Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Human Brain/Cloud Interface

The Internet comprises a decentralized global system that serves humanity’s collective effort to generate, process, and store data, most of which is handled by the rapidly expanding cloud. A stable, secure, real-time system may allow for interfacing the cloud with the human brain. One promising strategy for enabling such a system, denoted here as a “human brain/cloud interface” (“B/CI”), would be based on technologies referred to here as “neuralnanorobotics.” Future neuralnanorobotics technologies are anticipated to facilitate accurate diagnoses and eventual cures for the ∼400 conditions that affect the human brain. Neuralnanorobotics may also enable a B/CI with controlled connectivity between neural activity and external data storage and processing, via the direct monitoring of the brain’s ∼86 × 109 neurons and ∼2 × 1014 synapses. Subsequent to navigating the human vasculature, three species of neuralnanorobots (endoneurobots, gliabots, and synaptobots) could traverse the blood–brain barrier (BBB), enter the brain parenchyma, ingress into individual human brain cells, and autoposition themselves at the axon initial segments of neurons (endoneurobots), within glial cells (gliabots), and in intimate proximity to synapses (synaptobots). They would then wirelessly transmit up to ∼6 × 1016 bits per second of synaptically processed and encoded human–brain electrical information via auxiliary nanorobotic fiber optics (30 cm3) with the capacity to handle up to 1018 bits/sec and provide rapid data transfer to a cloud based supercomputer for real-time brain-state monitoring and data extraction. A neuralnanorobotically enabled human B/CI might serve as a personalized conduit, allowing persons to obtain direct, instantaneous access to virtually any facet of cumulative human knowledge. Other anticipated applications include myriad opportunities to improve education, intelligence, entertainment, traveling, and other interactive experiences. A specialized application might be the capacity to engage in fully immersive experiential/sensory experiences, including what is referred to here as “transparent shadowing” (TS). Through TS, individuals might experience episodic segments of the lives of other willing participants (locally or remote) to, hopefully, encourage and inspire improved understanding and tolerance among all members of the human family

Multi-Scale Mathematical Modelling of Brain Networks in Alzheimer's Disease

Perturbations to brain network dynamics on a range of spatial and temporal scales are believed to underpin neurological disorders such as Alzheimer’s disease (AD). This thesis combines quantitative data analysis with tools such as dynamical systems and graph theory to understand how the network dynamics of the brain are altered in AD and experimental models of related pathologies. Firstly, we use a biophysical neuron model to elucidate ionic mechanisms underpinning alterations to the dynamics of principal neurons in the brain’s spatial navigation systems in an animal model of tauopathy. To uncover how synaptic deficits result in alterations to brain dynamics, we subsequently study an animal model featuring local and long-range synaptic degeneration. Synchronous activity (functional connectivity; FC) between neurons within a region of the cortex is analysed using two-photon calcium imaging data. Long-range FC between regions of the brain is analysed using EEG data. Furthermore, a computational model is used to study relationships between networks on these different spatial scales. The latter half of this thesis studies EEG to characterize alterations to macro-scale brain dynamics in clinical AD. Spectral and FC measures are correlated with cognitive test scores to study the hypothesis that impaired integration of the brain’s processing systems underpin cognitive impairment in AD. Whole brain computational modelling is used to gain insight into the role of spectral slowing on FC, and elucidate potential synaptic mechanisms of FC differences in AD. On a finer temporal scale, microstate analyses are used to identify changes to the rapid transitioning behaviour of the brain’s resting state in AD. Finally, the electrophysiological signatures of AD identified throughout the thesis are combined into a predictive model which can accurately separate people with AD and healthy controls based on their EEG, results which are validated on an independent patient cohort. Furthermore, we demonstrate in a small preliminary cohort that this model is a promising tool for predicting future conversion to AD in patients with mild cognitive impairment

Intrinsic and synaptic membrane properties of neurons in the thalamic reticular nucleus

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2004-2005Le noyau réticulaire thalamique (RE) est une structure qui engendre des fuseaux, une oscillation bioélectrique de marque pendant les stades précoces du sommeil. De multiples propriétés neuronales, intrinsèques et synaptiques, sont impliquées dans la génération, la propagation, le maintien et la terminaison des ondes en fuseaux. D’un autre côté, ce rythme constitue un état spécial de l’activité du réseau qui est généré par le réseau lui-même et affecte les propriétés cellulaires du noyau RE. Cette étude se concentre sur ces sujets: comment les propriétés cellulaires et les propriétés du réseau sont inter-reliées et interagissent pour engendrer les ondes fuseaux dans les neurones du RE et leurs cibles, les neurones thalamocorticaux. La présente thèse fournit de nouvelles évidences montrant le rôle fondamental joué par les neurones du noyau RE dans la genèse des ondes en fuseaux, dû aux synapses chimiques établies par ces neurones. La propagation et la synchronisation de l’activité sont modulées par les synapses électriques entre les neurones réticulaires thalamiques, mais aussi par les composantes dépolarisantes secondaires des réponses synaptiques évoquées par le cortex. De plus, la forme générale et la terminaison des oscillations thalamiques sont probablement contrôlées en grande partie par les neurones du RE, lesquels expriment une conductance intrinsèque leurs procurant une membrane avec un comportement bistable. Finalement, les oscillations thalamiques en fuseaux sont aussi capables de moduler les propriétés membranaires et l’activité des neurones individuels du RE.The thalamic reticular nucleus (RE) is a key structure related to spindles, a hallmark bioelectrical oscillation during early stages of sleep. Multiple neuronal properties, both intrinsic and synaptic, are implicated in the generation, propagation, maintenance and termination of spindle waves. On the other hand, this rhythm constitutes a special state of network activity, which is generated within, and affects single-cell properties of the RE nucleus. This study is focused on these topics: how cellular and network properties are interrelated and interact to generate spindle waves in the pacemaking RE neurons and their targets, thalamocortical neurons. The present thesis provides new evidence showing the fundamental role played by the RE nucleus in the generation of spindle waves, due to chemical synapses established by its neurons. The propagation and synchronization of activity is modulated by electrical synapses between thalamic reticular neurons, but also by the secondary depolarizing component of cortically-evoked synaptic responses. Additionally, the general shaping and probably the termination of thalamic oscillations could be controlled to a great extent by RE neurons, which express an intrinsic conductance endowing them with membrane bistable behaviour. Finally, thalamic spindle oscillations are also able to modulate the membrane properties and activities of individual RE neurons

A new Mathematical Framework to Understand Single Neuron Computations

An important feature of the nervous system is its ability to adapt to new stimuli. This adaptation allows for optimal encoding of the incoming information by dynamically changing the coding strategy based upon the incoming inputs to the neuron. At the level of single cells, this widespread phenomena is often referred to as spike-frequency adaptation, since it manifests as a history-dependent modulation of the neurons firing frequency. In this thesis I focus on how a neuron is able to adapt its activity to a specific input as well as on the function of such adaptive mechanisms. To study these adaptive processes different approaches have been used, from empirical observations of neural activities to detailed modeling of single cells. Here, I approach these problems by using simplified threshold models. In particular, I introduced a new generalization of the integrate-and-fire model (GIF) along with a convex fitting method allowing for efficient estimation of model parameters. Despite its relative simplicity I show that this neuron model is able to reproduce neuron behaviors with a high degree of accuracy. Moreover, using this method I was able to show that cortical neurons are equipped with two distinct adaptation mechanisms. First, a spike-triggered current that captures the complex influx of ions generated after the emission of a spike. While the second is a movement of the firing threshold, which possibly reflects the slow inactivation of sodium channels induced by the spiking activity. The precise dynamics of these adaptation processes is cell-type specific, explaining the difference of firing activity reported in different neuron types. Consequently, neuronal types can be classified based on model parameters. In Pyramidal neurons spike-dependent adaptation lasts for seconds and follows a scale-free dynamics, which is optimally tuned to encodes the natural inputs that pyramidal neurons receive in vivo. Finally using an extended version of the GIF model, I show that adaptation is not only a spike-dependent phenomenon, but also acts at the subthreshold level. In Pyramidal neurons the dynamics of the firing threshold is influenced by the subthreshold membrane potential. Spike-dependent and voltage-dependent adaptation interact in an activity-dependent way to ultimately shape the filtering properties of the membrane on the input statistics. Equipped with such a mechanism, Pyramidal neurons behave as integrators at low inputs and as a coincidence detectors at high inputs, maintaining sensitivity to input fluctuations across all regimes

Induction and Maintenance of Synaptic Plasticity

Synaptic long-term modifications following neuronal activation are believed to be at the origin of learning and long-term memory. Recent experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states of a single synapse. The biochemical network involving calcium/calmodulin-dependent protein kinase II (CaMKII) and its regulating protein signaling cascade has been hypothesized to durably maintain the synaptic state in form of a bistable switch. Furthermore, it has been shown experimentally that CaMKII and associated proteins such as protein kinase A and calcineurin are necessary for the induction of long-lasting increases (long-term potentiation, LTP) and/or long-lasting decreases (long-term depression, LTD) of synaptic efficacy. However, the biochemical mechanisms by which experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such networks are still unknown. We present a detailed biochemical model of the calcium/calmodulin-dependent autophosphorylation of CaMKII and the protein signaling cascade governing the dephosphorylation of CaMKII. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentrations. Repetitive high calcium levels switch the system from a weakly- to a highly phosphorylated state (LTP). We show that the reverse transition (LTD) can be mediated by elevated phosphatase activity at intermediate calcium levels. It is shown that the CaMKII kinase-phosphatase system can qualitatively reproduce plasticity results in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. A reduced model based on the CaMKII system is used to elucidate which parameters control the synaptic plasticity outcomes in response to STDP protocols, and in particular how the plasticity results depend on the differential activation of phosphatase and kinase pathways and the level of noise in the calcium transients. Our results show that the protein network including CaMKII can account for (i) induction - through LTP/LTD-like transitions - and (ii) storage - due to its bistability - of synaptic changes. The model allows to link biochemical properties of the synapse with phenomenological 'learning rules' used by theoreticians in neural network studies