Mean field approximation of two coupled populations of excitable units

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the inter-ensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical inter-population couplings.Comment: 5 figure

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Ca2+-induced changes in energy metabolism and viability of melanoma cells

Cancer cells are characterized by a high rate of glycolysis, which is their primary energy source. We show here that a rise in intracellular-free calcium ion (Ca2+), induced by Ca2+-ionophore A23187, exerted a deleterious effect on glycolysis and viability of B16 melanoma cells. Ca2+-ionophore caused a dose-dependent detachment of phosphofructokinase (EC 2.7.1.11), one of the key enzymes of glycolysis, from cytoskeleton. It also induced a decrease in the levels of glucose 1,6-bisphosphate and fructose 1,6-bisphosphate, the two stimulatory signal molecules of glycolysis. All these changes occurred at lower concentrations of the drug than those required to induce a reduction in viability of melanoma cells. We also found that low concentrations of Ca2+-ionophore induced an increase in adenosine 5′-triphosphate (ATP), which most probably resulted from the increase in mitochondrial-bound hexokinase, which reflects a defence mechanism. This mechanism can no longer operate at high concentrations of the Ca2+-ionophore, which causes a decrease in mitochondrial and cytosolic hexokinase, leading to a drastic fall in ATP and melanoma cell death. The present results suggest that drugs which are capable of inducing accumulation of intracellular-free Ca2+ in melanoma cells would cause a reduction in energy-producing systems, leading to melanoma cell death. © 1999 Cancer Research Campaig

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Multi-gene phylogeny for Ophiostoma spp. reveals two new species from Protea infructescences

Ophiostoma represents a genus of fungi that are mostly arthropod-dispersed and have a wide global distribution. The best known of these fungi are carried by scolytine bark beetles that infest trees, but an interesting guild of Ophiostoma spp. occurs in the infructescences of Protea spp. native to South Africa. Phylogenetic relationships between Ophiostoma spp. from Protea infructescences were studied using DNA sequence data from the β-tubulin, 5.8S ITS (including the flanking internal transcribed spacers 1 and 2) and the large subunit DNA regions. Two new species, O. phasma sp. nov. and O. palmiculminatum sp. nov. are described and compared with other Ophiostoma spp. occurring in the same niche. Results of this study have raised the number of Ophiostoma species from the infructescences of serotinous Protea spp. in South Africa to five. Molecular data also suggest that adaptation to the Protea infructescence niche by Ophiostoma spp. has occurred independently more than once

Coupling and Elastic Loading Affect the Active Response by the Inner Ear Hair Cell Bundles

Active hair bundle motility has been proposed to underlie the amplification mechanism in the auditory endorgans of non-mammals and in the vestibular systems of all vertebrates, and to constitute a crucial component of cochlear amplification in mammals. We used semi-intact in vitro preparations of the bullfrog sacculus to study the effects of elastic mechanical loading on both natively coupled and freely oscillating hair bundles. For the latter, we attached glass fibers of different stiffness to the stereocilia and observed the induced changes in the spontaneous bundle movement. When driven with sinusoidal deflections, hair bundles displayed phase-locked response indicative of an Arnold Tongue, with the frequency selectivity highest at low amplitudes and decreasing under stronger stimulation. A striking broadening of the mode-locked response was seen with increasing stiffness of the load, until approximate impedance matching, where the phase-locked response remained flat over the physiological range of frequencies. When the otolithic membrane was left intact atop the preparation, the natural loading of the bundles likewise decreased their frequency selectivity with respect to that observed in freely oscillating bundles. To probe for signatures of the active process under natural loading and coupling conditions, we applied transient mechanical stimuli to the otolithic membrane. Following the pulses, the underlying bundles displayed active movement in the opposite direction, analogous to the twitches observed in individual cells. Tracking features in the otolithic membrane indicated that it moved in phase with the bundles. Hence, synchronous active motility evoked in the system of coupled hair bundles by external input is sufficient to displace large overlying structures

Estrogen receptor transcription and transactivation: Estrogen receptor alpha and estrogen receptor beta - regulation by selective estrogen receptor modulators and importance in breast cancer

Estrogens display intriguing tissue-selective action that is of great biomedical importance in the development of optimal therapeutics for the prevention and treatment of breast cancer, for menopausal hormone replacement, and for fertility regulation. Certain compounds that act through the estrogen receptor (ER), now referred to as selective estrogen receptor modulators (SERMs), can demonstrate remarkable differences in activity in the various estrogen target tissues, functioning as agonists in some tissues but as antagonists in others. Recent advances elucidating the tripartite nature of the biochemical and molecular actions of estrogens provide a good basis for understanding these tissue-selective actions. As discussed in this thematic review, the development of optimal SERMs should now be viewed in the context of two estrogen receptor subtypes, ERα and ERβ, that have differing affinities and responsiveness to various SERMs, and differing tissue distribution and effectiveness at various gene regulatory sites. Cellular, biochemical, and structural approaches have also shown that the nature of the ligand affects the conformation assumed by the ER-ligand complex, thereby regulating its state of phosphorylation and the recruitment of different coregulator proteins. Growth factors and protein kinases that control the phosphorylation state of the complex also regulate the bioactivity of the ER. These interactions and changes determine the magnitude of the transcriptional response and the potency of different SERMs. As these critical components are becoming increasingly well defined, they provide a sound basis for the development of novel SERMs with optimal profiles of tissue selectivity as medical therapeutic agents