Volumetric mapping of the functional neuroanatomy of the respiratory network in the perfused brainstem preparation of rats.

KEY POINTS: The functional neuroanatomy of the mammalian respiratory network is far from being understood since experimental tools that measure neural activity across this brainstem-wide circuit are lacking. Here, we use silicon multi-electrode arrays to record respiratory local field potentials (rLFPs) from 196-364 electrode sites within 8-10 mm3 of brainstem tissue in single arterially perfused brainstem preparations with respect to the ongoing respiratory motor pattern of inspiration (I), post-inspiration (PI) and late-expiration (E2). rLFPs peaked specifically at the three respiratory phase transitions, E2-I, I-PI and PI-E2. We show, for the first time, that only the I-PI transition engages a brainstem-wide network, and that rLFPs during the PI-E2 transition identify a hitherto unknown role for the dorsal respiratory group. Volumetric mapping of pontomedullary rLFPs in single preparations could become a reliable tool for assessing the functional neuroanatomy of the respiratory network in health and disease. ABSTRACT: While it is widely accepted that inspiratory rhythm generation depends on the pre-Bötzinger complex, the functional neuroanatomy of the neural circuits that generate expiration is debated. We hypothesized that the compartmental organization of the brainstem respiratory network is sufficient to generate macroscopic local field potentials (LFPs), and if so, respiratory (r) LFPs could be used to map the functional neuroanatomy of the respiratory network. We developed an approach using silicon multi-electrode arrays to record spontaneous LFPs from hundreds of electrode sites in a volume of brainstem tissue while monitoring the respiratory motor pattern on phrenic and vagal nerves in the perfused brainstem preparation. Our results revealed the expression of rLFPs across the pontomedullary brainstem. rLFPs occurred specifically at the three transitions between respiratory phases: (1) from late expiration (E2) to inspiration (I), (2) from I to post-inspiration (PI), and (3) from PI to E2. Thus, respiratory network activity was maximal at respiratory phase transitions. Spatially, the E2-I, and PI-E2 transitions were anatomically localized to the ventral and dorsal respiratory groups, respectively. In contrast, our data show, for the first time, that the generation of controlled expiration during the post-inspiratory phase engages a distributed neuronal population within ventral, dorsal and pontine network compartments. A group-wise independent component analysis demonstrated that all preparations exhibited rLFPs with a similar temporal structure and thus share a similar functional neuroanatomy. Thus, volumetric mapping of rLFPs could allow for the physiological assessment of global respiratory network organization in health and disease.

Fluctuation Scaling of Neuronal Firing and Bursting in Spontaneously Active Brain Circuits.

We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency - regularly firing neurons (RNs) - from 1 to 8Hz while 8% fired in burst with two dominant frequencies - bursting neurons (BNs) - corresponding to the inter-burst (2-6Hz) and intra-burst intervals (20-160Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.

Increasing Local Excitability of Brainstem Respiratory Nuclei Reveals a Distributed Network Underlying Respiratory Motor Pattern Formation.

The core circuit of the respiratory central pattern generator (rCPG) is located in the ventrolateral medulla, especially in the pre-Bötzinger complex (pre-BötC) and the neighboring Bötzinger complex (BötC). To test the hypothesis that this core circuit is embedded within an anatomically distributed pattern-generating network, we investigated whether local disinhibition of the nucleus tractus solitarius (NTS), the Kölliker-Fuse nuclei (KFn), or the midbrain periaqueductal gray area (PAG) can similarly affect the respiratory pattern compared to disinhibition of the pre-BötC/BötC core. In arterially-perfused brainstem preparations of rats, we recorded the three-phase respiratory pattern (inspiration, post-inspiration and late-expiration) from phrenic and vagal nerves before and after bilateral microinjections of the GABA(A)R antagonist bicuculline (50 nl, 10 mM). Local disinhibition of either NTS, pre-BötC/BötC, or KFn, but not PAG, triggered qualitatively similar disruptions of the respiratory pattern resulting in a highly significant increase in the variability of the respiratory cycle length, including inspiratory and expiratory phase durations. To quantitatively analyze these motor pattern perturbations, we measured the strength of phase synchronization between phrenic and vagal motor outputs. This analysis showed that local disinhibition of all brainstem target nuclei, but not the midbrain PAG, significantly decreased the strength of phase synchronization. The convergent perturbations of the respiratory pattern suggest that the rCPG expands rostrally and dorsally from the designated core but does not include higher mid-brain structures. Our data also suggest that excitation-inhibition balance of respiratory network synaptic interactions critically determines the network dynamics that underlie vital respiratory rhythm and pattern formation.

Excitation-inhibition balance regulates the patterning of spinal and cranial inspiratory motor outputs in rats in situ.

Spinal phrenic nerve activity (PNA) drives the diaphragm but cranial hypoglossal nerve activity (HNA) also expresses synchronous activity during inspiration. Here, we investigated the effects of local disinhibition (bilateral microinjections of bicuculline) of the nucleus tractus solitarius (NTS), the pre-Bötzinger complex and Bötzinger complex core circuit (pre-BötC/BötC) and the Kölliker-Fuse nuclei (KFn) on the synchronization of PNA and HNA in arterially-perfused brainstem preparations of rats. To quantitatively analyze the bicuculline effects on a putatively distributed inspiratory central pattern generator (i-CPG), we quantified the phase synchronization properties between PNA and HNA. The analysis revealed that bicuculline-evoked local disinhibition significantly reduced the strength of phase synchronization between PNA and HNA at any target site. However, the emergence of desynchronized HNA following disinhibition was more prevalent after NTS or pre-BötC/BötC microinjections compared to the KFn. We conclude that the primary i-CPG is located in a distributed medullary circuit whereas pontine contributions are restricted to synaptic gating of synchronous HNA and PNA.

Stochastic shielding and edge importance for Markov chains with timescale separation.

Nerve cells produce electrical impulses ("spikes") through the coordinated opening and closing of ion channels. Markov processes with voltage-dependent transition rates capture the stochasticity of spike generation at the cost of complex, time-consuming simulations. Schmandt and Galán introduced a novel method, based on the stochastic shielding approximation, as a fast, accurate method for generating approximate sample paths with excellent first and second moment agreement to exact stochastic simulations. We previously analyzed the mathematical basis for the method's remarkable accuracy, and showed that for models with a Gaussian noise approximation, the stationary variance of the occupancy at each vertex in the ion channel state graph could be written as a sum of distinct contributions from each edge in the graph. We extend this analysis to arbitrary discrete population models with first-order kinetics. The resulting decomposition allows us to rank the "importance" of each edge's contribution to the variance of the current under stationary conditions. In most cases, transitions between open (conducting) and closed (non-conducting) states make the greatest contributions to the variance, but there are exceptions. In a 5-state model of the nicotinic acetylcholine receptor, at low agonist concentration, a pair of "hidden" transitions (between two closed states) makes a greater contribution to the variance than any of the open-closed transitions. We exhaustively investigate this "edge importance reversal" phenomenon in simplified 3-state models, and obtain an exact formula for the contribution of each edge to the variance of the open state. Two conditions contribute to reversals: the opening rate should be faster than all other rates in the system, and the closed state leading to the opening rate should be sparsely occupied. When edge importance reversal occurs, current fluctuations are dominated by a slow noise component arising from the hidden transitions.

Anti-correlated cortical networks arise from spontaneous neuronal dynamics at slow timescales.

In the highly interconnected architectures of the cerebral cortex, recurrent intracortical loops disproportionately outnumber thalamo-cortical inputs. These networks are also capable of generating neuronal activity without feedforward sensory drive. It is unknown, however, what spatiotemporal patterns may be solely attributed to intrinsic connections of the local cortical network. Using high-density microelectrode arrays, here we show that in the isolated, primary somatosensory cortex of mice, neuronal firing fluctuates on timescales from milliseconds to tens of seconds. Slower firing fluctuations reveal two spatially distinct neuronal ensembles, which correspond to superficial and deeper layers. These ensembles are anti-correlated: when one fires more, the other fires less and vice versa. This interplay is clearest at timescales of several seconds and is therefore consistent with shifts between active sensing and anticipatory behavioral states in mice.

Kölliker-Fuse nuclei regulate respiratory rhythm variability via a gain-control mechanism.

Respiration varies from breath to breath. On the millisecond timescale of spiking, neuronal circuits exhibit variability due to the stochastic properties of ion channels and synapses. Does this fast, microscopic source of variability contribute to the slower, macroscopic variability of the respiratory period? To address this question, we modeled a stochastic oscillator with forcing; then, we tested its predictions experimentally for the respiratory rhythm generated by the in situ perfused preparation during vagal nerve stimulation (VNS). Our simulations identified a relationship among the gain of the input, entrainment strength, and rhythm variability. Specifically, at high gain, the periodic input entrained the oscillator and reduced variability, whereas at low gain, the noise interacted with the input, causing events known as "phase slips", which increased variability on a slow timescale. Experimentally, the in situ preparation behaved like the low-gain model: VNS entrained respiration but exhibited phase slips that increased rhythm variability. Next, we used bilateral muscimol microinjections in discrete respiratory compartments to identify areas involved in VNS gain control. Suppression of activity in the nucleus tractus solitarii occluded both entrainment and amplification of rhythm variability by VNS, confirming that these effects were due to the activation of the Hering-Breuer reflex. Suppressing activity of the Kölliker-Fuse nuclei (KFn) enhanced entrainment and reduced rhythm variability during VNS, consistent with the predictions of the high-gain model. Together, the model and experiments suggest that the KFn regulates respiratory rhythm variability via a gain control mechanism.

Effects of ion channel noise on neural circuits: an application to the respiratory pattern generator to investigate breathing variability.

Neural activity generally displays irregular firing patterns even in circuits with apparently regular outputs, such as motor pattern generators, in which the output frequency fluctuates randomly around a mean value. This "circuit noise" is inherited from the random firing of single neurons, which emerges from stochastic ion channel gating (channel noise), spontaneous neurotransmitter release, and its diffusion and binding to synaptic receptors. Here we demonstrate how to expand conductance-based network models that are originally deterministic to include realistic, physiological noise, focusing on stochastic ion channel gating. We illustrate this procedure with a well-established conductance-based model of the respiratory pattern generator, which allows us to investigate how channel noise affects neural dynamics at the circuit level and, in particular, to understand the relationship between the respiratory pattern and its breath-to-breath variability. We show that as the channel number increases, the duration of inspiration and expiration varies, and so does the coefficient of variation of the breath-to-breath interval, which attains a minimum when the mean duration of expiration slightly exceeds that of inspiration. For small channel numbers, the variability of the expiratory phase dominates over that of the inspiratory phase, and vice versa for large channel numbers. Among the four different cell types in the respiratory pattern generator, pacemaker cells exhibit the highest sensitivity to channel noise. The model shows that suppressing input from the pons leads to longer inspiratory phases, a reduction in breathing frequency, and larger breath-to-breath variability, whereas enhanced input from the raphe nucleus increases breathing frequency without changing its pattern. NEW & NOTEWORTHY: A major source of noise in neuronal circuits is the "flickering" of ion currents passing through the neurons' membranes (channel noise), which cannot be suppressed experimentally. Computational simulations are therefore the best way to investigate the effects of this physiological noise by manipulating its level at will. We investigate the role of noise in the respiratory pattern generator and show that endogenous, breath-to-breath variability is tightly linked to the respiratory pattern.

Spherical Harmonics Reveal Standing EEG Waves and Long-Range Neural Synchronization during Non-REM Sleep.

Previous work from our lab has demonstrated how the connectivity of brain circuits constrains the repertoire of activity patterns that those circuits can display. Specifically, we have shown that the principal components of spontaneous neural activity are uniquely determined by the underlying circuit connections, and that although the principal components do not uniquely resolve the circuit structure, they do reveal important features about it. Expanding upon this framework on a larger scale of neural dynamics, we have analyzed EEG data recorded with the standard 10-20 electrode system from 41 neurologically normal children and adolescents during stage 2, non-REM sleep. We show that the principal components of EEG spindles, or sigma waves (10-16 Hz), reveal non-propagating, standing waves in the form of spherical harmonics. We mathematically demonstrate that standing EEG waves exist when the spatial covariance and the Laplacian operator on the head's surface commute. This in turn implies that the covariance between two EEG channels decreases as the inverse of their relative distance; a relationship that we corroborate with empirical data. Using volume conduction theory, we then demonstrate that superficial current sources are more synchronized at larger distances, and determine the characteristic length of large-scale neural synchronization as 1.31 times the head radius, on average. Moreover, consistent with the hypothesis that EEG spindles are driven by thalamo-cortical rather than cortico-cortical loops, we also show that 8 additional patients with hypoplasia or complete agenesis of the corpus callosum, i.e., with deficient or no connectivity between cortical hemispheres, similarly exhibit standing EEG waves in the form of spherical harmonics. We conclude that spherical harmonics are a hallmark of spontaneous, large-scale synchronization of neural activity in the brain, which are associated with unconscious, light sleep. The analogy with spherical harmonics in quantum mechanics suggests that the variances (eigenvalues) of the principal components follow a Boltzmann distribution, or equivalently, that standing waves are in a sort of "thermodynamic" equilibrium during non-REM sleep. By extension, we speculate that consciousness emerges as the brain dynamics deviate from such equilibrium.

Decreased heart rate and enhanced sinus arrhythmia during interictal sleep demonstrate autonomic imbalance in generalized epilepsy.

We hypothesized that epilepsy affects the activity of the autonomic nervous system even in the absence of seizures, which should manifest as differences in heart rate variability (HRV) and cardiac cycle. To test this hypothesis, we investigated ECG traces of 91 children and adolescents with generalized epilepsy and 25 neurologically normal controls during 30 min of stage 2 sleep with interictal or normal EEG. Mean heart rate (HR) and high-frequency HRV corresponding to respiratory sinus arrhythmia (RSA) were quantified and compared. Blood pressure (BP) measurements from physical exams of all subjects were also collected and analyzed. RSA was on average significantly stronger in patients with epilepsy, whereas their mean HR was significantly lower after adjusting for age, body mass index, and sex, consistent with increased parasympathetic tone in these patients. In contrast, diastolic (and systolic) BP at rest was not significantly different, indicating that the sympathetic tone is similar. Remarkably, five additional subjects, initially diagnosed as neurologically normal but with enhanced RSA and lower HR, eventually developed epilepsy, suggesting that increased parasympathetic tone precedes the onset of epilepsy in children. ECG waveforms in epilepsy also displayed significantly longer TP intervals (ventricular diastole) relative to the RR interval. The relative TP interval correlated positively with RSA and negatively with HR, suggesting that these parameters are linked through a common mechanism, which we discuss. Altogether, our results provide evidence for imbalanced autonomic function in generalized epilepsy, which may be a key contributing factor to sudden unexpected death in epilepsy.

Abnormal cell-intrinsic and network excitability in the neocortex of serotonin-deficient Pet-1 knockout mice.

Neurons originating from the raphe nuclei of the brain stem are the exclusive source of serotonin (5-HT) to the cortex. Their serotonergic phenotype is specified by the transcriptional regulator Pet-1, which is also necessary for maintaining their neurotransmitter identity across development. Transgenic mice in which Pet-1 is genetically ablated (Pet-1(-/-)) show a dramatic reduction (∼80%) in forebrain 5-HT levels, yet no investigations have been carried out to assess the impact of such severe 5-HT depletion on the function of target cortical neurons. Using whole cell patch-clamp methods, two-dimensional (2D) multielectrode arrays (MEAs), 3D morphological neuronal reconstructions, and animal behavior, we investigated the impact of 5-HT depletion on cortical cell-intrinsic and network excitability. We found significant changes in several parameters of cell-intrinsic excitability in cortical pyramidal cells (PCs) as well as an increase in spontaneous synaptic excitation through 5-HT3 receptors. These changes are associated with increased local network excitability and oscillatory activity in a 5-HT2 receptor-dependent manner, consistent with previously reported hypersensitivity of cortical 5-HT2 receptors. PC morphology was also altered, with a significant reduction in dendritic complexity that may possibly act as a compensatory mechanism for increased excitability. Consistent with this interpretation, when we carried out experiments with convulsant-induced seizures to asses cortical excitability in vivo, we observed no significant differences in seizure parameters between wild-type and Pet-1(-/-) mice. Moreover, MEA recordings of propagating field potentials showed diminished propagation of activity across the cortical sheath. Together these findings reveal novel functional changes in neuronal and cortical excitability in mice lacking Pet-1.

Elevated serotonergic signaling amplifies synaptic noise and facilitates the emergence of epileptiform network oscillations.

Serotonin fibers densely innervate the cortical sheath to regulate neuronal excitability, but its role in shaping network dynamics remains undetermined. We show that serotonin provides an excitatory tone to cortical neurons in the form of spontaneous synaptic noise through 5-HT3 receptors, which is persistent and can be augmented using fluoxetine, a selective serotonin re-uptake inhibitor. Augmented serotonin signaling also increases cortical network activity by enhancing synaptic excitation through activation of 5-HT2 receptors. This in turn facilitates the emergence of epileptiform network oscillations (10-16 Hz) known as fast runs. A computational model of cortical dynamics demonstrates that these two combined mechanisms, increased background synaptic noise and enhanced synaptic excitation, are sufficient to replicate the emergence fast runs and their statistics. Consistent with these findings, we show that blocking 5-HT2 receptors in vivo significantly raises the threshold for convulsant-induced seizures.

On how correlations between excitatory and inhibitory synaptic inputs maximize the information rate of neuronal firing.

Cortical neurons receive barrages of excitatory and inhibitory inputs which are not independent, as network structure and synaptic kinetics impose statistical correlations. Experiments in vitro and in vivo have demonstrated correlations between inhibitory and excitatory synaptic inputs in which inhibition lags behind excitation in cortical neurons. This delay arises in feed-forward inhibition (FFI) circuits and ensures that coincident excitation and inhibition do not preclude neuronal firing. Conversely, inhibition that is too delayed broadens neuronal integration times, thereby diminishing spike-time precision and increasing the firing frequency. This led us to hypothesize that the correlation between excitatory and inhibitory synaptic inputs modulates the encoding of information of neural spike trains. We tested this hypothesis by investigating the effect of such correlations on the information rate (IR) of spike trains using the Hodgkin-Huxley model in which both synaptic and membrane conductances are stochastic. We investigated two different synaptic input regimes: balanced synaptic conductances and balanced currents. Our results show that correlations arising from the synaptic kinetics, τ, and millisecond lags, δ, of inhibition relative to excitation strongly affect the IR of spike trains. In the regime of balanced synaptic currents, for short time lags (δ ~ 1 ms) there is an optimal τ that maximizes the IR of the postsynaptic spike train. Given the short time scales for monosynaptic inhibitory lags and synaptic decay kinetics reported in cortical neurons under physiological contexts, we propose that FFI in cortical circuits is poised to maximize the rate of information transfer between cortical neurons. Our results also provide a possible explanation for how certain drugs and genetic mutations affecting the synaptic kinetics can deteriorate information processing in the brain.

Cardiorespiratory coupling: common rhythms in cardiac, sympathetic, and respiratory activities.

Cardiorespiratory coupling is an encompassing term describing more than the well-recognized influences of respiration on heart rate and blood pressure. Our data indicate that cardiorespiratory coupling reflects a reciprocal interaction between autonomic and respiratory control systems, and the cardiovascular system modulates the ventilatory pattern as well. For example, cardioventilatory coupling refers to the influence of heart beats and arterial pulse pressure on respiration and is the tendency for the next inspiration to start at a preferred latency after the last heart beat in expiration. Multiple complementary, well-described mechanisms mediate respiration's influence on cardiovascular function, whereas mechanisms mediating the cardiovascular system's influence on respiration may only be through the baroreceptors but are just being identified. Our review will describe a differential effect of conditioning rats with either chronic intermittent or sustained hypoxia on sympathetic nerve activity but also on ventilatory pattern variability. Both intermittent and sustained hypoxia increase sympathetic nerve activity after 2 weeks but affect sympatho-respiratory coupling differentially. Intermittent hypoxia enhances sympatho-respiratory coupling, which is associated with low variability in the ventilatory pattern. In contrast, after constant hypobaric hypoxia, 1-to-1 coupling between bursts of sympathetic and phrenic nerve activity is replaced by 2-to-3 coupling. This change in coupling pattern is associated with increased variability of the ventilatory pattern. After baro-denervating hypobaric hypoxic-conditioned rats, splanchnic sympathetic nerve activity becomes tonic (distinct bursts are absent) with decreases during phrenic nerve bursts and ventilatory pattern becomes regular. Thus, conditioning rats to either intermittent or sustained hypoxia accentuates the reciprocal nature of cardiorespiratory coupling. Finally, identifying a compelling physiologic purpose for cardiorespiratory coupling is the biggest barrier for recognizing its significance. Cardiorespiratory coupling has only a small effect on the efficiency of gas exchange; rather, we propose that cardiorespiratory control system may act as weakly coupled oscillator to maintain rhythms within a bounded variability.

Functional connectivity estimated from intracranial EEG predicts surgical outcome in intractable temporal lobe epilepsy.

This project aimed to determine if a correlation-based measure of functional connectivity can identify epileptogenic zones from intracranial EEG signals, as well as to investigate the prognostic significance of such a measure on seizure outcome following temporal lobe lobectomy. To this end, we retrospectively analyzed 23 adult patients with intractable temporal lobe epilepsy (TLE) who underwent an invasive stereo-EEG (SEEG) evaluation between January 2009 year and January 2012. A follow-up of at least one year was required. The primary outcome measure was complete seizure-freedom at last follow-up. Functional connectivity between two areas in the temporal lobe that were sampled by two SEEG electrode contacts was defined as Pearson's correlation coefficient of interictal activity between those areas. SEEG signals were filtered between 5 and 50 Hz prior to computing this correlation. The mean and standard deviation of the off diagonal elements in the connectivity matrix were also calculated. Analysis of the mean and standard deviation of the functional connections for each patient reveals that 90% of the patients who had weak and homogenous connections were seizure free one year after temporal lobectomy, whereas 85% of the patients who had stronger and more heterogeneous connections within the temporal lobe had recurrence of seizures. This suggests that temporal lobectomy is ineffective in preventing seizure recurrence for patients in whom the temporal lobe is characterized by weakly connected, homogenous networks. This pilot study shows promising potential of a simple measure of functional brain connectivity to identify epileptogenicity and predict the outcome of epilepsy surgery.

Decreased Hering-Breuer input-output entrainment in a mouse model of Rett syndrome.

Rett syndrome, a severe X-linked neurodevelopmental disorder caused by mutations in the gene encoding methyl-CpG-binding protein 2 (Mecp2), is associated with a highly irregular respiratory pattern including severe upper-airway dysfunction. Recent work suggests that hyperexcitability of the Hering-Breuer reflex (HBR) pathway contributes to respiratory dysrhythmia in Mecp2 mutant mice. To assess how enhanced HBR input impacts respiratory entrainment by sensory afferents in closed-loop in vivo-like conditions, we investigated the input (vagal stimulus trains) - output (phrenic bursting) entrainment via the HBR in wild-type and MeCP2-deficient mice. Using the in situ perfused brainstem preparation, which maintains an intact pontomedullary axis capable of generating an in vivo-like respiratory rhythm in the absence of the HBR, we mimicked the HBR feedback input by stimulating the vagus nerve (at threshold current, 0.5 ms pulse duration, 75 Hz pulse frequency, 100 ms train duration) at an inter-burst frequency matching that of the intrinsic oscillation of the inspiratory motor output of each preparation. Using this approach, we observed significant input-output entrainment in wild-type mice as measured by the maximum of the cross-correlation function, the peak of the instantaneous relative phase distribution, and the mutual information of the instantaneous phases. This entrainment was associated with a reduction in inspiratory duration during feedback stimulation. In contrast, the strength of input-output entrainment was significantly weaker in Mecp2 (-/+) mice. However, Mecp2 (-/+) mice also had a reduced inspiratory duration during stimulation, indicating that reflex behavior in the HBR pathway was intact. Together, these observations suggest that the respiratory network compensates for enhanced sensitivity of HBR inputs by reducing HBR input-output entrainment.

Quantifying interactions between real oscillators with information theory and phase models: application to cardiorespiratory coupling.

Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.

Information gain in the brain's resting state: A new perspective on autism.

Along with the study of brain activity evoked by external stimuli, an increased interest in the research of background, "noisy" brain activity is fast developing in current neuroscience. It is becoming apparent that this "resting-state" activity is a major factor determining other, more particular, responses to stimuli and hence it can be argued that background activity carries important information used by the nervous systems for adaptive behaviors. In this context, we investigated the generation of information in ongoing brain activity recorded with magnetoencephalography (MEG) in children with autism spectrum disorder (ASD) and non-autistic children. Using a stochastic dynamical model of brain dynamics, we were able to resolve not only the deterministic interactions between brain regions, i.e., the brain's functional connectivity, but also the stochastic inputs to the brain in the resting state; an important component of large-scale neural dynamics that no other method can resolve to date. We then computed the Kullback-Leibler (KLD) divergence, also known as information gain or relative entropy, between the stochastic inputs and the brain activity at different locations (outputs) in children with ASD compared to controls. The divergence between the input noise and the brain's ongoing activity extracted from our stochastic model was significantly higher in autistic relative to non-autistic children. This suggests that brains of subjects with autism create more information at rest. We propose that the excessive production of information in the absence of relevant sensory stimuli or attention to external cues underlies the cognitive differences between individuals with and without autism. We conclude that the information gain in the brain's resting state provides quantitative evidence for perhaps the most typical characteristic in autism: withdrawal into one's inner world.

Stochastic-shielding approximation of Markov chains and its application to efficiently simulate random ion-channel gating.

Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.

Disrupted ERK signaling during cortical development leads to abnormal progenitor proliferation, neuronal and network excitability and behavior, modeling human neuro-cardio-facial-cutaneous and related syndromes.

Genetic disorders arising from copy number variations in the ERK (extracellular signal-regulated kinase) MAP (mitogen-activated protein) kinases or mutations in their upstream regulators that result in neuro-cardio-facial-cutaneous syndromes are associated with developmental abnormalities, cognitive deficits, and autism. We developed murine models of these disorders by deleting the ERKs at the beginning of neurogenesis and report disrupted cortical progenitor generation and proliferation, which leads to altered cytoarchitecture of the postnatal brain in a gene-dose-dependent manner. We show that these changes are due to ERK-dependent dysregulation of cyclin D1 and p27(Kip1), resulting in cell cycle elongation, favoring neurogenic over self-renewing divisions. The precocious neurogenesis causes premature progenitor pool depletion, altering the number and distribution of pyramidal neurons. Importantly, loss of ERK2 alters the intrinsic excitability of cortical neurons and contributes to perturbations in global network activity. These changes are associated with elevated anxiety and impaired working and hippocampal-dependent memory in these mice. This study provides a novel mechanistic insight into the basis of cortical malformation which may provide a potential link to cognitive deficits in individuals with altered ERK activity.