Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell.
By convention it is written as Vm=Vinside−Voutside, thus a negative membrane potential means the cell interior is negative relative to the outside.It equals the interior potential minus the exterior potential. This is the energy per charge which is required to move a very small positive charge at constant velocity across the cell membrane from the exterior to the interior. Note, though, that if the charge is allowed to change velocity, the change of kinetic energy and production of radiation must be taken into account.
Typical values of membrane potential is normally given in units of millivolts and denoted as mV. In many animal cells, Vm is typically in the order of tens of millivolts. It commonly falls in the range of about −20 mV to −200 mV depending on the cell type and state. For such typical negative membrane potentials, positive work is required to move a positive charge from the interior to the exterior. However, thermal kinetic energy allows ions to overcome the potential difference. For a selectively permeable membrane, this permits a net flow against the gradient.
Although the entire cell is considered negative inside, the fluids in the cell are electrically neutral. The presence of the voltage is due to the thin layer of charge that accumulates at the surfaces of the cell membrane. The cell membrane is only a few nanometers thick, and as such, even a voltage of 100 mV across this thickness generates an electric field that is extremely strong on the cell membrane.
Description
All animal cells are surrounded by a membrane composed of a lipid bilayer with proteins embedded in it. The membrane serves both as a capacitor and as a diffusion barrier to the movement of ions. Ion pumps actively push ions across the membrane and establish concentration gradients across the membrane, and ion channels allow ions to move across the membrane down their electrochemical gradients. Ion channels and ion pumps are transmembrane proteins, and are electrically analogous to resistors and current sources (batteries), and contribute to the voltage across the two sides of the membrane.
All plasma membranes have an electrical potential across them, with the inside usually negative with respect to the outside. 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, it is used for transmitting signals between different parts of a cell.
Signals in neurons and muscle cells
Signals are generated in excitable cells 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 electric field can be quickly sensed by either adjacent or more distant ion channels in the membrane. Those ion channels can then open or close as a result of the potential change, reproducing the signal.
In non-excitable cells, and in excitable cells in their baseline states, the membrane potential is held at a relatively stable value, called the resting potential. For neurons, resting potential is defined as ranging from −80 to −70 millivolts; that is, the interior of a cell has a negative baseline voltage of a bit less than one-tenth of a volt. The opening and closing of ion channels can induce a departure from the resting potential. This is called a depolarization if the interior voltage becomes less negative (say from −70 mV to −60 mV), or a hyperpolarization if the interior voltage becomes more negative (say from −70 mV to −80 mV). In excitable cells, a sufficiently large depolarization can evoke an action potential, in which the membrane potential changes rapidly and significantly for a short time (on the order of 1 to 100 milliseconds), often reversing its polarity. 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 and some of which are voltage-gated. Because voltage-gated ion channels are controlled by the membrane potential, while the membrane potential itself is influenced by these same ion channels, feedback loops that allow for complex temporal dynamics arise, including oscillations and regenerative events such as action potentials.
Ion concentration gradients
Differences in the concentrations of ions on opposite sides of a cellular membrane lead to a voltage called the membrane potential.
Many ions have a concentration gradient across the membrane, including potassium (K+), which is at a high concentration inside and a low concentration outside the membrane. Sodium (Na+) and chloride (Cl−) ions are at high concentrations in the extracellular region, and low concentrations in the intracellular regions. These concentration gradients provide the potential energy to drive the formation of the membrane potential. This voltage is established when the membrane has permeability to one or more ions.
In the simplest case, illustrated in the top diagram ("Ion concentration gradients"), if the membrane is selectively permeable to potassium, these positively charged ions can diffuse down the concentration gradient to the outside of the cell, leaving behind uncompensated negative charges. This separation of charges is what causes the membrane potential.
The system as a whole is electro-neutral. The uncompensated positive charges outside the cell, and the uncompensated negative charges inside the cell, physically line up on the membrane surface and attract each other across the lipid bilayer. Thus, the membrane potential is physically located only in the immediate vicinity of the membrane. It is the separation of these charges across the membrane that is the basis of the membrane voltage.
The top diagram is only an approximation of the ionic contributions to the membrane potential. Other ions including sodium, chloride, calcium, and others play a more minor role, even though they have strong concentration gradients, because they have more limited permeability than potassium.
Physical basis The membrane potential in a cell derives ultimately from two factors: electrical force and diffusion. Electrical force arises from the mutual attraction between particles with opposite electrical charges (positive and negative) and the mutual repulsion between particles with the same type of charge (both positive or both negative). Diffusion arises from the statistical tendency of particles to redistribute from regions where they are highly concentrated to regions where the concentration is low.
Voltage
Voltage, which is synonymous with difference in electrical potential, is the ability to drive an electric current across a resistance. Indeed, the simplest definition of a voltage is given by Ohm's law: V=IR, where V is voltage, I is current and R is resistance. If a voltage source such as a battery is placed in an electrical circuit, the higher the voltage of the source the greater the amount of current that it will drive across the available resistance. The functional significance of voltage lies only in potential differences between two points in a circuit. The idea of a voltage at a single point is meaningless. It is conventional in electronics to assign a voltage of zero to some arbitrarily chosen element of the circuit, and then assign voltages for other elements measured relative to that zero point. There is no significance in which element is chosen as the zero point—the function of a circuit depends only on the differences not on voltages per se. However, in most cases and by convention, the zero level is most often assigned to the portion of a circuit that is in contact with ground.
The same principle applies to voltage in cell biology. In electrically active tissue, the potential difference between any two points can be measured by inserting an electrode at each point, for example one inside and one outside the cell, and connecting both electrodes to the leads of what is in essence a specialized voltmeter. By convention, the zero potential value is assigned to the outside of the cell and the sign of the potential difference between the outside and the inside is determined by the potential of the inside relative to the outside zero.
In mathematical terms, the definition of voltage begins with the concept of an electric field , a vector field assigning a magnitude and direction to each point in space. In many situations, the electric field is a conservative field, which means that it can be expressed as the gradient of a scalar function , that is, . This scalar field is referred to as the voltage distribution. The definition allows for an arbitrary constant of integration—this is why absolute values of voltage are not meaningful. In general, electric fields can be treated as conservative only if magnetic fields do not significantly influence them, but this condition usually applies well to biological tissue.
Because the electric field is the gradient of the voltage distribution, rapid changes in voltage within a small region imply a strong electric field; on the converse, if the voltage remains approximately the same over a large region, the electric fields in that region must be weak. A strong electric field, equivalent to a strong voltage gradient, implies that a strong force is exerted on any charged particles that lie within the region.
Ions and the forces driving their motion
Electrical signals within biological organisms are, in general, driven by ions.Johnston and Wu, p. 9. The most important cations for the action potential are sodium (Na+) and potassium (K+).Bullock, Orkand, and Grinnell, pp. 140–41. Both of these are monovalent cations that carry a single positive charge. Action potentials can also involve calcium (Ca2+),Bullock, Orkand, and Grinnell, pp. 153–54. which is a divalent cation that carries a double positive charge. The chloride anion (Cl−) plays a major role in the action potentials of some algae, but plays a negligible role in the action potentials of most animals.Schmidt-Nielsen, p. 483.
Ions cross the cell membrane under two influences: diffusion and electric fields. A simple example wherein two solutions—A and B—are separated by a porous barrier illustrates that diffusion will ensure that they will eventually mix into equal solutions. This mixing occurs because of the difference in their concentrations. The region with high concentration will diffuse out toward the region with low concentration. To extend the example, let solution A have 30 sodium ions and 30 chloride ions. Also, let solution B have only 20 sodium ions and 20 chloride ions. Assuming the barrier allows both types of ions to travel through it, then a steady state will be reached whereby both solutions have 25 sodium ions and 25 chloride ions. If, however, the porous barrier is selective to which ions are let through, then diffusion alone will not determine the resulting solution. Returning to the previous example, let's now construct a barrier that is permeable only to sodium ions. Now, only sodium is allowed to diffuse cross the barrier from its higher concentration in solution A to the lower concentration in solution B. This will result in a greater accumulation of sodium ions than chloride ions in solution B and a lesser number of sodium ions than chloride ions in solution A.