Membrane potential (also transmembrane potential or membrane voltage) is the difference in electrical potential between the interior and the exterior of a biological cell. Typical values of membrane potential range from –40 mV to –80 mV.
All animal cells are surrounded by a plasma membrane composed of a lipid bilayer with a variety of types of proteins embedded in it. The membrane potential arises primarily from the interaction between the membrane and the actions of two types of transmembrane proteins embedded in the plasma membrane. The membrane serves as both an insulator and a diffusion barrier to the movement of ions. Ion transporter/pump proteins actively push ions across the membrane to establish concentration gradients across the membrane, and ion channels allow ions to move across the membrane down those concentration gradients, a process known as facilitated diffusion. In the most fundamental example of this, the ion transporter Na+/K+-ATPase pumps sodium cations from the inside to the outside, and potassium cations from the outside to the inside of the cell. This establishes two concentration gradients: a gradient for sodium where its concentration is much higher outside than inside the cell, and a gradient for potassium where its concentration is much higher inside the cell than outside. Transmembrane potassium-selective leak channels allow potassium ions to diffuse across the membrane, down the concentration gradient that was established by the ATPase, creating a charge separation, and thus a voltage, across the membrane. In almost all cases, the ion that determines the so-called "resting" membrane potential of a cell is K+, although other ions do contribute in more minor ways. By convention, the sign of the membrane potential is the voltage inside relative to ground outside the cell. In the case of K+, its diffusion down its concentration gradient (toward the outside of the cell, in this case) creates transmembrane voltage that is negative relative to the outside of the cell, and typically –60 to –80 millivolts (mV) in amplitude.
Virtually all eukaryotic cells (including cells from animals, plants, and fungi) maintain a nonzero transmembrane potential, usually with a negative voltage in the cell interior as compared to the cell exterior. 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 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 electric field can quickly be detected by either adjacent or more distant ion channels in the membrane. Those ion channels can then depolarize, 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, typical values of the resting potential range from –70 to –80 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 more positive (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 that are chemically gated and some that 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.
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 (due to thermal energy).
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 E, 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 V, that is, E = –∇V. This scalar field V is referred to as the voltage distribution. Note that 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. The most important cations for the action potential are sodium (Na+) and potassium (K+). Both of these are monovalent cations that carry a single positive charge. Action potentials can also involve calcium (Ca2+), 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.
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. Since solution B has a lower concentration of both sodium and chloride, the barrier will attract both ions from solution A. However, only sodium will travel through the barrier. This will result in an accumulation of sodium in solution B. Since sodium has a positive charge, this accumulation will make solution B more positive relative to solution A. Positive sodium ions will be less likely to travel to the now-more-positive B solution. This constitutes the second factor controlling ion flow, namely electric fields. The point at which this electric field completely counteracts the force due to diffusion is called the equilibrium potential. At this point, the net flow of this specific ion (in this case sodium) is zero.
Every animal cell is enclosed in a plasma membrane, which has the structure of a lipid bilayer with many types of large molecules embedded in it. Because it is made of lipid molecules, the plasma membrane intrinsically has a high electrical resistivity, in other words a low intrinsic permeability to ions. However, some of the molecules embedded in the membrane are capable either of actively transporting ions from one side of the membrane to the other or of providing channels through which they can move.
In electrical terminology, the plasma membrane functions as a combined resistor and capacitor. Resistance arises from the fact that the membrane impedes the movement of charges across it. Capacitance arises from the fact that the lipid bilayer is so thin that an accumulation of charged particles on one side gives rise to an electrical force that pulls oppositely-charged particles toward the other side. The capacitance of the membrane is relatively unaffected by the molecules that are embedded in it, so it has a more or less invariant value estimated at about 2 µF/cm2 (the total capacitance of a patch of membrane is proportional to its area). The conductance of a pure lipid bilayer is so low, on the other hand, that in biological situations it is always dominated by the conductance of alternative pathways provided by embedded molecules. Thus, the capacitance of the membrane is more or less fixed, but the resistance is highly variable.
The thickness of a plasma membrane is estimated to be about 7-8 nanometers. Because the membrane is so thin, it does not take a very large transmembrane voltage to create a strong electric field within it. Typical membrane potentials in animal cells are on the order of 100 millivolts (that is, one tenth of a volt), but calculations show that this generates an electric field close to the maximum that the membrane can sustain—it has been calculated that a voltage difference much larger than 200 millivolts could cause dielectric breakdown, that is, arcing across the membrane.