Anisotropy and anharmonicity of atomic fluctuations in proteins: implications for X-ray analysis

The effects of anisotropy and anharmonicity of the atomic fluctuations on the results of crystallographic refinement of proteins are examined. Atomic distribution functions from a molecular dynamics simulation for lysozyme are introduced into a real-space (electron density) refinement procedure for individual atoms. Several models for the atomic probability distributions are examined. When isotropic, harmonic motion is assumed, the largest discrepancies between the true first moments (means) and second moments (B factors) of the positions calculated from the dynamics and the fitted values occur for probability densities with multiple peaks. The refined mean is at the center of the largest peak, and the refined B factor is slightly larger than that of the largest peak, unless the distance between the peaks is small compared to the peak width. The resulting values are often significantly different from the true first and second moments of the distribution. To improve the results, alternate conformations, rather than anharmonic corrections, should be included.     

A-type potassium channel clusters revealed using a new statistical analysis of loose patch data.

The spatial distribution of ion channels over the surface of a neuron is an important determinant of its excitable properties. We introduce two measures of channel clustering for use in patch-clamp experiments: a normalized chi-squared statistic (eta) and the number of zero-channel patches in a data set (Z). These statistics were calculated for data sets describing the distribution of A-type potassium channels on neurons of the nudibranch Doriopsilla and measurements of Ca-dependent outward current channels on bullfrog hair cells, as well as simulated channel distributions. When channels are clustered, eta is approximately equal to the amount of current in a cluster. The analysis shows that somatic A-channels in the nudibranch are distributed in clusters of approximately 50 channels each. The clusters are < 2 microns wide and are separated, on average, by 3.2 microns. Outward current channels on hair cells occur in clusters of approximately 27 channels each, in agreement with the original analysis. Channel clustering may reflect properties of the insertion or regulation of channels in the membrane.     

Statistical evaluation of ion-channel gating models based on distributions of log-likelihood ratios

The distributions of log-likelihood ratios (DeltaLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Xi, full model; Xi(R), submodel) were studied both theoretically and using simulated data. When Xi is true, DeltaLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When Xi(R) is true and corresponds to a distinct point in full parameter space, DeltaLL is Gamma-distributed (2DeltaLL is chi-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, Xi(R) corresponds to an infinite set of points in parameter space. The distribution of DeltaLL is a mixture of two components, one identically zero, the other approximated by a Gamma-distribution. This empirical distribution of DeltaLL, assuming Xi(R), allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Xi, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and DeltaLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of DeltaLL when Xi or Xi(R) is true.     

Dose distribution correction for the influence of magnetic field using a deep convolutional neural network for online MR-guided adaptive radiotherapy

PurposeThis study aimed to develop a deep convolutional neural network (CNN)-based dose distribution conversion approach for the correction of the influence of a magnetic field for online MR-guided adaptive radiotherapy.MethodsOur model is based on DenseNet and consists of two 2D input channels and one 2D output channel. These three types of data comprise dose distributions without a magnetic field (uncorrected), electron density (ED) maps, and dose distributions with a magnetic field. These data were generated as follows: both types of dose distributions were created using 15-field IMRT in the same conditions except for the presence or absence of a magnetic field with the GPU Monte Carlo dose in Monaco version 5.4; ED maps were acquired with planning CT images using a clinical CT-to-ED table at our institution. Data for 50 prostate cancer patients were used; 30 patients were allocated for training, 10 for validation, and 10 for testing using 4-fold cross-validation based on rectum gas volume. The accuracy of the model was evaluated by comparing 2D gamma-indexes against the dose distributions in each irradiation field with a magnetic field (true).ResultsThe gamma indexes in the body for CNN-corrected uncorrected dose against the true dose were 94.95% ± 4.69% and 63.19% ± 3.63%, respectively. The gamma indexes with 2%/2-mm criteria were improved by 10% in most test cases (99.36%).ConclusionsOur results suggest that the CNN-based approach can be used to correct the dose-distribution influences with a magnetic field in prostate cancer treatment.     

Deuterium oxide and temperature effects on the properties of endplate channels at the frog neuromuscular junction

The effects of deuterium oxide (D2O) and temperature on the properties of endplate channels were studied in voltage-clamped muscle fibers from the frog Rana pipiens. Studies were performed at temperatures of 8, 12, 16, and 20 degrees C. The single channel conductance (gamma) and mean channel lifetime (tau) were calculated from fluctuation analysis of the acetylcholine-induced end-plate currents. The reversal potential was determined by interpolation of the acetylcholine-induced current-voltage relation. The mean reversal potential was slightly more negative in D2O Ringer's (-7.9 +/- 0.1 mV [+/- SEM]) compared with H2O Ringer's (-5.2 +/- 0.6 mV, P less than 0.01). The single channel conductance was decreased in D2O. This decrease was greater than could be accounted for by the increased viscosity of D2O solutions, and the amount of the decrease was greater at higher temperatures. For example, gamma was 38.4 +/- 1.3 pS (+/- SEM) in H2O Ringer's and 25.7 +/- 1.0 pS in D2O Ringer's for a holding potential of -70 mV at 12 degrees C. The mean channel lifetime was significantly shorter in D2O, and the effect was greater at lower temperatures. There was not a strong effect of solvent on the temperature dependence of gamma. On the other hand, the temperature dependence of the reciprocal mean channel lifetime, alpha (where alpha = 1/tau), was strongly dependent upon the solvent. The single channel conductances showed no demonstrable voltage dependence over the range of -90 to -50 mV in both solvents. The reciprocal mean channel lifetime showed a voltage dependence, which could be described by the relation alpha = B exp(AV). The slope A was not strongly affected by either temperature or the solvent. On the other hand, the intercept B was a strong function of temperature and was weakly dependent upon the solvent, with most values greater in D2O. The D2O effects on alpha were what would be expected if they were due to the properties of D2O as a solvent (solvent isotope effects), while the D2O effects on gamma must also include the exchange of D for H in the vicinity of the selectivity filter (primary and/or secondary kinetic isotope effects).     

Block of neuronal chloride channels by tetraethylammonium ion derivatives

The block by the symmetric tetraethylammonium (TEA) ion derivatives tetrapropylammonium (TPrA), tetrabutylammonium (TBA), and tetrapentylammonium (TPeA) ions of fast chloride channels in acutely dissociated rat cortical neurons was studied with the excised inside- out configuration of the patch-clamp technique. When applied to the intracellular membrane surface, all three of the quaternary ammonium compounds (QAs) induced the appearance of short-lived closed states in a manner consistent with a blocking mechanism where the blocker preferentially binds to the open kinetic state and completely blocks ion current through the channel. The drug must leave the channel before the channel can return to a closed state. The mechanism of block was studied using one-dimensional dwell-time analysis. Kinetic models were fit to distributions of open and closed interval durations using the Q- matrix approach. The blocking rate constants for all three of the QAs were similar with values of approximately 12-20 x 10(6) M-1s-1. The unblocking rates were dependent on the size or hydrophobicity of the QA with the smallest derivative, TPrA, inducing a blocked state with a mean lifetime of approximately 90 microseconds, while the most hydrophobic derivative, TPeA, induced a blocked state with a mean lifetime of approximately 1 ms. Thus, it appears as though quaternary ammonium ion block of these chloride channels is nearly identical to the block of many potassium channels by these compounds. This suggests that there must be structural similarities in the conduction pathway between anion and cation permeable channels.     

The effects of bipolar electrode montage on conduction velocity estimation from the surface electromyogram.

This study examines the influence of the bipolar electrode montage on conduction velocity (CV) estimation. Electrode montage refers to the combination of two parameters, the inter-electrode distance (IED), the distance between the two electrodes of a bipolar pair, and the inter-signal distance (ISD), the distance between two bipolar signals used to calculate CV. Data from the biceps brachii (BB) and tibialis anterior (TA) of healthy subjects are analysed. Two approaches are used for CV estimation. The first returns a single value per epoch. The second is based on finding velocity values from individual peaks in the signal and results in a peak velocity (PV) distribution being generated per epoch. It is concluded that CV estimation is significantly dependent on the choice of the (IED, ISD) electrode montage. The main results are that the electrode montage affects (1) the mean PV and CV estimates, (typically P < 0.001), (2) the degree of spatial variability, and (3) the width of the PV distributions. The combination of a small IED and large an ISD is recommended.     

Fluxes theory in experiments with random distributed channels on vesicles

When channels are randomly distributed in a population of vesicles, disregarding the number of channels per vesicle, these channels follow a Poisson distribution. This has been verified in many cases, determining the average of channels per vesicle. However, to determine kinetic parameters in population studies, a mathematical expression for the mean flux of solute through channels per vesicle is necessary. Hence, here, this mean flux is calculated, assuming Poisson distributed channels in a population of vesicle. Moreover, this result has been generalized to any number of different kinds of channels (i.e., channels with different permeabilities). These results, useful for in vitro experiments with mixed both channels and vesicles, can be supplemented with those from other techniques, in order to understanding how the nature of the lipid membrane affects kinetic parameters of channel.     

Fluxes theory in experiments with random distributed channels on vesicles

When channels are randomly distributed in a population of vesicles, disregarding the number of channels per vesicle, these channels follow a Poisson distribution. This has been verified in many cases, determining the average of channels per vesicle. However, to determine kinetic parameters in population studies, a mathematical expression for the mean flux of solute through channels per vesicle is necessary. Hence, here, this mean flux is calculated, assuming Poisson distributed channels in a population of vesicle. Moreover, this result has been generalized to any number of different kinds of channels (i.e., channels with different permeabilities). These results, useful for in vitro experiments with mixed both channels and vesicles, can be supplemented with those from other techniques, in order to understanding how the nature of the lipid membrane affects kinetic parameters of channel.     

Stochastic description of the three-state model of the Na channel

The three-state model of the Na channel is formulated stochastically and various observable quantities calculated from this model. This model assumes that the Na channel can occupy one of three states--resting, open and inactivated--and that each channel is independent. This is a simplified representation of the model proposed by Aldrich et al. (1983) mainly with respect to the neuroblastoma. When the system contains many channels, the probability distribution of the numbers of the channels that occupy each of these states is a time-dependent multinomial distribution and the distribution of the first passage time from resting state to open state becomes an exponential decay function with higher components. The average and variance of the channel current calculated by the distribution show the time course with a single peak and its ratio converges to the current of a single channel. Stochastic treatment of the transient process developed here gives a method of estimating all of the transition rates and the number of channels in the system.     

Estimate of the Molecular Weight of the Sarcolemmal Sodium Channel Using H2O-D2O Centrifugation

The sodium channel saxitoxin binding component from rat sarcolemma was solubilized with NP-40 and centrifuged on sucrose gradients constructed in either D2O or H2O. When compared with a series of standard proteins the sedimentation behavior of the solubilized channel complex changed from an apparent S20,w of 9.1 in H2O to 6.1 in D2O. From these observations, a true partial specific volume of 0.83 ml/g was calculated for the complex. A Stokes radius of 8.6 nm was estimated from Sepharose 6-B chromatography in NP-40. The calculated protein molecular weight of the lipid-protein-detergent complex based on these data is 560,000. The complex contains about 56% protein, and the calculated molecular weight of this component is 314,000 if a v for the protein of 0.74 ml/g is assumed.     

Functional characterization of contractile vacuole isolated from Amoeba proteus

Contractile vacuoles (CVs) released from cells of Amoeba proteus were used to analyze its function in vitro. When CV was transferred to a hypertonic medium, its volume decreased within 10 sec. When it was subsequently returned to its original medium, it quickly started swelling. However, it ruptured before recovering its initial volume. These results suggested that the CV membrane is semi-permeable and that the fluid is collected by the osmotic gradient in vivo. The water permeability of membrane of isolated CV was calculated from the rate of osmotic volume change to be 0.94 microm/sec . OsM. This high value suggested that CV membrane is equipped with water channel. CV contracted (or burst) quickly upon addition of 1 mM ATP. Contraction was induced by ATP, but not by other nucleotides, GTP, ITP, ADP, or the analogues of ATP, AMP-PNP and ATPgammaS. It was suggested that the contraction of isolated CV was caused by increase in the tension of its membrane by ATP.     

Interactions Between Charged Residues in the Transmembrane Segments of the Voltage-sensing Domain in the hERG Channel

Studies on voltage-gated K channels such as Shaker have shown that positive charges in the voltage-sensor (S4) can form salt bridges with negative charges in the surrounding transmembrane segments in a state-dependent manner, and different charge pairings can stabilize the channels in closed or open states. The goal of this study is to identify such charge interactions in the hERG channel. This knowledge can provide constraints on the spatial relationship among transmembrane segments in the channel’s voltage-sensing domain, which are necessary for modeling its structure. We first study the effects of reversing S4’s positive charges on channel activation. Reversing positive charges at the outer (K525D) and inner (K538D) ends of S4 markedly accelerates hERG activation, whereas reversing the 4 positive charges in between either has no effect or slows activation. We then use the ‘mutant cycle analysis’ to test whether D456 (outer end of S2) and D411 (inner end of S1) can pair with K525 and K538, respectively. Other positive charges predicted to be able, or unable, to interact with D456 or D411 are also included in the analysis. The results are consistent with predictions based on the distribution of these charged residues, and confirm that there is functional coupling between D456 and K525 and between D411 and K538.     

A sieving method for rapid determination of size-frequency distribution of small gastropods. Example of the mud snail Hydrobia ventrosa (Gastropoda: Prosobranchia)

A sieving system using sieves of predefined mesh size has been developed for rapid size–frequency distribution analysis as a basis for the assessment of the secondary production of the hydrobiid species Hydrobia ventrosa Montagu of Lake Ichkeul in northern Tunisia (Mediterranean). The relationship between shell length (SL) and shell width (SW) SL = e^0.5005 SW^1.4306 calculated by a geometric mean regression is very highly significant allowing the application of sieves in mesh intervals of 0.1 mm for the determination of size–frequency distribution. The mean difference between sieved and measured size distributions, for different distribution patterns, only slightly exceeds 1%. The regression between shell length and ash-free dry mass (AFDM) fits an exponential model AFDM = e^{(-2.6591 + 0.9194 SL)}. Mean difference between estimated and observed biomass is in the 10% range. The elementary composition (C, H and N) of the ash-free dry mass is size-dependent. As a result, the proposed sieving method reduces by at least 20 times the data acquisition time (extraction, sorting and size-measuring), avoiding subsampling without significant loss of accuracy for secondary production studies of small gastropods.     

Mitogen induction of ion channels in murine T lymphocytes

Using gigohm-seal recording, we studied ion channel expression in resting and activated T lymphocytes from mice. Both the number of channels per cell and the predominant type of K+ channel depend upon the state of activation of the cell. Unstimulated T cells express small numbers of K+ channels, typically a dozen per cell, and are heterogeneous, usually expressing either type n or type l K+ channels (see DeCoursey, T. E., K. G. Chandy, S. Gupta, and M. D. Cahalan. 1987. Journal of General Physiology. 89:379-404). 1 d after stimulation by the murine T cell mitogen concanavalin A, large numbers of type n K+ channels appear in enlarged, activated cells. Type n channels appear in activated cells with a time course consistent with that reported for mitogen-induced enhancement of protein synthesis. Voltage-gated tetrodotoxin-sensitive Na+ channels present in about one-third of unstimulated cells from the MRL-n strain are increased approximately 10-fold after activation.     

An estimate of the number of Ca2+-dependent K+ channels in the human red cell

An original approach has been designed to count Ca2+-dependent K+ channels in the human red cell using a preparation of inside-out vesicles. The relative frequency of vesicles having no K+ channels is estimated from the fraction of 42K+ (or 86Rb+) which is not released from loaded vesicles on maximal stimulation with Ca2+. The mean number of channels per vesicle is then calculated from this figure assuming a Poisson distribution for the K+ channels. From this value and the mean vesicular radius, computed from the volume/surface ratio, the mean number of channels per cell can be estimated. A value of 142 +/- 27 (mean +/- S.E.) was obtained, which is well above that estimated by comparison of unitary conductance and tracer equilibration rate measurements (about 10 channels/cell, Grygorczyk, R. Schwarz, W. and Passow, H. (1984) Biophys. J. 45, 693-698), but compares favourably with the channel density inferred from comparison with the number of Na+ pumps in a similar preparation of inside-out vesicles (100-200/cell, Lew, V.L., Muallem, S. and Seymour, C.A. (1982) Nature 296, 742-744). The procedure described here can be considered for general application as an alternative to other known procedures.     

Sequential phosphorylation mediates receptor- and kinase-induced inhibition of TREK-1 background potassium channels

Background potassium channels determine membrane potential and input resistance and serve as prominent effectors for modulatory regulation of cellular excitability. TREK-1 is a two-pore domain background K+ channel (KCNK2, K2P2.1) that is sensitive to a variety of physicochemical and humoral factors. In this work, we used a recombinant expression system to show that activation of G alpha(q)-coupled receptors leads to inhibition of TREK-1 channels via protein kinase C (PKC), and we identified a critical phosphorylation site in a key regulatory domain that mediates inhibition of the channel. In HEK 293 cells co-expressing TREK-1 and either the thyrotropin-releasing hormone receptor (TRHR1) or the Orexin receptor (Orx1R), agonist stimulation induced robust channel inhibition that was suppressed by a bisindolylmaleimide PKC inhibitor but not by a protein kinase A blocker ((R(p))-cAMP-S). Channel inhibition by agonists or by direct activators of PKC (phorbol dibutyrate) and PKA (forskolin) was disrupted not only by alanine or aspartate mutations at an identified PKA site (Ser-333) in the C terminus, but also at a more proximal regulatory site in the cytoplasmic C terminus (Ser-300); S333A and S300A mutations enhanced basal TREK-1 current, whereas S333D and S300D substitutions mimicked phosphorylation and strongly diminished currents. When studied in combination, TREK-1 current density was enhanced in S300A/S333D but reduced in S300D/S333A mutant channels. Channel mutants were expressed and appropriately targeted to cell membranes. Together, these data support a sequential phosphorylation model in which receptor-induced kinase activation drives modification at Ser-333 that enables subsequent phosphorylation at Ser-300 to inhibit TREK-1 channel activity.     

Resonance energy transfer from a cylindrical distribution of donors to a plane of acceptors. Location of apo-B100 protein on the human low-density lipoprotein particle.

The resonance energy transfer (RET) from a cylindrical assembly of donors to acceptors in a plane was investigated, and the dependence the average RET rate (kT) on the cylinder's size, shape, and proximity to the acceptor plane was determined. This geometry provides a model for the RET from a donor-containing protein to acceptors embedded in an associated phospholipid mono- or bilayer. The determination of kT for a series of acceptors at different levels in the phospholipid layer is shown to provide information on the protein's relationship to the phospholipid layer. Two models for the donor (D) and acceptor (A) distributions are employed: (a) The D's and A's are uniformly distributed in the cylinder and the plane, respectively, and analytical expressions for kT in terms of experimental parameters are derived. (b) The RET rates between all D, A pairs within the cylinder and in the plane are calculated and averaged for a large number of random D and A distributions. The average transfer rates obtained by the two approaches are in agreement and the width of the frequency distribution of kT for the latter provides an estimate of the error to be expected when, as is usually the case, the true D and A locations are unknown. This methodology is illustrated by analyzing RET from the 37 tryptophan residues of the apo-B100 protein to a series of pyrenylphosphatidylcholine acceptors inserted in the phospholipid monolayer of the human low-density lipoprotein particle, and it is concluded that significant portions of the protein penetrate the phospholipid layer.     

On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems

This paper considers the asymptotic distribution of the likelihood ratio statistic T for testing a subset of parameter of interest θ, θ = (γ, η), H(0) : γ = γ(0), based on the pseudolikelihood L(θ, ??), where ?? is a consistent estimator of ?, the nuisance parameter. We show that the asymptotic distribution of T under H(0) is a weighted sum of independent chi-squared variables. Some sufficient conditions are provided for the limiting distribution to be a chi-squared variable. When the true value of the parameter of interest, θ(0), or the true value of the nuisance parameter, ?(0), lies on the boundary of parameter space, the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix, or from a mixture of multivariate normal distributions. A variety of examples are provided for which the limiting distributions of T may be mixtures of chi-squared variables. We conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments.     

Analytical calculation of intracellular calcium wave characteristics

We present a theoretical analysis of intracellular calcium waves propagated by calcium feedback at the inositol 1,4,5-trisphosphate (IP3) receptor. The model includes essential features of calcium excitability, but is still analytically tractable. Formulas are derived for the wave speed, amplitude, and width. The calculations take into account cytoplasmic Ca buffering, the punctate nature of the Ca release channels, channel inactivation, and Ca pumping. For relatively fast buffers, the wave speed is well approximated by V(infinity) = (J(eff)D(eff)/C0)1/2, where J(eff) is an effective, buffered source strength; D(eff) is the effective, buffered diffusion constant of Ca; and C(0) is the Ca threshold for channel activation. It is found that the saturability and finite on-rate of buffers must be taken into account to accurately derive the wave speed and front width. The time scale governing Ca wave propagation is T(r), the time for Ca release to reach threshold to activate further release. Because IP3 receptor inactivation is slow on this time scale, channel inactivation does not affect the wave speed. However, inactivation competes with Ca removal to limit wave height and front length, and for biological parameter ranges, it is inactivation that determines these parameters. Channel discreteness introduces only small corrections to wave speed relative to a model in which Ca is released uniformly from the surface of the stores. These calculations successfully predict experimental results from basic channel and cell parameters and explain the slowing of waves by exogenous buffers.