Biological membranes, capacitance

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. 

Casadio, R., Venturoli, G. and Melandri, B. A. (1988). Evaluation of the electrical capacitance in biological membranes at different phospholipid to protein ratios -a study in photosynthetic bacterial chromatophores based on electrochromic effects, Eur. Biophys. J., 16, 243-253. 

A novel method for the determination of surface charge density at a HMDE coated with a self-assembled phospholipid mono-layer mimicking a biological membrane has been described by Becucci etal. [7] Charge density was calculated by integrating the capacitance current, which flows at the constant potential as a consequence of slight contraction of mercury drop. 

This work led to the important conclusion that the capacitance of all biological membranes, including cellular membranes and those of subcellular organelles, such as mitochondria, is of the order of 1 yF/cm. This value is apparently independent of frequency in the total RF range at low audio frequencies, capacitance values increase with decreasing frequencies due to additional relaxation mechanisms in or near the membranes Q, 26). These mechanisms will not be discussed here and have been summarized elsewhere (1, 26). 

If f<total potential difference applied across the cell is developed across the membrane capacitance. In this limit, the induced membrane potential AV across a spherical cell is AV = 1.5 ER, where E represents the applied external field. Thus the cell samples the external field strength over its dimensions and delivers this integrated voltage to the membranes, which is a few mV at these low frequencies for cells larger than 10 ym and external fields of about 1 V/cm. These transmembrane potentials can be biologically significant. 

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-... 

In electrophysiology modeling biological membranes are typically treated as capacitors with constant capacitance. The basic equation for a capacitor is ... 

The impedance of the skin has been generally modeled by using a parallel resistance/capacitor equivalent circuit (Fig. 4a). The skin s capacitance is mainly attributed to the dielectric properties of the lipid-protein components of the human epidermis [5,8,9,12]. The resistance is associated primarily with the skin s stratum comeum layer [5,8,9,12]. Several extensions to the basic parallel resistor/capacitor circuit model have appeared in the literature [5,8,9,13]. Most involve two modified parallel resistor/capacitor combinations connected in series [5,8,9]. The interpretation of this series combination is that the first parallel resistor/capacitor circuit represents the stratum comeum and the second resistor/capacitor parallel combination represents the deeper tissues [5,8,9]. The modification generally employed is to add another resistance, either in series and/or in parallel with the original parallel resistor/capacitor combination [8,9]. Realize that because all of these circuits contain a capacitance, they will all exhibit a decrease in impedance as the frequency is increased. This is actually what is observed in all impedance measurements of the skin [5,6,8-15]. In addition, note that the capacitance associated with the skin is 10 times less than that calculated for a biological membrane [12]. This... 

Pure lipid membranes are electrical insulators with a specific capacitance of 1 tiF/cm, which separate two electrolytic compartments. The conductance of biological membranes is maiifly determined by highly specialized proteins that act as ion chaimels. For supported membranes to mimic the electrical properties of a biological membrane, it is necessary to measure its electrical characteristics. Even very small defects that are not... 

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. 

In the 1920s, impedance was applied to biological systems, including the resistance and capacitance of cells of vegetables and the dielectric response of blood suspensions. ° Impedance was also applied to muscle fibers, skin tissues, and other biological membranes. " The capacitance of the cell membranes was found to be a function of frequency, and Fricke observed a relationship between the frequency exponent of the impedance and the observed constant phase angle. In 1941, brothers Cole and Cole showed that the frequency-dependent complex... 

Table 9.1 provides the values of membrane resistance (/ ), capacitance (Cm), and thickness d) of artificial BLMs and natural cell membranes [11,18]. The resistance of artificial membranes is much higher than that of biological membranes. This results from the presence of translocators such as peptides and proteins in the cell membranes. The resistance of artificial membranes can however be reduced to the levels of natural cell membranes when ion translocators are inserted. Specific capacitance (C ) is the primary criterion to distinguish between solventless BLMs and black lipid films. Table 9.1 exhibits that the specific capacitance of the solventless BLMs (about 0.9 /itF cm ) approaches the values measured for natural cell membranes, and is almost twice the magnitude observed for black lipid membranes. These values of specific capacitance can be used to estimate the hydrocarbon thickness, d, of membranes using the equation... 

It is known that superoxide forms complexes with Ca ", thereby permitting formation of calcium peroxide. Since the majority of biological membranes translocate Ca or other alkali metal ions, the opportunity for interaction with superoxide within the membrane may be considerable (Ca " and calmodulin are required for superoxide production by leukocytes ). Under pathological circumstances calcium peroxide could be formed and lipid peroxidation initiated. The breakdown of membrane capacitance as a consequence of this may be deleterious in a number of ways. For example, the loss of a critical electric field may remove the driving force for energy-dependent processes associated with charge transfer. On the other hand, circumstances may be established which bring about unrestrained and unmodulated metabolic activity, as in cancer. 

The physical properties of bilayers are different from cell membranes in that they have extremely high resistance (10 J2/cm ) and usually a low capacitance (typically 0.5 tF/cm ). However, when the ionic permeability of bilayers is increased with various agents the resistance falls and the capacitance may increase producing models whose physical characteristics are, superficially at least, similar to biological membranes. 

Satyanarayana S et al (2006) Parylene micro membrane capacitive sensor array for chemical and biological sensing. Sens Actuators B 115 494-502... 

Biological membranes are capacitors. Let s calculate the capacitance of the membrane of a nerve cell. 

Impedimetric biosensors for whole cells have demonstrated two mechanisms in response. Considering the overall impedance of a biological cell as including the resistance and the capacitance of the cell membrane, the presence of intact cell membranes on the electrodes would contribute to the sensor s capacitance and/or resistance, and would determine the current flow and thus the sensor signal. However, when cells are attached to the electrode surface, they are usually separated by a gap of 10 -20 run (up to several hundred nanometers). This aqueous gap between the cell membrane and the electrode surface prevents a direct influence of the cell membrane capacitance on the impedance of the electrode. Therefore, the cell membrane resistances of these attached cells act as resistors on the IME surface and affect the interfacial resistance. The interfacial resistance is best represented as electron transfer resistance in the presence of a redox probe (e. g., [Fe(CN)6] / ) and can be sensitively monitored. Figure 10a presents a representative group of Nyquist plots of the impedance spectroscopic responses of an IME-based biosensor to different cell numbers of E. coli 0157 H7 at 10a antibodies, 10b 4.36 x 10 CFTJ/ml,... 

Since biological membranes quite generally have a specific capacitance of 1 pF/cm, this number transforms into a limit for the size of the membrane and this is 1000 ym, which is, for instance, a circular patch of 35 pm diameter or else a spherical cell with 18 pm diameter. This small size cannot be successfully impaled with electrodes of low enough internal resistance. Therefore measurements of single channel responses seem pretty hopeless with conventional techniques of recording. 

Fig. 2. Electric model used by the method BIS-STEP to interpret current response i to a step voltage of magnitude Vd. The extracellular resistance - Re, intracellular resistance - Ri, and membrane capacitance -Cm, stand for the biological segmental bioelectric impedance model. The capacitances - Ce and resistances - Rb are associated to the impedances of the two electrode-tissue interfaces.

The dielectric response of biological tissue has long been assumed linear. Thus an enzyme is treated as a hard sphere which relaxes linearly in an a. c. field at all but high field strengths [128]. In a suspension of cells, the electric field cannot penetrate to the interior of the cell at the low frequencies currently of interest in nonlinear dielectric spectroscopy [129], and is dropped almost entirely across the outer membrane of the cell which is predominantly capacitive at these frequencies, as was shown in Fig. 4. 

Where, V is the electrical potential difference across the membrane ie. Vm or Em and Ai]/, C = the capacitance of the membrane (dielectric) and q is the number of charges transported across the membrane. The term, A( )m is included as this represents a more consistent nomenclature, and would be better recognised by disciplines outside biology (e.g. Electrochemists), Ai]/, is the form utilised by biochemists (2) and Vm or Em is the form utilised by Physiologists (6). 

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