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

2019 ◽  
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.

scholarly journals Repetitive firing: a quantitative study of feedback in model encoders.

1977 ◽  
Vol 69 (6) ◽  
pp. 815-848 ◽  
Author(s):  
J F Fohlmeister ◽  
R E Poppele ◽  
R L Purple
Keyword(s):  
Spike Train ◽  
Transfer Functions ◽  
Accurate Method ◽  
Spike Trains ◽  
Repetitive Firing ◽  
Model Parameters ◽  
Sinusoidal Analysis ◽  
Leaky Integrator ◽  
Spike Train Data ◽  
The Times

Recognition of nonlinearities in the neuronal encoding of repetitive spike trains has generated a number of models to explain this behavior. Here we develop the mathematics and a set of tests for two such models: the leaky integrator and the variable-gamma model. Both of these are nearly sufficient to explain the dynamic behavior of a number of repetitively firing, sensory neurons. Model parameters can be related to possible underlying basic mechanisms. Summed and nonsummed, spike-locked negative feedback are examined in conjunction with the models. Transfer functions are formulated to predict responses to steady state, steps, and sinusoidally varying stimuli in which output data are the times of spike-train events only. An electrical analog model for the leaky integrator is tested to verify predicted responses. Curve fitting and parameter variation techniques are explored for the purpose of extracting basic model parameters from spike train data. Sinusoidal analysis of spike trains appear to be a very accurate method for determining spike-locked feedback parameters, and it is to a large extent a model independent method that may also be applied to neuronal responses.

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

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.

scholarly journals Validation of the Minimum-Error Method for Estimating Model Parameters from Neural Spike Train Data

2015 ◽  
Vol 19 (4) ◽  
pp. 111-114
Author(s):  
Huu Hoang ◽  
Isao T. Tokuda
Keyword(s):  
Spike Train ◽  
Model Parameters ◽  
Minimum Error ◽  
Neural Spike ◽  
Neural Spike Train ◽  
Spike Train Data ◽  
Error Method

Patch Clamp Recording in Brain Slices

2015 ◽  
Author(s):  
Luke Campagnola ◽  
Paul Manis
Keyword(s):  
Patch Clamp ◽  
Brain Slices ◽  
Neuronal Membrane ◽  
Electrical Noise ◽  
Patch Clamp Recording ◽  
Experimental Conditions ◽  
Neural Substrate ◽  
Hardware Configuration ◽  
Technical Issues

Patch clamp recording in brain slices allows unparalleled access to neuronal membrane signals in a system that approximates the in-vivo neural substrate while affording greater control of experimental conditions. In this chapter we discuss the theory, methodology, and practical considerations of such experiments including the initial setup, techniques for preparing and handling viable brain slices, and patching and recording signals. A number of practical and technical issues faced by electrophysiologists are also considered, including maintaining slice viability, visualizing and identifying healthy cells, acquiring reliable patch seals, amplifier compensation features, hardware configuration, sources of electrical noise and table vibration, as well as basic data analysis issues and some troubleshooting tips.

Decoding Poisson Spike Trains by Gaussian Filtering

2010 ◽  
Vol 22 (5) ◽  
pp. 1245-1271 ◽  
Author(s):  
Sidney R. Lehky
Keyword(s):  
Amplitude Spectrum ◽  
Spike Trains ◽  
Optimal Recovery ◽  
Rate Function ◽  
Gaussian Kernel ◽  
Gaussian Filtering ◽  
Low Pass ◽  
Spike Train Data ◽  
Fourier Amplitude Spectrum

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.

scholarly journals Spike Train Probability Models for Stimulus-Driven Leaky Integrate-and-Fire Neurons

2008 ◽  
Vol 20 (7) ◽  
pp. 1776-1795 ◽  
Author(s):  
Shinsuke Koyama ◽  
Robert E. Kass
Keyword(s):  
Spike Train ◽  
Point Process ◽  
Renewal Process ◽  
Spike Trains ◽  
Process Models ◽  
Time Varying ◽  
Integrate And Fire ◽  
Lack Of Fit ◽  
Point Process Models ◽  
Spike Train Data

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this letter we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time, the m-IMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit.

Capturing Spike Variability in Noisy Izhikevich Neurons Using Point Process Generalized Linear Models

2018 ◽  
Vol 30 (1) ◽  
pp. 125-148 ◽  
Author(s):  
Jacob Østergaard ◽  
Mark A. Kramer ◽  
Uri T. Eden
Keyword(s):  
Spike Train ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Spike Trains ◽  
Noisy Input ◽  
Statistical Sense ◽  
Active Research ◽  
Spike Train Data ◽  
Random Part ◽  
Different Levels

To understand neural activity, two broad categories of models exist: statistical and dynamical. While statistical models possess rigorous methods for parameter estimation and goodness-of-fit assessment, dynamical models provide mechanistic insight. In general, these two categories of models are separately applied; understanding the relationships between these modeling approaches remains an area of active research. In this letter, we examine this relationship using simulation. To do so, we first generate spike train data from a well-known dynamical model, the Izhikevich neuron, with a noisy input current. We then fit these spike train data with a statistical model (a generalized linear model, GLM, with multiplicative influences of past spiking). For different levels of noise, we show how the GLM captures both the deterministic features of the Izhikevich neuron and the variability driven by the noise. We conclude that the GLM captures essential features of the simulated spike trains, but for near-deterministic spike trains, goodness-of-fit analyses reveal that the model does not fit very well in a statistical sense; the essential random part of the GLM is not captured.

scholarly journals Inferring and validating mechanistic models of neural microcircuits based on spike-train data

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Josef Ladenbauer ◽  
Sam McKenzie ◽  
Daniel Fine English ◽  
Olivier Hagens ◽  
Srdjan Ostojic
Keyword(s):  
Parameter Estimation ◽  
Spike Train ◽  
Synthetic Data ◽  
Ground Truth ◽  
Neuronal Population ◽  
Mechanistic Models ◽  
Population Activity ◽  
Comprehensive Evaluations

Abstract The interpretation of neuronal spike train recordings often relies on abstract statistical models that allow for principled parameter estimation and model selection but provide only limited insights into underlying microcircuits. In contrast, mechanistic models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. Here we present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using derived likelihood functions, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Comprehensive evaluations on synthetic data, validations using ground truth in-vitro and in-vivo recordings, and comparisons with existing techniques demonstrate that parameter estimation is very accurate and efficient, even for highly subsampled networks. Our methods bridge statistical, data-driven and theoretical, model-based neurosciences at the level of spiking circuits, for the purpose of a quantitative, mechanistic interpretation of recorded neuronal population activity.

Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli

2005 ◽  
Vol 93 (6) ◽  
pp. 3270-3281 ◽  
Author(s):  
Roland Schaette ◽  
Tim Gollisch ◽  
Andreas V. M. Herz
Keyword(s):  
Stochastic Model ◽  
Spike Train ◽  
Response Variability ◽  
Model Parameters ◽  
Response Dynamics ◽  
Model Framework ◽  
Dynamic Stimuli ◽  
Recovery Function ◽  
Wide Range

Reliable accounts of the variability observed in neural spike trains are a prerequisite for the proper interpretation of neural dynamics and coding principles. Models that accurately describe neural variability over a wide range of stimulation and response patterns are therefore highly desirable, especially if they can explain this variability in terms of basic neural observables and parameters such as firing rate and refractory period. In this work, we analyze the response variability recorded in vivo from locust auditory receptor neurons under acoustic stimulation. In agreement with results from other systems, our data suggest that neural refractoriness has a strong influence on spike-train variability. We therefore explore a stochastic model of spike generation that includes refractoriness through a recovery function. Because our experimental data are consistent with a renewal process, the recovery function can be derived from a single interspike-interval histogram obtained under constant stimulation. The resulting description yields quantitatively accurate predictions of the response variability over the whole range of firing rates for constant-intensity as well as amplitude-modulated sound stimuli. Model parameters obtained from constant stimulation can be used to predict the variability in response to dynamic stimuli. These results demonstrate that key ingredients of the stochastic response dynamics of a sensory neuron are faithfully captured by a simple stochastic model framework.

scholarly journals Inferring and validating mechanistic models of neural microcircuits based on spike-train data

2018 ◽  
Author(s):  
Josef Ladenbauer ◽  
Sam McKenzie ◽  
Daniel Fine English ◽  
Olivier Hagens ◽  
Srdjan Ostojic
Keyword(s):  
Parameter Estimation ◽  
Spike Train ◽  
Synthetic Data ◽  
Ground Truth ◽  
Neuronal Population ◽  
Mechanistic Models ◽  
Population Activity ◽  
Comprehensive Evaluations

AbstractThe interpretation of neuronal spike train recordings often relies on abstract statistical models that allow for principled parameter estimation and model selection but provide only limited insights into underlying microcircuits. In contrast, mechanistic models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. Here we present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using derived likelihood functions, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Comprehensive evaluations on synthetic data, validations using ground truth in-vitro and in-vivo recordings, and comparisons with existing techniques demonstrate that parameter estimation is very accurate and efficient, even for highly subsampled networks. Our methods bridge statistical, data-driven and theoretical, model-based neurosciences at the level of spiking circuits, for the purpose of a quantitative, mechanistic interpretation of recorded neuronal population activity.

Sign in / Sign up

Export Citation Format

Share Document