Empirical mode decomposition of local field potential data from optogenetic experiments.

Introduction: This study investigated the effects of cocaine administration and parvalbumin-type interneuron stimulation on local field potentials (LFPs) recorded in vivo from the medial prefrontal cortex (mPFC) of six mice using optogenetic tools. Methods: The local network was subject to a brief 10 ms laser pulse, and the response was recorded for 2 s over 100 trials for each of the six subjects who showed stable coupling between the mPFC and the optrode. Due to the strong non-stationary and nonlinearity of the LFP, we used the adaptive, data-driven, Empirical Mode Decomposition (EMD) method to decompose the signal into orthogonal Intrinsic Mode Functions (IMFs). Results: Through trial and error, we found that seven is the optimum number of orthogonal IMFs that overlaps with known frequency bands of brain activity. We found that the Index of Orthogonality (IO) of IMF amplitudes was close to zero. The Index of Energy Conservation (IEC) for each decomposition was close to unity, as expected for orthogonal decompositions. We found that the power density distribution vs. frequency follows a power law with an average scaling exponent of ~1.4 over the entire range of IMF frequencies 2-2,000 Hz. Discussion: The scaling exponent is slightly smaller for cocaine than the control, suggesting that neural activity avalanches under cocaine have longer life spans and sizes.

Resource Allocation in the Noise-Free Striatal Beat Frequency Model of Interval Timing.

The Striatal Beat Frequency (SBF) model of interval timing uses many neural oscillators, presumably located in the frontal cortex (FC), to produce beats at a specific criterion time Tc. The coincidence detection produces the beats in the basal ganglia spiny neurons by comparing the current state of the FC neural oscillators against the long-term memory values stored at reinforcement time Tc. The neurobiologically realistic SBF model has been previously used for producing precise and scalar timing in the presence of noise. Here we simplified the SBF model to gain insight into the problem of resource allocation in interval timing networks. Specifically, we used a noise-free SBF model to explore the lower limits of the number of neural oscillators required for producing accurate timing. Using abstract sine-wave neural oscillators in the SBF-sin model, we found that the lower limit of the number of oscillators needed is proportional to the criterion time Tc and the frequency span (fmax - fmin) of the FC neural oscillators. Using biophysically realistic Morris-Lecar model neurons in the SBF-ML model, the lower bound increased by one to two orders of magnitude compared to the SBF-sin model.

Not All Mice Are Created Equal: Interval Timing Accuracy and Scalar Timing in 129, Swiss-Webster, and C57Bl/6 Mice.

Many species, including humans, show both accurate timing-appropriate time estimation in the seconds to minutes range-and scalar timing-time estimation error varies linearly with estimated duration. Behavioral paradigms aimed at investigating interval timing are expected to evaluate these dissociable characteristics of timing. However, when evaluating interval timing in models of neuropsychiatric disease, researchers are confronted with a lack of adequate studies about the parent (background) strains, since accuracy and scalar timing have only been demonstrated for the C57Bl/6 strain of mice (Buhusi et al., 2009). We used a peak-interval procedure with three intervals-a protocol in which other species, including humans, demonstrate accurate, scalar timing-to evaluate timing accuracy and scalar timing in three strains of mice frequently used in genetic and behavioral studies: 129, Swiss-Webster, and C57Bl/6. C57Bl/6 mice showed accurate, scalar timing, while 129 and Swiss-Webster mice showed departures from accuracy and/or scalar timing. Results suggest that the genetic background / strain of the mouse is a critical variable for studies investigating interval timing in genetically-engineered mice. Our study validates the PI procedure with multiple intervals as a proper technique, and the C57Bl/6 strain as the most suitable genetic background to date for behavioral investigations of interval timing in genetically engineered mice modeling human disorders. In contrast, studies using mice in 129, Swiss-Webster, or mixed-background strains should be interpreted with caution, and thorough investigations of accuracy and scalar timing should be conducted before a less studied strain of mouse is considered for use in timing studies.

Is the scalar property of interval timing preserved after hippocampus lesions?

Time perception is fundamental for decision-making, adaptation, and survival. In the peak-interval (PI) paradigm, one of the critical features of time perception is its scale invariance, i.e., the error in time estimation increases linearly with the to-be-timed interval. Brain lesions can profoundly alter time perception, but do they also change its scalar property? In particular, hippocampus (HPC) lesions affect the memory of the reinforced durations. Experiments found that ventral hippocampus (vHPC) lesions shift the perceived durations to longer values while dorsal hippocampus (dHPC) lesions produce opposite effects. Here we used our implementation of the Striatal Beat Frequency (SBFML) model with biophysically realistic Morris-Lecar (ML) model neurons and a topological map of HPC memory to predict analytically and verify numerically the effect of HPC lesions on scalar property. We found that scalar property still holds after both vHPC and dHPC lesions in our SBFML-HPC network simulation. Our numerical results show that PI durations are shifted in the correct direction and match the experimental results. In our simulations, the relative peak shift of the behavioral response curve is controlled by two factors: (1) the lesion size, and (2) the cellular-level memory variance of the temporal durations stored in the HPC. The coefficient of variance (CV) of the behavioral response curve remained constant over the tested durations of PI procedure, which suggests that scalar property is not affected by HPC lesions.

Dopamine receptor antagonists effects on low-dimensional attractors of local field potentials in optogenetic mice.

The goal of this study was to investigate the effects of acute cocaine injection or dopamine (DA) receptor antagonists on the medial prefrontal cortex (mPFC) gamma oscillations and their relationship to short term neuroadaptation that may mediate addiction. For this purpose, optogenetically evoked local field potentials (LFPs) in response to a brief 10 ms laser light pulse were recorded from 17 mice. D1-like receptor antagonist SCH 23390 or D2-like receptor antagonist sulpiride, or both, were administered either before or after cocaine. A Euclidian distance-based dendrogram classifier separated the 100 trials for each animal in disjoint clusters. When baseline and DA receptor antagonists trials were combined in a single trial, a minimum of 20% overlap occurred in some dendrogram clusters, which suggests a possible common, invariant, dynamic mechanism shared by both baseline and DA receptor antagonists data. The delay-embedding method of neural activity reconstruction was performed using the correlation time and mutual information to determine the lag/correlation time of LFPs and false nearest neighbors to determine the embedding dimension. We found that DA receptor antagonists applied before cocaine cancels out the effect of cocaine and leaves the lag time distributions at baseline values. On the other hand, cocaine applied after DA receptor antagonists shifts the lag time distributions to longer durations, i.e. increase the correlation time of LFPs. Fourier analysis showed that a reasonable accurate decomposition of the LFP data can be obtained with a relatively small (less than ten) Fourier coefficients.

Dynamic Network Activation of Hypothalamic MCH Neurons in REM Sleep and Exploratory Behavior.

Most brain neurons are active in waking, but hypothalamic neurons that synthesize the neuropeptide melanin-concentrating hormone (MCH) are claimed to be active only during sleep, particularly rapid eye movement (REM) sleep. Here we use deep-brain imaging to identify changes in fluorescence of the genetically encoded calcium (Ca2+) indicator GCaMP6 in individual hypothalamic neurons that contain MCH. An in vitro electrophysiology study determined a strong relationship between depolarization and Ca2+ fluorescence in MCH neurons. In 10 freely behaving MCH-cre mice (male and female), the highest fluorescence occurred in all recorded neurons (n = 106) in REM sleep relative to quiet waking or non-REM sleep. Unexpectedly, 70% of the MCH neurons had strong fluorescence activity when the mice explored novel objects. Spatial and temporal mapping of the change in fluorescence between pairs of MCH neurons revealed dynamic activation of MCH neurons during REM sleep and activation of a subset of the same neurons during exploratory behavior. Functional network activity maps will facilitate comparisons of not only single-neuron activity, but also network responses in different conditions and disease.SIGNIFICANCE STATEMENT Functional activity maps identify brain circuits responding to specific behaviors, including rapid eye movement sleep (REM sleep), a sleep phase when the brain is as active as in waking. To provide the first activity map of individual neurons during REM sleep, we use deep-brain calcium imaging in unrestrained mice to map the activity of hypothalamic melanin-concentrating hormone (MCH) neurons. MCH neurons were found to be synchronously active during REM sleep, and also during the exploration of novel objects. Spatial mapping revealed dynamic network activation during REM sleep and activation of a subset of the neurons during exploratory behavior. Functional activity maps at the cellular level in specific behaviors, including sleep, are needed to establish a brain connectome.

A Population-Based Model of the Temporal Memory in the Hippocampus.

Spatial and temporal dimensions are fundamental for orientation, adaptation, and survival of organisms. Hippocampus has been identified as the main neuroanatomical structure involved both in space and time perception and their internal representation. Dorsal hippocampus lesions showed a leftward shift (toward shorter durations) in peak-interval procedures, whereas ventral lesions shifted the peak time toward longer durations. We previously explained hippocampus lesion experimental findings by assuming a topological map model of the hippocampus with shorter durations memorized ventrally and longer durations more dorsal. Here we suggested a possible connection between the abstract topological maps model of the hippocampus that stored reinforcement times in a spatially ordered memory register and the "time cells" of the hippocampus. In this new model, the time cells provide a uniformly distributed time basis that covers the entire to-be-learned temporal duration. We hypothesized that the topological map of the hippocampus stores the weights that reflect the contribution of each time cell to the average temporal field that determines the behavioral response. The temporal distance between the to-be-learned criterion time and the time of the peak activity of each time cell provides the error signal that determines the corresponding weight correction. Long-term potentiation/depression could enhance/weaken the weights associated to the time cells that peak closer/farther to the criterion time. A coincidence detector mechanism, possibly under the control of the dopaminergic system, could be involved in our suggested error minimization and learning algorithm.

Inactivation of the Medial-Prefrontal Cortex Impairs Interval Timing Precision, but Not Timing Accuracy or Scalar Timing in a Peak-Interval Procedure in Rats.

Motor sequence learning, planning and execution of goal-directed behaviors, and decision making rely on accurate time estimation and production of durations in the seconds-to-minutes range. The pathways involved in planning and execution of goal-directed behaviors include cortico-striato-thalamo-cortical circuitry modulated by dopaminergic inputs. A critical feature of interval timing is its scalar property, by which the precision of timing is proportional to the timed duration. We examined the role of medial prefrontal cortex (mPFC) in timing by evaluating the effect of its reversible inactivation on timing accuracy, timing precision and scalar timing. Rats were trained to time two durations in a peak-interval (PI) procedure. Reversible mPFC inactivation using GABA agonist muscimol resulted in decreased timing precision, with no effect on timing accuracy and scalar timing. These results are partly at odds with studies suggesting that ramping prefrontal activity is crucial to timing but closely match simulations with the Striatal Beat Frequency (SBF) model proposing that timing is coded by the coincidental activation of striatal neurons by cortical inputs. Computer simulations indicate that in SBF, gradual inactivation of cortical inputs results in a gradual decrease in timing precision with preservation of timing accuracy and scalar timing. Further studies are needed to differentiate between timing models based on coincidence detection and timing models based on ramping mPFC activity, and clarify whether mPFC is specifically involved in timing, or more generally involved in attention, working memory, or response selection/inhibition.

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

Optogenetically evoked local field potential (LFP) recorded from the medial prefrontal cortex (mPFC) of mice during basal conditions and following a systemic cocaine administration were analyzed. Blue light stimuli were delivered to mPFC through a fiber optic every 2 s and each trial was repeated 100 times. As in the previous study, we used a surrogate data method to check that nonlinearity was present in the experimental LFPs and only used the last 1.5 s of steady activity to measure the LFPs phase resetting induced by the brief 10 ms light stimulus. We found that the steady dynamics of the mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar "8"-shaped attractors across different animals. Therefore, cocaine did not change the complexity of the recorded nonlinear data compared to the control case. The phase space of the reconstructed attractor is determined by the LFP time series and its temporally shifted versions by a multiple of some lag time. We also compared the change in the attractor shape between cocaine-injected and control using (1) dendrogram clustering and (2) Frechet distance. We found about 20% overlap between control and cocaine trials when classified using dendrogram method, which suggest that it may be possible to describe mathematically both data sets with the same model and slightly different model parameters. We also found that the lag times are about three times shorter for cocaine trials compared to control. As a result, although the phase space trajectories for control and cocaine may look similar, their dynamics is significantly different.

Scalar timing in memory: A temporal map in the hippocampus.

Many essential tasks, such as decision making, rate calculation and planning, require accurate timing in the second to minute range. This process, known as interval timing, involves many cortical areas such as the prefrontal cortex, the striatum, and the hippocampus. Although the neurobiological origin and the mechanisms of interval timing are largely unknown, we have developed increasingly accurate mathematical and computational models that can mimic some properties of time perception. The accepted paradigm of temporal durations storage is that the objective elapsed time from the short-term memory is transferred to the reference memory using a multiplicative "memory translation constant" K*. It is believed that K* has a Gaussian distribution due to trial-related variabilities. To understand K* genesis, we hypothesized that the storage of temporal memories follows a topological map in the hippocampus, with longer durations stored towards dorsal hippocampus and shorter durations stored toward ventral hippocampus. We found that selective removal of memory cells in this topological map model shifts the peak-response time in a manner consistent with the current experimental data on the effect of hippocampal lesions on time perception. This opens new avenues for experimental testing of our topological map hypothesis. We found numerically that the relative shift is determined both by the lesion size and its location and we suggested a theoretical estimate for the memory translation constant K*.

Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve.

We used the phase-resetting method to study a biologically relevant three-neuron network in which one neuron receives multiple inputs per cycle. For this purpose, we first generalized the concept of phase resetting to accommodate multiple inputs per cycle. We explicitly showed how analytical conditions for the existence and the stability of phase-locked modes are derived. In particular, we solved newly derived recursive maps using as an example a biologically relevant driving-driven neural network with a dynamic feedback loop. We applied the generalized phase-resetting definition to predict the relative-phase and the stability of a phase-locked mode in open loop setup. We also compared the predicted phase-locked mode against numerical simulations of the fully connected network.

A Consistent Definition of Phase Resetting Using Hilbert Transform.

A phase resetting curve (PRC) measures the transient change in the phase of a neural oscillator subject to an external perturbation. The PRC encapsulates the dynamical response of a neural oscillator and, as a result, it is often used for predicting phase-locked modes in neural networks. While phase is a fundamental concept, it has multiple definitions that may lead to contradictory results. We used the Hilbert Transform (HT) to define the phase of the membrane potential oscillations and HT amplitude to estimate the PRC of a single neural oscillator. We found that HT's amplitude and its corresponding instantaneous frequency are very sensitive to membrane potential perturbations. We also found that the phase shift of HT amplitude between the pre- and poststimulus cycles gives an accurate estimate of the PRC. Moreover, HT phase does not suffer from the shortcomings of voltage threshold or isochrone methods and, as a result, gives accurate and reliable estimations of phase resetting.

A generalized phase resetting method for phase-locked modes prediction.

We derived analytically and checked numerically a set of novel conditions for the existence and the stability of phase-locked modes in a biologically relevant master-slave neural network with a dynamic feedback loop. Since neural oscillators even in the three-neuron network investigated here receive multiple inputs per cycle, we generalized the concept of phase resetting to accommodate multiple inputs per cycle. We proved that the phase resetting produced by two or more stimuli per cycle can be recursively computed from the traditional, single stimulus, phase resetting. We applied the newly derived generalized phase resetting definition to predicting the relative phase and the stability of a phase-locked mode that was experimentally observed in this type of master-slave network with a dynamic loop network.

Non-equilibrium concentration fluctuations in superparamagnetic nanocolloids.

We investigate non-equilibrium concentration fluctuations during the free diffusion of a colloidal suspension against pure water. We investigate Fe2O3 superparamagnetic nanocolloids with sizes between 1 and 10 nm by means of a shadowgraph apparatus to determine the mixture mass diffusion coefficient and kinematic viscosity. The experiments were performed in three distinct conditions: Experiment 1 is without any magnetic field; Experiment 2 with a vertical magnetic field; Experiment 3 after turning off the magnetic field. We found no correlation between the kinematic viscosity coefficient and the external magnetic field. Conversely, we found that the mass diffusion coefficient decreases in the presence of the external magnetic field and slowly rebounds after the magnetic field was turned off.

Clocks within Clocks: Timing by Coincidence Detection.

The many existent models of timing rely on vastly different mechanisms to track temporal information. Here we examine these differences, and identify coincidence detection in its most general form as a common mechanism that many apparently different timing models share, as well as a common mechanism of biological circadian, millisecond and interval timing. This view predicts that timing by coincidence detection is a ubiquitous phenomenon at many biological levels, explains the reports of biological timing in many brain areas, explains the role of neural noise at different time scales at both biological and theoretical levels, and provides cohesion within the timing field.

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

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.

Direct imaging of long-range concentration fluctuations in a ternary mixture.

We used a direct imaging technique to investigate concentration fluctuations enhanced by thermal fluctuations in a ternary mixture of methanol (Me), cyclohexane (C), and partially deuterated cyclohexane (C*) within 1mK above its consolute critical point. The experimental setup used a low-coherence white-light source and a red filter to visualize fluctuation images. The red-filtered images were analyzed off-line using a differential dynamic microscopy algorithm that allowed us to determine the correlation time, τ, of concentration fluctuations. From τ, we determined the mutual mass diffusion coefficient, D, very near and above the critical point of Me-CC* mixtures. We also numerically estimated both the background and critical contributions to D and compared the results against our experimental values determined from τ. We found that the experimental value of D is close to the prediction based on Stokes-Einstein diffusion law with Kawasaki's correction.

Dimple coalescence and liquid droplets distributions during phase separation in a pure fluid under microgravity.

Phase separation has important implications for the mechanical, thermal, and electrical properties of materials. Weightless conditions prevent buoyancy and sedimentation from affecting the dynamics of phase separation and the morphology of the domains. In our experiments, sulfur hexafluoride (SF6) was initially heated about 1K above its critical temperature under microgravity conditions and then repeatedly quenched using temperature steps, the last one being of 3.6 mK, until it crossed its critical temperature and phase-separated into gas and liquid domains. Both full view (macroscopic) and microscopic view images of the sample cell unit were analyzed to determine the changes in the distribution of liquid droplet diameters during phase separation. Previously, dimple coalescences were only observed in density-matched binary liquid mixture near its critical point of miscibility. Here we present experimental evidences in support of dimple coalescence between phase-separated liquid droplets in pure, supercritical, fluids under microgravity conditions. Although both liquid mixtures and pure fluids belong to the same universality class, both the mass transport mechanisms and their thermophysical properties are significantly different. In supercritical pure fluids the transport of heat and mass are strongly coupled by the enthalpy of condensation, whereas in liquid mixtures mass transport processes are purely diffusive. The viscosity is also much smaller in pure fluids than in liquid mixtures. For these reasons, there are large differences in the fluctuation relaxation time and hydrodynamics flows that prompted this experimental investigation. We found that the number of droplets increases rapidly during the intermediate stage of phase separation. We also found that above a cutoff diameter of about 100 microns the size distribution of droplets follows a power law with an exponent close to -2, as predicted from phenomenological considerations.