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PubMed2003

Bifurcation and stability analysis of rotating chemical spirals in circular domains: boundary-induced meandering and stabilization.

Recent experimental and model studies have revealed that the domain size may strongly influence the dynamics of rotating spirals in two-dimensional pattern forming chemical reactions. Hartmann et al. [Phys. Rev. Lett. 76, 1384 (1996)], report a frequency increase of spirals in circular domains with diameters substantially smaller than the spiral wavelength in a large domain for the catalytic NO+CO reaction on a microstructured platinum surface. Accompanying simulations with a simple reaction-diffusion system reproduced the behavior. Here, we supplement these studies by a numerical bifurcation and stability analysis of rotating spirals in a simple activator-inhibitor model. The problem is solved in a co-rotating frame of reference. No-flux conditions are imposed at the boundary of the circular domain. At large domain sizes, eigenvalues and eigenvectors very close to those corresponding to infinite medium translational invariance are observed. Upon decrease of domain size, we observe a simultaneous change in the rotation frequency and a deviation of these eigenvalues from being neutrally stable (zero real part). The latter phenomenon indicates that the translation symmetry of the spiral solution is appreciably broken due to the interaction with the (now nearby) wall. Various dynamical regimes are found: first, the spiral simply tries to avoid the boundary and its tip moves towards the center of the circular domain corresponding to a negative real part of the "translational" eigenvalues. This effect is noticeable at a domain radius of R<R(cr,1). The spiral subsequently exhibits an oscillatory instability: the tip trajectory displays a meandering motion, which may be characterized as boundary-induced spiral meandering. A systematic study of the spiral rotation as a function of a control parameter and the domain size reveals that the meandering instability in large domains becomes suppressed, and the spiral rotation becomes rigid, at a critical radius R(cr,0). Boundary-induced meandering arises below a second critical radius R(cr,2)<R(cr,0).

Journal Article↗
PubMed2006

Active-feedback control of the magnetic boundary for magnetohydrodynamic stabilization of a fusion plasma.

Stable operation with control on magnetohydrodynamic modes has been obtained in the modified reversed field experiment employing a set of 192 feedback controlled saddle coils. Improvements of plasma temperature, confinement (twofold), and pulse length (threefold) and, as a consequence of the magnetic fluctuation reduction, strong mitigation of plasma-wall interaction and mode locking are reported.

Journal Article↗
PubMed1998

The effect of boundary selection on the stability and folding of the third fibronectin type III domain from human tenascin.

Correct selection of domain boundaries is critical for structural analysis of single domains from multimodular proteins. Folding and stability studies of the third fibronectin type III domain from human tenascin (TNfn31-90) have shown that it is moderately stable (Delta G(D-N)(H2O) approximately 5 kcal mol-1) and folds with two-state kinetics. In an attempt to stabilize the protein, five domains were constructed with different combinations of extensions to the N- and C-termini. Thermal denaturation studies show that a specific two amino acid (Gly-Leu) extension at the C-terminus is primarily responsible for a significant increase in stability. The Delta Delta G(D-N)(H2O) of the Gly-Leu extension (TNfn3(1-92)) is 2.7 +/- 0.3 kcal mol-1. Refolding kinetics do not differ significantly, but unfolding is slowed 40-fold. Mutation of leucine 92 to alanine does not affect stability, indicating that the stability of the extension does not come from the packing of the leucine side chain. Hydrogen exchange data suggest that the extension adds new hydrogen bonds and strengthens existing hydrogen bonds in the C-terminal interaction with the A-B and E-F loops. Removal of a very small number of hydrogen bonds substantially increases the unfolding rate, a phenomenon which may be important in stress-relaxation of FNIII-containing muscle proteins such as titin. These experiments demonstrate the importance of a small number of additional long-range interactions in the overall formation of a compact independently folding beta-sheet module.

Alanine↗
PubMed1999

Evaluation of a model that determines the stability limits of dynamic balance.

A recent model of balance control has revealed two types of boundaries describing stability limits for center of mass (CM) dynamics: torque boundaries and state boundaries. The purpose of this study was to determine if these boundaries correctly characterize empirical data. We analyzed 2367 trials from 10 subjects who recovered their balance after they voluntarily pulled on a handle. We hypothesized that if model predictions were valid, both types of boundaries should encompass the empirical trajectories. We also hypothesized that each trajectory's nearest distance to the torque boundaries (the torque safety margin) would be correlated with the center of pressure (COP) safety margin, defined as the COP's nearest distance to the edge of the feet. The results supported the accuracy of the model-derived boundaries, with torque boundaries encompassing 100% and state boundaries encompassing 99.8% of the trials. Moreover, torque safety margins were highly correlated with COP safety margins, supporting the use of COP safety margins for estimating relative stability in dynamic tasks where balance is maintained. The distributions of the trajectories also suggested that a safety margin-oriented control strategy might be a robust alternative to the hypothesis that the central nervous system strives to optimize motion. The distinctions among different safety margins are discussed.

Adult↗
PubMedDate not supplied

[Levels of homoiothermy and homoioosmy and probable reasons determining them].

Temperature of independently evolved homoiothermic animals (birds and animals) is maintained on the same level of 37-40 degrees C. Flying or preparing to fly insects are heated to the same temperature. This temperature is close to the lethal temperatures resulting in denaturation of proteins (Dolnik, 2003). Freshwater homoioosmy animals (annelids, mollusks, various groups of crustaceous, Cyclostomata and fishes) which independently occupied continental waters maintain internal salinity around 5-8% per hundred. The same level is retained in terrestrial and secondary marine animals (Khlebovich, 1974). In the case of decline in internal salinity below 5-8% per hundred the optical density of soluble tissue extracts increased, that could be explained by coagulation of tissue proteins. Therefore in the cases of homoiothermy and homoioosmy the values of regulated parameter are close to the parameters of protein complexes stability. It may be suggested that there are definitive advantages of governing regulated parameters exactly near boundaries of stability, out of which the process is terminated. Analogy could be found in control of reactions of nuclear synthesis and disintegration which are conducted under conditions which are close to the critical point of explosion. This statement can be regarded as a particular case of the Mopertui principle of the least operation.

Adaptation, Psychological↗
PubMed1984

The pericellular boundary layer modulates acetylcholine receptor stability in cultured myotubes.

Degradation of acetylcholine receptors in cultured chicken myotubes was measured by release into the medium of radioactivity from 125I-labeled alpha-bungarotoxin. Disturbance of the pericellular boundary layer by stirring of the culture medium shortened the half-life of receptor in the membrane from 24 to 12 h. The effect could not be explained by dissociation of toxin-receptor complexes or by conditioning of the bulk phase of the medium. The rates of synthesis and degradation of total cell protein and the degradation of lactoperoxidase-iodinated surface protein were not affected by medium stirring. The loss of glucosamine-labeled material from the cells was enhanced by stirring, however, and this resulted entirely from the increased shedding of high molecular weight glycosubstances from the cells. Cells in stirred cultures contained lower levels of surface coat material stainable with colloidal thorium. These results indicate that glycosubstances of the pericellular matrix protect ACh receptors from degradation.

Animals↗
PubMed1983

Information concerning colour derived from a single boundary.

Two experiments are described in which visual information is derived from a single moving boundary in the retinal image, all other boundaries being stabilized so that they contribute no visual information. In this situation the subject perceives the same colours on the two sides of the boundary as would be perceived in normal vision when, owing to eye-movements, all boundaries in the retinal image are moving relative to the retina. Thus complete information leading to perception of hue and saturation as well as brightness, and not merely differences of hue etc. on the two sides, can be derived from a single boundary.

Color Perception↗
PubMed1995

"Dynamical confinement" in neural networks and cell cycle.

In this paper randomization of well-known former mathematical models is proposed (i.e., the Hopfield model for neural networks and the Hahn model for the cell cycle) in order to facilitate the study of their asymptotic behavior: in fact, we replace the determination of the stability basins for attractors and boundaries by the study of a unique (or a small number of) invariant measure(s), whose distribution function maxima (or, respectively, percentile contour lines) correspond to the location of the attractors (or, respectively, boundaries of their stability basins). We give the name of "confinement" to this localization of the mass of the invariant measure(s). We intend to show here that the study of the confinement is in certain cases easier than the study of underlying attractors, in particular if these last are numerous and possess small stability basins (for example, for the first time we calculate the invariant measure in the random Hopfield model in a case for which the deterministic version exhibits many attractors, and in a case of phase transition). (c) 1995 American Institute of Physics.

Journal Article↗
PubMed2003

Role of feedforward control of movement stability in reducing slip-related balance loss and falls among older adults.

Human upright posture is inherently unstable. To counter the mechanical effect of a large-scale perturbation such as a slip, the CNS can make adaptive adjustments in advance to improve the stability of the body center-of-mass (COM) state (i.e., its velocity and position). Such feedforward control relies on an accurate internal representation of stability limits, which must be a function of anatomical, physiological, and environmental constraints and thus should be computationally deducible based on physical laws of motion. We combined an empirical approach with mathematical modeling to verify the hypothesis that an adaptive improvement in feedforward control of COM stability correlated with a subsequent reduction in balance loss. Forty-one older adults experienced a slip during a sit-to-stand task in a block of slip trials, followed by a block of nonslip trials and a re-slip trial. Their feedforward control of COM stability was quantified as the shortest distance between its state measured at seat-off (slip onset) and the mathematically predicted feasible stability region boundary. With adaptation to repeated slips, older adults were able to exponentially reduce their incidence of falls and backward balance loss, attributable significantly to their improvement in feedforward control of stability. With exposure to slip and nonslip conditions, subjects began to select "optimal" movements that improved stability under both conditions, reducing the reliance on prior knowledge of forthcoming perturbations. These results can be fully accounted for when we assume that an internal representation of the COM stability limits guides the adaptive improvements in the feedforward control of stability.

Adaptation, Physiological↗
PubMed1991

Boundaries and wounds, glia and glycoconjugates. Cellular and molecular analyses of developmental partitions and adult brain lesions.

During brain development, transient partitions of glia and glycoconjugates (glycoproteins, glycolipids, and glycosaminoglycans) surround forming functional units (e.g., nuclear divisions, whisker-related barrels, and neostriatal striosomes). These partitions, which we think of as boundaries, consist of dense aggregates of glial fibrillary acidic protein (GFAP)-positive radial glia, young astrocytes and their processes, and developmentally regulated glycoconjugates (e.g., J1/tenascin and the 473 proteoglycan) that can be thought of as recognition molecules present on membranes or perhaps within the extracellular matrix. When functional patterns have formed and appear to be stabilized, these boundaries are no longer detectable. Lesions of the developing brain show the existence of a more global astrocytic distribution suggestive of biochemically distinct subsets of astrocytes that reside within boundary versus nonboundary positions. Lesions of the adult brain, in addition to showing gliosis, reveal a reexpression of some of the same macromolecules present in transient brain boundaries during development. It is postulated that developmental boundaries and wounds in the adult brain possess some of the same inhibitory and possibly alluring molecular substrates for neuritic expansion.

Aging↗
PubMed1997

Dynamics of two-component biochemical systems in interacting cells; synchronization and desynchronization of oscillations and multiple steady states.

Systems of interacting cells containing a metabolic pathway with an autocatalytic reaction are investigated. The individual cells are considered to be identical and are described by differential equations proposed for the description of glycolytic oscillations. The coupling is realized by exchange of metabolites across the cell membranes. No constraints are introduced concerning the number of interacting systems, that is, the analysis applies also to populations with a high number of cells. Two versions of the model are considered where either the product or the substrate of the autocatalytic reaction represents the coupling metabolite (Model I and II, respectively). Model I exhibits a unique steady state while model II shows multistationary behaviour where the number of steady states increases strongly with the number of cells. The characteristic polynomials used for a local stability analysis are factorized into polynomials of lower degrees. From the various factors different Hopf bifurcations may result in leading for model I, either to asynchronous oscillations with regular phase shifts or to synchronous oscillations of the cells depending on the strength of the coupling and on the cell density. The multitude of steady states obtained for model II may be grouped into one class of states which are always unstable and another class of states which may undergo bifurcations leading to synchronous oscillations within subgroups of cells. From these bifurcations numerous different oscillatory regimes may emerge. Leaving the near neighbourhood of the boundary of stability, secondary bifurcations of the limit cycles occur in both models. By symmetry breaking the resulting oscillations for the individual cells lose their regular phase shifts. These complex dynamic phenomena are studied in more detail for a low number of interacting cells. The theoretical results are discussed in the light of recent experimental data on the synchronization of oscillations in populations of yeast cells.

Animals↗
PubMed1994

On the fittedness of organisms and the ascendency of ecosystems: toward a hierarchical model of network development.

The amount of information biological entities receive from and transmit to their environments (fittedness) influences their fitness and constrains the organization of the systems they constitute. The fittedness of an organism in an ecosystem modeled as a network of interacting organismal components (termed network fittedness) is measured by the diversity (strength and number) of its interactions with other components. Together, the fittedness of all ecosystem components is equal to the structural redundancy in the ecosystem. Redundancy is one part of the "overhead" by which the theoretically maximum organization of these pathways is reduced, thereby determining the actual degree of organization. Fittedness is hypothesized to increase or remain high early in network development because, in general, living entities must then deal with a more unpredictable environment. A hierarchical model of biological network development presented in terms of organisms and ecosystems shows how both network structural organization and the fittedness of components can increase through ecological and evolutionary time, if other parts of overhead decrease or the capacity of the system to process energy, matter, or information increases sufficiently. The model predicts the existence of a critical point when interacting components' shared environment is stabilized through boundary formation and the ecological replacement, evolution, and co-evolution of components, thereby allowing organismal fittedness to decrease and network organization to increase.

Animals↗
PubMed1994

Cultural transitions and epidemiology.

The analysis of cultural patterns, as an observational and qualitative tool in epidemiological research, is advanced. This approach to epidemiology, biomedicine, human and cultural ecology, focuses on the following theoretical points of view: (i) the intrinsic non-linearity of natural dynamics, (ii) the role of fluctuations in the evolution of self-organized systems, (iii) the reformulation of the homeostasis concept, through the hypothesis of the co-existence of different levels of boundaries of stability (the non-linear processes of adaptation) and the dynamics of transitions (the physiological jumps) between them, (iv) the image of the psychobiological status in peripheral cells (i.e. blood lymphocytes) due to the morphofunctional unity of neuroendocrine and immune systems, (v) the significance of emic/ethic operations used in cultural anthropology. In this conceptual framework, transitions among migrants or within populations, following sudden changes in cultural patterns, are particular events that can also be very interesting for epidemiological research; they can leave the marks of underlying intertwined psychobehavioral, metabolic and immune physiology; they can also be informative as regards the modulation of autonomy, disability, morbidity and mortality curves.

Anthropology, Cultural↗
PubMed1996

Pds1p is required for faithful execution of anaphase in the yeast, Saccharomyces cerevisiae.

To identify mutations that cause defects in mitosis, a collection of mutants in Saccharomyces cerevisiae was screened by a rapid visual assay for abnormal chromosome segregation. From this screen we identified one mutation, pds1-1 that was independently identified in an alternative screen for mutants that exhibit inviability after transient exposure to nocodazole and precocious disassociation of sister chromatids (Guacci, V., A. Yamamoto, A. Strunnikov, J. Kingsbury, E. Hogan, P. Meluh, and D. Koshland. 1993. CSH Symp. Quant. Biol. 58:677-685; Yamamoto, T.J., G. Li, B. Schaar, I. Szilak, and D.W. Cleveland. 1992. Nature (Lond.). 359:536-539). At 23 degrees C pds1-1 mutants exhibit frequent cell death and a 300-fold increase in chromosome loss compared to wild type. At 37 degrees C pds1-1 cells fail to elongate their spindles during anaphase. This spindle defect of pds1 mutants results from a temperature-sensitive step that occurs around the G1/S boundary about the time of spindle assembly. In the absence of spindle elongation pds1 mutants undergo cytokinesis, leading to the missegregation of both chromosomes and spindle pole bodies. After abnormal cell division pds1-1 mutants also initiate new rounds of DNA replication, spindle pole body duplication, and bud formation. Thus, in the pds1-1 mutant at 37 degrees C, cell cycle progression is uncoupled from the completion of anaphase. A pds1 deletion allele has similar phenotypes to the original allele. Taken together these results suggest that Pds1 protein plays an important role in chromosome segregation at 23 degrees C and an essential role for this process at 37 degrees C. The PDS1 gene encodes a novel 42-kD nuclear protein that has both basic and acidic domains. The level of PDS1 mRNA varies with the cell cycle with maximal accumulation around the G1/S boundary. The stability of Pds1 protein also appears to change during the cell cycle as overproduced Pds1p is stable in S and M but degraded in early G1. Therefore, expression of Pds1p is regulated apparently both transcriptionally and postranslationally during the cell cycle. The phenotypes of pds1 mutants and expression pattern of Pds1p are discussed in the context of other spindle-defective mutants and the knowledge that Pds1 protein is an inhibitor of anaphase (Yamamoto, T.J., G. Li, B. Schaar, I. Szilak, and D.W. Cleveland. 1992. Nature (Lond.). 359:536-539).

Amino Acid Sequence↗
PubMed2003

Local density approach for modeling fluids with density-dependent interactions.

In a recent paper [Phys. Rev. Lett. 86, 2038 (2001)] a simple fluid with a particular density-dependent pair potential was shown to exhibit, together with the vapor-liquid transition, a liquid-liquid phase separation and it was evidenced that, in order to adequately define the correct boundaries of stability, a simulation procedure based on the use of local densities had to be devised. It was found that for certain thermodynamic states the potential drives the system toward a phase separation that is otherwise frustrated by the change in the interactions induced by density fluctuations. Therefore, when integral equations or global density simulations are used, the critical points estimated from the thermodynamics are not associated with divergent correlations and vice versa. Here, we will explore in depth this fluid and introduce a detailed account of the proposed local density simulation technique. The results presented bear general significance for density-dependent potentials, like those of liquid metals or charge-stabilized colloids.

Journal Article↗
PubMed2004

Criticality, tricriticality, and crystallization in discretized models of electrolytes.

The Restricted Primitive Model of ionic systems is studied within a field-theoretic approach in order to provide a theoretic basis for the qualitative difference in the phase diagrams obtained in simulations for sigma/a=1,sigma/a=2, and sigma/a>/=3 ( a is the lattice constant and sigma is the ion diameter). The evolution of the phase diagrams from the case sigma/a=1 to the case sigma/a=square root[2] [nearest-neighbor ( NN ) occupancy excluded] is studied in the model with NN repulsion, 0</=J</= infinity, supplementing Coulomb forces. The boundary of stability of the charge-disordered phase with respect to short-wavelength charge fluctuations and the tricritical point are found in a mean-field ( MF ) approximation. Next, the effect of fluctuations is studied and we find that for J exceeding a particular value J0 a fluctuation-induced first-order phase transition should be expected instead of the continuous transition found in MF. At J= J0 the line of continuous transitions splits into two lines enclosing the two-phase region, whose thickness increases from zero when J>/= J0 increases. We argue that this transition corresponds to formation of a bcc ionic crystal. For high densities the ions form an fcc crystal, for which we find a fluctuation-induced first-order charge-ordered-charge-disordered transition, in agreement with recent simulation studies. Our results also shed light on the simulation results obtained for an off-lattice ionic system, for which a schematic phase diagram is constructed.

Journal Article↗