Network activity arising from optimal diameters of neuronal processes

Electrical coupling provides an important pathway for signal transmission between neurons. In several regions of the mammalian brain electrical synapses have been detected, and their role in the synchronization of neural networks and the generation of oscillations has been studied theoretically. Recently, it has been found that the amplitude of the postsynaptic potential is maximized for a specific diameter of the postsynaptic fiber. In this thesis, the impact of the fiber\u27s diameter on the success or failure of the action potential initiation and propagation is studied theoretically. Systems of two coupled neurons, as well as small networks, are investigated. The passive and voltage-dependent properties of the neurons are implemented using compartment modeling. The results of the simulations show that for neurons with non-branching dendrites an action potential is initiated only for a specific, optimal diameter. In contrast, for neurons with branching structures the signal transmission improves monotonically with increasing diameter. By studying a model network with a ring architecture it is demonstrated that network activity crucially depends on the diameter of the coupled fibers

神経細胞のマルチコンパートメントモデルにおける細胞外抵抗分布の役割 : 細胞外記録および細胞外電気刺激のための統一形式化

Tohoku University川島隆

Influence of the dentritic morphology on electrophysiological responses of thalamocortical neurons

Les neurones thalamiques de relai ont un rôle exclusif dans la transformation et de transfert de presque toute l'information sensorielle dans le cortex. L'intégration synaptique et la réponse électrophysiologique des neurones thalamiques de relai sont déterminées non seulement par l’état du réseau impliqué, mais ils sont également contrôlés par leurs propriétés intrinsèques tels les divers canaux ioniques voltage-dépendants ainsi que l’arborisation dendritique élaboré. Par conséquent, investiguer sur le profil complexe de morphologie dendritique et sur les propriétés dendritiques actives révèle des renseignements importants sur la fonction d'entrée-sortie de neurones thalamiques de relai. Dans cette étude, nous avons reconstruit huit neurones thalamocorticaux (TC) du noyau VPL de chat adulte. En se basant sur ces données morphologiques complètes, nous avons développé plusieurs modèles multicompartimentaux afin de trouver un rôle potentiellement important des arbres dendritiques des neurones de TC dans l'intégration synaptique et l’intégration neuronale. L'analyse des caractéristiques morphologiques des neurones TC accordent des valeurs précises à des paramètres géométriques semblables ou différents de ceux publiés antérieurement. En outre, cette analyse fait ressortir de tous nouveaux renseignements concernant le patron de connectivité entre les sections dendritiques telles que l'index de l'asymétrie et la longueur de parcours moyen (c'est-à-dire, les paramètres topologiques). Nous avons confirmé l’étendue des valeurs rapportée antérieurement pour plusieurs paramètres géométriques tels que la zone somatique (2956.24±918.89 m2), la longueur dendritique totale (168017.49±4364.64 m) et le nombre de sous-arbres (8.3±1.5) pour huit neurones TC. Cependant, contrairement aux données rapportées antérieurement, le patron de ramification dendritique (avec des cas de bifurcation 98 %) ne suit pas la règle de puissance de Rall 3/2 pour le ratio géométrique (GR), et la valeur moyenne de GR pour un signal de propagation est 2,5 fois plus grande que pour un signal rétropropagé. Nous avons également démontré une variabilité significative dans l'index de symétrie entre les sous-arbres de neurones TC, mais la longueur du parcours moyen n'a pas montré une grande variation à travers les ramifications dendritiques des différents neurones. Nous avons examiné la conséquence d’une distribution non-uniforme des canaux T le long de l'arbre dendritique sur la réponse électrophysiologique émergeante, soit le potentiel Ca 2+ à seuil bas (low-threshold calcium spike, LTS) des neurones TC. En appliquant l'hypothèse du «coût minimal métabolique», nous avons constaté que le neurone modélisé nécessite un nombre minimal de canaux-T pour générer un LTS, lorsque les canaux-T sont situés dans les dendrites proximales. Dans la prochaine étude, notre modèle informatique a illustré l'étendue d'une rétropropagation du potentiel d'action et de l'efficacité de la propagation vers des PPSEs générés aux branches dendritiques distales. Nous avons démontré que la propagation dendritique des signaux électriques est fortement contrôlée par les paramètres morphologiques comme illustré par les différents paliers de polarisation obtenus par un neurone à équidistance de soma pendant la propagation et la rétropropagation des signaux électriques. Nos résultats ont révélé que les propriétés géométriques (c.-à-d. diamètre, GR) ont un impact plus fort sur la propagation du signal électrique que les propriétés topologiques. Nous concluons que (1) la diversité dans les propriétés morphologiques entre les sous-arbres d'un seul neurone TC donne une capacité spécifique pour l'intégration synaptique et l’intégration neuronale des différents dendrites, (2) le paramètre géométrique d'un arbre dendritique fournissent une influence plus élevée sur le contrôle de l'efficacité synaptique et l'étendue du potentiel d'action rétropropagé que les propriétés topologiques, (3) neurones TC suivent le principe d’optimisation pour la distribution de la conductance voltage-dépendant sur les arbres dendritiques.Thalamic relay neurons have an exclusive role in processing and transferring nearly all sensory information into the cortex. The synaptic integration and the electrophysiological response of thalamic relay neurons are determined not only by a state of the involved network, but they are also controlled by their intrinsic properties; such as diverse voltage-dependent ionic channels as well as by elaborated dendritic arborization. Therefore, investigating the complex pattern of dendritic morphology and dendritic active properties reveals important information on the input-output function of thalamic relay neurons. In this study, we reconstructed eight thalamocortical (TC) neurons from the VPL nucleus of adult cats. Based on these complete morphological data, we developed several multi-compartment models in order to find a potentially important role for dendritic trees of TC neurons in the synaptic integration and neuronal computation. The analysis of morphological features of TC neurons yield precise values of geometrical parameters either similar or different from those previously reported. In addition, this analysis extracted new information regarding the pattern of connectivity between dendritic sections such as asymmetry index and mean path length (i.e., topological parameters). We confirmed the same range of previously reported value for several geometric parameters such as the somatic area (2956.24±918.89 m2), the total dendritic length (168017.49±4364.64 m) and the number of subtrees (8.3±1.5) for eight TC neurons. However, contrary to previously reported data, the dendritic branching pattern (with 98% bifurcation cases) does not follow Rall’s 3/2 power rule for the geometrical ratio (GR), and the average GR value for a forward propagation signal was 2.5 times bigger than for a backward propagating signal. We also demonstrated a significant variability in the symmetry index between subtrees of TC neurons, but the mean path length did not show a large variation through the dendritic arborizations of different neurons. We examined the consequence of non-uniform distribution of T-channels along the dendritic tree on the prominent electrophysiological response, the low-threshold Ca2+ spike (LTS) of TC neurons. By applying the hypothesis of “minimizing metabolic cost”, we found that the modeled neuron needed a minimum number of T-channels to generate low-threshold Ca2+ spike (LTS), when T-channels were located in proximal dendrites. In the next study, our computational model illustrated the extent of an action potential back propagation and the efficacy of forward propagation of EPSPs arriving at the distal dendritic branches. We demonstrated that dendritic propagation of electrical signals is strongly controlled by morphological parameters as shown by different levels of polarization achieved by a neuron at equidistance from the soma during back and forward propagation of electrical signals. Our results revealed that geometrical properties (i.e. diameter, GR) have a stronger impact on the electrical signal propagation than topological properties. We conclude that (1) diversity in the morphological properties between subtrees of a single TC neuron lead to a specific ability for synaptic integration and neuronal computation of different dendrites, (2) geometrical parameter of a dendritic tree provide higher influence on the control of synaptic efficacy and the extent of the back propagating action potential than topological properties, (3) TC neurons follow the optimized principle for distribution of voltage-dependent conductance on dendritic trees

Impact of Dendritic Size and Dendritic Topology on Burst Firing in Pyramidal Cells

Neurons display a wide range of intrinsic firing patterns. A particularly relevant pattern for neuronal signaling and synaptic plasticity is burst firing, the generation of clusters of action potentials with short interspike intervals. Besides ion-channel composition, dendritic morphology appears to be an important factor modulating firing pattern. However, the underlying mechanisms are poorly understood, and the impact of morphology on burst firing remains insufficiently known. Dendritic morphology is not fixed but can undergo significant changes in many pathological conditions. Using computational models of neocortical pyramidal cells, we here show that not only the total length of the apical dendrite but also the topological structure of its branching pattern markedly influences inter- and intraburst spike intervals and even determines whether or not a cell exhibits burst firing. We found that there is only a range of dendritic sizes that supports burst firing, and that this range is modulated by dendritic topology. Either reducing or enlarging the dendritic tree, or merely modifying its topological structure without changing total dendritic length, can transform a cell's firing pattern from bursting to tonic firing. Interestingly, the results are largely independent of whether the cells are stimulated by current injection at the soma or by synapses distributed over the dendritic tree. By means of a novel measure called mean electrotonic path length, we show that the influence of dendritic morphology on burst firing is attributable to the effect both dendritic size and dendritic topology have, not on somatic input conductance, but on the average spatial extent of the dendritic tree and the spatiotemporal dynamics of the dendritic membrane potential. Our results suggest that alterations in size or topology of pyramidal cell morphology, such as observed in Alzheimer's disease, mental retardation, epilepsy, and chronic stress, could change neuronal burst firing and thus ultimately affect information processing and cognition

Influence of the electrotonic architecture on single neurons dynamics : a computational approach

Dissertação de mestrado, Ciência Cognitiva, Universidade de Lisboa, Faculdade de Ciências, Faculdade de Letras, Faculdade de Medicina, Faculdade de Psicologia, 2014Na presente dissertação, investigamos de forma sistemática a forma como a morfologia dendrítica subjaz as diferenças na atividade elétrica neuronal que estão na base da geração de potenciais de ação. De forma a atingir este objetivo desenvolvemos uma medida que quantifica as duas maiores fontes de variabilidade morfológica: métrica e topologia, e ainda outros componentes estruturais como canais iónicos. Baseado na nova medida, propomos um novo mecanismo de sincronização que relaciona a estrutura dendritica à modulação de currente axial que flui da árvore dendrítica até ao soma. Esta hipótese afirma que quanto mais simétrica a estrutura electrotónica da célula é, mais currente irá chegar ao soma das dendrites devido à sincronização obtida em virtude da simetria estrutural. De forma a testar a hipótese de sincronização foram simuladas duas experiências usando modelos multi-compartimentais computacionais de células de Purkinje, Piramidais e células do córtex Visual. Na primeira abordagem, as estruturas das células foram quantificadas utilizando a nova medida e depois comparadas com a quantidade de currente axial proviniente das dendrites que atingia o soma. Na segunda abordagem, os potenciais de voltagem são medidos ao nível do compartimento axo-somático de forma a se poder analisar se diferenças encontradas na condição axial induzem diferenças na atividade de spiking da célula. Os resultados apoiam a hipótese de sincronização, pois neurónios com estruturas electrotónicas com níveis de simetria mais elevados, exibem os níveis mais elevados de currente axial a chegar ao soma para o mesmo estímulo. As diferenças encontradas na condição axial correlacionaram-se com o tempo que os neurónios levaram a atingir um potencial de ação, com os neurónios mais simétricos a requerer menos tempo para o fazer. No entanto, diferenças significativas não emergiram nos padrões de potenciais de ação, mas estes resultados podem ser explicados por algumas limitações no protocolo de estimulação. Em suma, os nossos resultados mostram que a medida desenvolvida é uma alternativa promissora às abordagens morfométricas tradicionais, pois pode ser utilizada com confiança para quantificar diferenças estruturais, podendo ser aplicada a vários tipos de neurónios, providenciando uma ligação entre estrutura e função.In this dissertation, we systematically investigate how dendritic morphology underlies the differences in the electrical dynamics of the cell that lead to spiking behaviour. To accomplish this goal we develop a new measure that provides a quantitative account of the two most relevant sources of morphological variability: metrics and topology, as well as of other structural components such as ion channels. Supported by the new measure, we propose a new synchronization mechanism that relates dendritic structure to the modulation of axial current that flows from the dendrites to the soma. This hypothesis states that the more symmetric the electrotonic structure of a cell is, the more current will reach the soma from the dendrites due to the synchronism obtained by virtue of structural symmetry. To test the synchronization hypothesis two simulation-based experiments using detailed multi-compartmental computational models of Purkinje, Pyramidal and Visual cortical cells were conducted. In the first approach, by means of the novel measure, the structure of the cells are quantified, and compared with the amount of axial current reaching the soma from the dendritic tree. In the second approach, voltage traces are measured at the axo-somatic compartment to analyse whether differences found in the axial current condition induce differences in the output spiking patterns. Our results support the synchronization hypothesis, as neurons with electrotonic structures with higher levels of symmetry exhibited the highest amount of current reaching the soma for the same stimulus. These differences correlated with the time that neurons required to spike, with more symmetrical neurons requiring less time to do so. Nevertheless, significant differences fail to emerge in the output spike trains, but these results can be explained by some limitations in the stimulation protocol. Overall, the results show that the proposed measure is a promising alternative to traditional morphometrics measures as it can be used with confidence to quantify structural differences, and can be applied across different types of neurons while providing a bridge between structure and function

Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca2+ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models

Solitonic Effects of the Local Electromagnetic Field on Neuronal Microtubules

Current wisdom in classical neuroscience suggests that the only direct action of the electric field in neurons is upon voltage-gated ion channels which open and close their gates during the passage of ions. The intraneuronal biochemical activities are thought to be modulated indirectly either by entering into the cytoplasm ions that act as\ud second messengers, or via linkage to the ion channels enzymes. In this paper we present a novel possibility for subneuronal processing of information by cytoskeletal microtubule tubulin tails and we show that the local electromagnetic field supports information that could\ud be converted into specific protein tubulin tail conformational states. Long-range collective coherent behavior of the tubulin tails could be modelled in the form of solitary waves such as sine-Gordon kinks, antikinks or breathers that propagate along the microtubule outer\ud surface, and the tubulin tail soliton collisions could serve as elementary computational gates that control cytoskeletal processes. The biological importance of the presented model is due to the unique biological enzymatic energase action of the tubulin tails, which is experimentally verified for controlling the sites of microtubule-associated protein\ud attachment and the kinesin transport of post-Golgi vesicles

The Theoretical Foundation of Dendritic Function

This collection of fifteen previously published papers, some of them not widely available, have been carefully chosen and annotated by Rall's colleagues and other leading neuroscientists.Wilfrid Rall was a pioneer in establishing the integrative functions of neuronal dendrites that have provided a foundation for neurobiology in general and computational neuroscience in particular. This collection of fifteen previously published papers, some of them not widely available, have been carefully chosen and annotated by Rall's colleagues and other leading neuroscientists. It brings together Rall's work over more than forty years, including his first papers extending cable theory to complex dendritic trees, his ground-breaking paper introducing compartmental analysis to computational neuroscience, and his studies of synaptic integration in motoneurons, dendrodendritic interactions, plasticity of dendritic spines, and active dendritic properties. Today it is well known that the brain's synaptic information is processed mostly in the dendrites where many of the plastic changes underlying learning and memory take place. It is particularly timely to look again at the work of a major creator of the field, to appreciate where things started and where they have led, and to correct any misinterpretations of Rall's work. The editors' introduction highlights the major insights that were gained from Rall's studies as well as from those of his collaborators and followers. It asks the questions that Rall proposed during his scientific career and briefly summarizes the answers.The papers include commentaries by Milton Brightman, Robert E. Burke, William R. Holmes, Donald R. Humphrey, Julian J. B. Jack, John Miller, Stephen Redman, John Rinzel, Idan Segev, Gordon M. Shepherd, and Charles Wilson

Computational modelling of reactive processes in lithium-metal batteries

This Thesis presents a computational phase-field model to describe the electrodeposition process that forms dendrites within lithium-metal batteries. We describe the evolution of a phase field, the lithium-ion concentration, and electric potential during a battery charge cycle. We simulate three-dimensional spike-like lithium structures in agreement with experimentally-observed dendrite growth rates and morphologies reported in the literature. This work constitutes a relevant step towards physical-based, quantitative models needed to achieve the commercial realisation of lithium-metal batteries