Elemente einer systemtheoretischen Betrachtung des Stoffwechsels

The discussion of general formal properties of metabolizing systems reveals the justification of applying tentatively General Systems Theory as a most general background. Whereas set-theoretical and graph-theoretical considerations, because of their very abstract nature, are obviously not well suited, the application of the theory of compartmented systems, elaborated on the basis of network or linear systems theories, seems to be useful. In metabolic studies physical models in the sense of computers operating as simulators are indispensable tools for research. A comparison between cybernetic and kinetic models demonstrates the many links and similarities rather than contrasts existing between them. Some epistemological problems are also included in the extended discussion of the concepts of information and energy, basical for these models.     

The structure of steady-state enzyme kinetic equations: a graph-theoretical algorithm for obtaining conditions for reduction in degree by common-factor cancellation

Many enzyme kinetic steady-state equations are so complicated that analysis of their predictions, preferably by graph-theoretical methods, without deriving the equations is desirable. An example of such a method is given here. It is a graph-theoretical algorithm for determining non-trivial relations between the rate constants of a mechanism that cause the numerator and denominator of its rate expression have a common factor so permitting the degree of the expression to be reduced. An algorithm for writing the several different forms of the reduced rate equation is also given. The algorithm is applied to some standard simple enzymic mechanisms that give relatively complicated rate equations.In the case of a 2:2 equation, the sign of curvature in a double reciprocal plot depends on the sign of the expression in the common-factor condition.     

Comparing DNA damage-processing pathways by computer analysis of chromosome painting data.

Chromosome aberrations are large-scale illegitimate rearrangements of the genome. They are indicative of DNA damage and informative about damage processing pathways. Despite extensive investigations over many years, the mechanisms underlying aberration formation remain controversial. New experimental assays such as multiplex fluorescent in situ hybridyzation (mFISH) allow combinatorial "painting" of chromosomes and are promising for elucidating aberration formation mechanisms. Recently observed mFISH aberration patterns are so complex that computer and graph-theoretical methods are needed for their full analysis. An important part of the analysis is decomposing a chromosome rearrangement process into "cycles." A cycle of order n, characterized formally by the cyclic graph with 2n vertices, indicates that n chromatin breaks take part in a single irreducible reaction. We here describe algorithms for computing cycle structures from experimentally observed or computer-simulated mFISH aberration patterns. We show that analyzing cycles quantitatively can distinguish between different aberration formation mechanisms. In particular, we show that homology-based mechanisms do not generate the large number of complex aberrations, involving higher-order cycles, observed in irradiated human lymphocytes.     

Consistent micro, macro and state-based population modelling

A population system can be modelled using a micro model focusing on the individual entities, a macro model where the entities are aggregated into compartments, or a state-based model where each possible discrete state in which the system can exist is represented. However, the concepts, building blocks, procedural mechanisms and the time handling for these approaches are very different. For the results and conclusions from studies based on micro, macro and state-based models to be consistent (contradiction-free), a number of modelling issues must be understood and appropriate modelling procedures be applied. This paper presents a uniform approach to micro, macro and state-based population modelling so that these different types of models produce consistent results and conclusions. In particular, we demonstrate the procedures (distribution, attribute and combinatorial expansions) necessary to keep these three types of models consistent. We also show that the different time handling methods usually used in micro, macro and state-based models can be regarded as different integration methods that can be applied to any of these modelling categories. The result is free choice in selecting the modelling approach and the time handling method most appropriate for the study without distorting the results and conclusions.     

Linear constraint relations in biochemical reaction systems: I. Classification of the calculability and the balanceability of conversion rates

Measurements provide the basis for process monitoring and control as well as for model development and validation. Systematic approaches to increase the accuracy and credibility of the empirical data set are therefore of great value. In (bio)chemical conversions, linear conservation relations such as the balance equations for charge, enthalpy, and/or chemical elements, can be employed to relate conversion rates. In a pactical situation, some of these rates will be measured (in effect, be calculated directly from primary measurements of, e.g., concentrations and flow rates), as others can or cannot be calculated from the measured ones. When certain measured rates can also be calculated from other measured rates, the set of equations, the accuracy and credibility of the measured rates can indeed be improved by, respectively, balancing and gross error diagnosis. The balanced conversion rates are more accurate, and form a consistent set of data, which is more suitable for further application (e.g., to calculate nonmeasured rates) than the raw measurements. Such an approach has drawn attention in previous studies. The current study deals mainly with the problem of mathematically classifying the conversion rates into balanceable and calculable rates, given the subset of measured rates. The significance of this problem is illustrated with some examples. It is shown that a simple matrix equation can be derived that contains the vector of measured conversion rates and the redundancy matrix R. Matrix R plays a predominant role in the classification problem. In supplementary articles, significance of the redundancy matrix R for an improved gross error diagnosis approach will be shown. In addition, efficient equations have been derived to calculate the balanceable and/or calculable rates. The method is completely based on matrix algebra (principally different from the graph-theoretical approach), and it is easily implemented into a computer program. (c) 1994 John Wiley & Sons, Inc.     

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two-step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph-theoretical approach FIRST and an all-atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse-graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse-graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions.     

Determining minimum energy conformations of polypeptides by dynamic programming

A combinatorial optimization approach is used for solving the multiple-minima problem when determining the low-energy conformations of short polypeptides. Each residue is represented by a finite number of discrete states corresponding to single residue local minima of the energy function. These precomputed values constitute a search table and define the conformational space for discrete minimization by a generalized dynamic programming algorithm that significantly limits the number of intermediate conformations to be generated during the search. Since dynamic programming involves stagewise decisions, it results in buildup-type procedures implemented in two different forms. The first procedure predicts a number of conformations by a completely discrete search and these are subsequently refined by local minimization. The second involves limited continuous local minimization within the combinatorial algorithm, generally restricted to two dihedral angles in a buildup step. Both procedures are tested on 17 short peptides previously studied by other global minimization methods but involving the same potential energy function. The discrete method is extremely fast, but proves to be successful only in 14 of the 17 test problems. The version with limited local minimization finds, however, conformations in all the 17 examples that are close to the ones previously presented in the literature or have lower energies. In addition, results are almost independent of the cutoff energy, the most important parameter governing the search. Although the limited local minimization increases the number of energy evaluations, the method still offers substantial advantages in speed.     

Generation of rules for expert systems by statistical methods of fermentation data analysis

Five new methods for determining the relations between kinetic data of fermentations are described and applied to an industrial antibotic fermentation process. The input data for these method are the elements of the distance matrix d_ij, which quantify the sum of the deviation squares between the time dependent kinetics x (t) of the fermentation runs i and j. For each measurable or calculable kinetic state variable, one n x n distance matrix must be calculated where n is the number of fermentation runs. All methods compare these distance matrices by statistical or graph-theoretical approaches. The algorithms obtained are universally applicable if enough kinetic data are available, especially from more than 10 comparable fermentation runs. The algorithms were developed for the use in knowledge acquisition modules of expert systems.     

Effects of extremely high-frequency electromagnetic radiation on the immune system and systemic regulation of homeostasis

Low-intensity of electromagnetic radiation of extremely high frequencies (EHF EMR) is effectively used in medical practice for diagnostics, prevention and treatment of a broad spectrum of diseases of different etiology. However, in spite of existence of many hypotheses about mechanisms of EHF EMR effects on the molecular and cellular levels of organization of living systems, there is not conception that could explain all diversity of the EHF-therapy effects from unified approach. In our opinion, the problem of determination of mechanisms of EHF EMR effects on living organism is divided into two basic tasks: first, determining subcellular structures which can receive radiation, and, second, studying physiological reactions of the organism which are caused by radiation. It is obviously, that investigation of functions of single cells and subcellular elements can not entirely explain therapeutic effects and mechanisms of EHF EMR influence on multicellular organism on the whole. Plenty of functional relationships between organs and systems of organs should be taken into account. In the present review, a realization of the EHF-therapy effects due to the influence on immune system functions and start of system mechanisms of maintenance of the homeostasis on the organism level is hypothesized. Potential targets for EHF EMR acception on the level of different systems of the organism are analysed. The material is formed so that functional relations between immune system and other regulatory systems (nervous and endocrine systems) are traced.     

Biocommunication and natural genome editing

The biocommunicative approach investigates communication processes within and among cells, tissues, organs and organisms as sign-mediated interactions, and nucleotide sequences as code, i.e. language-like text, which follows in parallel three kinds of rules: combinatorial (syntactic), context-sensitive (pragmatic), and content-specific (semantic). Natural genome editing from a biocommunicative perspective is competent agent-driven generation and integration of meaningful nucleotide sequences into pre-existing genomic content arrangements and the ability to (re-)combine and (re-)regulate them according to context-dependent (i.e. adaptational) purposes of the host organism.     

ACoM: A classification method for elementary flux modes based on motif finding

Elementary flux mode analysis is a powerful tool for the theoretical study of metabolic networks. However, when the networks are complex, the determination of elementary flux modes leads to combinatorial explosion of their number which prevents from drawing simple conclusions from their analysis. To deal with this problem we have developed a method based on the Agglomeration of Common Motifs (ACoM) for classifying elementary flux modes. We applied this algorithm to describe the decomposition into elementary flux modes of the central carbon metabolism in Bacillus subtilis and of the yeast mitochondrial energy metabolism. ACoM helps to give biological meaning to the different elementary flux modes and to the relatedness between reactions. ACoM, which can be viewed as a bi-clustering method, can be of general use for sets of vectors with values 0, +1 or −1.     

Homology,limbs, and genitalia

SUMMARY Similarities in genetic control between the main body axis and its appendages have been generally explained in terms of genetic co-option. In particular, arthropod and vertebrate appendages have been explained to invoke a common ancestor already provided with patterned body outgrowths or independent recruitment in limb patterning of genes or genetic cassettes originally used for purposes other than axis patterning. An alternative explanation is that body appendages, including genitalia, are evolutionarily divergent duplicates (paramorphs) of the main body axis. However, are all metazoan limbs and genitalia homologous? The concept of body appendages as paramorphs of the main body axis eliminates the requirement for the last common ancestor of limb-bearing animals to have been provided with limbs. Moreover, the possibility for an animal to express complex organs ectopically demonstrates that positional and special homology may be ontogenetically and evolutionarily uncoupled. To assess the homology of animal genitalia, we need to take into account three different sets of mechanisms, all contributing to their positional and/or special homology and respectively involved (1) in the patterning of the main body axis, (2) in axis duplication, followed by limb patterning mechanisms diverging away from those still patterning the main body axis (axis paramorphism), and (3) in controlling the specification of sexual/genital features, which often, but not necessarily, come into play by modifying already developed and patterned body appendages. This analysis demonstrates that a combinatorial approach to homology helps disentangling phylogenetic and ontogenetic layers of homology.     

Incremental truncation as a strategy in the engineering of novel biocatalysts

The application and success of combinatorial approaches to protein engineering problems have increased dramatically. However, current directed evolution strategies lack a combinatorial methodology for creating libraries of hybrid enzymes which lack high homology or for creating libraries of highly homologous genes with fusions at regions of non-identity. To create such hybrid enzyme libraries, we have developed a series of combinatorial approaches that utilize the incremental truncation of genes, gene fragments or gene libraries. For incremental truncation, Exonuclease III is used to create a library of all possible single base-pair deletions of a given piece of DNA. Incremental truncation libraries (ITLs) have applications in protein engineering as well as protein folding, enzyme evolution, and the chemical synthesis of proteins. In addition, we are developing a methodology of DNA shuffling which is independent of DNA sequence homology.     

A loop-mimetic inhibitor of the HCV-NS3 protease derived from a minibody

We have been interested for some time in establishing a strategy for deriving lead compounds from macromolecule ligands such as minibody variants. A minibody is a minimized antibody variable domain whose two loops are amenable to combinatorial mutagenesis. This approach can be especially useful when dealing with 'difficult' targets. One such target is the NS3 protease of hepatitis C virus (HCV), a human pathogen that is believed to infect about 100 million individuals worldwide and for which an effective therapy is not yet available. Based on known inhibitor specificity (residues P6-P1) of NS3 protease, we screened a number of minibodies from our collection and we were able to identify a competitive inhibitor of this enzyme. We thus validated an aspect of recognition by HCV NS3 protease, namely that an acid anchor is necessary for inhibitor activity. In addition, the characterization of the minibody inhibitor led to the synthesis of a constrained hexapeptide mimicking the bioactive loop of the parent macromolecule. The cyclic peptide is a lead compound prone to rapid optimization through solid phase combinatorial chemistry. We therefore confirmed that the potential of turning a protein ligand into a low molecular weight active compound for lead discovery is achievable and can complement more traditional drug discovery approaches.     

Combinatorics of saturated secondary structures of RNA.

Following Zuker (1986), a saturated secondary structure for a given RNA sequence is a secondary structure such that no base pair can be added without violating the definition of secondary structure, e.g., without introducing a pseudoknot. In the Nussinov-Jacobson energy model (Nussinov and Jacobson, 1980), where the energy of a secondary structure is -1 times the number of base pairs, saturated secondary structures are local minima in the energy landscape, hence form kinetic traps during the folding process. Here we present recurrence relations and closed form asymptotic limits for combinatorial problems related to the number of saturated secondary structures. In addition, Python source code to compute the number of saturated secondary structures having k base pairs can be found at the web servers link of bioinformatics.bc.edu/clotelab/.     

Evolutionary diversification of the flowers in angiosperms

Angiosperms and their flowers have greatly diversified into an overwhelming array of forms in the past 135 million years. Diversification was shaped by changes in climate and the biological environment (vegetation, interaction with other organisms) and by internal structural constraints and potentials. This review focuses on the development and structural diversity of flowers and structural constraints. It traces floral diversification in the different organs and organ complexes (perianth, androecium, gynoecium) through the major clades of extant angiosperms. The continuously improved results of molecular phylogenetics provide the framework for this endeavor, which is necessary for the understanding of the biology of the angiosperms and their flowers. Diversification appears to work with innovations and modifications of form. Many structural innovations originated in several clades and in special cases could become key innovations, which likely were hot spots of diversification. Synorganization between organs was an important process to reach new structural levels, from which new diversifications originated. Complexity of synorganization reached peaks in Orchidaceae and Apocynaceae with the independent evolution of pollinaria. Such a review throughout the major clades of angiosperms also shows how superficial and fragmentary our knowledge on floral structure in many clades is. Fresh studies and a multidisciplinary approach are needed.