Some considerations on relational equilibria

A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light of the theory.     

Physics,biology and sociology: II. Suggestion for a synthesis

In continuation of previous studies (Bull. Math. Biophysics,28, 283–308; 655–661, 1966;29, 139–152, 1967) it is shown that the difference between the “metric” aspects of physics and the “relational” aspects of biological and social sciences disappear by accepting the broader definition of “relation”, such as that given in mathematics and logic. A conceptual superstructure then becomes possible from which all three branches of knowledge may be derived, though none of them can be derived from the others.     

A note on imitative behavior

In a preceding paper (Bull. Math. Biophysics,27, 175–185) the distribution function ofφ=ɛ ₁-ɛ ₂,—the difference of excitations in the two mutually inhibiting centers, has been derived in terms of the distribution functionsf ₁(ɛ ₁) andf ₂(ɛ ₂) of the two excitations. In the present note some properties of the distribution functionf(ϕ) in terms of the propertiesf ₁(ɛ ₁) andf ₂(ɛ ₂) are derived.     

A discrete time neural network model with spiking neurons

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (“raster plots”). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.      

Biotransformation of soybean isoflavones by a marine <Emphasis Type="Italic">Streptomyces</Emphasis> sp. 060524 and cytotoxicity of the products

A marine Streptomyces sp. 060524 capable of hydrolyzing the glycosidic bond of isoflavone glycosides, was isolated by detecting its β-glucosidase activity. 5 isoflavone aglycones were isolated from culture filtrates in soybean meal glucose medium. They were identified as genistein (1), glycitein (2), daidzein (3), 3′,4′,5,7-tetrahydroxyisoflavone (4), and 3′,4′,7-trihydroxyisoflavone (5), based on UV, NMR and mass spectral analysis. The Streptomyces can selectively hydroxylate at the 3′-position in the daidzein and genistein to generate 3′-hydroxydaidzein and 3′-hydroxygenistein, respectively. The Strain biotransformed more than 90% of soybean isoflavone glycosides into their aglycones within 108 h. 3′-hydroxydaidzein and 3′-hydroxygenistein exhibited stronger cytotoxicity against K562 human chronic leukemia than daidzein and genistein.     

Two remarks on the mathematical biology of automobile driving

In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics 5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated.     

Parasitism and symbiosis in an N-person non-constant-sum continuous game

A non-constant-sum continuous game analyzed in a previous paper by one of the authors (A. Rapoport,Bull. Math. Biophysics,18, 15–30, 1956) is extended from two toN players with special emphasis onN=3. It is shown that the concept of stability becomes in this case one of “pairwise stability,” and depends on the so-called distribution matrix of rewards. The distribution matrix and the collusion structure jointly determine the end states of the game. Conditions which lead to the emergence of one, two, or no “parasites” are derived. An apparatus is described which provides a physical analogue of the game, making possible the isolation of behavioral variables under the prescribed conditions of the game.     

A note on epilepsies and similar disorders

This paper compares two previously published neural models for epilepsies (Bull. Math. Biophysics,33, 539–553, 1971;34, 71–78, 1972). The second model is developed in more detail and an attempt is made to bring it more in line with established neurological findings. The question of classification of some epilepsies is briefly discussed.     

Polar steroids from <Emphasis Type="Italic">Solaster endeca</Emphasis> starfish and the physiological activity of polar steroids from three starfish species

Four polyhydroxylated steroids, new (20R)-5α-cholestan-3β,6α,8,15α,24,26-hexaol (I) and known (20R,25S)-5α-cholestan-3β,6α,8,15β,16β,26-hexaol, (20R,25S)-5α-cholestan-3β,6α,15β,16β,26-pentaol, and marthasterone sulfate were isolated from the Solaster endeca starfish inhabiting the Sea of Okhotsk and characterized. Steroid (I) contains a 24,26-dihydroxylated side chain, which is unique for starfish polyols. The isolated steroids and related metabolites from two starfish species of the Evasterias genus (in total, 15 compounds) were weakly cytotoxic in a human HeLa cell culture and some of them were inhibitors of non-specific esterase from mouse Ehrlich carcinoma. The effects of these compounds on the p53 protein activity were studied in a yeast two-hybrid test system and both inhibitors and stimulators of this activity were found among them.     

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.     

Information content of chemical structures and some possible biological applications

The purpose of this paper is to calculate the amount of information contained in a chemical or biological structure, and to estimate the energy needed for obtaining an organization unit. The first problem is solved by applying H. J. Morowitz's reasoning (Bull. Math. Biophysics,17, 81–86, 1955) and, for the second one, calculations based upon bond formation heat are carried out.Information content theoretical physical entropy, real physical entropy, informational entropy or negentropy entropic information or neginformation, heat amount, as well as relationships between these system parameters, are defined and used. The investigation covers 63 chemical substances (inorganic and organic compounds). The numerical results should show that common organized systems happen to be between two extreme kinds of systems: highly disordered systems and ideally organized systems. Some speculative numerical applications are carried out regarding chlorophyllian photosynthesis and information amount accumulated through biological growth. It seems that Information Theory may predict some biocalorimetric results.     

The effect of heterogeneously-distributed RyR channels on calcium dynamics in cardiac myocytes

Calcium plays an essential role in excitation-contraction coupling in muscle, and derangements in calcium handling can produce a variety of potentially harmful conditions, especially in cardiac muscle. In cardiac tissue specialized invaginations of the sarcolemma, called T-tubules, penetrate deep into each sarcomere, and depolarization of the SL leads to an influx of calcium through voltage-sensitive channels in the T-tubules that in turn triggers further calcium release from the sarcoplasmic reticulum via ryanodine-sensitive calcium channels. Under certain conditions, such as elevated external Ca²⁺, cardiac cells can release calcium from the sarcoplasmic reticulum spontaneously, producing a calcium ’spark’ and propagating traveling waves of elevated Ca²⁺ concentration, without depolarization of the SL (Wier and Blatter, 1991a, Cell Calcium 12, 241–254; Williams, 1993, Cell Calcium 14, 724–735; Cheng et al., 1993a, Science 262, 740–744). However, under normal resting conditions these potentially harmful waves seldom occur. In this paper we investigate the role of the periodic distribution of ryanodine-sensitive channels in determining whether a spark can trigger a wave, using a modification of the kinetic model proposed by Tang and Othmer, 1994b, Biophys. J. 67, 2223–2235, for calcium-induced calcium release. We show that the spatial localization of these channels near the T-tubules has a significant effect on both wave propagation and the onset of oscillations in this system. Spatial localization provides a possible explanation for the differing effects of various experimental protocols on the system’s ability to propagate a traveling wave. Supported in part by NIH Grant GM29123.     

A note on relations between sets

From the definition of a strong and weakn-ary relation betweenn sets, given in a previous paper (Bulletin of Mathematical Biophysics,27, 477–492), it follows that for a given set ofn sets and givenn-ary relationR between them there can exist only one strong relation, but a large number of weak ones. An expression for the total number of possible weak relations is derived and the notion of the degree of weakness of a relation is introduced and discussed.     

Identification of a Potential Lead Structure for Designing New Antimicrobials to Treat Infections Caused by Staphylococcus epidermidis-Resistant Strains

Bacterial infections are a significant cause of morbidity and mortality among critically ill patients. The increase of antibiotic resistance in bacteria from human microbiota—such as Staphylococcus epidermidis, an important nosocomial pathogen that affects immunocompromised patients or those with indwelling devices—increased the desire for new antibiotics. In this study we designed, synthesized, and determined the antimicrobial activity of 27 thieno[2,3-b]pyridines (1, 2, 2a–2m, 3, 3a–3m) derivatives against a drug-resistant clinical S. epidermidis strain. In addition, we performed a structure-activity relationship analysis using a molecular modeling approach, and discuss the drug absorption, distribution, metabolism, excretion, and toxicity profile and Lipinski’s “rule of five,” which are tools to assess the relationship between structures and drug-like properties of active compounds. Our results showed that compound 3b (5-(1H-tetrazol-5-yl)-4-(3`-methylphenylamino)thieno[2,3-b]pyridine) was as active as oxacillin and chloramphenicol but with lower theoretical toxicity risks and a better drug likeness and drug score potential than chloramphenicol. All molecular modeling and biological results reinforced the promising profile of 3b for further experimental investigation and development of new antibacterial drugs. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Analysis of tracer experiments: IV. The kinetics of generalN compartment systems

The methods of C. W. Sheppard and A. S. Householder (Jour. App. Physcis,22, 510–20, 1951), H. D. Landahl (Bull. Math. Biophysics,16, 151–54, 1954) and H. E. Hart (Bull. Math. Biophysics,17, 87–94, 1955;ibid.,19, 61–72, 1957;ibid.,20, 281–87, 1958) are employed in studying the kinetics of generalN compartment systems. It is shown that the nature of the transfer processes occurring in fluid flow systems and the chemical processes occurring in quadratic systems and in catalyzed quadratic systems can in principle be completely determined for all polynomial dependencies. Systems involving three-body and higher-order interactions can be completely solved, however, only if supplementary information is available. Research supported by the Atomic Energy Commission, Contract AT (30-1)-1551.     

On relations between sets: III

The theory of relations between sets, proposed and outlined in previous publications (Bull. Math. Biophysics,23, 233–235, 1961;28, 117–124, 1966;28, 309–313, 1966), is tentatively expanded and generalized with a view to biological applications.     

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.     

Purification and characterization of UDP-glucose: anthocyanin 3′,5′-<Emphasis Type="Italic">O</Emphasis>-glucosyltransferase from <Emphasis Type="Italic">Clitoria ternatea</Emphasis>

A UDP-glucose: anthocyanin 3′,5′-O-glucosyltransferase (UA3′5′GT) (EC 2.4.1.-) was purified from the petals of Clitoria ternatea L. (Phaseoleae), which accumulate polyacylated anthocyanins named ternatins. In the biosynthesis of ternatins, delphinidin 3-O-(6″-O-malonyl)-β-glucoside (1) is first converted to delphinidin 3-O-(6″-O-malonyl)-β-glucoside-3′-O-β-glucoside (2). Then 2 is converted to ternatin C5 (3), which is delphinidin 3-O-(6″-O-malonyl)-β-glucoside-3′,5′-di-O-β-glucoside. UA3′5′GT is responsible for these two steps by transferring two glucosyl groups in a stepwise manner. Its substrate specificity revealed the regioselectivity to the anthocyanin′s 3′- or 5′-OH groups. Its kinetic properties showed comparable k _cat values for 1 and 2, suggesting the subequality of these anthocyanins as substrates. However, the apparent K _m value for 1 (3.89 × 10⁻⁵ M), which is lower than that for 2 (1.38 × 10⁻⁴ M), renders the k _cat/K _m value for 1 smaller, making 1 catalytically more efficient than 2. Although the apparent K _m value for UDP-glucose (6.18 × 10⁻³ M) with saturated 2 is larger than that for UDP-glucose (1.49 × 10⁻³ M) with saturated 1, the k _cat values are almost the same, suggesting the UDP-glucose binding inhibition by 2 as a product. UA3′5′GT turns the product 2 into a substrate possibly by reversing the B-ring of 2 along the C2-C1′ single bond axis so that the 5′-OH group of 2 can point toward the catalytic center. K. Kogawa, N. Kato, K. Kazuma, and N. Noda contributed equally to this work.     

Two exceptional sets of physiological clearance curves and their mathematical form: Test cases?

Amiodarone concentrationsy(t) have been measured from 1 min to more than 50 days following 10 min of infusion, with about 40 observations on each of six normal subjects (Tuckeret al., 1984,Eur. J. clin. Pharmacol. 26, 655–656). The form of the log-log plots—ln(y) vs ln(t)—is investigated. These appear to show three phases. First there is a rapid decrease ofy(t). then a straight line corresponding to a small negative power oft, ca −0.3, and this line changes continuously but quickly at about 0.5 day into a steeper line that is almost straight. For the curve fitting a simple “spline-type” device was successful. Two continuity conditions were imposed at the time of changeover, which was one of the unknown parameters. The results are compared in detail with those from a set of 15 radiocalcium curves obtained during 2 weeks or more from a single injection of⁴⁷Ca (Neeret al., 1967,J. clin. Invest. 46, 1364–1379). Again two power functions of time can be seen. The changeover is much more gradual than with amiodarone, and the fits are still better. Both sets of curves are fitted with fewer adjustable parameters than with the usual multiexponentials that are interpreted in terms of homogeneous compartments. Theoretical and practical implications are mentioned. There is much indirect evidence that hundreds of other clearance curves may consist largely of one or two of such power functions of time.     

Excitation of a magnetospheric MHD cavity by Kelvin-Helmholtz instability

The Kelvin-Helmholtz instability is investigated analytically by using a one-dimensional nonuniform model of the Earth’s magnetosphere and the adjacent solar wind region. Its properties are shown to be essentially governed by the presence of an MHD cavity that arises in the magnetosphere because of the non-uniformity of the latter and also because of the jump in the parameters of the medium at the magnetopause (the outer boundary of the magnetosphere). System oscillations constitute a discrete spectrum of eigenmodes, which are determined by the wave vector k _t along the tangential discontinuity and also by the mode number n = 0, 1, 2, …, playing the role of the wavenumber along a coordinate normal to the magnetopause. Analytic expressions are obtained for the frequency and instability growth rate of each eigenmode and for the functions describing its spatial structure. All these quantities depend parametrically on the solar wind velocity V _W , or more precisely, on the Doppler frequency shift ω _W = k _t · V _W . For each eigenmode, there is a lower instability threshold depending on the parameter ω _W and a sharp maximum in the growth rate at the eigenfrequency of the magnetospheric cavity. For ω _W values below the threshold, the properties of an eigenmode are highly sensitive to the type of solar wind nonuniformity. Three cases are considered: a uniform solar wind and solar winds in which the speed of sound increases or decreases away from the magnetopause.