Contributions of K+, Na+, and Cl− to the membrane potential of intact hamster vascular endothelial cells

The transmembrane potential (V_m) of vascular endothelial cells (EC) is an important property that may be involved in intra- and intercellular signal transduction for various vascular functions. In this study, V_m of intact aortic and vena caval EC from hamsters were measured using conventional microelectrodes. Vascular strips with the luminal surface upwards were suffused in a tissue chamber with krebs solution in physiological conditions. The resting V_m of aortic and vena caval EC was found to be ?40± 1 mV (n = 55) and ?43± 1 mV (n = 15), respectively. The V_m recordings were confirmed to have originated from EC by scanning and transmission electron microscopy combined with the comparison of electrical recordings between normal and endothelium-denuded aortic strips. The input resistance varied from 10–240 MΩ, which implied the presence of electrical coupling between vascular EC. Elevating the K⁺ level in the suffusate from 4.7 mM to 50 and 100 mM depolarized aortic EC by 19% and 29% and vena caval EC by 18% and 29%, respectively. These low percentages indicated a relatively small contribution of [K⁺] to the resting V_m of vascular EC. A positive correlation (r> 0.69) between the resting V_m and the magnitude of depolarization by the high [K⁺]₀ may be related to the involvement of voltage-dependent K⁺ channels. The hyperpolarization caused by lowering both [Na⁺]₀ and [CI^?]₀ suggested the disengagement of some electrogenic transport systems in the membrane, such as a Na⁺ -K⁺ -CI^? cotransporter. The transference number (t_ion), as an index of membrane conductance for specific ions, was calculated for K⁺ (15-20%), Na⁺ (16%), and Cl^? (9-15%), demonstrating that both Na⁺ and Cl^? as well as K⁺ contribute to the overall resting V_m. Our study documented some basic electrophysiology of the vascular EC when both structural and functional properties of the cell were maintained, thus furthering the understanding of the essential role of endothelial cells in mediating vascular functions. © 1993 Wiley-Liss, Inc.     

A mutant of Paramecium with increased relative resting potassium permeability

Fast-2, a membrane mutant of Paramecium aurelia, is due to a single-gene mutation and has behavioral abnormalities. Intracellular recordings through changes of external solutions were made. The mutant membrane hyperpolarized when it encountered solutions with low K⁺ concentration. This hyperpolarization and other associated activities were best observed in Ca- or Na-solutions devoid of K⁺. Membrane potential was plotted against the concentration of K⁺ (0.5 to 16 mM) in solutions of fixed Na⁺ or Ca⁺⁺ concentration. The slopes of the curves for the mutant membrane were steeper than those for the wild type at the lower concentrations of K⁺. Inclusion of 2 mM tetraethylammonium chloride (TEA-Cl) counteracted the mutational effects. Spontaneous action potentials in Ba-solution and the electrically evoked action potentials in various solutions are normal in this mutant. We conclude that the resting permeability to K⁺ relative to the permeabilities to Na⁺ and Ca⁺⁺ has been increased by the mutation.     

Sodium gradient dependence of proline and glycine uptake in rat renal brush-border membrane vesicles

The sodium-dependent entry of proline and glycine into rat renal brushborder membrane vesicles was examined. The high K_m system for proline shows no sodium dependence. The low K_m system for glycine entry is strictly dependent on a Na⁺ gradient but shows no evidence of the carrier system having any affinity for Na⁺. The low K_m system for proline and high K_m system for glycine transport appear to be shared. Both systems are stimulated by a Na⁺ gradient and appear to have an affinity for the Na⁺. The effect of decreasing the Na⁺ concentration in the ionic gradient is to alter the K_m for amino acid entry and, at low Na⁺ concentrations, to inhibit the V for glycine entry.     

Graded and All-or-None Electrogenesis in Arthropod Muscle : I. The effects of alkali-earth cations on the neuromuscular system of Romalea microptera

Graded electrically excited responsiveness of Romalea muscle fibers is converted to all-or-none activity by Ba⁺⁺, Sr⁺⁺, or Ca⁺⁺, the two former being much the more effective in this action. The change occurs with as little as 7 to 10 per cent of Na⁺ substituted by Ba⁺⁺. The spikes now produced have overshoots and may be extremely prolonged, lasting many seconds. During the spike the membrane resistance is lower than in the resting fiber, but the resting resistance and time constant are considerably increased by the alkali-earth ions. The excitability is also increased, spikes arising neurogenically from spontaneous repetitive discharges in the axon as well as myogenically from spontaneous activity in the muscle fibers. Repetitive responses frequently occur on intracellular stimulation with a brief pulse. The data indicate that the alkali-earth ions exert a complex of effects on the different action components of electrically excitable membrane. They may be described in terms of the ionic theory as follows: The resting K⁺ conductance is diminished. The sodium inactivation process is also diminished, and sodium activation may be increased. Together these changes can act to convert graded responsiveness to the all-or-none variety. The alkali-earth ions can also to some degree carry inward positive charge during activity, since spikes are produced when Na⁺ is fully replaced with the divalent ions.     

Fluctuation analysis of Na+ channels modified by batrachotoxin in myelinated nerve

(1) Single myelinated nerve fibres of Rana esculenta were treated with the steroidal alkaloid batrachotoxin, and Na⁺ currents and Na⁺-current fluctuations were measured near the resting potential under voltage-clamp conditions. Between test pulses fibres were held at hyperpolarizing membrane potentials. (2) The spectral density of Na⁺-current fluctuations was fitted by the sum of a $\text{1}\text{f}$ component and a Lorentzian function. The time constant $\text{τ}{}_{\mathrm{<mtext>c</mtext>}}\text{= 1/(2π?}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ obtained from the corner frequency ?_c of the Lorentzian function approximately agreed with the activation time constant τ_m of the macroscopic currents. (3) The conductance γ of a single Na⁺ channel modified by batrachotoxin was calculated from the integral of the Lorentzian function and the steady-state Na⁺ current. At the resting potential V = O we obtained γ = 1.6 pS, higher γ-values of 3.2 and 3.45 pS were found at V = ?8 and ?16 mV, respectively. (4) The conductance of a modified Na⁺ channel is significantly lower than the values 6.4 to 8.85 pS reported in the literature for normal Na⁺ channels. Hence, our experiments are in agreement with the view that batrachotoxin acts in an ‘all-or-none’ manner on Na⁺ channels and creates a distinct population of modified channels.     

Modulation of Na/H Antiporter Activity by Extreme pH and Salt in the Halotolerant Alga Dunaliella salina

The effect of different growth conditions on the activity of the Na⁺/H⁺ antiporter in Dunaliella salina has been investigated. Adaptation of D. salina cells to ammonia at alkaline pH or to high NaCl concentrations is associated with a pronounced increase in the plasma membrane Na⁺/H⁺ exchange activity. The enhanced activity is manifested both in vivo, by stimulation of Na⁺ influx into intact cells in response to internal acidification, and in vitro, by a larger ²²Na accumulation in plasma membrane vesicles in response to an induced pH gradient. Kinetic analysis shows that the stimulation does not result from a change of the K_m for Na⁺ but from an increase in the V_max. In contrast, adaptation of cells to a high LiCl concentration (0.8 m) depresses the activity of the Na⁺/H⁺ antiporter. Adaptation to ammonia is also associated with a large increase of three polypeptide bands in purified plasma membrane preparations, indicating that they may compose the antiporter polypeptides. These results suggest that adaptation to ammonia or to high salinity induces overproduction of the plasma membrane Na⁺/H⁺ antiporter in Dunaliella.     

Mechanisms underlying turgor regulation in the estuarine alga Vaucheria erythrospora (Xanthophyceae) exposed to hyperosmotic shock

Aquatic organisms are often exposed to dramatic changes in salinity in the environment. Despite decades of research, many questions related to molecular and physiological mechanisms mediating sensing and adaptation to salinity stress remain unanswered. Here, responses of Vaucheria erythrospora, a turgor‐regulating xanthophycean alga from an estuarine habitat, have been investigated. The role of ion uptake in turgor regulation was studied using a single cell pressure probe, microelectrode ion flux estimation (MIFE) technique and membrane potential (E_m) measurements. Turgor recovery was inhibited by Gd³⁺, tetraethylammonium chloride (TEA), verapamil and orthovanadate. A NaCl‐induced shock rapidly depolarized the plasma membrane while an isotonic sorbitol treatment hyperpolarized it. Turgor recovery was critically dependent on the presence of Na⁺ but not K⁺ and Cl^? in the incubation media. Na⁺ uptake was strongly decreased by amiloride and changes in net Na⁺ and H⁺ fluxes were oppositely directed. This suggests active uptake of Na⁺ in V. erythrospora mediated by an antiport Na⁺/H⁺ system, functioning in the direction opposite to that of the SOS1 exchanger in higher plants. The alga also retains K⁺ efficiently when exposed to high NaCl concentrations. Overall, this study provides insights into mechanisms enabling V. erythrospora to regulate turgor via ion movements during hyperosmotic stress.     

Kinetics of charge translocation in the passive downhill uptake mode of the Na/H antiporter NhaA of Escherichia coli

The Na⁺/H⁺ antiporter NhaA is the main Na⁺ extrusion system in E. coli. Using direct current measurements combined with a solid supported membrane (SSM), we obtained electrical data of the function of NhaA purified and reconstituted in liposomes. These measurements demonstrate NhaA's electrogenicity, its specificity for Li⁺ and Na⁺ and its pronounced pH dependence in the range pH 6.5-8.5. The mutant G338S, in contrast, presents a pH independent profile, as reported previously. A complete right-side-out orientation of the NhaA antiporter within the proteoliposomal membrane was determined using a NhaA-specific antibody based ELISA assay. This allowed for the first time the investigation of NhaA in the passive downhill uptake mode corresponding to the transport of Na⁺ from the periplasmic to the cytoplasmic side of the membrane. In this mode, the transporter has kinetic properties differing significantly from those of the previously investigated efflux mode. The apparent K_m values were 11 mM for Na⁺ and 7.3 mM for Li⁺ at basic pH and 180 mM for Na⁺ and 50 mM for Li⁺ at neutral pH. The data demonstrate that in the passive downhill uptake mode pH regulation of the carrier affects both apparent K_m as well as turnover (V_max).     

An analysis of conductance changes in squid axon

The membrane of the squid axon is considered on the basis of a pore model in which the distribution of the pore sizes strongly favors K⁺ transfer when there is no potential. Electrical asymmetry causes non-penetrating ions on the membrane capacitor to exert a mechanical force on both membrane surfaces and this force results in a deformation of the membrane pore system such that it assumes a distribution of sizes favoring the ions exerting mechanical force. The ions involved appear to be Ca⁺⁺ on the outside of the membrane and isethionate^-, (i^-) on the inside; as Ca⁺⁺ is equivalent in size to Na⁺, the charged membrane is potentially able to transfer Na⁺, when the ions deforming the membrane pore distribution are removed. A depolarization of the membrane leads to an opening of pores that will allow Na⁺ penetration and a release of the membrane from deformation. The pores revert to the zero-potential pore size distribution hence the Na permeability change is a transient. Calculation shows that the potassium conductance vs. displacement of membrane potential curve for the squid axon and the "inactivation" function, h, can be obtained directly from the assumed membrane distortion without the introduction of arbitrary parameters. The sodium conductance, because it is a transient, requires assumptions about the time constants with which ions unblock pores at the outside and the inside of the membrane.     

Basolateral K+ Conductance Establishes Driving Force for Cation Absorption by Outer Sulcus Epithelial Cells

Outer sulcus epithelial cells were recently found to actively reabsorb cations from the cochlear luminal fluid, endolymph, via nonselective cation channels in the apical membrane. Here we determined the transport properties of the basolateral membrane with the whole-cell patch clamp technique; the apical membrane contributed insignificantly to the recordings. Outer sulcus epithelial cells exhibited both outward and inward currents and had a resting membrane potential of −90.4 ± 0.7 mV (n= 78), close to the Nernst potential for K⁺ (−95 mV). The reversal potential depolarized by 54 mV for a tenfold increase in extracellular K⁺ concentration with a K⁺/Na⁺ permeability ratio of 36. The most frequently observed K⁺ current was voltage independent over a broad range of membrane potentials. The current was reduced by extracellular barium (10⁻⁵ to 10⁻³ m), amiloride (0.5 mm), quinine (1 mm), lidocaine (5 mm) and ouabain (1 mm). On the other hand, TEA (20 mm), charybdotoxin (100 nm), apamin (100 nm), glibenclamide (10 μm), 4-aminopyridine (1 mm) and gadolinium (1 mm) had no significant effect. These data suggest that the large K⁺ conductance, in concert with the Na⁺,K⁺-ATPase, of the basolateral membrane of outer sulcus cells provides the driving force for cation entry across the apical membrane, thereby energizing vectorial cation absorption by this epithelium and contributing to the homeostasis of endolymph.     

Voltage-dependent activation of Rac1 by Nav1.5 channels promotes cell migration

Ion channels can regulate the plasma membrane potential (V_m) and cell migration as a result of altered ion flux. However, the mechanism by which V_m regulates motility remains unclear. Here, we show that the Na_v1.5 sodium channel carries persistent inward Na⁺ current which depolarizes the resting V_m at the timescale of minutes. This Na_v1.5-dependent V_m depolarization increases Rac1 colocalization with phosphatidylserine, to which it is anchored at the leading edge of migrating cells, promoting Rac1 activation. A genetically encoded FRET biosensor of Rac1 activation shows that depolarization-induced Rac1 activation results in acquisition of a motile phenotype. By identifying Na_v1.5-mediated V_m depolarization as a regulator of Rac1 activation, we link ionic and electrical signaling at the plasma membrane to small GTPase-dependent cytoskeletal reorganization and cellular migration. We uncover a novel and unexpected mechanism for Rac1 activation, which fine tunes cell migration in response to ionic and/or electric field changes in the local microenvironment.     

Characterization of glutamate transport system in hydrophobic protein (H protein) of Bacillus subtilis

Hydrophobic protein (H protein) was isolated from membrane fractions of Bacillus subtilis and constituted into artificial membrane vesicles with lipid of B. substilis. Glutamate was accumulated into the vesicle when a Na⁺ gradient across the membrane was imposed. The maximum effect of Na⁺ on the transport was achieved at a concentration of about 40 mM, while the apparent K_m for Na⁺ was approximately 8 mM. On the other hand, K_m for glutamate in the presence of 50 mM Na⁺ was about 8 μM. Increasing the concentration of Na⁺ resulted in a decrease in K_m for glutamate, maximum velocity was not affected. The transport was sensitive to monensin (Na⁺ ionophore).Glutamate was also accumulated when pH gradient (interior alkaline) across the membrane was imposed or a membrane potential was induced with K⁺-diffusion potential. The pH gradient-driven glutamate transport was sensitive to carbonylcyanide m-chlorophenylhydrazone and the apparent K_m for glutamate was approximately 25 μM.These results indicate that two kinds of glutamate transport system were present in H protein: one is Na⁺ dependent and the other is H⁺ dependent.     

Single-Channel Analysis of a Delayed Rectifier K+ Channel in Xenopus Myelinated Nerve

Single-channel properties of a delayed rectifier voltage-gated K⁺ channel (I-type) were investigated in peripheral myelinated axons from Xenopus laevis. Channels activated between −60 and −40 mV with a potential of half-maximal activation, E₅₀, at −47.5 mV. Averaged single-channel currents activated with a time delay at all membrane potentials tested. Time to half-maximal activation decreased from 80 to 1.6 msec between −60 and +40 mV. The channel inactivated monoexponentially with a time constant of 10.9 sec at −40 mV. The time constant of deactivation was 126 msec at −80 mV and 16.9 msec at −110 mV. In symmetrical 105 mm K⁺, the single-channel conductance (γ) was 22 and 13 pS at negative and positive membrane potentials, respectively, at 13–15°C. In Na⁺-rich solution with 2.5 mm extracellular K⁺γ was 7 pS and the reversal potential was negative to −80 mV, indicating a high selectivity for K⁺ over Na⁺. γ depended on extracellular K⁺ concentration (K _D = 19.6 mm) and temperature (Q ₁₀= 1.45). External tetraethylammonium (TEA) reduced the apparent single-channel current amplitude at all potentials tested with a half-maximal inhibiting concentration (IC₅₀) of 0.6 mm. Open probability of the channel, but not single-channel current amplitude was decreased by extracellular dendrotoxin (DTX, IC₅₀= 6.8 nm) and mast cell degranulating peptide (MCDP, IC₅₀= 41.9 nm). In Ringer solution the membrane potential of macroscopic I-channel patches was about −65 mV and depolarized under TEA and DTX. It is concluded that besides their activation during action potentials, I-channels may also stabilize the resting membrane potential. Received: 2 June 1995/Revised: 13 October 1995     

Voltage dependent potassium fluxes and the significance of action potentials in Acetabularia

Membrane potential, V_m, and K⁺(⁸⁶Rb⁺) fluxes have been measured simultaneously on individual cells of Acetabularia mediterranea. During resting state (resting potential approx. ?170 mV) the K⁺ influx amounts to 0.24–0.6 pmol · cm^?2 · s^?1 and the K⁺ efflux to 0.2–1.5 pmol · cm^?2 s^?1. According to the K⁺ concentrations inside and outside the cell (40 : 1) the voltage dependent K⁺ flux (zero at V_m = E_K = ?90 mV) is stimulated approx. 40-fold for V_m more positive than E_K.It is calculated that during one action potential (temporary depolarization to V_m more positive than E_K) a cell looses the same amount of K⁺, which leaks in during 10–20 min in the resting state (V_m = ?170 mV). Since action potentials occur spontaneously in Acetabularia, they are therefore suggested to have a significant function for the K⁺ balance of this alga.     

An electrophysiological study of the membrane properties of the immature and mature oocyte of the Batstar,Patiria miniata

Immature oocyte membrane properties of a starfish, Patiria miniata, were investigated by microelectrode techniques. The resting membrane potential in artificial seawater (ASW) was ?78.5 ± 6.7 mV (n = 61, inside negative). This was mainly accounted for by a selective permeability to potassium ions. Potassium ion-selective microelectrodes were used to measure intracellular K⁺ ion activity, which was 350 mM. The sodium to potassium permeability ratio was 0.02 ± 0.01 (n = 4). The current-voltage relation was nonlinear. The I–V curve included both areas of inward and outward rectification. The dependence of inward rectification upon the K⁺ ion electrochemical gradient was demonstrated. The membrane was capable of a regenerative action potential due to permeability changes for Ca²⁺ and Na⁺ ions. The Ca and Na components of the action potential were identified. The Ca component was reversibly suppressed by cobalt and irreversibly blocked by D-600. The Na component was tetrodotoxin (TTX) insensitive. The excitable response of P. miniata oocytes is similar to that described by Miyazaki et al. (1975a) for those of the starfish Asterina pectinifera.Immature oocytes were stimulated to mature with 10^?5M 1-methyladenine (1-MA) during continuous monitoring of the membrane potential. The resting potential in ASW became more inside negative during maturation. This change of the passive membrane property of the oocyte may be accounted for by the increased selectivity to K⁺ ions. The specific membrane resistance near the resting potential increased from 4.2 ± 1.4 to 21 ± 8.7 kΩ·cm² (n = 15) during maturation, while the specific membrane capacitance decreased slightly from 2 ± 0.5 to 1.7 ± 0.6 μF/cm² (n = 5). Maturation had little effect upon the active membrane properties.     

Cation/proton antiport systems in escherichia coli: properties of the sodium/proton antiporter.

The sodium/proton antiport system of Escherichia coli has been characterized by the effect of Na⁺ on the pH gradient established by respiration in everted membrane vesicles. The system has equal affinity for Na⁺ and Li⁺. Between pH 7 and 9 dissipation of Δψ, membrane potential, has no effect on the affinity for Na⁺ but decreases the V of the antiport reaction. Uptake of ²²Na⁺ by everted membrane vesicles was observed using flow dialysis.     

Effect of peptide PV on the ionic permeability of lipid bilayer membranes

This paper reports the effects of peptide PV (primary structure: cyclo-(D-val-L-pro-L-val-D-pro)_δ) on the electrical properties of sheep red cell lipid bilayers. The membrane conductance (G_m) induced by PV in either Na⁺ or K⁺ medium is proportional to the concentration of PV in the aqueous phase. The PV concentration required to produce a comparable increase in G_m in K⁺ medium is about 10⁴ times greater than for its analogue, valinomycin (val). Although the selectivity sequence for PV and val is similar, K⁺ ≳ Rb⁺ > Cs⁺ > NH₄ ⁺ > TI⁺ > Na⁺ > Li⁺; the ratio of GGm in K⁺ to that in Na⁺ is about 10 for PV compared to > 10³ for val. When equal concentrations of PV are added to both sides of a bilayer, the membrane current approaches a maximum value independent of voltage when the membrane potential exceeds 100 mV. When PV is added to only one side of a bilayer separating identical salt solutions of either Na⁺ or K⁺ salts, rectification occurs such that the positive current flows more easily away rather than toward the side containing the carrier. Under these conditions, a large, stable, zero-current potential (VVm) is also observed, with the side containing PV being negative. The magnitude of this VVm is about 90 mV and relatively independent of PV concentration when the latter is larger than 2 Times; 10^–5 M. From a model which assumes that V_m equals the equilibrium potential for the PV-cation complexes (MS ⁺) and that the reaction between PV and cations is at equilibrium on the two membrane surfaces, we compute the permeability of the membrane to free PV to be about 10^–5 cm s^–1, which is about 10^–7 times the permeability of similar membranes to free val. This interpretation is supported by the fact that the observed values of V_m are in agreement with the calculated equilibrium potential for MS⁺ over a wide range of ratios of concentrations of total PV in the two bathing solutions, if the unstirred layers are taken into account in computing the MS⁺ concentrations at the membrane surfaces.     

Simultaneous Measurements of Cytoplasmic K Concentration and the Plasma Membrane Electrical Parameters in Single Membrane Samples of Chara corallina

The electrophysiological properties of cytoplasm-rich fragments (single membrane samples) prepared from internodal cells of Chara corallina were explored in conjunction with K⁺-sensitive microelectrode and current-voltage (I-V) measurements. This system eliminated the problem of the inaccessible cytoplasmic layer, while preserving many of the electrical characteristics of the intact cells. In 0.1 millimolar external K concentration (K_o⁺), the resting conductance (membrane conductance G_m, 0.85 ± 0.25 Siemens per square meter (±standard error)) of the single membrane samples, was dominated by the proton pump, as suggested by the response of the near-linear I-V characteristic to changes in external pH. Initial cytoplasmic K⁺ activities (a_K+), judged most reliable, gave values of 117 ± 67 millimolar; stable a_K+ values were 77 ± 31 millimolar. Equilibrium potentials for K⁺ (Nernst equilibrium potential) (E_K) calculated, using either of these data sets, were near the mean membrane potential (V_m). On a cell-to-cell basis, however, E_K was generally negative of the V_m, despite an electrogenic contribution from the Chara proton pump. When K_o⁺ was increased to 1.0 millimolar or above, G_m rose (by 8- to 10-fold in 10 millimolar K_o⁺), the steady state I-V characteristics showed a region of negative slope conductance, and V_m followed E_K. These results confirm previous studies which implicated a K_o⁺-induced and voltage-dependent permeability to K⁺ at the Chara plasma membrane. They provide an explanation for transitions between apparent K_o⁺-insensitive and K_o⁺-sensitive (`K⁺ electrode') behavior displayed by the membrane potential, as recorded in many algae and higher plant cells.     

Intracellular Na+, K+ and Cl− activities in Ehrlich ascites tumor cells

Ehrlich ascites tumor cell membrane potential (V_m) and intracellular Na⁺, K⁺ and Cl⁻ activities were measured under steady-state conditions in normal saline medium (Na⁺ = 154, K⁺ = 6, Cl⁻ = 150 mequiv./l). Membrane potential was estimated to be −23.3 ± 0.8 mV using glass microelectrodes. Intracellular ion activities were estimated with similar glass electrodes rendered ion-selective by incorporation of ion-specific ionophores. Measurements of V_m and ion-activity differences were made in the same populations of cells. Under these conditions the intracellular Na⁺, K⁺ and Cl⁻ activities are 4.6 ± 0.5; 68.3 ± 8.0; and 43.6 ± 2.1 mequiv./l, respectively. The apparent activity coefficients for Na⁺ and K⁺ are 0.18 ± 0.02 and 0.41 ± 0.05 respectively. These are significantly lower than the activity coefficients expected for the ions in physiological salt solutions (0.71 and 0.73, respectively). The activity coefficient for intracellular Cl⁻ (0.67 ± 0.03), however, is close to that of the medium (0.73), and the transmembrane electrochemical potential difference for Cl⁻ is not different from zero. The results establish that the energy available from the Na⁺ electrochemical gradient is much greater than previously estimated from chemical measurements.