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Background: Brain interdependencies can be studied from either a structural/anatomical perspective ("structural connectivity") or by considering statistical interdependencies ("functional connectivity" [FC]). Interestingly, while structural connectivity is by definition pairwise (white-matter fibers project from one region to another), FC is not. However, most FC analyses only focus on pairwise statistics and they neglect higher order interactions. A promising tool to study high-order interdependencies is the recently proposed O-Information, which can quantify the intrinsic statistical synergy and the redundancy in groups of three or more interacting variables. Methods: We analyzed functional magnetic resonance imaging (fMRI) data obtained at rest from 164 healthy subjects with ages ranging in 10 to 80 years and used O-Information to investigate how high-order statistical interdependencies are affected by age. Results: Older participants (from 60 to 80 years old) exhibited a higher predominance of redundant dependencies compared with younger participants, an effect that seems to be pervasive as it is evident for all orders of interaction. In addition, while there is strong heterogeneity across brain regions, we found a "redundancy core" constituted by the prefrontal and motor cortices in which redundancy was evident at all the interaction orders studied. Discussion: High-order interdependencies in fMRI data reveal a dominant redundancy in functions such as working memory, executive, and motor functions. Our methodology can be used for a broad range of applications, and the corresponding code is freely available. Impact statement Past research has showcased multiple changes to the brain's structural and functional properties caused by aging. Here we expand prior work through recent advancements in multivariate information theory, which provide richer and more theoretically principled analyses than existing alternatives. We show that the brains of older participants contain more redundant information at multiple spatial scales-that is, activation in different brain regions is less diverse, compared with younger participants-and identify a "redundancy core" constituted by prefrontal and motor cortices, which might explained impaired performance in the old population in functions such as working memory and executive control. ispartof: BRAIN CONNECTIVITY vol:11 issue:9 pages:734-744 ispartof: location:United States status: published

Brain activity during sleep transits between discretely described stages according to different brain dynamics. In particular, the slow-wave sleep stage (N2 and N3) presents events of interest for the memory consolidation process, such as slow oscillations and sleep spindles. Evidence exists that adequate timing between a slow oscillation and a sleep spindles, together with the increase in number and power, correlates with the performance in memory consolidation tasks. Nevertheless, how the results depend on the ongoing sleep stage is unclear, considering that stimulation is typically applied only at the N3 stage. Then, the effects of stimuli application in sleep macro-architecture during the same night are not well understood. Using a mean-field model of the thalamocortical activity, including dynamics of sleep cycle, we test the effects of stimuli application on the occurrence of slow-wave events. We evaluated three stimulation conditions in different time windows transiting from the N2 to N3 sleep stage. In our findings, closed-loop stimulation elicits higher quantity of slow oscillations and sleep spindles for near N3 brain dynamic. Further, closed-loop stimulation increases the co-occurrence of slow oscillations and sleep spindles. Interestingly, stimuli application does not significantly impact the trajectory of sleep dynamics, concordant with the null effect in sleep macro-architecture reported from experimental results. Finally, we noted that the lack of refractory periods in intra-thalamic dynamics results in a high occurrence of sleep spindles with stimuli application, which is not observed in the experimental results.

Field potential oscillations in the olfactory system of vertebrates and invertebrates are prominent and well-studied, but their functions remain nevertheless enigmatic. Spatial networks are thought to play a role in olfactory discrimination in different species, but their analysis is frequently complicated by behavior, learning and respiration (sniffing). Here, we show that in a sniffing-free model (trout), the relevant feature for discriminating odorant identity is the information conveyed by the oscillatory activity in a spatially distributed network, including the olfactory bulb and the telencephalic regions Vv and Dp. Specifically, information-based methods based on spectral decoding, information sharing, and information redundancy distinguished odorant identity across spatially distant regions while classical spectral analyses did not. Our study demonstrates that olfactory oscillations are carriers of spatially distributed odor information across the teleost olfactory system.

Integration and segregation are two fundamental principles of brain organization. The brain manages the transitions and balance between different functional segregated or integrated states through neuromodulatory systems. Recently, computational and experimental studies suggest a pro-segregation effect of cholinergic neuromodulation. Here, we studied the effects of the cholinergic system on brain functional connectivity using both empirical fMRI data and computational modeling. First, we analyzed the effects of nicotine on functional connectivity and network topology in healthy subjects during resting-state conditions and during an attentional task. Then, we employed a whole-brain neural mass model interconnected using a human connectome to simulate the effects of nicotine and investigate causal mechanisms for these changes. The drug effect was modeled decreasing both the global coupling and local feedback inhibition parameters, consistent with the known cellular effects of acetylcholine. We found that nicotine incremented functional segregation in both empirical and simulated data, and the effects are context-dependent: observed during the task, but not in the resting state. In-task performance correlates with functional segregation, establishing a link between functional network topology and behavior. Furthermore, we found in the empirical data that the regional density of the nicotinic acetylcholineα4β2correlates with the decrease in functional nodal strength by nicotine during the task. Our results confirm that cholinergic neuromodulation promotes functional segregation in a context-dependent fashion, and suggest that this segregation is suited for simple visual-attentional tasks.

The human brain generates a rich repertoire of spatio-temporal activity patterns, which support a wide variety of motor and cognitive functions. These patterns of activity change with age in a multi-factorial manner. One of these factors is the variations in the brain’s connectomics that occurs along the lifespan. However, the precise relationship between high-order functional interactions and connnectomics, as well as their variations with age are largely unknown, in part due to the absence of mechanistic models that can efficiently map brain connnectomics to functional connectivity in aging. To investigate this issue, we have built a neurobiologically-realistic whole-brain computational model using both anatomical and functional MRI data from 161 participants ranging from 10 to 80 years old. We show that the age differences in high-order functional interactions can be largely explained by variations in the connectome. Based on this finding, we propose a simple neurodegeneration model that is representative of normal physiological aging. As such, when applied to connectomes of young participant it reproduces the age-variations that occur in the high-order structure of the functional data. Overall, these results begin to disentangle the mechanisms by which structural changes in the connectome lead to functional differences in the ageing brain. Our model can also serve as a starting point for modelling more complex forms of pathological ageing or cognitive deficits.Author summaryModern neuroimaging techniques allow us to study how the human brain’s anatomical architecture (a.k.a. structural connectome) changes under different conditions or interventions. Recently, using functional neuroimaging data, we have shown that complex patterns of interactions between brain areas change along the lifespan, exhibiting increased redundant interactions in the older population. However, the mechanisms that underlie these functional differences are still unclear. Here, we extended this work and hypothesized that the variations of functional patterns can be explained by the dynamics of the brain’s anatomical networks, which are known to degenerate as we age. To test this hypothesis, we implemented a whole-brain model of neuronal activity, where different brain regions are anatomically wired using real connectomes from 161 participants with ages ranging from 10 to 80 years old. Analyzing different functional aspects of brain activity when varying the empirical connectomes, we show that the increased redundancy found in the older group can indeed be explained by precise rules affecting anatomical connectivity, thus emphasizing the critical role that the brain connectome plays for shaping complex functional interactions and the efficiency in the global communication of the human brain.

A physiologically-based scheme that incorporates inherent neurological fluctuations in the activation of intrinsic laryngeal muscles into a lumped-element vocal fold model is proposed. Herein, muscles are activated through a combination of neural firing rate and recruitment of additional motor units, both of which have stochastic components. The mathematical framework and underlying physiological assumptions are described, and the effects of the fluctuations are tested via a parametric analysis using a body-cover model of the vocal folds for steady-state sustained vowels. The inherent muscle activation fluctuations have a bandwidth that varies with the firing rate, yielding both low and high frequency components. When applying the proposed fluctuation scheme to the voice production model, changes in the dynamics of the system can be observed, ranging from fluctuations in the fundamental frequency to unstable behavior near bifurcation regions. The resulting coefficient of variation of the model parameters is not uniform with muscle activation. The stochastic components of muscle activation influence both the fine structure variability and the ability to achieve a target value for pitch control. These components can have a significant impact on the vocal fold parameters, as well as the outputs of the voice production model. Good agreement was found when contrasting the proposed scheme with prior experimental studies accounting for variability in vocal fold posturing and spectral characteristics of the muscle activation signal. The proposed scheme constitutes a novel and physiologically-based approach for controlling lumped-element models for normal voice production and can be extended to explore neuropathological conditions.

Neuromodulators, such as neuropeptides, can regulate and reconfigure neural circuits to alter their output, affecting in this way animal physiology and behavior. The interplay between the activity of neuronal circuits, their modulation by neuropeptides, and the resulting behavior, is still poorly understood. Here, we present a quantitative framework to study the relationships between the temporal pattern of activity of peptidergic neurons and of motoneurons duringDrosophilaecdysis behavior, a highly stereotyped motor sequence that is critical for insect growth. We analyzed, in the time and frequency domains, simultaneous intracellular calcium recordings of peptidergic CCAP (crustacean cardioactive peptide) neurons and motoneurons obtained from isolated central nervous systems throughout fictive ecdysis behavior inducedex vivoby Ecdysis triggering hormone. We found that the activity of both neuronal populations is tightly coupled in a cross-frequency manner, suggesting that CCAP neurons modulate the faster oscillation of motoneurons. To explore this idea further, we used a probabilistic logistic model to show that calcium dynamics in CCAP neurons can predict the oscillation of motoneurons, both in a simple model and in a conductance-base model capable of simulating many of the observed neural dynamics features. Finally, we developed an algorithm to quantify the motor behavior observed in videos of pupal ecdysis, and compared their features to the patterns of neuronal calcium activity recordedex vivo. We found that the motor activity of the intact animal is more regular than the motoneuronal activity recorded from theex vivopreparations during fictive ecdysis behavior; the analysis of movement patterns also allowed us to identify a new post-ecdysis phase.Author SummaryRepetitive movements such as walking, swimming, and flying are controlled by networks of neurons known as central patter generators. In many cases, the exact pattern of activity is modulated by neuropeptides, which are small signaling molecules that, unlike neurotransmitters, are broadly released within regions of the nervous system. Because of this mode of action, it can be difficult to discern the relationship between the temporal pattern of firing of peptidergic neurons and the timing of the resulting motor behavior. Here, we developed methods to analyze the patterns of activity of such weakly coupled systems as applied to ecdysis, the stereotyped sequence of behaviors used by insects to shed the remains of their old exoskeleton at the end of every molt. Key actors in this process are motoneurons (MN) and a set of neurons expressing the neuropeptide, Crustacean Cardioactive Peptide (CCAP). Combining real-time calcium imaging, frequency analysis, computational simulations, and image processing, we determined the relationships between the activity of CCAP neurons and the resulting motor output during pupal ecdysis in the fruit fly,Drosophila melanogaster. We found that several temporal features of the activity of CCAP neurons are highly coupled to the patter of activity motoneuronal pattern, suggesting an active role of CCAP neurons during ecdysis. We also developed quantitative approaches that allowed us to identify a new ecdysis sub-phase.

Slow-wave sleep cortical brain activity, conformed by slow-oscillations and sleep spindles, plays a key role in memory consolidation. The increase of the power of the slow-wave events, obtained by auditory sensory stimulation, positively correlates to memory consolidation performance. However, little is known about the experimental protocol maximizing this effect, which could be induced by the power of slow-oscillation, the number of sleep spindles, or the timing of both events’ co-occurrence. Using a mean-field model of thalamocortical activity, we studied the effect of several stimulation protocols, varying the pulse shape, duration, amplitude, and frequency, as well as a target-phase using a closed-loop approach. We evaluated the effect of these parameters on slow-oscillations (SO) and sleep-spindles (SP), considering: (i) the power at the frequency bands of interest, (ii) the number of SO and SP, (iii) co-occurrences between SO and SP, and (iv) synchronization of SP with the up-peak of the SO. The first three targets are maximized using a decreasing ramp pulse with a pulse duration of 50 ms. Also, we observed a reduction in the number of SO when increasing the stimulus energy by rising its amplitude. To assess the target-phase parameter, we applied closed-loop stimulation at 0º, 45º, and 90º of the phase of the narrow-band filtered ongoing activity, at 0.85 Hz as central frequency. The 0º stimulation produces better results in the power and number of SO and SP than the rhythmic or aleatory stimulation. On the other hand, stimulating at 45º or 90º change the timing distribution of spindles centers but with fewer co-occurrences than rhythmic and 0º phase. Finally, we propose the application of closed-loop stimulation at the rising zero-cross point using pulses with a decreasing ramp shape and 50 ms of duration for future experimental work.Author summaryDuring the non-REM (NREM) phase of sleep, events that are known as slow oscillations (SO) and spindles (SP) can be detected by EEG. These events have been associated with the consolidation of declarative memories and learning. Thus, there is an ongoing interest in promoting them during sleep by non-invasive manipulations such as sensory stimulation. In this paper, we used a computational model of brain activity that generates SO and SP, to investigate which type of sensory stimulus –shape, amplitude, duration, periodicity– would be optimal for increasing the events’ frequency and their co-occurrence. We found that a decreasing ramp of 50 ms duration is the most effective. The effectiveness increases when the stimulus pulse is delivered in a closed-loop configuration triggering the pulse at a target phase of the ongoing SO activity. A desirable secondary effect is to promote SPs at the rising phase of the SO oscillation.

In mammals, environmental cold sensing conducted by peripheral cold thermoreceptor neurons mostly depends on TRPM8, an ion channel that has evolved to become the main molecular cold transducer. This TRP channel is activated by cold, cooling compounds, such as menthol, voltage, and rises in osmolality. TRPM8 function is regulated by kinase activity that phosphorylates the channel under resting conditions. However, which specific residues, how this post-translational modification modulates TRPM8 activity, and its influence on cold sensing are still poorly understood. By mass spectrometry, we identified four serine residues within the N-terminus (S26, S29, S541, and S542) constitutively phosphorylated in the mouse ortholog. TRPM8 function was examined by Ca2+ imaging and patch-clamp recordings, revealing that treatment with staurosporine, a kinase inhibitor, augmented its cold- and menthol-evoked responses. S29A mutation is sufficient to increase TRPM8 activity, suggesting that phosphorylation of this residue is a central molecular determinant of this negative regulation. Biophysical and total internal reflection fluorescence-based analysis revealed a dual mechanism in the potentiated responses of unphosphorylated TRPM8: a shift in the voltage activation curve toward more negative potentials and an increase in the number of active channels at the plasma membrane. Importantly, basal kinase activity negatively modulates TRPM8 function at cold thermoreceptors from male and female mice, an observation accounted for by mathematical modeling. Overall, our findings suggest that cold temperature detection could be rapidly and reversibly fine-tuned by controlling the TRPM8 basal phosphorylation state, a mechanism that acts as a dynamic molecular brake of this thermo-TRP channel function in primary sensory neurons., This work was supported by Grants DICYT VRIDeI-USACH 022143PP to M.P. and R.M.; FONDECYT 1161733 to R.M. and M.P.; FONDECYT 1181076 to P.O.; Centro Basal AC3E FB0008 to P.O.; VRIDeI-USACH AP-539MM to R.M.; National Research Foundation of Korea NRF-2019R1A2C2003642 to K.-S.P.; MINECO PID2019-108194RB and the Severo Ochoa Program for Centers of Excellence in R&D SEV-2017-0723 to F.V.; the Millennium Nucleus of Ion Channel-Associated Diseases (MiNICAD) to R.M. and M.P.; and the Millennium Nucleus for the Study of Pain (MiNuSPain) to R.M. and M.P. R.M. also thanks VRIDeI-USACH for postdoctoral support to B.R. (02183MM). B.R. (21161660) and B.L. (21181611) thank Comisión Nacional de Investigación Científica y Tecnológica de Chile PhD fellowships. MiNICAD is a Millennium Nucleus supported by the Millennium Science Initiative of the Ministry of Science, Technology, Knowledge and Innovation (Chile). MiNuSPain is a Millennium Nucleus supported by the Millennium Science Initiative of the Ministry of Science, Technology, Knowledge and Innovation (Chile). The CINV is a Millennium Science Institute funded by Agencia Nacional de Investigación y Desarrollo de Chile Grant ICN09_022 of the Ministry of Science, Technology, Knowledge and Innovation (Chile).

Mathematical modeling has been and will continue to be central to the understanding of the emerging function of the nervous system. From the firing of action potentials – with their all-or-none characteristic – to the rich dynamical repertoire of neural networks, the equations and numerical models that describe them are a key part of our understanding of the nervous system. Moreover, they continue to be the subject of further research. In this chapter, we will describe what a mathematical model is and why it is useful. Then, we will describe models of neurons and networks of neurons, emphasizing on how the biophysical concepts are translated to equations.

TRPM8 is the main molecular entity responsible for cold sensing. This polymodal ion channel is activated by cold, cooling compounds such as menthol, voltage, and rises in osmolality. In corneal cold thermoreceptor neurons (CTNs), TRPM8 expression determines not only their sensitivity to cold, but also their role as neural detectors of ocular surface wetness. Several reports suggest that Protein Kinase C (PKC) activation impacts on TRPM8 function, however, the molecular bases of this functional modulation are still poorly understood. We explored PKC-dependent regulation of TRPM8 using Phorbol 12-Myristate 13-Acetate to activate this kinase. Consistently, recombinant TRPM8 channels, cultured trigeminal neurons, and free nerve endings of corneal CTNs revealed a robust reduction of TRPM8-dependent responses under PKC activation. In corneal CTNs, PKC activation decreased ongoing activity, a key parameter in the role of TRPM8-expressing neurons as humidity detectors, and also the maximal cold-evoked response, which were validated by mathematical modeling. Biophysical analysis indicated that PKC-dependent downregulation of TRPM8 is mainly due to a decreased maximal conductance value, and complementary noise analysis revealed a reduced number of functional channels at the cell surface, providing important clues to understanding the molecular mechanisms of how PKC activity modulates TRPM8 channels in CTNs.

Many experiments have evidenced that electrical and chemical synapses -- hybrid synapses -- coexist in most organisms and brain structures. The role of electrical and chemical synapse connection in diversity of neural activity generation has been investigated separately in networks of varying complexities. Nevertheless, theoretical understanding of hybrid synapses in diverse dynamical states of neural networks for self-organization and robustness still has not been fully studied. Here, we present a model of neural network built with hybrid synapses to investigate the emergence of global and collective dynamics states. This neural networks consists of excitatory and inhibitory population interacting together. The excitatory population is connected by excitatory synapses in small world topology and its adjacent neurons are also connected by gap junctions. The inhibitory population is only connected by chemical inhibitory synapses with all-to-all interaction. Our numerical simulations show that in the balanced networks with absence of electrical coupling, the synchrony states generated by this architecture are mainly controlled by heterogeneity among neurons and the balance of its excitatory and inhibitory inputs. In balanced networks with strong electrical coupling, several dynamical states arise from different combinations of excitatory and inhibitory weights. More importantly, we find that these states, such as synchronous firing, cluster synchrony, and various ripples events, emerge by slight modification of chemical coupling weights. For large enough electrical synapse coupling, the whole neural networks become synchronized. Our results pave a way in the study of the dynamical mechanisms and computational significance of the contribution of mixed synapse in the neural functions.

The cornea is extensively innervated by trigeminal ganglion cold thermoreceptor neurons expressing TRPM8 (transient receptor potential cation channel subfamily M member 8). These neurons respond to cooling, hyperosmolarity and wetness of the corneal surface. Surgical injury of corneal nerve fibers alters tear production and often causes dry eye sensation. The contribution of TRPM8-expressing corneal cold-sensitive neurons (CCSNs) to these symptoms is unclear. Using extracellular recording of CCSNs nerve terminals combined with in vivo confocal tracking of reinnervation, Ca2+ imaging and patch-clamp recordings of fluorescent retrogradely labeled corneal neurons in culture, we analyzed the functional modifications of CCSNs induced by peripheral axonal damage in male mice. After injury, the percentage of CCSNs, the cold- and menthol-evoked intracellular [Ca2+] rises and the TRPM8 current density in CCSNs were larger than in sham animals, with no differences in the brake K+ current IKD. Active and passive membrane properties of CCSNs from both groups were alike and corresponded mainly to those of canonical low- and high-threshold cold thermoreceptor neurons. Ongoing firing activity and menthol sensitivity were higher in CCSN terminals of injured mice, an observation accounted for by mathematical modeling. These functional changes developed in parallel with a partial reinnervation of the cornea by TRPM8(+) fibers and with an increase in basal tearing in injured animals compared with sham mice. Our results unveil key TRPM8-dependent functional changes in CCSNs in response to injury, suggesting that increased tearing rate and ocular dryness sensation derived from deep surgical ablation of corneal nerves are due to enhanced functional expression of TRPM8 channels in these injured trigeminal primary sensory neurons., This work was supported by Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grants 1161733 (R.M.), 1140520 (J.B.), 1181076 (P.O.), Retos Grants 2017 RSAF2017-83674-C2-1-R and C2-2-R MINECO Spain (C.B. and A.Í.-P), and by the Millennium Nucleus of Ion Channels-Associated Diseases (MiNICAD; R.M.). R.P. was supported by FONDECYT Postdoctoral Grant 3170249. MiNICAD is a Millennium Nucleus supported by the Millennium Science Initiative of the Ministry of Economy, Development and Tourism (Chile). The CINV is a Millennium Science Institute funded by the Ministry of Economy, Development and Tourism (Chile). R.M. thanks Pfizer (WI177114) for providing PBMCs and VRIDEI-USACH for support to G.U. and R.P.

Segregation and integration are two fundamental principles of brain structural and functional organization. Neuroimaging studies have shown that the brain transits between different functionally segregated and integrated states, and neuromodulatory systems have been proposed as key to facilitate these transitions. Although whole-brain computational models have reproduced this neuromodulatory effect, the role of local inhibitory circuits and their cholinergic modulation has not been studied. In this article, we consider a Jansen & Rit whole-brain model in a network interconnected using a human connectome, and study the influence of the cholinergic and noradrenergic neuromodulatory systems on the segregation/integration balance. In our model, we introduce a local inhibitory feedback as a plausible biophysical mechanism that enables the integration of whole-brain activity, and that interacts with the other neuromodulatory influences to facilitate the transition between different functional segregation/integration regimes in the brain., Author summary Segregation of brain activity refers to the fact that some brain regions are specialized to handle particular features of external and internal stimuli. However, to produce a coherent behavioral outcome, the brain must coordinate the activity of these specialized brain areas, and this is called integration of brain activity. Based on a fixed connectome (the brain anatomical structure), the neuromodulatory systems are one of the plausible candidates to manage the transitions of brain states in short timescales. Understanding the role of neuromodulators in brain dynamics and the segregation/integration balance is relevant, in particular, as it is known that in several neuropsychiatric disorders the segregation/integration balance its impaired. Here, we used a computational model of the whole brain to study the dual effect of the cholinergic and noradrenergic neuromodulatory systems in the switching from segregated to integrated brain states. The novelty of our work is the inclusion of a homeostatic local inhibitory loop. This specific inhibition, modulated by the cholinergic system, maintains the excitation/inhibition balance while promoting integration. Our work links the local effects of cholinergic neuromodulation, with the more global influences of the structural connectivity and neuromodulatory systems. This constitutes a step forward in the understanding of the neural mechanisms behind the segregation/integration balance of brain activity.

The multistable behavior of neural networks is actively being studied as a landmark of ongoing cerebral activity, reported in both functional Magnetic Resonance Imaging (fMRI) and electro- or magnetoencephalography recordings. This consists of a continuous jumping between different partially synchronized states in the absence of external stimuli. It is thought to be an important mechanism for dealing with sensory novelty and to allow for efficient coding of information in an ever-changing surrounding environment. Many advances have been made to understand how network topology, connection delays, and noise can contribute to building this dynamic. Little or no attention, however, has been paid to the difference between local chaotic and stochastic influences on the switching between different network states. Using a conductance-based neural model that can have chaotic dynamics, we showed that a network can show multistable dynamics in a certain range of global connectivity strength and under deterministic conditions. In the present work, we characterize the multistable dynamics when the networks are, in addition to chaotic, subject to ion channel stochasticity in the form of multiplicative (channel) or additive (current) noise. We calculate the Functional Connectivity Dynamics matrix by comparing the Functional Connectivity (FC) matrices that describe the pair-wise phase synchronization in a moving window fashion and performing clustering of FCs. Moderate noise can enhance the multistable behavior that is evoked by chaos, resulting in more heterogeneous synchronization patterns, while more intense noise abolishes multistability. In networks composed of nonchaotic nodes, some noise can induce multistability in an otherwise synchronized, nonchaotic network. Finally, we found the same results regardless of the multiplicative or additive nature of noise.

International audience; Long-range dependence (LRD) has been observed in a variety of phenomena in nature, and for several years also in the spiking activity of neurons. Often, this is interpreted as originating from a non-Markovian system. Here we show that a purely Markovian integrate-and-fire (IF) model, with a noisy slow adaptation term, can generate interspike intervals (ISIs) that appear as having LRD. However a proper analysis shows that this is not the case asymptotically. For comparison, we also consider a new model of individual IF neuron with fractional (non-Markovian) noise. The correlations of its spike trains are studied and proven to have LRD, unlike classical IF models. On the other hand, to correctly measure long-range dependence, it is usually necessary to know if the data are stationary. Thus, a methodology to evaluate stationarity of the ISIs is presented and applied to the various IF models. We explain that Markovian IF models may seem to have LRD because of non-stationarities.

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that – when isolated – can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data. Refereed/Peer-reviewed

In primary sensory neurons of the spinal and trigeminal somatosensory system, cold-sensitivity is strongly dependent on the functional balance between TRPM8 channels, the main molecular entity responsible for the cold-activated excitatory current, and Shaker-like Kv1.1-1.2 potassium channels, the molecular counterpart underlying the excitability brake current I

Cold allodynia is a common symptom of neuropathic and inflammatory pain following peripheral nerve injury. The mechanisms underlying this disabling sensory alteration are not entirely understood. In primary somatosensory neurons, cold sensitivity is mainly determined by a functional counterbalance between cold-activated TRPM8 channels and Shaker-like Kv1.1–1.2 channels underlying the excitability brake current IKD. Here we studied the role of IKDin damage-triggered painful hypersensitivity to innocuous cold. We found that cold allodynia induced by chronic constriction injury (CCI) of the sciatic nerve in mice, was related to both an increase in the proportion of cold-sensitive neurons (CSNs) in DRGs contributing to the sciatic nerve, and a decrease in their cold temperature threshold. IKDdensity was reduced in high-threshold CSNs from CCI mice compared with sham animals, with no differences in cold-induced TRPM8-dependent current density. The electrophysiological properties and neurochemical profile of CSNs revealed an increase of nociceptive-like phenotype among neurons from CCI animals compared with sham mice. These results were validated using a mathematical model of CSNs, including IKDand TRPM8, showing that a reduction in IKDcurrent density shifts the thermal threshold to higher temperatures and that the reduction of this current induces cold sensitivity in former cold-insensitive neurons expressing low levels of TRPM8-like current. Together, our results suggest that cold allodynia is largely due to a functional downregulation of IKDin both high-threshold CSNs and in a subpopulation of polymodal nociceptors expressing TRPM8, providing a general molecular and neural mechanism for this sensory alteration.SIGNIFICANCE STATEMENTThis paper unveils the critical role of the brake potassium current IKDin damage-triggered cold allodynia. Using a well-known form of nerve injury and combining behavioral analysis, calcium imaging, patch clamping, and pharmacological tools, validated by mathematical modeling, we determined that the functional expression of IKDis reduced in sensory neurons in response to peripheral nerve damage. This downregulation not only enhances cold sensitivity of high-threshold cold thermoreceptors signaling cold discomfort, but it also transforms a subpopulation of polymodal nociceptors signaling pain into neurons activated by mild temperature drops. Our results suggest that cold allodynia is linked to a reduction of IKDin both high-threshold cold thermoreceptors and nociceptors expressing TRPM8, providing a general model for this form of cold-induced pain.

In primary sensory neurons of the spinal and trigeminal somatosensory system, cold-sensitivity is strongly dependent on the functional balance between TRPM8 channels, the main molecular entity responsible for the cold-activated excitatory current, and Shaker-like Kv1.1–1.2 potassium channels, the molecular counterpart underlying the excitability brake current IKD. This slow-inactivating outward K+ current reduces the excitability of cold thermoreceptor neurons increasing their thermal threshold, and prevents unspecific activation by cold of neurons of other somatosensory modalities. Here we examine the main biophysical properties of this current in primary sensory neurons, its central role in cold thermotransduction, and its contribution to alterations in cold sensitivity triggered by peripheral nerve damage.

Motion detection is one of the most important and primitive computations performed by our visual system. Specifically in the retina, ganglion cells producing motion direction-selective responses have been addressed by different disciplines, such as mathematics, neurophysiology and computational modeling, since the beginnings of vision science. Although a number of studies have analyzed theoretical and mathematical considerations for such responses, a clear picture of the underlying cellular mechanisms is only recently emerging. In general, motion direction selectivity is based on a non-linear asymmetric computation inside a receptive field differentiating cell responses between preferred and null direction stimuli. To what extent can biological findings match these considerations? In this review, we outline theoretical and mathematical studies of motion direction selectivity, aiming to map the properties of the models onto the neural circuitry and synaptic connectivity found in the retina. Additionally, we review several compartmental models that have tried to fill this gap. Finally, we discuss the remaining challenges that computational models will have to tackle in order to fully understand the retinal motion direction-selective circuitry.

Hyperpolarization-activated currents (I(h)) are mediated by the expression of combinations of hyperpolarization-activated, cyclic nucleotide-gated (HCN) channel subunits (HCN1-4). These cation currents are key regulators of cellular excitability in the heart and many neurons in the nervous system. Subunit composition determines the gating properties and cAMP sensitivity of native I(h) currents. We investigated the functional properties of I(h) in adult mouse cold thermoreceptor neurons from the trigeminal ganglion, identified by their high sensitivity to moderate cooling and responsiveness to menthol. All cultured cold-sensitive (CS) neurons expressed a fast activating I(h), which was fully blocked by extracellular Cs(+) or ZD7288 and had biophysical properties consistent with those of heteromeric HCN1-HCN2 channels. In CS neurons from HCN1(-/-) animals, I(h) was greatly reduced but not abolished. We find that I(h) activity is not essential for the transduction of cold stimuli in CS neurons. Nevertheless, I(h) has the potential to shape the excitability of CS neurons. First, I(h) blockade caused a membrane hyperpolarization in CS neurons of about 5 mV. Furthermore, impedance power analysis showed that all CS neurons had a prominent subthreshold membrane resonance in the 5-7 Hz range, completely abolished upon blockade of I(h) and absent in HCN1 null mice. This frequency range matches the spontaneous firing frequency of cold thermoreceptor terminals in vivo. Behavioural responses to cooling were reduced in HCN1 null mice and after peripheral pharmacological blockade of I(h) with ZD7288, suggesting that I(h) plays an important role in peripheral sensitivity to cold.

After removal of the fast N-type inactivation gate, voltage-sensitive Shaker (Shaker IR) K channels are still able to inactivate, albeit slowly, upon sustained depolarization. The classical mechanism proposed for the slow inactivation observed in cell-free membrane patches—the so called C inactivation—is a constriction of the external mouth of the channel pore that prevents K+ ion conduction. This constriction is antagonized by the external application of the pore blocker tetraethylammonium (TEA). In contrast to C inactivation, here we show that, when recorded in whole Xenopus oocytes, slow inactivation kinetics in Shaker IR K channels is poorly dependent on external TEA but severely delayed by internal TEA. Based on the antagonism with internally or externally added TEA, we used a two-pulse protocol to show that half of the channels inactivate by way of a gate sensitive to internal TEA. Such gate had a recovery time course in the tens of milliseconds range when the interpulse voltage was −90 mV, whereas C-inactivated channels took several seconds to recover. Internal TEA also reduced gating charge conversion associated to slow inactivation, suggesting that the closing of the internal TEA-sensitive inactivation gate could be associated with a significant amount of charge exchange of this type. We interpreted our data assuming that binding of internal TEA antagonized with U-type inactivation (Klemic, K.G., G.E. Kirsch, and S.W. Jones. 2001. Biophys. J. 81:814–826). Our results are consistent with a direct steric interference of internal TEA with an internally located slow inactivation gate as a “foot in the door” mechanism, implying a significant functional overlap between the gate of the internal TEA-sensitive slow inactivation and the primary activation gate. But, because U-type inactivation is reduced by channel opening, trapping the channel in the open conformation by TEA would also yield to an allosteric delay of slow inactivation. These results provide a framework to explain why constitutively C-inactivated channels exhibit gating charge conversion, and why mutations at the internal exit of the pore, such as those associated to episodic ataxia type I in hKv1.1, cause severe changes in inactivation kinetics.

The role of TRPM8 channel in thermotransduction involves several aspects of complexity that make it difficult to understand intuitively. First, it is activated by several stimuli (cold, voltage, agonists and intracellular signaling) that interact with each other, raising the question of how these interactions occur. Experimental evidence in this type of polymodal channel may be misinterpreted if the consequences of a working hypothesis are not considered carefully. Second, in parallel with the identification of TRPM8 as the main molecular transducer of cold temperatures in cold thermoreceptors of the somatosensory system, a list of other ion channels have been shown to be involved in the activity of cold-sensitive neurons and nerve endings. The variety of firing patterns observed at cold sensitive nerve endings arises from a complex interaction of ion channels that operate on different time scales. Mathematical modeling has been instrumental in understanding these phenomena, showing the consequences of the hypotheses raised. Here we review some of the models that have been proposed in these two areas: the activation of TRPM8 and TRPV1 by voltage and temperature, and the generation of firing patterns of cold thermoreceptors. We finish this chapter with a mathematical model showing how the calcium-dependent adaptation of TRPM8 may account for the response of cold thermoreceptors to rapid changes in temperature.

Neural crest cells exhibit dramatic migration behaviors as they populate their distant targets. Using a line of zebrafish expressing green fluorescent protein (sox10:EGFP) in neural crest cells we developed an assay to analyze and quantify cell migration as a population, and use it here to characterize in detail the subtle defects in cell migration caused by ethanol exposure during early development. The challenge was to quantify changes in the in vivo migration of all Sox10:EGFP expressing cells in the visual field of time-lapse movies. To perform this analysis we used an Optical Flow algorithm for motion detection and combined the analysis with a fit to an affine transformation. Through this analysis we detected and quantified significant differences in the cell migrations of Sox10:EGFP positive cranial neural crest populations in ethanol treated versus untreated embryos. Specifically, treatment affected migration by increasing the left-right asymmetry of the migrating cells and by altering the direction of cell movements. Thus, by applying this novel computational analysis, we were able to quantify the movements of populations of cells, allowing us to detect subtle changes in cell behaviors. Because cranial neural crest cells contribute to the formation of the frontal mass these subtle differences may underlie commonly observed facial asymmetries in normal human populations., Les cellules de la crête neurale peuvent présenter des comportements migratoires cliniquement dramatiques lors de leur migration distante. En utilisant un marqueur exprimant la protéine fluorescente verte (SOX10: EGFP) dans les cellules de la crête neurale, nous avons développé un test pour analyser et quantifier la migration cellulaire en tant que population, et caractériser en détail les défauts subtils dans la migration cellulaire causée par l'exposition à l'éthanol, au début du développement neural. Le défi était de quantifier les changements dans la migration in vivo de toutes les cellues de type Sox10:EGFP observable dans le champ visuel des films réalisés à très basse fréquence. Pour réaliser cette analyse, nous avons utilisé un algorithme de flux optique pour la détection de mouvement et combiné l'analyse avec un ajustement par une transformation affine. Grâce à cette analyse, nous avons détectés et quantifiés des différences notoires dans les migrations cellulaires de populations soumises à l'éthanol, au regard d'embryons non traités. Plus précisément, la migration est affectée par unec augmentation de l'asymétrie gauche-droite des cellules migrantes et une modification de la direction des mouvements cellulaires. En appliquant cette analyse computationnelle, nous avons été en mesure de quantifier les mouvements de populations de cellules, permettant de détecter des changements subtils dans les comportements cellulaires. Les cellules de la crête neurale crânienne contribuant à la formation de la masse cranienne antérieure, ces asymétries sous-tendent fréquemment des asymétries faciales observés dans les populations humaines concernées.

Mammalian peripheral cold thermoreceptors respond to cooling of their sensory endings with an increase in firing rate and modification of their discharge pattern. We recently showed that cultured trigeminal coldsensitive (CS) neurons express a prominent hyperpolarization-activated current (Ih), mainly carried by HCN1 channels, supporting subthreshold resonance in the soma without participating in the response to acute cooling. However, peripheral pharmacological blockade of Ih, or characterization of HCN1-/- mice, reveals a deficit in acute cold detection. Here we investigated the role of Ih in CS nerve endings, where cold sensory transduction actually takes place. Corneal CS nerve endings in mice show a rhythmic spiking activity at neutral skin temperature that switches to bursting mode when the temperature is lowered. Ih blockers ZD7288 and ivabradine alter firing patterns of CS nerve endings, lengthening interspike intervals and inducing bursts at neutral skin temperature. We characterized the CS nerve endings from HCN1-/-mouse corneas and found that they behave similar to wild type, although with a lower slope in the firing frequency vs. temperature relationship, thus explaining the deficit in cold perception of HCN1-/- mice. The firing pattern of nerve endings from HCN1/ mice was also affected by ZD7288, which we attribute to the presence of HCN2 channels in the place of HCN1. Mathematical modeling shows that the firing phenotype of CS nerve endings from HCN1-/- mice can be reproduced by replacing HCN1 channels with the slower HCN2 channels rather than by abolishing Ih. We propose that Ih carried by HCN1 channels helps tune the frequency of the oscillation and the length of bursts underlying regular spiking in cold thermoreceptors, having important implications for neural coding of cold sensation. © 2012 the American Physiological Society., This work was supported by funds from the Chilean Comisión Nacional de Investigación Científica y Tecnológica (CONICYT) (PBCT PSD20 and FONDECYT 11090308 to P. Orio, FONDECYT 1100983 to R. Madrid, and ACT-1113 to P. Orio and R. Madrid), the Universidad de Valparaiso (DIPUV 51/2007 to P. Orio), the Universidad de Santiago de Chile (VRID-USACH to R. Madrid), and the Spanish MICIIN (BFU2008-04425 and CONSOLIDER-INGENIO 2010 CSD2007-00023 to C. Belmonte, SAF2010-14990 to F. Viana). O. González is a Fellow from the Foundation Maria Cristina Masaveu-Peterson and CajaSur (Spain). The CINV is funded by Grant P09-022-F of the Millennium Science Initiative (Ministerio de Economía, Chile).

In mammals a class of ion channels able to sense a wide range of temperatures (0-60 °C) has evolved. These molecular thermodynamic machines called thermo Transient Receptor Potential (thermoTRP) are spread through the different TRP channel subfamilies having members inside the TRPM (melastatin) subfamily, where TRPM2, TRPM3, TRPM4 and TRPM5 are heat-activated, whereas TRPM8 is activated by cold. The TRPV (vanilloid) subfamily contains four thermoTRP channels (TRPV1, TRPV2, TRPV3 and TRPV4), which are all activated by heat; and TRPA1 (ankyrin) channel which is activated by noxious cold (reviewed in [28, 107], Figure 1). More recently, a member of TRPC (canonical) subfamily, TRPC5, was identified as a cold receptor in the temperature range 37-25 °C [1].

Membrane voltage, ligand binding, mechanical force and temperature can all induce conformational changes that open ion channel pores. A key question in understanding ion channel function is how the protein domains involved in sensing stimuli (sensors) communicate with the pore to gate its opening and closing. TRP channels are considered six-transmembrane cation-permeable channels, distant relatives of voltage-gated potassium channels (Kv), which are known to be activated by membrane depolarization. Understanding the molecular nature of thermo-TRP channel gating offers a fair challenge to biophysicists. This chapter will summarize our present knowledge on the effect of voltage and temperature during thermo-TRP channel activation.

Membrane voltage, ligand binding, mechanical force and temperature can all induce conformational changes that open ion channel pores. A key question in understanding ion channel function is how the protein domains involved in sensing stimuli (sensors) communicate with the pore to gate its opening and closing. TRP channels are considered six-transmembrane cation-permeable channels, distant relatives of voltage-gated potassium channels (Kv), which are known to be activated by membrane depolarization. Understanding the molecular nature of thermo-TRP channel gating offers a fair challenge to biophysicists. This chapter will summarize our present knowledge on the effect of voltage and temperature during thermo-TRP channel activation.