Membranes nonlinear systems

Siegel, R.A. (2010) Oscillatory systems created with polymer membranes. Nonlinear Dynamics with Polymers, Wiley-Vch Verlag GmbH. 

Time-dependent flux decline is plotted in Figure 8. The C02 permeation rate, in units of SCFH/ft2.100 psi, was calculated from performance data for the fifteen elements in series. This rate corresponds to that which would be obtained for pure CO2 under similar partial pressure differences. After an initial (40 hrs) nonlinear flux decline, the C02 rate experienced a 10% loss over the next 1,000 hours (40 days). As this flux decline is a log/log relationship, only 6% more would be lost over the next three years, the minimum expected element lifetime. Membrane systems can be easily designed to adapt to a changing permeation rate by adjusting the feed flow rates and/or pressure, by allowing for addition of more elements in series after a period of time, and by using a progressive element replacement schedule. 

Abstract Neurotransmission in the nervous system is initiated at presynaptic terminals by fusion of synaptic vesicles with the plasma membrane and subsequent exocytic release of chemical transmitters. Currently, there are multiple methods to detect neurotransmitter release from nerve terminals, each with their own particular advantages and disadvantages. For instance, most commonly employed methods monitor actions of released chemical substances on postsynaptic receptors or artificial substrates such as carbon libers. These methods are closest to the physiological setting because they have a rapid time resolution and they measure the action of the endogenous neurotransmitters rather than the signals emitted by exogenous probes. However, postsynaptic receptors only indirectly report neurotransmitter release in a form modified by the properties of receptors themselves, which are often nonlinear detectors of released substances. Alternatively, released chemical substances... 

Autonomous phenomena in multicellular systems are considered in the section on bioelectric patterning in cell aggregates. A mathematical model is considered which describes the cell aggregate via macroscopic variables--concentrations and voltage. Cells are "smeared out" to formulate the theory in terms of continuum variables. A nonlinear integral operator is introduced to model the intercellular transport that corrects the cruder diffusion-like terms usually assumed. This transport term is explicitly related to the properties of cell membranes. 

Recently Frohlich has extended his ideas to give a possible explanation of the extraordinary high sensitivity of certain biological systems to very weak external electric and magnetic signals (2). The model is a combination of both, a nonlinear chemical reaction, which is based on long range interactions, and a ferroelectric term, which represent the specific dielectric properties of membranes. The model equations read ... 

The possible existence of highly polarized metastable states in biological model membranes has led us to a preliminary model for specific interactions in membranes (14). We have assumed that biomolecules are capable of nonlinear polarization oscillations, when they are sufficiently excited by metabolic energy or by external means, e.g. electric fields. Restricting to the case of two interacting molecules for simplicity, the dynamics of the system is given by a set of nonlinear differential equations for the polarization P. of the molecule i ... 

Finally, Section 2.4 analyses a simplified model of a bursting pancreatic /3-cell [12]. The purpose of this section is to underline the importance of complex nonlinear dynamic phenomena in biomedical systems. Living systems operate under far-from-equilibrium conditions. This implies that, contrary to the conventional assumption of homeostasis, many regulatory mechanisms are actually unstable and produce self-sustained oscillatory dynamics. The electrophysiological processes of the pancreatic /3-cell display (at least) two interacting oscillatory processes A fast process associated with the K+ dynamics and a much slower process associated with the Ca2+ dynamics. Together these two processes can explain the characteristic bursting dynamics in the membrane potential. 

The complete system responses are determined by the interactions, i.e. resonances, between the subthreshold and event-generating mechanisms. Again, in the HPA axis model, these interactions, so far, are rather simple and unidirectional. The circadian pacemaker modulates the H PA feedback loops in a nonlinear multiplicative way but is itself not influenced by the dynamics of the cortisol releasing processes. In contrast, in the neuronal and psychiatric models, the two subsystems are interlinked by a common control variable, the membrane voltage and the disease variable, respectively. These interlinks are a major source of very complex, inclusively chaotic dynamics [96, 111, 112]. 

Spiropyrans show promise for optical recording, three-dimensional optical memories,214 and holography.215 The dyes currently under study for these applications very probably will not be used merely dissolved in a bulk polymer matrix, but will be oriented in films and membranes, or adsorbed or vapor deposited on solid substrates to take advantage of the nonlinear optical properties of the colored forms. For example, thick (0.5 mm) PMMA films of 6-nitro-thiaBIPS can be used to record wavelength-multiplexed volume holograms with an infrared diode laser. This system is impractical at present because of fatigue and poor diffraction efficiencies.216... 

When two electrolyte solutions at different concentrations are separated by an ion--permeable membrane, a potential difference is generally established between the two solutions. This potential difference, known as membrane potential, plays an important role in electrochemical phenomena observed in various biomembrane systems. In the stationary state, the membrane potential arises from both the diffusion potential [1,2] and the membrane boundary potential [3-6]. To calculate the membrane potential, one must simultaneously solve the Nernst-Planck equation and the Poisson equation. Analytic formulas for the membrane potential can be derived only if the electric held within the membrane is assumed to be constant [1,2]. In this chapter, we remove this constant held assumption and numerically solve the above-mentioned nonlinear equations to calculate the membrane potential [7]. 

Most of the phenomena described in this monograph on photoreactive organic thin films are based on the isomerization of units deliberately built into molecules, molecular assemblies, or polymers. Most especially, the spectroscopic and isomerization behavior of these units determines the switching and triggering properties of the photoreactive systems and devices. Information storage and nonlinear optical properties, as well as photo-control of equilibria and of polymer, membrane, and other properties are exploited in applications. 

Recently, Kotowski et al. (1988) immobilized GOD by glutaraldehyde in a conductive lecithin polypyrrole bilayer membrane (BLM). The membrane was formed by polymerization of pyrrole in the presence of ferric chloride and was arranged between two electrodes. Addition of glucose leads to the formation of anodic peaks at 200 mV which reflect the electron transfer from reduced GOD to polypyrrole in the BLM system. The peak current exhibits a nonlinear dependence on the concentration of glucose between 1 and 20 mmol/1. 

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