Outline of a unified approach to physics,biology and sociology

The theory of organismic sets, introduced by N. Rashevsky (Bulletin of Mathematical Biophysics,29, 139–152, 1967;30, 163–174, 1968), is developed further. As has been pointed out, a society is a set of individuals plus the products of their activities, which result in their interactions. A multicellular organism is a set of cells plus the products of their activities, while a unicellular organism is a set of genes plus the products of their activities. It is now pointed out that a physical system is a set of elementary particles plus the product of their activities, such as transitions from one energy level to another. Therefore physical, biological and sociological phenomena can be considered from a unified set-theoretical point of view. The notion of a “world set” is introduced. It consists of the union of physical and of organismic sets. In physical sets the formation of different structure is governed preponderantly by analytical functions, which are special type of relations. In organismic sets, which represent biological organisms and societies, the formation of various structures is governed preponderantly by requirements that some relations, which are not functions, be satisfied. This is called the postulate of relational forces. Inasmuch as every function is a relation (F-relation) but not every relation is a function (Q-relation), it has been shown previously (Rashevsky,Bulletin of Mathematical Biophysics,29, 643–648, 1967) that the physical forces are only a special kind of relational force and that, therefore, the postulate of relational forces applies equally to physics, biology and sociology. By developing the earlier theory of organismic sets, we deduce the following conclusions: 1) A cell in which the genes are completely specialized, as is implied by the “one gene—one enzyme” principle, cannot be formed spontaneously. 2) By introducing the notion of organismic sets of different orders so that the elements of an organismic set of ordern are themselves organismic sets of order (n−1), we prove that in multicellular organisms no cell can be specialized completely; it performs, in addition to its special functions, also a number of others performed by other cells. 3) A differentiated multicellular organism cannot form spontaneously. It can only develop from simpler, less differentiated organisms. The same holds about societies. Highly specialized contemporary societies cannot appear spontaneously; they gradually develop from primitive, non-specialized societies. 4) In a multicellular organism a specialization of a cell is practically irreversible. 5) Every organismic set of ordern>1, that is, a multicellular organism as well as a society, is mortal. Civilizations die, and others may come in their place. 6) Barring special inhibitory conditions, all organisms multiply. 7) In cells there must exist specially-regulatory genes besides the so-called structural genes. 8) In basically identically-built organisms, but which are built from different material (proteins), a substitution of a part of one organism for the homologous part of another impairs the normal functioning (protein specificity of different species). 9) Even unicellular organisms show sexual differentiation and polarization. 10) Symbiotic and parasitic phenomena are included in the theory of organismic sets. Finally some general speculations are made in regard to the possibility of discovering laws of physics by pure mathematical reasoning, something in which Einstein has expressed explicit faith. From the above theory, such a thing appears to be possible. Also the idea of Poincaré, that the laws of physics as we perceive them are largely due to our psychobiological structure, is discussed.     

A remark on sensory deprivation from the point of view of organismic sets

It is shown that from the definition of organismic sets (Rashevsky,Organismic Sets. Some Reflections on the Nature of Life and Society, Holland, Michigan, Mathematical Biology, Inc. and Grosse Pointe, Michigan, J. M. Richards Laboratory) a complete sensory deprivation of an organismic set of ordern=2 should result in malfunctioning of the set. A generalization to higher order sets is suggested.     

A remark on the course of development of organismic sets

The basic postulate la, which governs the development of organismic sets, introduced previously (Bulletin of Mathematical Biophysics,31, 159–198, 1969), is generalized so as to contain also the rates of changes of the number and variety of differentQ-relations which determine an organismic set. It is thus brought closer to the Lagrangian principle in physics. It is pointed out that the postulate also provides a criterion of stability of an organismic set.     

Relational forces and structures produced by them

After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.     

Organismic sets: Outline of a general theory of biological and social organisms

The discussion as to whether societies are organisms andvice versa has been going on for a long time. The question is meaningless unless a clear definition of the term “organism” is made. Once such a definition is made, the question may be answered by studying whether there exists any relational isomorphism between what the biologist calls an organism and what the sociologist calls society. Such a study should also include animal societies studied by ecologists. Both human and animal societies are sets of individuals together with certain other objects which are the products of their activities. A multicellular organism is a set of cells together with some products of their activities. A cell itself may be regarded as a set of genes together with the products of their activities because every component of the cell is either directly or indirectly the result of the activities of the genes. Thus it is natural to define both biological and social organisms as special kinds of sets. A number of definitions are given in this paper which define what we call here organismic sets. Postulates are introduced which characterize such sets, and a number of conclusions are drawn. It is shown that an organismic set, as defined here, does represent some basic relational aspects of both biological organisms and societies. In particular a clarification and a sharpening of the Postulate of Relational Forces given previously (Bull. Math. Biophysics,28, 283–308, 1966) is presented. It is shown that from the basic definitions and postulates of the theory of organismic sets, it folows that only such elements of those sets will aggregate spontaneously, which are not completely “specialized” in the performance of only one activity. It is further shown that such “non-specialized” elements undergo a process of specialization, and as a result of it their spontaneous aggregation into organismic sets becomes impossible. This throws light on the problem of the origin of life on Earth and the present absence of the appearance of life by spontaneous generation. Some applications to problems of ontogenesis and philogenesis are made. Finally the relation between physics, biology, and sociology is discussed in the light of the theory of organismic sets.     

A note on the development of organismic sets

It is suggested that the development of organismic sets is governed not by the maximalization of the integral survival value, as suggested previously (Bull. Math. Biophysics,28, 283–308, 1966;29, 139–152, 1967;30, 163–174, 1968), but by maximizing the number of new relations which appear as an organismic set develops.     

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.     

Interactions between metazoans,autotrophs, mixotrophs and bacterioplankton in nutrient‐depleted high DOC environments: a long‐term experiment

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Impacts of elevated terrestrial nutrient loads and temperature on pelagic food‐web efficiency and fish production

Both temperature and terrestrial organic matter have strong impacts on aquatic food‐web dynamics and production. Temperature affects vital rates of all organisms, and terrestrial organic matter can act both as an energy source for lower trophic levels, while simultaneously reducing light availability for autotrophic production. As climate change predictions for the Baltic Sea and elsewhere suggest increases in both terrestrial matter runoff and increases in temperature, we studied the effects on pelagic food‐web dynamics and food‐web efficiency in a plausible future scenario with respect to these abiotic variables in a large‐scale mesocosm experiment. Total basal (phytoplankton plus bacterial) production was slightly reduced when only increasing temperatures, but was otherwise similar across all other treatments. Separate increases in nutrient loads and temperature decreased the ratio of autotrophic:heterotrophic production, but the combined treatment of elevated temperature and terrestrial nutrient loads increased both fish production and food‐web efficiency. CDOM: Chl a ratios strongly indicated that terrestrial and not autotrophic carbon was the main energy source in these food webs and our results also showed that zooplankton biomass was positively correlated with increased bacterial production. Concomitantly, biomass of the dominant calanoid copepod Acartia sp. increased as an effect of increased temperature. As the combined effects of increased temperature and terrestrial organic nutrient loads were required to increase zooplankton abundance and fish production, conclusions about effects of climate change on food‐web dynamics and fish production must be based on realistic combinations of several abiotic factors. Moreover, our results question established notions on the net inefficiency of heterotrophic carbon transfer to the top of the food web.     

Organismic sets: II. Some general considerations

The theory of organismic sets, developed in previous papers (Bull. Math. Biophysics,29, 139–152; 389–393; 643–647) is further generalized. To conform better with some biological and sociological facts the basic definitions are made more general. The conclusion is reached that every organismic setS _o is in general the union of three disjoined subsetsS _o1 ,S _o2 andS _o3 . Of these the subsetS _o1 , called the “core” is equivalent to an organismic set defined in previous publications. Its functioning is essential for the functioning ofS _o . The subsetsS _o2 andS _o3 , taken alone, are not organismic sets. The first of them is responsible for such biological or sociological functions which are not necessary for the “immediate” survival ofS _o but which are important for adaptation to changing environment and are therefore essential for a “long range survival.” The second one,S _o3 , is responsible for biological or social functions which are irrelevant for the survival ofS _o . Biological and sociological examples ofS _o2 andS _o3 are given. In addition to the fundamental theorem established in the first of the above mentioned papers, three new conclusions are derived. One is that in organismic sets of order higher than zero not all elements are specialized. The second is that every organismic set of order higher than zero is mortal. The third is that with increasing specialization the intensities of some activities in some elements ofS _o are reduced. Again the biological and sociological examples are given. At the end some very general speculations are made on the possible relation between biology and physics and on the possibility of “relationalizing” physics.     

The feeding habits of three Mediterranean sea anemone species,Anemonia viridis (Forskål),Actinia equina (Linnaeus) andCereus pedunculatus (Pennant)

The feeding habits of the Mediterranean sea anemonesCereus pedunculatus, Actinia equina andAnemonia viridis were examined mainly by analysing their coelenteron contents. The three species are opportunistic omnivorous suspension feeders. Main source of food forA. viridis andC. pedunculatus are crustaceans (mainly amphipods and decapods, respectively), while for the midlittoral speciesA. equina, it is organic detritus. Using the same method, the temporal and spatial changes in the diet ofA. viridis were examined. During the whole year, crustaceans seem to be the main source of food forA. viridis. The diet composition of this species, however, differs remarkably in space, possibly reflecting the different composition of the macrobenthic organismic assemblages in different areas. The data collected are compared with the limited bibliographical information.     

Metabolic regulation of pyruvate kinase isolated from autotrophically and heterotrophically grown Paracoccus denitrificans

Pyruvate kinase (ATP: pyruvate phosphotransferase (EC 2.7.1.40) was partially purified from both autotrophically and heterotrophycally grown Paracoccus denitrificans. The organism grown under heterotrophic conditions contains four times more pyruvate kinase than under autotrophic conditions. The enzyme isolated from both sources exhibited sigmoidal kinetics for both phosphoenolpyruvate (PEP) and ADP. The apparent M _m for ADP and PEP in the autotrophic enzyme were 0.63 mM ADP and 0.25 mM PEP. The effect of several low molecular weight metabolites on the pyruvate kinase activity was investigated. Ribose-5-phosphate, glucose-6-phosphate and AMP stimulated the reaction at low ADP levels; this stimulation was brought about by an alteration in the apparent K _m for ADP. The pyruvate kinases differ in their response to adenine nucleotides, but both preparations seem to be under adenylate control. The results are discussed in relation to the role of pyruvate kinase as a regulatory enzyme in P. denitrificans grown under both autotrophic and heterotrophic conditions.Non-Common Abbreviations PEP phosphoenolpyruvate - R-5-P ribose-5-phosphate - G-6-P glucose-6-phosphate - F-6-P fructose-6-phosphate - 3-PGA 3-phosphoglycerate     

Sporadic sustained nonperiodic oscillations in the activities of organismic sets

In combining the author's theories of organismic sets (Rashevsky,Bull. Math. Biophysics,31, 159–198, 1969a) and Robert Rosen's theory of (M, R)-systems (Bull. Math. Biophysics,20, 245–265, 1958), a conclusion is reached that the number of either normal or pathological phenomena in organismic sets may occur. Those phenomena are characterized by occurring spontaneously once in a while but are not exactly periodic. Some epilepsies are an example of such pathological phenomena in the brain.     

Organismic sets and biological epimorphism

It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.     

The influence of humic substances on lacustrine planktonic food chains

Humic substances (HS) might influence planktonic food chains in lakes in two ways: 1) by altering the physical or chemical environment and thus modifying autotrophic primary production and the dependent food chains; 2) by acting as a direct carbon/energy source for food chains. HS compete with phytoplankton for available quanta underwater and this effect is seen in the reduced euphotic zone depth in lakes with high concentrations of HS. Thus potential photosynthetic production is lower in the presence of HS. However, this effect can be offset in small lakes in which the depth of mixing is also reduced when HS concentrations are high. Complexation by HS of important nutrients such as iron and phosphorus may also restrict primary production. Evidence is accumulating that photosynthetic primary production is insufficient to support measured metabolic activity in humic lakes, which implies that metabolism of allochthonous HS underpins much of the observed activity. Studies of bacterial abundance and growth in the presence of HS support the view that bacteria are the most significant utilisers of HS. This use is apparently facilitated by photolysis of HS, particularly by short wavelength radiation. Bacteria are grazed by both micro-zooplankton (heterotrophic and mixotrophic flagellates and ciliates) and macrozooplankton. It is within this microbial community that the food chains derived from autotrophic and allotrophic sources interact. These effects of HS on food chains are discussed in relation to possible implications for the response of different lake types to eutrophication.     

Some considerations on relational equilibria

A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light of the theory.     

Natural transformations of organismic structures

The mathematical structures underlying the theories of organismic sets, (M, R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors. Their natural transformations allow the comparison of distinct entities, as well as the modelling of dynamics in “organismic” structures.     

The obligate autotroph — the demise of a concept

Autotrophy is a life style in which inorganic compounds provide for all nutritional needs of an organism. Implicit in this definition is the capacity of an organism to derive all cell carbon from CO₂ and to obtain ATP either photosynthetically or chemolithotrophically. The existence of bacteria with such potentials has been known since the work of Winogradsky in the 1880's. The question explored in this paper is whether bacteria exist that must of necessity live autotrophically, i.e., the obligate autotrophsensu Winogradsky. The evidence is briefly reviewed and leads to four conclusions. One: there is no obligatory coupling between phototrophy and autotrophy or between chemolithotrophy and autotrophy. Two: autotrophic bacteria are not uniquely inhibited by organic matter. Three: all putative obligate autotrophic bacteria so far tested assimilate and metabolize exogenously supplied organic compounds. Four: mixotrophy can exist with respect to autotrophic and heterotrophic biosynthetic mechanisms and/or to chemolithotrophic and chemoorganotrophic energy-generating processes. Examples remain of bacteria that have not been cultured in the absence of an inorganic energy source or light. Such forms are appropriately described as obligate chemolithotrophs or obligate phototrophs. The available evidence, briefly categorized above, suggest that none of these bacteria is, at the same time, an obligate autotroph. From ecological and evolutionary considerations, an absolute dependence on carbon dioxide for all carbon makes little sense, and bacteria with such a requirement would be an anachronism on earth as it now exists. A lecture delivered before the third meeting of the Northwest European Microbiological Group, on August 18, 1971 at Utrecht, the Netherlands. The work reported from the author's laboratory was supported by grants from the National Science Foundation.     

THE OXIDATION OF HYDROGEN SULFIDE BY BEGGIATOA

Knowledge of the conditions in which Beggiatoa is capable of autotrophic nutrition is incomplete. It is not known whether sulfur-free trichomes from heterotrophic cultures are able to return to the utilization of H₂S-oxidation. Devices were developed which permitted the supply of pure cultures of Beggiatoa, previously cultivated heterotrophically, with H₂S, O₂, and CO₂. Development in media devoid of organic nutrients was achieved, and subculturing under autotrophic conditions could be repeated indefinitely. The strains used behaved differently with respect to their tendency to grow autotrophically. The ability to dispense with organic substrates corresponds to the place in the groups to which they had previously been assigned. All the strains multiplied better when, under otherwise equal conditions, the inorganic medium was supplemented with acetate, very low concentrations of which were effective. This result may, however, be due to the selection of varieties by the isolation procedure. The mixotrophic tendency of our strains may not be a general feature of the genus. There are indications that the wider forms of Beggiatoa tend more toward autotrophic growth than the narrower ones.