Biomedical subjects

Stefan Schuster

Publications and source records attributed to Stefan Schuster.

33 records · Page 2Linked to original sources

PubMed2003

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations.

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.

Animals↗

PubMed2003

An example of the prisoner's dilemma in biochemistry.

Two strains of microorganisms that both use sugar as energy resource, but which may choose between two different pathways of ATP production, are studied from a game-theory point of view. We consider these pathways as distinct strategies to which we assign payoffs that are proportional to the expected steady-state number of individuals sustainable on the basis of these strategies. In a certain parameter range, we find that the payoffs fulfil the conditions for the prisoner's dilemma. Therefore, cooperative behaviour is unlikely to occur, unless additional factors intervene. In fact, the yeast Saccharomyces cerevisiae uses a competitive strategy by fermenting sugars even under aerobic conditions, thus wasting its own resource. The simple quantifiable structure of the model should enable access to an experimentally determined payoff matrix.

Adenosine Triphosphate↗

PubMed2003

A method for classifying metabolites in topological pathway analyses based on minimization of pathway number.

Metabolic pathway analysis based on the concept of elementary flux mode is a valuable tool for reconstruction of bacterial metabolisms and in predicting optimal conversion yields in biotechnology. However, pathway analysis of large and highly entangled metabolic networks meets the problem of combinatorial explosion of possible routes across the networks. Here we propose a method for coping with this problem by suitably classifying metabolites as external or internal. External metabolites are considered to have buffered concentrations while internal metabolites have to fulfil a balance condition at steady state. For many substances such as nutrients and excreted products, there are biochemical reasons to classify them as external. In addition, other substances (especially at central branching points) can operationally be considered external in order to avoid combinatorial explosion. We suggest to find such a classification of metabolites that minimizes the number of elementary flux modes (pathways). This is motivated by the objectives of finding such a description of the system that reduces as much as possible the amount of necessary data and of removing the ambiguity and arbitrariness in the classification of metabolites in an automated, systematic way. For networks of moderate size, the solution to this combinatorial minimization problem can be found by exhaustive search. To tackle also larger systems, a stochastic optimization program based on the Metropolis algorithm was developed. Both methods are applied, for illustration, to several reaction schemes including a larger network representing glutathione metabolism.

Combinatorial Chemistry Techniques↗

PubMed2003

Topological analysis of metabolic networks based on Petri net theory.

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.

Algorithms↗

PubMed2002

Metabolic network structure determines key aspects of functionality and regulation.

The relationship between structure, function and regulation in complex cellular networks is a still largely open question. Systems biology aims to explain this relationship by combining experimental and theoretical approaches. Current theories have various strengths and shortcomings in providing an integrated, predictive description of cellular networks. Specifically, dynamic mathematical modelling of large-scale networks meets difficulties because the necessary mechanistic detail and kinetic parameters are rarely available. In contrast, structure-oriented analyses only require network topology, which is well known in many cases. Previous approaches of this type focus on network robustness or metabolic phenotype, but do not give predictions on cellular regulation. Here, we devise a theoretical method for simultaneously predicting key aspects of network functionality, robustness and gene regulation from network structure alone. This is achieved by determining and analysing the non-decomposable pathways able to operate coherently at steady state (elementary flux modes). We use the example of Escherichia coli central metabolism to illustrate the method.

Biomass↗

PubMed2002

Virtual-reality techniques resolve the visual cues used by fruit flies to evaluate object distances.

Insects can estimate distance or time-to-contact of surrounding objects from locomotion-induced changes in their retinal position and/or size. Freely walking fruit flies (Drosophila melanogaster) use the received mixture of different distance cues to select the nearest objects for subsequent visits. Conventional methods of behavioral analysis fail to elucidate the underlying data extraction. Here we demonstrate first comprehensive solutions of this problem by substituting virtual for real objects; a tracker-controlled 360 degrees panorama converts a fruit fly's changing coordinates into object illusions that require the perception of specific cues to appear at preselected distances up to infinity. An application reveals the following: (1) en-route sampling of retinal-image changes accounts for distance discrimination within a surprising range of at least 8-80 body lengths (20-200 mm). Stereopsis and peering are not involved. (2) Distance from image translation in the expected direction (motion parallax) outweighs distance from image expansion, which accounts for impact-avoiding flight reactions to looming objects. (3) The ability to discriminate distances is robust to artificially delayed updating of image translation. Fruit flies appear to interrelate self-motion and its visual feedback within a surprisingly long time window of about 2 s. The comparative distance inspection practiced in the small fruit fly deserves utilization in self-moving robots.

Animals↗

PubMed2002

Treatment of multifunctional enzymes in metabolic pathway analysis.

In metabolic pathway analysis, it should be considered that many enzymes operate with low specificity (e.g. nucleoside diphosphokinase, uridine kinase, transketolase, aldolase), so that various substrates and products can be converted. Here, we analyze the effect of enzymes with low substrate specificity on the elementary flux modes (pathways). We also study the benefits of two different approaches to describing multifunctional enzymes. The usual description is in terms of (overall) enzymatic reactions. At a more detailed level, the reaction steps (half-reactions, hemi-reactions) of the formation and conversion of enzyme-substrate complexes are considered. Multifunctional enzymes operate according to various mechanisms. This is illustrated here by the reaction schemes for the different enzyme mechanisms of bifunctional enzymes. For enzymes with two or more functions, it is important to consider only linearly independent functions, because otherwise cyclic elementary modes would occur which do not perform any net transformation. However, the choice of linearly independent functions is not a priori unique. We give a method for making this choice unique by considering the extreme pathways of the hemi-reactions system. A formal application of the algorithm for computing elementary flux modes (pathways) yields the result that the number of such modes sometimes depend on the level of description if some reactions are reversible and the products of the multifunctional enzymes are external metabolites or some multifunctional enzymes partly share the same metabolites. However, this problem can be solved by appropriate interpretation of the definition of elementary modes and the correct choice of independent functions of multifunctional enzymes. The analysis is illustrated by a biochemical example taken from nucleotide metabolism, comparing the two ways of description for nucleoside diphosphokinase and adenylate kinase, and by several smaller examples.

Adenylate Kinase↗

PubMed2002

Calculability analysis in underdetermined metabolic networks illustrated by a model of the central metabolism in purple nonsulfur bacteria.

Metabolite balancing has turned out to be a powerful computational tool in metabolic engineering. However, the linear equation systems occurring in this analysis are often underdetermined. If it is difficult or impossible to find the missing constraints, it is nevertheless feasible in some cases to determine the values of a subset of the unknown rates. Here, a procedure for finding out which reaction rates can be uniquely calculated in underdetermined metabolic networks and computing these rates is given. The method is based on the null space to the stoichiometry matrix corresponding to the reactions with unknown rates. It is shown that this method is considerably easier to handle than an algorithm given previously (Van der Heijden et al., 1994a). Furthermore, a useful elementary representation of the null space is presented which is closely related with the elementary flux modes. This unique representation is central to a more general approach to observability/calculability analysis. In particular, it allows one to find, in an easy way, those sets of measurable rates that enable a calculation of a certain unknown rate. Besides, rates which are never calculable by metabolite balancing may be easily detected by this method. The applicability of these methods is illustrated by a model of the central metabolism in purple nonsulfur bacteria. The photoheterotrophic growth of these representatives of anoxygenic photosynthetic bacteria is stoichiometrically analyzed. Interesting metabolic constraints caused by the necessary balancing of NADPH can be detected in a highly underdetermined system. This is, to our knowledge, the first application of stoichiometric analysis to the metabolic network in this bacteria group using metabolite balancing techniques. A new software tool, the FluxAnalyzer, is introduced. It allows quantitative and structural analysis of metabolic networks in a graphical user interface.

Algorithms↗

PubMed2002

Calculating as many fluxes as possible in underdetermined metabolic networks.

A frequently occurring problem in Metabolic Flux Analysis is that the linear equation systems are underdetermined. A procedure for determining which reaction velocities can be calculated in underdetermined metabolic systems from measured rates and computing these velocities is given. The method is based on the null-space matrix to the stoichiometry matrix corresponding to the reactions with unknown velocities. Moreover, an elementary representation of the null-space is presented. This representation enables one to find those sets of measurable velocities that allow calculation of a certain non-measurable rate. The approach is illustrated by an example from monosaccharide metabolism.

Biological Transport↗

PubMed2002

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling.

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Animals↗

PubMed2002

Behavioral evidence for post-pause reduced responsiveness in the electrosensory system of Gymnotus carapo.

Gymnotiform weakly electric fish find their way in the dark using a continuously operating active sensory system. An electric organ generates a continuous train of discharges (electric organ discharges, EODs), and tuberous high-frequency electroreceptors monitor the pattern of transcutaneous current flow associated with each EOD. Here, I report that a prior interruption to the continuous train of EODs dramatically affects a response shown by many pulse-type gymnotids. In this so-called novelty response, fish normally raise their electrosensory sampling rate in response to novel sensory stimuli. The gymnotid Gymnotus carapo was induced to pause its EODs briefly, and the novelty response to sensory stimuli given post-pause was analyzed. Mechanosensory stimuli given as early as 20 EODs after a pause elicited clear novelty responses, but strong high-frequency electrical stimuli were ineffective at this time. Moreover, high-frequency electrical stimuli remained less efficient in eliciting normal-sized responses until approximately 2000 EODs, or 40s, after a pause. The post-pause inefficiency of high-frequency stimuli was not due to an inappropriate choice of intensity or their temporal patterning and did not result from the stimulation that caused the pausing. Low-frequency stimuli that also recruited ampullary electroreceptors were more efficient than high-frequency stimuli in eliciting post-pause responses. These findings show that continuous activity is required either to maintain sensitivity to high-frequency electrical stimuli or to ensure that such stimuli are able to modulate efficiently the pacemaker that sets the discharge frequency.

Animals↗

PubMed2002

Sensitivity to novel feedback at different phases of a gymnotid electric organ discharge.

Weakly electric fish communicate and electrolocate objects in the dark by discharging their electric organs (EOs) and monitoring the spatiotemporal pattern of current flow through their skin. In the South-American pulse-type gymnotid fish these organs often are intriguingly complex, comprising several hundreds of electrogenic cells (electrocytes) of various morphologies, innervation patterns and abilities to generate a spike, distributed over nearly the full length of the fish. An attractive idea is that different parts of the organ may serve distinct functions in electrocommunication and electrolocation. Recent studies support this notion and suggest that the currents produced during the final phase of the electric organ discharge (EOD) are used for communication. Here, we explore a method to directly assess the relevance of the various currents for electrolocation. In this new method, the pattern of current flow during a gymnotid EOD is changed selectively at distinct phases of the EOD so that currents generated by known electrocyte groups are affected. We have studied the roles played by the various currents for the detection of novel feedback at the trunk/tail region of the gymnotid fish Gymnotus carapo. An experimental animal rested in a cage and two electrodes were placed at a close distance to its trunk and tail. An electronic switch briefly connected these electrodes during a selected phase within an EOD and the shunting of EOD current that resulted from switch closure was directly monitored. G. carapo responded with an acceleration of its discharge rate to novelties in the EOD feedback that occurred only for a fraction of a single EOD. Controls in which the switch was closed during the silent intervals between successive EODs showed that the fish responded to the changes in EOD feedback and not to unrelated artefacts of the brief switch closure. Fish responded to shunting of current during all phases; the sensitivity was highest during the final headnegative phase but the magnitude of shunted current was largest in the preceeding phase. The current produced during the final part of the EOD is thus not reserved for communication as previously suggested but plays a predominant role in electrolocation at the trunk and tail region of G. carapo.

Animal Communication↗

PubMed2002

Predicting three-dimensional target motion: how archer fish determine where to catch their dislodged prey.

On locating an insect prey on a twig above the water surface, a group of archer fish can shoot it down using powerful jets of water. The insect, dislodged by one of the shots, falls on a ballistic path towards the water surface, where it is devoured by the first fish to arrive. We report that the archer fish can predict the point where the dislodged prey will later hit the water surface and move in a straight line towards that point, thus enabling it to arrive as fast as possible. Only about 100 ms after prey is dislodged, the fish initiate a quick turn that aligns their body axis right towards where the prey will later land, and not to the actual position of the prey at that moment. In contrast to other known examples of three-dimensional target interception in man and animals, archer fish can head straight to the predicted point of catch without the need of any further visual feedback. Moreover, archer fish can predict the point of incidence of a target, regardless of the angle at which the prey takes off with respect to the initial orientation of the fish. To perform this remarkable task, archer fish extract a minimum set of independent variables that fix the point of incidence, but do not extrapolate the target's spatial trajectory.

Animals↗

PubMed2002

Template-matching describes visual pattern-recognition tasks in the weakly electric fish Gnathonemus petersii.

Several insects use template-matching systems to recognize objects or environmental landmarks by comparing actual and stored retinal images. Such systems are not viewpoint-invariant and are useful only when the locations in which the images have been stored and where they are later retrieved coincide. Here, we describe that a vertebrate, the weakly electric fish Gnathonemus petersii, appears to use template-matching to recognize visual patterns that it had previously viewed from a fixed vantage point. This fish is nocturnal and uses its electrical sense to find its way in the dark, yet it has functional vision that appears to be well adapted to dim light conditions. We were able to train three fish in a two-alternative forced-choice procedure to discriminate a rewarded from an unrewarded visual pattern. From its daytime shelter, each fish viewed two visual patterns placed at a set distance behind a transparent Plexiglas screen that closed the shelter. When the screen was lifted, the fish swam towards one of the patterns to receive a food reward or to be directed back into its shelter. Successful pattern discrimination was limited to low ambient light intensities of approximately 10 lx and to pattern sizes subtending a visual angle greater than 3 degrees. To analyze the characteristics used by the fish to discriminate the visual training patterns, we performed transfer tests in which the training patterns were replaced by other patterns. The results of all such transfer tests can best be explained by a template-matching mechanism in which the fish stores the view of the rewarded training pattern and chooses from two other patterns the one whose retinal appearance best matches the stored view.

Animals↗

PubMedDate not supplied

A theory of optimal differential gene expression.

We investigate a model of optimal regulation, intended to describe large-scale differential gene expression. Relations between the optimal expression patterns and the function of genes are deduced from an optimality principle: the regulators have to maximise a fitness function which they influence directly via a cost term, and indirectly via their control on important cell variables, such as metabolic fluxes. According to the model, the optimal linear response to small perturbations reflects the regulators' functions, namely their linear influences on the cell variables. The optimal behaviour can be realised by a linear feedback mechanism. Known or assumed properties of response coefficients lead to predictions about regulation patterns. A symmetry relation predicted for deletion experiments is verified with gene expression data. Where the optimality assumption is valid, our results justify the use of expression data for functional annotation and for pathway reconstruction and suggest the use of linear factor models for the analysis of gene expression data.

Adaptation, Physiological↗