A hidden Markov model for decoding and the analysis of replay in spike trains

We present a hidden Markov model that describes variation in an animal’s position associated with varying levels of activity in action potential spike trains of individual place cell neurons. The model incorporates a coarse-graining of position, which we find to be a more parsimonious description of the system than other models. We use a sequential Monte Carlo algorithm for Bayesian inference of model parameters, including the state space dimension, and we explain how to estimate position from spike train observations (decoding). We obtain greater accuracy over other methods in the conditions of high temporal resolution and small neuronal sample size. We also present a novel, model-based approach to the study of replay: the expression of spike train activity related to behaviour during times of motionlessness or sleep, thought to be integral to the consolidation of long-term memories. We demonstrate how we can detect the time, information content and compression rate of replay events in simulated and real hippocampal data recorded from rats in two different environments, and verify the correlation between the times of detected replay events and of sharp wave/ripples in the local field potential.

[1]  B. McNaughton,et al.  Replay of Neuronal Firing Sequences in Rat Hippocampus During Sleep Following Spatial Experience , 1996, Science.

[2]  Albert K. Lee,et al.  Memory of Sequential Experience in the Hippocampus during Slow Wave Sleep , 2002, Neuron.

[3]  B. McNaughton,et al.  Memory trace reactivation in hippocampal and neocortical neuronal ensembles , 2000, Current Opinion in Neurobiology.

[4]  Matthijs A. A. van der Meer,et al.  Hippocampal Replay Is Not a Simple Function of Experience , 2010, Neuron.

[5]  Zhe Chen,et al.  An Overview of Bayesian Methods for Neural Spike Train Analysis , 2013, Comput. Intell. Neurosci..

[6]  Tzu-Tsung Wong,et al.  Generalized Dirichlet distribution in Bayesian analysis , 1998, Appl. Math. Comput..

[7]  David J. Foster,et al.  Reverse replay of behavioural sequences in hippocampal place cells during the awake state , 2006, Nature.

[8]  G. Buzsáki,et al.  Forward and reverse hippocampal place-cell sequences during ripples , 2007, Nature Neuroscience.

[9]  Wulfram Gerstner,et al.  Improved Similarity Measures for Small Sets of Spike Trains , 2011, Neural Computation.

[10]  Chris I. De Zeeuw,et al.  GATA-3 Is Involved in the Development of Serotonergic Neurons in the Caudal Raphe Nuclei , 1999, The Journal of Neuroscience.

[11]  J. O’Keefe,et al.  Phase relationship between hippocampal place units and the EEG theta rhythm , 1993, Hippocampus.

[12]  C. Rivera,et al.  Neurturin Evokes MAPK-Dependent Upregulation of Egr4 and KCC2 in Developing Neurons , 2011, Neural plasticity.

[13]  M. Wilson,et al.  Disruption of ripple‐associated hippocampal activity during rest impairs spatial learning in the rat , 2009, Hippocampus.

[14]  Brad E. Pfeiffer,et al.  Hippocampal place cell sequences depict future paths to remembered goals , 2013, Nature.

[15]  G. Dragoi,et al.  Preplay of future place cell sequences by hippocampal cellular assemblies , 2011, Nature.

[16]  Daniel T. Larose,et al.  Discovering Knowledge in Data: An Introduction to Data Mining , 2005 .

[17]  S. L. Scott.  Bayesian Methods for Hidden Markov Models , 2002 .

[18]  Matthew A. Wilson,et al.  A Bayesian nonparametric approach for uncovering rat hippocampal population codes during spatial navigation , 2016, Journal of Neuroscience Methods.

[19]  C. Robert,et al.  Computational and Inferential Difficulties with Mixture Posterior Distributions , 2000 .

[20]  Matthew A. Wilson,et al.  Hippocampal Replay of Extended Experience , 2009, Neuron.

[21]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[22]  Sen Cheng,et al.  Reactivation, Replay, and Preplay: How It Might All Fit Together , 2011, Neural plasticity.

[23]  G. Buzsáki,et al.  High-frequency network oscillation in the hippocampus. , 1992, Science.

[24]  J. Born,et al.  Hippocampal sharp wave-ripples linked to slow oscillations in rat slow-wave sleep. , 2006, Journal of neurophysiology.

[25]  B L McNaughton,et al.  Dynamics of the hippocampal ensemble code for space. , 1993, Science.

[26]  W. Wildman,et al.  Theoretical Neuroscience , 2014 .

[27]  Vipin Kumar,et al.  Introduction to Data Mining , 2022, Data Mining and Machine Learning Applications.

[28]  Nicolas Chopin,et al.  Inference and model choice for sequentially ordered hidden Markov models , 2007 .

[29]  Mattias P. Karlsson,et al.  Awake replay of remote experiences in the hippocampus , 2009, Nature Neuroscience.

[30]  J. O’Neill,et al.  Play it again: reactivation of waking experience and memory , 2010, Trends in Neurosciences.

[31]  G. Buzsáki,et al.  tFast Network Oscillations in the Hippocampal CA1 Region of the Behaving Rat , 1999, The Journal of Neuroscience.

[32]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[33]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[34]  Adam Johnson,et al.  Neural Ensembles in CA3 Transiently Encode Paths Forward of the Animal at a Decision Point , 2007, The Journal of Neuroscience.

[35]  M. Wilson,et al.  Theta Rhythms Coordinate Hippocampal–Prefrontal Interactions in a Spatial Memory Task , 2005, PLoS biology.

[36]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[37]  Yee Whye Teh,et al.  Fast MCMC sampling for Markov jump processes and extensions , 2012, J. Mach. Learn. Res..

[38]  Matthew A. Wilson,et al.  Uncovering spatial topology represented by rat hippocampal population neuronal codes , 2012, Journal of Computational Neuroscience.

[39]  C. Pavlides,et al.  Influences of hippocampal place cell firing in the awake state on the activity of these cells during subsequent sleep episodes , 1989, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[40]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[41]  B. McNaughton,et al.  Reactivation of Hippocampal Cell Assemblies: Effects of Behavioral State, Experience, and EEG Dynamics , 1999, The Journal of Neuroscience.

[42]  P. Good.  Permutation, Parametric, and Bootstrap Tests of Hypotheses (Springer Series in Statistics) , 1994 .

[43]  G. Buzsáki,et al.  Selective suppression of hippocampal ripples impairs spatial memory , 2009, Nature Neuroscience.

[44]  J. Csicsvari,et al.  Replay and Time Compression of Recurring Spike Sequences in the Hippocampus , 1999, The Journal of Neuroscience.

[45]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[46]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[47]  Andrew M. Wikenheiser,et al.  The balance of forward and backward hippocampal sequences shifts across behavioral states , 2013, Hippocampus.

[48]  D. R. Euston,et al.  Fast-Forward Playback of Recent Memory Sequences in Prefrontal Cortex During Sleep , 2007, Science.

[49]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[50]  G. Buzsáki.  Large-scale recording of neuronal ensembles , 2004, Nature Neuroscience.

[51]  Matthew A. Wilson,et al.  Neural Representation of Spatial Topology in the Rodent Hippocampus , 2013, Neural Computation.

[52]  M. Wilson,et al.  Temporally Structured Replay of Awake Hippocampal Ensemble Activity during Rapid Eye Movement Sleep , 2001, Neuron.

[53]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[54]  M. Khamassi,et al.  Replay of rule-learning related neural patterns in the prefrontal cortex during sleep , 2009, Nature Neuroscience.

[55]  E N Brown,et al.  A Statistical Paradigm for Neural Spike Train Decoding Applied to Position Prediction from Ensemble Firing Patterns of Rat Hippocampal Place Cells , 1998, The Journal of Neuroscience.

[56]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.

[57]  P. Good.  Permutation, Parametric, and Bootstrap Tests of Hypotheses , 2005 .

[58]  B. McNaughton,et al.  Memory reprocessing in corticocortical and hippocampocortical neuronal ensembles. , 1997, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[59]  Margaret F. Carr,et al.  Hippocampal replay in the awake state: a potential substrate for memory consolidation and retrieval , 2011, Nature Neuroscience.

[60]  B. McNaughton,et al.  Reactivation of hippocampal ensemble memories during sleep. , 1994, Science.

[61]  D. Brillinger.  Estimation of the Second-Order Intensities of a Bivariate Stationary Point Process , 1976 .

[62]  J. O’Keefe.  Place units in the hippocampus of the freely moving rat , 1976, Experimental Neurology.

[63]  M. Wilson,et al.  Coordinated Interactions between Hippocampal Ripples and Cortical Spindles during Slow-Wave Sleep , 1998, Neuron.

[64]  M. Wilson,et al.  Coordinated memory replay in the visual cortex and hippocampus during sleep , 2007, Nature Neuroscience.

[65]  B L McNaughton,et al.  Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. , 1998, Journal of neurophysiology.