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PubMed2001

The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca2+ release.

The fire-diffuse-fire model provides an idealized model of Ca2+ release within living cells. The effect of calcium pumps, which drive Ca2+ back into internal stores, is often neglected for mathematical simplicity. Here we show how to explicitly analyse such effects by extending the work of Keizer et al. [Keizer, J. E., G. D. Smith, S. Ponce Dawson and J. Pearson (1998). Saltatory propagation of Ca2+ waves by Ca2+ sparks. Biophys. J. 75, 595-600.]. For travelling waves, in which release events occur sequentially, we construct the speed of waves in terms of the time-scale at which pumps operate. An immediate consequence of this analysis is that the inclusion of calcium pumps leads to multiple solutions. A linear stability analysis determines those solution branches in parameter space which are stable. Numerical continuation is used to provide explicit examples of the bifurcation diagrams of the speed of waves as a function of physiologically significant system parameters.

Calcium↗
PubMed2004

Developmental waves in myxobacteria: A distinctive pattern formation mechanism.

In early stages of their development, starving myxobacteria organize their motion to produce a periodic pattern of traveling cell density waves. These waves arise from coordination of individual cell reversals by contact signaling when they collide. Unlike waves generated by reaction-diffusion instabilities, which annihilate on collision, myxobacteria waves appear to pass through one another unaffected. Here we analyze a mathematical model of these waves developed earlier [Proc. Natl. Acad. Sci. USA 98, 14 913 (2001)]]. The mechanisms which generate and maintain the density waves are clearly revealed by tracing the reversal loci of individual cells. An evolution equation of reversal point density is derived in the weak-signaling limit. Linear stability analysis determines parameters favorable for the development of the waves. Numerical solutions demonstrate the stability of the fully developed nonlinear waves.

Cell Communication↗
PubMed1982

Key for protein coding sequences identification: computer analysis of codon strategy.

The signal qualifying an AUG or GUG as an initiator in mRNAs processed by E. coli ribosomes is not found to be a systematic, literal homology sequence. In contrast, stability analysis reveals that initiators always occur within nucleic acid domains of low stability, for which a high A/U content is observed. Since no aminoacid selection pressure can be detected at N-termini of the proteins, the A/U enrichment results from a biased usage of the code degeneracy. A computer analysis is presented which allows easy detection of the codon strategy. N-terminal codons carry rather systematically A or U in third position, which suggests a mechanism for translation initiation and helps to detect protein coding sequences in sequenced DNA.

Amino Acid Sequence↗
PubMed2001

Quantitative analysis of the stabilization by substrate of Staphylococcus aureus PC1 beta-lactamase.

BACKGROUND: The stabilization of enzymes in the presence of substrates has been recognized for a long time. Quantitative information regarding this phenomenon is, however, rather scarce since the enzyme destroys the potential stabilizing agent during the course of the experiments. In this work, enzyme unfolding was followed by monitoring the progressive decrease of the rate of substrate utilization by the Staphylococcus aureus PC1 beta-lactamase, at temperatures above the melting point of the enzyme. RESULTS: Enzyme inactivation was directly followed by spectrophotometric measurements. In the presence of substrate concentrations above the K(m) values, significant stabilization was observed with all tested compounds. A combination of unfolding kinetic measurements and enzymatic studies, both under steady-state and non-steady-state regimes, allowed most of the parameters characteristic of the two concurrent phenomena (i.e. substrate hydrolysis and enzyme denaturation) to be evaluated. In addition, molecular modelling studies show a good correlation between the extent of stabilization, and the magnitude of the energies of interaction with the enzyme. CONCLUSIONS: Our analysis indicates that the enzyme is substantially stabilized towards heat-induced denaturation, independently of the relative proportions of non-covalent Henri-Michaelis complex (ES) and acyl-enzyme adduct (ES*). Thus, for those substrates with which the two catalytic intermediates are expected to be significantly populated, both species (ES and ES*) appear to be similarly stabilized. This analysis contributes a new quantitative approach to the problem.

Acylation↗
PubMed2003

Wave bifurcation and propagation failure in a model of Ca(2+) release.

The De Young Keizer model for intracellular calcium oscillations is based around a detailed description of the dynamics for inositol trisphosphate (IP(3)) receptors. Systematic reductions of the kinetic schemes for IP(3) dynamics have proved especially fruitful in understanding the transition from excitable to oscillatory behaviour. With the inclusion of diffusive transport of calcium ions the model also supports wave propagation. The analysis of waves, even in reduced models, is typically only possible with the use of numerical bifurcation techniques. In this paper we review the travelling wave properties of the biophysical De Young Keizer model and show that much of its behaviour can be reproduced by a much simpler Fire-Diffuse-Fire (FDF) type model. The FDF model includes both a refractory process and an IP(3) dependent threshold. Parameters of the FDF model are constrained using a comprehensive numerical bifurcation analysis of solitary pulses and periodic waves in the De Young Keizer model. The linear stability of numerically constructed solution branches is calculated using pseudospectral techniques. The combination of numerical bifurcation and stability analysis also allows us to highlight the mechanisms that give rise to propagation failure. Moreover, a kinematic theory of wave propagation, based around numerically computed dispersion curves is used to predict waves which connect periodic orbits. Direct numerical simulations of the De Young Keizer model confirm this prediction. Corresponding travelling wave solutions of the FDF model are obtained analytically and are shown to be in good qualitative agreement with those of the De Young Keizer model. Moreover, the FDF model may be naturally extended to include the discrete nature of calcium stores within a cell, without the loss of analytical tractability. By considering calcium stores as idealised point sources we are able to explicitly construct solutions of the FDF model that correspond to saltatory periodic travelling waves.

Algorithms↗
PubMed1990

A mathematical model for insulin kinetics. II. Extension of the model to include response to oral glucose administration and application to insulin-dependent diabetes mellitus (IDDM).

A generalized nonlinear mathematical model which incorporates beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term for glucose, is presented. Numerical simulations using this model lead to time variations of plasma glucose and insulin levels that are consistent with clinical observations in normal groups. The results obtained after suitable reduction in some of the parameters are in agreement with the clinical profile and laboratory data in insulin-dependent diabetes mellitus (IDDM). Linear stability analysis of the equations shows that there is a change in the nature of the stability in the transition from the normal case to IDDM, and it is the decrease in the beta cell function which causes this change.

Diabetes Mellitus, Type 1↗
PubMed2004

Electron-acoustic plasma waves: oblique modulation and envelope solitons.

Theoretical and numerical studies are presented of the amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, Boltzmann distributed hot electrons, and stationary ions. Perturbations oblique to the carrier EAW propagation direction have been considered. The stability analysis, based on a nonlinear Schrödinger equation, reveals that the EAW may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Different types of localized EA excitations are shown to exist.

Journal Article↗
PubMed2000

Electron-vibron-breather interaction

We study the interaction of breathers in the context of a coupled electron-vibron lattice system. Starting with single-site excitations, it is demonstrated that constellations exist for which the coexistence of electronic and vibronic breathers is assured. The energy exchange between the vibrational and electronic subsystems and its impact on the breather formation are discussed in detail. The coupled electron-vibron dynamics shows a tendency toward energy redistribution into the vibronic degrees of freedom at the expense of the electronic energy content. Attention is paid to the relaxation dynamics in the energy exchange and we discuss the attainment of a steady regime for the coupled electron-vibron dynamics starting from a nonequilibrium state. It is demonstrated that the presence of breathers has a strong impact on the relaxation dynamics. Breathers can assist the relaxation process. With the help of a linear stability analysis, we show why the electronic subsystem acts as an energy donor while the vibron system serves as the energy acceptor. To this end we investigate the existence and stability of localized breathing eigenmodes capable of energy trapping. A frequency analysis reveals that strong exchange also occurs due to a temporal transition from single-frequency breathers to those oscillating with two frequencies and their temporal resonance interaction. Finally, the self-stabilized electron-vibron system relaxes to a combined electron-vibron breather. On increasing the electron-vibron coupling strength, only a vibronic phonobreather of large amplitude survives, whereas the electronic subsystem tends to energy equipartition.

Journal Article↗
PubMed2000

A Multimethodological Approach for the Sustainable Management of Perifluvial Wetlands of the Po River (Italy).

/ Marginal aquatic systems (wetlands) of the Po River (Italy) have become the target of a renewed interest because of their value for recreation, natural reserves, and deposits of sand. To preserve these sites, wise management must be the objective of local administrations. In this paper a strategy for the sustainable use of 11 wetlands is presented. It uses simple economic analysis and multiple criteria techniques and provides suggestions to promote sustainability in terms of conservation of natural resources, economic self-sufficiency, and minimization of potential conflicts about the use of the wetlands. In the understanding that sustainability is framed in a long-term perspective, stability analysis is also considered and performed by means of loop analysis, a qualitative technique. Conditions for stability are then discussed about management opportunities.

Journal Article↗
PubMed2005

Modelling of predator-prey trophic interactions. Part I: two trophic levels.

A class of lumped parameter models to describe the local dynamics in a controlled environment of a two-trophic chain is considered. The class is characterized by a trophic function (functional response of predator to the abundance of prey) depending on the ratio of prey biomass x and a linear function of predator biomass y: f(qx/[(1-rho)k + rhoy]), where q is the efficiency of the predation process, k is a reference biomass, and rho (0 < or = rho < or = 1) specifies the predation model. The trophic function is defined only by some properties determining its shape. A stability analysis of the models has been performed by taking the parameters q and rho as bifurcation parameters: the regions in the (rho,q) plane of existence and stability of nonnegative equilibrium states and limit cycles are determined. This analysis shows that the behaviour of the models is qualitatively similar for 0 < or = rho < 1 (in particular the null state is always a saddle point), while the value rho=1 gives rise to some kind of structural instability of the system (in particular the null state becomes an attractor for sufficiently high predation efficiency).

Animals↗
PubMed2006

Linear stability of a draining film squeezed between two approaching droplets.

In the present paper we analyze the effect of infinitesimal non-axisymmetric perturbations in determining the critical gap thickness at which a draining, finite radius thin-film becomes unstable. The film is part of the suspending fluid trapped between two approaching deformable drops under the action of a flow field. We carry out a linear stability analysis in the context of a quasi-static approximation where the rate of growth of the disturbances is assumed to be much faster than the rate of film drainage. An analytical solution is derived for the model in the special case of a uniformly thick film, for two types of perturbation: fixed-end and free-end. It is shown, for this special case, when the hydrodynamic force pushing the drops together from the external flow is constant, that the four most unstable disturbances are of the free-end kind, associated with the lowest frequency modes of azimuthal variation in the film thickness. Higher modes are stabilized by surface tension. Our analysis also shows that adopting the unretarded form of the van der Waals disjoining pressure yields results similar to the analysis when electromagnetic retardation effects are included in the calculation. A second case is analyzed where the film is also of uniform thickness but its lateral extent and the gap thickness are both time-dependent. This case was included to extend the predictions to glancing drop-collisions where the external hydrodynamic force is time-dependent. We find that there is a maximum capillary number below which the film becomes unstable, and that there is range of angles in the trajectory where the film becomes unstable, but that outside this range the film is stable.

Journal Article↗
PubMed2001

Characterization and structural impact of five novel PROS1 mutations in eleven protein S-deficient families.

Heterozygozity for four novel missense mutations (W108C, W342R. E349K and L485S) and one novel 4 bp deletion (ACdelAAAG affecting codons 632-633) was identified in PROS1 of unrelated thrombosis prone Danish families with protein S type I or III deficiency. The 4 bp deletion results in a frameshift leading to replacement of the coding sequence for the 3 C-terminal amino acids by an abnormal extended sequence that codes for 9 amino acids. The E349K substitution was found in 7 families. Haplotype analysis using 7 microsatellite markers flanking PROS1 was consistent with a common founder for this mutation. The mutations reported here are most likely the cause of the protein S deficiency. Firstly, the four missense mutations cosegregate with the abnormal plasma protein S phenotype and lead to the loss of highly conserved amino acids. Secondly, computer analysis of structural models of protein S predicts that the substitutions could affect proper protein folding and/or stability. Analysis of platelet mRNA from subjects with the W108C, E349K, L485S mutation or the 4 bp deletion showed that mutated mRNA was expressed in significant amounts suggesting that mutated molecules are synthesized. Our results are compatible with defective protein folding/unstable molecules, impaired secretion and intracellular degradation of mutated protein, which appear to be the major molecular disease mechanisms for missense mutations and certain other mutations found in genetic disorders.

Adolescent↗
PubMed1993

[The stability of antibiotics administered in "and" with a parenteral nutrition mixture enriched with branched-chain amino acids. II. The cephalosporins].

Part I of these stability studies commented on the benefits, in terms of care and therapy, of the Y administration of antibiotics and parenteral nutrition. The aim of this study is to determine the stability of the cephalosporins ceftazidime, ceftriaxone, ceftizosime and cefotaxime in vitro, at therapeutic concentrations, infused together with a parenteral nutrition mixture with polyols, enriched in branched chained amino acids, and without lipids. A microbiological stability analysis was carried out on the antibiotics in the parenteral nutrition, and an HPLC aminogram was done to determine the concentration of amino acids in the infusion together with the antibiotic. As well, pH, osmolarity and colour change were measured in the antibiotics, in the parenteral nutrition used and in the joint infusion mixtures. It is concluded that parenteral nutrition can be jointly infused with cefotaxime and ceftazidime, at the concentrations studied, given the stability results obtained both with HPLC (antibiotics and amino acids) and microbiologically (antibiotics). At the same time, the microbiological analysis of ceftriaxone with the nutrition showed its stability in the study conditions. Its joint infusion with parenteral nutrition, studied by HPLC, confirmed the stability of the amino acids. The ceftizoxime analysed by HPLC remained stable during joint infusion with the parenteral nutrition.

Amino Acids, Branched-Chain↗
PubMed2003

Static and dynamic analysis of five anterior instrumentation systems for thoracolumbar scoliosis.

STUDY DESIGN: A nondestructive biomechanical investigation among five anterior spinal instrumentation systems for scoliosis. OBJECTIVES: The purpose of this study is to analyze the static and dynamic biomechanical stability of five different systems. SUMMARY OF BACKGROUND DATA: Although a variety of anterior spinal instrumentation systems for scoliosis are available, very few attempts have been made at comparative biomechanical studies. METHODS: Thirty calf spines were underwent static biomechanical tests, including flexion-extension, axial rotation, and lateral bending loading modes in the multisegmental spinal model. Five anterior instrumentation systems included: 1) Texas Scottish Rite Hospital system; 2) Bad Wildungen Metz; 3) anterior ISOLA; 4) Cotrel-Dubousset Hoph; and 5) Kaneda Anterior Scoliosis System. The initial and postfatigue stability after a cyclic loading test were analyzed by measuring the range of motion at instrumented segments compared to the intact within the same specimen (% to intact). RESULTS: Two-rod systems showed a significant decrease in range of motion compared to one-rod systems in flexion-extension (P < 0.001) and axial rotation (P < 0.05). In lateral bending, all systems demonstrated a significant decrease in range of motion of less than 40% to the intact (P < 0.001). After cyclical loading test, all systems increased in range of motion. In flexion-extension, one-rod systems depicted a significant increase in range of motion, compared to two-rod systems (P < 0.05). CONCLUSIONS: In the initial stability analysis, two-rod systems are superior to one-rod systems. For one-rod systems, repeated physiologic loading may result in reduced stability in flexion-extension.

Analysis of Variance↗
PubMed1990

Models for contact-mediated pattern formation: cells that form parallel arrays.

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.

Animals↗
PubMed2005

Phase stability relations in invariant systems.

Except for the trivial case of one-component systems, the conventional Schreinemakers phase stability analysis in invariant systems is shown to be thermodynamically and stoichiometrically inconsistent in that the partition of the stability relations into contributions coming from univariant subsystems is formulated only qualitatively. Although the stability relations in invariant systems are essentially additive (i.e., the stability relations in invariant system may be partitioned into a sum contributions coming from univariant subsystems), the quantitative form of this partition has never been considered. On the basis of a new approach to the stability of chemical species in multiple chemical reaction systems that has been recently developed by us (Fishtik, I. J. Phys. Chem. B, 2005, 109, 3851), we show how the stability relations in invariant systems may be uniquely partitioned into contributions coming from univariant reactions. This finding provides a simple algorithm for the construction of various types of thermodynamically consistent stability diagrams.

Journal Article↗
PubMed2000

Rotating hele-shaw cells with ferrofluids

We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a nonuniform, azimuthal magnetic field, applied tangential to the cell, tends to stabilize the interface. We verify that maximum growth rate selection of initial patterns is influenced by the applied field, which tends to decrease the number of interface ripples. We contrast these results with the situation in which a uniform magnetic field is applied normally to the plane defined by the rotating Hele-Shaw cell.

Journal Article↗
PubMed2004

The decrease in FlaA observed in a flaB mutant of Borrelia burgdorferi occurs posttranscriptionally.

The Lyme disease bacterium Borrelia burgdorferi is a motile spirochete with a flat-wave morphology. The periplasmic flagella, which are situated between the outer membrane sheath and cell cylinder, are essential for both the cell's wavy shape and motility. Here we focus on the structure and regulation of its periplasmic flagella. Previous studies have suggested that the periplasmic flagella consist of a polymer of the major filament protein FlaB and a minor protein, FlaA. We used immunoprecipitation methodology to present further evidence that FlaA is indeed a flagellar protein. In addition, in contrast to FlaA of the spirochete Brachyspira hyodysenteriae, B. burgdorferi FlaA did not impact the overall helical shape of the periplasmic flagella. We have previously shown that B. burgdorferi lacks the sigma factor-dependent cascade control of motility gene transcription found in other bacteria. To begin to understand motility gene regulation in B. burgdorferi, we examined the effects of an insertion mutation in flaB on the amounts of proteins encoded by motility genes. Of several motility gene-encoded proteins examined, only the amount of FlaA was decreased in the flaB mutant; it was 13% compared to the wild-type amount. Real-time reverse transcriptase PCR analysis indicated that this inhibition was not the result of a decrease in flaA mRNA. In addition, protein stability analysis suggested that FlaA was turned over in the flaB mutant. Our results indicate that the lack of FlaB negatively influences the amount of FlaA found in the cell and that this effect is at the level of either translational control or protein turnover.

Borrelia burgdorferi↗