Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes

Marmarelis, Vasilis Z.; Shin, Dong-Joon; Song, Dong; Hampson, Robert E.; Deadwyler, Sam A.; Berger, Theodore W.

doi:10.1007/s10827-012-0407-7

Cited by 25 publications

(35 citation statements)

References 114 publications

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“…This issue is particulary pertinent when dealing with large datasets such as those in this study. One approach developed by our group to deal with this issue is to extract the global Principal Dynamic Modes (PDMs) of the system (Marmarelis, 2004; Marmarelis et al, 2013, 2014). Essentially, the PDMs are an efficient system-specific set of basis functions which parsimoniously describe the linear dynamics of each input-output transformation.…”

Section: Methodsmentioning

confidence: 99%

“…The continuous ‘prethreshold’ signal was chosen over adding a threshold trigger and comparing true output spike train with an output ‘postthreshold’ spike train for two reasons. First, this allows us to avoid specifying the threshold trigger value, which relies on the somewhat arbitrary tradeoff between true-positive and false-negative spikes (Marmarelis et al, 2013). Also, similarity metrics between two spike trains often require the specification of a ‘binning parameter’ to determine the temporal resolution of the metric (van Rossum, 2001; Victor and Purpura, 1997).…”

Section: Methodsmentioning

confidence: 99%

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Model-based asessment of an in-vivo predictive relationship from CA1 to CA3 in the rodent hippocampus

et al. 2014

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Although an anatomical connection from CA1 to CA3 via the Entorhinal Cortex (EC) and through backprojecting interneurons has long been known it exist, it has never been examined quantitatively on the single neuron level, in the in-vivo nonpatholgical, nonperturbed brain. Here, single spike activity was recorded using a multi-electrode array from the CA3 and CA1 areas of the rodent hippocampus (N=7) during a behavioral task. The predictive power from CA3→CA1 and CA1→CA3 was examined by constructing Multivariate Autoregressive (MVAR) models from recorded neurons in both directions. All nonsignificant inputs and models were identified and removed by means of Monte Carlo simulation methods. It was found that 121/166 (73%) CA3→CA1 models and 96/145 (66%) CA1→CA3 models had significant predictive power, thus confirming a predictive ‘Granger’ causal relationship from CA1 to CA3. This relationship is thought to be caused by a combination of truly causal connections such as the CA1→EC→CA3 pathway and common inputs such as those from the Septum. All MVAR models were then examined in the frequency domain and it was found that CA3 kernels had significantly more power in the theta and beta range than those of CA1, confirming CA3’s role as an endogenous hippocampal pacemaker.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Model-based asessment of an in-vivo predictive relationship from CA1 to CA3 in the rodent hippocampus

et al. 2014

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“…Several related methods for PDM estimation have been proposed. 6,22,25 The method used here is similar to that proposed by Marmarelis et al 22 and is performed on both the self forward and feedback kernels to obtain a set of self and feedback PDMs as follows: Perform eigendecomposition on the second-order kernel (this is always possible, as the second-order self-kernels are symmetric). Retain all eigenvectors with a corresponding eigenvalue at least 1% of the maximum eigenvalue.…”

Section: Methodsmentioning

confidence: 99%

“…The PDMs can be ranked by singular value, which gives a rough indication of their relative importance, and the subset may be selected using this criterion. 22 However, at least in this work, we have found this ranking to be unreliable (with the exception of the highest ranked PDM), and we use a leave-one-out/add-one-in (LOO/AOI) algorithm to identify the reduced PDM basis set. This algorithm identifies two forward and four feedback PDMs that are significant, yielding a 27-parameter (27-P) basis-reduced model with performance comparable to that of the NARV model.…”

Section: Introductionmentioning

confidence: 99%

Principal Dynamic Mode Analysis of the Hodgkin–Huxley Equations

Eikenberry

Marmarelis

2015

Int. J. Neur. Syst.

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We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin–Huxley (H–H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.

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“…New hierarchical neural networks therefore are required to be constructed for encoding additional task-dependent features that were previously not relevant to successful performance. However, the evolution of successful hierarchical encoding depends to a large extent on frequent re-exposure to task events that can be categorized via specific firing of directly responsive “ Simple ” cells for eventual selective increased synaptic connectivity with “ Conjunctive ” and “ Trial Type ” ( TT ) cells (Marmarelis et al, 2013; Hampson et al, 2012c; Deadwyler and Hampson, 2004; Hampson and Deadwyler, 2003; Hampson et al, 2001). The resulting outcome of such hierarchically controlled plasticity is faster processing of previously unfamiliar information due to the sharing of some of the same Simple and Conjunctive cells in a previously hierarchical circuit established for other circumstances.…”

Section: Neurons and Networkmentioning

confidence: 99%

Neurons and networks organizing and sequencing memories

et al. 2015

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Hippocampal CA1 and CA3 neurons sampled randomly in large numbers in primate brain show conclusive examples of hierarchical encoding of task specific information. Hierarchical encoding allows multi-task utilization of the same hippocampal neural networks via distributed firing between neurons that respond to subsets, attributes or “categories” of stimulus features which can be applied in events in different contexts. In addition, such networks are uniquely adaptable to neural systems unrestricted by rigid synaptic architecture (i.e. columns, layers or “patches”) which physically limits the number of possible task-specific interactions between neurons. Also hierarchical encoding is not random; it requires multiple exposures to the same types of relevant events to elevate synaptic connectivity between neurons for different stimulus features that occur in different task-dependent contexts. The large number of cells within associated hierarchical circuits in structures such as hippocampus provides efficient processing of information relevant to common memory-dependent behavioral decisions within different contextual circumstances.

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Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes

Cited by 25 publications

References 114 publications

Model-based asessment of an in-vivo predictive relationship from CA1 to CA3 in the rodent hippocampus

Model-based asessment of an in-vivo predictive relationship from CA1 to CA3 in the rodent hippocampus

Principal Dynamic Mode Analysis of the Hodgkin–Huxley Equations

Neurons and networks organizing and sequencing memories

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