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Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E.coli.

MOTIVATION: The integrated dynamical modelling of mixed metabolic/genetic networks constitutes one of the challenges of systems biology. Furthermore, as most of available data about genetic and metabolic regulations are qualitative, there is a pressing need for rigorous qualitative mathematical approaches. RESULTS: On the basis of two established formalisms, the logical modelling of genetic regulatory networks and the Petri net modelling of metabolic networks, we propose a systematic approach for the modelling of regulated metabolic networks. This approach leans on previous work defining a systematic procedure to translate logical regulatory graphs into standard (discrete) Petri nets (PNs). This approach is illustrated by the qualitative modelling of the biosynthesis of tryptophan (Trp) in Escherichia coli, taking into account two types of regulatory feedbacks: the direct inhibition of the first enzyme of the pathway by the final product of the pathway, and the transcriptional inhibition of the Trp operon by the Trp-repressor complex. On the basis of this integrated PN model, we further indicate how available dynamical analysis tools can be applied to obtain significant insights in the behaviour of the system. AVAILABILITY: The software GINsim for the logical modelling of genetic regulatory networks together with the PN model of the regulated Trp biosynthesis pathway are available at: http://gin.univ-mrs.fr/GINsim.

Computer Simulation↗

Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic.

Modeling of metabolic pathway dynamics requires detailed kinetic equations at the enzyme level. In particular, the kinetic equations must account for metabolite effectors that contribute significantly to the pathway regulation in vivo. Unfortunately, most kinetic rate laws available in the literature do not consider all the effectors simultaneously, and much kinetic information exists in a qualitative or semiquantitative form. In this article, we present a strategy to incorporate such information into the kinetic equation. This strategy uses fuzzy logic-based factors to modify algebraic rate laws that account for partial kinetic characteristics. The parameters introduced by the fuzzy factors are then optimized by use of a hybrid of simplex and genetic algorithms. The resulting model provides a flexible form that can simulate various kinetic behaviors. Such kinetic models are suitable for pathway modeling without complete enzyme mechanisms. Three enzymes in Escherichia coli central metabolism are used as examples: phosphoenolpyruvate carboxylase; phosphoenolpyruvate carboxykinase; and pyruvate kinase I. Results show that, with fuzzy logic-augmented models, the kinetic data can be much better described. In particular, complex behavior, such as allosteric inhibition, can be captured using fuzzy rules. The resulting models, even though they do not provide additional physical meaning in enzyme mechanisms, allow the model to incorporate semiquantitative information in metabolic pathway models.

Bacterial Proteins↗

Long-term reversal of established autoimmunity upon transient blockade of the LFA-1/intercellular adhesion molecule-1 pathway.

Transgenic models and administration of mAbs directed against the LFA-1/intercellular adhesion molecule 1 (ICAM-1) pathway have shown that these costimulatory molecules play a key role in generating effector cells mediating inflammatory responses. In this report, durable remission of recent diabetes in nonobese diabetic (NOD) mice was induced by transient expression of an immunoadhesin gene encoding the soluble form of ICAM-1 (sICAM-1/Ig). A single i.v. injection of an adenovirus vector encoding the immunoadhesin gene led to 70% diabetes remission as opposed to 0% in mice injected with a control adenovirus vector. Despite the rapid decline of sICAM-1/Ig serum levels, diabetes remission remained stable in 50% of NOD mice for >6 mo. sICAM-1/Ig expression also led to long-term protection against diabetes in prediabetic NOD mice. sICAM-1/Ig in vitro induced an agonistic effect of T cell activation in a TCR-transgenic model, increasing T cell proliferation and IL-2 secretion. Importantly, protected mice were not immunosuppressed because they rejected skin allografts normally and developed immunity against the adenovirus vector. Rather, sICAM-1/Ig induced active tolerance, as assessed by the persistence of diabetogenic T cells in protected mice and the reversal of protection by immunosuppression with cyclophosphamide.

Adenoviridae↗

A theory of the Benham Top based on center-surround interactions in the parvocellular pathway.

A model color-opponent neuron was used to investigate the subjective colors evoked by the Benham Top (BT). Color-opponent inputs from cone-selective parvocellular (P) pathway neurons with center-surround receptive fields were subtracted with a short relative delay, yielding a small transient input in response to a white spot. This transient input was amplified by BT-like stimuli, modeled as a thin dark bar followed by full-field illumination. The narrow bar produced maximal activation of the P-pathway surrounds but only partial activation of the P-pathway centers. Due to saturation, subsequent removal of the bar had little effect on the P-pathway surrounds, whereas the transient input from the P-pathway centers was amplified via disinhibition. Responses to BT-like stimuli became weaker as surround sensitivity recovered, producing an effect analogous to the progression of perceived BT colors. Our results suggest that the BT-illusion arises because cone-selective neurons convey information about both color and luminance contrast, allowing the two signals become confounded.

Animals↗

A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description.

We developed and analyzed the mathematical model of the intrinsic pathway based on the current biochemical data on the kinetics of blood coagulation individual stages. The model includes eight differential equations describing the spatio-temporal dynamics of activation of factors XI, IX, X, II, I, VIII, V, and protein C. The assembly of tenase and prothrombinase complexes is considered as a function of calcium concentration. The spatial dynamics of coagulation was analyzed for the one-dimensional case. We examined the formation of active factors, their spreading, and growth of the clot from the site of injury in the direction perpendicular to the vessel wall, into the blood thickness. We assumed that the site of injury (in the model one boundary of the space segment under examination) becomes a source of the continuous influx of factor XIa. In the first part, we described the model, selected the parameters, etc. In the second part, we compared the model with experimental data obtained in the homogeneous system and analyzed the spatial dynamics of the clot growth.

Blood Coagulation↗

Evidence for identity between the equilibrium unfolding intermediate and a transient folding intermediate: a comparative study of the folding reactions of alpha-lactalbumin and lysozyme.

The refolding kinetics of alpha-lactalbumin at different concentrations of guanidine hydrochloride have been investigated by means of kinetic circular dichroism and stopped-flow absorption measurements. The refolding reaction consists of at least two stages, the instantaneous accumulation of the transient intermediate that has peptide secondary structure and the subsequent slow process associated with formation of tertiary structure. The transient intermediate is compared with the well-characterized equilibrium intermediate observed during the denaturant-induced unfolding. Stabilities of the secondary structures against the denaturant, affinities for Ca2+, and tryptophan absorption properties of the transient and equilibrium intermediates were investigated. In all of these respects, the transient intermediate is identical with the equilibrium one, demonstrating the validity of the use of the equilibrium intermediate as a model of the folding intermediate. Essentially the same transient intermediate was also detected in the folding of lysozyme, the protein known to be homologous to alpha-lactalbumin but whose equilibrium unfolding is represented as a two-state reaction. The stability and cooperativity of the secondary structure of the intermediate of lysozyme are compared with those of alpha-lactalbumin. The results show that the protein folding occurring via the intermediate is not limited to the proteins that show equilibrium intermediates. Although the unfolding equilibria of most proteins are well approximated as a two-state reaction, the two-state hypothesis may not be applicable to the folding reaction under the native condition. Two models of protein folding, intermediate-controlled folding model and multiple-pathway folding model, which are different in view of the role of the intermediate in determining the pathway of folding, are also discussed.

Guanidine↗

An intracellular signaling hierarchy determines direction of migration in opposing chemotactic gradients.

Neutrophils must follow both endogenous and bacterial chemoattractant signals out of the vasculature and through the interstitium to arrive at a site of infection. By necessity, in the setting of multiple chemoattractants, the neutrophils must prioritize, favoring end target chemoattractants (e.g., fMLP and C5a) emanating from the site of infection over intermediary endogenous chemoattractants (e.g., IL-8 and LTB4) encountered en route to sites of infection. In this study, we propose a hierarchical model of two signaling pathways mediating the decision-making process of the neutrophils, which allows end target molecules to dominate over intermediary chemoattractants. In an under agarose assay, neutrophils predominantly migrated toward end target chemoattractants via p38 MAPK, whereas intermediary chemoattractant-induced migration was phosphoinositide 3-kinase (PI3K)/Akt dependent. When faced with competing gradients of end target and intermediary chemoattractants, Akt activation was significantly reduced within neutrophils, and the cells migrated preferentially toward end target chemoattractants even at 1/1,000th that of intermediary chemoattractants. End target molecules did not require chemotactic properties, since the p38 MAPK activator, LPS, also inhibited Akt and prevented migration to intermediary chemoattractants. p38 MAPK inhibitors not only reversed this hierarchy, such that neutrophils migrated preferentially toward intermediary chemoattractants, but also allowed neutrophils to be drawn out of a local end target chemoattractant environment and toward intermediary chemoattractants unexpectedly in an exaggerated (two- to fivefold) fashion. This was entirely related to significantly increased magnitude and duration of Akt activation. Finally, end target chemoattractant responses were predominantly Mac-1 dependent, whereas nondominant chemoattractants used primarily LFA-1. These data provide support for a two pathway signaling model wherein the end target chemoattractants activate p38 MAPK, which inhibits intermediary chemoattractant-induced PI3K/Akt pathway, establishing an intracellular signaling hierarchy.

Calcium↗

Clinical pathway development: the Overlake Model.

Overlake Hospital Medical Center has developed a multi-faceted Care Management Model to improve clinical and fiscal outcomes for selected patient populations. The Clinical Pathway Component of this model has been applied to high-volume, high-loss DRG groups. Success of the program can be attributed to the unique multidisciplinary problem solving approach, team building and a focus beyond the inpatient hospital stay.

Chief Executive Officers, Hospital↗

Ontological integration of data models for cell signaling pathways by defining a factor of causality called 'signal'.

Databases have collected masses of information concerning cell signaling pathways that includes information on pathways, molecular interactions as well as molecular complexes. However we have no general data model to represent comprehensive properties of cell signaling pathways, so that this type of information has been represented by two different data models that we call 'binary relation' and 'state transition'. The disagreement between the existing models derives from lack of consensus about a factor of causality in reactions in cell signaling pathways, which is often called 'signal'. We developed an ontology named CSNO (Cell Signaling Networks Ontology) based on device ontology. As device ontology is a research product of knowledge engineering, CSNO is the first application of it to biological knowledge. CSNO defines the factor of causality called 'signal', offers an integrative viewpoint for the two different data models, explicates intrinsic distinctions between signaling and metabolic pathways, and eliminates ambiguity from representation of complex molecules.

Cell Physiological Phenomena↗

Corticofugal feedback can reduce the visual latency of responses to antagonistic stimuli.

A biophysically realistical model of the primary visual pathway is designed, including feedback connections from the visual cortex to the lateral geniculate nucleus (LGN) - the so-called corticofugal pathway. The model comprises up to 10,000 retina and LGN cells divided into the ON and the OFF pathway according to their contrast response characteristics. An additional 6000 cortical simple cells are modeled Apart from the direct excitatory afferent pathway we include strong mutual inhibition between the ON and the OFF subsystems. In addition, we propose a novel type of paradoxical corticofugal connection pattern which links ON dominated cortical simple cells to OFF-center LGN cells and vice versa. In accordance with physiological findings these connections are weakly excitatory and do not interfere with the steady-state responses to constant illumination, because during the steady-state inhibition arising from the active pathway effectively silences the non-stimulated pathway. At the moment of a contrast reversal the effect of the paradoxical connection pattern comes into play and the depolarization of the previously silent channel is accelerated, leading to a latency reduction of up to 4 ms using moderate synaptic weights. With increased weights reductions of more than 10 ms can be achieved. We introduce different synaptic characteristics for the feedback (AMPA, NMDA, AMPA + NMDA) and show that the strongest latency reduction is obtained for a combination of the membrane channels (i.e., AMPA + NMDA). The effect of the proposed paradoxical connection pattern is self-regulating; because the levels of inhibition and paradoxical excitation are always driven by the same inputs (strong inhibition is counter-balanced by a stronger paradoxical excitation and vice versa). In addition, the latency reduction for a contrast inversion which ends at a small absolute contrast level (small contrast step) is stronger than the reduction for an inversion with large final contrast (large contrast step). This leads to a more pronounced reduction in the reaction times for weak stimuli. Thus, reaction time differences for different contrast steps are smoothed out.

Contrast Sensitivity↗

Geriatric patients with depression. Improving outcomes using a multidisciplinary clinical path model.

Clinical pathways define multidisciplinary staff members' responsibilities, time lines, and patient outcomes. Although medical and surgical care settings frequently use them to improve quality, clinical, and fiscal outcomes for specific patient populations, staff members of psychiatric care settings have been hesitant to use clinical pathways because psychiatry emphasizes patient individuality. The authors describe the development and implementation of a psychiatric clinical pathway for geriatric patients with depression and identify common multidisciplinary interventions and a pattern of outcomes over the course of treatment for these patients. They also delineate quality and fiscal outcomes and future directions. Implementation of the pathway has been successful, and the development and implementation processes have applicability to other patient populations and care settings.

Aged↗

Glu192-->Gln substitution in thrombin yields an enzyme that is effectively inhibited by bovine pancreatic trypsin inhibitor and tissue factor pathway inhibitor.

Modeling studies have ascribed the remarkable resistance of thrombin to inhibition by the Kunitz type inhibitors, bovine pancreatic trypsin inhibitor (BPTI), and tissue factor pathway inhibitor (TFPI), to steric inhibition by the 60-loop insertion, especially Trp60D (in the chymotrypsin numbering system). Indeed, deletion of Pro60B, Pro60C, and Trp60D from this loop (des-PPW) enhances BPTI inhibition (Ki = 16 nM) (Le Bonniec, B. F., Guinto, E. R., MacGillivray, R. T. A., Stone, S. R., and Esmon, C. T. (1993) J. Biol. Chem. 268, 19055-19061). Activated protein C, however, lacks an equivalent insertion loop but is nevertheless resistant to inhibition by these Kunitz inhibitors. A unique feature of thrombin and activated protein C is the presence of Glu at position 192. Substitution of Glu192 with Gln in activated protein C dramatically enhances inhibition by BPTI and TFPI (Rezaie, A. and Esmon, C. T. (1993) J. Biol. Chem. 268, 19943-19948). We now demonstrate that thrombin E192Q (the Glu192-->Gln mutant) is inhibited by BPTI (Ki = 24 nM) or TFPI (Ki = 14 nM) much more effectively than wild type thrombin (Ki > 1 microM for both inhibitors). A thrombin mutant having both the des-PPW deletion and E192Q substitution binds BPTI (Ki = 35 pM) and TFPI (Ki = 25 pM) even tighter. BPTI can displace dansylarginine N-(-3-ethyl-1,5-pentanediyl)-amide from the active site of thrombin E192Q (Ki = 19 nM), indicating that BPTI interacts directly with the S1 binding site in thrombin. The E192Q mutation and PPW deletion contribute comparably and additively to the binding energy of thrombin with the Kunitz inhibitors. We suggest that access to the active center of thrombin is less restricted than predicted from previous studies.

Amino Acid Sequence↗

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

Biochemistry↗

A new model of cancer cachexia: contribution of the ubiquitin-proteasome pathway.

A new model of cachexia is described in which muscle protein metabolism related to the ubiquitin-proteasome pathway was investigated. Cloning of the colon-26 tumor produced a cell line, termed R-1, which induced cytokine (noninterleukin-1beta, interleukin-6 and tumor necrosis factor-alpha)-independent cachexia. Implantation of R-1 cells in mice elicited significant (20-30%) weight loss and decreased blood glucose by 70%, and adipose tissue levels declined by 95% and muscle weights decreased by 20-25%. Food intake was unaffected. The decrease in muscle weight reflected a decline in insoluble, but not soluble, muscle protein that was associated with a significant increase in net protein degradation. The rate of ubiquitin conjugation of proteins was significantly elevated in muscles of cachectic mice. Furthermore, the proteasome inhibitor lactacystin blocked the increase in protein breakdown but had no significant effect on proteolysis. Several markers of the ubiquitin-proteasome pathway, E2(14k) mRNA and E2(14k) protein and ubiquitin-protein conjugates, were not elevated. Future investigations with this new model should gain further insights into the mechanisms of cachexia and provide a background to evaluate novel and more efficacious therapies.

Animals↗

Regulating leukotriene synthesis: the role of nuclear 5-lipoxygenase.

Leukotrienes are lipid messengers involved in autocrine and paracrine cellular signaling. They are synthesized from arachidonic acid by the 5-lipoxygenase pathway. Current models of this enzymatic pathway recognize that a key step in initiating leukotriene synthesis is the calcium-mediated movement of enzymes, including 5-lipoxygenase, to intracellular membranes. However, 5-lipoxygenase can be imported into or exported from the nucleus before calcium activation. As a result, its subcellular localization will affect its ability to be activated by calcium, as well as the membrane to which it binds and its interaction with other enzymes. This commentary focuses on the role of 5-lipoxygenase compartmentation in determining its regulation and, ultimately, leukotriene synthesis.

Active Transport, Cell Nucleus↗

Prevention of thrombosis by topical application of tissue factor pathway inhibitor in a rabbit model of vascular trauma.

The extrinsic pathway of coagulation is initiated when tissue factor complexes with factor VII. A naturally occurring protein inhibitor of this complex, tissue factor pathway inhibitor (TFPI), has recently been isolated and the cDNA coding for this protein cloned. We used a rabbit ear artery model of crush/avulsion injury and microvascular repair to investigate the efficacy of TFPI as a topically applied antithrombotic agent. Traumatized arteries treated through lumenal irrigation with normal saline vehicle (controls) achieved patency rates of 8% and 0% at 1 and 7 postoperative days, respectively. Heparin irrigation (10 U/ml) resulted in patencies of 40% at both evaluation times. In contrast, TFPI at a dose of 20 micrograms/ml (0.2 ml total volume; 10 minute exposure) yielded a 91% patency rate at 1 day and 73% at 7 days postoperatively (p < 0.0005 vs controls). Prothrombin time and activated partial thromboplastin time values were not altered after topical treatment with TFPI. Scanning electron microscopy revealed dramatically inhibited thrombogenesis upon the injured surfaces of TFPI-treated vessels. These results suggest that TFPI used as a topically applied antithrombotic agent is effective for the prevention of thrombosis in microvascular anastomoses.

Administration, Topical↗

Analysis of antimalarial synergy between bestatin and endoprotease inhibitors using statistical response-surface modelling.

The pathway of hemoglobin degradation by erythrocytic stages of the human malarial parasite Plasmodium falciparum involves initial cleavages of globin chains, catalyzed by several endoproteases, followed by liberation of amino acids from the resulting peptides, probably by aminopeptidases. This pathway is considered a promising chemotherapeutic target, especially in view of the antimalarial synergy observed between inhibitors of aspartyl and cysteine endoproteases. We have applied response-surface modelling to assess antimalarial interactions between endoprotease and aminopeptidase inhibitors using cultured P. falciparum parasites. The synergies observed were consistent with a combined role of endoproteases and aminopeptidases in hemoglobin catabolism in this organism. As synergies between antimicrobial agents are often inferred without proper statistical analysis, the model used may be widely applied in studies of antimicrobial drug interactions.

Algorithms↗

Waves of pattern formation and signal pathways.

The model addresses the question of the origin of traveling waves, mimicking waves of the Hh and Dpp proteins such as found in development of the fly eye. These two proteins, which are part of an important signaling pathway to the genome, are found in a diverse array of developmental situations, for example in the formation of the proximal-distal axes in limbs. The complex intracellular biochemistry involved is modeled in the simplest way in both cases, with the intent that concepts be emphasized over biochemical detail.

Animals↗