Quantification of Clustering in Joint Interspike Interval Scattergrams of Spike Trains

Joint interval scattergrams are usually employed in determining serial correlations between events of spike trains. However, any inherent structures in such scattergrams that are often seen in experimental records are not quantifiable by serial correlation coefficients. Here, we develop a method to quantify clustered structures in any two-dimensional scattergram of pairs of interspike intervals. The method gives a cluster coefficient as well as clustering density function that could be used to quantify clustering in scattergrams obtained from first- or higher-order interval return maps of single spike trains, or interspike interval pairs drawn from simultaneously recorded spike trains. The method is illustrated using numerical spike trains as well as in vitro pairwise recordings of rat striatal tonically active neurons.     

Detection of spontaneous synaptic events with an optimally scaled template.

Spontaneous synaptic events can be difficult to detect when their amplitudes are close to the background noise level. Here we report a sensitive new technique for automatic detection of small asynchronous events. A waveform with the time course of a typical synaptic event (a template) is slid along the current or voltage trace and optimally scaled to fit the data at each position. A detection criterion is calculated based on the optimum scaling factor and the quality of the fit. An event is detected when this criterion crosses a threshold level. The algorithm automatically compensates for changes in recording noise. The sensitivity and selectivity of the method were tested using real and simulated data, and the influence of the template parameter settings was investigated. Its performance was comparable to that obtained by visual event detection, and it was more sensitive than previously described threshold detection techniques. Under typical recording conditions, all fast synaptic events with amplitudes of at least three times the noise standard deviation (3 sigma) could be detected, as could 75% of events with amplitudes of 2 sigma. The scaled template technique is implemented within a commercial data analysis application and can be applied to many standard electrophysiological data file formats.     

Analyzing recurrent and nonrecurrent terminal events data in discrete time

Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists' rank promotion data jointly analyzes the biochemists' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lung disease.     

Discrete-time nonparametric estimation for semi-Markov models of chain-of-events data subject to interval censoring and truncation

Chain-of-events data are longitudinal observations on a succession of events that can only occur in a prescribed order. One goal in an analysis of this type of data is to determine the distribution of times between the successive events. This is difficult when individuals are observed periodically rather than continuously because the event times are then interval censored. Chain-of-events data may also be subject to truncation when individuals can only be observed if a certain event in the chain (e.g., the final event) has occurred. We provide a nonparametric approach to estimate the distributions of times between successive events in discrete time for data such as these under the semi-Markov assumption that the times between events are independent. This method uses a self-consistency algorithm that extends Turnbull's algorithm (1976, Journal of the Royal Statistical Society, Series B 38, 290-295). The quantities required to carry out the algorithm can be calculated recursively for improved computational efficiency. Two examples using data from studies involving HIV disease are used to illustrate our methods.     

Interspike Interval Fluctuations in Aplysia Pacemaker Neurons

In recent years, several mathematical models have been put forth to explain the time sequence of spike discharges in single neurons, in terms of synaptic inputs or intrinsic mechanisms. All of these models have been hypothetical, in that intracellular events were assumed, and not measured directly. The purpose of the present work was to study the statistics of the discharge from a preparation where intracellular recording was possible, and relate the observed discharge to measurable cell parameters. Regularly firing “pacemaker neurons” in the visceral ganglion of Aplysia californica were studied, using intracellular stimulating and recording techniques. Measurements were obtained of average curves of membrane potential, threshold for spike initiation, membrane resistance, and fluctuations of potential in the intervals between spontanously occurring spikes. The timing of discharges from these neurons was described quantitatively by interspike-interval histograms, mean and standard deviation of intervals, skewness, and serial correlation coefficients. A mathematical model (contained in a simulation program for the IBM 7094 computer) was constructed, based on discrete fluctuations of membrane potential following each spike and other directly observed intracellular events. It was found that the model could quantitatively account for observed spike trains, including variations in the discharge from one cell to another.     

High resolution radiocarbon spike confirms tree ring dating with low sample depth

Radiocarbon (¹⁴C) has been used to date carbon-rich objects in Earth science, archeology, and history since the 1940s. New methods, using spikes in ¹⁴C caused by solar proton events, can be used to annually date wood when crossdating is not possible, such as when sample size is low, samples are floating in time, or external disturbances lead to insecure dates. Here, we use a spike in radiocarbon during a solar energetic particle (SEP) event in 774/775 CE to confirm crossdating of a poorly-replicated King Billy pine (Athrotaxis selaginoides) chronology. Low sample depth between 1498 and 1523 CE (two trees) prevented confident dating of the early period of the chronology. Three core samples with strong correlation with the master chronology that likely included the 774/775 CE Miyake SEP event were identified for radiocarbon isotope analysis. We sectioned segments centered on the estimated 774/775 CE date and then isolated the holocellulose in each sample. Samples were sent to an accelerator mass spectrometry (AMS) for radiocarbon measurements. The AMS data confirmed the crossdating accuracy of the tree ring series and reinforces the applicability of this technique to anchor poorly dated tree ring series in time. In addition, we found sample processing with a microtome proved superior for holocellulose extractions and yielded more accurate ¹⁴C measurements. We recommend sampling with a microtome, processing at least three samples per year, and including sample masses greater than 100 ug C to confirm dating using radiocarbon spikes.     

Analyzing time‐ordered event data with missed observations

A common problem with observational datasets is that not all events of interest may be detected. For example, observing animals in the wild can difficult when animals move, hide, or cannot be closely approached. We consider time series of events recorded in conditions where events are occasionally missed by observers or observational devices. These time series are not restricted to behavioral protocols, but can be any cyclic or recurring process where discrete outcomes are observed. Undetected events cause biased inferences on the process of interest, and statistical analyses are needed that can identify and correct the compromised detection processes. Missed observations in time series lead to observed time intervals between events at multiples of the true inter‐event time, which conveys information on their detection probability. We derive the theoretical probability density function for observed intervals between events that includes a probability of missed detection. Methodology and software tools are provided for analysis of event data with potential observation bias and its removal. The methodology was applied to simulation data and a case study of defecation rate estimation in geese, which is commonly used to estimate their digestive throughput and energetic uptake, or to calculate goose usage of a feeding site from dropping density. Simulations indicate that at a moderate chance to miss arrival events (p = 0.3), uncorrected arrival intervals were biased upward by up to a factor 3, while parameter values corrected for missed observations were within 1% of their true simulated value. A field case study shows that not accounting for missed observations leads to substantial underestimates of the true defecation rate in geese, and spurious rate differences between sites, which are introduced by differences in observational conditions. These results show that the derived methodology can be used to effectively remove observational biases in time‐ordered event data.     

A Bayesian multi-risks survival (MRS) model in the presence of double censorings

Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi-risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right-censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate-specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer.     

Methods for short time series analysis of cell-based biosensor data.

This paper describes two approaches for sensing changes in spiking cells when only a limited amount of spike data is available, i.e., dynamically constructed local expansion rates and spike area distributions. The two methods were tested on time series from cultured neuron cells that exhibit spiking both autonomously and in the presence of periodic stimulation. Our tested hypothesis was that minute concentrations of toxins could affect the local statistics of the dynamics. Short data sets having relatively few spikes were generated from experiments on cells before and after being treated with a small concentration of channel blocker. In spontaneous spiking cells, local expansion rates show a sensitivity that correlates with channel concentration level, while stimulated cells show no such correlation. Spike area distributions on the other hand showed measurable differences between control and treated conditions for both types of spiking, and a much higher degree of sensitivity. Because these methods are based on analysis of short time series analysis, they might provide novel means for cell drug and toxin detection.     

A measure of explained variation for event history data

Summary There is no shortage of proposed measures of prognostic value of survival models in the statistical literature. They come under different names, including explained variation, correlation, explained randomness, and information gain, but their goal is common: to define something analogous to the coefficient of determination R² in linear regression. None however have been uniformly accepted, none have been extended to general event history data, including recurrent events, and many cannot incorporate time‐varying effects or covariates. We present here a measure specifically tailored for use with general dynamic event history regression models. The measure is applicable and interpretable in discrete or continuous time; with tied data or otherwise; with time‐varying, time‐fixed, or dynamic covariates; with time‐varying or time‐constant effects; with single or multiple event times; with parametric or semiparametric models; and under general independent censoring/observation. For single‐event survival data with neither censoring nor time dependency it reduces to the concordance index. We give expressions for its population value and the variance of the estimator and explore its use in simulations and applications. A web link to R software is provided.     

Using Simulation to Interpret a Discrete Time Survival Model in a Complex Biological System: Fertility and Lameness in Dairy Cows

The ever-growing volume of data routinely collected and stored in everyday life presents researchers with a number of opportunities to gain insight and make predictions. This study aimed to demonstrate the usefulness in a specific clinical context of a simulation-based technique called probabilistic sensitivity analysis (PSA) in interpreting the results of a discrete time survival model based on a large dataset of routinely collected dairy herd management data. Data from 12,515 dairy cows (from 39 herds) were used to construct a multilevel discrete time survival model in which the outcome was the probability of a cow becoming pregnant during a given two day period of risk, and presence or absence of a recorded lameness event during various time frames relative to the risk period amongst the potential explanatory variables. A separate simulation model was then constructed to evaluate the wider clinical implications of the model results (i.e. the potential for a herd’s incidence rate of lameness to influence its overall reproductive performance) using PSA. Although the discrete time survival analysis revealed some relatively large associations between lameness events and risk of pregnancy (for example, occurrence of a lameness case within 14 days of a risk period was associated with a 25% reduction in the risk of the cow becoming pregnant during that risk period), PSA revealed that, when viewed in the context of a realistic clinical situation, a herd’s lameness incidence rate is highly unlikely to influence its overall reproductive performance to a meaningful extent in the vast majority of situations. Construction of a simulation model within a PSA framework proved to be a very useful additional step to aid contextualisation of the results from a discrete time survival model, especially where the research is designed to guide on-farm management decisions at population (i.e. herd) rather than individual level.     

Short loop length and high thermal stability determine genomic instability induced by G‐quadruplex‐forming minisatellites

G‐quadruplexes (G4) are polymorphic four‐stranded structures formed by certain G‐rich nucleic acids, with various biological roles. However, structural features dictating their formation and/or function in vivo are unknown. In S. cerevisiae, the pathological persistency of G4 within the CEB1 minisatellite induces its rearrangement during leading‐strand replication. We now show that several other G4‐forming sequences remain stable. Extensive mutagenesis of the CEB25 minisatellite motif reveals that only variants with very short (≤ 4 nt) G4 loops preferentially containing pyrimidine bases trigger genomic instability. Parallel biophysical analyses demonstrate that shortening loop length does not change the monomorphic G4 structure of CEB25 variants but drastically increases its thermal stability, in correlation with the in vivo instability. Finally, bioinformatics analyses reveal that the threat for genomic stability posed by G4 bearing short pyrimidine loops is conserved in C. elegans and humans. This work provides a framework explanation for the heterogeneous instability behavior of G4‐forming sequences in vivo, highlights the importance of structure thermal stability, and questions the prevailing assumption that G4 structures with short or longer loops are as likely to form in vivo.     

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.     

Joint model of recurrent events and a terminal event with time‐varying coefficients

Joint modeling of recurrent events and a terminal event has been studied extensively in the past decade. However, most of the previous works assumed constant regression coefficients. This paper proposes a joint model with time‐varying coefficients in both event components. The proposed model not only accommodates the correlation between the two type of events, but also characterizes the potential time‐varying covariate effects. It is especially useful for evaluating long‐term risk factors' effect that could vary with time. A Gaussian frailty is used to model the correlation between event times. The nonparametric time‐varying coefficients are modeled using cubic splines with penalty terms. A simulation study shows that the proposed estimators perform well. The model is used to analyze the readmission rate and mortality jointly for stroke patients admitted to Veterans Administration (VA) Hospitals.     

A Deconvolution-Based Method with High Sensitivity and Temporal Resolution for Detection of Spontaneous Synaptic Currents In?Vitro and?In?Vivo

Spontaneous postsynaptic currents (PSCs) provide key information about the mechanisms of synaptic transmission and the activity modes of neuronal networks. However, detecting spontaneous PSCs in vitro and in vivo has been challenging, because of the small amplitude, the variable kinetics, and the undefined time of generation of these events. Here, we describe a, to our knowledge, new method for detecting spontaneous synaptic events by deconvolution, using a template that approximates the average time course of spontaneous PSCs. A recorded PSC trace is deconvolved from the template, resulting in a series of delta-like functions. The maxima of these delta-like events are reliably detected, revealing the precise onset times of the spontaneous PSCs. Among all detection methods, the deconvolution-based method has a unique temporal resolution, allowing the detection of individual events in high-frequency bursts. Furthermore, the deconvolution-based method has a high amplitude resolution, because deconvolution can substantially increase the signal/noise ratio. When tested against previously published methods using experimental data, the deconvolution-based method was superior for spontaneous PSCs recorded in vivo. Using the high-resolution deconvolution-based detection algorithm, we show that the frequency of spontaneous excitatory postsynaptic currents in dentate gyrus granule cells is 4.5 times higher in vivo than in vitro.     

A Hybrid Technique for the Periodicity Characterization of Genomic Sequence Data

Many studies of biological sequence data have examined sequence structure in terms of periodicity, and various methods for measuring periodicity have been suggested for this purpose. This paper compares two such methods, autocorrelation and the Fourier transform, using synthetic periodic sequences, and explains the differences in periodicity estimates produced by each. A hybrid autocorrelation—integer period discrete Fourier transform is proposed that combines the advantages of both techniques. Collectively, this representation and a recently proposed variant on the discrete Fourier transform offer alternatives to the widely used autocorrelation for the periodicity characterization of sequence data. Finally, these methods are compared for various tetramers of interest in C. elegans chromosome I.     

Lipid Mixing and Content Release in Single-Vesicle, SNARE-Driven Fusion Assay with 1-5 ms Resolution

A single-vesicle, fluorescence-based, SNARE-driven fusion assay enables simultaneous measurement of lipid mixing and content release with 5 ms/frame, or even 1 ms/frame, time resolution. The v-SNARE vesicles, labeled with lipid and content markers of different color, dock and fuse with a planar t-SNARE bilayer supported on glass. A narrow (<5 ms duration), intense spike of calcein fluorescence due to content release and dequenching coincides with inner-leaflet lipid mixing within 10 ms. The spike provides more sensitive detection of productive hemifusion events than do lipid labels alone. Consequently, many fast events previously thought to be prompt, full fusion events are now reclassified as productive hemifusion. Both full fusion and hemifusion occur with a time constant of 5-10 ms. At 60% phosphatidylethanolamine lipid composition, productive and dead-end hemifusion account for 65% of all fusion events. However, quantitative analysis shows that calcein is released into the space above the bilayer (vesicle bursting), rather than the thin aqueous space between the bilayer and glass. Evidently, at the instant of inner-leaflet mixing, flattening of the vesicle increases the internal pressure beyond the bursting point. This may be related to in vivo observations suggesting that membrane lysis often competes with membrane fusion.     

Local phenomena and distribution of molecular species during the unfolding of heme-free myoglobin in the presence of GdnHCl and urea as seen by time-resolved fluorescence spectroscopy

We have used time-resolved fluorescence spectroscopy for following the unfolding of apomyoglobin in urea and guanidine hydrochloride (GdnHCl). The data have been compared with those obtained using classical techniques such as CD and steady-state emission spectroscopy. Both the average intensity of the lifetimes and the size of the librational cone of the fluorophores, as measured by time-resolved fluorescence, increased with denaturant concentration and their changes largely preceded the modifications detectable with CD and the shift of the maximum of emission spectra. The data indicate that the changes in the local environments of the tryptophans were completed when the global modification monitored by CD and the emission spectra was still minimal. This suggests that an initial event in the denaturation of apomyoglobin is localized at the tryptophan residues. The correlation times of native apomyoglobin showed the rotational diffusion characteristics of a rigid rotor. In 3.6 M GdnHCl and 7.5 M urea, where the secondary structure is practically absent, the correlation times of the two systems became very short, as expected from the motion of a flexible polymer. In GdnHCl, under conditions of partial unfolding, it was not possible to detect the presence of native totally folded molecular species.     

Seed size and seed germination in the Mediterranean fire-prone shrub <Emphasis Type="Italic">Cistus </Emphasis><Emphasis Type="Italic">ladanifer</Emphasis>

The germination response of different sized seeds from individuals of a Mediterranean fire-prone shrub (Cistus ladanifer) was investigated in relation to pre-germination heating. A control (no heating), a low temperature during a short exposure time (50°C during 5 min), a high temperature during a short exposure time (100°C during 5 min) and a high temperature during a long exposure time (100°C during 15 min) were applied to seeds from different individual plants with different mean seed weight. These pre-germination treatments resemble natural germination scenarios for the studied species, absence of fire, low intensity pasture fire, typical Mediterranean shrub fire, and severe fire with high fuel load. Mean seed weight only showed a marginally significant positive correlation with the proportion of germinated seeds whatever the pre-germination treatment. These results suggest that seed dormancy is unrelated to seed size and that under the experimental conditions used in this study, the effect of seed size on seed germination is low. Nevertheless, larger seeds could be favoured in natural conditions, especially under the high competition scenario which arise after wildfires. Control seeds showed a negative correlation between seed size and germination velocity suggesting that lighter seeds could take advantage from early germination in recruitment events in the absence of wildfires. Nevertheless, even the lower pre-germination heating treatment turns this correlation in not significant, suggesting a strong selection pressure (unrelated to seed size) for early germination after fire events. In our study, different sized seeds of C. ladanifer seem to perform better under different germination scenarios suggesting that seed size variation could be maintained by the alternation of recruitments without wildfires and recruitments after wildfire events.