Reptation theory of ion channel gating.

Reptation theory is a highly successful approach for describing polymer dynamics in entangled systems. In turn, this molecular process is the basis of viscoelasticity. We apply a modified version of reptation dynamics to develop an actual physical model of ion channel gating. We show that at times longer than microseconds these dynamics predict an alpha-helix-screw motion for the amphipathic protein segment that partially lines the channel pore. Such motion has been implicated in several molecular mechanics studies of both voltage-gated and transmitter-gated channels. The experimental probability density function (pdf) for this process follows t-3/2 which has been observed in several experimental systems. Reptation theory predicts that channel gating will occur on the millisecond time scale and this is consistent with experimental results from single-channel recording. We examine the consequences of reptation over random barriers and we show that, to first order, the pdf remains unchanged. In the case of a charged helix undergoing reptation in the presence of a transmembrane potential we show that the tail of the pdf will be exponential. We provide a list of practical experimental predictions to test the validity of this physical theory.     

Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel.

The synthetic channel [acetyl-(LeuSerSerLeuLeuSerLeu)3-CONH2]6 (pore diameter approximately 8 A, length approximately 30 A) is a bundle of six alpha-helices with blocked termini. This simple channel has complex properties, which are difficult to explain, even qualitatively, by traditional theories: its single-channel currents rectify in symmetrical solutions and its selectivity (defined by reversal potential) is a sensitive function of bathing solution. These complex properties can be fit quantitatively if the channel has fixed charge at its ends, forming a kind of macrodipole, bracketing a central charged region, and the shielding of the fixed charges is described by the Poisson-Nernst-Planck (PNP) equations. PNP fits current voltage relations measured in 15 solutions with an r.m.s. error of 3.6% using four adjustable parameters: the diffusion coefficients in the channel's pore DK = 2.1 x 10(-6) and DCl = 2.6 x 10(-7) cm2/s; and the fixed charge at the ends of the channel of +/- 0.12e (with unequal densities 0.71 M = 0.021e/A on the N-side and -1.9 M = -0.058e/A on the C-side). The fixed charge in the central region is 0.31e (with density P2 = 0.47 M = 0.014e/A). In contrast to traditional theories, PNP computes the electric field in the open channel from all of the charges in the system, by a rapid and accurate numerical procedure. In essence, PNP is a theory of the shielding of fixed (i.e., permanent) charge of the channel by mobile charge and by the ionic atmosphere in and near the channel's pore. The theory fits a wide range of data because the ionic contents and potential profile in the channel change significantly with experimental conditions, as they must, if the channel simultaneously satisfies the Poisson and Nernst-Planck equations and boundary conditions. Qualitatively speaking, the theory shows that small changes in the ionic atmosphere of the channel (i.e., shielding) make big changes in the potential profile and even bigger changes in flux, because potential is a sensitive function of charge and shielding, and flux is an exponential function of potential.     

Three-dimensional Poisson-Nernst-Planck theory studies: influence of membrane electrostatics on gramicidin A channel conductance

A recently introduced real-space lattice methodology for solving the three-dimensional Poisson-Nernst-Planck equations is used to compute current-voltage relations for ion permeation through the gramicidin A ion channel embedded in membranes characterized by surface dipoles and/or surface charge. Comparisons to a variety of experimental results, presented herein, have proven largely successful. Strengths and weaknesses of the method are discussed.     

A cell survival model with saturable repair after irradiation

Summary A cell survival model with saturable repair has been developed. The model is based on the assumption that after irradiation the cell can be in one of the following three states: In state A the viable cells have no lesions, in state C cells carry lethal lesions and in state B cells exhibit potentially lethal lesions which can be repaired by a saturable enzymatic repair system or which are converted to lethal lesions. The model incorporates five parameters. The applicability of the model has been demonstrated by fitting 11 experimental data sets obtained with different cell lines, different kinds of radiation and variable repair times simulated by liquid holding recovery or inhibition of repair processes by different agents. The model and the results obtained are discussed in relation to published results.Dedicated to Prof. K.G. Zimmer on his 75th birthday     

A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel.

A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed.     

General continuum theory for multiion channel. II. Application to acetylcholine channel.

The general theory (Levitt, D. G. 1990. Biophys. J. 59:271-277) is applied to a model channel that resembles the acetylcholine receptor channel (ACH). The model incorporates the known features of the ACH geometry and fixed charge locations. The channel has a wide mouth facing the outer solution, tapering to a narrow region facing the interior of the cell. Rings of fixed negative charge are placed at the two surfaces where the bilayer begins, corresponding to the known charges at the ends of the M2 segment. It is assumed that the forces acting on the ion are electrostatic: ion-channel wall, ion-ion, Born image and applied voltage. Analytical expressions for these forces are derived that take account of the low dielectric lipid region. In addition, there is a local hard sphere repulsive force that prevents ions from piling up on each other in regions of the channel with a high fixed charge density. A classical continuum theory is used to obtain an expression for the diffusion coefficient in the channel. The model can mimic the major qualitative and, in many cases, quantitative experimental features of the ACH channel: current-voltage relation, conductance versus concentration and interaction between monovalent and divalent ions. The model calculations were also compared with the site directed mutagenesis experiments of Imoto, K., C. Busch, B. Sakmann, M. Mishina, T. Konno, J. Nakai, H. Bujo, Y. Mori, K. Fukuda, and S. Numa. (1988. Nature (Lond.). 335:645-648) in which the charge at the ends of the channel was systematically varied.     

Facilitated diffusion of p-nitrophenyl-alpha-D-maltohexaoside through the outer membrane of Escherichia coli. Characterization of LamB as a specific and saturable channel for maltooligosaccharides

LamB, an outer membrane protein of Escherichia coli, is a component of the maltose-maltooligosaccharide transport system. We used p-nitrophenyl-alpha-D-maltohexaoside, a chromogenic analog of maltohexaose, and a periplasmic amylase that hydrolyzes this compound to study the LamB-mediated diffusion of p-nitrophenyl-alpha-D-maltohexaoside into the periplasm. Using this approach, we were able to characterize LamB in vivo as a saturable channel for maltooligosaccharides. Permeation through LamB follows Michaelis-Menten kinetics, with a Km of 0.13 mM and a Vmax of 3.3 nmol/min/10(9) cells. Previous studies suggested that maltose-binding protein increases the rate of maltooligosaccharide diffusion through LamB. We show here that, at least in strains that are unable to transport maltooligosaccharides into the cytoplasm, maltose-binding protein does not influence the rate of substrate diffusion. The periplasmic amylase had been previously described as being of the alpha-type. We have now purified this protein and analyzed its mode of action using chromogenic maltooligosaccharides of varying length. Analysis of the hydrolytic products revealed that the enzyme recognizes its substrate from the nonreducing that the enzyme recognizes its substrate from the nonreducing end and preferentially liberates maltohexaose, in contrast to the behavior of classical alpha-amylases that are endohydrolases. Using p-nitrophenyl-alpha-D-maltohexaoside as a substrate, we determined a Km of 3 microM and a Vmax of 0.14 mumol/min/mg of protein.     

A specific and saturable spermine-binding component present in bovine testis membranes

To determine if polyamine (PA)-binding components were present in testis membranes, a membrane fraction derived from homogenates of immature bovine testes was utilized in a radioligand assay. [14C]Spermine ([14C] Sp) bound to a spermine-binding component (SpBC) in a saturable manner and radioligand-binding data were analyzed and fit to a one-site model. Estimates of the binding constant (Kd = 7.2 +/- 1.2 X 10(-6) M) and of the concentration of sites (11.6 +/- 1.6 X 10(-6) M) were determined assuming a one-to-one stoichiometry. Metal cations (Ca+2, Mg+2, Mn+2 and Na+) as chloride salts had no effect on binding of [14C]Sp to SpBC when tested at concentrations up to 10 mM. Not all polyamines tested were effective competitors for [14C]Sp binding, which had an ID50 of 21.0 +/- 2.0 microM. The inhibitory potencies for putrescine and spermidine relative to spermine were 3.1 +/- 0.43 X 10(-4) and 0.1 +/- 0.01 (nmol/nmol) respectively, illustrating the specificity of SpBC binding. In addition, acetylation of polyamines, which is generally associated with degradation and interconversion of polyamines, resulted in a reduction of potency of 25.2 +/- 2.0-fold of spermine and 31.1 +/- 10.6-fold of spermidine in the SpBC radioligand assay. Binding of SpBC was decreased by tryptic digestion of the membrane fraction, suggesting that protein may be a part of the SpBC. Neuraminidase treatment had no effect on [14C]Sp binding but phospholipase-C digestion increased [14C]Sp binding.(ABSTRACT TRUNCATED AT 250 WORDS)     

Regulation of connexin43 oligomerization is saturable

We have used connexin constructs containing a C-terminal di-lysine-based endoplasmic reticulum (ER) retention/retrieval signal (HKKSL) transfected into HeLa cells to study early events in connexin oligomerization. Using this approach, we found that Cx43-HKKSL stably expressed at moderate levels by HeLa cells was retained in the ER and prevented from oligomerization. However, Cx43-HKKSL stably overexpressed by HeLa cells escaped from the ER and localized to a perinuclear region of the cell that included the Golgi apparatus. Overexpressed Cx43-HKKSL oligomerized into hexamers and also formed Triton X-100 insoluble, intracellular complexes that resembled gap junctions. Thus, the ability of HeLa cells to inhibit Cx43 oligomerization was saturable. HeLa cells stably overexpressing Cx43-HKKSL may provide a useful model system to evaluate pharmacologic agents and/or cDNAs encoding chaperones with the potential to regulate initial steps in Cx43 oligomerization.     

First-principle study of the native defects in GaAs saturable absorbers

The change of atom configuration in GaAs, caused by intrinsic point defects (Ga and As vacancies, Ga and As antisites, Ga and As interstitials), is first calculated by a plane wave pseudo-potential method with the generalised gradient approximation in the frame of density functional theory, and the most stable structure is obtained. Then, the formation energy of each kind of the native defect is calculated, by which the possibilities of the six kinds of point defects to be formed during crystal growth are analysed. The defect energy levels corresponding to each kind of the native point defect and their electron occupancy are analysed from the aspect of density of states. Finally, the elastic constants of GaAs saturable absorbers with native point defects are calculated, and the impacts on the elastic properties brought by native point defects are studied. The values of defect energy levels obtained will be helpful in ascertaining the mechanism of the EL2 deep level in the GaAs saturable absorber, and the analysis of the elastic properties of a GaAs crystal with native point defects will be helpful in guiding the application of the GaAs crystal as a saturable absorber in passively Q-switched lasers.     

Statistical analysis of channel current from a membrane patch. II. A stochastic theory of a multi-channel system in the steady-state

A general stochastic theory is presented for analysis of current records of a patch containing an arbitrary number (N) of independent homologous channels in the steady-state. We give the "basic theorem" that at the instant of any open (or shut) transition of a channel, the other N-1 channels are located in each state with a probability equal to those in the steady-state, if enough transitions are observed. Using the "basic theorem", we derived: (a) the time-dependent open and shut frequencies after a definite type of transition, and (b) the probability density functions (pdf) of the duration of any period between two successive transitions. Briefly, the main results obtained were: (1) The time-dependent open (or shut) transition frequency after every shut (or open) transition at t = 0 in an N-channel patch, fJSh,Op(t)(N) (or fJOp,Sh(t)(N)), is the same as that of a one-channel patch except for the value of the constant. (2) In the all-shut (or all-open) period of a patch, the average duration of the period is 1/N, and the slowest exponential decay constant contained in the pdf is N times those of a single channel patch, respectively. (3) An example calculation for small N showed that the stochastic properties of a single channel can be obtained even when N is uncertain, if the channel open probability is small and exponential decay constants are separated. (4) When the channels are in equilibrium, the pdf of duration of every type of period in the patch is described by a sum of exponential terms with positive coefficients. This also holds for fJSh,Op(t)(N) and fJOp,Sh(t)(N).     

Growth kinetics of Lactobacillus acidophilus under ohmic heating

Lactobacillus acidophilus OSU133 was inoculated into MRS broth in a fermenter vessel and incubated at 30, 35, or 45 degrees C with agitation. Incubation temperatures were attained by conventional or ohmic heating. An electrical current at low (15 V) or high (40 V) voltage was used to heat the culture directly during fermentations under ohmic heating. The growth parameters (lag period, minimum generation time, and maximum growth) and changes in pH were determined during fermentation. Metabolic activities (consumption of glucose and production of lactic acid and bacteriocin) were determined during fermentation at 35 degrees C under both heating methods. Lag period for L. acidophilus was affected appreciably by the method of heating, but the magnitude of these changes depended on the fermentation temperature. When fermentation was done at 30 degrees C, lag period decreased by 94% under low-voltage ohmic, compared with conventional, heating methods. Ohmic heating did not change the generation time significantly and caused slight, but significant (p < 0.01) decrease in maximum growth. Therefore, the electric current enhances the early stages, but it inhibits the late stages of growth. Ohmic, compared with conventional, heating resulted in higher final pH and lower bacteriocin activity in the fermented medium. However, ohmic heating at 35 degrees C had minimal effect on glucose utilization and lactic acid production by L. acidophilus. Results show that measurement of the electric current when ohmic heating is done at a constant voltage may be used in monitoring such fermentations. In conclusion, ohmic heating is potentially useful in certain applications related to fermented foods. (c) 1996 John Wiley & Sons, Inc.     

Gravity dependency of the gramicidin A channel conductivity

Theoretical investigations involving the membrane-solution interface have revealed that the density of the solution varies appreciably within interfacial layers adjacent to charged membrane surfaces. The hypothesis that gravity interacts with this configuration and modifies transport rates across horizontal and vertical membranes differently was supported by initial experiments with gramicidin A channels in phosphatidylserine (PS) membranes in 0.1 M KCl. Channel conductivity was found to be about 1.6 times higher in horizontal membranes than in vertical membranes. Here we present the results of further experiments with gramicidin A channels (incorporated into charged PS- and uncharged phosphatidylcholine (PC) membranes in KCl- and CsCl-solutions) to demonstrate that the hypothesis is more generally applicable. Again, channel conductivity was found to be higher in horizontal PS membranes by a factor of between 1.20 and 1.75 in 0.1 M CsCl. No difference in channel conductivity was found for uncharged PC membranes in 0.1 M KCl and in 0.1 M CsCl. However, for PC membranes in 0.05 M KCl the channel conductivity was significantly higher in horizontal membranes by a factor of between 1.07 and 1.14. These results are consistent with the results of our model calculations of layer density and extension, which showed that the layer formation is enhanced by increasing membrane surface charge and decreasing electrolyte ion concentration. The mechanism of gravity interaction with membrane transport processes via interface reactions might be utilized by biological systems for orientational behaviour in the gravity field, which has been observed even for cellular systems. Received: 16 October 1995 / Accepted: 23 April 1996     

The structure of the gramicidin A transmembrane channel

Gramicidin A is a linear polypeptide antibiotic that facilitates the diffusion of monovalent cations across lipid bilayer membranes by forming channels. It has been proposed that the conducting channel is a dimer which is in equilibrium with nonconducting monomers in the membrane. To directly test this model in several independent ways, we have prepared and purified a series of gramicidin C derivatives. All of these derivatives are fully active analogs of gramicidin A, and each derivative has a useful chromophore esterified to the phenolic hydroxyl of tyrosine #11. Simultaneous conductance and fluorescence measurements on planar lipid bi-layer membranes containing dansyl gramicidin C yielded four conclusions: (1) A plot of the logarithm of the membrane conductance versus the logarithm of the membrane fluorescence had a slope of 2.0 ± 0.3, over a concentration range for which nearly all the gramicidin was monomeric. Hence, the active channel is a dimer of the nonconducting species. (2) In a membrane in which nearly all of the gramicidin was dimeric, the number of channels was approximately equal to the number of dimers. Thus, most dimers are active channels and so it should be feasible to carry out spectroscopic studies of the conformation of the transmembrane channel. (3) The association constant for dimerization is more than 1,000-fold larger in a glycerolester membrane with 26 Å-hydrocarbon thickness than in a 47 Å-glycerolester membrane. The dimerization constant in a 48 Å-phosphatidyl choline membrane was 200 times larger than in a 47 Å-glycerolester membrane, showing that it depends on the type of lipid as well as on the thickness of the hydrocarbon core. (4) We were readily able to detect 10^?14 mole cm^?2 of dansyl gramicidin C in a bilayer membrane, which corresponds to 60 fluorescent molecules per square μm. The fluorescent techniques described here should be sufficiently sensitive for fluorescence studies of reconstituted gates and receptors in planar bilayer membranes. An alternative method of determining the number of molecules of gramicidin in the channel is to measure the fraction of hybrid channels present in a mixture of 2 chemically different gramicidins. The single-channel conductance of p-phenylazo-benzene-sulfonyl ester gramicidin C (PABS gramicidin C) was found to be 0.68 that of gramicidin A. In membranes containing a mixture of these 2 gramicidins, a hybrid channel was evident in addition to 2 pure channels. The hybrid channel conductance was 0.82 that of gramicidin A. Fluorescence energy transfer from dansyl gramicidin C to diethylamino-phenylazobenzene-sulfonyl ester gramicidin C (DPBS gramicidin C), provided an independent way to measure the fraction of hybrid channels on liposomes. For both techniques the fraction of hybrid channels was found to be 2ad where a² and d² were the fractions of the 2 kinds of pure channels. This result strongly supports a dimer channel and the hybrid data excludes the possibility of a tetramer channel. The study of hybrid species by conductance and fluorescence techniques should be generally useful in elucidating the subunit structure of oligomeric assemblies in membranes. The various models which have been proposed for the conformation of the gramicidin transmembrane channel are briefly discussed.     

A selective filter model of the potassium channel

A model based on analogy between filter and crown-ether molecule in a two-phase system organic solvent-water is proposed for potassium channel selective filter. The selectivity of K+-channel can be quantitatively described by this model.     

A series-parallel model of the voltage-gated sodium channel

A series-parallel model of the kinetics of the voltage-gated sodium channel is described. It goes some way towards reconciling the time-courses of the gating and macroscopic sodium currents in the squid giant axon with the molecular structure of the channel.     

A large-conductance anion channel of the Golgi complex

An acidic lumenal pH is vital for the proper posttranslational modifications and sorting of proteins and lipids from the Golgi complex. We characterized ion channels present in Golgi fractions that have been cleared of transiting proteins. A large conductance anion channel was observed in approximately 30% of successful channel incorporations into the planar lipid bilayer. The channel, GOLAC-2, has six levels (one closed and five open). The open states are each approximately 20% increments of the maximal, 325 pS conductance. The channel was approximately 6 times more selective for Cl(-) over K(+). Binomial analysis of percent occupancy for each conducting level supports the hypothesis of five independent conducting pathways. The conducting levels can coordinately gate because full openings and closings were often observed. Addition of 3 to 5 mM reduced glutathione to the cis chamber caused dose-dependent increases in single channel conductance, indicating that the channel may be regulated by the oxidation-reduction state of the cell. We propose that GOLAC-2 is a co-channel complex consisting of five identical pores that have a coordinated gating mechanism. GOALC-2 may function as a source of counter anions for the H(+)-ATPase and may be involved in regulating charge balance and membrane potential of the Golgi complex.