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.     

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 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.     

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.     

Abstract biological systems as sequential machines: Behavioral reversibility

Rosen’s identification of abstract biological systems, called (M,R)-systems, with sequential machines is formally characterized. It is then shown that the determination of environmental alterations of (M,R)-systems from a knowledge of the response sequence and the structure of the system, which we call behavioral reversibility, can be interpreted as information-losslessness of sequential machines. Applying this relationship, necessary conditions for behavioral reversibility are derived. It is further shown that, similar to Rosen’s work on structural reversibility, (M,R)-systems are behaviorally reversible only if the number of physically realizable mappings are restricted.     

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.     

Cytotoxic activity of withanolides isolated from Tunisian Datura metel L

Withanolide-type steroids, withametelin Q (1) and 12α-hydroxydaturametelin B (2) along with three known withanolides, were isolated from leaves of Datura metel L. (Solanaceae). The respective structures, characterized mainly by NMR spectroscopy, were identified as (20R,22R,24R)-21,24-epoxy-1α,3β-dihydroxywitha-5,25(27)-dienolide-3-O-β-d-glucopyranoside (1) and (20R,22R,24R)-12α,21,27-trihydroxy-1-oxowitha-2,5,24-trienolide-27-O-β-d-glucopyranoside (2). The cytotoxicity of isolated compounds was evaluated against human lung carcinoma cells (A549) and human colorectal adenocarcinoma cells (DLD-1), respectively. Compound 2 exhibited cytotoxicity against A549 and DLD-1 cell lines, with IC₅₀ values of 7 and 2.0 μM, respectively. However, for compounds 6 and 7, cytotoxicities were higher against DLD-1 cells with IC₅₀ values of 0.6 and 0.7 μM. Both compounds blocked the cell cycle in the S-phase and induced apoptosis.     

Effect of the structure of dietary epoxylignan on its cytotoxic activity: relationship between the structure and the activity of 7,7′-epoxylignan and the introduction of apoptosis by caspase 3/7

We compared the cytotoxic activities of dietary epoxylignans and their stereoisomers and found (?)-verrucosin, which is (7S,7′R,8R,8′R)-7,7′-epoxylignan, to be the most cytotoxic epoxylignan against HeLa cells (IC₅₀ = 6.6 μM). On the other hand, the activity was about a factor of 10 less against HL-60. In this research on the relationship between the structure and cytotoxic activity of (?)-verrucosin 13, the 7-(4-methoxyphenyl)-7′-(3,4-dimethoxyphenyl) derivative 60, for which the activity (IC₅₀ = 2.4 μM) is three times greater than (?)-verrucosin 13, was discovered. The induction of apoptosis by caspase 3/7 was observed upon treatment with the (?)-verrucosin derivative.     

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.     

Synthesis of Annonaceous Acetogenins from Muricatacin

Synthetic studies of annonaceous acetogenins starting from (?)-muricatacin (1a) or (+)-muricatacin are described, involving (?)-muricatacin (1a), mono-THF acetogenin, solamin (2), reticulatacin (3), (15R, 16R, 19S, 20S)-cis-solamin (4a) and (15S, 16S, 19R, 20R)-cis-solamin (4b), non-adjacent bis-THF acetogenin, 4-deoxygigantecin (5), and epoxide-bearing acetogenin, (15S, 16R, 19S, 20R)-diepomuricanin (6a).     

Compounds with neuroprotective activity from the medicinal plant Machilus thunbergii

The dichloromethane fraction of the bark of Machilus thunbergii Sieb. et Zucc. (Lauraceae) significantly protected primary cultures of rat cortical cells exposed to the excitotoxic amino acid, L-glutamate. Through the activity-guided isolation from the CH₂Cl₂ fraction, (+)-9′-hydroxygalbelgin (1), isogalcatin B (2), (7S,8S,8′R)-3′,4′-dimethoxy-3,4,-methylenedioxylignan-7-ol (3), 1-hydroxy-7-hydroxymethyl-6-methoxyxanthone (4), 5,7-dimethoxy-3′,4′-methylenedioxyflavan-3-ol (5), (+)-(3S,4S,6R)-3,6-dihydroxypiperitone (6), protocatechuic acid methyl ester (7) and tyrosol (8) were obtained. All of them had significant neuroprotective activities against glutamate-induced neurotoxicity in primary cultures of rat cortical cells at concentrations ranging from 0.1 μM to 10.0 μM and were comparable to MK-801, a well-known inhibitor of glutamate receptor.     

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.     

Biotransformation of zerumbone by <Emphasis Type="Italic">Caragana chamlagu</Emphasis>

Suspension cultured cells of Caragana chamlagu (Leguminosae) converted zerumbone (1) into zerumbone epoxide (2) as the intermediate, (2R,3R,7R)-2,3-epoxy-9-humulen-8-one (3) and (2R,3S,7R)-2,3-epoxy-9-humulen-8-one (4) as new sesquiterpenes in 11%, 36% and 21% yields, respectively.     

柯拉斯那沉香的生物活性成分研究

为了解柯拉斯那(Aquilaria crassna)的化学成分,从其所产沉香中分离得到10个化合物,经波谱分析分别鉴定为:6,8-羟基-2-(2-苯乙基)色酮(1),6,8-二羟基-2-[2-(4-甲氧基苯)乙基]色酮(2),rel-(1a R,2R,3R,7b S)-1a,2,3,7b-tetrahydro-2,3-dihydroxy-5-(2-phenylethyl)-7H-oxireno[f][1]benzopyran-7-one(3),rel-(1a R,2R,3R,7b S)-1a,2,3,7b-tetrahydro-2,3-dihydroxy-[2-(4-methoxyphenyl)-ethyl]-7H-oxireno[f][1]benzopyran-7-one(4),rel-(1a R,2R,3R,7b S)-1a,2,3,7b-tetrahydro-2,3-dihydroxy-5-[2-(3-hydroxy-4-methoxyphenyl)-ethyl]-7H-oxireno[f][1]benzopyran-7-one(5),oxidoagarochromone B(6),oxidoagarochromone C(7),(5S,6R,7S,8R)-2-[2-(3′-hydroxy-4′-methoxyphenyl)ethyl]-5,6,7,8-tetrahydroxy-5,6,7,8-tetrahydrochromone(8),6,7-cis-dihydroxy-2-(2-phenylethyl)-5,6,7,8-tetrahydrochromone(9),N-trans-feruloyltyramine(10)。化合物3~5和8~10为首次从柯拉斯那沉香中分离得到。化合物1,3,6,7,9和10对乙酰胆碱酯酶具有一定的抑制活性,化合物4对人慢性髓原白血病细胞株K-562和人胃癌细胞株SGC-7901均具有较小的抑制作用,化合物1和3对人肝癌细胞株BEL-7402也有抑制活性。     

Synthesis of Both the Enantiomers of 3-Octanol,the Pheromone of Various Species of Ants

(2S,3R,1′S,2′S)-Serricorole (1) and (2S,3R,1′R)-serricorone (2), sex pheromone components of the cigarette beetle (Lasioderma serricorne F.), were synthesized, starting from the enantiomers of methyl 3-hydroxypentanoate. The stereochemistry of the naturally occurring 1 was determined to be 2S,3R,1′S,2′S, and that of 2 to be 2S,3R,1′RS by comparing between the CD spectra of the natural and synthetic samples.     

Efficient Synthesis of (22R,23R,24S)-22,23-Isopropylidenedioxy-5α-ergost-2-en-6-one,a Key Intermediate in the Preparation of Brassinolide

(22R,23R,24S)-22,23-Isopropylidenedioxy-5α-ergost-2-en-6-one 2b is an important intermediate of brassinolide. We found that the enone 2b can be prepared by transformation of (22R,23R,24S)-3α,5-cyclo-22,23-isopropylidenedioxy-5α-ergostan-6-one 5b with catalytic amount of both p-TsOH and NaBr in DMF under reflux. 5b was prepared from (22R,23R,24S)-3α,5-cyclo-22,23-dihydroxy-6β-methoxy-5α-ergostane 9b or a 6β-benzyloxy compound 9c, which was obtained in a manner similar to Mori’s brassinolide synthesis. The enone 2b was eventually prepared via a benzyl ether 9c from stigmasterol 3a in a 15.5% yield in 11 steps.     

Synthesis and Antimicrobial Activity of Optically Active trans-Cycloheximide Isomers

Optically active tiraras-cycloheximide isomers such as cycloheximide [(2S,4S,6R,αR)-form (1)], naramycin B[(25,4S,6RαR)-form(4)], and new stereoisomers (2S,4S,6S,αS)-form (8) and (2S,4S,6R,αS)-from (9) were synthesized by an aldol condensation of trans-2,4-dimethyl-l-cyclohexanone (5b), with 4-(2-oxoethyl)-2,6-piperidinedione(6). The antimicrobial activity of trans- cycloheximide isomers (1, 4, 8, and 9) was examined against S. cerevisiae and P. oryzae. The stereoisomers 1 and 4 exhibited marked antimicrobial activity against both microorganisms as compared with their C- α-epimers 8 and 9.     

Identification and Characterization of a Mycobacterial (2R,3R)-2,3-Butanediol Dehydrogenase

Bacterial strain B-009, capable of using racemic 1,2-propanediol (PD), was identified as a rapid-growing member of the genus Mycobacterium. The strain is phylogenetically related to M. gilvum, but has slightly different physiological characteristics. An NAD⁺-dependent enantioselective alcohol dehydrogenase, which acts on R-PD, was purified from the strain. The enzyme was a homodimer of a peptide coded by a 1047-bp gene (mbd1). A highly conserved sequence for medium-chain dehydrogenase/reductases with a preference for secondary alcohols was found in the gene. Hydroxyacetone was produced from R-PD by an enzymatic reaction, indicating that position 2 of the substrate was oxidized. The enzyme activity was highest for (2R,3R)-2,3-butanediol (R,R-BD), enabling the enzyme to be identified as (2R,3R)-2,3-butanediol dehydrogenase (R,R-BD-DH). A homology search revealed M. gilvum, M. vanbaalenii, and M. semegmatis to have ORFs similar to mbd1, suggesting the widespread distribution of genes encoding R,R-BD-DH among mycobacterial strains.     

Preparation of Optically Pure cis-2,4-Dimethyl-l-cyclohexanones,the Key Intermediates in Cycloheximide Synthesis,Using Microbial Resolution

Asymmetric hydrolysis of acetate (10) of (±)-t-2,t-4-dimethyl-r-l-cyclohexanol with Bacillus subtilis var. niger gave (?)-(lS,2S,4S)-2,4-dimethyl-l-cyclohexanol (6a) and (+)-(1R,2R,4R)-acetate (10b) with high optical purities. Optically pure (?) and (+)-alcohols (6a and 6b) were prepared via corresponding 3,5-dinitrobenzoates. Oxidation of alcohols (6a and 6b) with chromic acid gave optically pure (?)-(2S,4S) and (+)-(2R,4R)-2,4-dimethyl-l-cyclohexanones (2a and 2b), respectively.