Capacitance bilayer membranes

As first shown by Hladky and Haydon 7,8), it is possible to observe the current due to a single transmembrane channel by using extensions of the planar lipid hilaver approach of Mueller and Rudin 9). The basic system is shown in Fig. 2 and is commonly referred to as the black lipid membrane (BLM) method. This is because, as the lipid in the hole between the two chambers thins, the areas that have become planar bilayers are seen as black. Additional terms are bilayer lipid membranes or planar lipid bilayer membranes. These lipid bilayer membranes, particularly those which are solvent free, have capacitances which are very close to those of biological membranes. 

A variety of methods have been developed to study exocytosis. Neurotransmitter and hormone release can be measured by the electrical effects of released neurotransmitter or hormone on postsynaptic membrane receptors, such as the neuromuscular junction (NMJ see below), and directly by biochemical assay. Another direct measure of exocytosis is the increase in membrane area due to the incorporation of the secretory granule or vesicle membrane into the plasma membrane. This can be measured by increases in membrane capacitance (Cm). Cm is directly proportional to membrane area and is defined as Cm = QAJV, where Cm is the membrane capacitance in farads (F), Q is the charge across the membrane in coulombs (C), V is voltage (V) and Am is the area of the plasma membrane (cm2). The specific capacitance, Q/V, is the amount of charge that must be deposited across 1 cm2 of membrane to change the potential by IV. The specific capacitance, mainly determined by the thickness and dielectric constant of the phospholipid bilayer membrane, is approximately 1 pF/cm2 for intracellular organelles and the plasma membrane. Therefore, the increase in plasma membrane area due to exocytosis is proportional to the increase in Cm. 

First of all, the capacitance of lecithin-hexadecane membrane is about 0.62 yF/cm. This value is smaller than the capacitance of biological membranes, i.e., 1 yF/cm2. The difference is perhaps partially due to the absence of proteins in artificial membranes. In addition, it is known that the presence of solvents decreases the values of membrane capacitance. For example, membranes formed by the Montal-Mueller Method (21), which are believed to be free of solvents, have a capacitance of 0.7 yF/cm2 (22). Thus, the capacitance of bilayer membranes shown in this figure may be in error by about 0.1 yF/cm2 because of the presence of solvent molecules. However, it is more important to note that membrane capacitance is independent of frequency, which provides unequivocal evidence that there is no relaxation process in lipid membranes in this frequency range. Coster and Smith (23) reported that they observed a frequency dispersion of membrane capacitance of artificial layers at very... 

The frequency response of various chemical constituents of nerve membrane was studied. Biological membranes in general consist of lipids and proteins. Firstly, impedance characteristics of artificial lipid bilayer membranes are examined using lecithin-hexadecane preparations. It was observed that the capacitance of plain lipid membranes was independent of frequency between 100 Hz and 20 KHz. Moreover, application of external voltages has no effect up to 200 mV. Secondly, membrane capacitance and conductance of nerve axon were investigated. There are three components in nerve membranes, i.e., conductance, capaci-... 

At frequencies below 63 Hz, the double-layer capacitance began to dominate the overall impedance of the membrane electrode. The electric potential profile of a bilayer membrane consists of a hydrocarbon core layer and an electrical double layer (49). The dipolar potential, which originates from the lipid bilayer head-group zone and the incorporated protein, partially controls transmembrane ion transport. The model equivalent circuit presented here accounts for the response as a function of frequency of both the hydrocarbon core layer and the double layer at the membrane-water interface. The value of Cdl from the best curve fit for the membrane-coated electrode is lower than that for the bare PtO interface. For the membrane-coated electrode, the model gives a polarization resistance, of 80 kfl compared with 5 kfl for the bare PtO electrode. Formation of the lipid membrane creates a dipolar potential at the interface that results in higher Rdl. The incorporated rhodopsin may also extend the double layer, which makes the layer more diffuse and, therefore, decreases C. ... 

PhotocontroUed Transport Phenomenon in Lipid Bilayer Membranes. Photocontrolled ion transport across lipid bilayer membranes using photoresponsive compounds such as azobenzene derivatives has been of great interest for potential applications in optoelectronic devices and optical transducers. Most research has exploited membrane capacitance change because of the disruption of membrane structures resulting from photoisomerization of azoben-zene-containing compounds incorporated into the lipid bilayers. Others have used the volumetric change of azobenzene moieties associated with photoisomerization. 

Techniques for using a silicon-based light addressable potentiometric sensor (LAPS) to measure the electrical properties of phospholipid bilayer membranes were developed. Membrane conductance, capacitance, and potential could all be measured when the membrane was painted on an aperture between the silicon surface and a controlling electrode. The sensor was tested by observing changes in membrane properties on the addition of simple ion carriers and channels. 

Planar bilayer membranes are characterized by their electrical response since the insulating bilayer membrane and the two conducting ionic solutions are electrically equivalent to a capacitor with the membrane as the dielectric. The current through a capacitor is directly proportional to the rate of change of the voltage on the capacitor, i = C dV/dt. The capacitance, in turn, is related to the thickness of the membrane and its dielectric constant. The membrane capacitance is determined by applying a ramp potential with a constant dV/dt across the membrane to give a constant current that can be converted to the mem-... 

For a simple planar bilayer membrane the impedance studies produce one semicircle on the complex plane plots according to the model RsiRmCm), from which the resistance, R, and capacitance, Cm, of the membrane can be simply determined. 

Let us look at the example of interactions between phosphatidylethanolamine and a-tocopherol in bilayer membranes [515]. In this case, the formation of lipid domains consisting of phosphatidylethanolamine, 1, and phosphatidylethanolami-ne-a-tocopherol, 3, of a certain composition is observed. Assuming that only these two domains exist in the membrane and that the electrical parameters are additive, one can write an equation for the capacitance and resistance of the membrane ... 

Weaver JC, Powell KT, Mintzer RA, Ling H, Sloan SR (1984) The electrical capacitance of bilayer membranes the contribution of transient aqueous pores. Bioelectrochem Bioenerg 12 393-412... 

EXAMPLE 21.3 The capacitance of a nerve cell membrane. Assume that a nerve cell is a long cylinder enclosed by a thin planar bilayer membrane of lipids (see Figure 21.7). You can treat the lipid bilayer as a parallel plate capacitor. Lipid bilayers have oil-like interiors, for which we will assume D = 2, and thickness approximately d 20 A. Equation (21.13) gives the capacitance per unit area as... 

With a method in hand for routinely constructing cytochrome c oxidase modified electrodes that exhibited direct electron transfer between the electrode and the oxidase, amperometry was used to detect reduced cytochrome c in solution at the oxidase-modified electrodes in a flow injection analysis format [69]. The dialysis cell was equipped with a wall jet inlet to direct cytochrome c solution past the oxidase-modified electrodes. Figure 12 shows the current response for three sequential reduced cytochrome c injections. Control experiments conducted at bilayer modified electrodes containing no oxidase showed current responses that are about 2% of those shown in Figure 12. This response may be due to changes in electrode capacitance and/or cytochrome c reacting at bilayer defect sites on the electrode. QCM measurements showed that no cytochrome c incorporated into the bilayer. However, cytochrome c was electrostatically held at the surface of the bilayer membrane at lower ionic strength [69]. 

Simple considerations show that the membrane potential cannot be treated with computer simulations, and continuum electrostatic methods may constimte the only practical approach to address such questions. The capacitance of a typical lipid membrane is on the order of 1 j.F/cm-, which corresponds to a thickness of approximately 25 A and a dielectric constant of 2 for the hydrophobic core of a bilayer. In the presence of a membrane potential the bulk solution remains electrically neutral and a small charge imbalance is distributed in the neighborhood of the interfaces. The membrane potential arises from... 

A = approximate area of the bilayer lipid membrane G = membrane conductance Gj = specific membrane conductance Cm = membrane capacitance C, = specific membrane capacitance. 

A solution of brain lipids was brushed across a small hole in a 5-ml. polyethylene pH cup immersed in an electrolyte solution. As observed under low power magnification, the thick lipid film initially formed exhibited intense interference colors. Finally, after thinning, black spots of poor reflectivity suddenly appeared in the film. The black spots grew rapidly and evenutally extended to the limit of the opening (5, 10). The black membranes have a thickness ranging from 60-90 A. under the electron microscope. Optical and electrical capacitance measurements have also demonstrated that the membrane, when in the final black state, corresponds closely to a bimolecular leaflet structure. Hence, these membranous structures are known as bimolecular, black, or bilayer lipid membranes (abbreviated as BLM). The transverse electrical and transport properties of BLM have been studied usually by forming such a structure interposed between two aqueous phases (10, 17). 

Movileanu et al. [127] used reconstituted planar PC bilayers (black lipid bilayers) to study the effect exerted by quercetin (29) on their electrical properties. Quercetin inserted into model membranes, which resulted in an increase in their conductance and electrical capacitance. Clear pH dependence of quercetin (29) binding to membranes was observed. Capacitance changes were the most pronounced at low pH, which was attributed to the deeper insertion of quercetin (29) into the bilayer in acidic conditions. The authors postulated that quercetin inside the membrane interacted with both the hydrophobic domain and polar headgroups of PC. 

Figure 1. Membrane capacitance and conductance of lecithin bilayers. Curve 1 membrane capacitance ((— X —) measured values at high frequencies before correction for series resistance) Curve 2 membrane conductance ((— X —) measured conductances without correction for series resistance).

Channel activity is best studied electrochemically as charged species cross a cell membrane or artificial lipid bilayer. There is a difference in electrical potential between the interior and exterior of a cell leading to the membrane itself having a resting potential between -50 and -100 mV. This can be determined by placing a microelectrode inside the cell and measuring the potential difference between it and a reference electrode placed in the extracellular solution. Subsequent changes in electrical current or capacitance are indicative of a transmembrane flux of ions. 

Electrical properties of membranes. Biological membranes serve as barriers to the passage of ions and polar molecules, a fact that is reflected in their high electrical resistance and capacitance. The electrical resistance is usually 10 ohms cm, while the capacitance is 0.5-1.5 microfarad (pF) cm . The corresponding values for artificial membranes are 10 ohms cm and 0.6 - 0.9 pF cm . The lower resistance of biological membranes must result from the presence of proteins and other ion-carrying substances or of pores in the membranes. The capacitance values for the two types of membrane are very close to those expected for a bilayer with a thickness of 2.5 nm and a dielectric constant of 2. 4 The electrical potential gradient is steep. 

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