Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium.

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines

Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space

Chronic and acute implants of multi-electrode arrays that cover several mm$^2$ of neural tissue provide simultaneous access to population signals like extracellular potentials and the spiking activity of 100 or more individual neurons. While the recorded data may uncover principles of brain function, its interpretation calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Such models can facilitate the search of mechanisms underlying observed spatiotemporal activity patterns in cortex. Multi-layer spiking neuron network models of local cortical circuits covering ~1 mm$^2$ have been developed, integrating experimentally obtained neuron-type specific connectivity data and reproducing features of in-vivo spiking statistics. With forward models, local field potentials (LFPs) can be computed from the simulated spiking activity. To account for the spatial scale of common neural recordings, we extend a local network and LFP model to 4x4 mm$^2$. The upscaling preserves the neuron densities, and introduces distance-dependent connection probabilities and delays. As detailed experimental connectivity data is partially lacking, we address this uncertainty in model parameters by testing parameter combinations within biologically plausible bounds. Based on model predictions of spiking activity and LFPs, we find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations observed in sensory cortex. In contrast with the weak spike-train correlations, the correlation of LFP signals is strong and distance-dependent, compatible with experimental observations. Enhanced spatial coherence in the low-gamma band may explain the recent experimental report of an apparent band-pass filter effect in the spatial reach of the LFP.Comment: 44 pages, 9 figures, 5 table

when channels cooperate or capacitance varies

Die elektrische Signalverarbeitung in Nervenzellen basiert auf deren erregbarer Zellmembran. Üblicherweise wird angenommen, dass die in der Membran eingebetteten leitfähigen Ionenkanäle nicht auf direkte Art gekoppelt sind und dass die Kapazität des von der Membran gebildeten Kondensators konstant ist. Allerdings scheinen diese Annahmen nicht für alle Nervenzellen zu gelten. Im Gegenteil, verschiedene Ionenkanäle “kooperieren” und auch die Vorstellung von einer konstanten spezifischen Membrankapazität wurde kürzlich in Frage gestellt. Die Auswirkungen dieser Abweichungen auf die elektrischen Eigenschaften von Nervenzellen ist das Thema der folgenden kumulativen Dissertationsschrift. Im ersten Projekt wird gezeigt, auf welche Weise stark kooperative spannungsabhängige Ionenkanäle eine Form von zellulärem Kurzzeitspeicher für elektrische Aktivität bilden könnten. Solche kooperativen Kanäle treten in der Membran häufig in kleinen räumlich getrennte Clustern auf. Basierend auf einem mathematischen Modell wird nachgewiesen, dass solche Kanalcluster als eine bistabile Leitfähigkeit agieren. Die dadurch entstehende große Speicherkapazität eines Ensembles dieser Kanalcluster könnte von Nervenzellen für stufenloses persistentes Feuern genutzt werden -- ein Feuerverhalten von Nutzen für das Kurzzeichgedächtnis. Im zweiten Projekt wird ein neues Dynamic Clamp Protokoll entwickelt, der Capacitance Clamp, das erlaubt, Änderungen der Membrankapazität in biologischen Nervenzellen zu emulieren. Eine solche experimentelle Möglichkeit, um systematisch die Rolle der Kapazität zu untersuchen, gab es bisher nicht. Nach einer Reihe von Tests in Simulationen und Experimenten wurde die Technik mit Körnerzellen des *Gyrus dentatus* genutzt, um den Einfluss von Kapazität auf deren Feuerverhalten zu studieren. Die Kombination beider Projekte zeigt die Relevanz dieser oft vernachlässigten Facetten von neuronalen Membranen für die Signalverarbeitung in Nervenzellen.Electrical signaling in neurons is shaped by their specialized excitable cell membranes. Commonly, it is assumed that the ion channels embedded in the membrane gate independently and that the electrical capacitance of neurons is constant. However, not all excitable membranes appear to adhere to these assumptions. On the contrary, ion channels are observed to gate cooperatively in several circumstances and also the notion of one fixed value for the specific membrane capacitance (per unit area) across neuronal membranes has been challenged recently. How these deviations from the original form of conductance-based neuron models affect their electrical properties has not been extensively explored and is the focus of this cumulative thesis. In the first project, strongly cooperative voltage-gated ion channels are proposed to provide a membrane potential-based mechanism for cellular short-term memory. Based on a mathematical model of cooperative gating, it is shown that coupled channels assembled into small clusters act as an ensemble of bistable conductances. The correspondingly large memory capacity of such an ensemble yields an alternative explanation for graded forms of cell-autonomous persistent firing – an observed firing mode implicated in working memory. In the second project, a novel dynamic clamp protocol -- the capacitance clamp -- is developed to artificially modify capacitance in biological neurons. Experimental means to systematically investigate capacitance, a basic parameter shared by all excitable cells, had previously been missing. The technique, thoroughly tested in simulations and experiments, is used to monitor how capacitance affects temporal integration and energetic costs of spiking in dentate gyrus granule cells. Combined, the projects identify computationally relevant consequences of these often neglected facets of neuronal membranes and extend the modeling and experimental techniques to further study them

Phenomenological modeling of diverse and heterogeneous synaptic dynamics at natural density

This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement them in software, and perform simulations reflecting experiments. This path is demonstrated with respect to four key aspects of synaptic signaling: the connectivity of brain networks, synaptic transmission, synaptic plasticity, and the heterogeneity across synapses. Each step and aspect of the modeling and simulation workflow comes with its own challenges and pitfalls, which are highlighted and addressed in detail.Comment: 35 pages, 3 figure

Local signal processing in mouse horizontal cell dendrites

Most neurons in the central nervous system have elaborate dendritic arbours which come in a large variety of sizes and morphologies (Lefebvre et al., 2015). For many decades, dendrites have been thought to simply relay presynaptic signals to the soma and to the axon terminal system by acting as “passive cables”. However, it has become clear that dendrites are capable of much more than passively integrating synaptic input, they can also act independently and modulate presynaptic signals (reviewed by Branco and Häusser, 2010). Dendritic signal processing has been reported to support sophisticated functions in the cortex, hippocampus, and cerebellum as well as in the retina. In the latter case, multiple processing within one dendrite is essential to process considerable amounts of information from the outside world but, at the same time to use space efficiently: The retina needs to be thin and transparent to reduce light scattering within the tissue. Dendritic processing has already been described in inner retinal neurons (Euler et al., 2002; Grimes et al., 2010; Oesch et al., 2005; Sivyer and Williams, 2013). In the outer retina, the horizontal cell (HC) dendrites, which are directly postsynaptic to the cone photoreceptors (cones) have recently been suggested to be plausible candidates for local signal processing (Grassmeyer and Thoreson, 2017; Jackman et al., 2011; Vroman et al., 2014) despite their involvement in global tasks such as contrast enhancement. To test this hypothesis physiologically, I used two-photon imaging to record calcium (Ca2+) signals in cones and HCs, as well as, cone glutamate release in mouse retinal slices. I used green (578 nm) and ultra violet (UV, 360 nm) light stimuli and recorded from different retinal regions to specifically activate different combinations of medium (M-) and short (S-) wavelength-sensitive opsin expressed in cones. This approach allowed to assess if signals from individual cones remain “isolated” within a local dendritic region of a HC, or if they spread across the entire dendritic tree or, in the electrically coupled HC network. In contrast to what one would expect in a purely globally acting HC (network), responses measured in neighbouring HC compartments varied markedly in their chromatic preference suggesting that HC dendrites are able to process cone input in a highly local manner. Moreover, I found local HC feedback to play a role in shaping the temporal properties of cone output

Synaptic consolidation: from synapses to behavioral modeling

Synaptic plasticity, a key process for memory formation, manifests itself across different time scales ranging from a few seconds for plasticity induction up to hours or even years for consolidation and memory retention. We developed a three-layered model of synaptic consolidation that accounts for data across a large range of experimental conditions. Consolidation occurs in the model through the interaction of the synaptic efficacy with a scaffolding variable by a read-write process mediated by a tagging-related variable. Plasticity-inducing stimuli modify the efficacy, but the state of tag and scaffold can only change if a write protection mechanism is overcome. Our model makes a link from depotentiation protocols in vitro to behavioral results regarding the influence of novelty on inhibitory avoidance memory in rats

Neuronal filopodia borne along tips and shafts of dendrites comprise two distinct populations as evidenced by differences in structure and dynamics

Ever since their discovery in 1880 by Ramon y Cajal, dendritic spines have evoked considerable interest in the field of cellular and molecular neuroscience. Subsequent studies into their morphogenesis, and into synaptogenesis, brought into the spotlight their putative precursors – the dendritic filopodia. This set off several lines of investigation into filopodial structure and function, notable among which is the work by Portera-Cailliau et al. who showed in 2003 that growth cone filopodia differ from shaft filopodia in terms of densities and lengths, and in their response to blocking of synaptic transmission, and of ionotropic glutamate receptors. However, they observed these differences only up to postnatal day 5. In 2010, Korobova and Svitkina reported the existence of a different actin organization in shaft filopodia at 10 days in vitro (DIV). This work fills the gap between those two studies, investigating differences between tip and shaft filopodia at 4, 7, 10 and 14 DIV, and examining structure and dynamics, as well as responses to developmental cues, specifically, Semaphorin3A (Sema3A). Using confocal microscopy to visualize filopodial membrane and actin we found that shaft filopodia are shorter than tip filopodia, and show a less dense presentation along the dendrite. We then employed the quantitative phase imaging technology of Spatial Light Interference Microscopy (SLIM) for analysis of mass change dynamics of individual filopodia. We found that tip and shaft filopodia show similar dynamics early on, but further on in development by 7 DIV shaft filopodia slow down considerably while tip filopodia continue to show fast increases and decreases in mass. Further analysis of growth rates showed that both types filopodia exhibit exponential growth during their extension, implying that the bigger the filopodium the faster it grows. Next we sought to examine the functional ramifications of these differences in tip and shaft filopodia. We investigated the differential responses of the two populations to Sema3A. We found that a 24 h exposure to Sema3A at 0-1 DIV leads to accelerated maturation of shaft filopodia as evidenced by (1) an increase in dendritic branching, (2) an acceleration of maturation into spines, and (3) into synapses. An analysis of the underlying dynamics showed that Sema3A treatment results in (1) tip filopodial movement becoming more deterministic, (2) an increase in average growth and shrinkage rates in shaft filopodia, and, (3) an increase in speed of the fastest growth and shrinkage in tip and shaft filopodia at 4 and 7 DIV. Together these findings show that Sema3A is a unique cue that acts on both tip filopodia and shaft filopodia, but with different outcomes – the former to increase dendrite lengths, and the latter to increase branching, spinogenesis and synaptogenesis. Bath application of Sema3A also elicits an axonal response, which might itself affect the cells as a whole, and could confound the filopodial read out. To avoid this, we supplemented bath application studies with investigations using microfluidic devices that enable focal, dendrite specific application of Sema3A, and, also, better replicate the in vivo layered structure of the hippocampus. Our results held true even with this sub-cellular administration of Sema3A. Taken together our findings provide further evidence for differences in the two dendritic filopodial populations – those borne on the tips, and those along the shafts, and help deconstruct the role of Sema3A in dendritic development. A greater comprehension of this diversity in the filopodial population, and its role in shaping the development of neuronal networks will not only further our understanding of the nervous system, but will also help unravel the mechanistic bases of developmental disorders and diseases

Modelling human choices: MADeM and decision‑making

Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)

CA1 pyramidal cells as computational units: From inputs to output

Pyramidal cells of the CA1 area in the hippocampus are one of the most studied neurons nowadays due to their role in memory formation or spatial navigation. CA1 pyramidal cells possess an apical dendrite which receives excitatory synaptic input mainly from CA3 axons. To better understand apical synaptic input to these neurons, a new recording technique is proposed to measure excitatory synaptic input applied onto neurons. First, the theoretical derivations are presented. Then, the technique is applied to measure CA1 pyramidal cells and finally a computational model studies in depth the influence of the distance between synaptic input and recording on the estimation. The conclusion is that the method cannot improve current experimental techniques. In addition, in some cases the axon of a neuron stems out of a dendrite rather than out of the soma. This particular morphology favors synaptic inputs onto this dendrite to generate action potentials. A computational model is applied to characterize the propagation of synapses from dendrites to the axon in a neuron with this feature. The model shows that electronic propagation is responsible of this favorable action potential generation. Finally, extracellular stimulation of the axons of CA1 pyramidal cells generates ectopic action potentials with a bimodal distribution of time to arrive to the soma. The computational model suggests that this bimodal distribution is due to two different sites of action potential initiation, namely the axon initial segment and the first node of ranvier