they can still have very different equilibrium potentials, provided their outside and/or inside concentrations differ. take, for example, the equilibrium potentials of potassium and sodium in neurons. the potassium equilibrium potential ek is −84 mv with 5 mm potassium outside and 140 mm inside. on the other hand, the sodium equilibrium potential, ena, is approximately +66 mv with approximately 12 mm sodium inside and 140 mm outside. changes to membrane potential during development a neuron's resting membrane potential actually changes during the development of an organism. in order for a neuron to eventually adopt its full adult function, its potential must be tightly regulated during development. as an organism progresses through development the resting membrane potential becomes more negative. glial cells are also differentiating and proliferating as development progresses in the brain. the addition of these glial cells increases the organism's ability to regulate extracellular potassium. the drop in extracellular potassium can lead to a decrease in membrane potential of 35 mv. cell excitability cell excitability is the change in membrane potential that is necessary for cellular responses in various tissues. cell excitability is a property that is induced during early embriogenesis. excitability of a cell has also been defined as the ease with which a response may be triggered. the resting and threshold potentials forms the basis of cell excitability and these processes are fundamental for the generation of graded and action potentials. the most important regulators of cell excitability are the extracellular electrolyte concentrations (i.e. na+, k+, ca2+, cl−, mg2+) and associated proteins. important proteins that regulate cell excitability are voltage-gated ion channels, ion transporters (e.g. na+/k+-atpase, magnesium transporters, acid–base transporters), membrane receptors and hyperpolarization-activated cyclic-nucleotide-gated channels. for example, potassium channels and calcium-sensing receptors are important regulators of excitability in neurons, cardiac myocytes and many other excitable cells like astrocytes. calcium ion is also the most important second messenger in excitable cell signaling. activation of synaptic receptors initiates long-lasting changes in neuronal excitability. thyroid, adrenal and other hormones also regulate cell excitability, for example, progesterone and estrogen modulate myometrial smooth muscle cell excitability. many cell types are considered to have an excitable membrane. excitable cells are neurons, myocytes (cardiac, skeletal, smooth), vascular endothelial cells, pericytes, juxtaglomerular cells, interstitial cells of cajal, many types of epithelial cells (e.g. beta cells, alpha cells, delta cells, enteroendocrine cells, pulmonary neuroendocrine cells, pinealocytes), glial cells (e.g. astrocytes), mechanoreceptor cells (e.g. hair cells and merkel cells), chemoreceptor cells (e.g. glomus cells, taste receptors), some plant cells and possibly immune cells. astrocytes display a form of non-electrical excitability based on intracellular calcium variations related to the expression of several receptors through which they can detect the synaptic signal. in neurons, there are different membrane properties in some portions of the cell, for example, dendritic excitability endows neurons with the capacity for coincidence detection of spatially separated inputs. equivalent circuit equivalent circuit for a patch of membrane, consisting of a fixed capacitance in parallel with four pathways each containing a battery in series with a variable conductance electrophysiologists model the effects of ionic concentration differences, ion channels, and membrane capacitance in terms of an equivalent circuit, which is intended to represent the electrical properties of a small patch of membrane. the equivalent circuit consists of a capacitor in parallel with four pathways each consisting of a battery in series with a variable conductance. the capacitance is determined by the properties of the lipid bilayer, and is taken to be fixed. each of the four parallel pathways comes from one of the principal ions, sodium, potassium, chloride, and calcium. the voltage of each ionic pathway is determined by the concentrations of the ion on each side of the membrane; see the reversal potential section above. the conductance of each ionic pathway at any point in time is determined by the states of all the ion channels that are potentially permeable to that ion, including leakage channels, ligand-gated channels, and voltage-gated ion channels. reduced circuit obtained by combining the ion-specific pathways using the goldman equation for fixed ion concentrations and fixed values of ion channel conductance, the equivalent circuit can be further reduced, using the goldman equation as described below, to a circuit containing a capacitance in parallel with a battery and conductance. in electrical terms, this is a type of rc circuit (resistance-capacitance circuit), and its electrical properties are very simple. starting from any initial state, the current flowing across either the conductance or the capacitance decays with an exponential time course, with a time constant of τ = rc, where c is the capacitance of the membrane patch, and r = 1/gnet is the net resistance. for realistic situations, the time constant usually lies in the 1—100 millisecond range. in most cases, changes in the conductance of ion channels occur on a faster time scale, so an rc circuit is not a good approximation; however, the differential equation used to model a membrane patch is commonly a modified version of the rc circuit equation. resting potential when the membrane potential of a cell goes for a long period of time without changing significantly, it is referred to as a resting potential or resting voltage. this term is used for the membrane potential of non-excitable cells, but also for the membrane potential of excitable cells in the absence of excitation. in excitable cells, the other possible states are graded membrane potentials (of variable amplitude), and action potentials, which are large, all-or-nothing rises in membrane potential that usually follow a fixed time course. excitable cells include neurons, muscle cells, and some secretory cells in glands. even in other types of cells, however, the membrane voltage can undergo changes in response to environmental or intracellular stimuli. for example, depolarization of the plasma membrane appears to be an important step in programmed cell death. the interactions that generate the resting potential are modeled by the goldman equation. this is similar in form to the nernst equation shown above, in that it is based on the charges of the ions in question, as well as the difference between their inside and outside concentrations. however, it also takes into consideration the relative permeability of the plasma membrane to each ion in question. e m = r t f ln ⁡ ( p k [ k + ] o u t + p n a [ n a + ] o u t + p c l [ c l − ] i n p k [ k + ] i n + p n a [ n a + ] i n + p c l [ c l − ] o u t ) =\ln }_ }+p_ }_ }+p_ }_ }} }_ }+p_ }_ }+p_ }_ }}}\right)}} the three ions that appear in this equation are potassium (k+), sodium (na+), and chloride (cl−). calcium is omitted, but can be added to deal with situations in which it plays a significant role. being an anion, the chloride terms are treated differently from the cation terms; the intracellular concentration is in the numerator, and the extracellular concentration in the denominator, which is reversed from the cation terms. pi stands for the relative permeability of the ion type i. in essence, the goldman formula expresses the membrane potential as a weighted average of the reversal potentials for the individual ion types, weighted by permeability. (although the membrane potential changes about 100 mv during an action potential, the concentrations of ions inside and outside the cell do not change significantly. they remain close to their respective concentrations when then membrane is at resting potential.) in most animal cells, the permeability to potassium is much higher in the resting state than the permeability to sodium. as a consequence, the resting potential is usually close to the potassium reversal potential. the permeability to chloride can be high enough to be significant, but, unlike the other ions, chloride is not actively pumped, and therefore equilibrates at a reversal potential very close to the resting potential determined by the other ions. values of resting membrane potential in most animal cells usually vary between the potassium reversal potential (usually around -80 mv) and around -40 mv. the resting potential in excitable cells (capable of producing action potentials) is usually near -60 mv—more depolarized voltages would lead to spontaneous generation of action potentials. immature or undifferentiated cells show highly variable values of resting voltage, usually significantly more positive than in differentiated cells. in such cells, the resting potential value correlates with the degree of differentiation: undifferentiated cells in some cases may not show any transmembrane voltage difference at all. maintenance of the resting potential can be metabolically costly for a cell because of its requirement for active pumping of ions to counteract losses due to leakage channels. the cost is highest when the cell function requires an especially depolarized value of membrane voltage. for example, the resting potential in daylight-adapted blowfly (calliphora vicina) photoreceptors can be as high as -30 mv. this elevated membrane potential allows the cells to respond very rapidly to visual inputs; the cost is that maintenance of the resting potential may consume more than 20% of overall cellular atp. on the other hand, the high resting potential in undifferentiated cells does not necessarily incur a high metabolic cost. this apparent paradox is resolved by examination of the origin of that resting potential. little-differentiated cells are characterized by extremely high input resistance, which implies that few leakage channels are present at this stage of cell life. as an apparent result, potassium permeability becomes similar to that for sodium ions, which places resting potential in-between the reversal potentials for sodium and potassium as discussed above. the reduced leakage currents also mean there is little need for active pumping in order to compensate, therefore low metabolic cost. graded potentials as explained above, the potential at any point in a cell's membrane is determined by the ion concentration differences between the intracellular and extracellular areas, and by the permeability of the membrane to each type of ion. the ion concentrations do not normally change very quickly (with the exception of ca2+, where the baseline intracellular concentration is so low that even a small influx may increase it by orders of magnitude), but the permeabilities of the ions can change in a fraction of a millisecond, as a result of activation of ligand-gated ion channels. the change in membrane potential can be either large or small, depending on how many ion channels are activated and what type they are, and can be either long or short, depending on the lengths of time that the channels remain open. changes of this type are referred to as graded potentials, in contrast to action potentials, which have a fixed amplitude and time course. as can be derived from the goldman equation shown above, the effect of increasing the permeability of a membrane to a particular type of ion shifts the membrane potential toward the reversal potential for that ion. thus, opening na+ channels shifts the membrane potential toward the na+ reversal potential, which is usually around +100 mv. likewise, opening k+ channels shifts the membrane potential toward about –90 mv, and opening cl− channels shifts it toward about –70 mv (resting potential of most membranes). thus, na+ channels shift the membrane potential in a positive direction, k+ channels shift it in a negative direction (except when the membrane is hyperpolarized to a value more negative than the k+ reversal potential), and cl− channels tend to shift it towards the resting potential. graph displaying an epsp, an ipsp, and the summation of an epsp and an ipsp graded membrane potentials are particularly important in neurons, where they are produced by synapses—a temporary change in membrane potential produced by activation of a synapse by a single graded or action potential is called a postsynaptic potential. neurotransmitters that act to open na+ channels typically cause the membrane potential to become more positive, while neurotransmitters that activate k+ channels typically cause it to become more negative; those that inhibit these channels tend to have the opposite effect. whether a postsynaptic potential is considered excitatory or inhibitory depends on the reversal potential for the ions of that current, and the threshold for the cell to fire an action potential (around –50mv). a postsynaptic current with a reversal