Membrane potential responses of paramecium caudatum to external Na+

The membrane potential responses of Paramecium caudatum to Na+ ions were examined to understand the mechanisms underlying the sensation of external inorganic ions in the ciliate by comparing the responses of the wild type and the behavioral mutant. Wild-type cells exhibited initial continuous backward swimming followed by repeated transient backward swimming in the Na+-containing test solution. A wild-type cell impaled by a microelectrode produced initial action potentials and a sustained depolarization to an application of the test solution. The prolonged depolarization, the depolarizing afterpotential, took place subsequently after stimulation. The ciliary reversal of the cell was closely associated with the depolarizing responses. When the application of the test solution was prolonged, the wild-type cell produced sustained depolarization overlapped by repeated transient depolarization. A behavioral mutant defective in the Ca2+ channel, CNR (caudatum non reversal), produced a sustained depolarization but no action potential or depolarizing afterpotential. The mutant cell responded to prolonged stimulation with sustained depolarization overlapped by transient depolarization, although it did not show backward swimming. The results suggest that Paramecium shows at least two kinds of membrane potential responses to Na+ ions: a depolarizing afterpotential mediating initial backward swimming and repeated transient depolarization responsible for the repeated transient backward swimming.     

Ca2+ Current-Deficient Pawn Mutants are Promoted to Queens During Chronic Depolarization of Paramecium tetraurelia

Chronic KCl-induced depolarization of Paramecium tetraurelia enhances Ca²⁺-dependent backward swimming behavior over a period of 8–24 hr. Here, we investigated the electrophysiological mechanisms underlying this adaptive phenomenon using voltage-clamp techniques. Cells that had been adapted to 20 mm KCl showed several significant changes in the properties of the Ca²⁺ current that mediates ciliary reversal in Paramecium (I _Ca ), including a positive shift in voltage sensitivity and a significant slowing of inactivation. In seeking an explanation for these changes, we examined the effects of chronic depolarization on mutants that do not normally express a Ca²⁺ current or swim backward. Surprisingly, pawn B mutant cells slowly regained the ability to reverse their cilia during KCl exposure with a time course that mirrored behavioral adaptation of the wild type. This behavior was accompanied by expression of a novel Ca²⁺ current (I _QUEEN ) whose voltage sensitivity was shifted positive with respect to the wild-type Ca²⁺ current and that was slow to inactivate. Coincidental expression of I _QUEEN in the wild type during adaptation would readily explain the observed changes in I _Ca kinetics. We also examined the effects of chronic depolarization on Dancer, a mutant suggested previously to have an I _Ca inactivation defect. The mutant phenotype could be suppressed or exaggerated greatly by manipulating extracellular KCl concentration, suggesting that Dancer lesion instead causes inappropriate regulation of I _QUEEN . Received: 23 April 1999/Revised: 29 June 1999     

Isolation and characterization of magbane, a magnesium-lethal mutant of paramecium.

Discerning the mechanisms responsible for membrane excitation and ionic control in Paramecium has been facilitated by the availability of genetic mutants that are defective in these pathways. Such mutants typically are selected on the basis of behavioral anomalies or resistance to ions. There have been few attempts to isolate ion-sensitive strains, despite the insights that might be gained from studies of their phenotypes. Here, we report isolation of "magbane," an ion-sensitive strain that is susceptible to Mg2+. Whereas the wild type tolerated the addition of > or =20 mm MgCl2 to the culture medium before growth was slowed and ultimately suppressed (at >40 mm), mgx mutation slowed growth at 10 mm. Genetic analysis indicated that the phenotype resulted from a recessive single-gene mutation that had not been described previously. We additionally noted that a mutant that was well described previously (restless) is also highly sensitive to Mg2+. This mutant is characterized by an inability to control membrane potential when extracellular K+ concentrations are lowered, due to inappropriate regulation of a Ca2+-dependent K+ current. However, comparing the mgx and rst mutant phenotypes suggested that two independent mechanisms might be responsible for their Mg2+ lethality. The possibility that mgx mutation may adversely affect a transporter that is required for maintaining low intracellular Mg2+ is considered.     

New Mutants of Paramecium Tetraurelia Defective in a Calcium Control Mechanism: Genetic and Behavioral Characterizations

The k-shy mutants of Paramecium tetraurelia are altered in several Ca2+-dependent functions which regulate ciliary motility. The isolation, genetics, and phenotypes of these mutants are described. Of six independent isolates, all contained recessive single-factor mutations and comprise two unlinked loci, ksA and ksB. All k-shy strains showed prolonged backward swimming responses to depolarizing stimuli, but gave infrequent responses to some stimuli. At least four k-shy strains displayed temperature sensitivity. Neither ksA nor ksB was allelic or linked to dancer, a mutation causing weak Ca2+ current inactivation and prolonged backward swimming. Analysis of ks+; Dn double mutants revealed synergism between the two mutations. The ksA mutant survived Ba2+ solutions longer than wild type, but was more sensitive to K+. Together with previous studies, these results are consistent with a defect in reducing intracellular Ca2+ causing both prolonged ciliary reversal and reduced Ca2+ channel activity due to more active Ca2+-dependent feedback mechanisms. The integration of the Ca2+-dependent stimulatory and inhibitory functions is therefore dependent on ks+ gene functions. The ksA mutant was rescued by microinjection of wild-type cytoplasm, suggesting a possible behavioral assay for factors related to the ksA+ gene product.     

Isolation and Characterization of Paramecium Mutants Defective in Their Response to Magnesium

Four mutant strains of Paramecium tetraurelia with a reduced ability to respond behaviorally to Mg(2+) have been isolated. Voltage-clamp analyses showed that their Mg(2+) insensitivity is associated with a reduced Ca(2+) -dependent Mg(2+) current. The four mutants, which have been dubbed ``eccentric,' result from recessive mutations in two unlinked loci, xntA and xntB. Further analysis of xntA(1) showed it to be unlinked to any of the behavioral mutants of P. tetraurelia described previously, but it is allelic to d4-521, a ``K(+)-resistant' strain, and d4-596, a ``Ba(2+)-shy' mutant. The varied pleiotropic effects of xntA(1), which include increased resistance to Ni(2+) and Zn(2+) poisoning, suggest that the locus encodes a central regulator of cell function in Paramecium.     

Calcium current activated upon hyperpolarization of Paramecium tetraurelia

Hyperpolarization of Paramecium tetraurelia under conditions where K+ currents are suppressed elicits an inward current that activates rapidly toward a peak at 25-80 ms and decays thereafter. This peak current (Ihyp) is not affected by removing Cl ions from the microelectrodes used to clamp membrane potential, or by changing extracellular Cl- concentration, but is lost upon removing extracellular Ca2+. Ihyp is also lost upon replacing extracellular Ca2+ with equimolar concentrations of Ba2+, Co2+, Mg2+, Mn2+, or Sr2+, suggesting that the permeability mechanism that mediates Ihyp is highly selective for Ca2+. Divalent cations also inhibit Ihyp when introduced extracellularly, in a concentration- and voltage-dependent manner. Ba2+ inhibits Ihyp with an apparent dissociation constant of 81 microM at -110 mV, and with an effective valence of 0.42. Ihyp is also inhibited reversibly by amiloride, with a dissociation constant of 0.4 mM. Ihyp is not affected significantly by changes in extracellular Na+, K+, or H+ concentration, or by EGTA injection. Also, it is unaffected by manipulations or mutations that suppress the depolarization-activated Ca2+ current or the various Ca(2+)-dependent currents of Paramecium. We suggest that Ihyp is mediated by a novel, hyperpolarization-activated calcium conductance that is distinct from the one activated by depolarization.     

K<Superscript>+</Superscript>-induced Ca<Superscript>2+</Superscript> Conductance Responsible for the Prolonged Backward Swimming in K<Superscript>+</Superscript>-agitated Mutant of <Emphasis Type="Italic">Paramecium caudatum</Emphasis>

The K⁺-agitated (Kag) mutant of Paramecium caudatum shows prolonged backward swimming in K⁺-rich solution. To understand the regulation mechanisms of the ciliary motility in P. caudatum, we examined the membrane electrical properties of the Kag mutant. The duration of the backward swimming of the Kag in K⁺-rich solution was about 10 times longer than that of the wild type. In response to an injection of the outward current, the wild type produced an initial action potential and a subsequent membrane depolarization due to I-R potential drop, while the Kag exhibited repetitive action potentials during the depolarization. Under voltage-clamp conditions, the depolarization-activated transient inward current exhibited by the Kag was slightly smaller than that exhibited by the wild type. In response to an application of K⁺-rich solution, both the wild type and the Kag exhibited a depolarizing afterpotential representing the activation of the K⁺-induced Ca²⁺ conductance. The inactivation time course of the K⁺-induced Ca²⁺ conductance of Kag was about 10 times longer than that of the wild type. This difference corresponds well with the difference in behavioral responses between Kag and wild type to K⁺-rich solution. We conclude that the overreaction of the Kag mutant to the K⁺-rich solution is caused by slowing down of the inactivation of the K⁺-induced Ca²⁺ conductance.     

Identification of an algal carbon fixation-enhancing factor extracted from Paramecium bursaria

The green ciliate Paramecium bursaria contains several hundred symbiotic Chlorella species. We previously reported that symbiotic algal carbon fixation is enhanced by P. bursaria extracts and that the enhancing factor is a heat-stable, low-molecular-weight, water-soluble compound. To identify the factor, further experiments were carried out. The enhancing activity remained even when organic compounds in the extract were completely combusted at 700 degrees C, suggesting that the factor is an inorganic substance. Measurement of the major cations, K+, Ca2+, and Mg2+, by an electrode and titration of the extract resulted in concentrations of 0.90 mM, 0.55 mM, and 0.21 mM, respectively. To evaluate the effect of these cations, a mixture of the cations at the measured concentrations was prepared, and symbiotic algal carbon fixation was measured in the solution. The results demonstrated that the fixation was enhanced to the same extent as with the P. bursaria extract, and thus this mixture of K+, Ca2+, and Mg2+ was concluded to be the carbon fixation-enhancing factor. There was no effect of the cation mixture on free-living C. vulgaris. Comparison of the cation concentrations of nonsymbiotic and symbiotic Paramecium extracts revealed that the concentrations of K+ and Mg2+ in nonsymbiotic Paramecium extracts were too low to enhance symbiotic algal carbon fixation, suggesting that symbiotic P. bursaria provide suitable cation conditions for photosynthesis to its symbiotic Chlorella.     

Primary mutations in calmodulin prevent activation of the Ca(++)-dependent Na+ channel in Paramecium.

Paramecium tetraurelia behavioral mutant cam12 displays a "fast-2" behavioral phenotype: it fails to respond to Na+ stimuli. Electrophysiologically, it lacks a Ca(++)-dependent Na+ current. Genetics and DNA sequencing showed the primary defect of cam12 to be in the calmodulin gene (Kink et al., 1990). To correlate calmodulin structure and function in Paramecium, we elucidated the primary structure of cam12 calmodulin. Peptide sequencing confirmed the two point mutations predicted by the DNA sequence: a glycine-to-glutamate substitution at position 40 and an aspartate-to-asparagine substitution at position 50. Our results further showed that lysine 13 and lysine 115 were methylated normally in cam12. It is likely that the electrophysiological abnormalities of cam12 are a direct reflection of the amino-acid substitutions, as opposed to improper posttranslational modification.     

An Intragenic Suppressor of a Calmodulin Mutation in Paramecium: Genetic and Biochemical Characterization

We describe a suppressor of the calmodulin mutant cam1 in Paramecium tetraurelia. The cam1 mutant, which has a SER----PHE change at residue 101 of the third calcium-binding domain, inhibits the activity of the Ca(2+)-dependent K+ current and causes exaggerated behavioral responses to most stimuli. An enrichment scheme, based on an increased sensitivity to Ba2+ in cam1 cells, was used to isolate suppressors. One such suppressor, designated cam101, restores both the activity of the Ca(2+)-dependent K+ current and behavioral responses of the cells. We show that the cam101 mutant is an intragenic suppressor of cam1, based on genetic and microinjection data. The cam101 calmodulin is shown to be similar to wild-type calmodulin in terms of its ability to stimulate calmodulin-dependent phosphodiesterase at low concentrations of free calcium. However, the cam101 calmodulin has a reduced affinity for a monoclonal antibody to wild-type Paramecium calmodulin, as does the parental cam1 calmodulin, and a different mobility on acid-urea gels relative to both wild-type and cam1 calmodulin. We have been able to demonstrate that the isolation of intragenic suppressors of a calmodulin mutation is possible, which allows for the further genetic analysis of structure-function relationships in the calmodulin molecule.     

The molecular basis for the alternative stable phenotype in a behavioral mutant of Paramecium tetraurelia

In the sexual reproduction of Paramecium tetraurelia, the somatic nucleus (macronucleus) undergoes massive genomic rearrangement, including gene amplification and excision of internal eliminated sequences (IESs), in its normal developmental process. Strain d4-662, one of the pawn mutants, is a behavioral mutant of P. tetraurelia that carries a recessive allele of pwB662. ThepwB gene in the macronucleus of the strain has an insertion of the IES because a base substitution within the IES prevents its excision during gene rearrangement. Cultures of this strain frequently contain cells reverting to the wild type in the behavioral phenotype. The mutant and revertant cells maintained stable clonal phenotypes under the various environmental conditions examined unless they underwent sexual reproduction. After sexual reproduction, both mutant and revertant produced 2.7-7.1% reverted progeny. A molecular analysis performed on the macronuclear DNA of the mutant and revertant of d4-662 showed that much less than 1% of the mutant IES was precisely excised at every sexual reproduction of the strain. Therefore, the alternative phenotype of strain d4-662 seems to be caused by an alternative excision of the mutant IES.     

A Mendelian Mutation Affecting Mating-Type Determination Also Affects Developmental Genomic Rearrangements in Paramecium Tetraurelia

In Paramecium tetraurelia, mating type is determined during the differentiation of the somatic macronucleus from a zygotic nucleus genetically competent for both types, O and E. Determination of the developing macronucleus is controlled by the parental macronucleus through an unknown mechanism resulting in the maternal inheritance of mating types. The pleiotropic mutation mtF(E) affects macronuclear differentiation. Determination for E is constitutive in mutant homozygotes; a number of unrelated mutant characters are also acquired during development. We have examined the possibility that the mutation causes a defect in the developmental rearrangements of the germ-line genome. We show that the excision of an IES (internal eliminated sequence) interrupting the coding sequence of a surface antigen gene is impaired in the mutant, resulting in an alternative macronuclear version of the gene. Once established, the excision defect is indefinitely transmitted across sexual generations in the cytoplasmic lineage, even in a wild-type genetic context. Thus, the processes of mating-type determination and excision of this IES, in addition to their common sensitivity to the mtF(E) mutation, show a similar maternal inheritance of developmental alternatives in wild-type cells, suggesting a molecular model for mating-type determination.     

An automated assay for quantifying the swimming behavior of Paramecium and its use to study cation responses

Paramecium tetraurelia is a ciliated protist that alters its swimming behavior in response to various stimuli. Like the sensory responses of many organisms, these responses in Paramecium show adaptation to continued stimulation. For quantitative studies of the initial response to stimulation, and of the time course of adaptation, we have developed a computerized motion analysis assay that can detect deviations from the normal swimming pattern in a population of cells. The motion of an average of ten cells was quantified during periods ranging from 15 to 60 seconds, with a time resolution of 1/15 seconds. During normal forward swimming, the maximum deviation from a straight-line path was less than 17 degrees. Path deviations above this threshold value were defined as changes in swimming direction. The percentage of total path time that cells spent deviating from forward swimming was defined as percent directional changes (PDC). This parameter was used to construct dose-response curves for the behavioral effects of various externally added cations known to induce behavioral changes and also to show the time course of adaptation to a depolarizing K+ stimulus. This assay is a valuable tool for studies of chemoeffectors or mutations that alter the swimming behavior of Paramecium and may also be applicable to other motile organisms.     

Identification of the Ca2+ conductance responsible for K+-induced backward swimming in Paramecium caudatum

Membrane potential responses of Paramecium caudatum to an application of K+-rich solution were examined to understand the mechanisms underlying K+-induced backward swimming. A wild-type cell impaled by a microelectrode produced action potentials followed by a sustained depolarization in response to an application of a K+-rich test solution. After termination of the application, a prolongation of the depolarization (depolarizing after-potential) took place. Behavioral mutants incapable of exhibiting K+-induced backward swimming did not show depolarizing afterpotentials. Upon short application of K+-rich solution, the timing and duration of the ciliary reversal of the wild-type cell coincided well with the K+-induced depolarization. The duration of the depolarizing afterpotential decreased as the duration of the application increased. The depolarizing afterpotential recovered slowly after it had been suppressed by a preceding application of the K+-rich solution. By injection of an outward current into the wild-type cell, the action potentials were evoked normally during the period when the K+-induced depolarizing afterpotential was suppressed. We concluded that the prolongation of the depolarizing membrane potential response following the application of the K+-rich solution represents the Ca2+ conductance responsible for the K+-induced backward swimming in P. caudatum and that the characteristics of the K+-induced Ca2+ conductance are distinct from those of the Ca2+ conductance responsible for the action potentials.     

Cold-sensitive responses in the Paramecium membrane

A transient depolarization was recorded in response to the cooling of a deciliated Paramecium. The amplitude of the depolarization was almost proportional to the cooling rate. Therefore, the cells are sensitive to the rate of temperature change. The input resistance of the membrane transiently increased during the cooling. When constant current was applied to shift the resting membrane potential to a negative or positive level, the initial depolarization in response to cooling decreased, and the following hyperpolarization during cooling reversed to a gradual depolarization during a positive shift. The potential at which the reversal occurred was independent of K+ concentration and was slightly dependent on Ca2+ concentration (10 mV/log[Ca2+]o). The amplitude of the initial depolarization decreased with the increase in K+ and was not affected by Ca2+. These results are discussed in terms of changes in membrane conductances in response to cooling.     

Extracellular GTP Causes Membrane-Potential Oscillations through the Parallel Activation of Mg2+ and Na+ Currents in Paramecium tetraurelia

Paramecium tetraurelia responds to extracellular GTP (≥ 10 nm) with repeated episodes of prolonged backward swimming. These backward swimming events cause repulsion from the stimulus and are the behavioral consequence of an oscillating membrane depolarization. Ion substitution experiments showed that either Mg²⁺ or Na⁺ could support these responses in wild-type cells, with increasing concentrations of either cation increasing the extent of backward swimming. Applying GTP to cells under voltage clamp elicited oscillating inward currents with a periodicity similar to that of the membrane-potential and behavioral responses. These currents were also Mg²⁺- and Na⁺-dependent, suggesting that GTP acts through Mg²⁺-specific (I _Mg) and Na⁺-specific (I _Na) conductances that have been described previously in Paramecium. This suggestion is strengthened by the finding that Mg²⁺ failed to support normal behavioral or electrophysiological responses to GTP in a mutant that specifically lacks I _Mg (``eccentric'), while Na<sup>+</sup> failed to support GTP responses in ``fast-2,' a mutant that specifically lacks I _Na. Both mutants responded normally to GTP if the alternative cation was provided. As I _Mg and I _Na are both Ca²⁺-dependent currents, the characteristic GTP behavior could result from oscillations in intracellular Ca²⁺ concentration. Indeed, applying GTP to cells in the absence of either Mg²⁺ or Na⁺ revealed a minor inward current with a periodicity similar to that of the depolarizations. This current persisted when known voltage-dependent Ca²⁺ currents were blocked pharmacologically or genetically, which implies that it may represent the activation of a novel purinergic-receptor–coupled Ca²⁺ conductance. Received: 28 October 1996/Revised: 24 December 1996     

Responses of the ciliates tetrahymena and paramecium to vertebrate odorants and tastants

The ciliates Tetrahymena and Paramecium respond to strong depolarizing stimuli with Ca(2+)-based action potentials, ciliary reversals, and consequent bouts of backward and forward swimming called "avoidance reactions" (ARs). We found that several representative tastants and odorants cause repetitive ARs in Tetrahymena and Paramecium at low (nM to microM) concentrations. Tetrahymena responded well to capsaicin, quinine, quinacrine, denatonium benzoate, eugenol, piperine, chloroquine, carvacrol, allyl isothiocyanate (AITC), and menthol. Chemosensory adaptation was seen with carvacrol, eugenol, quinacrine, and capsaicin. Cross-adaptation was seen between some of these compounds, suggesting possible similarities in their chemosensory transduction or adaptation pathways. Paramecium only responded well to AITC, quinacrine, piperine, and eugenol (with the effective concentration for 50% response [EC(50)] values in the microM range) while chemosensory adaptation was only seen to eugenol in Paramecium, suggesting possible species differences. Tetrahymena and Paramecium may have primitive receptors that can recognize these and other compounds or some of these compounds can act independently of specific receptors.     

Properties of a Sodium Channel (Nax) Activated by Strong Depolarization of Xenopus Oocytes

Short (<1 sec) duration depolarization of Xenopus laevis oocytes to voltages greater than +40 mV activates a sodium-selective channel (Na(x)) with sodium permeability five to six times greater than the permeability of other monovalent cations examined, including K+, Rb+, Cs+, TMA+, and Choline+. The permeability to Li+ is about equal to that of Na+. This channel was present in all oocytes examined. The kinetics, voltage dependence and pharmacology of Na(x)distinguish it from TTX-sensitive or epithelial sodium channels. It is also different from the sodium channel of Xenopus oocytes activated by prolonged depolarization, which is more highly selective for Na+, requires prolonged depolarization to be activated, and is blocked by Li+. Intracellular Mg2+ reversibly inhibits Na(x), whereas extracellular Mg2+ does not have an inhibitory effect. Intracellular Mg2+ inhibition of Na(x), is voltage dependent, suggesting that Mg2+ binding occurs within the membrane field. Eosin is also a reversible voltage-dependent intracellular inhibitor of Na(x), suggesting that a P-type ATPase may mediate the current. An additional cytoplasmic factor is involved in maintaining Na(x) since the current runs down in internally perfused oocytes and excised membrane patches. The rundown is reversible by reintroduction of the membrane patch into oocyte cytoplasm. The cytoplasmic factor is not ATP, because ATP has no effect on Na(x) current magnitude in either cut-open or inside-out patch preparations. Extracellular Gd3+ is also an inhibitor of Na(x). Na(x) activation follows a sigmoid time course. Its half-maximal activation potential is +100 mV and the effective valence estimated from the steepness of conductance activation is 1.0. Na(x) deactivates monoexponentially upon return to the holding potential (-40 mV). The deactivation rate is voltage dependent, increasing at more negative membrane potentials.     

Inhibition of Mg2+ current by single-gene mutation in Paramecium

Eccentric is a newly-isolated mutant of Paramecium tetraurelia that fails to swim backwards in response to Mg²⁺. In the wild type, this backward swimming results from Mg²⁺ influx via a Mg²⁺-specific ion conductance (I _Mg. Voltage-clamp analysis confirmed that, as suspected, step changes in membrane potential over a physiological range fail to elicit I _Mg from eccentric. Further electrophysiological investigation revealed a number of additional ion-current defects in eccentric: (i) The Ca²⁺ current activated upon depolarization inactivates more slowly in eccentric than in the wild type, and it requires longer to recover from this inactivation. (ii) The Ca²⁺-dependent Na⁺ current deactivates significantly faster in the mutant, (iii) The two K⁺ currents observed upon hyperpolarization are reduced by >60% in eccentric. It is difficult to envision how these varied pleiotropic effects could result from loss of a single ion current. Rather, they suggest that the eccentric mutation affects a global regulatory system. Two plausible hypotheses are discussed.We are grateful to Dr. Yoshiro Saimi for his comments and suggestions on this work, and for the support of the Lucille P. Markey Charitable trust and the National Institutes of Health (GM22714 and GM38646).     

Phenotypic and Genetic Analysis of ``chameleon,'''' a Paramecium Mutant with an Enhanced Sensitivity to Magnesium

Three mutant strains of Paramecium tetraurelia with an enhanced sensitivity to magnesium have been isolated. These new ``Chameleon' mutants result from partial- or codominant mutations at a single locus, Cha. Whereas the wild type responded to 5 mM Mg(2+) by swimming backward for 10-15 sec, Cha mutants responded with ~30 sec backward swimming. Electrophysiological analysis suggested that this behavior may be caused by slowing in the rate at which a Mg(2+)-specific ion conductance deactivates following membrane excitation. This would be consistent with an observed increase in the sensitivity of Cha mutants to nickel poisoning, since Ni(2+) is also able to enter the cell via this pathway. More extensive behavioral analysis showed that Cha cells also overresponded to Na(+), but there was no evidence for a defect in intracellular Ca(2+) homeostasis that might account for a simultaneous enhancement of both the Mg(2+) and Na(+) conductances. The possibility that the Cha locus may encode a specific regulator of the Mg(2+)- and Na(+)-permeabilities is considered.