Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Rhythmogenic and Premotor Functions of Dbx1 Interneurons in the Pre-Bötzinger Complex and Reticular Formation: Modeling and Simulation Studies

Breathing in mammals depends on rhythms that originate from the preBötzinger complex (preBötC) of the ventral medulla and a network of brainstem and spinal premotor neurons. The rhythm-generating core of the preBötC, as well as some premotor circuits, consists of interneurons derived from Dbx1-expressing precursors but the structure and function of these networks remain incompletely understood. We previously developed a cell-specific detection and laser ablation system to interrogate respiratory network structure and function in a slice model of breathing that retains the preBötC, premotor circuits, and the respiratory related hypoglossal (XII) motor nucleus such that in spontaneously rhythmic slices, cumulative ablation of Dbx1 preBötC neurons decreased XII motor output by half after only a few cell deletions, and then decelerated and terminated rhythmic function altogether as the tally increased. In contrast, cumulatively deleting Dbx1 premotor neurons decreased XII motor output monotonically, but did not affect frequency nor stop functionality regardless of the ablation tally. This dissertation presents several network modeling and cellular modeling studies that would further our understanding of how respiratory rhythm is generated and transmitted to the XII motor nucleus. First, we propose that cumulative deletions of Dbx1 preBötC neurons preclude rhythm by diminishing the amount of excitatory inward current or disturbing the process of recurrent excitation rather than structurally breaking down the topological network. Second, we establish a feasible configuration for neural circuits including an Erdős-Rényi preBötC network and a small-world reticular premotor network with interconnections following an anti-preferential attachment rule, which is the only configuration that produces consistent outcomes with previous experimental benchmarks. Furthermore, since the performance of neuronal network simulations is, to some extent, affected by the nature of the cellular model, we aim to develop a more realistic cellular model based on the one we adopted in previous network studies, which would account for some recent experimental findings on rhythmogenic preBötC neurons

Релаксационные автоколебания в системе из двух синаптически связанных импульсных нейронов

We consider a mathematical model of synaptic interaction between two pulse neuron elements. Each of the neurons is modeled by a singularly-perturbed difference-differential equation with delay. Coupling is assumed to be at the threshold, and time delay is taken into consideration. Problems of existence and stability of relaxation periodic movements for obtained systems are considered. It turns out that the ratio between the delay due to internal causes in a single neuron model and the delay in the coupling link between oscillators is crucial. Existence and stability of a uniform cycle of the problem is proved for the case where the delay in the link is less than a period of a single oscillator that depends on the internal delay. As the delay grows, the in-phase regime becomes more complex, particularly, it is shown that by choosing a suitable delay, we can obtain more complex relaxation oscillation and inside a period interval the system can exhibit not one but several high-amplitude splashes. This means that bursting-effect can appear in a system of two synaptic coupled oscillators of neuron type due to a delay in a coupling link.Рассматривается математическая модель синаптического взаимодействия пары импульсных нейронных элементов. Моделью каждого из отдельных нейронов является сингулярно возмущенное дифференциально-разностное уравнение с запаздыванием. Связь между элементами предполагается пороговой, кроме того, в ней учитывается запаздывание по времени. Изучаются вопросы о существовании и устойчивости в полученных системах релаксационных периодических движений. Как оказалось, принципиальным является соотношение между запаздыванием, обусловленным внутренними факторами в модели одиночного импульсного нейрона, и запаздыванием в цепи связи между осцилляторами. При условии, что запаздывание в цепи связи меньше, чем обусловленный внутренним запаздыванием период колебаний уединенного осциллятора, доказывается существование и устойчивость однородного цикла задачи. Увеличение запаздывания приводит к усложнению синфазного режима, в частности, показано, что за счет подходящего выбора этой величины релаксационные колебания в изучаемой системе могут усложняться и на промежутке периода система может иметь не один, а несколько всплесков большой амплитуды. Это означает, что bursting-эффект может возникать в системе из двух синаптически связанных осцилляторов нейронного типа за счет запаздывания в цепи связи

Electroencephalographic field influence on calcium momentum waves

Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential $\mathbf{A}$. The bottom-up process considered are $\mathrm{Ca}^{2+}$ waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of $\mathbf{A}$ on $\mathrm{Ca}^{2+}$ momentum, $\mathbf{p}$. The canonical momentum of a charged particle in an electromagnetic field, $\mathbf{\Pi} = \mathbf{p} + q \mathbf{A}$ (SI units), is calculated, where the charge of $\mathrm{Ca}^{2+}$ is $q = - 2 e$, $e$ is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG $\mathbf{A}$ can be quite influential on the momentum $\mathbf{p}$ of $\mathrm{Ca}^{2+}$ ions, in both classical and quantum mechanics. Molecular scales of $\mathrm{Ca}^{2+}$ wave dynamics are coupled with $\mathbf{A}$ fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting $\mathbf{A}$ models to EEG data as reported here, building tripartite models to develop $\mathbf{A}$ models, and studying long coherence times of $\mathrm{Ca}^{2+}$ waves in the presence of $\mathbf{A}$ due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the $\mathbf{p} + q \mathbf{A}$ interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.Comment: Final draft. http://ingber.com/smni14_eeg_ca.pdf may be updated more frequentl

Neuronal oscillations: from single-unit activity to emergent dynamics and back

L’objectiu principal d’aquesta tesi és avançar en la comprensió del processament d’informació en xarxes neuronals en presència d’oscil lacions subumbrals. La majoria de neurones propaguen la seva activitat elèctrica a través de sinapsis químiques que són activades, exclusivament, quan el corrent elèctric que les travessa supera un cert llindar. És per aquest motiu que les descàrregues ràpides i intenses produïdes al soma neuronal, els anomenats potencials d’acció, són considerades la unitat bàsica d’informació neuronal, és a dir, el senyal mínim i necessari per a iniciar la comunicació entre dues neurones. El codi neuronal és entès, doncs, com un llenguatge binari que expressa qualsevol missatge (estímul sensorial, memòries, etc.) en un tren de potencials d’acció. Tanmateix, cap funció cognitiva rau en la dinàmica d’una única neurona. Circuits de milers de neurones connectades entre sí donen lloc a determinats ritmes, palesos en registres d’activitat colectiva com els electroencefalogrames (EEG) o els potencials de camp local (LFP). Si els potencials d’acció de cada cèl lula, desencadenats per fluctuacions estocàstiques de les corrents sinàptiques, no assolissin un cert grau de sincronia, no apareixeria aquesta periodicitat a nivell de xarxa. Per tal de poder entendre si aquests ritmes intervenen en el codi neuronal hem estudiat tres situacions. Primer, en el Capítol 2, hem mostrat com una cadena oberta de neurones amb un potencial de membrana intrínsecament oscil latori filtra un senyal periòdic arribant per un dels extrems. La resposta de cada neurona (pulsar o no pulsar) depèn de la seva fase, de forma que cada una d’elles rep un missatge filtrat per la precedent. A més, cada potencial d’acció presinàptic provoca un canvi de fase en la neurona postsinàptica que depèn de la seva posició en l’espai de fases. Els períodes d’entrada capaços de sincronitzar les oscil lacions subumbrals són aquells que mantenen la fase d’arribada dels potencials d’acció fixa al llarg de la cadena. Per tal de què el missatge arribi intacte a la darrera neurona cal, a més a més, que aquesta fase permeti la descàrrega del voltatge transmembrana. En segon cas, hem estudiat una xarxa neuronal amb connexions tant a veïns propers com de llarg abast, on les oscil lacions subumbrals emergeixen de l’activitat col lectiva reflectida en els corrents sinàptics (o equivalentment en el LFP). Les neurones inhibidores aporten un ritme a l’excitabilitat de la xarxa, és a dir, que els episodis en què la inhibició és baixa, la probabilitat d’una descàrrega global de la població neuronal és alta. En el Capítol 3 mostrem com aquest ritme implica l’aparició d’una bretxa en la freqüència de descàrrega de les neurones: o bé polsen espaiadament en el temps o bé en ràfegues d’elevada intensitat. La fase del LFP determina l’estat de la xarxa neuronal codificant l’activitat de la població: els mínims indiquen la descàrrega simultània de moltes neurones que, ocasionalment, han superat el llindar d’excitabilitat degut a un decreixement global de la inhibició, mentre que els màxims indiquen la coexistència de ràfegues en diferents punts de la xarxa degut a decreixements locals de la inhibició en estats globals d’excitació. Aquesta dinàmica és possible gràcies al domini de la inhibició sobre l’excitació. En el Capítol 4 considerem acoblament entre dues xarxes neuronals per tal d’estudiar la interacció entre ritmes diferents. Les oscil lacions indiquen recurrència en la sincronització de l’activitat col lectiva, de manera que durant aquestes finestres temporals una població optimitza el seu impacte en una xarxa diana. Quan el ritme de la població receptora i el de l’emissora difereixen significativament, l’eficiència en la comunicació decreix, ja que les fases de màxima resposta de cada senyal LFP no mantenen una diferència constant entre elles. Finalment, en el Capítol 5 hem estudiat com les oscil lacions col lectives pròpies de l’estat de son donen lloc al fenomen de coherència estocàstica. Per a una intensitat òptima del soroll, modulat per l’excitabilitat de la xarxa, el LFP assoleix una regularitat màxima donant lloc a un període refractari de la població neuronal. En resum, aquesta Tesi mostra escenaris d’interacció entre els potencials d’acció, característics de la dinàmica de neurones individuals, i les oscil lacions subumbrals, fruit de l’acoblament entre les cèl lules i ubiqües en la dinàmica de poblacions neuronals. Els resultats obtinguts aporten funcionalitat a aquests ritmes emergents, agents sincronitzadors i moduladors de les descàrregues neuronals i reguladors de la comunicació entre xarxes neuronals.The main objective of this thesis is to better understand information processing in neuronal networks in the presence of subthreshold oscillations. Most neurons propagate their electrical activity via chemical synapses, which are only activated when the electric current that passes through them surpasses a certain threshold. Therefore, fast and intense discharges produced at the neuronal soma (the action potentials or spikes) are considered the basic unit of neuronal information. The neuronal code is understood, then, as a binary language that expresses any message (sensory stimulus, memories, etc.) in a train of action potentials. Circuits of thousands of interconnected neurons give rise to certain rhythms, revealed in collective activity measures such as electroencephalograms (EEG) and local field potentials (LFP). Synchronization of action potentials of each cell, triggered by stochastic fluctuations of the synaptic currents, cause this periodicity at the network level.To understand whether these rhythms are involved in the neuronal code we studied three situations. First, in Chapter 2, we showed how an open chain of neurons with an intrinsically oscillatory membrane potential filters a periodic signal coming from one of its ends. The response of each neuron (to spike or not) depends on its phase, so that each cell receives a message filtered by the preceding one. Each presynaptic action potential causes a phase change in the postsynaptic neuron, which depends on its position in the phase space. Those incoming periods that are able to synchronize the subthreshold oscillations, keep the phase of arrival of action potentials fixed along the chain. The original message reaches intact the last neuron provided that this phase allows the discharge of the transmembrane voltage.I the second case, we studied a neuronal network with connections to both long range and close neighbors, in which the subthreshold oscillations emerge from the collective activity apparent in the synaptic currents. The inhibitory neurons provide a rhythm to the excitability of the network. When inhibition is low, the likelihood of a global discharge of the neuronal population is high. In Chapter 3 we show how this rhythm causes a gap in the discharge frequency of neurons: either they pulse single spikes or they fire bursts of high intensity. The LFP phase determines the state of the neuronal network, coding the activity of the population: its minima indicate the simultaneous discharge of many neurons, while its maxima indicate the coexistence of bursts due to local decreases of inhibition at global states of excitation. In Chapter 4 we consider coupling between two neural networks in order to study the interaction between different rhythms. The oscillations indicate recurrence in the synchronization of collective activity, so that during these time windows a population optimizes its impact on a target network. When the rhythm of the emitter and receiver population differ significantly, the communication efficiency decreases as the phases of maximum response of each LFP signal do not maintain a constant difference between them.Finally, in Chapter 5 we studied how oscillations typical of the collective sleep state give rise to stochastic coherence. For an optimal noise intensity, modulated by the excitability of the network, the LFP reaches a maximal regularity leading to a refractory period of the neuronal population.In summary, this Thesis shows scenarios of interaction between action potentials, characteristics of the dynamics of individual neurons, and the subthreshold oscillations, outcome of the coupling between the cells and ubiquitous in the dynamics of neuronal populations . The results obtained provide functionality to these emerging rhythms, triggers of synchronization and modulator agents of the neuronal discharges and regulators of the communication between neuronal networks

Learning Universal Computations with Spikes

Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to inputs and the self-sustained generation of complex activity patterns, e.g. for locomotion. Many such computations require previous building of intrinsic world models. Here we show how spiking neural networks may solve these different tasks. Firstly, we derive constraints under which classes of spiking neural networks lend themselves to substrates of powerful general purpose computing. The networks contain dendritic or synaptic nonlinearities and have a constrained connectivity. We then combine such networks with learning rules for outputs or recurrent connections. We show that this allows to learn even difficult benchmark tasks such as the self-sustained generation of desired low-dimensional chaotic dynamics or memory-dependent computations. Furthermore, we show how spiking networks can build models of external world systems and use the acquired knowledge to control them

Extended field-of-view ultrathin microendoscopes with built-in aberration correction for high-resolution functional imaging with minimal invasiveness

TB

Investigating the neurovascular coupling in the cerebellar granular layer.

The neurovascular coupling (NVC) or functional hyperemia is the mechanism whereby neuronal activity controls cerebral blood flow (CBF). The tight coupling between neuronal activation and blood vessels diameter modifications ensures the proper supply of oxygen and nutrients to the central nervous system. In the brain, CBF adaptations are governed by vasoactive agents and their action on the vascular system (Iadecola, 2017). This phenomenon is also involved in the genesis of the blood-oxygen-level-dependent (BOLD) signals used by neuroimaging techniques, like functional magnetic resonance imaging (fMRI), to map changes in brain activity. Although being highly investigated, the interpretation of activity-dependent BOLD responses is widely debated (Hall et al., 2016). The complexity of investigating BOLD neurophysiological basis, i.e. NVC mechanisms, resulted in the inability to define a comprehensive theory for BOLD signals interpretation. In this work of thesis, the attention was focused on NVC mechanisms in the cerebellum. In this region, NVC has been previously investigated in the molecular layer, where interneurons activation has been found as the main player, unlike Purkinje cells spiking activity (Cauli et al., 2004; Thomsen et al., 2004). Surprisingly, there was no information about the role of the granular layer in cerebellar NVC before our investigations. In the granular layer, NVC is mediated by granule cells through an NMDA receptor/NO-dependent system acting on pericytes (Mapelli et al., 2017). The latter are contractile cells able to regulate the caliber of brain capillaries (Attwell et al., 2016),which are thought to be involved in the genesis of BOLD signals (Hall et al., 2016). Recent investigations using human fMRI demonstrated that cerebellar vermis lobule V and hemisphere lobule VI showed respectively linear and non-linear BOLD responses during the same motor task performance (Alahmadi et al., 2017). In mouse cerebellar slices, vermis lobule V and hemisphere lobule VI responded with different non-linear neurovascular events to several frequency patterns of neuronal activation, suggesting that NVC and thus BOLD signals might be region-dependent in the cerebellum (Gagliano et al., 2018 in preparation). In conclusion, granule cells, pericytes and capillaries may drive the basic neurovascular mechanisms of the cerebellum, but different cerebellar regions (vermis and hemisphere) could differently contribute to the genesis of cerebellar BOLD signals. These results might reflect different functions of these cerebellar areas following the same input