation, which is accompanied by a radical change of the relevant microenvironment, the original fundamental frequency also disappears. Consequently, this kind of special frequency termed activating low frequency can serve as a dynamic criterion in identifying whether a biomacromolecule is in its native state. The energy of a phonon excited by this kind of low-frequency vibration is of the same order of magnitude as the average enthalpy value per residue measured during conformational change in some protein molecules. Therefore, there must be some intrinsic relation between the allosteric transitions of protein molecules and their low-frequency motions.

Identification of low-frequency modes in protein molecules

It is demonstrated that the observed low-frequency motions with wave numbers of 22 cm-1 and 25 cm-1 for insulin and lysozyme respectively originate from the accordion-like motions of the principal helices therein. The calculated results based on such a model are in good agreement with the observed values. During calculations the role of the internal microenvironment upon the low-frequency motion is naturally revealed, so as to elucidate as well why this kind of low-frequency motion is so sensitive to the conformations of proteins observed.

Energy transfer mechanisms in mitochondria

The problem of free energy transfer and transduction in mitochondria is reviewed from the point of view of conservative and dissipative mechanisms. Excited states are inherently dissipative and are not considered viable possibilities. If the free energy is already a local minimum and present in the form of potential energy, conservative transfer is possible within a properly designed medium. The design features are compatible with what is known about mitochondria.