A Comprehensive Specimen-Specific Multiscale Data Set for Anatomical and Mechanical Characterization of the Tibiofemoral Joint

Understanding of tibiofemoral joint mechanics at multiple spatial scales is essential for developing effective preventive measures and treatments for both pathology and injury management. Currently, there is a distinct lack of specimen-specific biomechanical data at multiple spatial scales, e.g., joint, tissue, and cell scales. Comprehensive multiscale data may improve the understanding of the relationship between biomechanical and anatomical markers across various scales. Furthermore, specimen-specific multiscale data for the tibiofemoral joint may assist development and validation of specimen-specific computational models that may be useful for more thorough analyses of the biomechanical behavior of the joint. This study describes an aggregation of procedures for acquisition of multiscale anatomical and biomechanical data for the tibiofemoral joint. Magnetic resonance imaging was used to acquire anatomical morphology at the joint scale. A robotic testing system was used to quantify joint level biomechanical response under various loading scenarios. Tissue level material properties were obtained from the same specimen for the femoral and tibial articular cartilage, medial and lateral menisci, anterior and posterior cruciate ligaments, and medial and lateral collateral ligaments. Histology data were also obtained for all tissue types to measure specimen-specific cell scale information, e.g., cellular distribution. This study is the first of its kind to establish a comprehensive multiscale data set for a musculoskeletal joint and the presented data collection approach can be used as a general template to guide acquisition of specimen-specific comprehensive multiscale data for musculoskeletal joints.     

Bilateral edge filter: photometrically weighted, discontinuity based edge detection

Edge-detection algorithms have the potential to play an increasingly important role both in single particle analysis (for the detection of randomly oriented particles), and in tomography (for the segmentation of 3D volumes). However, the majority of traditional linear filters are significantly affected by noise as well as artefacts, and offer limited selectivity. The Bilateral edge filter presented here is an adaptation of the Bilateral filter [Jiang, W., Baker, M.L., Wu, Q., Bajaj, C., Chiu, W., 2003. Applications of a bilateral denoising filter in biological electron microscopy. J. Struct. Biol. 144, 114-122] designed for enhanced edge detection. It uses photometric weighting to identify significant discontinuities (representing edges), minimizing artefacts and noise. Compared with common edge-detectors (LoG, Marr-Hildreth) the Bilateral edge filter yielded significantly better results. Indeed data was of a similar quality to that of the Canny edge-detector, which is considered as a leading standard in edge detection [Basu, M., 2002. Gaussian-based edge-detection methods-a survey. IEEE Trans. Syst. Man Cybern. C Appl. Rev. 32, 252-260]. Compared to the Canny edge-detector the Bilateral edge-detector has the advantages that it only requires the adjustment of a single parameter, is theoretically faster for reasonably sized images, and can be used in selective contrast enhancement of images. The simplicity and speed of the filter for single particle and tomographic analysis are discussed.     

Noise Reduction in Electron Tomographic Reconstructions Using Nonlinear Anisotropic Diffusion

Electron tomography is a powerful technique capable of giving unique insights into the three-dimensional structural organization of pleomorphic biological objects. However, visualization and interpretation of the resulting volumetric data are hampered by an extremely low signal-to-noise ratio, especially when ice-embedded biological specimens are investigated. Usually, isosurface representation or volume rendering of such data is hindered without any further signal enhancement. We propose a novel technique for noise reduction based on nonlinear anisotropic diffusion. The approach combines efficient noise reduction with excellent signal preservation and is clearly superior to conventional methods (e.g., low-pass and median filtering) and invariant wavelet transform filtering. The gain in the signal-to-noise ratio is verified and demonstrated by means of Fourier shell correlation. Improved visualization performance after processing the 3D images is demonstrated with two examples, tomographic reconstructions of chromatin and of a mitochondrion. Parameter settings and discretization stencils are presented in detail.     

Applications of a bilateral denoising filter in biological electron microscopy

Due to the sensitivity of biological sample to the radiation damage, the low dose imaging conditions used for electron microscopy result in extremely noisy images. The processes of digitization, image alignment, and 3D reconstruction also introduce additional sources of noise in the final 3D structure. In this paper, we investigate the effectiveness of a bilateral denoising filter in various biological electron microscopy applications. In contrast to the conventional low pass filters, which inevitably smooth out both noise and structural features simultaneously, we found that bilateral filter holds a distinct advantage in being capable of effectively suppressing noise without blurring the high resolution details. In as much, we have applied this technique to individual micrographs, entire 3D reconstructions, segmented proteins, and tomographic reconstructions.     

Blind noise reduction for multisensory signals using ICA and subspace filtering, with application to EEG analysis

 In many applications of signal processing, especially in communications and biomedicine, preprocessing is necessary to remove noise from data recorded by multiple sensors. Typically, each sensor or electrode measures the noisy mixture of original source signals. In this paper a noise reduction technique using independent component analysis (ICA) and subspace filtering is presented. In this approach we apply subspace filtering not to the observed raw data but to a demixed version of these data obtained by ICA. Finite impulse response filters are employed whose vectors are parameters estimated based on signal subspace extraction. ICA allows us to filter independent components. After the noise is removed we reconstruct the enhanced independent components to obtain clean original signals; i.e., we project the data to sensor level. Simulations as well as real application results for EEG-signal noise elimination are included to show the validity and effectiveness of the proposed approach. Received: 6 November 2000 / Accepted in revised form: 12 November 2001     

Extracellular iron reduction is mediated in part by neutral red and hydrogenase in Escherichia coli

Both microbial iron reduction and microbial reduction of anodes in fuel cells can occur by way of soluble electron mediators. To test whether neutral red (NR) mediates iron reduction, as it does anode reduction, by Escherichia coli, ferrous iron levels were monitored in anaerobic cultures grown with amorphous iron oxide. Ferrous iron levels were 19.4 times higher in cultures fermenting pyruvate in the presence of NR than in the absence of NR. NR did not stimulate iron reduction in cultures respiring with nitrate. To explore the mechanism of NR-mediated iron reduction, cell extracts of E. coli were used. Cell extract-NADH-NR mixtures had an enzymatic iron reduction rate almost 15-fold higher than the chemical NR-mediated iron reduction rate observed in controls with no cell extract. Hydrogen was consumed during stationary phase (in which iron reduction was detectable) especially in cultures containing both NR and iron oxide. An E. coli hypE mutant, with no hydrogenase activity, was also impaired in NR-mediated iron reduction activity. NR-mediated iron reduction rates by cell extracts were 1.5 to 2 times higher with hydrogen or formate as the electron source than with NADH. Our findings suggest that hydrogenase donates electrons to NR for extracellular iron reduction. This process appears to be analogous to those of iron reduction by bacteria that use soluble electron mediators (e.g., humic acids and 2,6-anthraquinone disulfonate) and of anode reduction by bacteria using soluble mediators (e.g., NR and thionin) in microbial fuel cells.     

Extracellular Iron Reduction Is Mediated in Part by Neutral Red and Hydrogenase in Escherichia coli

Both microbial iron reduction and microbial reduction of anodes in fuel cells can occur by way of soluble electron mediators. To test whether neutral red (NR) mediates iron reduction, as it does anode reduction, by Escherichia coli, ferrous iron levels were monitored in anaerobic cultures grown with amorphous iron oxide. Ferrous iron levels were 19.4 times higher in cultures fermenting pyruvate in the presence of NR than in the absence of NR. NR did not stimulate iron reduction in cultures respiring with nitrate. To explore the mechanism of NR-mediated iron reduction, cell extracts of E. coli were used. Cell extract-NADH-NR mixtures had an enzymatic iron reduction rate almost 15-fold higher than the chemical NR-mediated iron reduction rate observed in controls with no cell extract. Hydrogen was consumed during stationary phase (in which iron reduction was detectable) especially in cultures containing both NR and iron oxide. An E. coli hypE mutant, with no hydrogenase activity, was also impaired in NR-mediated iron reduction activity. NR-mediated iron reduction rates by cell extracts were 1.5 to 2 times higher with hydrogen or formate as the electron source than with NADH. Our findings suggest that hydrogenase donates electrons to NR for extracellular iron reduction. This process appears to be analogous to those of iron reduction by bacteria that use soluble electron mediators (e.g., humic acids and 2,6-anthraquinone disulfonate) and of anode reduction by bacteria using soluble mediators (e.g., NR and thionin) in microbial fuel cells.     

Transformation of carbon tetrachloride in an anaerobic packed-bed reactor without addition of another electron donor

Carbon tetrachloride (52 M) was biodegraded for more than 72% in an anaerobic packed-bed reactor without addition of an external electron donor. The chloride mass balance demonstrated that all carbon tetrachloride transformed was completely dechlorinated. Chloroform and dichloromethane were sometimes also found as transformation products, but neither accumulated to significant levels in comparison to the amount of carbon tetrachloride transformed. Transformation of carbon tetrachloride in the absence of an added electron donor suggests that carbon tetrachloride itself is the source of energy for the biological reaction observed, and possibly the source of carbon for cell growth. No such mechanism is yet known. The pathway of carbon tetrachloride transformation is not clear; it may be dehalogenated by hydrolytic reduction to carbon monoxide or formic acid which are electron demanding transformations. Carbon monoxide or formic acid may be further utilized and serve as electron donor. Complete dechlorination of carbon tetrachloride according to this pathway is independent of a second electron donor or electron acceptor, as with a fermentation process. Vancomycin, an inhibitor of gram positive eubacteria, severely inhibited carbon tetrachloride transformation in batch incubations with an enrichment culture from the reactor, indicating that gram positive eubacteria were involved in carbon tetrachloride transformation. Batch experiments with bromoethanesulfonic acid, used to inhibit methanogens, and molybdate, an inhibitor of sulfate reduction in sulfate reducing bacteria, demonstrated that neither methanogens nor sulfate reducers were involved in the complete dechlorination of carbon tetrachloride.     

Preprocessing of two-dimensional gel electrophoresis images

Proteomics produces a huge amount of two-dimensional gel electrophoresis images. Their analysis can yield a lot of information concerning proteins responsible for different diseases or new unidentified proteins. However, an automatic analysis of such images requires an efficient tool for reducing noise in images. This allows proper detection of the spots' borders, which is important in protein quantification (as the spots' areas are used to determine the amounts of protein present in an analyzed mixture). Also in the feature-based matching methods the detected features (spots) can be described by additional attributes, such as area or shape. In our study, a comparison of different methods of noise reduction is performed in order to find out a method best suited for reducing noise in gel images. Among the compared methods there are the classical methods of linear filtering, e.g., the mean and Gaussian filtering, the nonlinear method, i.e., median filtering, and also the methods better suited for processing of nonstationary signals, such as spatially adaptive linear filtering and filtering in the wavelet domain. The best results are obtained by filtering of gel images in the wavelet domain, using the BayesThresh method of threshold value determination.     

The discriminative bilateral filter: an enhanced denoising filter for electron microscopy data

Advances in three-dimensional (3D) electron microscopy (EM) and image processing are providing considerable improvements in the resolution of subcellular volumes, macromolecular assemblies and individual proteins. However, the recovery of high-frequency information from biological samples is hindered by specimen sensitivity to beam damage. Low dose electron cryo-microscopy conditions afford reduced beam damage but typically yield images with reduced contrast and low signal-to-noise ratios (SNRs). Here, we describe the properties of a new discriminative bilateral (DBL) filter that is based upon the bilateral filter implementation of Jiang et al. (Jiang, W., Baker, M.L., Wu, Q., Bajaj, C., Chiu, W., 2003. Applications of a bilateral denoising filter in biological electron microscopy. J. Struc. Biol. 128, 82-97.). In contrast to the latter, the DBL filter can distinguish between object edges and high-frequency noise pixels through the use of an additional photometric exclusion function. As a result, high frequency noise pixels are smoothed, yet object edge detail is preserved. In the present study, we show that the DBL filter effectively reduces noise in low SNR single particle data as well as cellular tomograms of stained plastic sections. The properties of the DBL filter are discussed in terms of its usefulness for single particle analysis and for pre-processing cellular tomograms ahead of image segmentation.     

Characterization of the redox components of transplasma membrane electron transport system from Leishmania donovani promastigotes

An investigation has been made of the points of coupling of four nonpermeable electron acceptors e.g., alpha-lipoic acid (ALA), 5,5'-dithiobis (2-nitroaniline-N-sulphonic acid) (DTNS), 1,2-naphthoquinone-4-sulphonic acid (NQSA) and ferricyanide which are mainly reduced via an interaction with the redox sites present in the plasma membrane of Leishmania donovani promastigotes. ALA, DTNS, NQSA and ferricyanide reduction and part of O2 reduction is shown to take place on the exoplasmic face of the cell, for it is affected by external pH and agents that react with the external surface. Redox enzymes of the transplasma membrane electron transport system orderly transfer electron from one redox carrier to the next with the molecular oxygen as the final electron acceptor. The redox carriers mediate the transfer of electrons from metabolically generated reductant to nonpermeable electron acceptors and oxygen. At a pH of 6.4, respiration of Leishmania cells on glucose substrate shut down almost completely upon addition of an uncoupler FCCP and K+-ionophore valinomycin. The most pronounced effects on O2 uptake were obtained by treatment with antimycin A, 2-heptadecyl-4-hydroxyquinone-N-oxide, paracholoromercuribenzene sulphonic acid and trifluoperazine. Relatively smaller effects were obtained by treatment with potassium cyanide. Inhibition observed with respect to the reduction of the electron acceptors ALA, DTNS, NQSA and ferricyanide was not similar in most cases. The redox chain appears to be branched at several points and it is suggested that this redox chain incorporate iron-sulphur center, b-cytochromes, cyanide insensitive oxygen redox site, Na+ and K+ channel, capsaicin inhibited energy coupling site and trifluoperazine inhibited energy linked P-type ATPase. We analyzed the influence of ionic composition of the medium on reduction of electron acceptors in Leishmania donovani promastigotes. Our data suggest that K+ have some role for ALA reduction and Na+ for ferricyanide reduction. No significant effects were found with DTNS and NQSA reduction when Na+ or K+ was omitted from the medium. Stimulation of ALA, DTNS, NQSA and ferricyanide reduction was obtained by omitting Cl- from the medium. We propose that this redox system may be an energy source for control of membrane function in Leishmania cells.     

Electron microscopic identification and morphologic preservation of enriched populations of lung cells isolated by laser flow cytometry and cell sorting: a new technique

There is increasing need to verify the identities of cell subpopulations enriched by laser flow cytometry and fluorescence-activated cell sorting (FACS). When cell subpopulations isolated from whole organs or tissues have similar characteristics (e.g., size, granularity, staining), light, phase contrast or fluorescence microscopy may not provide sufficient resolution to identify isolated cells accurately and many flow cytometric parameters (e.g., viability, fluorescence) require the cells to be live at the point of analysis where the cell transects the laser beam. In some studies, cells identified by fluorescence microscopy as a highly enriched subpopulation were found by electron microscopy to contain significant populations of other cell types. A technique, fixation-in-flow (FIF), has been developed to increase ability to correlate morphological and laser analyses of cell subpopulations. Sheath fluid is replaced by fixative, permitting fixation to be initiated immediately after laser beam analysis of live cells. This new procedure yields improved cytoarchitectural preservation of recovered cell subpopulation(s) for evaluation by transmission or scanning electron microscopy. This report presents results from applying the methodology to identify more accurately cell subpopulations of the distal lung, specifically type II pneumocytes, Clara cells and pulmonary macrophages. A modification of this procedure was employed to isolate fibroblast subpopulations from murine lung fibroblasts grown in vitro and the procedure is being used to determine the responses of cultured fibroblasts to other permutations (e.g., X-irradiation, cytokines).     

Stimulation of corneal differentiation by interaction between cell surface and extracellular matrix. I. Morphometric analysis of transfilter "induction".

The present study was undertaken to determine whether or not physical contact with the substratum is essential for the stimulatory effect of extracellular matrix (ECM) on corneal epithelial collagen synthesis. Previous studies showed that collagenous substrata stimulate isolated epithelia to produce three times as much collagen as they produce on noncollagenous substrate; killed collagenous substrata (e.g., lens capsule) are just as effective as living substrata (e.g., living lens) in promoting the production of new corneal stroma in vitro. In the experiments to be reported here, corneal epithelia were placed on one side of Nucleopore filters of different pore sizes and killed lens capsule on the other, with the expectation that contact of the reacting cells with the lens ECM should be limited by the number and size of the cell processes that can tranverse the pores. Transfilter cultures were grown for 24 h in [3H]proline-containing median and incorporation of isotope into hot trichloroacetic acid-soluble protein was used to measure corneal epithelial collagen production. Epithelial collagen synthesis increases directly as the size of the pores in the interposed filter increases and decreases as the thickness of the filter layer increases. Cell processes within Nucleopore filters were identified with the transmission electron microscope with difficulty; with the scanning electron microscope, however, the processes could easily be seen emerging from the undersurface of even 0.1-mum pore size filters. Morphometric techniques were used to show that cell surface area thus exposed to the underlying ECM is linearly correlated with enhancement of collagen synthesis. Epithelial cell processes did not pass through ultrathin (25-mum thick) 0.45-mum pore size Millipore filters nor did "induction" occur across them. The results are discussed in relation to current theories of embryonic tissue interaction.     

Efficient automatic noise reduction of electron tomographic reconstructions based on iterative median filtering

A simple, fast and efficient noise-reduction protocol for three-dimensional electron tomographic reconstructions of biological material is presented. The approach is based on iterative application of median filtering and shows promise for automatic noise reduction as a pre-processor for automated data analysis tools which aim at segmentation, feature extraction and pattern recognition. The application of this algorithm produces encouraging results for a wide variety of experimental and synthetic electron tomographic reconstructions.     

Taurine reduction in anaerobic respiration of Bilophila wadsworthia RZATAU.

Organosulfonates are important natural and man-made compounds, but until recently (T. J. Lie, T. Pitta, E. R. Leadbetter, W. Godchaux III, and J. R. Leadbetter. Arch. Microbiol. 166:204-210, 1996), they were not believed to be dissimilated under anoxic conditions. We also chose to test whether alkane- and arenesulfonates could serve as electron sinks in respiratory metabolism. We generated 60 anoxic enrichment cultures in mineral salts medium which included several potential electron donors and a single organic sulfonate as an electron sink, and we used material from anaerobic digestors in communal sewage works as inocula. None of the four aromatic sulfonates, the three unsubstituted alkanesulfonates, or the N-sulfonate tested gave positive enrichment cultures requiring both the electron donor and electron sink for growth. Nine cultures utilizing the natural products taurine, cysteate, or isethionate were considered positive for growth, and all formed sulfide. Two clearly different pure cultures were examined. Putative Desulfovibrio sp. strain RZACYSA, with lactate as the electron donor, utilized sulfate, aminomethanesulfonate, taurine, isethionate, and cysteate, converting the latter to ammonia, acetate, and sulfide. Strain RZATAU was identified by 16S rDNA analysis as Bilophila wadsworthia. In the presence of, e.g., formate as the electron donor, it utilized, e.g., cysteate and isethionate and converted taurine quantitatively to cell material and products identified as ammonia, acetate, and sulfide. Sulfite and thiosulfate, but not sulfate, were utilized as electron sinks, as was nitrate, when lactate was provided as the electron donor and carbon source. A growth requirement for 1,4-naphthoquinone indicates a menaquinone electron carrier, and the presence of cytochrome c supports the presence of an electron transport chain. Pyruvate-dependent disappearance of taurine from cell extracts, as well as formation of alanine and release of ammonia and acetate, was detected. We suspected that sulfite is an intermediate, and we detected desulfoviridin (sulfite reductase). We thus believe that sulfonate reduction is one aspect of a respiratory system transferring electrons from, e.g., formate to sulfite reductase via an electron transport system which presumably generates a proton gradient across the cell membrane.     

Practical Image Restoration of Thick Biological Specimens Using Multiple Focus Levels in Transmission Electron Microscopy

Three-dimensional electron tomographic studies of thick specimens such as cellular organelles or supramolecular structures require accurate interpretations of transmission electron micrograph intensities. In addition to microscope lens aberrations, thick specimen imaging is complicated by additional distortions resulting from multiple elastic and inelastic scattering. Extensive analysis of the mechanism of image formation using electron energy-loss spectroscopy and imaging as well as exit wavefront reconstruction demonstrated that multiple scattering does not contribute to the coherent component of the exit wave (Hanet al.,1996, 1995). Although exit wavefront restored images showed enhanced contrast and resolution, that technique, which requires the collection of more than 30 images at different focus levels, is not practical for routine data collection in 3D electron tomography, where usually over 100 projection views are required for each reconstruction. Using a 0.7-μm-thick specimen imaged at 200 keV, the accuracy of reconstructions using small numbers of defocused images and a simple linear filter (Schiske, 1968) was assessed by comparison to the complete exit wave restoration. We demonstrate that only four optimal focus levels are required to effectively restore the coherent component (deviation 5.1%). By contrast, the optimal single image (zero defocus) shows a 25.5% deviation to the exit wave restoration. Two pairs of under- and over-defocus images should be taken: one pair at quite high defocus (>10 μm) to differentiate the coherent (single elastic scattering) from the incoherent (multiple elastic and inelastic scattering) components, and the second pair to optimize information content at the highest desired resolution (e.g., 5 μm for (2.5 nm)⁻¹resolution). We also propose a new interpretation of the restored amplitude and phase components where the specimen mass-density is proportional to the logarithm of the amplitude component and linearly related to the phase component. This approach should greatly facilitate the collection of high resolution tomographic data from thick samples.     

中国希瓦氏菌D14^T的厌氧腐殖质呼吸

实验证明,希瓦氏菌新种(ShewanellacinicaD14T)在厌氧条件下可以利用多种有机酸盐和甲苯等环境有毒污染物作为电子供体,以腐殖质作为唯一末端电子受体进行厌氧呼吸(即醌呼吸)。电子在细胞膜呼吸链的传递过程中,偶联能量的产生来支持菌体的生长,1mmol/LAQDS可支持细胞增殖约60倍。电子供体的氧化和唯一电子受体腐殖质还原之间存在着动态的偶联过程,随着电子供体量的增加腐殖质还原的量也随之增加。典型呼吸链抑制剂诸如:抑制Fe-S中心的Cu2 ,甲基萘醌类似物标桩菌素,抑制甲基萘醌氧化型向还原型转化的双香豆素和细胞色素P450的专一抑制物甲吡酮等对腐殖质的还原有着极为显著的抑制作用,为进一步证明希瓦氏菌(Shewanellacinica)D14T可利用腐殖质进行厌氧呼吸提供了有力的佐证。而D14T在进行腐殖质呼吸的同时,对于甲苯,苯胺等环境有毒物质的有效降解则具有着重要的环境学意义。     

On the value of knowing a z* ion for what it is

Computer simulation of database searches of electron transfer dissociation (ETD) spectra using both "bottom up" and "top down" approaches was performed to evaluate the utility of knowing a priori which product ions contain the C-terminus (i.e., the z* ions). In this work, knowledge of the identities of the z* ions was used to exclude putative identifications that are based solely on the mass matching of undifferentiated product ions derived from an experiment with those derived from in silico fragmentation. The benefit from knowing which ions are z* ions was found to be heavily dependent on the quality of the ETD spectra, in terms of sequence coverage afforded by the product ions, the amount of noise in the spectra (i.e., extraneous peaks that do not directly reflect primary structure), and mass measurement accuracy. Under conditions in which the likelihood for misidentifications are high without a priori knowledge of ion types (e.g., b-, y-, c-, or z-ions), a knowledge of which product ions are z* ions allows discrimination against false-positive identifications. Relatively little benefit from knowing which ions are z* ions was noted when product spectra reflected relatively high sequence coverage and when a low fraction of the products ions were due to extraneous peaks (i.e., spectra with relatively little noise). In all cases, specificity is higher with higher mass measurement accuracy with the consequent reduction in benefit from knowledge of which ions are z* ions.     

Spike Inference from Calcium Imaging Using Sequential Monte Carlo Methods

As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies, the signals of interest—spike trains and/or time varying intracellular calcium concentrations—are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing sequential Monte Carlo methods (particle filters) based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing error bars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence (e.g., refractoriness) of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate temporal superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation maximization with only a very limited amount of data (e.g., ∼5-10 s or 5-40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.