Some theorems in topology and a possible biological implication

In a previous paper (Bull. Math. Biophysics,16, 317–48, 1954) a transformationT of one graph into another was suggested, which may describe the relations between organisms of different complexity. In this paper some topological properties of the transformationT are studied. It is shown that the fundamental group of the transformed graph is homomorph to the fundamental group of the original graph. An expression is derived for the number of points in a point base of the transformed graph in terms of the number of points of the point base of the original when the point base of the latter consists only of residual points, and it is shown that the ratio of the number of points of the point base to the total number of points of the graph is in that case greater in the transformed graph than in the original. A combinatorial problem arising in connection with the transformationT is solved by deriving the number of possible ways in whichn-n _i indistinguishable elements may be arranged inn _i classes, permitting some of then _i classes to be empty. The possible biological meaning of the increased ratio of the number of points of the point base to the total number of points of the graph is discussed. It is suggested that it may be interpreted as a decrease of regenerating ability with increase of differentiation of the organism. Those considerations suggest the possibility of deriving some general biological laws from the consideration of the properties of the transformation only, regardless of the choice of the primordial graph.     

Contributions to topological biology: Some considerations on the primordial graph and on some possible transformations

This paper is a continuation of some discussions published previously (Bull. Math. Biophysics,16, 317–347, 1954). A different example of a primordial graph is suggested and discussed. Then six different types of geometric transformations, similar in some respects to the one discussed in the previous paper are proposed. Another set of seven different transformations which emphasize the central role of the circulatory system is described. A theorem about the “lumping” of several points of a graph into one point is proved and possible biological aspects of it are discussed.     

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 contribution to Rashevsky’s mathematical theory of development

The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.     

Optimal sequence alignment using affine gap costs

When comparing two biological sequences, it is often desirable for a gap to be assigned a cost not directly proportional to its length. If affine gap costs are employed, in other words if opening a gap costsv and each null in the gap costsu, the algorithm of Gotoh (1982,J. molec. Biol. 162, 705) finds the minimum cost of aligning two sequences in orderMN steps. Gotoh's algorithm attempts to find only one from among possibly many optimal (minimum-cost) alignments, but does not always succeed. This paper provides an example for which this part of Gotoh's algorithm fails and describes an algorithm that finds all and only the optimal alignments. This modification of Gotoh's algorithm still requires orderMN steps. A more precise form of path graph than previously used is needed to represent accurately all optimal alignments for affine gap costs.     

Identification of methionine oxidation in human recombinant erythropoietin by mass spectrometry: Comparative isoform distribution and biological activity analysis

Background: Oxidative degradation of human recombinant erythropoietin (hrEPO) may occur in manufacturing process or therapeutic applications. This unfavorable alteration may render EPO inefficient or inactive. We investigated the effect of methionine/54 oxidative changes on the amino acid sequences, glycoform distribution and biological activity of hrEPO. Methods: Mass spectrometry was applied to verify the sequence and determine the methionine oxidation level of hrEPO. Isoform distribution was studied by capillary zone electrophoresis method. In vivo normocythemic mice assay was used to assess the biological activity of three different batches (A, B, and C) of the proteins. Results: Nano-LC/ESI/MS/MS data analyses confirmed the amino acid sequences of all samples. The calculated area percent of three isoforms (2–4 of the 8 obtained isoforms) were decreased in samples of C, B, and A with 27.3, 16.7, and 6.8% of oxidation, respectively. Specific activities were estimated as 53671.54, 95826.47, and 112994.93?mg/mL for the samples of A, B, and C, respectively. Conclusion: The observed decrease in hrEPO biological activity, caused by increasing methionine oxidation levels, was rather independent of its amino acid structure and mainly associated with the higher contents of acidic isoforms.     

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.     

A note on a variational problem in biology and sociology

The author's suggestion that the behavior of an individual or of a society may be described not by maximizing the satisfaction function but by maximizing the integral of it over a period of time (Rashevsky,Mathematical Biology of Social Behavior, rev. ed., p. 233, Chicago: The University of Chicago Press) has been considered applicable to other biological functions in a recent paper by R. Rosen (Bull. Math. Biophysics,24, 279–290, 1962). It is pointed out that the possibility of introducing such variational principles into biology or sociology requires that the corresponding functions depend explicitly and in a nonlinear manner on the rate of change of some of the variables. An example of a satisfaction function is given that describes the behavior of an individual who derives more satisfaction from the process of approaching a goal than from the actual goal itself.     

The representation of biological systems from the standpoint of the theory of categories

A mathematical framework for a rigorous theory of general systems is constructed, using the notions of the theory of Categories and Functors introduced by Eilenberg and MacLane (1945,Trans. Am. Math. Soc.,58, 231–94). A short discussion of the basic ideas is given, and their possible application to the theory of biological systems is discussed. On the basis of these considerations, a number of results are proved, including the possibility of selecting a unique representative (a “canonical form”) from a family of mathematical objects, all of which represent the same system. As an example, the representation of the neural net and the finite automaton is constructed in terms of our general theory.     

A set-theoretical approach to biology

In a preceding paper (Bull. Math. Biophysics 20, 71–93, 1958) the principle of biotopological mapping was formulated in terms of a continuous mapping of an abstract space, made from the set of biological properties which characterize the organism, by an appropriate definition of neighborhoods. In this paper it is shown that we may consider directly the mappings of the different sets of properties which characterize different organisms without taking recourse to abstract spaces. All the verificable conclusions made in the preceding paper remain valid. A serious difficulty mentioned previously is, however, avoided and the possibility of more general predictions is established.     

炭团木霉中非核糖体多肽基因NRPS1的功能研究

[目的] 木霉属真菌是应用最为广泛和潜力最大的生防真菌,其产生的典型化合物哌珀霉素（peptaibols）类抗生素在生物防治中发挥重要作用。本研究采用基因组挖掘技术（genome mining）发现炭团木霉（Trichoderma hypoxylon）的潜在哌珀霉素生物合成基因簇及对病原菌的防治作用。[方法] 生物信息学分析预测合成哌珀霉素的基因簇,利用Quick-change技术构建基因骨架敲除盒,通过PEG介导的原生质体转化方法获得敲除突变株,通过平板对峙法和菌丝生长毒力实验验证该基因簇对炭团木霉生物活性的影响。[结果] 基因挖掘鉴定一个非核糖体多肽合成酶（nonribosomal peptide synthetases,NRPS）可能合成哌珀霉素类抗生素,命名为NRPS1,对该基因进行部分敲除,成功获得3株NRPS1缺失突变株。对峙实验表明,突变株对寄生曲霉（Aspergillus parasiticus）、尖孢镰刀菌（Fusarium oxysporum）、黑白轮枝菌（Verticillium alboatrum）等9株植物病原真菌的抑制作用与野生株相比显著下降,且突变株的粗提物的抑菌活性明显弱于野生型。[结论] NRPS1是一个潜在的哌珀霉素合成基因,该基因在宿主与病原真菌对抗过程中起关键作用,该研究为炭团木霉哌珀霉素结构解析及生物防治机理研究奠定了基础。     

西藏青稞根际细菌群落结构及多样性

【目的】分析西藏不同种植区青稞根际土壤细菌群落结构及其影响因素，揭示特定环境下根际细菌生物标志物，为发掘研究优异根际促生菌及其作用提供参考。【方法】采用16S rRNA基因高通量测序技术和数据统计分析，比较了西藏5个市青稞种植区根际土壤细菌群落组成和结构差异，分析了青稞根际细菌生物标志物及群落结构变化的驱动因素。【结果】通过测序45个根际土壤样品获得10 715个操作分类单元（operational taxonomic units，OTUs），共43门、1 244属、2 783种，其中放线菌门（Actinobacteriota）、变形菌门（Proteobacteria）、绿弯菌门（Chloroflexi）、酸杆菌门（Acidobacteriota）、拟杆菌门（Bacteroidota）、厚壁菌门（Firmicutes）、芽单胞菌门（Gemmatimonadota）、粘球菌门（Myxococcota）和髌骨细菌门（Patescibacteria）为优势菌门，相对丰度占比94.92%-96.56%。五个市的根际细菌群落结构存在明显的差异，组间差异大于组内差异（R=0.226 9，P=0.001），其中放线菌门、绿弯菌门、酸杆菌门、拟杆菌门和髌骨细菌门丰度存在显著性差异（P<0.05）。五个市青稞根际土壤存在潜在生物标志物，拉萨和山南只有3个和6个特有细菌进化支，共现网络更为复杂、OTUs间联系更为紧密。变形菌门、绿弯菌门、放线菌门和酸杆菌门是青稞根际土壤中主要的关键细菌门，内生菌门、Methylomirabilota和蓝细菌分别是林芝市、日喀则市和山南市的特有关键类群。青稞根际细菌群落结构的变化主要与环境因子pH、全钾（total potassium，TK）、速效钾（available potassium，AK）、碳磷比（C：P）和海拔有关，其中TK是影响根际土壤细菌群落最重要的因子（r²=0.621 4，P=0.001）。【结论】西藏青稞根际细菌多样性丰富，5市间存在显著差异，且不同生长区青稞根际具有特有的生物标志物，为进一步研究特有根际细菌在青稞生长和环境适应中的作用，发掘优异根际促生菌提供参考。     

On relations between sets: II

The notion of relations between sets, defined in a previous publication (Bull. Math. Biophysics,23, 233–235, 1961) is generalized and some biological examples are given. A generalization ton-ary relation is suggested.     

Laboratory evolution of peroxide-mediated cytochrome P450 hydroxylation Joo H,Lin Z,Arnold FH. Nature 1999; 399: 670–673

Abstract

The article entitled Laboratory evolution of peroxide-mediated cytochrome P450 hydroxylations, by Hyun Joo, Zhanglin Lin and Francis H. Arnold of the Division of Chemistry and Chemical Engineering, California Institute of Technology, recently communicated in Nature,¹ is an excellent example of the revolution in the biological sciences. We frequently hear that we are in the midst of an informational revolution. If one simply considers the fact that all biological information exists in DNA, it is possible to envision the biological informational revolution. Alternatively, the term technological revolution is applied to the many recent advances in several fields, including the biological sciences. Both the informational and technological revolution can be readily recognized in the article by Joo and colleagues.     

Organismic sets and biological epimorphism

It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.     

蝇蛹俑小蜂对橘小实蝇和瓜实蝇的偏好性

【背景】蝇蛹俑小蜂是实蝇类害虫蛹期的一种重要寄生蜂,对压制下一代实蝇类害虫的种群数量具有重要作用,但有关其对不同实蝇害虫的寄生特性尚缺乏研究。【方法】采用"H"型装置和培养皿测定方法,研究了蝇蛹俑小蜂的寄主选择偏好性。【结果】蝇蛹俑小蜂在橘小实蝇蛹和瓜实蝇蛹共存的情况下,偏好在橘小实蝇蛹上停留,且寄生率较高,最高寄生率达61.11%。【结论与意义】本研究为合理利用蝇蛹俑小蜂控制实蝇类害虫提供了理论基础。     

Organismic supercategores: II. On multistable systems

The representation of biological systems in terms of organismic supercategories, introduced in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious.     

Topological biology: A note on Rashevsky's transformation T.

In the bio-topological transformation between graphs denoted by (T ⁽¹⁾ X) N. Rashevsky (Bull. Math. Biophysics,18, 173–88, 1956) considers the number of fundamental sets which (a) have only one specialized point as source (and no other sources), (b) have no points in common (are “disjoined”); he proves that this number is an invariant of the transformation. In this note we show that Rashevsky's Theorem can be extended as follows:The number of fundamental sets of the first category is an invariant of the transformation. We must, however, count the subsidiary points of the transformed graph as specialized points. We recall that fundamental sets of the first category are those whose sources consist of specialized points only (Trucco,Bull. Math. Biophysics,18, 65–85, 1956). But in this modified version of the Theorem the fundamental sets may have more than one source and need not be disjoined.     

假结核耶尔森氏菌中Phd-Doc毒素-抗毒素系统的功能鉴定

【背景】毒素-抗毒素系统在微生物体内广泛存在,在微生物对抗外界不良环境方面发挥重要作用。【目的】以模式细菌假结核耶尔森氏菌(Yersinia pseudotuberculosis,Yptb)为材料,探究其编码的Phd-Doc毒素-抗毒素系统的作用机制和生物学功能。【方法】通过生物信息学方法预测Yptb中编码的Phd-Doc毒素-抗毒素系统,通过毒性分析、基因表达分析及蛋白相互作用对其进行鉴定;通过抗生素胁迫、氧胁迫、生物被膜形成等实验研究Phd-Doc在体内发挥的生物学功能。【结果】生物信息学分析鉴定出一对Phd-Doc毒素-抗毒素系统,发现二者共转录且相互作用;毒素蛋白Doc能够引起大肠杆菌形态发生变化并抑制其生长,抗毒素蛋白Phd能中和Doc的毒性;Phd-Doc毒素-抗毒素系统具有自调控抑制效应;phd-doc的缺失对Yptb自身的生长无影响,而且毒素蛋白Doc在野生型Yptb内过表达并未显示毒性;phd-doc在转录水平上响应了抗生素胁迫和氧胁迫,其中,对氯霉素胁迫最为敏感,但并不影响Yptb的生长;同时,Phd-Doc能够影响Yptb的生物被膜形成能力。【结论】Yptb中Phd-Doc毒素-抗毒素系统的功能鉴定对于更好地了解在多变的外部环境下微生物的定殖和响应机制具有重要意义。