Estimating the number of channels in patch-clamp recordings: application to kinetic analysis of multichannel data from voltage-operated channels.

Important kinetic information of voltage-operated ion channels can be obtained by estimating the open probability, the availability, and the first latency, and by applying run analysis. In the case of multichannel patches, estimation of the number of available channels is a prerequisite for the above analysis. Here we describe a method for calculation of the a posteriori probability of the number of available channels in each sweep by using the Bayes formula. This probability serves as a measure for the number of channels and allows for first latency determination and run analysis. The methods described were applied to simulated and experimental data obtained from L-type Ca2+ channel recordings.     

Methods for patch clamp capacitance recordings from the calyx

We demonstrate the basic techniques for presynaptic patch clamp recording at the calyx of Held, a mammalian central nervous system nerve terminal. Electrical recordings from the presynaptic terminal allow the measurement of action potentials, calcium channel currents, vesicle fusion (exocytosis) and subsequent membrane uptake (endocytosis). The fusion of vesicles containing neurotransmitter causes the vesicle membrane to be added to the cell membrane of the calyx. This increase in the amount of cell membrane is measured as an increase in capacitance. The subsequent reduction in capacitance indicates endocytosis, the process of membrane uptake or removal from the calyx membrane. Endocytosis, is necessary to maintain the structure of the calyx and it is also necessary to form vesicles that will be filled with neurotransmitter for future exocytosis events. Capacitance recordings at the calyx of Held have made it possible to directly and rapidly measure vesicular release and subsequent endocytosis in a mammalian CNS nerve terminal. In addition, the corresponding postsynaptic activity can be simultaneously measured by using paired recordings. Thus a complete picture of the presynaptic and postsynaptic electrical activity at a central nervous system synapse is achievable using this preparation. Here, the methods for slice preparation, morphological features for identification of calyces of Held, basic patch clamping techniques, and examples of capacitance recordings to measure exocytosis and endocytosis are presented.     

Bayesian restoration of single-channel patch clamp recordings.

The technique of patch clamp recording makes possible the measurement of current flowing through a single ion channel in a cell membrane. Examination of such recordings suggests that the current is quantal in nature, alternating in a seemingly random manner between "on" and "off," but the recordings are corrupted by noise from a variety of sources. In this paper we propose and illustrate methods for restoring the underlying quantal signal from such noisy measurements. The methods use a Markov chain prior distribution for the underlying quantal process and base the restoration on the resulting posterior distribution.     

Estimating the dimensionality of the manifold underlying multi-electrode neural recordings

It is generally accepted that the number of neurons in a given brain area far exceeds the number of neurons needed to carry any specific function controlled by that area. For example, motor areas of the human brain contain tens of millions of neurons that control the activation of tens or at most hundreds of muscles. This massive redundancy implies the covariation of many neurons, which constrains the population activity to a low-dimensional manifold within the space of all possible patterns of neural activity. To gain a conceptual understanding of the complexity of the neural activity within a manifold, it is useful to estimate its dimensionality, which quantifies the number of degrees of freedom required to describe the observed population activity without significant information loss. While there are many algorithms for dimensionality estimation, we do not know which are well suited for analyzing neural activity. The objective of this study was to evaluate the efficacy of several representative algorithms for estimating the dimensionality of linearly and nonlinearly embedded data. We generated synthetic neural recordings with known intrinsic dimensionality and used them to test the algorithms’ accuracy and robustness. We emulated some of the important challenges associated with experimental data by adding noise, altering the nature of the embedding of the low-dimensional manifold within the high-dimensional recordings, varying the dimensionality of the manifold, and limiting the amount of available data. We demonstrated that linear algorithms overestimate the dimensionality of nonlinear, noise-free data. In cases of high noise, most algorithms overestimated the dimensionality. We thus developed a denoising algorithm based on deep learning, the “Joint Autoencoder”, which significantly improved subsequent dimensionality estimation. Critically, we found that all algorithms failed when the intrinsic dimensionality was high (above 20) or when the amount of data used for estimation was low. Based on the challenges we observed, we formulated a pipeline for estimating the dimensionality of experimental neural data.     

Blind patch clamp recordings in embryonic and adult mammalian brain slices

To obtain electrophysiological recordings in brain slices, sophisticated and expensive pieces of equipment can be used. However, costly microscope equipment with infrared differential interference contrast optics is not always necessary or even desirable. For instance, obtaining a randomized unbiased sample in a given preparation would be better accomplished if cells were not directly visualized before recording. In addition, some preparations require thick slices, and direct visualization is not possible. Here we describe a protocol for the 'blind patch clamp method' that we developed several years ago to perform electrophysiological recordings in mammalian brain slices using a standard patch clamp amplifier, dissecting microscope and recording chamber. Overall, it takes approximately 3-4 h to set up this procedure.     

Estimating the pKa values of basic and acidic side chains in ion channels using electrophysiological recordings: a robust approach to an elusive problem

As a step toward gaining a better understanding of the physicochemical bases of pK(a)-value shifts in ion channels, we have previously proposed a method for estimating the proton affinities of systematically engineered ionizable side chains from the kinetic analysis of single-channel current recordings. We reported that the open-channel current flowing through mutants of the (cation-selective) muscle nicotinic acetylcholine receptor (AChR) engineered to bear single basic residues in the transmembrane portion of the pore domain fluctuates between two levels of conductance. Our observations were consistent with the idea that these fluctuations track directly the alternate protonation-deprotonation of basic side chains: protonation of the introduced basic group would attenuate the single-channel conductance, whereas its deprotonation would restore the wild-type-like level. Thus, analysis of the kinetics of these transitions was interpreted to yield the pK(a) values of the substituted side chains. However, other mechanisms can be postulated that would also be consistent with some of our findings but according to which the kinetic analysis of the fluctuations would not yield true pK(a)s. Such mechanisms include the pH-dependent interconversion between two conformations of the channel that, while both ion permeable, would support different cation-conduction rates. In this article, we present experimental evidence for the notion that the fluctuations of the open-channel current observed for the muscle AChR result from the electrostatic interaction between fixed charges and the passing cations rather than from a change in conformation. Hence, we conclude that bona fide pK(a) values can be obtained from single-channel recordings.     

Resolution of patch capacitance recordings and of fusion pore conductances in small vesicles

We investigated the noise levels in cell-attached patch capacitance recordings with a lock-in amplifier. The capacitance noise level decreases with increasing sine wave frequency up to 20-40 kHz. With a 20-mV rms sine wave the rms noise level above 8 kHz is <50 aF. With increasing sine wave amplitudes a further reduction down to 14 aF could be achieved. Capacitance measurements with a lock-in amplifier may also be used to measure the conductance of fusion pores connecting the vesicular lumen to the extracellular space. It is estimated that at noise levels of 14 aF fusion pore conductances between 20 pS and 700 pS may be resolved in vesicles with 380-aF capacitance by using a 50-kHz sine wave. This corresponds to vesicles with a approximately 110-nm diameter. It is suggested that with low-noise techniques fusion pores may be detectable in vesicles approaching the size of large synaptic vesicles.     

Estimating the spatial position of marine mammals based on digital camera recordings

Estimating the spatial position of organisms is essential to quantify interactions between the organism and the characteristics of its surroundings, for example, predator–prey interactions, habitat selection, and social associations. Because marine mammals spend most of their time under water and may appear at the surface only briefly, determining their exact geographic location can be challenging. Here, we developed a photogrammetric method to accurately estimate the spatial position of marine mammals or birds at the sea surface. Digital recordings containing landscape features with known geographic coordinates can be used to estimate the distance and bearing of each sighting relative to the observation point. The method can correct for frame rotation, estimates pixel size based on the reference points, and can be applied to scenarios with and without a visible horizon. A set of R functions was written to process the images and obtain accurate geographic coordinates for each sighting. The method is applied to estimate the spatiotemporal fine‐scale distribution of harbour porpoises in a tidal inlet. Video recordings of harbour porpoises were made from land, using a standard digital single‐lens reflex (DSLR) camera, positioned at a height of 9.59 m above mean sea level. Porpoises were detected up to a distance of ~3136 m (mean 596 m), with a mean location error of 12 m. The method presented here allows for multiple detections of different individuals within a single video frame and for tracking movements of individuals based on repeated sightings. In comparison with traditional methods, this method only requires a digital camera to provide accurate location estimates. It especially has great potential in regions with ample data on local (a)biotic conditions, to help resolve functional mechanisms underlying habitat selection and other behaviors in marine mammals in coastal areas.     

Estimating the total number of protein folds.

Many seemingly unrelated protein families share common folds. Theoretical models based on structure designability have suggested that a few folds should be very common while many others have low probability. In agreement with the predictions of these models, we show that the distribution of observed protein families over different folds can be modeled with a highly-stretched exponential. Our results suggest that there are approximately 4,000 possible folds, some so unlikely that only approximately 2,000 folds existing among naturally-occurring proteins. Due to the large number of extremely rare folds, constructing a comprehensive database of all existent folds would be difficult. Constructing a database of the most-likely folds representing the vast majority of protein families would be considerably easier.     

Voltage-clamp measurement of visually-evoked conductances with whole-cell patch recordings in primary visual cortex

Whole cell patch recordings have been realized in the primary visual cortex of the anesthetized and paralyzed cat, in order to better characterize input resistance and time constant of visual cortical cells in vivo. Measurements of conductance changes evoked by visual stimulation were derived from voltage clamp recordings achieved in continuous mode at two or more different subtreshold holding potentials. They show that the magnitude of the conductance increase can reach up to 300% of the mean conductance at rest. The observation of similar changes for the preferred and antagonist responses, when flashing ON and OFF, a test stimulus in pure ON and OFF subfields supports the hypothesis of a role for shunting inhibition in the spatial organization of simple receptive fields.     

Micromolded PDMS planar electrode allows patch clamp electrical recordings from cells

The patch clamp method measures membrane currents at very high resolution when a high-resistance 'gigaseal' is established between the glass microelectrode and the cell membrane (Pflugers Arch. 391 (1981) 85; Neuron 8 (1992) 605). Here we describe the first use of the silicone elastomer, poly(dimethylsiloxane) (PDMS), for patch clamp electrodes. PDMS is an attractive material for patch clamp recordings. It has low dielectric loss and can be micromolded (Annu. Rev. Mat. Sci. 28 (1998) 153) into a shape that mimics the tip of the glass micropipette. Also, the surface chemistry of PDMS may be altered to mimic the hydrophilic nature of glass (J. Appl. Polym. Sci. 14 (1970) 2499; Annu. Rev. Mat. Sci. 28 (1998) 153), thereby allowing a high-resistance seal to a cell membrane. We present a planar electrode geometry consisting of a PDMS partition with a small aperture sealed between electrode and bath chambers. We demonstrate that a planar PDMS patch electrode, after oxidation of the elastomeric surface, permits patch clamp recording on Xenopus oocytes. Our results indicate the potential for high-throughput patch clamp recording with a planar array of PDMS electrodes.     

Estimating the number of terrestrial organisms on the moon

NASA policy requires that the number and spatial distribution of terrestrial organisms deposited on the Moon be estimated. This paper describes the way in which such an ‘inventory’ is being maintained, and some of the conclusions that may be drawn from it. This work was conducted under Contract W-12,853, Planetary Programs, Office of Space Science and Applications, NASA Headquarters, Washington, D.C.     

Estimating the number of species in a stochastic abundance model

Consider a stochastic abundance model in which the species arrive in the sample according to independent Poisson processes, where the abundance parameters of the processes follow a gamma distribution. We propose a new estimator of the number of species for this model. The estimator takes the form of the number of duplicated species (i.e., species represented by two or more individuals) divided by an estimated duplication fraction. The duplication fraction is estimated from all frequencies including singleton information. The new estimator is closely related to the sample coverage estimator presented by Chao and Lee (1992, Journal of the American Statistical Association 87, 210-217). We illustrate the procedure using the Malayan butterfly data discussed by Fisher, Corbet, and Williams (1943, Journal of Animal Ecology 12, 42-58) and a 1989 Christmas Bird Count dataset collected in Florida, U.S.A. Simulation studies show that this estimator compares well with maximum likelihood estimators (i.e., empirical Bayes estimators from the Bayesian viewpoint) for which an iterative numerical procedure is needed and may be infeasible.     

Single-channel recordings from purified acetylcholine receptors reconstituted in bilayers formed at the tip of patch pipets

The channel of the purified acetylcholine receptor from Torpedo californica electric organ reconstituted in lipid vesicles was assayed by direct electrical recording using patch-clamp pipets. High-resistance seals were obtained by gentle suction of vesicles into the pipet or after the formation of lipid bilayers from monolayers at the tip of the pipet. Single-channel currents were activated by three cholinergic ligands: acetylcholine, carbamylcholine, and suberyldicholine. The single-channel conductance, gamma, was 40 +/- 5 pS in 0.5 M NaCl, irrespective of the agonist used. The distributions of channel open times were fitted by a sum of two exponentials. The lifetimes of the two exponential components were a factor of 2 longer for suberyldicholine than for acetylcholine or carbamylcholine. At desensitizing concentrations of agonists the single events appeared in paroxysms of channel activity followed by quiescent periods. These results suggest that the full cycle of solubilization, purification, and reconstitution of this membrane receptor can be achieved without impairment of channel function.     

Estimating effective paternity number in social insects and the effective number of alleles in a population

Estimating paternity and genetic relatedness is central to many empirical and theoretical studies of social insects. The two important measures of a queen's mating number are her actual number of mates and her effective number of mates. Estimating the effective number of mates is mathematically identical to the problem of estimating the effective number of alleles in population genetics, a common measure of genetic variability introduced by Kimura & Crow (1964). We derive a new bias-corrected estimator of effective number of types (mates or alleles) and compare this new method to previous methods for estimating true and effective numbers of types using Monte Carlo simulations. Our simulation results suggest that the examined estimators of the true number of types have very similar statistical properties, whereas the estimators of effective number of types have quite different statistical properties. Moreover, our new proposed estimator of effective number of types is approximately unbiased, and has considerably lower variance than the original estimator. Our new method will help researchers more accurately estimate intracolony genetic relatedness of social insects, which is an important measure in understanding their ecology and social behaviour. It should also be of use in population genetic studies in which the effective number of alleles is of interest.     

Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

Advances in recording technologies have given neuroscience researchers access to large amounts of data, in particular, simultaneous, individual recordings of large groups of neurons in different parts of the brain. A variety of quantitative techniques have been utilized to analyze the spiking activities of the neurons to elucidate the functional connectivity of the recorded neurons. In the past, researchers have used correlative measures. More recently, to better capture the dynamic, complex relationships present in the data, neuroscientists have employed causal measures—most of which are variants of Granger causality—with limited success. This paper motivates the directed information, an information and control theoretic concept, as a modality-independent embodiment of Granger’s original notion of causality. Key properties include: (a) it is nonzero if and only if one process causally influences another, and (b) its specific value can be interpreted as the strength of a causal relationship. We next describe how the causally conditioned directed information between two processes given knowledge of others provides a network version of causality: it is nonzero if and only if, in the presence of the present and past of other processes, one process causally influences another. This notion is shown to be able to differentiate between true direct causal influences, common inputs, and cascade effects in more two processes. We next describe a procedure to estimate the directed information on neural spike trains using point process generalized linear models, maximum likelihood estimation and information-theoretic model order selection. We demonstrate that on a simulated network of neurons, it (a) correctly identifies all pairwise causal relationships and (b) correctly identifies network causal relationships. This procedure is then used to analyze ensemble spike train recordings in primary motor cortex of an awake monkey while performing target reaching tasks, uncovering causal relationships whose directionality are consistent with predictions made from the wave propagation of simultaneously recorded local field potentials.     

Single channel recordings from calcium-activated potassium channels in cultured rat muscle

Single channel recordings from cultured rat skeletal muscle have revealed a large conductance (230 pS) channel with a high selectivity for K⁺ over Na⁺. In excised patches of membrane, the probability of channel opening is sensitive to micromolar concentrations of calcium ions at the intracellular surface of the patch. Channel openings appear grouped together into bursts whose duration increases with Ca²⁺ and membrane depolarization. Statistical analysis of the individual open times during each burst showed that there are two distinct open states of similar conductance but dissimilar average lifetimes. These channels might contribute to a macroscopic calcium-activated potassium conductance in rat skeletal muscle and other preparations.     

Estimating the number of clusters in multivariate data by self-organizing maps

Determining the structure of data without prior knowledge of the number of clusters or any information about their composition is a problem of interest in many fields, such as image analysis, astrophysics, biology, etc. Partitioning a set of n patterns in a p-dimensional feature space must be done such that those in a given cluster are more similar to each other than the rest. As there are approximately Kn/K! possible ways of partitioning the patterns among K clusters, finding the best solution is very hard when n is large. The search space is increased when we have no a priori number of partitions. Although the self-organizing feature map (SOM) can be used to visualize clusters, the automation of knowledge discovery by SOM is a difficult task. This paper proposes region-based image processing methods to post-processing the U-matrix obtained after the unsupervised learning performed by SOM. Mathematical morphology is applied to identify regions of neurons that are similar. The number of regions and their labels are automatically found and they are related to the number of clusters in a multivariate data set. New data can be classified by labeling it according to the best match neuron. Simulations using data sets drawn from finite mixtures of p-variate normal densities are presented as well as related advantages and drawbacks of the method.     

Estimating the effective number of breeders from heterozygote excess in progeny

The heterozygote-excess method is a recently published method for estimating the effective population size (Ne). It is based on the following principle: When the effective number of breeders (Neb) in a population is small, the allele frequencies will (by chance) be different in males and females, which causes an excess of heterozygotes in the progeny with respect to Hardy-Weinberg equilibrium expectations. We evaluate the accuracy and precision of the heterozygote-excess method using empirical and simulated data sets from polygamous, polygynous, and monogamous mating systems and by using realistic sample sizes of individuals (15-120) and loci (5-30) with varying levels of polymorphism. The method gave nearly unbiased estimates of Neb under all three mating systems. However, the confidence intervals on the point estimates of Neb were sufficiently small (and hence the heterozygote-excess method useful) only in polygamous and polygynous populations that were produced by <10 effective breeders, unless samples included > approximately 60 individuals and 20 multiallelic loci.     

Estimating the patch size of larval fishes during colonization on coral reefs

Fish larvae were sampled daily over a period of 14 days using six crest nets spaced at 200 m intervals on a coral reef on the west coast of Moorea Island, French Polynesia, to estimate the extent to which ichthyonekton arriving at one location reflected ichthyonekton arriving at neighbouring areas. Each night, the six crest nets were colonized by larval fishes from the same location.