The DNA-protein coding problem

The DNA-protein coding problem is given a general algebraic formulation, the consequences of which are then explored by standard mathematical methods. To keep the treatment self-contained, the mathematical techniques to be used are explained in detail. It is demonstrated that there exista priori a countably infinite number of different abstract DNA-protein codes, thereby showing that inductive attempts to construct such a code will most likely be fruitless. A notion of ergodicity is then introduced, which imposes a number of restrictions on the admissible codes, and, in fact, these considerations enable us toderive a small portion of a code which, if our hypothesis of ergodicity is correct, must occur in nature. Finally, we discuss briefly the problem as to whether there can exist more than one DNA-protein code in nature.     

An hypothesis of freese and the DNA-protein coding problem

Freese’s Hypothesis states that a single specific alteration in the sequence of nucleotides of an information-bearing DNA molecule results in a specific mutational effect. Within the framework of the DNA-protein coding problem developed elsewhere, and assuming the quasi-ergodicity of the general coding process, it is shown that Freese’s Hypothesis allows us to derive expressions for the length of the smallest mutable DNA molecule and to obtain a bound for the maximal number of allelic molecules of fixed length. To illustrate these ideas, calculations are carried out on appropriate data from bacternophage and man, and the results are shown to differ by a factor of 10 (modulo the rather crude approximations used). It is further shown that, if ρ(N) and ϱ(N) are respectively the number of information-bearing words of lengthN in a given code and the number of words of lengthN, then the number lim ρ(N)/ϱ(N) depends sensitively on the parameter ∈ which specifiesN→∞ the given code. The implications of this result for the spontaneous aggregation of a sufficient number of information-bearing words to characterize an organism are discussed. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

A note on relations between sets

From the definition of a strong and weakn-ary relation betweenn sets, given in a previous paper (Bulletin of Mathematical Biophysics,27, 477–492), it follows that for a given set ofn sets and givenn-ary relationR between them there can exist only one strong relation, but a large number of weak ones. An expression for the total number of possible weak relations is derived and the notion of the degree of weakness of a relation is introduced and discussed.     

Some remarks on molecular biology

The binding energy of a very long molecular chain, composed of different classes of molecules, depends in general on the order of the molecules. It is shown that under very general conditions there exists for a givenbrutto chemical composition of a chain, a class of chains which is characterized by a total binding energy which is equal to the total binding energy of any other prescribed chain of different composition within the limits of unsharpness of the energy level. This establishes a criterion formapping of a class of configurations of long chain molecules on another class. To the extent that a mapping constitutes a generalized code those results contribute to the theory of molecular codes. Applying to our results the results of a previous paper (1959,Bull. Math. Biophysics,21, 309–326), we arrive at the conclusion that the self-replication of a living molecule may be the property not of a particular structure but of classes of structures.     

Mn2+对A/O-BAF系统处理效能和细菌群落多样性的影响

【目的】通过考察Mn²⁺对A/O-BAF系统处理效能及微生物群落多样性的影响,研究了15℃下不同浓度Mn²⁺对A/O-BAF系统处理效能的影响,并通过高通量测序考察了细菌群落多样性的变化情况。【方法】在温度15°C、水力负荷0.50 m³/(m²·h)、气水比10:1的条件下,在进水中投加Mn²⁺,考察反应器处理效能的变化情况,并通过高通量测序对BAF生物膜样品进行分析。【结果】2.0 mg/L Mn²⁺作用下A/O-BAF系统的COD、NH₄⁺-N、TN、TP去除率分别提高3.51%、2.21%、6.26%和12.13%;4.0 mg/L Mn²⁺作用下COD、NH₄⁺-N、TN、TP去除率分别提高了4.24%、1.92%、7.75%和10.73%;Mn²⁺作用下A/O-BAF系统内反硝化细菌和亚硝酸菌的数量明显增加,硝酸菌...     

On relations between sets: II

The notion of relations between sets, defined in a previous publication (Bull. Math. Biophysics,23, 233–235, 1961) is generalized and some biological examples are given. A generalization ton-ary relation is suggested.     

椰子木蛾的产卵节律及其对寄主植物的产卵选择性

【背景】椰子木蛾是近年来新入侵我国棕榈科植物的害虫,研究其产卵习性可为监测和防治该虫提供参考。【方法】在室内条件下,观察、记录了椰子木蛾雌成虫的产卵节律及其对不同寄主植物的产卵选择性。【结果】椰子木蛾最高日产卵量可达34.4粒·头-1,且主要集中在羽化后4 d内产卵,占总产卵量的54.1%;产卵活动主要发生在夜间23:00到次日8:00;在椰子、蒲葵、大王棕、槟榔和散尾葵等寄主植物上的产卵量无显著差异,为89.3~147.7粒·头-1,但产卵位置存在差别。【结论与意义】椰子木蛾雌成虫具有较强的繁殖能力和产卵节律性,且在不同寄主植物上的产卵量一致。     

Ecosystem and Ecotomo: A Nature or Society-Nature Relationship?

The notion of entorno is discussed and its mutual dependence upon the organism is emphasised. Both the etymology and meaning of ethos, oikos, entorno and ecotomo are discussed. The intimate relation between Ethology and Ecology is also shown. A reference background is given to explain how the commonly considered isolated components organism/society and entorno/nature articulate in the form of a relation. It is argued that the integrated concepts that originated the notion of ecosystem have been set aside. The term ecotomo is proposed, which refers to any territorial unit that, considered at a local, regional or global level, emerges from the society-nature relationship.     

A sociological approach to biology

The paper develops further some suggestions made previously (Bulletin of Mathematical Biophysics,28, 283–308, 1966) that certain biological phenomena may be more easily interpreted from a “sociological” point of view by considering the organism as a social aggregate of cells and a cell as a social aggregate of genes. In this light the problems of origin of life on earth, of aging, and of parasitism and symbiosis are discussed. The notion of social aggregates of different orders is introduced.     

Some remarks on the mathematical bio-sociology of the relativity of injustice

The author's theory of the adoption of certain types of behavior patterns (Rashevsky, N., 1957, “Contributions to the Theory Initiative Behavior”.Bull. Maths. Biophysics,19, 91–119; 1968,Looking at History through Mathematics, Cambridge, Massachusetts: M.I.T. Press) consisting of elementary behaviors for each of which there is an opposite one and the two are mutually exclusive, is applied to describe the changes in the general type of behavior of a society. The elementary acts of which the whole problem consists may be either overt activities or beliefs or opinions. The general behavior patternsadopted by the society are considered as the “proper” or “just” ones. Any deviation from it in either one or more of the component elementary behaviors is considered as “unjust” and is subject to some punitive action. The total number of possible mutually exclusive behavior patterns is very large but finite. Within this very large range of possible patterns, we find that this notion of justice is relative, because changes from any behavior pattern to any other may occur. It is further shown that the amount of punishment for the deviation from the accepted pattern in order to be effective as well as efficient must be applied in different ways to different individuals even for the same transgression.     

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.     

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.     

A monograph of <Emphasis Type="Italic">Ascogrammitis</Emphasis>, a new genus of grammitid ferns (Polypodiaceae)

This paper describes Ascogrammitis, a new genus of grammitid ferns formerly combined under Terpsichore. Seventeen species are recognized, including five new ones: A. clavigera, A. colombiensis, A. loxensis, A. oxapampensis, and A. tungurahuae. New combinations are made for A. alan-smithii, A. anfractuosa, A. angustipes, A. athyrioides, A. clathrata, A. cuencana, A. david-smithii, A. dilatata, A. nana, A. pichinchae, A. pichinchensis, A. stuebelii, and a lectotype is chosen for Polypodium induens. A key is provided to distinguish the species, and illustrations are provided for 12 species. The genus occurs primarily in neotropical cloud forests, with the greatest diversity in the Andes. Ascogrammitis is one of two monophyletic groups of grammitid ferns that are consistently associated with Acrospermum, an epibiotic bitunicate ascomycete that produces black clavate fruiting bodies.     

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.     

What is Nummulites depressus Kenawy 1978? Evolution of Nummulites fabianii group in the Middle Eocene of Egypt

New species Nummulites vetustufabianiin. sp. is described from the El Hamra Formation, Gara El Hamra section Bahariya Oasis Western Desert. The biometrical measurements include maximum and minimum diameter of the successive radii and heights of whorls, length/height ratio, number of chambers and the marginal cord thickness of each whorl for the megalospheric generation as well as the diameter of proloculus were elaborated to differentiate between some allied granulated species such as Nummulites depressus, Nummulites decrouezae, Nummulites cuvillieri and N. vetustufabianiin. sp.Nummulites fabianii group has lateral distribution for the entire Tethys basin, hence such biometrical studies are needed to emphasise the polyphyletic nature of the group.     

Identification of DNA-binding protein target sequences by physical effective energy functions: free energy analysis of lambda repressor-DNA complexes.

Background  

Specific binding of proteins to DNA is one of the most common ways gene expression is controlled. Although general rules for the DNA-protein recognition can be derived, the ambiguous and complex nature of this mechanism precludes a simple recognition code, therefore the prediction of DNA target sequences is not straightforward. DNA-protein interactions can be studied using computational methods which can complement the current experimental methods and offer some advantages. In the present work we use physical effective potentials to evaluate the DNA-protein binding affinities for the λ repressor-DNA complex for which structural and thermodynamic experimental data are available.     

Identification of further <Emphasis Type="Italic">Craterostigma plantagineum cdt</Emphasis> mutants affected in abscisic acid mediated desiccation tolerance

The resurrection plant (Craterostigma plantagineum) is desiccation tolerant. However, callus derived from this plant, when propagated in vitro, requires exogenously applied abscisic acid (ABA) in order to survive desiccation. Treatment of callus tissue with ABA induces most of the genes that are induced by dehydration in the whole plant. This property has been exploited for the isolation of mutants that show dominant phenotypes resulting from the ectopic expression of endogenous genes induced by the insertion of a foreign promoter. Here we describe new T-DNA tagged Craterostigma desiccation-tolerant (cdt) mutants with different molecular and physiological characteristics, suggesting that different pathways of desiccation tolerance are affected. One of the mutants, cdt-2, constitutively expresses known osmoprotective Lea genes in callus and leaf tissue. Further analysis of this mutant revealed that the tagged locus is similar to a previously characterised gene, CDT-1, which codes for a signalling molecule that confers desiccation tolerance. The nature of the T-DNA insertion provides insight into the mechanism by which the CDT-1/2 gene family functions in ABA signal transduction.     

Spirits of Uncertainty: Eventologies of Nature on China’s Frontiers

ABSTRACT

Studies of the environmental spirit world have been pursuing two main lines of inquiry: (1) that indigenous claims on ecological thought, including beliefs in chthonic spirits and mountain deities, are the outcome of a global process of abstraction and the commoditisation of nature which acts as technology of governmentality for the production of discursive formations through which neoliberal environmental subjectivities can emerge and (2) that the pitfalls of the nature/culture dualism can be avoided by giving priority to nonhuman subjectivities and positing sociologies of nature as subordinate to ontologies of the self-other divide or action-orienting cosmologies of local ‘nature’. The contributors of this collection engage with the spirit worlds and other invisible agents that constitute the everyday landscape of a number of ethnic groups in western China. While declining to engage with the notion of animism or subscribing to totalising ‘cosmologies’, the authors prefer to extract the eventfulness of haphazard and radically uncertain interactions with spirits or wondrous signs apt to be transformed into marvels and rumours. The ethnographies presented in this collection reveal an eventology of spirit worlds and landscape on China’s borderlands, an inquiry that – unlike history – does not study ‘events’ as such but the relation between what is deemed to be an event, a surprise, or a manifestation of wonder and what is deemed to be the innate, natural, ordinary, everyday life.     

The Symptom

The symptom (which here refers to both the clinical or ‘objective’ sign, that is, the sign that physicians believe cannot lie, and the patient’s subjective revelation of disorder, which is always considered suspect) has been relegated by a number of semioticians to a category of signs often considered of little consequence, a ‘natural’ sign signaling some specific condition or state within the body whose object stands in a strictly biological and securely determined relationship to the symptom. I believe the symptom, however, is deep, rich, and symbolic in every sense, signifying the misadventures of a body impaled by its perceptual skills and history within its own unique Umwelt or sign-world. Unfortunately, the notion of a sign which reflects biologically coded events alone suggests the body is without the ability to think, learn, and produce a story of unlimited semiosis. This should seem especially problematic to those biosemioticians who find analogic codes of much greater importance than the supposedly digital codes of DNA. I suggest that the disordered and disorderly body and the Umwelt within which it survives offer biosemioticians and those who pursue semiotic models in other disciplines an important opportunity to jointly and more fully explore the experienced world of health and illness, a world in which culture and nature are fully interpenetrated.     

Analysis of tracer experiments: IV. The kinetics of generalN compartment systems

The methods of C. W. Sheppard and A. S. Householder (Jour. App. Physcis,22, 510–20, 1951), H. D. Landahl (Bull. Math. Biophysics,16, 151–54, 1954) and H. E. Hart (Bull. Math. Biophysics,17, 87–94, 1955;ibid.,19, 61–72, 1957;ibid.,20, 281–87, 1958) are employed in studying the kinetics of generalN compartment systems. It is shown that the nature of the transfer processes occurring in fluid flow systems and the chemical processes occurring in quadratic systems and in catalyzed quadratic systems can in principle be completely determined for all polynomial dependencies. Systems involving three-body and higher-order interactions can be completely solved, however, only if supplementary information is available. Research supported by the Atomic Energy Commission, Contract AT (30-1)-1551.