Concept of energy in biological systems

Beside the concept of material inputs and outputs of components of the representation of biological systems given to us by Rosen, the concept of energy is incorporated. The interaction of material and energy is represented by a cartesian product; and separate material and energetical mappings are considered as the new representation of components. These developments generate aMα category, and it is shown thatMα is isomorphic to theM category of previous developments.     

Concept of energy in biological systems and the effects of irradiations of low energies on enzyme-substrate systems

The recent mathematical formalization of the concepts of matter and extrinsical energy, which are used for the relational representation of biological systems, is employed in the analysis of the important experimental discoveries of Comorosanet al. related to low energy electromagnetic irradiations on enzyme substrates. By means of the present analysis one of the properties inherent to the experimental phenomena is more precisely exposed, and theoretical developments corresponding to “energetical evolutions” in a biological system (Leguizamón, 1976) may now have an experimental basis. Important limitations are introduced for the validity of the commutativity and associativity of cartesian product of sets, when they represent matter and its linked extrinsical energy. In connection with this last aspect, new important knowledge is obtained for the relational mathematical representation of biological systems.     

Transfers between biological and environmental systems

A newM _γ categorical representation of biological systems is developed which is an extension of previously reported work (Leguizamón, 1975a, b; 1976). In this representation, each material physical nature going to a component or produced by it, is given by a set whose cardinality corresponds to the quantity of the material physical nature. Biological and environmental diagrams, respectively represented byM _γ andE categories, are used in order to obtain a theory of transfers between both systems. From the mathematical representation of this theory, the transfers are classified as: material-energetic, exclusively energetic and theoretical material-theoretical energetic. These concepts are incorporated into a diagram, and later, a set of axioms is given, in order to have the previous developments as a new categoryT. This paper was made possible by a Fellowship from the Consejo Nacional de Investigationes Científicas y Técnicas of the República Argentina.     

Some remarks on topological biology

With reference to several recent papers by the author, it is pointed out that within the principle of biotopological mapping a choice of a primordial graph and of a particular transformation defines a system of abstract biology, similar to systems of abstract geometries. The study of such abstract systems is necessary before one can be found which is isomorphic to the actual biological world. A brief survey of the structure and properties of the system based on the choice of the primordial graph and of the transformationT defined in a previous paper (Bull. Math. Biophysics,16, 317–48, 1954) is made. Two more topological theorems are demonstrated, which, interpreted biologically, lead to the conclusion that the higher an organism, the more adaptable it is. Finally a criticism of that particular system of abstract biology is made, and its inadequacy for the representation of the actual biological phenomena pointed out, and a suggestion is made for a possible point set topological approach to biology.     

Abstract representations of biological systems in supercategories

An abstract representation of biological systems from the standpoint of the theory of supercategories is presented. The relevance of such representations forG-relational biologies is suggested. In section A the basic concepts of our representation, that is class, system, supercategory and measure are introduced. Section B is concerned with the mathematical representation starting with some axioms and principles which are natural extensions of the current abstract representations in biology. Likewise, some extensions of the principle of adequate design are introduced in section C. Two theorems which present the connection between categories and supercategories are proved. Two other theorems concerning the dynamical behavior of biological and biophysical systems are derived on the basis of the previous considerations. Section D is devoted to a general study of oscillatory behavior in enzymic systems, some general quantitative relations being derived from our representation. Finally, the relevance of these results for a quantum theoretic approach to biology is discussed.     

Organismic supercategores: II. On multistable systems

The representation of biological systems in terms of organismic supercategories, introduced in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious.     

A note on abstract relational biologies

It is shown that the class of abstract block diagrams of (M, ℜ)-systems which can be constructed out of the objects and mappings of a particular subcategoryG ₀ of the categoryG of all sets depends heavily on the structure ofG ₀, and in particular on the number of sets of mappingsH(A, B) which are empty inG ₀. In the context ofG ₀-systems, there-fore, each particular categoryG ₀ gives rise to a different “abstract biology” in the sense of Rashevsky. A number of theorems illustrating the relation between the structure of a categoryG ₀ and the embeddability of an arbitrary mapping αεG ₀ into an (M, ℜ)-system are proved, and their biological implication is discussed. This research was supported by the United States Air Force through the Air Force Office of Scientific Reserch of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

On the Semio-Mathematical Nature of Codes

The relational structure of RNA, DNA, and protein bears an interesting similarity to the determination problem in category theory. In this paper, we present this deep-structure similarity and use it as a springboard for discussing some abstract properties of coding in various systems. These abstract properties, in turn, may shed light on the evolution of the DNA world from a semiotic perspective. According to the perspective adopted in this paper, living systems are not information processing systems but “meaning-making” systems. Therefore, what flows in the genetic system is not “information” but “value.” We define meaning, meaning-making, and value and then use these terms to explain the abstract dynamics of coding, which can illuminate many forms of sign-mediated activities in biosystems.     

Phase behavior of hydrated lipid bilayer composed of binary mixture of phospholipids with different head groups

Phase behavior of hydrated lipid bilayer was investigated for the mixtures of two phospholipid species chosen from phosphatidic acid (PA), phosphatidylcholine (PC), phosphatidylethanolamine (PE), and phosphatidylglycerol (PG) with the same acyl chains. The pseudo-binary phase diagrams constructed by a differential scanning calorimetry (DSC) were analyzed based on a thermodynamic model applying the Bragg–Williams approximation for non-ideality of mixing. The interchange energy parameters, ρ₀, derived from this approach were positive for all mixture systems in both gel and liquid–crystalline phase bilayers, and increased in the order PG/PE<PC/PA<PC/PE<PG/PA with a few exception. This suggests that the energetical disadvantage for the mixed-pair formation relative to the like-pair formation in the hydrated bilayer increases in this order. In addition, the ρ₀ values increased with the increase in the acyl chain length of the phospholipids. These experimental results were discussed in terms of an intermolecular interaction of the phospholipid species in hydrated bilayer.     

Did Acidic Stress Resistance in Vertebrates Evolve as Na+/H+ Exchanger-Mediated Ammonia Excretion in Fish?

How vertebrates evolved different traits for acid excretion to maintain body fluid pH homeostasis is largely unknown. The evolution of Na⁺/H⁺ exchanger (NHE)-mediated NH₄⁺ excretion in fishes is reported, and the coevolution with increased ammoniagenesis and accompanying gluconeogenesis is speculated to benefit vertebrates in terms of both internal homeostasis and energy metabolism response to acidic stress. The findings provide new insights into our understanding of the possible adaptation of fishes to progressing global environmental acidification. In human kidney, titratable H⁺ and NH₄⁺ comprise the two main components of net acid excretion. V-type H⁺-ATPase-mediated H⁺ excretion may have developed in stenohaline lampreys when they initially invaded freshwater from marine habitats, but this trait is lost in most fishes. Instead, increased reliance on NHE-mediated NH₄⁺ excretion is gradually developed and intensified during fish evolution. Further investigations on more species will be needed to support the hypothesis. Also see the video abstract here https://youtu.be/vZuObtfm-34 .     

Complexity versus Uncertainty: The Question of Staying Alive

Some real objects show a very particular tendency: that of becomingindependent with regard to the uncertainty of their surroundings. This isachieved by the exchange of three quantities: matter, energy andinformation. A conceptual framework, based on both Non-equilibriumThermodynamic and the Mathematical Theory of Communication is proposedin order to review the concept of change in living individuals. Three mainsituations are discussed in this context: passive independence inconnection with resistant living forms (such as seeds, spores, hibernation,...), active independence in connection with the life span of aliving individual (whether an ant or an ant farm), and the newindependence in connection with the general debate of biological evolution.     

Comparative and evolutionary aspects of the photosynthetic electron transfer system of purple bacteria

The cyclic electron transfer system in purple bacteria is composed of the photosynthetic reaction center, the cytochromebc ₁ complex, cytochromec ₂, and ubiquinone. These components share many characteristics with those of photosynthesis and respiration in other organisms. Studies of the cyclic electron transfer system have provided useful insights about the evolution and general mechanisms of membranous energy-conserving systems. The photosynthetic system in purple bacteria may represent a prototype of highly efficient, energy-conserving electron transfer systems in the organisms. Recipient of the Botanical Society Award of Young Scientists, 1992     

The optimization of L-lysine fermentation and a mass transfer model

The efficiency of L-lysine biosynthesis is essentially determined by the power input and aeration ratio in the stirred fermenter. A mass transfer model was developed by means of the results of lysine fermentations in four geometrically similar fermenters with working volumes of 10 1, 50 1, 100 1 and 2500 1 which allows the optimization of lysine fermentation from the energetical point of view. The usefullness of this k_La-model is demonstrated with an example where the power input for an unknown fermenter is calculated.     

Entropy and information in evolving biological systems

Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state to another in a manner that generates structures which allows the system to continue to persist. Two classes of energetic transformations allow this; heat-generating transformations, resulting in a net loss of energy from the system, and conservative transformations, changing unusable energy into states that can be stored and used subsequently. All conservative transformations in biological systems are coupled with heat-generating transformations; hence, inherent biological production, or genealogical proesses, is positively entropic. There is a self-organizing phenomenology common to genealogical phenomena, which imparts an arrow of time to biological systems. Natural selection, which by itself is time-reversible, contributes to the organization of the self-organized genealogical trajectories. The interplay of genealogical (diversity-promoting) and selective (diversity-limiting) processes produces biological order to which the primary contribution is genealogical history. Dynamic changes occuring on times scales shorter than speciation rates are microevolutionary; those occuring on time scales longer than speciation rates are macroevolutionary. Macroevolutionary processes are neither redicible to, nor autonomous from, microevolutionary processes.Authorship alphabetical     

The representation of biological systems from the standpoint of the theory of categories

A mathematical framework for a rigorous theory of general systems is constructed, using the notions of the theory of Categories and Functors introduced by Eilenberg and MacLane (1945,Trans. Am. Math. Soc.,58, 231–94). A short discussion of the basic ideas is given, and their possible application to the theory of biological systems is discussed. On the basis of these considerations, a number of results are proved, including the possibility of selecting a unique representative (a “canonical form”) from a family of mathematical objects, all of which represent the same system. As an example, the representation of the neural net and the finite automaton is constructed in terms of our general theory.     

A relational theory of biological systems II

The general Theory of Categories is applied to the study of the (M, R)-systems previously defined. A set of axioms is provided which characterize “abstract (M, R)-systems”, defined in terms of the Theory of Categories. It is shown that the replication of the repair components of these systems may be accounted for in a natural way within this framework, thereby obviating the need for anad hoc postulation of a replication mechanism. A time-lag structure is introduced into these abstract (M, R)-systems. In order to apply this structure to a discussion of the “morphology” of these systems, it is necessary to make certain assumptions which relate the morphology to the time lags. By so doing, a system of abstract biology is in effect constructed. In particular, a formulation of a general Principle of Optimal Design is proposed for these systems. It is shown under what conditions the repair mechanism of the system will be localized into a spherical region, suggestive of the nuclear arrangements in cells. The possibility of placing an abstract (M, R)-system into optimal form in more than one way is then investigated, and a necessary and sufficient condition for this occurrence is obtained. Some further implications of the above assumptions are then discussed.     

Algorithms for effective querying of compound graph-based pathway databases

Background  

Graph-based pathway ontologies and databases are widely used to represent data about cellular processes. This representation makes it possible to programmatically integrate cellular networks and to investigate them using the well-understood concepts of graph theory in order to predict their structural and dynamic properties. An extension of this graph representation, namely hierarchically structured or compound graphs, in which a member of a biological network may recursively contain a sub-network of a somehow logically similar group of biological objects, provides many additional benefits for analysis of biological pathways, including reduction of complexity by decomposition into distinct components or modules. In this regard, it is essential to effectively query such integrated large compound networks to extract the sub-networks of interest with the help of efficient algorithms and software tools.     

From reproduction to production,stomata are the master regulators

The best predictor of leaf level photosynthetic rate is the porosity of the leaf surface, as determined by the number and aperture of stomata on the leaf. This remarkable correlation between stomatal porosity (or diffusive conductance to water vapour g_s) and CO₂ assimilation rate (A) applies to all major lineages of vascular plants (Figure 1) and is sufficiently predictable that it provides the basis for the model most widely used to predict water and CO₂ fluxes from leaves and canopies. Yet the Ball–Berry formulation is only a phenomenological approximation that captures the emergent character of stomatal behaviour. Progressing to a more mechanistic prediction of plant gas exchange is challenging because of the diversity of biological components regulating stomatal action. These processes are the product of more than 400 million years of co‐evolution between stomatal, vascular and photosynthetic tissues. Both molecular and structural components link the abiotic world of the whole plant with the turgor pressure of the epidermis and guard cells, which ultimately determine stomatal pore size and porosity to water and CO₂ exchange (New Phytol., 168, 2005, 275). In this review we seek to simplify stomatal behaviour by using an evolutionary perspective to understand the principal selective pressures involved in stomatal evolution, thus identifying the primary regulators of stomatal aperture. We start by considering the adaptive process that has locked together the regulation of water and carbon fluxes in vascular plants, finally examining specific evidence for evolution in the proteins responsible for regulating guard cell turgor.     

A note on replication in (M,R)-systems

The condition which allows the existence of induced replication maps in (M,R)-systems is shown to place strong restrictions on the “richness” of the category from which these systems can be constructed. This condition also admits of a simple biological interpretation, which can be checked empirically, and which may offer insight into the physical and biological realizations of these abstract systems.