Some remarks on topological biology

With reference to several recent papers by the author, it is pointed out that within the principle of biotopological mapping a choice of a primordial graph and of a particular transformation defines a system of abstract biology, similar to systems of abstract geometries. The study of such abstract systems is necessary before one can be found which is isomorphic to the actual biological world. A brief survey of the structure and properties of the system based on the choice of the primordial graph and of the transformationT defined in a previous paper (Bull. Math. Biophysics,16, 317–48, 1954) is made. Two more topological theorems are demonstrated, which, interpreted biologically, lead to the conclusion that the higher an organism, the more adaptable it is. Finally a criticism of that particular system of abstract biology is made, and its inadequacy for the representation of the actual biological phenomena pointed out, and a suggestion is made for a possible point set topological approach to 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.     

多层生物介质传感器的特性研究（英文）

目的 多层生物介质的生物传感器被广泛应用于各大领域,其检测特性对于传感器优劣的评估尤为重要。本文目的在于量化表征多层生物介质的电学特征。方法 基于生物电阻抗谱技术来探究多层生物介质的电化学阻抗谱特性,并结合保角映射的方法来量化表征多层生物介质,阐明其对阻抗的影响规律,继而为生物传感器的研制与开发提供理论基础。有效提取各生物介质层修饰后电阻抗参数(Z^*),从而量化表征多层生物介质层的电阻抗谱特性。结果 对多层模型进行了理论计算并构建了相关试验测试系统,研究结果表明,随着生物介质层的逐步修饰,检测区域电阻抗参数(Z^*)在f=0.1～50 MHz下持续上升,理论计算结果趋势与试验结果趋势较好吻合,论证了此理论计算方法的正确性。结论 本文证实了可根据生物电阻抗谱和保角映射方法量化表征多层生物介质的电阻抗谱特性,对生物传感器的研制与开发有一定的实用价值。     

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.     

Relational forces and structures produced by them

After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.     

Characterization and mapping of R Pi-ber , a novel potato late blight resistance gene from Solanum berthaultii

Phytophthora infestans, the causal agent of late blight, threatens potato production worldwide. An important tool in the management of the disease is the use of resistant varieties. Eleven major resistance genes have been identified and introgressed from Solanum demissum. However, new sources of resistance are continually sought. Here, we report the characterization and refined genetic localization of a resistance gene previously identified as Rber in a backcross progeny of Solanum tuberosum and Solanum berthaultii. In order to further characterize Rber, we developed a set of P. infestans isolates capable of identifying each of the 11 R-genes known to confer resistance to late blight in potato. Our results indicate that Rber is a new resistance gene, different from those recognized in S. demissum, and therefore, it has been named R _Pi-ber according to the current system of nomenclature. In order to add new molecular markers around R _Pi-ber , we used a PCR-based mapping technique, named MASP-map, which located R _Pi-ber in a 3.9 cM interval between markers CT240 and TG63 on potato chromosome X. The location of R _Pi-ber coincides with an area involved in resistance to different pathogens of potato and tomato.     

On the Semio-Mathematical Nature of Codes

The relational structure of RNA, DNA, and protein bears an interesting similarity to the determination problem in category theory. In this paper, we present this deep-structure similarity and use it as a springboard for discussing some abstract properties of coding in various systems. These abstract properties, in turn, may shed light on the evolution of the DNA world from a semiotic perspective. According to the perspective adopted in this paper, living systems are not information processing systems but “meaning-making” systems. Therefore, what flows in the genetic system is not “information” but “value.” We define meaning, meaning-making, and value and then use these terms to explain the abstract dynamics of coding, which can illuminate many forms of sign-mediated activities in biosystems.     

A visualization of 3D proteome universe: Mapping of a proteome ensemble into 3D space based on the protein-structure composition

To visualize a bird’s-eye view of an ensemble of proteomes for various species, we recently developed a novel method of mapping a proteome ensemble into Three-Dimensional (3D) vector space. In this study, the “proteome” is defined as the entire set of all proteins encoded in a genome sequence, and these proteins were dealt with at the level of the SCOP Fold. First, we represented the proteome of a species s by a 1053-dimensional vector x(s), where its length ∣x(s)∣ represents the overall amount of all the SCOP Folds in the proteome, and its unit vector x(s)/∣x(s)∣ represents the relative composition of the SCOP Folds in the proteome and the size of the dimension, 1053, is the number of all possible Folds in the proteome ensemble given. Second, we mapped the vector x(s) to the 3D vector y(s), based on the two simple principles: (1) ∣y(s)∣ = ∣x(s)∣, and (2) the angle between y(s) and y(t) maximally correlates with the angle between x(s) and x(t). We applied to the mapping of a proteome ensemble for 456 species, which were retrieved from the Genomes TO Protein structures and functions (GTOP) database. As a result, we succeeded in the mapping in that the properties of the 1053-dimensional vectors were quantitatively conserved in the 3D vectors. Particularly, the angles between vectors before and after the mapping highly correlated with each other (correlation coefficients were 0.95–0.96). This new mapping method will allow researchers to intuitively interpret the visual information presented in the maps in a highly effective manner.     

Multiple relational equilibria: Polymorphism,metamorphosis and other possibly similar phenomena

In a preceding paper (Rashevsky, 1969. “Outline of a Unified Approach to Physics, Biology and Sociology.”Bulletin of Mathematical Biophysics,31, 159–198) certain isomorphisms between biological and social systems on the one hand and physical systems on the other were studied. The notion or relational forces, of which ordinary physical forces are a particular case, was introduced. In the present paper an attempt is made to establish analogies between stable equilibria in physical systems, equilibria due to physical forces, and stable equilibria in biological and social systems which are due to purely relational forces. The notion of relational forces causing multiple equilibria similar to multiple equilibria in some physical systems is studied, and it is outlined how this notion may possibly help the understanding of such phenomena as polymorphism, metamorphosis and the existence of rudimentary organs or rudimentary functions.     

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.     

Mathematical biology of automobile driving: III

In a previous paper (Bull. Math. Biophysics,22, 257–262, 1960), an expression for the probability that a car jumps off a road as a function of the speed and the size of the car was derived mostly from geometric and kinematic considerations, introducing only the reaction time as a biological parameter. In subsequent papers (Bull. Math. Biophysics,29, 181–186, 187–188, 1967) a more detailed study was made of the exact shape of the tracking curve of the car which involved several biological parameters of the driver. In the present paper the results of the previous studies are combined, and a more general equation for the probability of jumping off the road is obtained. This probability, as in the earlier study, increases with the speedv, widths _o and lengthl _o of the car, and decreases with widths of the lane. However, this probability also depends on several parameters which characterize the psychobiological constitution of the driver. Unpublished experiments by Ehrlich, which corroborate the general conclusions, are briefly described.     

Suggestions for a mathematical biology of some pathological phenomena in the central nervous system,with special reference to some epilepsies

A neural model which was published in a preceding paper (Bull. Math. Biophysics,33, 539–553, 1971) and which explains the appearance of spontaneous sporadic outbursts of hyperactivity in some individuals, is elaborated further, with special reference tosome epilepsies. It is concluded thatsome epilepsies may be of purely psychogenic nature and amenable to psychotherapy. In particular such epilepsies may be arrested by appropriate conditioning. A case of such arrest has actually been described in medical literature.     

Nucleosome Positioning,Nucleosome Spacing and the Nucleosome Code

Abstract

Nucleosome positioning has been the subject of intense study for many years. The properties of micrococcal nuclease, the enzyme central to these studies, are discussed. The various methods used to determine nucleosome positions in vitro and in vivo are reviewed critically. These include the traditional low resolution method of indirect end-labelling, high resolution methods such as primer extension, monomer extension and nucleosome sequencing, and the high throughput methods for genome-wide analysis (microarray hybridisation and parallel sequencing). It is established that low resolution mapping yields an averaged chromatin structure, whereas high resolution mapping reveals the weighted superposition of all the chromatin states in a cell population. Mapping studies suggest that yeast DNA contains information specifying the positions of nucleosomes and that this code is made use of by the cell. It is proposed that the positioning code facilitates nucleosome spacing by encoding information for multiple alternative overlapping nucleosomal arrays. Such a code might facilitate the shunting of nucleosomes from one array to another by ATP-dependent chromatin remodelling machines.     

Methane in Water: An Ab Initio Study

Abstract

In preceding publications we discussed some properties of pure water in condensed phases using an ab initio approach. Here this study is used as a basis of comparison for analysing the behaviour of water as a solvent in the presence of an apolar molecule. Our analysis is focused on the process of organization of the hydrogen bonding network around the solute. For this purpose we perform some ab initio calculations for a system of 32 water molecules and one methane molecule at 300 K; in particular, the average molecular dipole moment of water is determined and the result is compared with that of pure water. Next the attention is switched to the methane molecule; related properties such as excluded volume and sphericity of its shape are illustrated and discussed. A comparison with results obtained using classical approaches suggests that some classical models of water can be considered to be still valid when they are used to analyse the water-methane system.     

Other developments regarding the concept of energy in biological systems

In order to recognize the realizability of inputs with different physical natures through a component, Yoneda's Lemma is applied. The major utility of this Lemma is when the components produce only energy. From this, it is assumed that a new material input must exist which was not recognized in the original developments in biological systems representation. Moreover, simple transfers of energy, between objects, components, and among both objects and components are developed under the generic name; energetical evolution. Thus, energetical evolution appears as anew element in the abstract representation of biological systems. These new concepts are incorporated into a new abstract diagram and a newM _β category. This paper was made possible by a Fellowship from the Consejo Nacional de Investigaciones Científicas y Técnicas of the República Argentina.     

Further studies of some aspects of a neurobiophysical model of schizophrenia

The neurobiophysical model of schizophrenia discussed previously (Bull. Math. Biophysics,26, 167–185, 1964;27, 21–26, 1965) is generalized further, to include catatonic and stuporous states. It is concluded that the development of schizophrenia will proceed through different stages of catatonic and non-catatonic states, depending on parameters which characterize on one hand the general inhibition of the individual, on the other hand what may be called his “stability.” Suggestions for possible clinical verifications of the conclusions are made.     

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.     

Molecular set theory: II. An aspect of the biomathematical theory of sets

In an earlier paper (Molecular Set Theory: I.Bull. Math. Biophysics,22, 285–307, 1960) the author proposed a “Molecular Set Theory” as a formal mathematical meta-theoretic system for representing complex reactions not only of biological interest, but also of general chemical interest. The present paper is a refinement and extension of the earlier work along more formal algebraic lines. For example the beginnings of an algebra of molecular transformations is presented. It also emphasizes that this development, together with the genetical set theory of Woodger's and Rashevsky's set-theoretic contributions to Relational Biology, points to the existence of a biomathematical theory of sets which is not deducible from the general mathematical, abstract theory of sets.     

A note on topological biology

In line with a recent suggestion by the author (Bull. Math. Biophysics,20, 267–73, September, 1958) that not only does the organism as a whole map on the primordial, but that each organ can also be thus mapped, it is shown that the previously introduced abstract spaces, which represent an organism, contain subspaces which map continuously on the space of the primordial. Several theorems about those subspaces are proven.     

功能作图(functional mapping)分析大肠杆菌和金黄色葡萄球菌之间的竞争互作

【背景】功能作图(functionalmapping)模型是基于统计方法的分析生物体动态复杂性状发育的全基因组作图方法,旨在定位性状发育过程中的数量性状位点(quantitative trait loci, QTL),将功能作图应用于微生物研究有助于解析复杂的互作过程。【目的】利用功能作图定位两种微生物在动态生长发育过程中发挥显著作用的QTL,通过基因功能注释找到影响微生物表型生长的基因。【方法】将大肠杆菌和金黄色葡萄球菌各100个菌株单独培养和一一配对共同培养,将取得的各菌株生长丰度表型数据和单核苷酸多态性(singlenucleotidepolymorphism,SNP)数据进行关联分析,找到同一物种在不同培养条件下对生长起作用的显著QTL。【结果】通过功能作图分析,在大肠杆菌中定位到217个QTL,金黄色葡萄球菌中定位到152个QTL;通过功能聚类和基因注释分析发现,QTL所在候选基因中金黄色葡萄球菌scdA、sdrC、sdrD、ftsA和大肠杆菌phr、nagC、eptA、ppsA、priA、flim基因对微生物的生长发挥了较大作用。【结论】本文借助功能作图定位了大肠杆菌和金黄...