End-point targeted molecular dynamics: large-scale conformational changes in potassium channels

Large-scale conformational changes in proteins that happen often on biological time scales may be relatively rare events on the molecular dynamics time scale. We have implemented an approach to targeted molecular dynamics called end-point targeted molecular dynamics that transforms proteins between two specified conformational states through the use of nonharmonic "soft" restraints. A key feature of the method is that the protein is free to discover its own conformational pathway through the plethora of possible intermediate states. The method is applied to the Shaker K(v)1.2 potassium channel in implicit solvent. The rate of cycling between the open and closed states was varied to explore how slow the cycling rate needed to be to ensure that microscopic reversibility along the transition pathways was well approximated. Results specific to the K(+) channel include: 1), a variation in backbone torsion angles of residues near the Pro-Val-Pro motif in the inner helix during both opening and closing; 2), the identification of possible occlusion sites in the closed channel located among Pro-Val-Pro residues and downstream; 3), a difference in the opening and closing pathways of the channel; and 4), evidence of a transient intermediate structural substate. The results also show that likely intermediate conformations during the opening-closing process can be generated in computationally tractable simulation times.

Physiological predictors of performance in cross-country skiing from treadmill tests in male and female subjects

In order to study which parameter that best corresponds to performance during cross-country skiing, seven male and nine female cross-country skiers were tested with treadmill tests. Parameters measured or computed by metabolic gas measurements were the anaerobic threshold (AT), threshold of decompensated metabolic acidosis (TDMA), the exercise intensity where the Respiratory exchange ratio reaches 1.0 (R = 1) and peak oxygen (O2) uptake (VO2peak). Onset of blood lactate accumulation (OBLA, 4 mmol.l-1 blood lactate) was also measured. The various parameters were measured in percentage of maximal heart rate, percentage of peak O2 uptake, VO2 ml.kg-1.min-1, VO2 ml.min-1.kg-2/3 and VO2 l.min-1. Results from four large competitions were also collected to rank the subjects. With correlation analysis, it was revealed that in male subjects a high OBLA was associated with good ranking results (r = (-0.829) - (-0.964); P < 0.05-0.001). In female subjects, the best association with competition results was found for R = 1 (r = (-0.715) - (-0.810); P < 0.05). Concerning VO2 measurements, for male subjects the unit l.min-1 is suggested to be used and for female subjects either the units l.min-1, ml.min-1.kg-2/3, or ml.kg-1.min-1 could be used when predicting performance in cross-country skiing. In conclusion, treadmill tests can be used for the prediction of performance in cross-country skiing. Further, various parameters from treadmill tests in men and women are best used as predictors of performance in cross-country skiing.

A brominated flame retardant, 2,2',4,4',5-pentabromodiphenyl ether: uptake, retention, and induction of neurobehavioral alterations in mice during a critical phase of neonatal brain development

Polybrominated diphenyl ethers (PBDEs) are used in large quantities as flame retardant additives. In a recent study, we have seen that neonatal exposure to some brominated flame retardants can cause permanent aberrations in spontaneous motor behavior that seem to worsen with age. In view of an increasing amount of PBDEs in mother's milk and in the environment, the present study was undertaken to investigate whether there is a critical and limited phase, during neonatal life, for induction of persistent neurotoxic effects of 2,2',4,4',5-pentaBDE (PBDE 99). Neonatal NMRI male mice were exposed on day 3, 10, or 19 to 8 mg 2,2',4,4',5-pentaBDE/kg body weight. Uptake and retention of 2,2',4,4',5-penta[(14)C]BDE were studied in the mouse brain after exposure to 1.5 M becquerel (Bq) 2,2',4,4',5-penta[(14)C]BDE /kg body weight (bw) on postnatal day 3, 10, or 19. Spontaneous motor behavior was observed in 4-month-old mice. Mice exposed to 2,2',4,4',5-pentaBDE on day 3 or 10 showed significantly impaired spontaneous motor behavior, whereas no effect was seen in mice exposed on day 19. Neonatal mice exposed to 2,2',4,4',5-penta[(14)C]BDE 99 on postnatal day 3, 10, or 19 were sacrificed 24 h or 7 days posttreatment. The amount of radioactivity, given as per mille ( per thousand) of total amount administered, was between 3.7 and 5.1 per thousand in the three different age categories at 24 h after administration. Seven days after the administration, 2,2',4,4',5-penta[(14)C]BDE or its metabolites could still be detected in the brain. The amount of radioactivity in the brain was not higher in mice exposed on day 3 or 10 when compared to exposure on day 19. Thus, the behavioral disturbances observed in adult mice following neonatal exposure to 2,2',4,4',5-pentaBDE are induced during a defined critical period of neonatal brain development.

Molecular simulation of dioleoylphosphatidylcholine lipid bilayers at differing levels of hydration

The structure and dynamics of the lipid and water components of dioleoylphosphatidylcholine bilayers at various levels of hydration were studied using molecular dynamics (MD) simulations. Equilibration of these systems proceeded by use of a hybrid MD and configurational-bias Monte Carlo technique using one atmosphere of pressure normal to the membrane and a set point for the lateral area derived from experimental Bragg spacings, combined with experimentally derived specific volumes for each of the system components. Membrane surface tensions were observed to be of the order of tens of dyn/cm. The transbilayer molecular fragment peak positions at low hydration were found to agree with experimental neutron and x-ray scattering profiles and previously published simulations. For hydration levels of 5.4, 11.4, and 16 waters/lipid, molecular fragment distributions and order parameters for the headgroup, lipid chains, and water were quantified. Spin-lattice relaxation rates and lateral self-diffusion coefficients of water agreed well with results from experimental nuclear magnetic resonance studies. Relaxation rates of the choline segments and chemical shift anisotropies for the phosphate and carbonyls were computed. Headgroup orientation, as measured by the P-N vector, showed enhanced alignment with the membrane surface at low hydration. The sign of the membrane dipole potential reversed at low hydration, with the membrane interior negative relative to the interlamellar region. Calculation of the number of water molecules in the headgroup hydration shell, as a function of hydration level, supports the hypothesis that the break point in the curve of Bragg spacing versus hydration level near 12 waters/lipid, observed experimentally by Hristova and White (1988. Biophys. J. 74:2419-2433), marks the completion of the first hydration shell.

Hierarchical approach to predicting permeation in ion channels

A hierarchical computational strategy combining molecular modeling, electrostatics calculations, molecular dynamics, and Brownian dynamics simulations is developed and implemented to compute electrophysiologically measurable properties of the KcsA potassium channel. Models for a series of channels with different pore sizes are developed from the known x-ray structure, using insights into the gating conformational changes as suggested by a variety of published experiments. Information on the pH dependence of the channel gating is incorporated into the calculation of potential profiles for K(+) ions inside the channel, which are then combined with K(+) ion mobilities inside the channel, as computed by molecular dynamics simulations, to provide inputs into Brownian dynamics simulations for computing ion fluxes. The open model structure has a conductance of approximately 110 pS under symmetric 250 mM K(+) conditions, in reasonable agreement with experiments for the largest conducting substate. The dimensions of this channel are consistent with electrophysiologically determined size dependence of quaternary ammonium ion blocking from the intracellular end of this channel as well as with direct structural evidence that tetrabutylammonium ions can enter into the interior cavity of the channel. Realistic values of Ussing flux ratio exponents, distribution of ions within the channel, and shapes of the current-voltage and current-concentration curves are obtained. The Brownian dynamics calculations suggest passage of ions through the selectivity filter proceeds by a "knock-off" mechanism involving three ions, as has been previously inferred from functional and structural studies of barium ion blocking. These results suggest that the present calculations capture the essential nature of K(+) ion permeation in the KcsA channel and provide a proof-of-concept for the integrated microscopic/mesoscopic multitiered approach for predicting ion channel function from structure, which can be applied to other channel structures.

Brominated flame retardants: a novel class of developmental neurotoxicants in our environment?

Brominated flame retardants are a novel group of global environmental contaminants. Within this group the polybrominated diphenyl ethers (PBDE) constitute one class of many that are found in electrical appliances, building materials, and textiles. PBDEs are persistent compounds that appear to have an environmental dispersion similar to that of polychlorinated biphenyls (PCBs) and dichlorodiphenyltrichloroethane (DDT). Levels of PBDEs are increasing in mother's milk while other organohalogens have decreased in concentration. We studied for developmental neurotoxic effects two polybrominated diphenyl ethers, 2,2',4,4'-tetrabromodiphenyl ether (PBDE 47) and 2,2',4,4',5-pentabromodiphenyl ether (PBDE 99)--congeners that dominate in environmental and human samples--together with another frequently used brominated flame retardant, tetrabromo-bis-phenol-A (TBBPA). The compounds were given to 10-day-old NMRI male mice, as follows: PBDE 47, 0.7 mg (1.4 micromol), 10.5 mg (21.1 micromol)/kg body weight (bw); PBDE 99, 0.8 mg (1.4 micromol), 12.0 mg (21.1 micromol)/kg bw; TBBPA, 0.75 mg (1.4 micromol), 11.5 mg (21.1 micromol)/kg bw. Mice serving as controls received 10 mL/kg bw of the 20% fat emulsion vehicle in the same manner. The present study has shown that neonatal exposure to PBDE 99 and PBDE 47 can cause permanent aberrations in spontaneous behavior, evident in 2- and 4-month-old animals. This effect together with the habituation capability was more pronounced with increasing age, and the changes were dose-response related. Furthermore, neonatal exposure to PBDE 99 also affected learning and memory functions in adult animals. These are developmental defects that have been detected previously in connection with PCBs.

Combined Monte Carlo and molecular dynamics simulation of hydrated lipid-cholesterol lipid bilayers at low cholesterol concentration

We have applied a hybrid equilibration and sampling procedure for the atomic level simulation of a hydrated lipid bilayer to systems consisting of dipalmitoyl phosphatidylcholine (DPPC) and cholesterol, and palmitoyl-oleyl phosphatidylcholine (POPC) at low (approximately 6%) cholesterol concentration. The procedure is applied to bilayers of 94 molecules of DPPC, 6 molecules of cholesterol, and 3205 water molecules, and to bilayers of 120 molecules of POPC, 8 molecules of cholesterol, and 4268 water molecules, at a temperature of 325 K. After equilibration, three separate 400-ps continuous molecular dynamics runs, separated by 10,000 configurational bias Monte Carlo steps, were carried out for each system. Properties of the systems were calculated and averaged over the three separate runs. Results of the simulations are presented and compared with experimental data and with other recent simulations of DPPC and cholesterol, and of pure DPPC, and pure POPC. Certain properties of the bilayers are indistinguishable from cholesterol-free bilayers, including lateral diffusion and electron density. Other properties, most notably the order parameter profile, show the effect of cholesterol even at low concentrations.

Clinical competence in pain assessment

Our knowledge about the content of the clinical knowledge used by nurses in a surgical recovery unit for assessment of postoperative pain is fairly limited. The aim of the present study was to analyse and describe the variations of nurses' conceptions of the impact of clinical experience on competence in post-operative pain assessment. The informants consist of critical care nurses. A phenomenographical approach has been applied to tape-recorded interview data. The results reveal that clinical competence in pain assessment was described in three categories: (a) to be able to see; (b) to be able to differentiate; (c) to be able to give. The observations articulate what nurses perceive that they have learnt from experience in performing many clinical pain assessments and point to some difficulties in using a single-data source for the development of valid and truthful professional knowledge. In the development of professional experience, it is of the utmost importance to be able to change perspective from what is most frequent and general to what is special and unique, to base one's standpoint on the individual patient's experience and integrate this with previous professional experience.

Potent competitive interactions of some brominated flame retardants and related compounds with human transthyretin in vitro

Brominated flame retardants such as polybrominated diphenyl ethers (PBDEs), pentabromophenol (PBP), and tetrabromobisphenol A (TBBPA) are produced in large quantities for use in electronic equipment, plastics, and building materials. Because these compounds have some structural resemblance to the thyroid hormone thyroxine (T(4)), it was suggested that they may interfere with thyroid hormone metabolism and transport, e.g., by competition with T(4) on transthyretin (TTR). In the present study, we investigated the possible interaction of several brominated flame retardants with T(4) binding to TTR in an in vitro competitive binding assay, using human TTR and 125 I-T(4) as the displaceable radioligand. Compounds were tested in at least eight different concentrations ranging from 1.95 to 500 nM. In addition, we investigated the structural requirements of these and related ligands for competitive binding to TTR. We were able to show very potent competition binding for TBBPA and PBP (10.6- and 7.1-fold stronger than the natural ligand T(4), respectively). PBDEs were able to compete with T(4)-TTR binding only after metabolic conversion by induced rat liver microsomes, suggesting an important role for hydroxylation. Brominated bisphenols with a high degree of bromination appeared to be more efficient competitors, whereas chlorinated bisphenols were less potent compared to their brominated analogues. These results indicate that brominated flame retardants, especially the brominated phenols and tetrabromobisphenol A, are very potent competitors for T(4) binding to human transthyretin in vitro and may have effects on thyroid hormone homeostasis in vivo comparable to the thyroid-disrupting effects of PCBs.

Biochemical responses of fish sac fry and a primary cell culture of fish hepatocytes exposed to polychlorinated naphthalenes

Chlorinated naphthalenes are planar halogenated aromatic compounds, which are widespread in the environment. Knowledge of their biochemical and toxicological actions in aquatic biota is, however, limited. The objective of this study was to assess the toxicity of highly chlorinated naphthalene congeners found in the aquatic environment on fish sac fry and to study their effects on xenobiotic metabolizing enzymes (CYP) using a short-term primary culture of fish hepatocytes and liver microsomes. A few days after hatching, rainbow trout sac fry were administered either Hallovax 1014, a mixture of 1,2,3,4,6,7-hexachloronaphthalene and 1,2,3,5,6, 7-hexachloronaphthalene (HxCN-mix), or 1,2,3,4,5,6, 7-heptachloronaphthalene (HpCN) (0.08, 0.8, and 4 microg/sac fry injected into the yolk sac). The exposure was terminated 2 weeks later. The naphthalene preparations did not cause any clinical signs of toxicity or difference in mortality rates between the control and treated groups. Immunohistochemical analysis of CYP1A expression in the treated sac fry revealed that staining was most pronounced in the hepatocytes and thereafter in kidney tubular epithelial cells. Moderate CYP1A staining was also seen in the mucosal epithelium of pyloric caecae and mild staining in the epithelium of olfactory organ. Staining in control sac fry was weak or absent. Exposure of the primary cell culture of trout hepatocytes to a low doses (</=10 ng/ml) of the chlorinated naphthalenes increased significantly CYP1A-associated EROD activity and CYP1A mRNA content, HxCN-mix being the most potent and thereafter HpCN and Hallovax 1014. The higher doses (50-100 ng/ml) of each naphthalene also inhibited EROD activity. However, the content of CYP1A mRNA or the intensity of the CYP1A protein band (58 kDa) recognized by anti-trout CYP1A peptide antibodies were not decreased with increasing polychlorinated naphthalene (PCN) concentration, indicating that the inhibition was not due to reduced protein synthesis. Furthermore, in vitro analyses of the inhibitory potential of PCNs on CYP1A activity with trout liver microsomes suggested that these naphthalene preparations may be CYP1A substrates and act as competitive inhibitors of CYP1A catalyst. Our results demonstrate that highly chlorinated naphthalenes are potent modulators of fish CYP1A enzyme and suggest that hepatocytes and tubular epithelial cells are the cell types that may be vulnerable to their metabolic products for cell injury in fish sac fry.

Combined Monte Carlo and molecular dynamics simulation of fully hydrated dioleyl and palmitoyl-oleyl phosphatidylcholine lipid bilayers

We have applied a new equilibration procedure for the atomic level simulation of a hydrated lipid bilayer to hydrated bilayers of dioleyl-phosphatidylcholine (DOPC) and palmitoyl-oleyl phosphatidylcholine (POPC). The procedure consists of alternating molecular dynamics trajectory calculations in a constant surface tension and temperature ensemble with configurational bias Monte Carlo moves to different regions of the configuration space of the bilayer in a constant volume and temperature ensemble. The procedure is applied to bilayers of 128 molecules of POPC with 4628 water molecules, and 128 molecules of DOPC with 4825 water molecules. Progress toward equilibration is almost three times as fast in central processing unit (CPU) time compared with a purely molecular dynamics (MD) simulation. Equilibration is complete, as judged by the lack of energy drift in 200-ps runs of continuous MD. After the equilibrium state was reached, as determined by agreement between the simulation volume per lipid molecule with experiment, continuous MD was run in an ensemble in which the lateral area was restrained to fluctuate about a mean value and a pressure of 1 atm applied normal to the bilayer surface. Three separate continuous MD runs, 200 ps in duration each, separated by 10,000 CBMC steps, were carried out for each system. Properties of the systems were calculated and averaged over the three separate runs. Results of the simulations are presented and compared with experimental data and with other recent simulations of POPC and DOPC. Analysis of the hydration environment in the headgroups supports a mechanism by which unsaturation contributes to reduced transition temperatures. In this view, the relatively horizontal orientation of the unsaturated bond increases the area per lipid, resulting in increased water penetration between the headgroups. As a result the headgroup-headgroup interactions are attenuated and shielded, and this contributes to the lowered transition temperature.

Flame retardant exposure: polybrominated diphenyl ethers in blood from Swedish workers

Polybrominated diphenyl ethers (PBDEs) are used as additives in polymers and textiles to prohibit the development of fires. Because of the production and use of PBDEs, their lipophilic characteristics, and persistence, these compounds have become ubiquitous environmental contaminants. The aim of the present study was to determine potential exposures of PBDEs to clerks working full-time at computer screens and personnel at an electronics-dismantling plant, with hospital cleaners as a control group. Five PBDE congeners--2,2',4,4'-tetraBDE; 2,2',4,4',5,5'-hexaBDE; 2,2',4,4',5, 6'-hexaBDE; 2,2',3,4,4',5',6-heptaBDE; and decaBDE--were quantified in blood serum from all three categories of workers. Subjects working at the dismantling plant showed significantly higher levels of all PBDE congeners in their serum as compared to the control group. Decabromodiphenyl ether is present in concentrations of 5 pmol/g lipid weight (lw) in the personnel dismantling electronics; these concentrations are comparable to the concentrations of 2,2',4, 4'-tetraBDE. The latter compound was the dominating PBDE congener in the clerks and cleaners. The major compound in personnel at the dismantling plant was 2,2',3,4,4',5',6-heptaBDE. Concentrations of this PBDE congener are almost twice as high as for 2,2',4, 4'-tetraBDE in these workers and seventy times the level of this heptaBDE in cleaners. The total median PBDE concentrations in the serum from workers at the electronics-dismantling plant, clerks, and cleaners were 37, 7.3, and 5.4 pmol/g lw, respectively. The results show that decabromodiphenyl ether is bioavailable and that occupational exposure to PBDEs occurs at the electronics-dismantling plant.

Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. I. Structure of the molecular complex

This paper reports on a simulation of a gramicidin channel inserted into a fluid phase DMPC bilayer with 100 lipid molecules. Two lipid molecules per leaflet were removed to insert the gramicidin, so the resulting preparation had 96 lipid molecules and 3209 water molecules. Constant surface tension boundary conditions were employed. Like previous simulations with a lower lipid/gramicidin ratio (Woolf, T. B., and B. Roux. 1996. Proteins: Struct., Funct., Genet. 24:92-114), it is found that tryptophan-water hydrogen bonds are more common than tryptophan-phospholipid hydrogen bonds. However, one of the tryptophan NH groups entered into an unusually long-lived hydrogen bonding pattern with two glycerol oxygens of one of the phospholipid molecules. Comparisons were made between the behavior of the lipids adjacent to the channel with those farther away. It was found that hydrocarbon chains of lipids adjacent to the channel had higher-order parameters than those farther away. The thickness of the lipid bilayer immediately adjacent to the channel was greater than it was farther away. In general, the lipids adjacent to the membrane had similar orientations to those seen by Woolf and Roux, while those farther away had similar orientations to those pertaining before the insertion of the gramicidin. A corollary to this observation is that the thickness of the hydrocarbon region adjacent to the gramicidin was much thicker than what other studies have identified as the "hydrophobic length" of the gramicidin channel.

Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. II. Rates and mechanisms of water transport

A gramicidin channel in a fluid phase DMPC bilayer with excess lipid and water has been simulated. By use of the formal correspondence between diffusion and random walk, a permeability for water through the channel was calculated, and was found to agree closely with the experimental results of Rosenberg and Finkelstein (Rosenberg, P.A., and A. Finkelstein. 1978. J. Gen. Physiol. 72:327-340; 341-350) for permeation of water through gramicidin in a phospholipid membrane. By using fluctuation analysis, components of resistance to permeation were computed for movement through the channel interior, for the transition step at the channel mouth where the water molecule solvation environment changes, and for the process of diffusion up to the channel mouth. The majority of the resistance to permeation appears to occur in the transition step at the channel mouth. A significant amount is also due to structurally based free energy barriers within the channel. Only small amounts are due to local friction within the channel or to diffusive resistance for approaching the channel mouth.

Using theory and simulation to understand permeation and selectivity in ion channels

It is clear that the function of ion channels must flow from their structure. With recent advances in computational power and methodology, it appears feasible to correlate structure to ion channel permeation at an atomistically detailed level of description. The overall strategy is to structure the calculations in a hierarchy, ranging from coarse-grained thermodynamic and kinetic descriptions to fine-grained molecular dynamics descriptions with atomic detail. Each level of description is connected to the others by appropriate statistical mechanical theory. The coarse-grained descriptions can be correlated directly with electrophysiological experiment. The fine-grained descriptions are used to parameterize the coarse-grained descriptions and to describe the permeation process at the most detailed level. This strategy has so far had varying degrees of success. It has successfully described water permeation through lipid bilayers and gramicidin channels. It has revealed the essential events of ion permeation through gramicidin channels at an atomistically detailed level. The role of channel protein motions in permeation has been elucidated. However, it appears that force fields used to describe molecular dynamics must be refined further to achieve completely accurate predictions of the permeation of such small ions as sodium. Channels with more complex structure and more multiion occupancy than gramicidin pose major computational challenges with respect to sampling protein conformations and ion distributions involved in the permeation process. Possible approaches to meeting these challenges are discussed.

[Nursing theories--friends or foes? Student nurses' perspective]

Nursing researchers consider nursing theories too theoretical and complicated to apply in practice. In this study student nurses in their last term are being interviewed about their ideas of nursing theories. A lot of different views emerged. The conclusion to make from this study is that a frequent presentation both practical and theoretical is required in order to make theories more accessible to nursing students. It is also important that different kinds of theories are exposed to give the students the possibility to find the theory most suited for the personality. This also gives the student the advantage to choose the essence from each theory. This is a way to establish a natural relationship between students and nursing theories and thereby the students will find easier ways to apply nursing theories in different nursing actions.

Selectivity of electron-donor- and electron-acceptor-bonded silica packing materials for hydrophobic environmental contaminants in polar and non-polar eluents

Electron-acceptor-bonded stationary phases, 2-(nitrophenyl)ethylsilyl (NPE) and 3-(p-nitrophenoxy)propylsilyl (NPO), and electron-donor-bonded phases, 3-(N-carbazolyl)propylsilyl (CZP), 2-(1-pyrenyl)ethylsilyl (PYE), and 5-coronenylpentylsilyl (COP), were prepared from silica particles and their selectivities were examined in both polar and non-polar solvents for specific isomers of polychlorodibenzo-p-dioxins (PCDDs), hexachloronaphthalenes (HxCNs) and planar and non-planar polychlorobiphenyl (PCB) congeners. Although no single stationary phase was able to separate all the isomer pairs that are coproduced during the synthesis of the PCDDs and HxCNs, pairs can be separated by selecting a suitable stationary phase and solvent. The separation of mixtures of PCDD isomers were found to be most successful with PYE and NPO phases, which yielded the opposite elution orders for each isomer pair that is produced as a mixture. Similar results were obtained for the HxCN isomers that were separated on PYE and CZP phases. The COP phase provided easier separation of non-ortho-substituted and mono-ortho-substituted PCBs from the other PCBs based on the planarity than PYE phase.

Computer simulation studies of biological membranes: progress, promise and pitfalls

Because of the complexity of biological membranes, computer simulations are useful adjuncts to experimental work in their study. Simulations of model membranes have provided new insights. Progress in simulating more biologically realistic membranes will require further development of statistical mechanical theory applied specifically to these systems, in conjunction with the use of powerful computers.

Distribution of Polychlorinated Naphthalene Congeners inEnvironmental and Source-Related Samples

Polychlorinated naphthalene (CN) congener profiles inenvironmental and source related samples were compared graphically and byprincipal component analysis. Samples investigated included biological,sediment, water, and air samples, technical polychlorinated biphenyl (PCB)and polychlorinated naphthalene (PCN) formulations, as well as municipalwaste incineration (MWI) fly ash and graphite electrode sludge. Biologicalsamples showed a preferential enrichment of planar, 1,3,5,7-substitutedtetra-, penta-, and hexachlorinated congeners and most of these samplesshowed profiles that displayed some similarity to those found in thetechnical PCB formulations. Sediment samples representing diffuse pollution,i.e., sediment samples from remote sites, showed an elevatedabundance of the planar hexa- and heptaCN congeners(1,2,3,4,6,7-/1,2,3,5,6,7- and 1,2,3,4,5,6,7-). The CN congener profile foundin these sediment samples and the two air samples were more similar to thetechnical PCB formulations than to the investigated MWI and graphite sludgesamples. Samples from three PCB contaminated lakes displayed similar congenerprofiles as Aroclor 1242, 1254 and Clophen A40. Two sediment samples and apike sample collected from the vicinity of a chloroalkali plant showedprofiles that were closely related to the investigated graphite electrodesludge sample. None of the environmental samples displayed profiles similarto low or medium chlorinated technical PCN (Halowax 1099, 1013, and 1014).

Solvation, water permeation, and ionic selectivity of a putative model for the pore region of the voltage-gated sodium channel

This paper describes a molecular dynamics and molecular mechanics study of the solvation and selectivity of the narrow pore and vestibule region of a model-built structure for the voltage-gated sodium channel. The particular structure used was one proposed by Guy and Durell. However, many of the features we saw would likely be shared with other possible models for this channel, such as the one proposed by Lipkind and Fozzard. It was found that the water mobility was reduced in the channel and the water orientations were significantly ordered by the channel environment. Water mobility depended on protein mobility; in a computer experiment in which the protein was artificially frozen, channel water at 300 degrees K was immobilized. Water motions were defined in significant part by a series of discrete moves from one pattern of hydrogen bonding with particular amino acids to another. However, there are so many different hydrogen bonding patterns that a description of the motion in terms of transitions among a small number of discrete states is not appropriate. In the model whose solvation we explored, several charged residues seem to play a particularly significant role in determining solvation and water motions. Based on energy minimization studies, the structure clearly shows selectivity for univalent cations over anions.

Computational studies of ion-water flux coupling in the airway epithelium. II. Role of specific transport mechanisms

Ion and water balance by the in vivo airway epithelium was investigated utilizing dynamic computer modeling. Parameters of the osmotically significant transport processes were varied to assess the sensitivity of water transport and fluid composition to transport perturbations. Establishment and regulation of water secretion represent a coordinated function of at least seven different ion transport processes: basolateral passive potassium transport, basolateral active sodium-potassium transport, basolateral sodium-potassium-chloride cotransport, apical passive sodium and chloride transport, and diffusion of sodium and chloride across the paracellular path. We found that apical chloride permeability at a level reported for cystic fibrosis is sufficient to cause the airway dehydration characteristic of cystic fibrosis. Given the reduction in apical chloride permeability in cystic fibrosis, a reduction in apical sodium permeability can potentially compensate completely for the airway dehydration associated with the cystic fibrosis genetic defect. Other simulations presented here address the importance of various membrane transport processes in airway epithelium water balance and the sensitivity of epithelium water balance to ion transport perturbations.

Computational studies of ion-water flux coupling in the airway epithelium. I. Construction of model

A mathematical model of ion and water transport across the airway epithelium is presented. The model consists of 12 state variables representing ion concentrations, volumes, and membrane potentials. All osmotically significant membrane transport processes for which there is conclusive experimental evidence are included: passive apical sodium and chloride movement, basolateral sodium-potassium pumping, basolateral sodium-potassium-chloride cotransport, passive basolateral potassium movement, nonselective passive paracellular ion motion, and water transport across all membranes. Ion movements are described by Michaelis-Menten kinetics or by the constant field flux equation. Model parameters are established with Ussing chamber data. Model behavior is validated by comparing in vitro simulations with experimental results. The model accurately reproduces short-circuit chloride and sodium fluxes, short-circuit current, and open-circuit membrane potentials from Ussing chamber data in the secreting and nonsecreting states. The model is then used to describe the behavior of the airway epithelium in vivo, in which case the apical electrolyte compartment is small and of variable size and ionic composition.

Incorporation of surface tension into molecular dynamics simulation of an interface: a fluid phase lipid bilayer membrane

In this paper we report on the molecular dynamics simulation of a fluid phase hydrated dimyristoylphosphatidylcholine bilayer. The initial configuration of the lipid was the x-ray crystal structure. A distinctive feature of this simulation is that, upon heating the system, the fluid phase emerged from parameters, initial conditions, and boundary conditions determined independently of the collective properties of the fluid phase. The initial conditions did not include chain disorder characteristic of the fluid phase. The partial charges on the lipids were determined by ab initio self-consistent field calculations and required no adjustment to produce a fluid phase. The boundary conditions were constant pressure and temperature. Thus the membrane was not explicitly required to assume an area/phospholipid molecule thought to be characteristic of the fluid phase, as is the case in constant volume simulations. Normal to the membrane plane, the pressure was 1 atmosphere, corresponding to the normal laboratory situation. Parallel to the membrane plane a negative pressure of -100 atmospheres was applied, derived from the measured surface tension of a monolayer at an air-water interface. The measured features of the computed membrane are generally in close agreement with experiment. Our results confirm the concept that, for appropriately matched temperature and surface pressure, a monolayer is a close approximation to one-half of a bilayer. Our results suggest that the surface area per phospholipid molecule for fluid phosphatidylcholine bilayer membranes is smaller than has generally been assumed in computational studies at constant volume. Our results confirm that the basis of the measured dipole potential is primarily water orientations and also suggest the presence of potential barriers for the movement of positive charges across the water-headgroup interfacial region of the phospholipid.

Liquid-gel partitioning using Lipidex in the determination of polychlorinated biphenyls, naphthalenes, dibenzo-p-dioxins and dibenzofurans in blood plasma

A method was developed for the transfer of fat, polychlorinated biphenyls (PCBs), naphthalenes (PCNs), dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs) from blood plasma into the lipophilic gel Lipidex 5000. Subsequent elution of the gel separated about 70% of the fat from the analytes. Different adsorbents and activated charcoal were applied for further purification of the sample and separation of analytes. Identification and determination of the chlorinated compounds were made by gas chromatography with electron-capture detection (GC-ECD) or gas chromatography-mass spectrometry (GC-MS). Recoveries were studied by addition of Halowax 1014 and different congeners of PCBs, PCNs, PCDDs and PCDFs to 50 ml of plasma. The mean recoveries of the individual compounds studied were 72-99%. By using the liquid-gel partitioning technique emulsions were avoided. Concentrations of lipids in plasma obtained by the present method agreed well with the concentrations obtained using liquid-liquid partitioning with chloroform-methanol.

Gas chromatographic retention behaviour of polychlorinated naphthalenes on non-polar, polarizable, polar and smectic capillary columns

Six commercially available gas chromatography columns were investigated for performance in separating polychlorinated naphthalenes (PCNs). Retention behaviour on the investigated phases is compared and retention data for 40 congeners on a 5% phenyl-methylpolysiloxane column is reported. For all columns, except the octylmethylpolysiloxane and the smectic, a relation between substitution pattern and retention was found, where substitution in adjacent positions as well as alpha-substitution increase the retention time. A mathematical model based on these findings was developed and used to predict the relative retention of all congeners from di- up to octachloronaphthalene, on a 5% phenyl-methylpolysiloxane column.

Brownian dynamics study of a multiply-occupied cation channel: application to understanding permeation in potassium channels

The behavior of a multiply-occupied cation-selective channel has been computed by Brownian dynamics. The length, cross-section, ion-ion repulsion force, and ionic mobility within the channel are all estimated from data and physical reasoning. The only free parameter is a partition energy at the mouth of the channel, defining the free energy of an ion in the channel compared to the bath. It is presumed that this partition energy is associated with the energetics of exchanging a bulk hydration environment for a channel hydration environment. Varying the partition energy alone, keeping all other parameters fixed, gives approximately the full range of magnitudes of single channel conductances seen experimentally for K channels. Setting the partition energy at -11 kT makes the computed channel look similar to a squid axon K channel with respect to magnitude of conductance, shape of the I-V curve, non-unity of Ussing flux ratio exponents, decrease of current and increase of conductance with extracellular ion accumulation, and saturation at high ion concentration in the bathing solution. The model includes no preferred binding sites (local free energy minima) for ions in the channel. Therefore it follows that none of the above-mentioned properties of K channels are strong evidence for the existence of such sites. The model does not show supersaturation of current at very high bathing concentrations nor any pronounced voltage-dependence of the Ussing flux ratio exponent, suggesting that these features would require additional details not included in the model presented herein.

Ethoxyresorufin O-deethylase (EROD) and aryl hydrocarbon hydroxylase (AHH)-inducing potency and lethality of chlorinated naphthalenes in chicken (Gallus domesticus) and eider duck (Somateria mollissima) embryos

The 7-ethoxyresorufin O-deethylase (EROD)- and aryl hydrocarbon hydroxylase (AHH)-inducing potencies and lethalities of a technical preparation of polychlorinated naphthalenes (PCNs) (Halowax 1014, approximate congener ratio: 20% tetrachloronaphthalenes, 40% pentachloronaphthalenes, 40% hexachloronaphthalenes), a mixture of 50% 1,2,3,5,6,7-hexachloronaphthalene and 50% 1,2,3,4,6,7-hexachloronaphthalene (HxCN-mix), and 1,2,3,4,5,6,7-heptachloronaphthalene (HpCN) were studied in chicken (Gallus domesticus) and eider duck (Somateria mollissima) embryos. Mortality and hepatic EROD activity were determined on day 10 of incubation in chicken embryos exposed to various doses of the PCNs via the air-sacs of the eggs on day 7. The HxCN-mix and Halowax 1014 proved to have both embryolethal and EROD-inducing properties, while the HpCN had low EROD-inducing potency and embryolethality. ED50 values for EROD induction by the HxCN-mix and Halowax 1014 were estimated to be 0.06 mg/kg egg and 0.2 mg/kg egg, respectively. Fifty percent of the chicken embryos died (6/12) when given 3.0 mg/kg of the HxCN-mix while a similar dose of Halowax 1014 caused mortality in 4 out of 12 chicken embryos. The dose-response curve for EROD induction by Halowax 1014 exhibited a decline after the maximal level was reached. When Halowax 1014 (1.0 mg/kg egg) was coinjected with 3,3',4,4',5-pentachlorobiphenyl (PCB IUPAC #126) (0.1 microgram/kg egg) no additive effects on EROD activity were found, but when the same dose of Halowax 1014 was coinjected with a dose of PCB #126, known to cause maximal induction (1.0 microgram/kg egg), the resulting EROD activity was lower than that caused solely by 1.0 micrograms PCB #126/kg egg.(ABSTRACT TRUNCATED AT 250 WORDS)

The nature of ion and water barrier crossings in a simulated ion channel

Using a combination of techniques, including molecular dynamics, time-correlation analysis, stochastic dynamics, and fitting of continuum diffusion theory to electrophysiological data, a characterization is made of thermally driven sodium, water, and D2O motion within the gramicidin A channel. Since the channel contents are constrained to move in a single-file fashion, the motion that corresponds to experimentally measurable rates of permeation of the membrane is the motion of the center of mass of the channel contents. We therefore emphasize channel contents center-of-mass motion in our analysis of molecular dynamics computations. The usual free energy calculation techniques would be of questionable validity when applied to such motion. As an alternative to those techniques, we postulate a periodic sinusoidal free energy profile (related to the periodic structure of the helical channel) and deduce the fluid dynamic diffusion coefficient and the height and spacing of the free energy barriers from the form of the mean-square-deviation function, using stochastic computations. The fluid dynamic friction in each case appears similar to that for aqueous solution. However, the diffusive motions are modulated by a spatially periodic free energy profile with a periodicity characteristic of an L-D pair of amino acids in the gramicidin helix, approximately 1.7 A in the model we use. The barrier height depends on which substance is moving in the channel, but in each case is several times thermal energy. For barriers of this width and height, the motion is intermediate between the low-friction (transition-state) and high-friction (Brownian) limits. Thus, neither of these formalisms that have been used commonly to describe membrane permeation gives an accurate picture of the underlying physical process (although the Brownian description seems closer to correct). The non-Markovian Langevin equation must be solved to describe properly the statistics of the process. The "channel state of matter" characteristic of the channel contents appears to have some properties typical of the solid and some typical of the liquid state. The magnitude of the local friction and nature of the ion solvation are similar to the liquid state, but the periodicities of structure, free energy, and dynamics are somewhat solid-like. The alignment of water dipoles in the channel bears some resemblance to the orientational ordering of a nematic liquid crystal, but unlike a nematic liquid crystal, the waters have a degree of translational order as well. Thus, the "channel state" is not adequately described by analogy to either the solid or liquid states or to liquid crystals but must be dealt with as its own characteristic type of condensed matter.

Functional significance of the A-current

This work considers the response to simulated synaptic inputs of an excitable membrane model. The model is essentially of the Hodgkin-Huxley type, but contains an A-current in addition to sodium and delayed-rectifier potassium channels. The results were compared with previous simulations in which the stimulus was an injected current. These two types of stimuli give somewhat different results because synaptic stimuli directly change the membrane resistance, whereas injected current does not. The results of synaptic stimulation were similar to injected current in that very low frequencies of action potentials were elicited only where the stimulus was slightly above threshold. For most of the range of synaptic inputs that produced oscillatory behavior, the A-current had little effect on oscillation frequency. With synaptic stimuli as with injected current, the model membrane's spiking behavior does not begin immediately when an excitatory stimulus is imposed on a quiescent state. The delay before spiking is closely related to the inactivation time of the A-current. The synaptic results were different from the injected current results in that when substantial inhibition was present, the ability to produce very-low-frequency spiking was absent, even just above the excitatory threshold. The higher the degree of inhibition, the narrower the range of spike frequencies that could be elicited by excitation. At very high inhibition, no degree of excitation could elicit spiking.

Molecular dynamics computations and solid state nuclear magnetic resonance of the gramicidin cation channel

This paper reports on a coupled approach to determining the structure of the gramicidin A ion channel, utilizing solid state nuclear magnetic resonance (NMR) of isotopically labeled gramicidin channels aligned parallel to the magnetic field direction, and molecular dynamics (MD). MD computations using an idealized right-handed beta-helix as a starting point produce a refined molecular structure that is in excellent agreement with atomic resolution solid state NMR data. The data provided by NMR and MD are complementary to each other. When applied in a coordinated manner they provide a powerful approach to structure determination in molecular systems not readily amenable to x-ray diffraction.

Time-correlation analysis of simulated water motion in flexible and rigid gramicidin channels

Molecular dynamics simulations have been done on a system consisting of the polypeptide membrane channel former gramicidin, plus water molecules in the channel and caps of waters at the two ends of the channel. In the absence of explicit simulation of the surrounding membrane, the helical form of the channel was maintained by artificial restraints on the peptide motion. The characteristic time constant of the artificial restraint was varied to assess the effect of the restraints on the channel structure and water motions. Time-correlation analysis was done on the motions of individual channel waters and on the motions of the center of mass of the channel waters. It is found that individual water molecules confined in the channel execute higher frequency motions than bulk water, for all degrees of channel peptide restraint. The center-of-mass motion of the chain of channel waters (which is the motion that is critical for transmembrane transport, due to the mandatory single filing of water in the channel) does not exhibit these higher frequency motions. The mobility of the water chain is dramatically reduced by holding the channel rigid. Thus permeation through the channel is not like flow through a rigid pipe; rather permeation is facilitated by peptide motion. For the looser restraints we used, the mobility of the water chain was not very much affected by the degree of restraint. Depending on which set of experiments is considered, the computed mobility of our water chain in the flexible channel is four to twenty times too high to account for the experimentally measured resistance of the gramicidin channel to water flow. From this result it appears likely that the peptide motions of an actual gramicidin channel embedded in a lipid membrane may be more restrained than in our flexible channel model, and that these restraints may be a significant modulator of channel permeability. For the completely rigid channel model the "trapping" of the water molecules in preferred positions throughout the molecular dynamics run precludes a reasonable assessment of mobility, but it seems to be quite low.

Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels

In this paper we calculate surface conformation and deformation free energy associated with the incorporation of gramicidin channels into phospholipid bilayer membranes. Two types of membranes are considered. One is a relatively thin solvent-free membrane. The other is a thicker solvent-containing membrane. We follow the approach used for the thin membrane case by Huang (1986) in that we use smectic liquid crystal theory to evaluate the free energy associated with distorting the membrane to other than a flat configuration. Our approach is different from Huang, however, in two ways. One is that we include a term for surface tension, which Huang did not. The second is that one of our four boundary conditions for solving the fourth-order differential equation describing the free energy of the surface is different from Huang's. The details of the difference are described in the text. Our results confirm that for thin membranes Huang's neglect of surface tension is appropriate. However, the precise geometrical form that we calculate for the surface of the thin membrane in the region of the gramicidin channel is somewhat different from his. For thicker membranes that have to deform to a greater extent to accommodate the channel, we find that the contribution of surface tension to the total energy in the deformed surface is significant. Computed results for the shape of the deformed surface, the total energy in the deformed surface, and the contributions of different components to the total energy, are presented for the two types of membranes considered. These results may be significant for understanding the mechanisms of dimer formation and breakup, and the access resistance for ions entering gramicidin channels.

Water and polypeptide conformations in the gramicidin channel. A molecular dynamics study

Theoretical studies of ion channels address several important questions. The mechanism of ion transport, the role of water structure, the fluctuations of the protein channel itself, and the influence of structural changes are accessible from these studies. In this paper, we have carried out a 70-ps molecular dynamics simulation on a model structure of gramicidin A with channel waters. The backbone of the protein has been analyzed with respect to the orientation of the carbonyl and the amide groups. The results are in conformity with the experimental NMR data. The structure of water and the hydrogen bonding network are also investigated. It is found that the water molecules inside the channel act as a collective chain; whereas the conformation in which all the waters are oriented with the dipoles pointing along the axis of the channel is a preferred one, others are also accessed during the dynamics simulation. A collective coordinate involving the channel waters and some of the hydrogen bonding peptide partners is required to describe the transition of waters from one configuration to the other.

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.

Application of Brownian motion theory to the analysis of membrane channel ionic trajectories calculated by molecular dynamics

This paper shows how Brownian motion theory can be used to analyze features of individual ion trajectories in channels as calculated by molecular dynamics, and that its use permits more precise determinations of diffusion coefficients than would otherwise be possible. We also show how a consideration of trajectories of single particles can distinguish between effects due to the magnitude of the diffusion coefficient and effects due to barriers and wells in the potential profile, effects which can not be distinguished by consideration of average fluxes.

Stochastic theory of ion movement in channels with single-ion occupancy. Application to sodium permeation of gramicidin channels

The electrodiffusion equations were solved for the one-ion channel both by the analytical method due to Levitt and also by Brownian dynamic simulations. For both types of calculations equilibration of ion distribution between the bath and the ends of the channel was assumed. Potential profiles were found that give good fits to published data on Na+ permeation of gramicidin channels. The data were best fit by profiles that have no relative energy maximum at the mouth of the channel. This finding suggests that alignment of waters or channel charged groups inside the channel in response to an ion's approach may provide an energetically favorable situation for entry sufficient to overcome the energy required for removing bulk waters of hydration. An alternative possibility is that the barrier to ion entry is situated outside the region restricted to single-ion occupancy. Replacement of valine with more polar amino acids at the No. 1 location was found to correspond to a deepening of the potential minima near the channel mouths, an increase in height of the central barrier to ion translocation across the channel, and possibly a reduction in the mobility of the ion-water complex in the channel. The Levitt theory was extended to calculate passage times for ions to cross the channel and the blocking effects of ions that entered the channel but didn't cross. These quantities were also calculated by the Brownian dynamics method.

Basolateral membrane chloride transport in isolated epithelia of frog skin

Isotopic methodology was used to characterize Cl- transport in isolated epithelia of frog skin (northern Rana pipiens) bathed in Cl--rich Ringer solution and short-circuited. Cl- content of epithelia measured when loaded to 36Cl specific activity equilibrium averaged 139.6 neq/mg dry wt. The kinetics of 36Cl efflux was biexponential and consistent with binding or compartmentalization of approximately 30% of tissue Cl- within the intracellular pool. Because efflux of 36Cl to the apical solution was immeasurable, it was concluded that apical membranes were virtually impermeable to Cl- and that basolateral membranes were highly permeable to Cl- with a mean unidirectional Cl- efflux of 21.7 microA/cm2. Both furosemide (1 mM) and 4-acetamido-4'-isothiocyanostilbene-2,2'-disulfonic acid (5 X 10(-4) M) inhibited markedly the basolateral membrane chloride fluxes within seconds, as measured in chamber experiments. As inhibition of Cl- flux occurred in the absence of a change of the electrical parameters of apical and basolateral membranes, the mechanisms of Cl- transport appeared to be electroneutral and, for the most part at least, not coupled to the fluxes of Na+ and K+. Transepithelial Cl- fluxes averaged near 1 microA/cm2, proceeding via transport routes in parallel to the cells of the stratified epithelium. No correlation existed between the "shunt" resistance measured in the presence of 100 microM amiloride (greater than 1,000 omega X cm2) and the partial conductance to Cl-.

Frequency entrainment of squid axon membrane

Sinusoidally varying stimulating currents were applied to space-clamped squid giant axon membranes in a double sucrose gap apparatus. Stimulus parameters varied were peak-to-peak current amplitude, frequency, and DC offset bias. In response to these stimuli, the membranes produced action potentials in varying patterns, according to variation of input stimulus parameters. For some stimulus parameters the output patterns were stable and obviously periodic with the periods being simple multiples of the input period; for other stimulus parameters no obvious periodicity was manifest in the output. The experimental results were compared with simulations using a computer model which was modified in several ways from the Hodgkin-Huxley model to make it more representative of our preparation. The model takes into account K+ accumulation in the periaxonal space, features of Na+ inactivation which are anomalous to the Hodgkin-Huxley model, sucrose gap hyperpolarization current, and membrane current noise. Many aspects of the experiments are successfully simulated but some are not, possibly because some very slow process present in the preparation is not included in the model.

The standard Hodgkin-Huxley model and squid axons in reduced external Ca++ fail to accommodate to slowly rising currents

Accommodation may be defined as an increase in the threshold of an excitable membrane when the membrane is subjected to a sustained subthreshold depolarizing stimulus. Some excitable membranes show accommodation in response to currents which rise linearly at a very slow rate. In this report we point out a theoretical and an experimental counterexample, i.e., a nerve model and an axon which do not accommodate. The nerve model is the standard Hodgkin-Huxley axon, which Hodgkin and Huxley expected not to be excited by a very slowly rising current. This expectation is often quoted as fact, in spite of contrary calculations which we confirm. We have found that squid axons in seawater with reduced divalent cation concentration also do not accommodate to slowly rising currents.

Interactions of cell volume, membrane potential, and membrane transport parameters

Equations have been written and solved that describe for animal cells the relationships among membrane transport, cell volume, membrane potential, and distribution of permeant solute. The essential system consists of n + 2 equations, where n is the number of permeant solute species. The n of the equations are the n transport equations for the permeant species, one for each species. The other two equations are statements of 1) the condition for bulk electroneutrality inside the cell and 2) the condition for isotonicity between the interior and exterior of the cell. Numerical solutions have been obtained in both the steady-state and time-varying cases for transport equations that are physically and phenomenologically reasonable. In addition to numerical solutions analytic expressions are presented that show the ranges of membrane parameters essential for volume regulation; for values of membrane parameters beyond explicitly defined bounds, the equations do not have real, positive solutions for cell volume.

A fully coupled transient excited state model for the sodium channel. II. Implications for action potential generation, threshold, repetitive firing, and accommodation

The axon membrane is simulated by standard Hodgkin-Huxley leakage and potassium channels plus a coupled transient excited state kinetic scheme for the sodium channel. This scheme for the sodium channel is as proposed previously by the author. Simulations are presented showing the form of the action potential, threshold behavior, accommodation, and repetitive firing. It is seen that the form of the individual action potential, its all-or-none nature, and its refractory period are well simulated by this model, as they are by the standard Hodgkin-Huxley model. However, the model differs markedly from the Hodgkin-Huxley model with respect to repetitive firing and accommodation to stimulating currents of slowly rising intensity, in ways that are shown to be related to those features of the sodium inactivation which are anomalous to the H-H model. The tendency for repetitive firing is highly dependent on that parameter which primarily determines the existence of the inactivation shift in voltage clamp experiments, in such a way that the more pronounced the inactivation shift, the less the tendency for repetitive firing. The tendency for accommodation is highly dependent on that parameter which primarily determines the 'tauc-tauh' separation, in such a way that the greater the separation the greater the tendency for the membrane to accommodate without firing action potentials to a slowly rising current.

A fully coupled transient excited state model for the sodium channel. I. Conductance in the voltage clamped case

The behavior under voltage clamp conditions of a coupled kinetic scheme for the sodium channel is examined. The scheme is given diagrammatically by: Numerical simulations are presented which show that this model fits the voltage clamp data which are well described by the Hodgkin-Huxley equations, but also gives the sorts of behavior anomalous to the Hodgkin-Huxley model which have been seen experimentally. Further, straightforward changes in parameter values are shown to be capable of mimicking the ways in which some axonal preparations differ from others. Detailed, but admittedly heuristic, arguments are presented for the propositions that: 1) the model is minimal; i.e. no simpler kinetic model will fit the array of data simulated, and: 2) the transient excited state is necessary; i.e. no model of comparable simplicity with pure voltage dependent kinetics will fit the array of data simulated.