Remark on an interesting problem in topological biology

The possibility of several homotopic classes of mappings of the graph of an organism onto the primordial graph (Bull. Math. Biophysics,16, 317–48, 1954) is considered. An application of this possibility is suggested for the theoretical determination as to what type of new biological functions may be acquired by certain cells which originally perform a different biological function.     

A contribution to Rashevsky’s mathematical theory of development

The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.     

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.     

Contributions to relational biology

The principle of biotopological mapping (Rashevsky, 1954,Bull. Math. Biophysics,16, 317–48) is given a generalized formulation, as the principle of relational epimorphism in biology. The connection between this principle and Robert Rosen’s representation of organisms by means of categories (1958,Bull. Math. Biophysics,20, 317–41) is studied. Rosen’s theory of (M,R)-systems, (1958,Bull. Math. Biophysics,20, 245–60) is generalized by dropping the assumption that only terminalM _i components are sending inputs into theR _i components. It is shown that, if the primordial organism is an (M,R)-system, then the higher organisms, obtained by a construction well discussed previously (1958,Bull. Math. Biophysics,20, 71–93), are also (M,R)-systems. Several theorems about such derived (M,R)-systems are demonstrated. It is shown that Rosen’s concept of an organism as a set of mappings throws light on phenomena of synesthesia and also leads to the conclusion that Gestalt phenomena must occur not only in the fields of visual and auditory perception but in perceptions of any modality.     

A note on the geometrization of biology

In connection with a recently proposed topological model of an organism (Bull. Math. Biophysics,18, 31–56, 1956), it is pointed out that the dependence of some properties of the studied topological spaces on the type of space in which they are imbedded reflects some aspects of the dependence of the organism on its environment.     

Primordial germ cell proliferation is impaired in Fused Toes mutant embryos

Over the first 4 days of their life, primordial germ cells invade the endoderm, migrate into and through the developing hindgut, and traverse to the genital ridge where they cluster and ultimately inhabit the nascent gonad. Specific signal–receptor combinations between primordial germ cells and their immediate environment establish successful migration and colonization. Here we demonstrate that disruption of a cluster of six genes on murine chromosome 8, as exemplified by the Fused Toes (Ft) mutant mouse model, results in severely decreased numbers of primordial germ cells within the early gonad. Primordial germ cell migration appeared normal within Ft mutant embryos; however, germ cell counts progressively decreased during this time. Although no difference in apoptosis was detected, we report a critical decrease in primordial germ cell proliferation by E12.5. The six genes within the Ft locus include the IrxB cluster (Irx3, -5, -6), Fts, Ftm, and Fto, of which only Ftm, Fto, and Fts are expressed in primordial germ cells of the early gonad. From these studies, we have discovered that the Ft locus on mouse chromosome 8 is associated with cell cycle deficits within the primordial germ cell population that initiates just before translocation into the genital ridge.     

兰州唐古特白刺根际微生物分离鉴定

【目的】从兰州唐古特白刺根际分离得到对植物有潜在促生效果的功能微生物，为研发相关菌种制剂的研究奠定基础。【方法】通过平板划线法从其根际分离纯化出6株细菌，并对菌株进行形态特征观察、革兰氏染色等一系列生理生化试验。用藜麦检测各菌株的促生功能，并对具有优良促生作用的1个菌株16S rRNA基因进行分子鉴定及基因草图绘制。【结果】根据生化鉴定结果，6株细菌分别属于不动杆菌属(Acinetobacter)、土壤杆菌属(Agrobacterium)、类芽孢杆菌属(Paenibacillus)、芽孢杆菌属(Bacillus)、鞘氨醇单胞菌属(Sphingomonas)和假单胞菌属(Pseudomonas)。其中，16S rRNA基因鉴定BC4属于肠杆菌属(Enterobacter)，具有较好的促生效果。【结论】BC4具有较好的促生效果，为兰州唐古特白刺菌种资源的开发和利用提供了一定的理论依据。     

A note on biotopology of reproduction

In a recent paper (Bull. Math. Biophysics, 20, 245, 1958), Robert Rosen applied topological considerations to the study of an organism as a whole. Those considerations have no direct relation to the principle of biotopological mapping. They rather represent a topological model of an organism, especially a model of the repair mechanisms which organisms possess for lost or impaired parts. In this note it is shown that the model introduced by Rosen may possibly be derived from the principle of biotopological mapping plus a proper definition of the primordial. Such a derivation may also provide a clue to a proper biotopological approach to the problem of multiplication of organisms.     

Residui di Leccete pure e miste sulla Murgia di Putignano

Summary

Purpose of this paper is to point out the residues of Quercus Ilex woods in the hilly region of Murgia di Putignano (Puglia) which lies inside the distribution area of Q. trojana, now the main wood-forming tree-species of this territory.

Fourteen different small Q. Ilex stands are mentioned, as marked on alleged map. One of them (n° 1 on the map) has been more carefully studied through a whole year, and all plants growing in it have been collected.     

Stenogrammitis, a new genus of grammitid ferns segregated from Lellingeria (Polypodiaceae)

Stenogrammitis , a new genus of grammitid ferns, is segregated from Lellingeria based on morphological and molecular evidence. It differs from Lellingeria by linear leaves usually less than 5 mm wide, clathrate iridescent rhizome scales that are glabrous except for a single apical cilium, veins unbranched and only one per segment, fertile veins usually with the dark sclerenchyma visible beneath the sporangia, and x = 33. In contrast, Lellingeria has broader laminae, veins pinnate within the segments, and fertile veins not visible beneath the sporangia. Melpomene, which is sister to Stenogrammitis and Lellingeria, differs from those two genera by reddish setae on the leaves and rhizome scales papillate at the apex. Some species of Stenogrammitis are also distinctive by hemidimorphic laminae that have the fertile portion less dissected than the sterile. Stenogrammitis is pantropical and currently comprises 24 species, 12 of which occur in the Neotropics, six in Africa, four in Madagascar, and two on Pacific Islands. New combinations are made for Stenogrammitis aethiopica, S. anamorphosa, S. ascensionensis, S. boivinii, S. delitescens, S. jamesonii, S. hartii, S. hellwigii, S. hildebrandtii, S. limula, S. luetzelburgii, S. myosuroides, S. nutata, S. oosora, S. paucipinnata, S. prionodes, S. pumila, S. ruglessii, S. rupestris, S. saffordii, S. strangeana, S. tomensis, S. subcoriacea, and S. wittigiana. Lectotypifications are made for Grammitis muscosa, Polypodium itatiayense, P. oosorum var. micropecten, P. serrulatum forma major, P. serrulatum forma minor, S. luetzelburgii, S. myosuroides, and S. wittigiana. Illustrations are presented for the diagnostic characters of the genus, as well as a map with the geographical distribution.     

Some theorems in topology and a possible biological implication

In a previous paper (Bull. Math. Biophysics,16, 317–48, 1954) a transformationT of one graph into another was suggested, which may describe the relations between organisms of different complexity. In this paper some topological properties of the transformationT are studied. It is shown that the fundamental group of the transformed graph is homomorph to the fundamental group of the original graph. An expression is derived for the number of points in a point base of the transformed graph in terms of the number of points of the point base of the original when the point base of the latter consists only of residual points, and it is shown that the ratio of the number of points of the point base to the total number of points of the graph is in that case greater in the transformed graph than in the original. A combinatorial problem arising in connection with the transformationT is solved by deriving the number of possible ways in whichn-n _i indistinguishable elements may be arranged inn _i classes, permitting some of then _i classes to be empty. The possible biological meaning of the increased ratio of the number of points of the point base to the total number of points of the graph is discussed. It is suggested that it may be interpreted as a decrease of regenerating ability with increase of differentiation of the organism. Those considerations suggest the possibility of deriving some general biological laws from the consideration of the properties of the transformation only, regardless of the choice of the primordial graph.     

Contributions to topological biology: Some considerations on the primordial graph and on some possible transformations

This paper is a continuation of some discussions published previously (Bull. Math. Biophysics,16, 317–347, 1954). A different example of a primordial graph is suggested and discussed. Then six different types of geometric transformations, similar in some respects to the one discussed in the previous paper are proposed. Another set of seven different transformations which emphasize the central role of the circulatory system is described. A theorem about the “lumping” of several points of a graph into one point is proved and possible biological aspects of it are discussed.     

APPARENT PREDATION OF MICROCYSTIS AERUGINOSA KüTZ. EMEND ELENKIN BY A SAPROSPIRA-LIKE BACTERIUM IN A HYPERTROPHIC LAKE (HARTBEESPOORT DAM,SOUTH AFRICA)

SUMMARY

The cyanobacterium Microcystis aeruginosa is the dominant autotroph in hypertrophic Hartbeespoort Dam, South Africa. Tn early summer (November) of 1983 and 1984 Microcystis colonies were heavily colonized by a gram-negative, spiral-shaped organism whose filaments appeared as si.ngle cells under both the light and scanning electron microscope. DNA staining with 4'6 diamidino-2-phenylindole (DAPI) revealed that each filament consisted of a number of bow-shaped cells. The organism has been tentatively identified as a bacterium, Saprospira albida, on the basis of it morphology. The Microcystis cells at the site of colonization were apochlorotic suggesting lysis by Saprospira.     

Oxidative-stress-induced production of pyocyanin by Xanthomonas campestris and its effect on the indicator target organism, Escherichia coli

Pyocyanin, a potential antimicrobial agent, was secreted by Xanthomonas campestris. Treatments with agents causing oxidative stress in the organism caused up to 4.4-fold increase in pyocyanin production. Pyocyanin added in the extracellular space did not affect growth rate of X. campestris, but decreased maximum cell concentration and specific product formation. However, the growth of Escherichia coli, the indicator target organism, was affected by pyocyanin. There was also a significant increase in the intracellular reactive oxygen species (ROS) concentration and antioxidant enzyme [catalase, superoxide dismutase (SOD)] concentrations, in the presence of pyocyanin. The intracellular ROS concentrations in E. coli formed upon exposure to pyocyanin, which is an indicator of the toxicity, was dependent on the growth phase of the organism. Studies with mutants of E. coli showed that intracellular ROS concentration was not significantly affected by the absence of the regulon OxyR, but, was significantly higher in cases when the regulon rpoS or the genes katG or katE were absent. Journal of Industrial Microbiology & Biotechnology (2000) 25, 266–272. Received 08 May 2000/ Accepted in revised form 04 August 2000     

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 note on population growth under random dispersal

An approximation method using a sine function is used to solve the second degree growth equation for the case in which an organism may simultaneously become dispersed throughout a uniform region. The resulting expression for a special case is compared with the expression obtained by R. Barakat (1959,Bull. Math. Biophysics,21, 141–51), giving the first two terms, by an iterative, procedure. The agreement is satisfactory.     

Effects of BMP4/SMAD signaling pathway on mouse primordial follicle growth and survival via up‐regulation of Sohlh2 and c‐kit

Bone morphogenetic protein 4 (BMP4) is essential for the development of primordial follicles, although its underlying mechanism remains largely unknown. By using cultured ovaries, the effects of BMP4 and the potential signal transduction pathways were investigated. Ovaries from 3‐day‐old female mouse pups were maintained in organ culture in the absence (control) or presence of BMP4 (100 ng/ml). At different culture time, the effects of BMP4 on primordial follicle growth and survival were assayed by follicle count and TUNEL labeling. The expression of phospho‐SMAD1/5/8, Sohlh2, and c‐kit were measured by immunohistochemistry, RT‐PCR, and Western blotting. Immunohistochemistry was also performed to determine the expression pattern of BMP4, pSMAD1/5/8, Sohlh2, and c‐kit in vivo during ovarian development. The results showed treatments of ovaries with BMP4 resulted in a significant (P < 0.05) increase on the primordial‐to‐primary follicle transition. The oocytes of primordial follicles treated with BMP4 were also less likely to undergo apoptosis. BMP4 enhanced the phosphorylation of SMAD1/5/8 and up‐regulated the expression of Sohlh2 and c‐kit in primordial follicles. During ovarian development in vivo, Sohlh2, and c‐kit exhibited similar expression patterns to BMP4 and pSMAD1/5/8 in primordial follicles. The present studies suggest that BMP4/SMAD signaling pathway initiate primordial follicle growth and prevented oocyte apoptosis via up‐regulation of Sohlh2 and c‐kit. Mol. Reprod. Dev. 80: 70–78, 2013. © 2012 Wiley Periodicals, Inc.     

Revision and typification of Brazilian Augusta (Rubiaceae, Rondeletieae), with ecological observations on the riverine vegetation of the cerrado and Atlantic forests

A revision of Brazilian Augusta and general comments on the systematics of this genus are presented. The complex taxonomic history of this taxon has caused confusion over its correct nomenclature. The peculiar geographic distribution of Augusta has stimulated field observations and analysis of the ecology of the Brazilian ecosystems where this taxon occurs, which are here presented. The five Brazilian species of Augusta described by Pohl are here treated as ecotypes of A. longifolia. This species has two distinct varieties: var. Longifolia, widespread throughout the Brazilian cerrado, and var. parvifolia, endemic to the Atlantic forest near Rio de Janeiro. Typification, list of representative specimens, and distribution map of A. longifolia are also included.     

Orientation by helical motion—III. Microorganisms can orient to stimuli by changing the direction of their rotational velocity

Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.     

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.