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PubMed2002

Stripe patterns in the magnetic reorientation of a glass-forming nematic liquid crystal.

We study spontaneous pattern formation in a glass-forming nematic liquid crystal during the magnetically induced dynamic Fréedericksz transition. Pattern growth rates and wavelengths as functions of the magnetic field are extracted from optical transmission textures of thin planar cells. The characteristics of the observed stripe pattern can be related to viscoelastic parameters of the nematic by means of a linear stability analysis of director fluctuation modes. The viscous properties of the material allow to vary the time scales of the experiment with temperature by orders of magnitude, leaving the spatial structure of the pattern essentially unchanged. We find that the ratios of shear and rotational viscosity coefficients relevant for the pattern wavelength selection remain constant in the temperature range investigated, whereas their absolute values change by almost two orders.

Journal Article↗
PubMed2005

Undulation versus Frederiks instability in nematic elastomers in an external electric field.

We study the behaviour of a nematic side-chain elastomer under the influence of an external static electric field for a specific geometry. For this investigation, the nematic elastomer is considered to be a perfect insulator. On the basis of a macroscopic description we generalize the classical Frederiks transition in a low-molecular-weight (LMW) nematic liquid crystal to the elastomeric case. We predict, using a linear stability analysis, that the onset of the instability can be qualitatively different from the LMW case: in liquid crystalline elastomers an undulation instability can arise at onset. Whether the analogue of a Frederiks instability or an undulation instability occurs first depends on the sample thickness as well as on the material parameters. It turns out that the parameter which describes the coupling between the deformations of the elastomer and the relative rotations between the elastomer and the director field of the nematic phase is most important for the predicted response of the system. Furthermore, we find that the magnitude of the critical electric field is much higher in the elastomeric than in the low-molecular-weight case.

Journal Article↗
PubMed2006

Spinodal wrinkling in thin-film poly(ethylene oxide)/polystyrene bilayers.

Optical microscopy and atomic force microscopy were used to study a novel roughness-induced wrinkling instability in thin-film bilayers of poly(ethylene oxide) (PEO) and polystyrene (PS). The observed wrinkling morphology is manifested as a periodic undulation at the surface of the samples and occurs when the bilayers are heated above the melting temperature of the semi crystalline PEO (T(m) = 63 Celsius) layer. During the wrinkling of the glassy PS capping layers the system selects a characteristic wavelength that has the largest amplitude growth rate. This initial wavelength is shown to increase monotonically with increasing thickness of the PEO layer. We also show that for a given PEO film thickness, the wavelength can be varied independently by changing the thickness of the PS capping layers. A model based upon a simple linear stability analysis was developed to analyse the data collected for the PS and PEO film thickness dependences of the fastest growing wavelength in the system. The predictions of this theory are that the strain induced in the PS layer caused by changes in the area of the PEO/PS interface during the melting of the PEO are sufficient to drive the wrinkling instability. A consideration of the mechanical response of the PEO and PS layers to the deformations caused by wrinkling then allows us to use this simple theory to predict the fastest growing wavelength in the system.

Computer Simulation↗
PubMed1991

Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters.

1. An equivalent circuit model of the R15 bursting neuron in Aplysia has been combined with a fluid compartment model, resulting in a model that incorporates descriptions of most of the membrane ion channels that are known to exist in the somata of R15, as well as providing a Ca2+ balance on the cell. 2. A voltage-activated, calcium-inactivated Ca2+ current (denoted the slow inward current ISI) was sufficient to produce bursting activity without invoking any other calcium-dependent currents (such as a nonspecific cation current, INS, or a calcium-activated K+ current, IK,Ca). Furthermore, many characteristics of a typical R15 burst could be simulated, such as a parabolic variation in interspike interval, the depolarizing afterpotential (DAP), and the progressive decrease in the undershoots of spikes during a burst. 3. The dynamic activity of R15 was analyzed by separately characterizing two different temporal domains; the fast dynamics associated with action potentials and the slow dynamics associated with low-amplitude oscillations lasting tens of seconds ("slow waves"). The slow dynamics were isolated by setting the Na+ conductance (gNa) to zero and then studied by the use of a system of equations reduced to two variables: intracellular concentration of Ca2+ and membrane potential. The fixed point of the system was located at the intersection of the nullclines for these two variables. A stability analysis of the fixed point was then used to determine whether a given set of parameters would produce slow-wave activity. 4. If the reduced model predicted slow-wave oscillations for a given set of parameters with gNa set to zero, then bursting activity was observed for the same set of parameters in the full model with gNa reset to its control value. However, for certain sets of parameters with gNa at its usual value, the full model exhibited bursting activity because of a slow oscillation produced by the activation of INS by action potentials. This oscillation resulted from an interaction between the fast and slow dynamics that the reduced model alone could not predict and was not observed when gNa was subsequently set to zero. If gNS was also set to zero, this discrepancy disappeared.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed2006

An integrated computational/experimental model of tumor invasion.

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.g., of cell nutrients, driving shape instability and invasive tumor morphologies, and stabilizing mechanical forces, e.g., cell-to-cell and cell-to-matrix adhesion. To test this hypothesis, we here obtain variable-based statistics for input to the mathematical model from in vitro human and rat glioblastoma cultures. A linear stability analysis of the model predicts that glioma spheroid morphology is marginally stable. In agreement with this prediction, for a range of variable values, unbounded growth of the tumor mass and invasion of the environment are observed in vitro. The mechanism of invasion is recursive subspheroid component development at the tumor viable rim and separation from the parent spheroid. Results of computer simulations of the mathematical model closely resemble the morphologies and spatial arrangement of tumor cells from the in vitro model. We propose that tumor morphogenesis in vivo may be a function of marginally stable environmental conditions caused by spatial variations in cell nutrients, oxygen, and growth factors, and that controlling these conditions by decreasing spatial gradients could benefit treatment outcomes, whereas current treatment, and especially antiangiogenic therapy, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability.

Animals↗
PubMed2000

On the synthesis of brain-state-in-a-box neural models with application to associative memory.

In this article we present techniques for designing associative memories to be implemented by a class of synchronous discrete-time neural networks based on a generalization of the brain-state-in-a-box neural model. First, we address the local qualitative properties and global qualitative aspects of the class of neural networks considered. Our approach to the stability analysis of the equilibrium points of the network gives insight into the extent of the domain of attraction for the patterns to be stored as asymptotically stable equilibrium points and is useful in the analysis of the retrieval performance of the network and also for design purposes. By making use of the analysis results as constraints, the design for associative memory is performed by solving a constraint optimization problem whereby each of the stored patterns is guaranteed a substantial domain of attraction. The performance of the designed network is illustrated by means of three specific examples.

Association Learning↗
PubMed2004

Rapid processing and unsupervised learning in a model of the cortical macrocolumn.

We study a model of the cortical macrocolumn consisting of a collection of inhibitorily coupled minicolumns. The proposed system overcomes several severe deficits of systems based on single neurons as cerebral functional units, notably limited robustness to damage and unrealistically large computation time. Motivated by neuroanatomical and neurophysiological findings, the utilized dynamics is based on a simple model of a spiking neuron with refractory period, fixed random excitatory interconnection within minicolumns, and instantaneous inhibition within one macrocolumn. A stability analysis of the system's dynamical equations shows that minicolumns can act as monolithic functional units for purposes of critical, fast decisions and learning. Oscillating inhibition (in the gamma frequency range) leads to a phase-coupled population rate code and high sensitivity to small imbalances in minicolumn inputs. Minicolumns are shown to be able to organize their collective inputs without supervision by Hebbian plasticity into selective receptive field shapes, thereby becoming classifiers for input patterns. Using the bars test, we critically compare our system's performance with that of others and demonstrate its ability for distributed neural coding.

Afferent Pathways↗
PubMed2005

A theoretical study of hypothalamo-pituitary-adrenocortical axis dynamics.

Does the hypothalamo-pituitary-adrenocortical (HPA) axis itself generate oscillations? The affirmative answer to this question is commonly assumed, because a regular daily rhythm of its hormones is observed. We offer another plausible explanation of the origin of this pattern: HPA just responds to an external pacemaker. A qualitative mathematical model is constructed wherein all the terms in the equations are physicochemically interpretable. Linear stability analysis shows that this system does not generate oscillations. Computer simulation yields oscillations that are the system's response to an external pulsing activator, implying that the observed pattern does not have to be an intrinsic property of this system.

Adrenal Cortex Hormones↗
PubMed1994

Identification and characterization of an antisense RNA transcript (gfg) from the human basic fibroblast growth factor gene.

Basic fibroblast growth factor (bFGF) is an autocrine growth factor that is overexpressed in glial tumor cells and promotes their unregulated proliferation. We have previously reported that increased messenger RNA (mRNA) stability contributes to the elevated steady state levels of bFGF mRNA in human U87-MG glioma cells. Stability of bFGF mRNA is regulated by a natural antisense transcript in Xenopus oocytes, but the mammalian equivalent of this transcript has not previously been described. We were interested in identifying the human equivalent of this antisense transcript in order to study its role in bFGF mRNA stability. Analysis of the 3'-untranslated region of the 6.7-kilobase human bFGF mRNA revealed two areas of greater than 75% homology to exons 3 and 4 of the Xenopus antisense transcript, separated by 4300 basepairs of nonhomologous sequence. We used reverse transcription-polymerase chain reaction to amplify, clone, and sequence a 301-basepair fragment of the antisense splice variant from U87-MG cells. The clone (gfg-1) is 73% identical to the Xenopus sequence, with a conserved splice junction and an open reading frame. Strand-specific gfg-1 complementary RNA probes detect a 1.5-kilobase mRNA transcript in normal rat tissues and human T47D breast cancer cells, which contain very low levels of bFGF mRNA. In contrast, antisense transcript expression was undetectable by Northern hybridization in U87-MG cells, which overexpress the bFGF sense mRNA. The reciprocal relationship between bFGF sense and antisense expression suggests that antisense transcripts may regulate bFGF expression in mammalian cells, and that disruption of normal sense/antisense mRNA ratios may lead to overexpression of bFGF in some tumors.

Animals↗
PubMed2000

[Investigation on the marker substances of crude drugs in formulations. II. Marker substances for the identification of Cistanchis Herba in drinkable preparations].

There are few reports about marker substances for the identification of Cistanchis Herba in formulations. First, constituent analysis was performed by HPLC for screening of a marker substance, using several lots of Cistanchis Herba and its fluid extract. As a result, two components were clearly detected, which were thought to be good marker substances and identified to be echinacoside and acteoside by structural analysis. Stability testing of these two marker substances in various pH and temperature conditions was carried out, which suggested that they are stable and suitable enough for the identification. Therefore, the identification methods of Cistanchis Herba and its fluid extract in formulations were investigated using five different kinds of commercial drinkable preparations with authentic standard of echinacoside and acteoside as marker substances. Consequently, echinacoside and acteoside were clearly detected in all formulations investigated, using an HPLC-photodiode array detector system. Echinacoside and acteoside will be successfully used as marker substances for the identification of Cistanchis Herba and its fluid extract in formulations.

Chemistry, Pharmaceutical↗
PubMed2003

The comparison of intrinsic rates of increase among chromosome-substituted lines resistant and susceptible to organophosphate insecticides in Drosophila melanogaster.

To investigate the genetic basis of the seasonal fluctuations in resistance to three organophosphates, observed within a natural population of Drosophila melanogaster (Meigen), we compared the intrinsic rate of increase, generation time and net reproduction rate among chromosome substitution lines derived from a resistant and a susceptible line, obtained from this natural population. There was significant variation among substituted lines; lines possessing the third chromosome from the resistant line, which confers resistance to the three organophosphates, generally showed lower mean values of these fitness measures. Chromosomal analyses also indicated significant negative contributions of the third chromosome from the resistant line. However, significant positive contributions of the interactions among chromosomes from the resistant line to these fitness measures were also detected. We further conducted a local stability analysis, in which each chromosome-substituted line was assumed to be introduced at a low frequency into the initial susceptible population. It was demonstrated that the resistance factor(s) on the third chromosome tend to decrease in their frequency under both density-independent and juvenile density-regulated conditions. Based on these results, a possible explanation for the seasonal fluctuations in resistance to the three organophosphates observed in the natural population was proposed.

Animals↗
PubMed2002

Suppression of self-pulsing behavior in erbium-doped fiber lasers with a semiconductor optical amplifier.

We experimentally demonstrate that the stability of cw and mode-locked erbium-doped fiber ring lasers can be improved significantly with a semiconductor optical amplifier (SOA) inside the cavity. The fast saturable gain of the SOA suppresses significantly the self-pulsing that is due to ion pairs in the erbium-doped fiber, which acts as a saturable absorber. A linear stabilization analysis of the laser system agrees with our experimental results.

Journal Article↗
PubMed2005

Two-mode injection locking in vertical-cavity surface-emitting lasers.

We report on the dynamics that accompany polarization switching induced by orthogonal optical injection in a vertical-cavity surface-emitting laser (VCSEL). As the injection strength increases, the VCSEL bifurcates to injection-locked steady states and time-periodic and possibly chaotic dynamics. Of particular interest is a two-mode injection-locking solution, i.e., locking of the two VCSEL polarization modes. A detailed stability analysis unveils new bistability mechanisms in optical injection problems.

Journal Article↗
PubMed2006

Channel density regulation of firing patterns in a cortical neuron model.

Modifying the density and distribution of ion channels in a neuron (by natural up- and downregulation or by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In this investigation we analyzed how the impulse patterns are regulated by the density of voltage-gated channels in a neuron model based on voltage-clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf-bifurcation threshold dynamics, respectively. Single, strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The relationship found here between channel densities and oscillatory behavior may partly explain the difference between the principal spiking patterns previously described for crab axons (class 1 and 2) and cortical neurons (regular firing and fast spiking).

Action Potentials↗
PubMed2000

The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response.

In order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account. The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.

Disease Transmission, Infectious↗
PubMed2000

The interaction between uric acid level and other risk factors on the development of gout among asymptomatic hyperuricemic men in a prospective study.

OBJECTIVE: To investigate the incidence of gout and the interaction between uric acid level and other risk factors in the development of gout. METHODS: Two hundred twenty-three asymptomatic hyperuricemic men initially studied in 1991-92 were reassessed in 1996-97. Gout was clinically diagnosed by a senior rheumatologist based on history and physical according to the clinical criteria of Wallace. Basic demographic and lifestyle variables as well as biochemical data were collected in both baseline and followup periods. Both the stability analysis and the analysis of repeated relationships were applied. RESULTS: The 5-year cumulative incidence of gout was 18.83% (42/223). The risk factors for gout based on the analysis of repeated relationships were uric acid level, alcohol consumption, use of diuretics, and obesity. The only predictor of gout at baseline was uric acid level. After adjusting for baseline uric acid level, followup uric acid increase, persistent alcohol consumption, use of diuretics in the followup period, and body mass index increase were independent predictors for gout among asymptomatic hyperuricemic men. Excessive alcohol consumption, particularly if occasional, was the most important factor in the development of gout, even when the concentration of uric acid level was below 8 mg/dl. CONCLUSION: Uric acid level is the key factor for prevention of gout and needs constant monitoring. Other contributing or possible etiologic factors such as alcohol consumption, diuretics use, and excess weight gain carry an increased risk of gout attack among patients with hyperuricemia.

Adult↗