1.
Action potential
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In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of cells, called excitable cells, which include neurons, muscle cells. In other types of cells, their function is to activate intracellular processes. In muscle cells, for example, a potential is the first step in the chain of events leading to contraction. In beta cells of the pancreas, they provoke release of insulin, action potentials in neurons are also known as nerve impulses or spikes, and the temporal sequence of action potentials generated by a neuron is called its spike train. A neuron that emits an action potential is often said to fire, action potentials are generated by special types of voltage-gated ion channels embedded in a cells plasma membrane. When the channels open they allow a flow of sodium ions, which changes the electrochemical gradient. This then causes more channels to open, producing an electric current across the cell membrane. The process proceeds explosively until all of the ion channels are open. The rapid influx of ions causes the polarity of the plasma membrane to reverse. As the sodium channels close, sodium ions can no longer enter the neuron, potassium channels are then activated, and there is an outward current of potassium ions, returning the electrochemical gradient to the resting state. After an action potential has occurred, there is a transient negative shift, in animal cells, there are two primary types of action potentials. One type is generated by voltage-gated sodium channels, the other by voltage-gated calcium channels, sodium-based action potentials usually last for under one millisecond, whereas calcium-based action potentials may last for 100 milliseconds or longer. In some types of neurons, slow calcium spikes provide the force for a long burst of rapidly emitted sodium spikes. In cardiac muscle cells, on the hand, an initial fast sodium spike provides a primer to provoke the rapid onset of a calcium spike. Nearly all cell membranes in animals, plants and fungi maintain a voltage difference between the exterior and interior of the cell, called the membrane potential. A typical voltage across a cell membrane is –70 mV. In most types of cells the membrane potential usually stays fairly constant, some types of cells, however, are electrically active in the sense that their voltages fluctuate over time
2.
Membrane potential
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Membrane potential is the difference in electric potential between the interior and the exterior of a biological cell. With respect to the exterior of the cell, typical values of membrane potential range from –40 mV to –80 mV, all animal cells are surrounded by a membrane composed of a lipid bilayer with proteins embedded in it. The membrane serves as both an insulator and a barrier to the movement of ions. Ion pumps and ion channels are electrically equivalent to a set of batteries and resistors inserted in the membrane, and therefore create a voltage between the two sides of the membrane. Virtually all eukaryotic cells maintain a non-zero transmembrane potential, usually with a voltage in the cell interior as compared to the cell exterior ranging from –40 mV to –80 mV. The membrane potential has two basic functions, first, it allows a cell to function as a battery, providing power to operate a variety of molecular devices embedded in the membrane. Second, in electrically excitable cells such as neurons and muscle cells, signals are generated by opening or closing of ion channels at one point in the membrane, producing a local change in the membrane potential. This change in the field can be quickly affected by either adjacent or more distant ion channels in the membrane. Those ion channels can open or close as a result of the potential change. In non-excitable cells, and in cells in their baseline states. For neurons, typical values of the potential range from –70 to –80 millivolts, that is. The opening and closing of ion channels can induce a departure from the resting potential and this is called a depolarization if the interior voltage becomes less negative, or a hyperpolarization if the interior voltage becomes more negative. Action potentials are generated by the activation of certain voltage-gated ion channels, in neurons, the factors that influence the membrane potential are diverse. They include numerous types of ion channels, some of which are chemically gated, the membrane potential in a cell derives ultimately from two factors, electrical force and diffusion. Electrical force arises from the attraction between particles with opposite electrical charges and the mutual repulsion between particles with the same type of charge. Diffusion arises from the tendency of particles to redistribute from regions where they are highly concentrated to regions where the concentration is low. Voltage, which is synonymous with difference in potential, is the ability to drive an electric current across a resistance. Indeed, the simplest definition of a voltage is given by Ohms law, V=IR, where V is voltage, I is current and R is resistance
3.
Chloride
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The chloride ion /ˈklɔəraɪd/ is the anion Cl−. It is formed when the element chlorine gains an electron or when a compound such as chloride is dissolved in water or other polar solvents. Chloride salts such as sodium chloride are often soluble in water. It is an essential electrolyte located in all body fluids responsible for maintaining acid/base balance, transmitting nerve impulses and regulating fluid in, less frequently, the word chloride may also form part of the common name of chemical compounds in which one or more chlorine atoms are covalently bonded. For example, methyl chloride, with the standard name chloromethane is a compound with a covalent C−Cl bond in which the chlorine is not an anion. A chloride ion is much larger than an atom,167 and 99 pm. The ion is colorless and diamagnetic, in aqueous solution, it is highly soluble in most cases, however, some chloride salts, such as silver chloride, lead chloride, and mercury chloride are slightly soluble in water. In aqueous solution, chloride is bound by the end of the water molecules. Some chloride-containing minerals include the chlorides of sodium, potassium, and magnesium, called serum chloride, the concentration of chloride in the blood is regulated by the kidneys. A chloride ion is a component of some proteins, e. g. it is present in the amylase enzyme. The chlor-alkali industry is a consumer of the worlds energy budget. This process converts sodium chloride into chlorine and sodium hydroxide, which are used to make many other materials and chemicals, in the petroleum industry, the chlorides are a closely monitored constituent of the mud system. An increase of the chlorides in the mud system may be an indication of drilling into a high-pressure saltwater formation and its increase can also indicate the poor quality of a target sand. Chloride is also a useful and reliable chemical indicator of river / groundwater fecal contamination, as chloride is a non-reactive solute, many water regulating companies around the world utilize chloride to check the contamination levels of the rivers and potable water sources. Chloride salts such as sodium chloride are used to preserve food, chloride is an essential electrolyte, trafficking in and out of cells through chloride channels and playing a key role in maintaining cell homeostasis and transmitting action potentials in neurons. Characteristic concentrations of chloride in model organisms are, in both E. coli and budding yeast are 10-200mM, in mammalian cell 5-100mM and in blood plasma 100mM, chloride can be oxidized but not reduced. The first oxidation, as employed in the process, is conversion to chlorine gas. Chlorine can be oxidized to other oxides and oxyanions including hypochlorite, chlorine dioxide, chlorate
4.
Cable theory
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Classical cable theory uses mathematical models to calculate the electric current along passive neurites, particularly the dendrites that receive synaptic inputs at different sites and times. Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances c m, the capacitance of a neuronal fiber comes about because electrostatic forces are acting through the very thin lipid bilayer. The resistance in series along the fiber r l is due to the significant resistance to movement of electric charge. Cable theory in neuroscience has roots leading back to the 1850s. The models resembled the partial differential equations used by Fourier to describe heat conduction in a wire, the 1870s saw the first attempts by Hermann to model neuronal electrotonic potentials also by focusing on analogies with heat conduction. Further mathematical theories of nerve fiber conduction based on cable theory were developed by Cole and Hodgkin, Offner et al. two key papers from this era are those of Davis and Lorente de Nó and Hodgkin and Rushton. The 1950s saw improvements in techniques for measuring the activity of individual neurons. Thus cable theory became important for analyzing data collected from intracellular microelectrode recordings, scientists like Coombs, Eccles, Fatt, Frank, Fuortes and others now relied heavily on cable theory to obtain functional insights of neurons and for guiding them in the design of new experiments. Note, various conventions of rm exist, here rm and cm, as introduced above, are measured per membrane-length unit. Thus rm is measured in ohm·meters and cm in farads per meter and this is in contrast to Rm and Cm, which represent the specific resistance and capacitance respectively of one unit area of membrane. A current injected into the fiber at position x =0 would move along the inside of the fiber unchanged. The more holes, the faster the water escape from the hose. Similarly, in an axon, some of the current traveling longitudinally through the axoplasm will escape through the membrane, if im is the current escaping through the membrane per length unit, m, then the total current escaping along y units must be y·im. The capacitance will cause a flow of charge towards the membrane on the side of the cytoplasm and this current is usually referred to as displacement current The flow will only take place as long as the membranes storage capacity has not been reached. I c can then be expressed as, where c m is the membranes capacitance, combining equations and gives a first version of a cable equation, which is a second-order partial differential equation. By a simple rearrangement of equation it is possible to make two important terms appear, namely the length constant denoted λ and the time constant denoted τ, the following sections focus on these terms. The length constant, λ, is a parameter that indicates how far a stationary current will influence the voltage along the cable, the larger the value of λ, the farther the charge will flow. The higher the resistance, r l, the smaller the value of λ, the harder it will be for current to travel through the axoplasm
