Life,information theory,and topology

The information content of an organism determines to a large extent its ability to perform the basic vital functions: selection of food, breaking up of the food molecules into appropriate parts, selection of those parts, and their assimilation. The information content needed is very large and requires a sufficiently large complexity of the organism. The information content of an organism is largely determined by the information content of the constituent organic molecules. The information content of the latter is in its turn determined by the number of physically distinguishable atoms or radicals of which the molecule is composed. The different arrangements of atoms in a molecule are represented by the structural formula, which is basically a graph. It is shown that the topology of this graph also determines to a large extent the information content. Different points of a graph may be physically indistinguishable; in general, however, they are different in regard to their topological properties. A study of the relations between the topological properties of graphs and their information content is suggested, and several theorems are demonstrated. A relation between topology and living processes is thus found also on the molecular level.     

From protein-protein interactions to protein co-expression networks: a new perspective to evaluate large-scale proteomic data

The reductionist approach of dissecting biological systems into their constituents has been successful in the first stage of the molecular biology to elucidate the chemical basis of several biological processes. This knowledge helped biologists to understand the complexity of the biological systems evidencing that most biological functions do not arise from individual molecules; thus, realizing that the emergent properties of the biological systems cannot be explained or be predicted by investigating individual molecules without taking into consideration their relations. Thanks to the improvement of the current -omics technologies and the increasing understanding of the molecular relationships, even more studies are evaluating the biological systems through approaches based on graph theory. Genomic and proteomic data are often combined with protein-protein interaction (PPI) networks whose structure is routinely analyzed by algorithms and tools to characterize hubs/bottlenecks and topological, functional, and disease modules. On the other hand, co-expression networks represent a complementary procedure that give the opportunity to evaluate at system level including organisms that lack information on PPIs. Based on these premises, we introduce the reader to the PPI and to the co-expression networks, including aspects of reconstruction and analysis. In particular, the new idea to evaluate large-scale proteomic data by means of co-expression networks will be discussed presenting some examples of application. Their use to infer biological knowledge will be shown, and a special attention will be devoted to the topological and module analysis.     

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.     

Outline of a unified approach to physics,biology and sociology

The theory of organismic sets, introduced by N. Rashevsky (Bulletin of Mathematical Biophysics,29, 139–152, 1967;30, 163–174, 1968), is developed further. As has been pointed out, a society is a set of individuals plus the products of their activities, which result in their interactions. A multicellular organism is a set of cells plus the products of their activities, while a unicellular organism is a set of genes plus the products of their activities. It is now pointed out that a physical system is a set of elementary particles plus the product of their activities, such as transitions from one energy level to another. Therefore physical, biological and sociological phenomena can be considered from a unified set-theoretical point of view. The notion of a “world set” is introduced. It consists of the union of physical and of organismic sets. In physical sets the formation of different structure is governed preponderantly by analytical functions, which are special type of relations. In organismic sets, which represent biological organisms and societies, the formation of various structures is governed preponderantly by requirements that some relations, which are not functions, be satisfied. This is called the postulate of relational forces. Inasmuch as every function is a relation (F-relation) but not every relation is a function (Q-relation), it has been shown previously (Rashevsky,Bulletin of Mathematical Biophysics,29, 643–648, 1967) that the physical forces are only a special kind of relational force and that, therefore, the postulate of relational forces applies equally to physics, biology and sociology. By developing the earlier theory of organismic sets, we deduce the following conclusions: 1) A cell in which the genes are completely specialized, as is implied by the “one gene—one enzyme” principle, cannot be formed spontaneously. 2) By introducing the notion of organismic sets of different orders so that the elements of an organismic set of ordern are themselves organismic sets of order (n−1), we prove that in multicellular organisms no cell can be specialized completely; it performs, in addition to its special functions, also a number of others performed by other cells. 3) A differentiated multicellular organism cannot form spontaneously. It can only develop from simpler, less differentiated organisms. The same holds about societies. Highly specialized contemporary societies cannot appear spontaneously; they gradually develop from primitive, non-specialized societies. 4) In a multicellular organism a specialization of a cell is practically irreversible. 5) Every organismic set of ordern>1, that is, a multicellular organism as well as a society, is mortal. Civilizations die, and others may come in their place. 6) Barring special inhibitory conditions, all organisms multiply. 7) In cells there must exist specially-regulatory genes besides the so-called structural genes. 8) In basically identically-built organisms, but which are built from different material (proteins), a substitution of a part of one organism for the homologous part of another impairs the normal functioning (protein specificity of different species). 9) Even unicellular organisms show sexual differentiation and polarization. 10) Symbiotic and parasitic phenomena are included in the theory of organismic sets. Finally some general speculations are made in regard to the possibility of discovering laws of physics by pure mathematical reasoning, something in which Einstein has expressed explicit faith. From the above theory, such a thing appears to be possible. Also the idea of Poincaré, that the laws of physics as we perceive them are largely due to our psychobiological structure, is discussed.     

Concepts of an architectonic approach to transformation morphology

This paper is about a general methodology for pattern transformation. Patterns are network representations of the relations among structures and functions within an organism. Transformation refers to any realistic or abstract transformation relevant to biology, e.g. ontogeny, evolution and phenotypic clines. The main aim of the paper is a methodology for analyzing the range of effects on a pattern due to perturbing one or more of its structures and/or functions (transformation morphology). Concepts relevant to such an analysis of pattern transformation are reviewed and several new ones introduced: pattern unit; direct and indirect functional demands; compatibility and trade-off; integrating, adding and decoupling; functional effectiveness; spatial, profile and other architectonic constraints; domains of structure-function relations; goal and process adaptability; multiple pathways. The paper is written from the the perspective of architectonic morphology, viz. functional morphology focusing on the relation between anatomical coherence and the compatibility of functions. The advantages and disadvantages of inductive and deductive approaches are discussed.     

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.     

Saccharomyces cerevisiae as a model organism: a comparative study

Background

Model organisms are used for research because they provide a framework on which to develop and optimize methods that facilitate and standardize analysis. Such organisms should be representative of the living beings for which they are to serve as proxy. However, in practice, a model organism is often selected ad hoc, and without considering its representativeness, because a systematic and rational method to include this consideration in the selection process is still lacking.

Methodology/Principal Findings

In this work we propose such a method and apply it in a pilot study of strengths and limitations of Saccharomyces cerevisiae as a model organism. The method relies on the functional classification of proteins into different biological pathways and processes and on full proteome comparisons between the putative model organism and other organisms for which we would like to extrapolate results. Here we compare S. cerevisiae to 704 other organisms from various phyla. For each organism, our results identify the pathways and processes for which S. cerevisiae is predicted to be a good model to extrapolate from. We find that animals in general and Homo sapiens in particular are some of the non-fungal organisms for which S. cerevisiae is likely to be a good model in which to study a significant fraction of common biological processes. We validate our approach by correctly predicting which organisms are phenotypically more distant from S. cerevisiae with respect to several different biological processes.

Conclusions/Significance

The method we propose could be used to choose appropriate substitute model organisms for the study of biological processes in other species that are harder to study. For example, one could identify appropriate models to study either pathologies in humans or specific biological processes in species with a long development time, such as plants.     

Study of biological networks using graph theory

As an effective modeling, analysis and computational tool, graph theory is widely used in biological mathematics to deal with various biology problems. In the field of microbiology, graph can express the molecular structure, where cell, gene or protein can be denoted as a vertex, and the connect element can be regarded as an edge. In this way, the biological activity characteristic can be measured via topological index computing in the corresponding graphs. In our article, we mainly study the biology features of biological networks in terms of eccentric topological indices computation. By means of graph structure analysis and distance calculating, the exact expression of several important eccentric related indices of hypertree network and X-tree are determined. The conclusions we get in this paper illustrate that the bioengineering has the promising application prospects.     

Detection in an experiment of a previously unknown phenomenon of the malignant transformation of bacteria as affected by antibiotics or phenol

The experimental study of bacteria exposed to antibiotics or phenol has revealed the hitherto unknown process of their malignant transformation. These facts are of universal importance for life sciences, as they bring about changes in the knowledge of the main processes in the life and development of organisms. The discovery of this phenomenon will help in achieving the correct solutions of cardinal problems in biology and medicine.     

The cell theory--history, present state and prospects (on the 150th anniversary of the development of the cell theory)

The main stages of history of this most important biological conception are presented and the state of the modern cell theory and its future prospects are considered. Since 1839, when T. Schwann expounded his conception of the cell, a long pathway in cognition of the cell function and organization has been covered. From the original picture of the complex organism as a "cellular state", made up of relatively independent "elementary organisms", i.e. cells the modern biology has come to the idea of the cell as an integral system either being a part of a complex organism, or living free in the nature (protists). The cell represents certain qualitatively peculiar level in a complex evolutionary established hierarchy of biological systems. Some particular tight relations, existing between cytology, as a fundamental biological science and molecular biology, genetics, ecology and other biological disciplines are considered. The importance of the cell conception is ascertained for practical aims, especially in medicine.     

Design and implementation of a qualitative simulation model of lambda phage infection

MOTIVATION: Molecular biology databases hold a large number of empirical facts about many different aspects of biological entities. That data is static in the sense that one cannot ask a database 'What effect has protein A on gene B?' or 'Do gene A and gene B interact, and if so, how?'. Those questions require an explicit model of the target organism. Traditionally, biochemical systems are modelled using kinetics and differential equations in a quantitative simulator. For many biological processes however, detailed quantitative information is not available, only qualitative or fuzzy statements about the nature of interactions. RESULTS: We designed and implemented a qualitative simulation model of lambda phage growth control in Escherichia coli based on the existing simulation environment QSim. Qualitative reasoning can serve as the basis for automatic transformation of contents of genomic databases into interactive modelling systems that can reason about the relations and interactions of biological entities.      

Can we build synthetic,multicellular systems by controlling developmental signaling in space and time?

Using biological machinery to make new, functional molecules is an exciting area in chemical biology. Complex molecules containing both 'natural' and 'unnatural' components are made by processes ranging from enzymatic catalysis to the combination of molecular biology with chemical tools. Here, we discuss applying this approach to the next level of biological complexity -- building synthetic, functional biotic systems by manipulating biological machinery responsible for development of multicellular organisms. We describe recent advances enabling this approach, including first, recent developmental biology progress unraveling the pathways and molecules involved in development and pattern formation; second, emergence of microfluidic tools for delivering stimuli to a developing organism with exceptional control in space and time; third, the development of molecular and synthetic biology toolsets for redesigning or de novo engineering of signaling networks; and fourth, biological systems that are especially amendable to this approach.     

Synthetic Genomics and Synthetic Biology Applications Between Hopes and Concerns

New organisms and biological systems designed to satisfy human needs are among the aims of synthetic genomics and synthetic biology. Synthetic biology seeks to model and construct biological components, functions and organisms that do not exist in nature or to redesign existing biological systems to perform new functions. Synthetic genomics, on the other hand, encompasses technologies for the generation of chemically-synthesized whole genomes or larger parts of genomes, allowing to simultaneously engineer a myriad of changes to the genetic material of organisms. Engineering complex functions or new organisms in synthetic biology are thus progressively becoming dependent on and converging with synthetic genomics. While applications from both areas have been predicted to offer great benefits by making possible new drugs, renewable chemicals or clean energy, they have also given rise to concerns about new safety, environmental and socio-economic risks – stirring an increasingly polarizing debate. Here we intend to provide an overview on recent progress in biomedical and biotechnological applications of synthetic genomics and synthetic biology as well as on arguments and evidence related to their possible benefits, risks and governance implications.     

A comparison of set-theoretical and graph-theoretical approaches in topological biology

Two somewhat different approaches to topological biology have been developed in recent years. The latest, set-theoretical approach leads rather immediately to a number of conclusions which are verified experimentally. It also predicts a number of new biological relations. The older, graph-theoretical approach does not lead directly to those conclusions but suggests a number of combinatorial relations between number of organs and number of cell types. Such suggestions are absent from the set-theoretical approach. It is shown that the above-mentioned combinatorial relations are independent of the graph-theoretical method proper and can be introduced into the set-theoretical approach through the addition of an independent postulate. A possible addition to the principle of biotopological mapping is suggested, which brings into focus the relations between the organism and its individual organs and which has a predictive value.     

Additive functions in boolean models of gene regulatory network modules

Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome's evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate.     

Organismic sets: Outline of a general theory of biological and social organisms

The discussion as to whether societies are organisms andvice versa has been going on for a long time. The question is meaningless unless a clear definition of the term “organism” is made. Once such a definition is made, the question may be answered by studying whether there exists any relational isomorphism between what the biologist calls an organism and what the sociologist calls society. Such a study should also include animal societies studied by ecologists. Both human and animal societies are sets of individuals together with certain other objects which are the products of their activities. A multicellular organism is a set of cells together with some products of their activities. A cell itself may be regarded as a set of genes together with the products of their activities because every component of the cell is either directly or indirectly the result of the activities of the genes. Thus it is natural to define both biological and social organisms as special kinds of sets. A number of definitions are given in this paper which define what we call here organismic sets. Postulates are introduced which characterize such sets, and a number of conclusions are drawn. It is shown that an organismic set, as defined here, does represent some basic relational aspects of both biological organisms and societies. In particular a clarification and a sharpening of the Postulate of Relational Forces given previously (Bull. Math. Biophysics,28, 283–308, 1966) is presented. It is shown that from the basic definitions and postulates of the theory of organismic sets, it folows that only such elements of those sets will aggregate spontaneously, which are not completely “specialized” in the performance of only one activity. It is further shown that such “non-specialized” elements undergo a process of specialization, and as a result of it their spontaneous aggregation into organismic sets becomes impossible. This throws light on the problem of the origin of life on Earth and the present absence of the appearance of life by spontaneous generation. Some applications to problems of ontogenesis and philogenesis are made. Finally the relation between physics, biology, and sociology is discussed in the light of the theory of organismic sets.     

Lattices and lattice-valued relations in biology

Rashevsky's treatment of general binary relations between sets of biological elements is extended using the novel mathematical concept of lattice-valued relation (l.v.r.). This yields a quantitative measure of the strength of the relations between components of a biological organism, and some illustrative examples are given. Specific l.v.r.'s are used to define (more precisely than in Rashevsky's preliminary theory of binary relations) the biologically important relationships amongst hormones, metabolism and energy exchange involved in metabolic reactions. The ‘strongest link’ between the set of hormones and the set of metabolic reactions is quantified using a special l.v.r., and other specific biological realisations of lattice-valued relations in abstract-relational biology are presented. L.v.r.'s may also be regarded as a form ofG-relation in relational biology, or as a particular case of generating diagrams. Further possible developments of this approach, using more complex tools of the newly developed mathematical theory of lattice-valued relations, such as function space l.v.r., group l.v.r., l.v.r. morphisms, l.v.r. homology andn-ary l.v.r.'s are suggested.