Categories of (ℓ, ℛ)-systems

We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.     

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.     

Rapid discrimination of commercial strawberry cultivars using Fourier transform infrared spectroscopy data combined by multivariate analysis

To determine whether pattern recognition based on metabolite fingerprinting for whole cell extracts can be used to discriminate cultivars metabolically, leaves and fruits of five commercial strawberry cultivars were subjected to Fourier transform infrared (FT-IR) spectroscopy. FT-IR spectral data from leaves were analyzed by principal component analysis (PCA) and Fisher’s linear discriminant function analysis. The dendrogram based on hierarchical clustering analysis of these spectral data separated the five commercial cultivars into two major groups with originality. The first group consisted of Korean cultivars including ‘Maehyang’, ‘Seolhyang’, and ‘Gumhyang’, whereas in the second group, ‘Ryukbo’ clustered with ‘Janghee’, both Japanese cultivars. The results from analysis of fruits were the same as of leaves. We therefore conclude that the hierarchical dendrogram based on PCA of FT-IR data from leaves represents the most probable chemotaxonomical relationship between cultivars, enabling discrimination of cultivars in a rapid and simple manner. The authors Suk Weon Kim and Sung Ran Min contributed equally to this work.     

Construction of a dense genetic linkage map for apple rootstocks using SSRs developed from Malus ESTs and Pyrus genomic sequences

Marker-assisted selection (MAS) offers quick and reliable prediction of the phenotypes of seedlings in large populations and thus opens new approaches for selection to breeders of apple (Malus x domestica Borkh.). The development of framework maps enables the discovery of genetic markers linked to desired traits. Although genetic maps have been reported for apple scion cultivars, none has previously been constructed for apple rootstocks. We report the construction of framework genetic maps in a cross between ‘M.9’ (‘Malling 9’) and ‘R.5’ (‘Robusta 5’) apple rootstocks. The maps comprise 224 simple sequence repeat (SSR) markers, 18 sequence-characterised amplified regions, 14 single nucleotide polymorphisms and 42 random amplified polymorphic DNAs. A new set of 47 polymorphic SSRs was developed from apple EST sequences and used for construction of this rootstock map. All 17 linkage groups have been identified and aligned to existing apple genetic maps. The maps span 1,175.7 cM (‘M.9’) and 1,086.7 cM (‘R.5’). To improve the efficiency of mapping markers to this framework map, we developed a bin mapping set. Applications of these new genetic maps include the elucidation of the genetic basis of the dwarfing effect of the apple rootstock ‘M.9’ and the analysis of disease and insect resistance traits such as fire blight (Erwinia amylovora), apple scab (Venturia inaequalis) and woolly apple aphid (Eriosoma lanigerum). Markers for traits mapped in this population will be of direct use to apple breeders for MAS and for identification of causative genes by map-based cloning.     

Thidiazuron-induced shoot organogenesis from mature leaf explants of scented <Emphasis Type="Italic">Pelargonium capitatum</Emphasis> cultivars

Shoot organogenesis from mature leaf tissues of two scented Pelargonium capitatum cultivars, ‘Attar of Roses’ and ‘Atomic Snowflake’, grown in the greenhouse, were optimized in the presence of thidiazuron (TDZ). The protocol involved preculture of leaf sections on basal Murashige and Skoog (MS) medium supplemented with 10 μM TDZ, 4.4 μM of 6-benzyladenine (BA) and 5.4 μM α-naphtaleneacetic acid (NAA) for a period of 2 weeks and followed by subculture of explants to a fresh medium containing 4.4 μM BA and 5.4 μM NAA. Frequency of regeneration reached approximately 93% for both cultivars, with the induction of more than 100 shoots per explant. Regenerated plantlets were rooted on half-strength MS medium supplemented with 4.4 mM sucrose and 8.6 μM of Indole-3-acetic acid (IAA). All regenerated shoots from both cultivars developed roots when transferred to organic soil mix, acclimatized, and successfully transferred to greenhouse conditions. When regenerated shoots were transferred to hydroponic conditions, frequency of survival was 76.2 and 61.9% for ‘Attar of Roses’ and ‘Atomic Snowflake’, respectively.     

Effect of low doses of gamma irradiation on in vitro growth of grapevine

Shoot tips and single node explants of two rootstocks (R.99 and 3309) and two varieties (‘Helwani’ and ‘Cabernet Franc’) of grapevine cultured on DSD1 media for a period of 60 days, were irradiated with 0, 2, 5 and 7 Gy doses of gamma irradiation. Shoot length of ‘Helwani’ and ‘Cabernet Franc’ was increased by 7 Gy irradiation. The 5 Gy dose increased the number of roots in plants of the two rootstocks and ‘Helwani’. Root length of ‘Helwani’ and ‘Cabernet Franc’ at the 2 and 7 Gy doses were significantly higher than those of the non-irradiated control. A similar effect was noticed on R.99 rootstock subjected to 5 Gy. Five Gy also increased the dry weight of the R.99 rootstock, whereas 2 and 7 Gy had a similar effect on ‘Helwani’ and ‘Cabernet Franc’. Number of leaves of plants exposed to 5 and 7 Gy was increased when compared with the non-irradiated control. This revised version was published online in June 2006 with corrections to the Cover Date.     

Some comments on re-estalishability

The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an (ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958.     

In vitro propagation of Gladiolus hybridus Hort.: Synergistic effect of heat shock and sucrose on morphogenesis

Three cultivars (cvs.) of Gladiolus hybridus Hort., namely ‘Her Majesty’, ‘Aldebaran’ and ‘Bright Eye’ were successfully micropropagated. The cultures were established using intact cormels or segments of cormels and inflorescence axes on Murashige and Skoog (1962; MS) medium. The response depended on media supplements; both callus formation or direct induction of shoot buds was observed. Shoot differentiation from callus could be obtained on MS medium containing 1.0 μM BA (6–benzyladenine) and 10.0 μM NAA (α-naphthalene acetic acid) in all three cultivars. The same could be achieved by giving a heat shock (HS; 50 °C, 1h) to callus cultures (in case of ‘Her Majesty’ and ‘Aldebaran’ only) maintained on the basal medium. In these two cultivars, high sucrose concentration (0.232, 0.290 or 0.348 M) also favoured growth and proliferation of shoot cultures on a plant growth regulator-free medium at 20 °C in comparison to the cultures kept at 25 °C. On the other hand, shoot cultures maintained on the basal medium at 25 °C containing normal (0.058 M, i.e., 2.0%, w/v) sucrose concentration responded similar to those maintained at 20 °C on a high sucrose medium; reduced response was observed on normal sucrose containing medium at 20 °C. Heat shock enhanced shoot proliferation in the cultures maintained on basal medium, but induced prolific rooting in shoot cultures, within 5 days of HS, on high sucrose (optimum 0.232 M) medium. While the number of roots increased at higher sucrose concentrations in the medium in case of cvs. ‘Her Majesty’ and ‘Aldebaran’, the same was found to be independent of sucrose concentration in cv. ‘Bright Eye’. Generally the rooted plants produced on high sucrose (0.232 M) medium in comparison to medium with normal sucrose concentration showed better survival (ca. 90% as against 40%) in the soil. This revised version was published online in June 2006 with corrections to the Cover Date.     

Some algebraic properties of (M,R)-systems

On the basis of Rosen's representation of (M, R)-systems as sequential machines (Rosen,Bull. Math. Biophys.,26, 103–111, 1964), the existence of projective limits in categories of general (M, R)-systems is proved.     

Evolution of the Genetic Triplet Code via Two Types of Doublet Codons

Explaining the apparent non-random codon distribution and the nature and number of amino acids in the ‘standard’ genetic code remains a challenge, despite the various hypotheses so far proposed. In this paper we propose a simple new hypothesis for code evolution involving a progression from singlet to doublet to triplet codons with a reading mechanism that moves three bases each step. We suggest that triplet codons gradually evolved from two types of ambiguous doublet codons, those in which the first two bases of each three-base window were read (‘prefix’ codons) and those in which the last two bases of each window were read (‘suffix’ codons). This hypothesis explains multiple features of the genetic code such as the origin of the pattern of four-fold degenerate and two-fold degenerate triplet codons, the origin of its error minimising properties, and why there are only 20 amino acids. Reviewing Editor: Dr. Laura Landweber An erratum to this article can be found at .     

Patterns of host ant use by sympatric populations of <Emphasis Type="Italic">Maculinea alcon</Emphasis> and <Emphasis Type="Italic">M. ‘rebeli’</Emphasis> in the Carpathian Basin

Maculinea butterflies show social parasitism via obligatory myrmecophily as their larvae are adopted and raised to pupation by Myrmica ants. Suitable hosts differ for different Maculinea species, and host ant specificity can further differ at the population-level. Although early studies suggested single ant species as main hosts for each Maculinea species, it has recently become clear that their host ant specificity is more complex. Maculinea alcon and Maculinea ‘rebeli’ have variously been separated according to adult and larval morphology, phenology, and their use of different ecosystems, including host plant and host ant species. However, recent genetic evidence has questioned their separation as good species. Here we compare the use of host ants by M. alcon and M. ‘rebeli’ at the regional scale in NE-Hungary and Transylvania (Romania), where molecular studies have found no species-level separation between the two forms. We opened 778 nests of Myrmica ants and searched for Maculinea specimens (larvae, pupae and exuviae) shortly before imago emergence from the nest in seven M. alcon sites, six M. ‘rebeli’- sites and one site where both M. alcon and M. ‘rebeli’ are syntopic. In all, Maculinea caterpillars were found in the nests of seven different ant species (M. alcon was recorded mainly with Myrmica scabrinodis and occasionally with M. salina and M. vandeli; M. ‘rebeli’ used mainly M. scabrinodis, M. sabuleti and M. schencki and occasionally M. lonae and M. specioides). Myrmica scabrinodis was found to be a general host of both M. alcon and M. ‘rebeli’, which is the first record for a common host ant of these two closely related butterflies within the same region. However there were also differences in host ant use patterns between the sites occupied by the two Maculinea taxa, which reflect differences in Myrmica communities between the two types of habitat. Possible explanations for the similar but not identical host use patterns of M. alcon and M. ‘rebeli’, and their relevance for the question of whether they are separate species are discussed. Received 27 November 2007; revised 28 May 2008; accepted 11 June 2008.     

Production and molecular characterization of potential seedless cybrid plants between pollen sterile Satsuma mandarin and two seedy <Emphasis Type="Italic">Citrus</Emphasis> cultivars

Cytoplasmic male sterility (CMS) is known to be controlled by mitochondrial genome in higher plants including Satsuma mandarin (Citrus unshiu Marc.). Citrus symmetric fusion experiments often produce diploid cybrids possessing nuclear DNA from the mesophyll parent and mitochondrial DNA (mtDNA) from the embryogenic callus parent. Therefore, it is possible to transfer CMS from Satsuma mandarin as callus parent to seedy citrus cultivars as leaf one by somatic cybridization. Herein, symmetric fusion technique was adopted to create cybrids for potential seedlessness by transferring CMS from Citrus unshiu Marc. cv. Guoqing No. 1 (G1) to two traditional Chinese seedy citrus cultivars, ‘Shatian’ pummelo (C. grandis (L) Osbeck) and ‘Bingtang’ orange (C. sinensis (L) Osbeck). Flow cytometry analysis showed that 19 plants recovered from G1 + ‘Bingtang’ orange and 17 of 35 plants regenerated from G1 + ‘Shatian’ pummelo were diploid. The remaining plants from G1 + ‘Shatian’ pummelo were tetraploid. The diploid plants from the two combinations were confirmed as true cybrids by simple sequence repeat (SSR) and cleaved amplified polymorphic sequence (CAPS) analysis, with nuclear DNA from their corresponding leaf parent and mtDNA from their common suspension parent, G1 Satsuma mandarin. The remaining plants from G1 + ‘Shatian’ pummelo were identified as somatic hybrids with mtDNA from G1. The chloroplast simple sequence repeat (cp-SSR) analysis revealed somatic hybrid/cybrid plants from the two combinations in most cases possessed either of their parental chloroplast type, and two plants from G1 +‘Shatian’ pummelo and all embryoids analyzed from G1 + ‘Bingtang’ orange possessed chloroplast DNA (cpDNA) from both parents. These results demonstrated that we succeeded in introducing mtDNA from G1 Satsuma mandarin into the two target seedy citrus cultivars for potential seedlessness through symmetric fusion.     

The influence of plant growth regulators and storage on root induction and growth in <Emphasis Type="Italic">Pelargonium zonale</Emphasis> cuttings

The effects of post harvest application of ethylene, abscisic acid (ABA), indole-3-butyric acid (IBA) treatments or dark storage on root induction and continued growth of regenerated roots in Pelargonium cuttings were investigated using hydroponics in the greenhouse. Ethylene markedly increased rooting percentage in ‘Greco’ and ‘Surfing’, reduced the number of roots per cutting in ‘Surfing’ and had no effect on the total root lengths in the two cultivars. Ethylene treatment reduced fresh root mass in ‘Surfing’, increased dry root mass and reduced root water content in both cultivars. ABA (50 μM) enhanced rooting percentage in ‘Greco’, reduced the number of roots per cutting, reduced total root lengths and fresh root mass in both cultivars. ABA increased dry root mass and reduced root water content in ‘Surfing’ but this effect was not apparent in ‘Greco’. Storing cuttings in the dark for 4 days had no effect on rooting percentage and number of roots per cutting in ‘Greco’ and ‘Surfing’. However, dark storage reduced total root lengths in ‘Surfing’ and reduced fresh root mass in ‘Greco’. Dark storage had no effect on dry root mass and water content in both cultivars. Applying 4 μl l⁻¹ IBA in the rooting solution induced maximum (100%) root induction in ‘Surfing’. However, IBA reduced the number of roots per cutting in ‘Greco’, reduced total root lengths and fresh root mass in the two cultivars. IBA treatment profoundly increased and reduced dry root mass and root water content, respectively, in ‘Greco’ and ‘Surfing’. The enhanced root induction observed after IBA and ABA applications could be ascribed to their influence on ethylene biosynthesis, since ethylene treatment increased rooting percentage in both cultivars. However, high ABA (100 μM) and IBA (12 μl l⁻¹) levels or dark storage reduced the ability of induced roots to continue growth. We attribute our results to plant stress-response mechanism and ethylene appears to play an important role in the process of root initiation and root growth in Pelargonium cuttings.     

Peroxidase involvement in the defense response of red raspberry to Didymella applanata (Niessl/Sacc.)

Peroxidase activity of red raspberry canes was dependent on the cultivar and influenced the subsequent lignification. After inoculation with Didymella applanata, responsible for the spur blight cane disease, the activity of soluble cytoplasmic enzyme increased in the moderately resistant ‘Latham’ and susceptible ‘Malling Promise’, similarly for syringaldazine and guaiacol as hydrogen donors. Systemic induction found in ‘Latham’ was recognized as a symptom of defence mechanism responsible for fungal restriction. Locally enhanced peroxidase activity in the ‘M.Promise’ tissues was related to the local lignification and/or may be associated with the loss of cell integrity caused by pathogen penetration. Pathogen-induced changes of cell wall peroxidases were similar in both cultivars mentioned above. No influence of the infection was found in the high susceptible Zeva cultivar. Using native-PAGE analysis and horizontal starch electrophoresis of soluble fraction five constitutive acidic isoperoxidases were detected in ‘Latham’ and three in ‘M. Promise’. The infection process was accompanied by the appearance of two new anodic isoforms.     

Cryopreservation of horse-chestnut (Aesculus hippocastanum L. ) somatic embryos using three different freezing methods

Cryopreservation of somatic embryos of Aesculus hippocastanum L. cultured on nutritive media containing abscisic acid (ABA) at concentrations of 0.75 μM, 7.5 μM and 75.0 μM was evaluated for three cooling methods: (i) slow freezing with cryoprotectants, (ii) fast freezing with cryoprotectants, and (iii) fast freezing with desiccation techniques. The ‘cryoprotectant’ freezing techniques included the embryo pretreatment on ABA containing medium for 4 days, followed by cryoprotective treatment in liquid medium containing 0.5 M dimethylsulfoxide, 0.5 M glycerol, 1.0 M sucrose, and cooled at slow, and rapid rates. Embryos pretreated on a medium containing 0.75 μM ABA, and cooled to −35 °C at 1°C /min, held for 30 min at this transfer temperature and then immersed in liquid nitrogen (LN) had the best embryo recovery (43%). The ‘desiccation’ method involved an air drying step of similar ABA-pretreated, non-cryoprotected embryos followed by rapid cooling. Embryos precultured on 0.75 μM ABA, then subjected to a 4 h period of air desiccation (water content reduction to 13%) showed about the same level of survival (46%) as found with the ‘cryoprotectant’ slow freezing technique. The air-dry ‘desiccation’ method is easier to apply than the more complicated ‘cryoprotectant’ method. This revised version was published online in June 2006 with corrections to the Cover Date.     

Two strategies for investigating the evolution of behavior

In this paper I distinguish and characterize two strategies, both prominent in contemporary biology, for investigating the evolution of behavior. The ‘Lorenzian Strategy’ is taxon-focused, holistic, and particularistic, and relies heavily on naturalistic observation as well as careful experimental manipulation of target systems; it tends to produce detailed knowledge of concrete historical instances of the evolution of behavior in particular lineages. The ‘Analytic Strategy’ is principle-focused, generative, and taxonomically universal; it relies on the development of mathematical principles (simple analytic models) of the evolution of behavior at an abstract level, and uses experimentation to garner support for the empirical relevance for these. The strategies hence employ different methods and produce different sorts of knowledge, hence they are neither inconsistent nor redundant, but complementary, and indeed they both play important roles in the contemporary biology of animal behavior.     

Evolution of early determinate tomato cultivars during the last three decades as a result of research conducted at Warsaw Agricultural University

Earliness is a crucial factor of tomato field production in Poland. A. Michalska and B. Kubicki (1978) conducted the first investigations on tomato earliness at the Department of Plant Genetics and Breeding. The main conclusions from these studies indicated that it was possible to obtain varieties earlier than ‘New Yorker’ as a result of transgression. The two new varieties (‘Alfa’ and ‘Akord F₁’) proved to be two weeks earlier than ‘New Yorker’. However, earliness was correlated with smaller fruit weight (30–40 g). At the next stage of experiment some improvement was achieved both in the size of fruit (45 g for ‘Beta’ up to 70 g for ‘Alka’) as well as colour intensity and good flavour. With the next few years fruit weight was still increased (up to 100 g for ‘Maskarena’) and a higher level of firmness was obtained (mid firm fruits for ‘Maskarena’ and ‘Delta’). At present, the Polish Research Centre for Cultivar Testing recommends our varieties ‘Betalux’, ‘Promyk’ and ‘Delta’ as standards.     

Using a limited mapping strategy to identify major QTLs for resistance to grapevine powdery mildew (<Emphasis Type="Italic">Erysiphe necator</Emphasis>) and their use in marker-assisted breeding

A limited genetic mapping strategy based on simple sequence repeat (SSR) marker data was used with five grape populations segregating for powdery mildew (Erysiphe necator) resistance in an effort to develop genetic markers from multiple sources and enable the pyramiding of resistance loci. Three populations derived their resistance from Muscadinia rotundifolia ‘Magnolia’. The first population (06708) had 97 progeny and was screened with 137 SSR markers from seven chromosomes (4, 7, 9, 12, 13, 15, and 18) that have been reported to be associated with powdery or downy mildew resistance. A genetic map was constructed using the pseudo-testcross strategy and QTL analysis was carried out. Only markers from chromosome 13 and 18 were mapped in the second (04327) and third (06712) populations, which had 47 and 80 progeny, respectively. Significant QTLs for powdery mildew resistance with overlapping genomic regions were identified for different tissue types (leaf, stem, rachis, and berry) on chromosome 18, which distinguishes the resistance in ‘Magnolia’ from that present in other accessions of M. rotundifolia and controlled by the Run1 gene on chromosome 12. The ‘Magnolia’ resistance locus was termed as Run2.1. Powdery mildew resistance was also mapped in a fourth population (08391), which had 255 progeny and resistance from M. rotundifolia ‘Trayshed’. A locus accounting for 50% of the phenotypic variation mapped to chromosome 18 and was named Run2.2. This locus overlapped the region found in the ‘Magnolia’-based populations, but the allele sizes of the flanking markers were different. ‘Trayshed’ and ‘Magnolia’ shared at least one allele for 68% of the tested markers, but alleles of the other 32% of the markers were not shared indicating that the two M. rotundifolia selections were very different. The last population, 08306 with 42 progeny, derived its resistance from a selection Vitis romanetii C166-043. Genetic mapping discovered a major powdery mildew resistance locus termed Ren4 on chromosome 18, which explained 70% of the phenotypic variation in the same region of chromosome 18 found in the two M. rotundifolia resistant accessions. The mapping results indicate that powdery mildew resistance genes from different backgrounds reside on chromosome 18, and that genetic markers can be used as a powerful tool to pyramid these loci and other powdery mildew resistance loci into a single line.     

A consensus map of rye integrating mapping data from five mapping populations

A consensus map of rye (Secale cereale L.) was constructed using JoinMap 2.0 based on mapping data from five different mapping populations, including ‘UC90’ × ‘E-line’, ‘P87’ × ‘P105’, ‘I_0.1-line’ × ‘I_0.1-line’, ‘E-line’ × ‘R-line’, and ‘Ds2’ × ‘RxL10’. The integration of the five mapping populations resulted in a 779-cM map containing 501 markers with the number of markers per chromosome ranging from 57 on 1R to 86 on 4R. The linkage sizes ranged from 71.5 cM on 2R to 148.7 cM on 4R. A comparison of the individual maps to the consensus map revealed that the linear locus order was generally in good agreement between the various populations, but the 4R orientations were not consistent among the five individual maps. The 4R short arm and long arm assignments were switched between the two population maps involving the ‘E-line’ parent and the other three individual maps. Map comparisons also indicated that marker order variations exist among the five individual maps. However, the chromosome 5R showed very little marker order variation among the five maps. The consensus map not only integrated the linkage data from different maps, but also greatly increased the map resolution, thus, facilitating molecular breeding activities involving rye and triticale.     

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.