Roberto Fernández Galán

Computational Physics, Neuroscience
PhD
29.58

Publications

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    Roberto Fernández Galán, G Bard Ermentrout, Nathaniel N Urban
  • Pavel Anatolyevich Puzerey, Michael J Decker, Roberto Fernandez Galan
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    ABSTRACT: 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 reuptake 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.
    Journal of Neurophysiology 08/2014; DOI:10.1152/jn.00031.2014 · 3.04 Impact Factor
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    Pavel A Puzerey, Roberto F Galán
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    ABSTRACT: 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.
    Frontiers in Computational Neuroscience 06/2014; 8:59. DOI:10.3389/fncom.2014.00059 · 2.23 Impact Factor
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    ABSTRACT: 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.
    Progress in brain research 01/2014; 209:191-205. DOI:10.1016/B978-0-444-63274-6.00010-2 · 5.10 Impact Factor
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    José L Pérez Velázquez, Roberto F Galán
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    ABSTRACT: 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.
    Frontiers in Neuroinformatics 12/2013; 7:37. DOI:10.3389/fninf.2013.00037
  • Journal of Critical Care 12/2013; 28(6):e34. DOI:10.1016/j.jcrc.2013.07.020 · 2.19 Impact Factor
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    ABSTRACT: 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.
    PLoS ONE 10/2013; 8(10):e77916. DOI:10.1371/journal.pone.0077916 · 3.53 Impact Factor
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    ABSTRACT: We present an efficient approach to discriminate between typical and atypical brains from macroscopic neural dynamics recorded as magnetoencephalograms (MEG). Our approach is based on the fact that spontaneous brain activity can be accurately described with stochastic dynamics, as a multivariate Ornstein-Uhlenbeck process (mOUP). By fitting the data to a mOUP we obtain: 1) the functional connectivity matrix, corresponding to the drift operator, and 2) the traces of background stochastic activity (noise) driving the brain. We applied this method to investigate functional connectivity and background noise in juvenile patients (n = 9) with Asperger's syndrome, a form of autism spectrum disorder (ASD), and compared them to age-matched juvenile control subjects (n = 10). Our analysis reveals significant alterations in both functional brain connectivity and background noise in ASD patients. The dominant connectivity change in ASD relative to control shows enhanced functional excitation from occipital to frontal areas along a parasagittal axis. Background noise in ASD patients is spatially correlated over wide areas, as opposed to control, where areas driven by correlated noise form smaller patches. An analysis of the spatial complexity reveals that it is significantly lower in ASD subjects. Although the detailed physiological mechanisms underlying these alterations cannot be determined from macroscopic brain recordings, we speculate that enhanced occipital-frontal excitation may result from changes in white matter density in ASD, as suggested in previous studies. We also venture that long-range spatial correlations in the background noise may result from less specificity (or more promiscuity) of thalamo-cortical projections. All the calculations involved in our analysis are highly efficient and outperform other algorithms to discriminate typical and atypical brains with a comparable level of accuracy. Altogether our results demonstrate a promising potential of our approach as an efficient biomarker for altered brain dynamics associated with a cognitive phenotype.
    PLoS ONE 04/2013; 8(4):e61493. DOI:10.1371/journal.pone.0061493 · 3.53 Impact Factor
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    ABSTRACT: We present an efficient approach to discriminate between typical and atypical brains from macroscopic neural dynamics recorded as magnetoencephalograms (MEG). Our approach is based on the fact that spontaneous brain activity can be accurately described with stochastic dynamics, as a multivariate Ornstein-Uhlenbeck process (mOUP). By fitting the data to a mOUP we obtain: 1) the functional connectivity matrix, corresponding to the drift operator, and 2) the traces of background stochastic activity (noise) driving the brain. We applied this method to investigate functional connectivity and background noise in juvenile patients (n = 9) with Asperger's syndrome, a form of autism spectrum disorder (ASD), and compared them to age-matched juvenile control subjects (n = 10). Our analysis reveals significant alterations in both functional brain connectivity and background noise in ASD patients. The dominant connectivity change in ASD relative to control shows enhanced functional excitation from occipital to frontal areas along a parasagittal axis. Background noise in ASD patients is spatially correlated over wide areas, as opposed to control, where areas driven by correlated noise form smaller patches. An analysis of the spatial complexity reveals that it is significantly lower in ASD subjects. Although the detailed physiological mechanisms underlying these alterations cannot be determined from macroscopic brain recordings, we speculate that enhanced occipital-frontal excitation may result from changes in white matter density in ASD, as suggested in previous studies. We also venture that long-range spatial correlations in the background noise may result from less specificity (or more promiscuity) of thalamo-cortical projections. All the calculations involved in our analysis are highly efficient and outperform other algorithms to discriminate typical and atypical brains with a comparable level of accuracy. Altogether our results demonstrate a promising potential of our approach as an efficient biomarker for altered brain dynamics associated with a cognitive phenotype.
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    ABSTRACT: 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.
    Frontiers in Neural Circuits 04/2013; 7:42. DOI:10.3389/fncir.2013.00042 · 2.95 Impact Factor
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    ABSTRACT: 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.] 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.
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    ABSTRACT: 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.
    Physical Review E 02/2013; 87(2-1):022709. DOI:10.1103/PhysRevE.87.022709 · 2.33 Impact Factor
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    Nicolaus T Schmandt, Roberto F Galán
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    ABSTRACT: 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 approxi-mation theoretically and in simulations of stochastic ion-channel gating in neurons. Introduction.—Markov chains provide realistic models of numerous random processes in physics [1], chemistry [1], biology [2], engineering [3,4], and quantitative finance [5]. However, stochastic simulations of Markov chains are computationally expensive. Recently published methods from various groups use diffusive and Gaussian approxi-mations to implement these simulations more efficiently [6–12]. These approximations are less accurate with small numbers of transitioning elements, in which case the oc-cupation numbers could have large fluctuations (high noise). Here we propose an efficient alternative to accu-rately simulate Markov chains regardless of fluctuations size: the stochastic-shielding approximation. This approxi-mation is applicable when only a subset of states in the model is relevant (e.g., because they are the only observ-able states), or equivalently, when there are hidden (not observable) states. The name ''stochastic shielding'' stems from the fact that fluctuations in the occupation number of hidden units that are not directly connected to the relevant states have no effect on the mean and little or no effect on the variance of the occupation numbers in the relevant states. In Fig. 1, state 2 shields the relevant state 3 from fluctuations in transitions to and from state 1. Thus, to simulate the stochastic dynamics of Markov chains, ran-dom numbers are only needed for transitions to and from relevant states, whereas all other transitions may be re-placed with their mean values, reducing the computation time significantly. We illustrate our method in the context of ion-channel gating to demonstrate that our approximation is effective with both constant and state-dependent transition rates, which corresponds to voltage-clamp and current-clamp conditions, respectively. Analysis of single-channel re-cordings reveals that ion-channel gating can be described by stochastic Markov chain models [13–16] and their random currents can cause large variability in the timing of neuronal firing [17], which may deteriorate information processing in the brain [13]. Results.—Consider Fig. 1 as an example of a general Markov chain. N i ðtÞ denotes the occupation number of the ith state at time t, and ij is the transition rate from the ith state to the jth state, which may depend explicitly or implicitly on time. The total number of elements N in the Markov chain is preserved, so at any point in time one has P i N i ðtÞ ¼ N. N 3 ðtÞ is the only observable state, which in a model of channel gating corresponds to the conducting state. Changes in occupation numbers between times t and t þ dt are given by
    Physical Review Letters 09/2012; 109(11). DOI:10.1103/PhysRevLett.109.118101 · 7.73 Impact Factor
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    ABSTRACT: 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.
    The Journal of Neuroscience : The Official Journal of the Society for Neuroscience 06/2012; 32(25):8663-77. DOI:10.1523/JNEUROSCI.1107-12.2012 · 6.75 Impact Factor
  • Roberto Fernández Galán
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    ABSTRACT: Neurons can respond with highly consistent spike patterns to repetitions of the same stimulus. Analogously, similar neurons receiving a common stimulus can fire highly consistent spike patterns. The former phenomenon is referred to as spike-time reliability, whereas the latter is an example of stochastic synchronization. Both phenomena are quite general and in fact, they also manifest in simplified models of single neuron dynamics, like phase oscillator models, in which the activity of the neuron is determined by its phase-response curve, which in turn is determined by the membrane conductances. Here, we use two measures of spike-time reliability and stochastic synchronization for real neurons and conductance-based models that have been recently introduced in the theory of phase oscillators: the Lyapunov exponent of the oscillator dynamics and the variance of the phase difference between two identical oscillators. Analyzing data from simulations and experiments, we show that, in response to manipulations of membrane conductances, a change of the phase-response curve leading to lower variance of the relative phase is a good predictor of increased spike-time reliability and stochastic synchronization in real and simulated neurons.We also explain why the Lyapunov exponent is not sufficient by itself. Our approach is then exemplified by investigating the effect of certain potassium currents, A and A-like currents, on spike-time precision. Finally, we discuss the biological relevance of our results.
    Phase Response Curves in Neuroscience: Theory, Experiment, and Analysis, Edited by Nathan W. Schultheiss, Astrid A. Prinz, Robert J. Butera, 01/2012: chapter 10: pages 237-255; Springer., ISBN: 978-1-4614-0738-6
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    ABSTRACT: The transient oscillatory model of odor identity encoding seeks to explain how odorants with spatially overlapped patterns of input into primary olfactory networks can be discriminated. This model provides several testable predictions about the distributed nature of network oscillations and how they control spike timing. To test these predictions, 16 channel electrode arrays were placed within the antennal lobe (AL) of the moth Manduca sexta. Unitary spiking and multi site local field potential (LFP) recordings were made during spontaneous activity and in response to repeated presentations of an odor panel. We quantified oscillatory frequency, cross correlations between LFP recording sites, and spike-LFP phase relationships. We show that odor-driven AL oscillations in Manduca are frequency modulating (FM) from ∼100 to 30 Hz; this was odorant and stimulus duration dependent. FM oscillatory responses were localized to one or two recording sites suggesting a localized (perhaps glomerular) not distributed source. LFP cross correlations further demonstrated that only a small (r < 0.05) distributed and oscillatory component was present. Cross spectral density analysis demonstrated the frequency of these weakly distributed oscillations was state dependent (spontaneous activity = 25-55 Hz; odor-driven = 55-85 Hz). Surprisingly, vector strength analysis indicated that unitary phase locking of spikes to the LFP was strongest during spontaneous activity and dropped significantly during responses. Application of bicuculline, a GABA(A) receptor antagonist, significantly lowered the frequency content of odor-driven distributed oscillatory activity. Bicuculline significantly reduced spike phase locking generally, but the ubiquitous pattern of increased phase locking during spontaneous activity persisted. Collectively, these results indicate that oscillations perform poorly as a stimulus-mediated spike synchronizing mechanism for Manduca and hence are incongruent with the transient oscillatory model.
    Frontiers in Neuroengineering 10/2011; 4:12. DOI:10.3389/fneng.2011.00012
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    G Karl Steinke, Roberto F Galán
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    ABSTRACT: Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.
    PLoS Computational Biology 10/2011; 7(10):e1002207. DOI:10.1371/journal.pcbi.1002207 · 4.83 Impact Factor
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    ABSTRACT: We consider optimization of phase response curves for stochastic synchronization of noninteracting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronization efficiency, the optimal phase response curve is obtained. We show that the optimal shape mutates from a sinusoid to a sawtooth as the constraint on its squared amplitude is varied.
    Physical Review E 07/2011; 84(1 Pt 2):016229. DOI:10.1103/PhysRevE.84.016229 · 2.33 Impact Factor
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    G Karl Steinke, Roberto F Galán
    BMC Neuroscience 01/2011; 12:1-2. DOI:10.1186/1471-2202-12-S1-P108 · 2.85 Impact Factor
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    Roberto Fernández Galán, Thomas E Dick, David M Baekey
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    ABSTRACT: We have combined neurophysiologic recording, statistical analysis, and computational modeling to investigate the dynamics of the respiratory network in the brainstem. Using a multielectrode array, we recorded ensembles of respiratory neurons in perfused in situ rat preparations that produce spontaneous breathing patterns, focusing on inspiratory pre-motor neurons. We compared firing rates and neuronal synchronization among these neurons before and after a brief hypoxic stimulus. We observed a significant decrease in the number of spikes after stimulation, in part due to a transient slowing of the respiratory pattern. However, the median interspike interval did not change, suggesting that the firing threshold of the neurons was not affected but rather the synaptic input was. A bootstrap analysis of synchrony between spike trains revealed that both before and after brief hypoxia, up to 45% (but typically less than 5%) of coincident spikes across neuronal pairs was not explained by chance. Most likely, this synchrony resulted from common synaptic input to the pre-motor population, an example of stochastic synchronization. After brief hypoxia most pairs were less synchronized, although some were more, suggesting that the respiratory network was transiently "rewired" after the stimulus. To investigate this hypothesis, we created a simple computational model with feed-forward divergent connections along the inspiratory pathway. Assuming that (1) the number of divergent projections was not the same for all presynaptic cells, but rather spanned a wide range and (2) that the stimulus increased inhibition at the top of the network; this model reproduced the reduction in firing rate and bootstrap-corrected synchrony subsequent to hypoxic stimulation observed in our experimental data.
    Frontiers in Computational Neuroscience 09/2010; 4. DOI:10.3389/fncom.2010.00131 · 2.23 Impact Factor

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