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Results for “Stability analysis”

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At least 631 records · Page 35Linked to original sources
PubMed2004

Speed of pattern appearance in reaction-diffusion models: implications in the pattern formation of limb bud mesenchyme cells.

It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearance in a Turing reaction-diffusion system using linear stability analysis. It is shown that the sign of the change in appearance speed is qualitatively decided if the system is under the diffusion-driven instability condition, and this is confirmed by numerical simulations. Numerical simulations also show that a small change in parameter value induced easily detectable differences in the appearance speed of patterns. Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells-reinforcement of lateral inhibition and earlier appearance of pattern. These qualitative properties and easy detectability make this feature a promising tool to elucidate the underlying mechanisms of biological pattern formation where the quantitative parameters are difficult to obtain.

Animals↗
PubMed2004

Stability of cardiac waves.

Cardiac waves can fail to propagate when the membrane potential of the cells in the wavefront rises too slowly. The sodium channel inactivation gates play an important role in this process of propagation block. Simple models including inactivation gates can have travelling waves of constant form with two possible velocities. A stability analysis demonstrates that the slower velocity is always unstable, and in limited parameter regimes the faster velocity can also be unstable. Waves with the lower velocity propagate a finite distance before they dissipate due to this instability and this distance is calculated. The distance can be large suggesting that they might be seen in certain pathological conditions. The analytical results are compared with numerical simulations of the simplified model and a detailed cardiac ionic model.

Action Potentials↗
PubMed2005

Interaction of the IP3-Ca2+ and MAPK signaling systems in the Xenopus blastomere: a possible frequency encoding mechanism for the control of the Xbra gene expression.

The intense periodic calcium activity experimentally observed in the Xenopus embryo at the Mid Blastula Transition stage is closely related to the competence of the embryonic cells of the marginal zone to respond to the posterior-mesodermal inducting signals from the Fibroblast Growth Factor (FGF). In this work we do a stability analysis and study numerically an extension of a mathematical model previously introduced by us [Diaz, J., Baier, G., Martinez-Mekler, G., Pastor, N., 2002. Interaction of the IP(3)-Ca(2+) and the FGF-MAPK signaling pathways in the Xenopus laevis embryo: a qualitative approach to the mesodermal induction problem. Biophys. Chem. 97, 55-72] for the interaction of the Inositol 1,4,5-triphosphate-Calcium (IP(3)-Ca(2+)) and the Mitogen-Activated Protein Kinase (MAPK) signaling pathways at the Mid Blastula Transition stage or stage 8 of development. This allows us to consider the effect of the oscillatory calcium dynamics on the FGF input signal carried by the MAP kinase (ERK) into the nucleus. We find that this interaction of the pathways induces a limit cycle behavior for ERK with frequency-encoding characteristics. We believe that this periodic increase of the ERK levels in the nucleus is related to the ability of the cell to express posteriorizing mesodermal features induced by the FGF signal at stage 8.

Algorithms↗
PubMed2005

Dynamics of the 'echo' effect in a phytoplankton system with nitrogen fixation.

Consideration of nitrogen fixation adds a positive nonlinear feedback to plankton ecosystem models. We investigate the consequences of this feedback for secondary phytoplankton blooms and the response of phytoplankton dynamics to physical forcing. The dynamics of phytoplankton, Trichodesmium (the nitrogen fixer), and nutrients is modeled with a system of three differential equations. The model includes two types of nonlinear interactions: the competition of phytoplankton and Trichodesmium for light, and the positive feedback resulting from Trichodesmium recycling. A typical simulation of the model in time, with forcing by a varying mixed-layer depth, reveals a clear successional sequence including a secondary or 'echo' bloom of the phytoplankton. We explain this sequence of events through the stability analysis of three different steady states of the model. Our analysis shows the existence of a critical biological parameter, the ratio of normalized growth rates, determining the occurrence of 'echo' blooms and the specific sequence of events following a physical perturbation. The interplay of positive and negative feedbacks appears essential to the timing and the type of events following such a perturbation.

Algorithms↗
PubMed2005

A Michaelis-Menten-style model for the autocatalytic enzyme prostaglandin H synthase.

Prostaglandin H synthase (PGHS) is an autocatalytic enzyme which plays a key role in the arachidonic acid metabolic pathway. PGHS mediates the formation of prostaglandin H2, the precursor for a number of prostaglandins which are important in a wide variety of biological processes, including inflammation, blood clotting, renal function, and tumorigenesis. Here we present a Michaelis-Menten-style model for PGHS. A stability analysis determines when the reaction becomes self-sustaining, and can help explain the regulation of PGHS activity in vivo. We also consider a quasi-steady-state approximation (QSSA) for the model, and present conditions under which the QSSA is expected to be a good approximation. Applying the QSSA for this model can be useful in computationally intensive modeling endeavors involving PGHS.

Catalysis↗
PubMed2005

Nonlinear waves in double-stranded DNA.

We propose a nonlinear model derived from first principles, to describe bubble dynamics of DNA. Our model equations include a term derived from the dissipative effect of intermolecular vibrational modes. Such modes are excited by the propagating bubble, and we term this 'curvature dissipation'. The equations that we derive allow for stable pinned localized kinks which form the bubble. We perform the stability analysis and specify the energy requirements for the motion of the localized solutions. Our findings are consistent with properties of DNA dynamics, and can be used in models for denaturation bubbles, RNA and DNA transcription, nucleotide excision repair and meiotic recombination.

DNA↗
PubMed2004

Theoretical modeling of photo-induced wave propagation in liquid-crystalline Langmuir monolayers.

A phenomenological model of wave propagation in photo-excited liquid-crystalline Langmuir monolayers is constructed. The spontaneous splay deformation of the liquid-crystalline order and the anisotropy of photo-excitation of molecules are taken into account in this model. Numerical simulations of the model well reproduce qualitative features of the wave propagation phenomenon observed in recent experiments. A linear stability analysis of the model equations reveals that an interplay between the spontaneous splay deformation and the anisotropy of the photo-excitation can lead to the wave propagation.

Crystallization↗
PubMed2005

Effect of molecular weight heterogeneity on drug encapsulation efficiency of gelatin nano-particles.

Influence of molecular weight heterogeneity and drug solubility, drug loading and hydrodynamic conditions on drug release kinetics from gelatin nanoparticles were investigated. Also to assess the ability of gelatin nanoparticles as a potential intravascular probe for diagnostic purposes and in improving the biodelivery of cycloheximide (CHX), which is being used as a representative drug. Comparative characterization of 75 Bloom (type B, bovine), 175 and 300 Bloom (type A, porcine) gelatin nanoparticles was done to understand the phase behavior and hydrodynamic properties of gelatin chains and its nanoparticles. Gelatin nanoparticles were prepared by two-step desolvation method. Dynamic light scattering studies were performed to estimate hydrodynamic radii as well as intermolecular interaction. Effects of parameters like pH, temperature and molecular weight on the size and stability of the nanoparticles were studied. Transmission electron microscopy (TEM) and atomic force microscopy (AFM) measurements were done for size and stability analysis. Enhanced visco-elastic properties of nanoparticles were observed as compared to normal solutions of gelatin.

Gelatin↗
PubMed2005

Simulation of a mathematical model of the role of the TFPI in the extrinsic pathway of coagulation.

Blood coagulation is a complex physiological process. With the development of biochemistry and molecular biology, especially the discovery of the tissue factor pathway inhibitor (TFPI) and further research, the researches of tissue factor (TF) and TFPI have been the hot topics now. Based on this result, we provide a new concept of blood coagulation system and provide a dynamic model to describe the role of TFPI of this pathway. Through stability analysis of the equilibrium point and numerical simulations, we obtain some important conclusions. All these results may have great significance for lesions of cardiac vessels and cerebral vessels, haemophilia, DIC, thrombosis formation and malignancy.

Blood Coagulation↗
PubMed2004

Decomposing the total variation in a nested random effects model of neighborhood, household, and individual components when the dependent variable is dichotomous: implications for adolescent marijuana use.

Multilevel modeling techniques have become a useful tool that enables substance abuse researchers to more accurately identify the contribution of multiple levels of influence on drug-related attitudes and behaviors. However, it is difficult to determine the relative importance of the different hierarchical levels because, in the case of dichotomous outcomes, the variance components estimation involves calculations using a log-odds metric at the lowest level of estimation. We present methods introduced by Goldstein and Rasbash [Goldstein, H., Rasbash, J., 1996. Improved approximations for multilevel models with binary responses. J. Roy. Stat. Soc. A 159, 505-513.] to convert the variance components from the log-odds to the probability metric. This method provides a more logical and interpretable way to examine variation for nonlinear outcomes, which tend to be heavily utilized in substance use research. Using data from the National Household Survey on Drug Abuse [Substance Abuse and Mental Health Services Administration (SAMHSA), 2001. 1999 National Household Survey on Drug Abuse. Data Collection Final Report. Office of Applied Studies (OAS), Rockville, MD. Available at . Accessed on July 1, 2003.], we partition variation among individual, household, and neighborhood levels for the binary outcome of past year marijuana use to illustrate this approach. We also conduct a stability analysis to examine the robustness across different estimation procedures commonly available in commercial multilevel software packages. Finally, we partition the variance components using a conventional continuously distributed outcome and compare the relative magnitudes across binary and continuous outcomes.

Adolescent↗
PubMed2003

Determination of metformin in plasma using a new ion pair solid phase extraction technique and ion pair liquid chromatography.

This article describes the development of the first ion pair solid phase extraction technique (IPSPE), which has been applied to the extraction of metformin from plasma samples. In addition an ion pair chromatographic method was developed for the specific HPLC determination of metformin. Several extraction and HPLC methods have been described previously for metformin, however, most of them did not solve the problems associated with the high polarity of this drug. Drug recovery in the developed method was found to be more than 98%. The limit of detection and limit of quantification was 3 and 5 ng/ml, respectively. The intraday and interday precision (measured by coefficient of variation, CV%) was always less than 9%. The accuracy (measured by relative error, R.E.%) was always less than 6.9%. Stability analysis showed that metformin is stable for at least 3 months when stored at -70 degrees C. The method has been applied to 150 patient samples as part of a medication adherence study.

Chromatography, High Pressure Liquid↗
PubMed2005

The development and validation of liquid chromatography method for the simultaneous determination of metformin and glipizide, gliclazide, glibenclamide or glimperide in plasma.

This article describes the development of SPE and HPLC methods for the simultaneous determination of metformin and glipizide, gliclazide, glibenclamide or glimperide in plasma. Several extraction and HPLC methods have been described previously for the determination of each of these analytes in plasma separately. The simultaneous determination of these analytes is important for the routine monitoring of diabetic patients who take combination medications and for studying the pharmacokinetics of the combined dosage forms. In addition this developed method can serve as a standard method for the plasma determination of these analytes therefore saving time, effort and money. The recoveries of the developed methods were found to be between 76.3% and 101.9%. The limits of quantification were between 5 and 22.5 ng/ml. The intraday and interday precision (measured by coefficient of variation, CV%) was always less than 9%. The accuracy (measured by relative error %) was always less than 12%. Stability analysis showed that all analytes are stable for at least 3 months when stored at -70 degrees C.

Chromatography, High Pressure Liquid↗
PubMed2005

Effect of thermal treatment on interfacial properties of beta-lactoglobulin.

The changes in the secondary conformation and surface hydrophobicity of beta-lactoglobulin subjected to different thermal treatments were characterized at pH values of 7, 5.5 and 4 using circular dichroism (CD) and hydrophobic dye binding. Heating resulted in a decrease in alpha-helix content with a corresponding increase in random coil at all pH values, this change being more pronounced for small heating times. Heating also resulted in an increase in surface hydrophobicity as a result of partial denaturation, this increase being more pronounced at pH 4. Thermal treatment resulted in a shift of the spread monolayer isotherm at air-water interface to smaller area per molecule due to increased flexibility and more loop formation. Thermal treatment led to an increase in interfacial shear elasticity and viscosity of adsorbed beta-lactoglobulin layer at pH 5.5 and 7. Interfacial shear elasticity, shear viscosity, stability of beta-lactoglobulin stabilized emulsion and average coalescence time of a single droplet at a planar oil-water interface with adsorbed protein layer exhibited a maximum for protein subjected to 15 min heat treatment at pH 7. At pH 5.5, the interfacial shear rheological properties and average single drop coalescence time were maximum for 15 min heat treatment whereas emulsion stability was maximum for 5 min heat treatment. At pH 7, thermal treatment was found to enhance foam stability. Analysis of thin film drainage indicated that interfacial shear rheological properties do not influence thin film drainage.

Circular Dichroism↗
PubMed2005

Nonlinear evolution of thin liquid films dewetting near soft elastomeric layers.

The nonlinear evolution of thin liquid films dewetting near soft elastomeric layers is examined in this work. Evolution equations are derived by applying the lubrication approximation and assuming that van der Waals forces in the liquid cause the dewetting and that the solid can be described as a linear viscoelastic material. Two cases are examined: (i) a liquid layer resting on an elastomer bounded from below by a rigid substrate, and (ii) an elastomer overlying a thin liquid film bounded from below by a rigid substrate. Linear stability analysis is carried out to obtain asymptotic relations which are then compared against solutions of the full characteristic equations. In the liquid-on-solid case, numerical solutions of the evolution equations show that van der Waals forces cause thinning of the liquid film and thickening of the elastomeric solid beneath film depressions. Inclusion of a short-range repulsive force suggests that regular patterns may form in which ridges of fluid rest on depressions in the solid. In the solid-on-liquid case, the van der Waals forces cause the solid layer to break up before the liquid film can dewet. The results presented here support the idea that the dewetting of thin liquid films might be exploited to create topographically patterned surfaces on soft polymeric solids.

Journal Article↗
PubMed2006

Dynamics of thin liquid films on surfaces with a time-periodic wettability.

The dynamics of thin liquid films on surfaces whose wettability changes in a time-periodic manner are examined in this work. A nonlinear evolution equation based on the lubrication approximation is used to describe the film height, and attractions due to van der Waals forces are incorporated. Film wettability is varied through an imposed sinusoidal modulation of the Hamaker constant. A linear stability analysis predicts that if the mean Hamaker constant is negative, disturbances at the film surface will eventually decay regardless of the amplitude and frequency of the oscillation. However, numerical solution of the evolution equation shows that the film can rupture at a given frequency if the amplitude is sufficiently large. The associated characteristic wavelength can be predicted from results for constant-wettability surfaces if an appropriate effective Hamaker constant is used. For positive mean Hamaker constants, film rupture can be accelerated, delayed, or prevented depending on how the Hamaker constant changes early in the oscillation cycle. The effects of spatial gradients in wettability are also considered, and it is found that oscillation can delay but not prevent rupture. Inclusion of short-range repulsive forces leads to the formation of droplet-like structures separated by ultra-thin films, but this can be prevented by sufficiently large and slow oscillations of the Hamaker constant. The results of this work may find use in applications that make use of surfaces whose wettability can be controlled by external stimuli.

Journal Article↗
PubMed2006

Instability of a two-layer thin liquid film with surfactants: Dewetting waves.

Dewetting dynamics of a liquid film composed of two superposed ultra-thin layers of immiscible liquids resting on a solid substrate is investigated in the case when surfactants are present at the liquid-liquid interface. Two cases are considered: insoluble surfactant and surfactant soluble in the lower liquid. The dependence of Hamaker constants on the surfactant concentration is taken into account. A system of three strongly nonlinear evolution equations describing large (comparable to the layer thicknesses), long-wave perturbations of the liquid-liquid and liquid-gas interfaces, as well as the surfactant concentration, is derived for each case in the lubrication approximation. The linear stability analysis shows that in the presence of surfactants, oscillatory dewetting instability can occur. Numerical simulations of this system of nonlinear evolution equations are performed. It is found that in the case of oscillatory instabilities, the system exhibits either standing or traveling "dewetting waves." The weakly nonlinear analysis explains this phenomenon.

Journal Article↗
PubMed2005

Modelling the compartmentalization of splicing factors.

Splicing factor (SF) compartments, also known as speckles, are heterogeneously distributed compartments within the nucleus of eukaryotic cells that are enriched in pre-mRNA SFs. We derive a fourth-order aggregation-diffusion model that describes a possible mechanism underlying the organization of SFs into speckles. The model incorporates two hypotheses, namely (1) that self-organization of dephosphorylated SFs, modulated by a phosphorylation-dephosphorylation cycle, is responsible for the formation and disappearance of speckles, and (2) that an underlying nuclear structure plays a major role in the organization of SFs. A linear stability analysis about homogeneous steady-state solutions of the model reveals how the self-interaction among dephosphorylated SFs can result in the onset of spatial patterns. A detailed bifurcation analysis of the model describes how phosphorylation and dephosphorylation modulate the onset of the compartmentalization of SFs.

Animals↗
PubMed2006

Construction of genetic oscillators with interlocked feedback networks.

To understand how a gene regulatory network functioning as an oscillator is built, a precise mathematical description of the network and its dynamical properties are developed in this paper. Our approach is based on analyzing the effect of interactions between smaller subnetworks with simple dynamics. We relate an oscillatory behavior of the network to the destabilization phenomenon of a steady state caused by the interactions in a simple discrete map. When source of the instability of the steady state rather than the oscillatory behavior itself is considered, linear stability analysis and feedback control theory can be employed. Moreover, the amplitudes robust against change in delay can also be obtained from the discrete map. The main ideas are illustrated by constructing a genetic oscillator termed a "repressilator" and analyzing the occurrence of cellular rhythms, although the theoretical results hold for a general class of biological systems. The method can be directly applied to design, construct genetic oscillators, and further control their dynamics, even for large-scale networks.

Animals↗