Decoding Poisson Spike Trains by Gaussian Filtering

The temporal waveform of neural activity is commonly estimated by low-pass filtering spike train data through convolution with a gaussian kernel. However, the criteria for selecting the gaussian width σ are not well understood. Given an ensemble of Poisson spike trains generated by an instantaneous firing rate function λ(t), the problem was to recover an optimal estimate of λ(t) by gaussian filtering. We provide equations describing the optimal value of σ using an error minimization criterion and examine how the optimal σ varies within a parameter space defining the statistics of inhomogeneous Poisson spike trains. The process was studied both analytically and through simulations. The rate functions λ(t) were randomly generated, with the three parameters defining spike statistics being the mean of λ(t), the variance of λ(t), and the exponent α of the Fourier amplitude spectrum 1/fα of λ(t). The value of σopt followed a power law as a function of the pooled mean interspike interval I, σopt = aIb, where a was inversely related to the coefficient of variation CV of λ(t), and b was inversely related to the Fourier spectrum exponent α. Besides applications for data analysis, optimal recovery of an analog signal waveform λ(t) from spike trains may also be useful in understanding neural signal processing in vivo.

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Inferring the collective dynamics of neuronal populations from single-trial spike trains using mechanistic models

10.1101/671909 ◽

2019 ◽

Cited By ~ 2

Author(s):

Christian Donner ◽

Manfred Opper ◽

Josef Ladenbauer

Keyword(s):

Population Dynamics ◽

Spike Train ◽

Spike Trains ◽

Neuronal Membrane ◽

Model Parameters ◽

Mechanistic Models ◽

Single Trial ◽

Experimental Conditions ◽

Spike Train Data

AbstractMulti-neuronal spike-train data recorded in vivo often exhibit rich dynamics as well as considerable variability across cells and repetitions of identical experimental conditions (trials). Efforts to characterize and predict the population dynamics and the contributions of individual neurons require model-based tools. Abstract statistical models allow for principled parameter estimation and model selection, but possess only limited interpretive power because they typically do not incorporate prior biophysical constraints. Here we present a statistically principled approach based on a population of doubly-stochastic integrate-and-fire neurons, taking into account basic biophysics. This model class comprises an idealized description for the dynamics of the neuronal membrane voltage in response to fast independent and slower shared input fluctuations. To efficiently estimate the model parameters and compare different model variants we compute the likelihood of observed single-trail spike trains by leveraging analytical methods for spiking neuron models combined with inference techniques for hidden Markov models. This allows us to reconstruct the shared input variations, classify their dynamics, obtain precise spike rate estimates, and quantify how individual neurons couple to the low-dimensional overall population dynamics, all from a single trial. Extensive evaluations based on simulated data show that our method correctly identifies the dynamics of the shared input process and accurately estimates the model parameters. Validations on ground truth recordings of neurons in vitro demonstrate that our approach successfully reconstructs the dynamics of hidden inputs and yields improved fits compared to a typical phenomenological model. Finally, we apply the method to a neuronal population recorded in vivo, for which we assess the contributions of individual neurons to the overall spiking dynamics. Altogether, our work provides statistical inference tools for a class of reasonably constrained, mechanistic models and demonstrates the benefits of this approach to analyze measured spike train data.

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Method for stationarity-segmentation of spike train data with application to the Pearson cross-correlation

Journal of Neurophysiology ◽

10.1152/jn.00186.2013 ◽

2013 ◽

Vol 110 (2) ◽

pp. 562-572 ◽

Cited By ~ 8

Author(s):

Claudio S. Quiroga-Lombard ◽

Joachim Hass ◽

Daniel Durstewitz

Keyword(s):

Correlation Functions ◽

Cross Correlation ◽

Simulated Data ◽

Weak Sense ◽

Spike Trains ◽

Data Sets ◽

Stimulus Movement ◽

Spike Train Data ◽

Definition Of

Correlations among neurons are supposed to play an important role in computation and information coding in the nervous system. Empirically, functional interactions between neurons are most commonly assessed by cross-correlation functions. Recent studies have suggested that pairwise correlations may indeed be sufficient to capture most of the information present in neural interactions. Many applications of correlation functions, however, implicitly tend to assume that the underlying processes are stationary. This assumption will usually fail for real neurons recorded in vivo since their activity during behavioral tasks is heavily influenced by stimulus-, movement-, or cognition-related processes as well as by more general processes like slow oscillations or changes in state of alertness. To address the problem of nonstationarity, we introduce a method for assessing stationarity empirically and then “slicing” spike trains into stationary segments according to the statistical definition of weak-sense stationarity. We examine pairwise Pearson cross-correlations (PCCs) under both stationary and nonstationary conditions and identify another source of covariance that can be differentiated from the covariance of the spike times and emerges as a consequence of residual nonstationarities after the slicing process: the covariance of the firing rates defined on each segment. Based on this, a correction of the PCC is introduced that accounts for the effect of segmentation. We probe these methods both on simulated data sets and on in vivo recordings from the prefrontal cortex of behaving rats. Rather than for removing nonstationarities, the present method may also be used for detecting significant events in spike trains.

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Frequency-preference response in covalent modification cycles under substrate sequestration conditions

npj Systems Biology and Applications ◽

10.1038/s41540-021-00192-8 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Juliana Reves Szemere ◽

Horacio G. Rotstein ◽

Alejandra C. Ventura

Keyword(s):

Frequency Response ◽

Covalent Modification ◽

Protein Abundance ◽

Dynamic Features ◽

Signaling Systems ◽

Low Pass ◽

Low Pass Filters ◽

Periodic Inputs ◽

Preferred Frequency Response

AbstractCovalent modification cycles (CMCs) are basic units of signaling systems and their properties are well understood. However, their behavior has been mostly characterized in situations where the substrate is in excess over the modifying enzymes. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations, leading to substrate sequestration by the enzymes. In this enzyme-in-excess regime, CMCs have been shown to exhibit signal termination, the ability of the product to return to a stationary value lower than its peak in response to constant stimulation, while this stimulation is still active, with possible implications for the ability of systems to adapt to environmental inputs. We characterize the conditions leading to signal termination in CMCs in the enzyme-in-excess regime. We also demonstrate that this behavior leads to a preferred frequency response (band-pass filters) when the cycle is subjected to periodic stimulation, whereas the literature reports that CMCs investigated so far behave as low-pass filters. We characterize the relationship between signal termination and the preferred frequency response to periodic inputs and we explore the dynamic mechanism underlying these phenomena. Finally, we describe how the behavior of CMCs is reflected in similar types of responses in the cascades of which they are part. Evidence of protein abundance in vivo shows that enzymes and substrates are present in comparable concentrations, thus suggesting that signal termination and frequency-preference response to periodic inputs are also important dynamic features of cell signaling systems, which have been overlooked.

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GluA1 Phosphorylation Alters Evoked Firing PatternIn Vivo

Neural Plasticity ◽

10.1155/2012/286215 ◽

2012 ◽

Vol 2012 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Balázs Barkóczi ◽

Gábor Juhász ◽

Robert G. Averkin ◽

Imre Vörös ◽

Petra Vertes ◽

...

Keyword(s):

Synaptic Plasticity ◽

Spike Trains ◽

Temporal Coding ◽

Relative Contribution ◽

Ampa Receptor Subunit ◽

Ampa And Nmda Receptors ◽

Characteristic Features ◽

Evoked Activity

AMPA and NMDA receptors convey fast synaptic transmission in the CNS. Their relative contribution to synaptic output and phosphorylation state regulate synaptic plasticity. The AMPA receptor subunit GluA1 is central in synaptic plasticity. Phosphorylation of GluA1 regulates channel properties and trafficking. The firing rate averaged over several hundred ms is used to monitor cellular input. However, plasticity requires the timing of spiking within a few ms; therefore, it is important to understand how phosphorylation governs these events. Here, we investigate whether the GluA1 phosphorylation (p-GluA1) alters the spiking patterns of CA1 cellsin vivo. The antidepressant Tianeptine was used for inducing p-GluA1, which resulted in enhanced AMPA-evoked spiking. By comparing the spiking patterns of AMPA-evoked activity with matched firing rates, we show that the spike-trains after Tianeptine application show characteristic features, distinguishing from spike-trains triggered by strong AMPA stimulation. The interspike-interval distributions are different between the two groups, suggesting that neuronal output may differ when new inputs are activated compared to increasing the gain of previously activated receptors. Furthermore, we also show that NMDA evokes spiking with different patterns to AMPA spike-trains. These results support the role of the modulation of NMDAR/AMPAR ratio and p-GluA1 in plasticity and temporal coding.

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Dynamics of neurons in the cat lateral geniculate nucleus: in vivo electrophysiology and computational modeling

Journal of Neurophysiology ◽

10.1152/jn.1995.74.3.1222 ◽

1995 ◽

Vol 74 (3) ◽

pp. 1222-1243 ◽

Cited By ~ 73

Author(s):

P. Mukherjee ◽

E. Kaplan

Keyword(s):

Computational Modeling ◽

Spike Train ◽

Lateral Geniculate Nucleus ◽

Transfer Functions ◽

Temporal Frequency ◽

Relay Cell ◽

Lateral Geniculate ◽

Low Pass ◽

Band Pass

1. We investigated the time domain transformation that thalamocortical relay cells of the cat lateral geniculate nucleus (LGN) perform on their retinal input, and used computational modeling to explore the biophysical properties that determine the dynamics of the LGN relay cells in vivo. 2. We recorded simultaneously the input (S potentials) and output (action potentials) of 50 cat LGN relay cells stimulated by drifting sinusoidal gratings of varying temporal frequency. The temporal modulation transfer functions (TMTFs) of the neurons were derived from these data. The burstiness of the LGN spike trains was also assessed using objective criteria. 3. We found that the form of the TMTF was quite variable among cells, ranging from low-pass to strongly band-pass. The optimal temporal frequency of band-pass neurons was between 2 and 8 Hz. In addition, the TMTF of some cells was nonstationary: their temporal tuning changed with time. 4. The temporal tuning of a cell was directly related to the degree of burstiness of its spike train. Tonically firing relay cells had low-pass TMTFs, whereas the most bursty neurons exhibited the most sharply band-pass transfer functions. This was also true for single cells that altered their temporal tuning: a shift to more band-pass tuning was associated with increased burstiness of the spike train, and vice versa. 5. We constructed a computer simulation of the LGN relay cell. The model was a simplified five-channel version of the thalamocortical neuron model of McCormick and Huguenard. It incorporated the quantitative kinetics of the Ca2+ T channel, as well as the Hodgkin-Huxley Na+ and K+ channels, as the only active membrane currents. To simulate the in vivo dynamics of the relay cell, the input to the model consisted of trains of synaptic potentials, recorded as S potentials in our physiological experiments. 6. When the resting membrane potential of the model neuron was relatively depolarized, the model's TMTF was low-pass, with no bursting evident in the simulated spike train. At hyperpolarized resting membrane potentials, however, the modeled TMTF was band-pass, with frequent burst discharges. Thus the biophysical model reproduced not only the range of dynamics seen in real LGN relay cells, but also the dependence of the overall dynamics on the burstiness of the spike train. However, neither of these phenomena could be simulated without the T channel. Thus the simulations demonstrated that the T-type Ca2+ channel was necessary and sufficient to explain the LGN dynamics observed in physiological experiments.(ABSTRACT TRUNCATED AT 400 WORDS)

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LiquidCNA: tracking subclonal evolution from longitudinal liquid biopsies using somatic copy number alterations

10.1101/2021.01.05.425414 ◽

2021 ◽

Author(s):

Eszter Lakatos ◽

Helen Hockings ◽

Maximilian Mossner ◽

Michelle Lockley ◽

Trevor A. Graham

Keyword(s):

Copy Number ◽

Evolutionary Dynamics ◽

Cost Effective ◽

Copy Number Alterations ◽

Liquid Biopsies ◽

Metastatic Lung ◽

Low Pass ◽

Somatic Copy Number Alterations

AbstractCell-free DNA (cfDNA) measured via liquid biopsies provides a way for minimally-invasive monitoring of tumour evolutionary dynamics during therapy. Here we present liquidCNA, a method to track subclonal evolution from longitudinally collected cfDNA samples based on somatic copy number alterations (SCNAs). LiquidCNA utilises SCNA profiles derived through cost-effective low-pass whole genome sequencing to automatically and simultaneously genotype and quantify the size of the dominant subclone without requiring prior knowledge of the genetic identity of the emerging clone. We demonstrate the accuracy of liquidCNA in synthetically generated sample sets and in vitro and in silico mixtures of cancer cell lines. Application in vivo in patients with metastatic lung cancer reveals the progressive emergence of a novel tumour sub-population. LiquidCNA is straightforward to use, computationally inexpensive and enables continuous monitoring of subclonal evolution to understand and control therapy-induced resistance.

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Estimation of neuronal firing rate using Bayesian Adaptive Kernel Smoother (BAKS)

10.1101/204818 ◽

2017 ◽

Author(s):

Nur Ahmadi ◽

Timothy G. Constandinou ◽

Christos-Savvas Bouganis

Keyword(s):

Firing Rate ◽

Spike Train ◽

Prior Distribution ◽

Kernel Smoothing ◽

Neuronal Firing ◽

Gaussian Kernel ◽

Single Trial ◽

Adaptive Kernel ◽

Neuronal Firing Rate ◽

Spike Train Data

AbstractNeurons use sequences of action potentials (spikes) to convey information across neuronal networks. In neurophysiology experiments, information about external stimuli or behavioral tasks has been frequently characterized in term of neuronal firing rate. The firing rate is conventionally estimated by averaging spiking responses across multiple similar experiments (or trials). However, there exist a number of applications in neuroscience research that require firing rate to be estimated on a single trial basis. Estimating firing rate from a single trial is a challenging problem and current state-of-the-art methods do not perform well. To address this issue, we develop a new method for estimating firing rate based on kernel smoothing technique that considers the bandwidth as a random variable with prior distribution that is adaptively updated under a Bayesian framework. By carefully selecting the prior distribution together with Gaussian kernel function, an analytical expression can be achieved for the kernel bandwidth. We refer to the proposed method as Bayesian Adaptive Kernel Smoother (BAKS). We evaluate the performance of BAKS using synthetic spike train data generated by biologically plausible models: inhomogeneous Gamma (IG) and inhomogeneous inverse Gaussian (IIG). We also apply BAKS to real spike train data from non-human primate (NHP) motor and visual cortex. We benchmark the proposed method against the established and previously reported methods. These include: optimized kernel smoother (OKS), variable kernel smoother (VKS), local polynomial fit (Locfit), and Bayesian adaptive regression splines (BARS). Results using both synthetic and real data demonstrate that the proposed method achieves better performance compared to competing methods. This suggests that the proposed method could be useful for understanding the encoding mechanism of neurons in cognitive-related tasks. The proposed method could also potentially improve the performance of brain-machine interface (BMI) decoder that relies on estimated firing rate as the input.

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