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.     

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.     

Abstract biological systems as sequential machines II: Strong connectedness and reversibility

It was previously shown that the abstract biological systems called. (ℳ, ℛ)-systems could be regarded formally as sequential machines, and that when this was done, the reversibility of environmentally induced structural changes in these systems was closely related to the strong connectedness of the corresponding machines. In the present work it is shown that the sequential machines arising in this way are characterized by the property that the size of the input alphabet is very small compared with the size of the set of states of the machine. It is further shown that machines with this property almost always fail to be strongly connected. Therefore, it follows that one of the following alternatives holds: either most environmentally induced structural alterations are not environmentally reversible, or else many mappings in the category from which the (ℳ, ℛ)-systems are formed must not be physically realizable.     

Abstract biological systems as sequential machines: III. Some algebraic aspects

Using the relationship between (M,R) and sequential machines developed in previous work, it is shown that the totality of (M,R) which can be formed over a given categoryA itself forms a category in a natural fashion.     

Abstract biological systems as sequential machines

It is shown that a rather close relationship exists between the (ℳ,ℛ)-systems, defined previously as prototypes of abstract biological systems, and the sequential machines which have been studied by various authors. The theory of sequential machines is reformulated in a way suitable for its application to the study of the intertransformability of (ℳ,ℛ)-systems as a result of environmental alteration. The important concept of strong connectedness is most useful in this direction, and is used to derive a number of results on intertransformability. Some suggestions are made for further studies along these lines.     

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.     

A note on replication in (M,R)-systems

The condition which allows the existence of induced replication maps in (M,R)-systems is shown to place strong restrictions on the “richness” of the category from which these systems can be constructed. This condition also admits of a simple biological interpretation, which can be checked empirically, and which may offer insight into the physical and biological realizations of these abstract systems.     

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.     

On the reversibility of environmentally induced alterations in abstract biological systems

The environmentally induced alterations in structure of (M, ℜ) which were described previously (R. Rosen,Bull. Math. Biophysics,23, 165–171, 1961) are examined from the standpoint of determining under what circumstances they can be reversed by further environmental interactions. For simplicity we consider only the case of (M, ℜ)-systems possessing one “metabolic” and one “genetic” component. In the case of environmentally induced alteration of the “metabolic” component alone, a necessary and sufficient condition is given for the reversibility of the alteration. In the case of alteration of the “genetic” component, the situation becomes more complex; several partial results are given, but a full analysis is not available at this time. Some possible biological implications of this analysis 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 and Grant no. AF-AFOSR-9-63.     

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.     

A note on abstract relational biologies

It is shown that the class of abstract block diagrams of (M, ℜ)-systems which can be constructed out of the objects and mappings of a particular subcategoryG ₀ of the categoryG of all sets depends heavily on the structure ofG ₀, and in particular on the number of sets of mappingsH(A, B) which are empty inG ₀. In the context ofG ₀-systems, there-fore, each particular categoryG ₀ gives rise to a different “abstract biology” in the sense of Rashevsky. A number of theorems illustrating the relation between the structure of a categoryG ₀ and the embeddability of an arbitrary mapping αεG ₀ into an (M, ℜ)-system are proved, and their biological implication is discussed. This research was supported by the United States Air Force through the Air Force Office of Scientific Reserch of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

Experience with using Ellenberg’s <Emphasis Type="Italic">R</Emphasis> indicator values in Slovakia: Oligotrophic and mesotrophic submontane broad-leaved forests

Ellenberg’s indicator values have been suggested as useful method of estimating site conditions using plants. We examined whether Ellenberg’s R values are suitable for indicating soil reaction and if calibration to physical pH measurements can improve bioindication in oligotrophic and mesotrophic submontane broad-leaved forests in Slovakia. Vegetation relevés and pH-H₂O and pH-CaCl₂ soil reaction were recorded for this purpose. Ellenberg’s R values (R _e) were compared to Jurko’s indicator values (R _j) and a set of species R values and tolerances (T), which were calibrated with physical pH data using the weighted averaging (R _w, T _w) and Huisman-Olff-Fresco modelling (R _h, T _h). Original R _e values were then recalibrated with measured pH data to establish new, adjusted set of scores (R _c, T _c) at Ellenberg’s scale. The Re values are significantly correlated with the other R values, and they demonstrate similar frequency distribution to R _j and R _w values for the studied species pool. The frequency distribution becomes similar across all the R values when indifferent species were excluded. The performance of all the indicator values in terms of bioindication was tested. Relevé means of the R values were regressed on the field pH measurements. The performance of bioindication varied from 36% to 49% of the explained variance for pH-CaCl₂, with the R _e and R _c values yielding 46% and 49% respectively. The bioindication slightly improved for all calibrated methods (R _w, R _h and R _c) when species were weighted inversely with their tolerances — the performance varied from 42% to 51%, and the R _c values performed most effectively. We concluded that Ellenberg’s R values represent a powerful system for bioindicating soil acidity when compared to the other alternatives, with pH-CaCl₂ showing better results than pH-H₂O. Recalibration of Ellenberg’s values to the measured data improved the indicator system.     

AnO(N 2 logN) restriction map comparison and search algorithm

We present anO(R logP) time,O(M+P ² ) space algorithm for searching a restriction map withM sites for the best matches to a shorter map withP sites, whereR, the number of matching site pairs, is bounded byMP. As first proposed by Watermanet al. (1984,Nucl. Acids Res. 12, 237–242) the objective function used to score matches is additive in the number of unaligned sites and the discrepancies in the distances between adjacent aligned sites. Our algorithm is basically a sparse dynamic programming computation in which “candidate lists” are used to model the future contribution of all previously computed entries to those yet to be computed. A simple modification to the algorithm computes the distance between two restriction maps withM andN sites, respectively, inO(MN(logM+logN)) time. This author’s work was supported in part by National Library of Medicine Grant R01-LM4960. This author’s work was supported in part by National Library of Medicine Grant R01-LM5110.     

Cellular systems as sequential machines: Stability properties

In previous studies of (M,R) (Rosen, 1961; Demetrius, 1966), it was assumed that changes in the structure of (M,R) which were induced by environmental alternations occurred without error. Here, the effect of both “genetic” and “metabolic” malfunctions on the behavior of (M,R) is examined and a subclass of these systems whose behavior is invulnerable to such errors is specified.     

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.     

Somatic embryogenesis from stigmas and styles of grapevine

Summary An in vitro protocol has been developed for callus indiction, somatic embryogenesis, and plant regeneration from stigma-style culture of grapevine. Four different grapevine cultivars (Vitis vinifera L.: cvs. ‘Bombino Nero’, ‘Greco di Tufo’, ‘Merlot’, and ‘Sangiovese’) were tested. Exlants were cultured on Nitsch and Nitsch medium (NN) supplemented with various combinations of 6-benzylaminopurine (BA: 4.5 and 9.0 μM) and β-naphthoxyacetic acid (NOA; 5.0 and 9.9 μM). Sucrose (88 mM) was used as the carbon source. Somatic embryogenesis was induced within 3–7 mo. after culture initiation. Even though explants of different origin (unfertilized ovules and anthers) regenerated somatic embryos, the higher embryogenic potential was observed in stigma and style explants, with the exception of ‘Merlot’, which regenerated somatic embryos only from unfertilized ovules. The percentages of stigma-style explants producing somatic embryos was 7% in ‘Bombino Nero’ (cultured on NN medium supplemented 9.0 μM BA and 9.9 μM NOA). 14% in ‘Greco di Tufo’ (4.5 μM BA and 9.9 μM NOA), and 8% in ‘Sangiovese’ (9.0 μM BA and 9.9 μM NOA). The presence of growth regulators (BA and NOA) in the medium was essential for induction of somatic embryogenesis. Plants were regenerated on hormone-free NN medium containing 88 mM sucrose.     

Sporadic sustained nonperiodic oscillations in the activities of organismic sets

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

Efficient and simple plant regeneration via organogenesis from leaf segment cultures of persimmon (Diospyros kaki thunb.)

Summary An efficient and simple plant regeneration system via organogenesis from leaf segments of persimmon (Diospyros kaki Thunb.) cultivars ‘Fuyu’ and ‘Nishimurawase’ has been developed. The regeneration capacity was influenced by the culture vessels, gelling agents, plant growth regulators, and light conditions. Leaf explants taken from in vitro shoots were cultured on a modified Murashige and Skoog medium (MS1/2N), for 16 wk without transfer to fresh medium. Adventious shoots appeared after 4 and 8 wk in culture of ‘Nishimurawase’ and ‘Fuyu’ tissues, respectively. The culture of leaf explants in Erlenmeyer flasks with medium containing 4 g l⁻¹ agar enhanced shoot formation in comparison to media with increased agar concentrations. Optimal shoot regeneration was obtained with 5 mg l⁻¹ (22.8 μM) zeatin and 0.1 mg l⁻¹ (0.05 μM) indole-3-butyric acid (IBA) for ‘Nishimurawase’, and 10 mg l⁻¹ (45.6 μM) zeatin and 0.1 mg l⁻¹ (0.05 μM) IBA for ‘Fuyn’. Shoot regeneration frequencies in both cultivars were 100%, and shoot numbers per explant reached up to 9.2 for ‘Nishimurawase’ and 2.2 for ‘Fuyu’. Dark incubation during the first 4–5 wk was the most effective condition to successfully influence shoot regeneration in both cultivars. While dark incubation was essential for adventitious shoot formation by ‘Fuyu’, it was only slightly beneficial to ‘Nishimurawase’. More than 80% of the regenerated shoots rooted within 4 wk on hormone-free MS1/2N demium after having been dipped for 30 s in 250 mg l⁻¹ (1.1. mM) IBA solution.     

Highly efficient embryogenesis and plant regeneration of tall fescue (Festuca arundinacea Schreb.) from mature seed-derived calli

Summary We report a protocol for efficient plant regeneration of four tall fescue (Festuca arundinacea Schreb.) cultivars (‘Surpro’, ‘Coronado’, ‘Summer Lawn’, and ‘Fawn’) via somatic embryogenesis. Calli were initiated from mature seeds grown on modified Murashige and Skoog (MMS) medium supplemented with 7.0mgl⁻¹ (31.7μM) 2,4-dichlorophenoxyacetic acid (2,4-D) and 0.05 mgl⁻¹ (0.23 μM) kinetin (Kin). Calli were maintained and proliferated by subculture at monthly intervals on MMS medium containing 4.5 mgl⁻¹ (20.4 μM) 2,4-D and 0.2mgl⁻¹ (0.9 μM) Kin. Somatic embryos (SE) were induced from seed-derived calli on SE-induction medium (MMS supplemented with 2.0 mgl⁻¹ 2,4-D and 0.2mgl⁻¹ Kin). Plantlets were regenerated from somatic embryogenic calli grown on modified SH medium supplemented with 2 mgl⁻¹ Kin. Using this optimized protocol, 78.6–82.3% of mature seeds of all four cultivars produced SE clusters, of which 93.5–95.3% regenerated into plants within 10 wk. The regenerants showed no phenotypic abnormalities.     

On the biotopology of protein biosynthesis

The present paper is an attempt to outline a possible approach to the study of concrete cellular systems in terms of relational biology as developed by Rashevsky and Rosen. The basic ideas and the formalism of Rosen’s (M,R)-systems, proposed as a model of abstract biological systems, are used in order to represent the cellular protein biosynthesis. A diagram corresponding to the activation of amino acids and synthesis of amino-acyl-transfer RNA, the attachment of _t RNA to a specific codon of messenger RNA and peptide bond synthesis with the release of a protein molecule, is constructed. The systemM thus obtained for the synthesis of a proteinp _k receives a set of environmental inputs, that is, the twently naturally occurring amino acids and emits a single output, thep _k protein. The problem of noncontractibility of inputs in the system is then analyzed. In our context, it is found that the noncontractibility is not associated with the whole amino acid setS _pk but with an “essential amino acid set” , so that and represent the set of amino acids which can be replaced or absent. According to our considerations, the biochemical concept of “essential amino acid” acquires a new significance, that is, what seems “essential” is linked with the ability to form a giventRNA _t ∼a _i complex in a suitable augmented dependent set essential for the biosynthesis of a functional protein. Eventually the discussion of re-establishability leads to some important biological implications concerning the existence of ambiguous codons and the degeneracy phenomenon in the genetic code, as anecessary biochemical tool involved in adaptive processes.