Relationship between cadmium sensitivity and degree of plasma membrane fatty acid unsaturation in Saccharomyces cerevisiae

The sensitivity of Saccharomyces cerevisiae to the redox-active metal copper has recently been found to be influenced by cellular fatty acid composition. This study sought to investigate whether fatty acid composition affected plasma membrane permeabilisation and whole-cell toxicity induced by the redox-inactive metal cadmium. S. cerevisiae NCYC 1383 was enriched with the polyunsaturated fatty acids linoleate (18:2) and linolenate (18:3) by growth in 18:2- or 18:3-supplemented medium. Incorporation of the exogenous fatty acids resulted in them comprising more than 65% of the total fatty acids in plasma membrane lipids. Inhibition of cell division in the presence of Cd(NO₃)₂ was accentuated by growth in the presence of a polyunsaturated fatty acid. Furthermore, susceptibility to Cd²⁺-induced plasma membrane permeabilisation increased with the degree of fatty acid unsaturation. Thus, during exposure to Cd²⁺, K⁺ efflux from 18:2- and 18:3-enriched cells was up to 2.5-fold or 3-fold greater, respectively than that from unsupplemented cells. In addition, reductions in cell viability during exposure to Cd²⁺ were most marked in polyunsaturated-fatty-acid-supplemented cells. At certain times, unsupplemented Cd²⁺-exposed cells displayed up to 7-fold greater viability than supplemented Cd²⁺-exposed cells. The study demonstrates that the toxicity of the redox-inactive metal Cd²⁺ towards S. cerevisiae becomes markedly amplified with increased cellular and plasma membrane fatty acid unsaturation. Received: 14 March 1997 / Received revision: 4 June 1997 / Accepted: 7 June 1997     

Sodium-cotransport systems in intestine and kidney of the winter flounder

Summary Brush-border membrane vesicles were isolated from the intestine and kidney of the winter flounder,Pseudopleuronectes americanus, and the transport ofd-glucose,l-alanine and sodium was examined by a rapid filtration technique.d-glucose,l-alanine, and sodium entered the same osmotically reactive space suggesting that uptake into vesicles represents transport across rather than binding to the membrane. d-glucose andl-alanine uptake by intestinal and renal brush-border membrane vesicles was stimulated by sodium as compared to potassium or choline. In the presence of a sodium chloride gradient, overshooting uptake was observed indicating a transient intravesicular accumulation ofd-glucose andl-alanine. The sodium-dependentd-glucose uptake was inhibited by phlorizin andd-galactose while the transport ofl-alanine was inhibited byl-phenylalanine. The sodium-dependent transport ofd-glucose andl-alanine was affected by the electrical potential difference across the vesicle membrane; the addition of valinomycin in the presence of an inwardly directed potassium chloride gradient inhibited sodium-dependent solute uptake, whereas replacing chloride or gluconate with more permeant anions, such as SCN^–, stimulated uptake. Similar results were obtained with intestinal and renal membranes; they document the presence of sodium/d-glucose and sodium/l-alanine cotransport systems in the brush-border membrane of intestine and kidney.Sodium uptake into brush border membrane vesicles from the flounder intestine and kidney was saturable (tracer replacement) and trans-stimulated (tracer coupling), indicating transport via facilitated diffusion systems. Additionally, sodium uptake was only slightly affected by superimposing diffusion potentials demonstrating that the majority of sodium transport was by electroneutral coupled processes. In both the intestinal and kidney brush-border membrane vesicles sodium uptake was inhibited by an inwardly directed proton gradient suggesting the presence of a sodium/proton exchange mechanism. In intestinal, but not in renal membrane preparations, sodium uptake was stimulated by chloride. Chloride stimulation was abolished after preincubation with furosemide indicating the presence of an additional coupled sodium-chloride transport in the intestinal brush-border membranes.The experiments were carried out at the Mount Desert Island Biological Laboratory, Salsbury Cove, Maine 04672, USAAddress effective February 1, 1980: Albert Einstein College of Medicine, Department of Physiology, 1300 Morris Park Avenue, Bronx, New York 10461, USA     

Fluidization of Membrane Lipids Enhances the Tolerance of Saccharomyces cerevisiae to Freezing and Salt Stress

Unsaturated fatty acids play an essential role in the biophysical characteristics of cell membranes and determine the proper function of membrane-attached proteins. Thus, the ability of cells to alter the degree of unsaturation in their membranes is an important factor in cellular acclimatization to environmental conditions. Many eukaryotic organisms can synthesize dienoic fatty acids, but Saccharomyces cerevisiae can introduce only a single double bond at the Δ⁹ position. We expressed two sunflower (Helianthus annuus) oleate Δ¹² desaturases encoded by FAD2-1 and FAD2-3 in yeast cells of the wild-type W303-1A strain (trp1) and analyzed their effects on growth and stress tolerance. Production of the heterologous desaturases increased the content of dienoic fatty acids, especially 18:2Δ^9,12, the unsaturation index, and the fluidity of the yeast membrane. The total fatty acid content remained constant, and the level of monounsaturated fatty acids decreased. Growth at 15°C was reduced in the FAD2 strains, probably due to tryptophan auxotrophy, since the trp1 (TRP1) transformants that produced the sunflower desaturases grew as well as the control strain did. Our results suggest that changes in the fluidity of the lipid bilayer affect tryptophan uptake and/or the correct targeting of tryptophan transporters. The expression of the sunflower desaturases, in either Trp⁺ or Trp⁻ strains, increased NaCl tolerance. Production of dienoic fatty acids increased the tolerance to freezing of wild-type cells preincubated at 30°C or 15°C. Thus, membrane fluidity is an essential determinant of stress resistance in S. cerevisiae, and engineering of membrane lipids has the potential to be a useful tool of increasing the tolerance to freezing in industrial strains.     

Improved ethanol tolerance of Saccharomyces cerevisiae strains by increases in fatty acid unsaturation via metabolic engineering

To enhance the ethanol tolerance of Saccharomyces cerevisiae, the Arabidopsis thaliana FAD2 gene and/or the S. cerevisiae OLE1 gene were over-expressed in this yeast. The transformant over-expressing both these genes could not only synthesize dienoic fatty acids but also increased the unsaturated fatty acid content of membrane lipid and then showed the highest viability in the presence of 15% (v/v) ethanol.     

Physiological role of d-amino acid-N-acetyltransferase of Saccharomyces cerevisiae: detoxification of d-amino acids

Saccharomyces cerevisiae is sensitive to d-amino acids: those corresponding to almost all proteinous l-amino acids inhibit the growth of yeast even at low concentrations (e.g. 0.1 mM). We have determined that d-amino acid-N-acetyltransferase (DNT) of the yeast is involved in the detoxification of d-amino acids on the basis of the following findings. When the DNT gene was disrupted, the resulting mutant was far less tolerant to d-amino acids than the wild type. However, when the gene was overexpressed with a vector plasmid p426Gal1 in the wild type or the mutant S. cerevisiae as a host, the recombinant yeast, which was found to show more than 100 times higher DNT activity than the wild type, was much more tolerant to d-amino acids than the wild type. We further confirmed that, upon cultivation with d-phenylalanine, N-acetyl-d-phenylalanine was accumulated in the culture but not in the wild type and hpa3Δ cells overproducing DNT cells. Thus, d-amino acids are toxic to S. cerevisiae but are detoxified with DNT by N-acetylation preceding removal from yeast cells.     

Blood-endothelial cell and blood-brain transport ofl-proline, α-aminoisobutyric acid,andl-alanine

We report the application of multiple time regression analysis with the in situ brain perfusion technique to measure the rates of passage between blood and brain for [¹⁴C]l-proline, [¹⁴C]l-alanine, and [¹⁴C] α-aminoisobutyric acid (AIB) and their rapidly reversible volumes following perfusion of these amino acids from 10 to 60 seconds. We also report on their mechanism of transport. Proline diffused through the blood-brain barrier with a transfer coefficient (K_in) of 0.55 ± 0.15 × 10⁻⁴ ml/s/g and had no reversible compartment. AIB had a low K_in of 0.68±0.14×10⁻⁴ ml/s/g and a significant reversible volume of 4.34±0.51×10⁻³ ml/g in parietal cortex.l-alanine had the highest transfer coefficient, 3.11±0.26 × 10⁻⁴ ml/s/g, and a reversible volume of 10.03±0.93×10⁻³ ml/g in the same cerebral region. Postwash procedures which remove any radiotracer in the vasculature and capillary depletion were performed for alanine and AIB, as they had significant reversible compartments, to test the possibility of rapid efflux from the endothelial cells. Results obtained from wash and capillary depletion procedures suggest that a rapid efflux could occur from endothelial cells after entry of alanine and AIB. Mechanisms of transport forl-alanine and AIB were investigated using amino acids (5 mM) as substrates and inhibitors of different amino acid transport systems. AIB transport was reduced by plasma andl-leucine and unchanged by sodium-free buffer, confirming its passage by the L₁ system.l-alanine uptake was sodium-independent and not reduced by plasma.l-serine,l-cysteine,l-leucine andl-phenylalanine produced similar inhibition (66%) whilel-alanine produced a lower inhibition (41%).l-arginine increased alanine uptake in cortex and thalamus. Addingl-serine tol-phenylalanine reduced the uptake only in cortex and hippocampus. These data suggest thatl-alanine is transported by another L transport system different from the L₁ system at the luminal membrane.     

Modification of cell membrane lipids inMicrococcus lysodeikticus induced by pantoyl lactone

Summary Growth ofMicroccoccus lysodeikticus in the presence of pantoyl lactone brings about both qualitative and quantitative changes in cell membrane lipids. Significant amounts of the two major phospholipids (phosphatidylglycerol and diphosphatidylglycerol) are converted to lyso forms; the largest conversion occurs in the phosphatidylglycerol. In addition, amounts of several phospholipid fatty acids are changed. Physical alteration of the cell membrane can be demonstrated using differential scanning calorimetry. Although growth and transport are significantly inhibited when pantoyl lactone is present, cells possessing altered cell membrane phospholipids and phospholipid fatty acids, brought about by growth in the presence of pantoyl lactone, transportd-alanine,l-glutamic andl-aspartic acid normally when washed free of the pantoyl lactone.     

Changes of Saccharomyces cerevisiae cell membrane components and promotion to ethanol tolerance during the bioethanol fermentation

During bioethanol fermentation process, Saccharomyces cerevisiae cell membrane might provide main protection to tolerate accumulated ethanol, and S. cerevisiae cells might also remodel their membrane compositions or structure to try to adapt to or tolerate the ethanol stress. However, the exact changes and roles of S. cerevisiae cell membrane components during bioethanol fermentation still remains poorly understood. This study was performed to clarify changes and roles of S. cerevisiae cell membrane components during bioethanol fermentation. Both cell diameter and membrane integrity decreased as fermentation time lasting. Moreover, compared with cells at lag phase, cells at exponential and stationary phases had higher contents of ergosterol and oleic acid (C_18:1) but lower levels of hexadecanoic (C_16:0) and palmitelaidic (C_16:1) acids. Contents of most detected phospholipids presented an increase tendency during fermentation process. Increased contents of oleic acid and phospholipids containing unsaturated fatty acids might indicate enhanced cell membrane fluidity. Compared with cells at lag phase, cells at exponential and stationary phases had higher expressions of ACC1 and HFA1. However, OLE1 expression underwent an evident increase at exponential phase but a decrease at following stationary phase. These results indicated that during bioethanol fermentation process, yeast cells remodeled membrane and more changeable cell membrane contributed to acquiring higher ethanol tolerance of S. cerevisiae cells. These results highlighted our knowledge about relationship between the variation of cell membrane structure and compositions and ethanol tolerance, and would contribute to a better understanding of bioethanol fermentation process and construction of industrial ethanologenic strains with higher ethanol tolerance.     

Role of phospholipid head groups in ethanol tolerance of Saccharomyces cerevisiae

Pre-incubation of cells of Saccharomyces cerevisiae with 2 M-ethanol led to decreased rates of L-alanine uptake, H+ efflux and fermentation rate. However, these responses were modified in yeast cells with altered phospholipid composition. Using L-alanine transport and H+ efflux as indices of ethanol tolerance, it was observed that cells enriched with phosphatidylserine had greater tolerance to ethanol. This resulted from altered charge of membrane phospholipids rather than changes in membrane fluidity. It is suggested that the anion:zwitterion ratio of phospholipids may be one of the important determinants of ethanol tolerance in S. cerevisiae.     

Studies on isolated subcellular components of cat pancreas

Summary Transport of alanine was studied in isolated plasma membrane vesicles from cat pancreas using a rapid filtration technique. The uptake is osmotically sensitive and the kinetics ofl-alanine transport are biphasic showing a saturable and a nonsaturable component. The saturable component is seen only when a sodium gradient directed from the medium to the vesicular space is present. Under this condition an overshooting uptake ofl-but not ofd-alanine occurs. The Na⁺ gradient stimulated uptake ofl-alanine is inhibited byl-serine andl-leucine and stimulated when the membrane vesicles had been preloaded withl-alanine,l-serine orl-leucine.The ionophore monensin inhibits stimulation of uptake caused by a sodium gradient. In the presence of valinomycin or carbonyl cyanidep-trifluoromethoxyphenylhydrazone (CFCCP), the sodium-dependent transport is augmented in vesicles preloaded with K₂SO₄ or H⁺ ions (intravesicular pH 5.5), respectively. In the presence of different anions, the Na⁺-dependent transport is stimulated according to increasing anionic penetration through membranes (lipid solubility). We conclude that a sodium dependent electrogenic amino acid transport system is present in pancreatic plasma membranes.     

Secondary transport of amino acids in Nitrosomonas europaea

Nitrosomonas europaea is capable of incorporating exogenously supplied amino acids. Studies in whole cells revealed that at least eight amino acids are actively accumulated, probably by the action of three different transport systems, each with high affinity ( molar range) for several amino acids. Evidence for the action of secondary mechanisms of transport was obtained from efflux, counterflow and exchange experiments. More detailed information was obtained from studies in liposomes in which solubilized integral membrane proteins of N. europaea were incorporated. Uptake of l-alanine in these liposomes could be driven by artificially imposed pH gradients and electrical potentials, but not by chemical sodium-ion gradients. These observations indicate that l-alanine is transported by a H⁺/alanine symport system. The ecological significance of secondary amino acid transport systems in autotrophic ammonium-oxidizing bacteria is discussed.     

The outer membrane TolC is involved in cysteine tolerance and overproduction in <Emphasis Type="Italic">Escherichia coli</Emphasis>

l-Cysteine is an important amino acid in terms of its industrial applications. We previously found marked production of l-cysteine directly from glucose in recombinant Escherichia coli cells by the combination of enhancing biosynthetic activity and weakening the degradation pathway. Further improvements in l-cysteine production are expected to use the amino acid efflux system. Here, we identified a novel gene involved in l-cysteine export using a systematic and comprehensive collection of gene-disrupted E. coli K-12 mutants (the Keio collection). Among the 3,985 nonessential gene mutants, tolC-disrupted cells showed hypersensitivity to l-cysteine relative to wild-type cells. Gene expression analysis revealed that the tolC gene encoding the outer membrane channel is essential for l-cysteine tolerance in E. coli cells. However, l-cysteine tolerance is not mediated by TolC-dependent drug efflux systems such as AcrA and AcrB. It also appears that other outer membrane porins including OmpA and OmpF do not participate in TolC-dependent l-cysteine tolerance. When a low-copy-number plasmid carrying the tolC gene was introduced into E. coli cells with enhanced biosynthesis, weakened degradation, and improved export of l-cysteine, the transformants exhibited more l-cysteine tolerance and production than cells carrying the vector only. We concluded that TolC plays an important role in l-cysteine tolerance probably due to its export ability and that TolC overexpression is effective for l-cysteine production in E. coli. Natthawut Wiriyathanawudhiwong and Iwao Ohtsu contributed equally to this work.     

Establishment of l-arabinose fermentation in glucose/xylose co-fermenting recombinant Saccharomyces cerevisiae 424A(LNH-ST) by genetic engineering

Cost-effective and efficient ethanol production from lignocellulosic materials requires the fermentation of all sugars recovered from such materials including glucose, xylose, mannose, galactose, and l-arabinose. Wild-type strains of Saccharomyces cerevisiae used in industrial ethanol production cannot ferment d-xylose and l-arabinose. Our genetically engineered recombinant S. cerevisiae yeast 424A(LNH-ST) has been made able to efficiently ferment xylose to ethanol, which was achieved by integrating multiple copies of three xylose-metabolizing genes. This study reports the efficient anaerobic fermentation of l-arabinose by the derivative of 424A(LNH-ST). The new strain was constructed by over-expression of two additional genes from fungi l-arabinose utilization pathways. The resulting new 424A(LNH-ST) strain exhibited production of ethanol from l-arabinose, and the yield was more than 40%. An efficient ethanol production, about 72.5% yield from five-sugar mixtures containing glucose, galactose, mannose, xylose, and arabinose was also achieved. This co-fermentation of five-sugar mixture is important and crucial for application in industrial economical ethanol production using lignocellulosic biomass as the feedstock.     

l- andd-alanine transport in brush border membrane vesicles from lepidopteran midgut: Evidence for two transport systems

Summary In brush border membrane vesicles from the midgut ofPhilosamia cynthia larvae (Lepidoptera) thel- andd-alanine uptake is dependent on a potassium gradient and on transmembrane electrical potential difference. Each isomer inhibits the uptake of the other form: inhibition ofl-alanine uptake byd-alanine is competitive, whereas inhibition ofd-alanine uptake byl-alanine is noncompetitive. Transstimulation experiments as well as the different pattern of specificity to cations suggest the existence of two transport systems. Kinetic parameters for the two transporters have been calculated both when K_out>K_in and K_out=K_in.d-alanine is actively transported also by the whole midgut, but it is not metabolized by the intestinal tissue.     

Effect of l-azetidine 2-carboxilic acid on the activity of the general amino-acid permease from Saccharomyces cerevisiae var. ellipsoideus

Addition of the l-proline analogue l-azetidine 2-carboxylic acid to growing cultures of Saccharomyces cerevisiae var. ellipsoideus promoted fast deactivation of the general aminoacid permease, measured as l-valine uptake, without an immediate decrease in the growth rate. Cells preincubated with the analogue for 3 h were unable to restore either growth ability or general aminoacid permease activity in analogue-free medium. Eadie-Hofstee plots of l-valine uptake in the presence of the analogue are consistent with a strong reduction in the number of active molecules of the general amino-acid permease located in the plasma membrane. Inhibitory effects on protein synthesis were seen after preincubations of the yeast with the analogue for 3 h although a 30 min preincubation had no effect.Abbreviations GAP general amino-acid permease - AZC l-azetidine 2-carboxylic acid - YNB yeast nitrogen base - YE Yeast extract     

Ionic and non-ionic compounds in the germination of spores of bacillus megaterium texas

Summary Germination requirements of suspensions of spores of Bacillus megaterium, Texas strain, an l-alanine-inosine type, have been examined employing a decrease in optical density as the criterion of germination. In deionized water, l-alanine and inosine were devoid of germinative powers. They were effective only in conjunction with any one of a large variety of salts. Data are given for germination by the monovalent and divalent alkali metal chlorides. The potassium halides were germinative; potassium fluoride was the best. Salts of organic acids, including fatty acids and polycarboxylic acids, were germinative. The need for inosine could be bypassed by various salts, e.g., ammonium propionate or salts of dipicolinic acid. Also, l-alanine was replaceable by a variety of amino acids, provided suitable ions were present. In the presence of magnesium chloride, sodium dipicolinate could substitute for either inosine or l-alanine, but not both. Salts of n-hexylamine and n-heptylamine bypassed the need for both l-alanine and inosine. A primary role for ions in germination is proposed and a secondary, augmentative action is attributed to l-alanine and inosine.     

Double mutation of the <Emphasis Type="Italic">PDC1</Emphasis> and <Emphasis Type="Italic">ADH1</Emphasis> genes improves lactate production in the yeast <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> expressing the bovine lactate dehydrogenase gene

Expression of a heterologous l-lactate dehydrogenase (l-ldh) gene enables production of optically pure l-lactate by yeast Saccharomyces cerevisiae. However, the lactate yields with engineered yeasts are lower than those in the case of lactic acid bacteria because there is a strong tendency for ethanol to be competitively produced from pyruvate. To decrease the ethanol production and increase the lactate yield, inactivation of the genes that are involved in ethanol production from pyruvate is necessary. We conducted double disruption of the pyruvate decarboxylase 1 (PDC1) and alcohol dehydrogenase 1 (ADH1) genes in a S. cerevisiae strain by replacing them with the bovine l-ldh gene. The lactate yield was increased in the pdc1/adh1 double mutant compared with that in the single pdc1 mutant. The specific growth rate of the double mutant was decreased on glucose but not affected on ethanol or acetate compared with in the control strain. The aeration rate had a strong influence on the production rate and yield of lactate in this strain. The highest lactate yield of 0.75 g lactate produced per gram of glucose consumed was achieved at a lower aeration rate.     

Stimulation of olfactory receptors alters regulation of [Cai] in olfactory neurons of the catfish (Ictalurus punctatus)

Summary Intracellular calcium was measured in single olfactory neurons from the channel catfish (Icatalurus punctatus) using the fluorescent Ca²⁺ indicator fura 2. In 5% of the cells, olfactory stimuli (amino acids) elicited an influx of calcium through the plasma membrane which led to a rapid transient increase in intracellular calcium concentration. Amino acids did not induce release of calcium from internal stores in these cells. Some cells responded specifically to one stimulus (l-alanine,l-arginine,l-norleucine andl-glutamate) while one cell responded to all stimuli. An increase in intracellular calcium could also be elicited in 50% of the cells by direct G-protein stimulation using aluminum fluoride. Because the fraction of cells which respond to direct G-protein stimulation is substantially larger than the fraction of cells responding to amino acids, we tested for possible damage of receptor proteins due to exposure of the olfactory neurons to papain during cell isolation. We find that pretreatment with papain does not alter specific binding ofl-alanine andl-arginine to olfactory receptor sites in isolated olfactory cilia. The results are discussed in terms of their relevance to olfactory transduction.     

Effects of ethanol,octanoic and decanoic acids on fermentation and the passive influx of protons through the plasma membrane of Saccharomyces cerevisiae

Ethanol, octanoic and decanoic acids are known toxic products of alcoholic fermentation and inhibit yeast functions such as growth and fermentation. pH-stat measurements showed that, in a concentration range up to 20 mg/l, octanoic and decanoic acids increase the rate of passive H⁺ influx across the plasma membrane of Saccharomyces cerevisiae IGC 3507. Decanoic acid was more active than octanoic acid, which agrees with its higher liposolubility. The fatty acids probably act as H⁺ carriers, since the magnitude of the effect depended on pH and correlated with the concentration of protonated fatty acids. Esterification of the fatty acids partially abolished the enhancing effect on passive H⁺ influx. Passive H⁺ influx showed saturation kinetics with half-maximal activity at 6.6 M H⁺ (pH 5.2). Contrary to previous findings, ethanol inhibited H⁺ influx exponentially up to a concentration of 8% (v/v). At higher concentrations, ethanol reactivated H⁺ influx; the original rate of H⁺ uptake was reached at 14% (v/v) ethanol. In the same concentration ranges that affected passive H⁺ influx, ethanol, octanoic and decanoic acids inhibited the fermentation rate. This inhibitory effect of the fatty acids on fermentation rate depended on liposolubility, pH, and esterification in the same way as that found for their effect on passive H⁺ influx. Inhibition of fermentation by octanoic and decanoic acids could therefore result from their effect on the rate of passive H⁺ influx. Correspondence to: S. Stevens     

Transport-limited fermentation and growth of Saccharomyces cerevisiae and its competitive inhibition

Summary The anaerobic glucose uptake (at 20°, pH 3.5) by resting cells of Saccharomyces cerevisiae followed unidirectional Michaelis-Menten kinetics and was competitively inhibited by l-sorbose; K _m and K _i were respectively 5.6×10^-4 m and 1.8×10^-1 m; V _max was 6.5×10^-8 moles mg^-1 min^-1. The aerobic uptake of glucose by resting yeast was also inhibited by l-sorbose but did not follow unidirectional Michaelis-Menten kinetics. Glucose-limited growth in the chemostat of a respiration-deficient mutant of S. cerevisiae was competitively inhibited by l-sorbose. As predicted by theory for transport-limited growth in the chemostat (van Uden, 1967) the steady state glucose concentrations were linear functions of the l-sorbose concentrations with different slopes at different dilution rates; K _m and K _i were respectively 7.2×10^-4 m and 1.8×10^-1 m. It is concluded that glucose transport was the rate-limiting step of anaerobic fermentation of S. cerevisiae and of growth of the mutant and that l-sorbose is a competitive inhibitor of active glucose transport in this yeast. The latter conclusion is accommodated in the transport model of van Steveninck and Rothstein (1965).