Some notes on complexity in vegetation

Abstract. Vegetation is considered as a complex system with many subsystems. The system functions by using solar radiation as energy source and producing biomass and biodiversity. The different subsystems are connected by feedback loops and interact in a process of self-organisation. It appears impossible to characterize this system with mathematical expressions, because most of the basic processes are non-linear. Instead, vegetation can be described with dynamical models. Selection, competition as well as positive interactions can occur. The model accounts for the general dynamics, particularly fluctuations (when the system is in a steady state) and the climax situation. Many problems remain open: e.g. arbitrary limits of the system and its subsystems, macrostate/microstate relationships, thresholds and attractors. Single aspects of the subsystems can be linearized, but not the system as a whole and consequently its behaviour remains unpredictable.     

The Bio-Logic and machinery of plant morphogenesis

Morphogenesis (the development of organic form) requires signal-trafficking and cross-talking across all levels of organization to coordinate the operation of metabolic and genomic networked systems. Many biologists are currently converging on the pictorial conventions of computer scientists to render biological signaling as logic circuits supervising the operation of one or more signal-activated metabolic or gene networks. This approach can redact and simplify complex morphogenetic phenomena and allows for their aggregation into diagrams of larger, more "global" networked systems. This conceptualization is discussed in terms of how logic circuits and signal-activated subsystems work, and it is illustrated for examples of increasingly more complex morphogenetic phenomena, e.g., auxin-mediated cell expansion, entry into the mitotic cell cycle phases, and polar/lateral intercellular auxin transport. For each of these phenomena, a posited circuit/subsystem diagram draws rapid attention to missing components, either in the logic circuit or in the subsystem it supervises. These components must be identified experimentally if each of these basic phenomena is to be fully understood. Importantly, the power of the circuit/subsystem approach to modeling developmental phenomena resides not in its pictorial appeal but in the mathematical tools that are sufficiently strong to reveal and quantify the synergistics of networked systems and thus foster a better understanding of morphogenesis.     

The malignant transformation as a metabolic steady state transition: The possible significance of the phasing of enzyme synthesis and related aspects

It has been suggested by Sel'kov and by the author that the malignant transformation may be due to a transition between alternative steady states at the metabolic level without necessarily involving a genetic defect. It had previously been indicated by the author that the properties of a cell can be expected to reflect its pattern of temporal organisation. These two aspects are now considered in relation to one another by examining the behaviour of a coupled enzymic system (involving substrate inhibition characteristics) which is capable of exhibiting multiple steady states. It is shown that the phasing of the synthesis of the enzymes concerned during the cell cycle (normal or disturbed as a result of the action of agents) can determine whether a transition occurs or not and also if it is stable or not. It is also pointed out that the phasing between the fluctuations in the levels of inhibitors and activators of the enzymes involved and in their isozyme patterns can be equally significant in these respects. Hence a transition can be effected by a variety of agents acting at diverse sites within or without the cell. The transition is discussed as an example of a process that may be involved in the malignant transformation. It is emphasized that once a transition has occurred in a cell, there is no reason to presuppose that the new state cannot be inherited by the progeny of that cell, despite the removal of the causative agent: reversal is possible, however, and is discussed as an explanation for abortive oncogenic transformation. Other aspects briefly discussed in relation to metabolic steady state transitions include - the random nature and distribution of transformation in culture; the heterogeneity of transformed cells; resistance to transformation; the significance of the timing and duration of action of an oncogenic agent; the effect of gene duplication on the ‘fixation’ of the transformation; cell death. Finally it is pointed out that the same considerations are likely to apply to other systems exhibiting multiple steady states as a result of the existence of the phenomenon of hysteresis and hence probably to genetic switch systems also.     

Simultaneous modelling of metabolic, genetic and product-interaction networks

The creation of cell models from annotated genome information, as well as additional data from other databases, requires both a format and medium for its distribution. Standards are described for the representation of the data in the form of Document Type Definitions (DTDs) for XML files. Separate DTDs are detailed for genetic, metabolic and gene product-interaction networks, which can be used to hold information on individual subsystems, or which may be combined to create a whole cell DTD. In the execution of this work, a fifth DTD was also created for a metabolite thesaurus, which allows incorporation of metabolite synonyms and generic nomenclature data into the models. A gene-regulation classification scheme was also created, to facilitate incorporation of gene regulatory information in an efficient manner. The work is described with particular reference to the metabolic network of Escherichia coli, which contains 808 individual enzymes. The assignment of confidence levels to these data, through the use of Gene Ontology evidence codes, is highlighted. In silico investigations may now be performed using the mathematical simulation workbench, DBsolve, which incorporates the facility to introduce data directly from XML.     

Dynamic metabolic flux analysis (DMFA): a framework for determining fluxes at metabolic non-steady state

Metabolic flux analysis (MFA) is a key tool for measuring in vivo metabolic fluxes in systems at metabolic steady state. Here, we present a new method for dynamic metabolic flux analysis (DMFA) of systems that are not at metabolic steady state. The advantages of our DMFA method are: (1) time-series of metabolite concentration data can be applied directly for estimating dynamic fluxes, making data smoothing and estimation of average extracellular rates unnecessary; (2) flux estimation is achieved without integration of ODEs, or iterations; (3) characteristic metabolic phases in the fermentation data are identified automatically by the algorithm, rather than selected manually/arbitrarily. We demonstrate the application of the new DMFA framework in three example systems. First, we evaluated the performance of DMFA in a simple three-reaction model in terms of accuracy, precision and flux observability. Next, we analyzed a commercial glucose-limited fed-batch process for 1,3-propanediol production. The DMFA method accurately captured the dynamic behavior of the fed-batch fermentation and identified characteristic metabolic phases. Lastly, we demonstrate that DMFA can be used without any assumed metabolic network model for data reconciliation and detection of gross measurement errors using carbon and electron balances as constraints.     

NIBBS-search for fast and accurate prediction of phenotype-biased metabolic systems

Understanding of genotype-phenotype associations is important not only for furthering our knowledge on internal cellular processes, but also essential for providing the foundation necessary for genetic engineering of microorganisms for industrial use (e.g., production of bioenergy or biofuels). However, genotype-phenotype associations alone do not provide enough information to alter an organism's genome to either suppress or exhibit a phenotype. It is important to look at the phenotype-related genes in the context of the genome-scale network to understand how the genes interact with other genes in the organism. Identification of metabolic subsystems involved in the expression of the phenotype is one way of placing the phenotype-related genes in the context of the entire network. A metabolic system refers to a metabolic network subgraph; nodes are compounds and edges labels are the enzymes that catalyze the reaction. The metabolic subsystem could be part of a single metabolic pathway or span parts of multiple pathways. Arguably, comparative genome-scale metabolic network analysis is a promising strategy to identify these phenotype-related metabolic subsystems. Network Instance-Based Biased Subgraph Search (NIBBS) is a graph-theoretic method for genome-scale metabolic network comparative analysis that can identify metabolic systems that are statistically biased toward phenotype-expressing organismal networks. We set up experiments with target phenotypes like hydrogen production, TCA expression, and acid-tolerance. We show via extensive literature search that some of the resulting metabolic subsystems are indeed phenotype-related and formulate hypotheses for other systems in terms of their role in phenotype expression. NIBBS is also orders of magnitude faster than MULE, one of the most efficient maximal frequent subgraph mining algorithms that could be adjusted for this problem. Also, the set of phenotype-biased metabolic systems output by NIBBS comes very close to the set of phenotype-biased subgraphs output by an exact maximally-biased subgraph enumeration algorithm ( MBS-Enum ). The code (NIBBS and the module to visualize the identified subsystems) is available at http://freescience.org/cs/NIBBS.     

Shifts in growth strategies reflect tradeoffs in cellular economics

The growth rate‐dependent regulation of cell size, ribosomal content, and metabolic efficiency follows a common pattern in unicellular organisms: with increasing growth rates, cell size and ribosomal content increase and a shift to energetically inefficient metabolism takes place. The latter two phenomena are also observed in fast growing tumour cells and cell lines. These patterns suggest a fundamental principle of design. In biology such designs can often be understood as the result of the optimization of fitness. Here we show that in basic models of self‐replicating systems these patterns are the consequence of maximizing the growth rate. Whereas most models of cellular growth consider a part of physiology, for instance only metabolism, the approach presented here integrates several subsystems to a complete self‐replicating system. Such models can yield fundamentally different optimal strategies. In particular, it is shown how the shift in metabolic efficiency originates from a tradeoff between investments in enzyme synthesis and metabolic yields for alternative catabolic pathways. The models elucidate how the optimization of growth by natural selection shapes growth strategies.     

Application of type synthesis theory to the redesign of a complex surgical instrument

Surgical instruments consist of basic mechanical components such as gears, links, pivots, sliders, etc., which are common in mechanical design. This paper describes the application of a method in the analysis and design of complex surgical instruments such as those employed in laparoscopic surgery. This is believed to be the first application of type synthesis theory to a complex medical instrument. Type synthesis is a methodology that can be applied during the conceptual phase of mechanical design. A handle assembly from a patented laparoscopic surgical stapler is used to illustrate the application of the design method developed. Type synthesis is applied on specific subsystems of the mechanism within the handle assembly where alternative design concepts are generated. Chosen concepts are then combined to form a new conceptual design for the handle assembly. The new handle assembly is improved because it has fewer number of parts, is a simpler design and is easier to assemble. Surgical instrument designers may use the methodology presented here to analyze the mechanical subsystems within complex instruments and to create new options that may offer improvements to the original design.     

Defining and measuring autophagosome flux—concept and reality

The autophagic system is involved in both bulk degradation of primarily long-lived cytoplasmic proteins as well as in selective degradation of cytoplasmic organelles. Autophagic flux is often defined as a measure of autophagic degradation activity, and a number of methods are currently utilized to assess autophagic flux. However, despite major advances in measuring various molecular aspects of the autophagic machinery, we remain less able to express autophagic flux in a highly sensitive, robust, and well-quantifiable manner. Here, we describe a conceptual framework for defining and measuring autophagosome flux at the single-cell level. The concept discussed here is based on the theoretical framework of metabolic control analysis, which distinguishes between the pathway along which there is a flow of material and the quantitative measure of this flow. By treating the autophagic system as a multistep pathway with each step characterized by a particular rate, we are able to provide a single-cell fluorescence live-cell imaging-based approach that describes the accurate assessment of the complete autophagosome pool size, the autophagosome flux, and the transition time required to turn over the intracellular autophagosome pool. In doing so, this perspective provides clarity on whether the system is at steady state or in a transient state moving towards a new steady state. It is hoped that this theoretical account of quantitatively measuring autophagosome flux may contribute towards a new direction in the field of autophagy, a standardized approach that allows the establishment of systematic flux databases of clinically relevant cell and tissue types that serve as important model systems for human pathologies.     

Matrix proof of flow,volume and mean transit time theorems for regional and compartmental systems

The relations (inflow) = (dose)/(area under indicator curve), and (volume of distribution) = (throughflow) × (mean transit time) are derived by a matrix method for a system of interconnected subsystems, within which spatial indicator activity gradients may exist, and for compartments, within which the indicator activity is spatially uniform. The inflow theorem, is different from the outflow theorem. Equivalent labeling of multi-input systems reduces them formally to single input systems. Foreign indicator flow-volume kinetics are more general than, and include as a special case, tracer flux-mass (metabolic) kinetics. Volume of distribution in the indicator steady state may be different from the equilibrium volume of distribution.     

Prolidase and prolidase deficiency

Prolidase deficiency seems to be a rather rare metabolic disorder. However, many new cases can be detected because screening is easy to perform and enzymatic confirmation allows the differentiation from other iminodipeptidurias . Clinical symptoms are briefly reviewed, while biological considerations and prolidase properties are exhaustively described. Methods for investigating urinary iminodipeptides are given with results. Moreover, several collagen modifications observed in this disorder led us to formulate a hypothesis for their mechanism. Genetic considerations and treatment attempts are discussed.     

1H-NMR-based metabolomics for cancer targeting and metabolic engineering –A review

Nuclear magnetic resonance (NMR) spectroscopy acts as the best tool that can be used in tissue engineering scaffolds to investigate unknown metabolites. Moreover, metabolomics is a systems approach for examining in vivo and in vitro metabolic profiles, which promises to provide data on cancer metabolic alterations. However, metabolomic profiling allows for the activity of small molecules and metabolic alterations to be measured. Furthermore, metabolic profiling also provides high-spectral resolution, which can then be linked to potential metabolic relationships. An altered metabolism is a hallmark of cancer that can control many malignant properties to drive tumorigenesis. Metabolite targeting and metabolic engineering contribute to carcinogenesis by proliferation, and metabolic differentiation. The resulting the metabolic differences are examined with traditional chemometric methods such as principal component analysis (PCA), and partial least squares-discriminate analysis (PLS-DA). In this review, we examine NMR-based activity metabolomic platforms that can be used to analyze various fluxomics and for multivariant statistical analysis in cancer. We also aim to provide the reader with a basic understanding of NMR spectroscopy, cancer metabolomics, target profiling, chemometrics, and multifunctional tools for metabolomics discrimination, with a focus on metabolic phenotypic diversity for cancer therapeutics.     

Multiplicity of Steady States in Glycolysis and Shift of Metabolic State in Cultured Mammalian Cells

Cultured mammalian cells exhibit elevated glycolysis flux and high lactate production. In the industrial bioprocesses for biotherapeutic protein production, glucose is supplemented to the culture medium to sustain continued cell growth resulting in the accumulation of lactate to high levels. In such fed-batch cultures, sometimes a metabolic shift from a state of high glycolysis flux and high lactate production to a state of low glycolysis flux and low lactate production or even lactate consumption is observed. While in other cases with very similar culture conditions, the same cell line and medium, cells continue to produce lactate. A metabolic shift to lactate consumption has been correlated to the productivity of the process. Cultures that exhibited the metabolic shift to lactate consumption had higher titers than those which didn’t. However, the cues that trigger the metabolic shift to lactate consumption state (or low lactate production state) are yet to be identified. Metabolic control of cells is tightly linked to growth control through signaling pathways such as the AKT pathway. We have previously shown that the glycolysis of proliferating cells can exhibit bistability with well-segregated high flux and low flux states. Low lactate production (or lactate consumption) is possible only at a low glycolysis flux state. In this study, we use mathematical modeling to demonstrate that lactate inhibition together with AKT regulation on glycolysis enzymes can profoundly influence the bistable behavior, resulting in a complex steady-state topology. The transition from the high flux state to the low flux state can only occur in certain regions of the steady state topology, and therefore the metabolic fate of the cells depends on their metabolic trajectory encountering the region that allows such a metabolic state switch. Insights from such switch behavior present us with new means to control the metabolism of mammalian cells in fed-batch cultures.     

Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics

This paper presents a new mathematical framework for modeling of in vivo dynamics and for metabolic re-design: the linlog approach. This approach is an extension of metabolic control analysis (MCA), valid for large changes of enzyme and metabolite levels. Furthermore, the presented framework combines MCA with kinetic modeling, thereby also combining the merits of both approaches. The linlog framework includes general expressions giving the steady-state fluxes and metabolite concentrations as a function of enzyme levels and extracellular concentrations, and a metabolic design equation that allows direct calculation of required enzyme levels for a desired steady state when control and response coefficients are available. Expressions giving control coefficients as a function of the enzyme levels are also derived. The validity of the linlog approximation in metabolic modeling is demonstrated by application of linlog kinetics to a branched pathway with moiety conservation, reversible reactions and allosteric interactions. Results show that the linlog approximation is able to describe the non-linear dynamics of this pathway very well for concentration changes up to a factor 20. Also the metabolic design equation was tested successfully.     

Coupling and internal noise sustain synchronized oscillation in calcium system

In this work, the effects of coupling on two calcium subsystems were investigated, the cooperation between coupling and internal noise was also considered. When two non-identical subsystems are in steady state, coupling can induce oscillations, and distinctly enlarge the oscillatory region in bifurcation diagram. Besides, coupling can make the two non-identical oscillators synchronized. With the increment of the coupling strength, the cross-correlation time of the two oscillators firstly increases and then decreases to be constant, showing the synchronization without tuning coupling strength. When internal noise is considered, similar phenomena can also be obtained under the cooperation between coupling and internal noise.     

A multiple-staining procedure for the detection of different DNA fragments on a single blot.

We have developed a method that implies the use of a particular type of substrate which can be used in combination with alkaline phosphatase in detecting nucleic acid on filters. The method allows the detection of several different nucleic acid sequences on a single filter. In consecutive steps, the target DNA molecules are hybridized with different digoxigenin-labeled DNA probes. After each hybridization step, digoxigenin is detected with an antibody-alkaline phosphatase conjugate. This enzyme is subsequently visualized by a color reaction using different 2-hydroxy-3-naphthoic acid anilide (naphthol AS) phosphates as substrates in combination with varying diazonium salts. The multiple-staining procedure is based on the fact that the probe DNA-antibody complex can be removed while the color precipitate remains stably bound at its place on the filter. This allows several repeated hybridizations with other digoxigenin-labeled probes followed by antibody detection and color reaction with other naphthol AS phosphate-diazonium salt combinations. Aside from the ability to simultaneously visualize different target DNAs on a single filter, this new method provides several important features that are more powerful than the conventional 5-bromo-4-chloro-3-indolyl phosphate-nitro blue tetrazolium (BCIP-NBT) color reaction for alkaline phosphatase. The colors are more stable and brilliant than BCIP-NBT; their development is faster, the resolution of closely spaced bands is greater, and the background is much lower. The detection limit for alkaline phosphates is as good as with BCIP-NBT (0.1 pg of DNA). One major advantage is the simplicity of removing the colors by ethanol incubation. In this paper, the method is described using the example of Southern blotted DNA fragments.(ABSTRACT TRUNCATED AT 250 WORDS)     

System-size resonance for intracellular and intercellular calcium signaling

Dynamical behaviors of unidirectionally, linearly coupled as well as isolated calcium subsystems are investigated by taking into account the internal noise resulting from finite system size and thus small numbers of interacting molecules. For an isolated calcium system, the internal noise can induce stochastic oscillations for a steady state close to the Hopf-bifurcation point, and the regularity of those stochastic oscillations depends resonantly on the system size, exhibiting system-size resonance. For the coupled system consisting of two subsystems, the system-size resonance effect observed in the subsystem subject to coupling is significantly amplified due to the nontrivial effects of coupling.     

Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering

Rational metabolic engineering requires powerful theoretical methods such as pathway analysis, in which the topology of metabolic networks is considered. All metabolic capabilities in steady states are composed of elementary flux modes, which are minimal sets of enzymes that can each generate valid steady states. The modes of the fructose-2,6-bisphosphate cycle, the combined tricarboxylic-acid-glyoxylate-shunt system and tryptophan synthesis are used here for illustration. This approach can be used for many biotechnological applications such as increasing the yield of a product, channelling a product into desired pathways and in functional reconstruction from genomic data.     

Regulated multicistronic expression technology for mammalian metabolic engineering

Contemporary basic research is rapidly revealing increasingly complex molecular regulatory networks which are often interconnected via key signal integrators. These connections among regulatory and catalytic networks often frustrate bioengineers as promising metabolic engineering strategies are bypassed by compensatory metabolic responses or cause unexpected, undesired outcomes such as apoptosis, product protein degradation or inappropriate post- translational modification. Therefore, for metabolic engineering to achieve greater success in mammalian cell culture processes and to become important for future applications such as gene therapy and tissue engineering, this technology must be enhanced to allow simultaneous, in cases conditional, reshaping of metabolic pathways to access difficult-to-attain cell states. Recent advances in this new territory of multigene metabolic engineering are intimately linked to the development of multicistronic expression technology which allows the simultaneous, and in some cases, regulated expression of several genes in mammalian cells. Here we review recent achievements in multicistronic expression technology in view of multigene metabolic engineering. This revised version was published online in August 2006 with corrections to the Cover Date.     

A structured kinetic modeling framework for the dynamics of hybridoma growth and monoclonal antibody production in continuous suspension cultures

A structured kinetic model is developed to describe the dynamics of hybridoma growth and the production of monoclonal antibodies and metabolic waste products in suspension culture. The crucial details of known metabolic processes in hybridoma cells are incorporated by dividing the cell mass into four intracellular metabolic pools. The model framework and structure allow the dynamic calculation of the instantaneous specific growth rate of a hybridoma culture. The steady state and dynamic simulations of the model equations exhibit excellent agreement with experimentally observed trends in substrate utilization and product formation. The model represents the first to include any degree of metabolic detail and structure in describing a hybridoma culture. In so doing, it provides the basic modeling framework for incorporating further details of metabolism and can be a useful tool to study various strategies for enhancing hybridoma growth as well as viability and the production of monoclonal antibodies in suspension cultures.