Low-dimensional attractor for neural activity from local field potentials in optogenetic mice

Abstract

We used optogenetic mice to investigate possible nonlinear responses of the medial prefrontal cortex (mPFC) local network to light stimuli delivered by a 473 nm laser through a fiber optics. Every 2 s, a brief 10 ms light pulse was applied and the local field potentials (LFPs) were recorded with a 10 kHz sampling rate. The experiment was repeated 100 times and we only retained and analyzed data from six animals that showed stable and repeatable response to optical stimulations. The presence of nonlinearity in our data was checked using the null hypothesis that the data were linearly correlated in the temporal domain, but were random otherwise. For each trail, 100 surrogate data sets were generated and both time reversal asymmetry and false nearest neighbor (FNN) were used as discriminating statistics for the null hypothesis. We found that nonlinearity is present in all LFP data. The first 0.5 s of each 2 s LFP recording were dominated by the transient response of the networks. For each trial, we used the last 1.5 s of steady activity to measure the phase resetting induced by the brief 10 ms light stimulus. After correcting the LFPs for the effect of phase resetting, additional preprocessing was carried out using dendrograms to identify “similar” groups among LFP trials. We found that the steady dynamics of mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar “8”-shaped attractors across different animals. Our results also open the possibility of designing a low-dimensional model for optical stimulation of the mPFC local network.

Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice

“…The goal was to investigate the effects of acute cocaine on mPFC gamma oscillation and their relationship to more permanent cortical changes of long-term use of stimulants. We previously carried out a similar data mining study on the same animals under control conditions (Oprisan et al, 2015 ). The present study is a continuation of Oprisan et al ( 2015 ) in which the same mice were systemically injected with cocaine.…”

“…We previously carried out a similar data mining study on the same animals under control conditions (Oprisan et al, 2015 ). The present study is a continuation of Oprisan et al ( 2015 ) in which the same mice were systemically injected with cocaine. We performed a nonlinear time series analysis of LFPs recorded from PV+ neurons using time reversal asymmetry and false nearest neighbor (FNN) statistics between the original signal and surrogate data (Oprisan et al, 2015 ) to identify the nonlinearity in the data set.…”

“…Ongoing oscillatory activity could be reset by sensory inputs, such as visual (Kambe et al, 2015 ; Woelders et al, 2017 ) or auditory (Mercier et al, 2013 ) stimuli, or by extrinsic stimuli, such as deep brain stimulation (Tass, 2003 ), or temperature (Rensing and Ruoff, 2002 ). We measured the phase resetting induced by brief light stimuli using both the autocorrelation (Oprisan, 2013 ; Oprisan et al, 2015 ) and the Hilbert's transform (Oprisan, 2017 ) methods. The phase resetting correction allowed an accurate estimate of the delay (lag) time and embedding dimension of LFP data (Oprisan and Canavier, 2002 ; Oprisan et al, 2003 , 2015 ).…”

“…We measured the phase resetting induced by brief light stimuli using both the autocorrelation (Oprisan, 2013 ; Oprisan et al, 2015 ) and the Hilbert's transform (Oprisan, 2017 ) methods. The phase resetting correction allowed an accurate estimate of the delay (lag) time and embedding dimension of LFP data (Oprisan and Canavier, 2002 ; Oprisan et al, 2003 , 2015 ).…”

A generalized phase resetting method for phase-locked modes prediction

“…Delay embedding reconstruction of the phase space gave a low dimensional attractor suggesting a phase coupled model of medial prefrontal cortex that is reset by light stimuli [29]. …”