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.     

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.     

The Enigma of <Emphasis Type="Italic">Solanum maglia</Emphasis> in the Origin of the Chilean Cultivated Potato, <Emphasis Type="Italic">Solanum tuberosum</Emphasis> Chilotanum Group<Superscript>1</Superscript>

The Enigma of Solanum maglia in the Origin of the Chilean Cultivated Potato, Solanum tuberosum Chilotanum Group. Landrace potato cultivars occur in two broad geographic regions: the high Andes from western Venezuela south to northern Argentina (Solanum tuberosum Andigenum Group, “Andigenum”), and lowland south-central Chile (S. tuberosum Chilotanum Group, “Chilotanum”), with a coastal desert and 560 km between southernmost populations of Andigenum and Chilotanum. Unlike Andigenum landraces, Chilotanum landraces are adapted to long days and carry a 241 base pair plastid DNA deletion. However, Andigenum and Chilotanum landraces are morphologically similar. We investigated a hypothesis that Chilotanum landraces arose from Solanum maglia, a rare tuber-bearing species found in Chile and Argentina. This hypothesis was formulated first based on morphological analyses of starch grains of extant and preserved (12,500 years before present) S. maglia, and on putative sympatry of extant S. maglia and Chilotanum landraces. Our new starch grain analyses fail to support this hypothesis; we could find no evidence of current sympatric distributions, and S. maglia lacks the 241-bp plastid deletion. However, microsatellite data group all accessions of S. maglia exclusively with Chilotanum, which is supported by our previous observation at the single locus of the waxy gene. These results could be interpreted in various ways, but all explanations have problems. One explanation is that S. maglia is a progenitor of Chilotanum. However, the plastid deletion in Chilotanum but not S. maglia cannot be easily explained. Another explanation is that Chilotanum was formed by hybridization between S. maglia and pre-Chilotanum, but this conflicts with prior cladistic analyses. These new data shed light on aspects of this question and highlight various evolutionary scenarios, but the origin of Chilotanum and the involvement of S. maglia in its origin remain an enigma.     

Il Gametofito Tetramegasporiale di Tulipa Oculus-Solis St. Am. Var. Praecox (Ten.)

Summary

We take here into consideration the embryologic study of Tulipa Oculus-solis St. Am v. praecox, a species which became naturalized in the northern Sardinia, and we notice that contemporaneously to the development of the embryo-sac according to Euphorbia dulcis type (85% frequency), which was already described by Bambacioni (1931), we may have also the development according to Adoxa type (15% frequency).

We show here the hypothesis that the possibility of developping the embryo-sac according to unlike types (but genically kindred ones) is not depending upon an early or a delayed vacuolisation, caused by either external or internal casual factors, but on the contrary is the manifestation of a peculiar tendency which is connected with the particular genetic caracteristic of the Species.     

Abstract mathematical molecular biology: II some relational consequences of the “one gene-one enzyme” hypothesis

Following the program outlined in a previous paper (Bull. Math. Biophysics,23, 237–260, 1961), a further abstract study is made of some simple relational systems which possess some properties of living organisms. It is shown that the “one gene-one enzyme” hypothesis leads to the conclusion that either all genes are built of the same chemical building blocks, or that at least all genes have a number of building blocks in common. A consistent relational application of the “one gene-one enzyme” hypothesis leads moreover to the conclusion that replication is not an inherent property of a gene. Rather there must be a set of enzymes which “copy” the genes. The number of enzymes in this set must be less than the number of genes and therefore the activity of those “copying” enzymes cannot be absolutely specific.     

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 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.     

Comments on the approximate solution of the diffusion equation: II

On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed. This work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the Mathematics Panel, Oak Ridge National Laboratory.     

Probability distributions associated with distinct hits on targets

Some probability distributions connected with distinct hits on targets, using two different firing schemes, are developed. It is assumed that any shot has a probabilityp, not necessarily unity, of hitting the target at which it was aimed. The development uses a well-known expression for the probability that exactlyt ofN possible events occur simultaneously. Some of the formulae developed here include as special cases the probabilities derived separately and by more complicated arguments in papers by N. Rashevsky. (Bull. Math. Biophysics,17, 45–50, 1955) and A. Rapoport (Bull. Math. Biophysics,13, 133–38, 1951).     

On the action of sulfanilamide

Summary The better activity (in vitro) of various sulfanilamide compounds as compared with sulfanilamide itself is only quantitative,i.e., an equal activity is obtained with lower concentrations. It is shown, that the activity of the studied drugs is so narrowly related to their adsorption in the bacteria (B. coli), that probably the varying activity of the studied compounds is due to differences in adsorbability. For different drugs the adsorbed amount was equal for concentrations with equal activity.The concentration of p. aminobenzoic acid which re-establishes growth — in cultures containing the studied compounds in concentrations of equal activity — was equal in all cases. This fact corroborates the hypothesis, that activity and adsorption are correlated and shows, that the mechanism of action (in vitro) is the same in all cases.Ninth communication: K. C.Winkler, Antonie van Leeuwenhoek9, 115, 1943.     

Some consequences of Henri Poincaré's hypothesis about the biological nature of the three-dimensionality of our space

Henri Poincaré (Derniere Pansées, Paris, Flamerion, 1920) makes the interesting suggestion that our space is three-dimensional because ourvoluntary movements are those of quasi-rigid bodies in three dimensional space. Inasmuch as according to the theory of organismic sets (Rashevsky,Bulletin of Mathematical Biophysics,31, 159–198, 1969) organisms are conceivable, perhaps in some remote parts of the universe, for which the primary voluntary changes may be not spatial movements but changes of other physical qualities, it is pointed out that the acceptance of Poincaré's hypothesis will require an invariance of the physical laws in an abstractn-hyperspace with respect to the choice ofm<n coordinates as the basic frame of reference.     

Systematic relationships within the Vibrionaceae (Bacteria: Gammaproteobacteria): steps toward a phylogenetic taxonomy

A phylogenetic hypothesis is presented for all 95 species of the family Vibrionaceae (Bacteria: Gammaproteobacteria) based on a combined analysis of eight molecular loci (16S rRNA, gyrB, recA, rpoA, gapA, mreB, topA, atpA) for up to 9337 nucleotide characters. Members of this taxon exhibit diverse life histories, including bioluminescence, pathogenicity to human and marine organisms, symbiosis, quorum sensing and extremophilic environment living, making a hypothesis of phylogenetic history important to studies addressing these traits from an evolutionary perspective. It is proposed that this phylogenetic set of relationships replaces previous phenetic hypotheses and be used to construct a phylogenetic taxonomy. Recent taxonomic proposals, including the validity of four, instead of one, families representing the 95 species and historical notions of genera within the group are compared with the presented phylogenetic hypothesis. Character support is traced through the tree and is used to address these taxonomic proposals. Photobacterium is not a monophyletic group as it is currently delimited. Aliivibrio is found within Photobacterium, suggesting a new definition for Photobacterium that includes all species of Aliivibrio. Enterovibrio, Salinivibrio and Grimontia, previously thought to be distinct from and basal to Photobacterium and Vibrio, are found nested deeply within a large Vibrio clade. © The Willi Hennig Society 2010.     

The effects of quantity and quality of prey on population fluctuations in three seabird species

Capsule Population sizes of Common Guillemots Uria aalge, Razorbills Alca torda and Lesser Black‐backed Gulls Larus fuscus were associated with prey abundance but not prey quality.

Aims To examine how the abundance and quality of prey fish affects seabird population size and to test the ‘junk‐food’ or nutritional stress hypothesis.

Methods Analysis of long‐term seabird population size data and Sprat Sprattus sprattus biomass and age‐related weight data using a correlative approach.

Results De‐trended seabird and Sprat population data showed that the abundance of Sprat, the main prey species, was associated with the abundance of seabirds, while no effect of age‐related size of prey on seabird population size was found.

Conclusion As the Sprat population increased so did the seabird populations, regardless of decreases in ‘quality’ of Sprats, implying that more prey fish simply seem to mean more food in this marine ecosystem. No support for the ‘junk‐food’ hypothesis was found and the results contradict suggestions from earlier studies that prey quality is important to top‐predators in the Baltic Sea.     

A new species of Pleuridium from Australia

Abstract

A new species, Pleuridium curvisetum, is described. It has an arched seta similar to that of P. arnoldii and was collected, sometimes in association with that species, in alpine country in Australia. P. arnoldii was first recorded from New Zealand. A comparison of the two species revealed some features, including a bistratose margin to the leaf subula, not previously reported for P. arnoldii.     

On multipole theory in electrocardiography

This paper continues a comparison of the Taylor series and spherical harmonic forms of multipole representations initiated by Yeh (Bull. Math. Biophysics,24, 197–207, 1962). It is shown that while transformations from Taylor series form into spherical harmonic form is always possible, the inverse cannot be accomplished as suggested by Yeh; corrected transformation equations are given. It is also shown that direct measurement of Taylor coefficients, as outlined in Yeh, Martinek, and de Beaumont (Bull. Math. Biophysics,20, 203–216, 1958), is actually not possible. Accordingly, only the spherical harmonic coefficients can be determined by measurement of surface potentials, as in electrocardiography.     

Passiflora tacanensis, a new species of Passiflora subgenus Decaloba supersection Cieca from Mexico

Passiflora tacanensis, a new species from southern Mexico, is described and illustrated. It was discovered during the course of a taxonomic revision ofPassiflora subgenusDecaloba supersectionCieca and is assigned to that group of apetalous passion flowers.Passiflora tacanensis is known only from one fruiting herbarium specimen that was collected in southern Mexico on Volcán Tacaná in a high mesophytic forest. It is distinguished from its closest relatives,P. coriacea, P. sexocellata, P. mcvaughiana, andP. xiikzodz, by its foliose stipules, leaves that lack laminar nectaries but possess petiolar nectaries, and wide seeds with a chalazal beak that is not well developed.     

Hydrogel composite of lanthanum and Halorubrum ejinoor sp. cell lysate as an adsorbing material

Objectives

Although halophilic archaea are rich in natural environments, their biotechnological applications are not as prevalent as those of other extremophiles, such as thermophiles and alkaliphiles. This study presents an simple method to prepare a hydrogel composite using crude cell lysate of a halophilic archaea, Halorubrum ejinoor sp. (H.e.) which was isolated from a saline lake in Inner Mongolia, China. Furthermore, formation mechanism and potential applications of the hydrogel as an adsorbing material are discussed.

Results

Halorubrum ejinoor sp. (H.e.) cell lysate was firstly prepared by adding pure water onto the H.e. cell pellet, followed by a short incubation at 60 °C. The cell lysate was injected into different metal ion (or H⁺) solutions to obtain the hydrogel composite. It was observed that H⁺, Fe³⁺, La³⁺, Cu²⁺, and Ca²⁺ induced gelation of the cell lysate, while Fe²⁺, Co²⁺, Ni²⁺, Mg²⁺, Na⁺, and K⁺ did not. DNA and extracellular polysaccharides (EPS) in the H.e. cell lysate were found to be responsible for the gelation reaction. These results suggest that DNA and EPS should be crosslinked by metal ions (or H⁺) and form a networked structure in which the metal ion (or H⁺) serves as an anchor point. Potential application of the hydrogel as an adsorbing material was explored using La³⁺-induced H.e. hydrogel composite. The hydrogel composite can adsorb the fluoride, phosphate and DNA-binding carcinogenic agents, such as acridine orange.

Conclusions

The simplicity and cost effectiveness of the preparation method might make H.e. hydrogel a promising adsorbing material. This work is expected to expand the technical applications of haloarchaea.

     

Effects of the winter beechmast crop on bird occurrence in British gardens

Capsule Woodland birds were significantly less likely to occur in gardens in years of high beechmast crop.

Aim To test the hypothesis that woodland species that feed on beechmast will have significantly lower occurrence rates at garden feeders in mast years.

Methods Weekly winter occurrence rates at garden feeders between 1970/71 and 1999/2000 for 40 species were analysed in relation to annual beechmast abundance, classified into low, medium and high years. A repeated-measures logistic regression model was used to assess whether beechmast abundance explained further significant variation additional to underlying seasonal and annual trends.

Results Seven species that commonly feed on beechmast showed significantly lower occurrence in gardens in years of highest beechmast abundance: Great Spotted Woodpecker Dendrocopos major, Woodpigeon Columba palumbus, Great Tit Parus major, Coal Tit Periparus ater, Nuthatch Sitta europaea, Jay Garrulus glandarius and Chaffinch Fringilla coelebs. Blackbird Turdus merula and Siskin Carduelis spinus, which showed similar significant patterns, are likely to take beechmast as elements of their diet. Pied Wagtail Motacilla alba was the only insectivorous species to show significant effects, but occurrence was lowest in years of intermediate beechmast abundance. For the latter species, this may have been due to confounding effects of temperature, but there were no such confounding effects of either temperature, or the number of bird feeders provided in gardens, for the other nine species.

Conclusion Use of artificial food sources by birds in gardens is influenced by resources in the surrounding countryside, suggesting that food provided in gardens may play a significant part in the population dynamics of these species, that population monitoring without consideration of the garden habitat may be deficient, and that volunteer-based garden bird recording may provide data that can be used as an indicator of changes in the wider countryside.     

3-Arylidene-5-(4-isobutylphenyl)-2(3H)-furanones: a new series of anti-inflammatory and analgesic compounds having antimicrobial activity

An ideal anti-inflammatory drug should have the desired effect in minimum dose with minimum side effects. Antimicrobial actions associated with such agents will be an added advantage as they broaden the spectrum of the compounds. Promising anti-inflammatory and antimicrobial activity together with low ulcerogenic properties of some 2(3H)-furanones, synthesized in our previous study, prompted us to investigate the effect of the isobutyl group on their pharmacological profile. Since compounds 3, 9, 13, and 14 have both anti-inflammatory and analgesic effects in addition to low ulcerogenic incidence, they were selected for investigation of their inhibitory effects on various cyclo-oxygenase enzymes. It was found that they were more selective toward COX-2 enzymes. An MIC of 6.25 μg/mL was recorded for compounds 3, 13, and 14 against S. aureus, E. coli, R. oryza, and P. citrum. The study supports the development of furanone derivatives as potential anti-inflammatory agents with antimicrobial activity.     

Synopsis of the tribe Bocageeae (Annonaceae), with revisions of Cardiopetalum,Froesiodendron, Trigynaea,Bocagea, and Hornschuchia

The tribal name Bocageeae Endlicher is reestablished and the tribe is circumscribed on the basis of solitary internodal ebracteate pedicels that are articulated at the base, and pollen shed in polyads of eight or more grains. Septate anther locules, large pollen size, and seed appendages are prevalent in the tribe. Intectate pollen with free-standing columellae, rare in Annonaceae, occurs not only in the genusTrigynaea but also in some species ofBocagea andHornschuchia. As defined here, the Bocageeae include seven neotropical genera:Cymbopetalum, Porcelia, Bocagea, Cardiopetalum, Froesiodendron, Hornschuchia, andTrigynaea. The latter five genera are revised and the treatments include ten new species:Cardiopetalum plicatum, Froesiodendron urceocalyx, Hornschuchia lianarum, H. santosii, H. leptandra, Trigynaea cinnamomea, T. lanceipetala, T. triplinervis, T. lagaropoda, andT. axilliflora, all from tropical South America. A new combination,Froesiodendron longicuspe, changes the rank of that taxon from subspecies to species.Cardiopetalum surinamense is removed fromFroesiodendron and reassigned toCardiopetalum on the basis of its connate petals, dehiscent monocarps, and seeds with bilobed arils. A cladogram provides an explicit hypothesis of intergeneric relationships in the tribe. The new combinationOnychopetalum periquino, based onTrigynaea periquino, is made.