Fast state-space methods for inferring dendritic synaptic connectivity

We present fast methods for filtering voltage measurements and performing optimal inference of the location and strength of synaptic connections in large dendritic trees. Given noisy, subsampled voltage observations we develop fast l[subscript 1]-penalized regression methods for Kalman state-space models of the neuron voltage dynamics. The value of the l[subscript 1]-penalty parameter is chosen using cross-validation or, for low signal-to-noise ratio, a Mallows’ C[subscript p]-like criterion. Using low-rank approximations, we reduce the inference runtime from cubic to linear in the number of dendritic compartments. We also present an alternative, fully Bayesian approach to the inference problem using a spike-and-slab prior. We illustrate our results with simulations on toy and real neuronal geometries. We consider observation schemes that either scan the dendritic geometry uniformly or measure linear combinations of voltages across several locations with random coefficients. For the latter, we show how to choose the coefficients to offset the correlation between successive measurements imposed by the neuron dynamics. This results in a “compressed sensing” observation scheme, with an important reduction in the number of measurements required to infer the synaptic weights.National Science Foundation (U.S.) (CAREER Grant)McKnight Foundation (Scholar Award)National Science Foundation (U.S.) (Grant IIS-0904353)Columbia College. Rabi Scholars Progra

Modern Statistical/Machine Learning Techniques for Bio/Neuro-imaging Applications

Developments in modern bio-imaging techniques have allowed the routine collection of a vast amount of data from various techniques. The challenges lie in how to build accurate and efficient models to draw conclusions from the data and facilitate scientific discoveries. Fortunately, recent advances in statistics, machine learning, and deep learning provide valuable tools. This thesis describes some of our efforts to build scalable Bayesian models for four bio-imaging applications: (1) Stochastic Optical Reconstruction Microscopy (STORM) Imaging, (2) particle tracking, (3) voltage smoothing, (4) detect color-labeled neurons in c elegans and assign identity to the detections

Design and implementation of multi-signal and time-varying neural reconstructions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Several efficient procedures exist to digitally trace neuronal structure from light microscopy, and mature community resources have emerged to store, share, and analyze these datasets. In contrast, the quantification of intracellular distributions and morphological dynamics is not yet standardized. Current widespread descriptions of neuron morphology are static and inadequate for subcellular characterizations. We introduce a new file format to represent multichannel information as well as an open-source Vaa3D plugin to acquire this type of data. Next we define a novel data structure to capture morphological dynamics, and demonstrate its application to different time-lapse experiments. Importantly, we designed both innovations as judicious extensions of the classic SWC format, thus ensuring full back-compatibility with popular visualization and modeling tools. We then deploy the combined multichannel/time-varying reconstruction system on developing neurons in live Drosophila larvae by digitally tracing fluorescently labeled cytoskeletal components along with overall dendritic morphology as they changed over time. This same design is also suitable for quantifying dendritic calcium dynamics and tracking arbor-wide movement of any subcellular substrate of interest.Peer reviewe

Developmental and interspecies comparison of morphology and plasticity in neuronal circuits involved in olfactory information processing

The anterior piriform cortex (aPCx) is a three layered paleocortex receiving afferent inputs from the olfactory bulb as well as local and long-range associational inputs. Neurons in layer 2 are segregated into layer 2A and layer 2B according to their position, morphology and implementation in the sensory and associative circuits. The dendritic architecture of these neurons is determined during postnatal development and plays an important role for the functionality and circuit integration of the two cell types. Here, confocal imaging, electrophysiology, morphometry and Ca2+ imaging, were combined in order to study the development of the dendritic arborizations for both subtypes of layer 2 neurons. Three different growth phases were identified: branch complexity determination, branch elongation and pruning, occurring at different time windows during development. Layer 2A and layer 2B neurons showed morphological differences between their apical and basal dendrites from the very first postnatal days; as well as phase-specific differences during development associated to differences in circuit implementation. During the first postnatal week, early spontaneous network activity in layer 2 of the aPCx displayed differences between layer 2A and layer 2B neurons in their functional connectivity, reflected in the morphological dissimilarities between their basal dendritic trees during the period of branch complexity determination. Additionally, strong differences in growth phase three were observed. Pruning was exclusive for layer 2B neurons and selective for apical dendrites receiving layer 1A sensory inputs. These differences between layer 2A and layer 2B cells in their morphological and functional development exhibit the close association between circuit specificity and neuronal development. Finally, synaptic plasticity in the mossy fiber (MF) pathway of the hippocampus in shrews was investigated and compared to mice. Although hippocampal structure in shrews is preserved, short and long-term plasticity at the MF synapsis was lower compared to mice, suggesting different involvement of these synapses in the behavioral outcome of different species.Der Cortex piriformis anterior (aPCx auf Englisch) ist ein dreischichtiger Paläokortex, der sensorische afferente Eingänge aus dem Riechkolben sowie intracerebrale assoziative Eingänge empfängt. Die Neuronen in Schicht 2 werden nach ihrer Position, Morphologie und Einbindung in die sensorischen und rekurrenten Netzwerke in die Schichten 2A und 2B unterteilt. Die dendritische Architektur dieser Neurone wird während der postnatalen Entwicklung festgelegt und spielt eine wichtige Rolle für die Funktionalität und Netzwerkintegration der beiden Zelltypen. Hier wurden konfokales Imaging, Elektrophysiologie, Morphometrie und Kalzium-Imaging kombiniert, um die Entwicklung der Dendritenbäume für beide Subtypen von Schicht-2-Neuronen zu untersuchen. Es wurden drei verschiedene Wachstumsphasen identifiziert: Bestimmung der Komplexität der Verzweigung, Verlängerung der Verzweigung und strukturelle Vereinfachung, die in verschiedenen Zeitfenstern während der Entwicklung auftreten. Neurone der Schicht 2A und der Schicht 2B zeigten bereits in den ersten postnatalen Tagen morphologische Unterschiede zwischen ihren apikalen und basalen Dendriten sowie phasenspezifische Unterschiede während der Entwicklung, die mit Unterschieden in der Netzwerkimplementierung verbunden sind. Während der ersten postnatalen Woche zeigte die frühe spontane Netzwerkaktivität in Schicht 2 des aPCx Unterschiede in der funktionellen Konnektivität zwischen Neuronen der Schicht 2A und Schicht 2B, die sich in den morphologischen Unterschieden zwischen ihren basalen Dendritenbäumen während der Bestimmung der Verzweigungskomplexität widerspiegelten. Außerdem wurden starke Unterschiede in der dritten Wachstumsphase beobachtet. Die strukturelle Vereinfachung fand ausschließlich bei Neuronen der Schicht 2B statt und war selektiv für apikale Dendriten, die sensorische Inputs der Schicht 1A erhielten. Diese Unterschiede zwischen Zellen der Schicht 2A und der Schicht 2B in ihrer morphologischen und funktionellen Entwicklung zeigen den engen Zusammenhang zwischen Netzwerkspezifität und neuronaler Entwicklung. Schließlich wurde die synaptische Plastizität des Moosfaser (MF)-Trakts des Hippocampus bei Spitzmäusen untersucht und mit der von Mäusen verglichen. Obwohl die Struktur des Hippocampus bei Spitzmäusen erhalten ist, war die Kurz- und Langzeitplastizität an den MF-Synapsen im Vergleich zu Mäusen geringer, was auf eine unterschiedliche Beteiligung dieser Synapsen an spezifisch adaptierte Verhaltensweisen der beiden Spezies hindeutet

Characterizing single-cell computation using all-optical interrogation of cortical dendrites in vivo

Pyramidal neurons in the mouse neocortex develop elaborate dendritic compartments that integrate signals to generate stimulus-specific responses. Parameters such as the origin, strength, and location of inputs on the dendritic arbor define computations performed by dendrites to modulate neuronal activity. Although the role of dendrites in synaptic integration has been studied in brain slices in vitro, little is known about how their integrative properties functionally relate to dendritic computations in vivo. The small size of dendrites and mechanical instability of the brain have precluded the use of direct methods such as in vivo patch clamp recording for making functional measurements of dendritic activity during behavior. In this thesis, I have optimized existing optical methods to selectively target and monitor responses in single dendrites in the mouse neocortex, providing a proof-of-principle for all-optical interrogation of dendritic computation. I used an ultra-sparse expression strategy to express the powerful channelrhodopsin ChRmine and the highly sensitive calcium indicator GCaMP8s in Layer 2/3 pyramidal neurons in primary visual cortex (V1) for simultaneous optical stimulation and recording of basal dendrites. Previously, our lab developed a protocol for all-optical interrogation experiments (Russell et al. 2022), using a spatial light modulator (SLM) to activate cellular targets in an awake, head-fixed mouse. We re-configured this approach to optically stimulate single dendritic segments, or combinations of dendritic segments from different dendrites of the same neuron. Challenges included optimizing the relative expression of ChRmine and GCaMP8s in the soma and dendrites to both allow efficient activation and avoid overexpression, as well as calibration of the SLM to reliably target single dendrites (~1-2 µm diameter) while accounting for movement caused by respiration or running. Two-photon imaging of GCaMP8s responses revealed intensity-dependent calcium signals in dendrites with increasing laser power and number of targets. Analysis of somatic activation driven by dendritic optogenetic stimulation revealed supra- or sub-linear summation of multiple dendritic targets depending on the spatial pattern of stimulation. Applying this technique to probe dendritic integration during sensory stimulus processing or animal behavior could provide us with one of the tools needed to understand the role of single-neuron processing in neural computations in the brain

Why Are Computational Neuroscience and Systems Biology So Separate?

Despite similar computational approaches, there is surprisingly little interaction between the computational neuroscience and the systems biology research communities. In this review I reconstruct the history of the two disciplines and show that this may explain why they grew up apart. The separation is a pity, as both fields can learn quite a bit from each other. Several examples are given, covering sociological, software technical, and methodological aspects. Systems biology is a better organized community which is very effective at sharing resources, while computational neuroscience has more experience in multiscale modeling and the analysis of information processing by biological systems. Finally, I speculate about how the relationship between the two fields may evolve in the near future

Low-rank graphical models and Bayesian inference in the statistical analysis of noisy neural data

We develop new methods of Bayesian inference, largely in the context of analysis of neuroscience data. The work is broken into several parts. In the first part, we introduce a novel class of joint probability distributions in which exact inference is tractable. Previously it has been difficult to find general constructions for models in which efficient exact inference is possible, outside of certain classical cases. We identify a class of such models that are tractable owing to a certain "low-rank" structure in the potentials that couple neighboring variables. In the second part we develop methods to quantify and measure information loss in analysis of neuronal spike train data due to two types of noise, making use of the ideas developed in the first part. Information about neuronal identity or temporal resolution may be lost during spike detection and sorting, or precision of spike times may be corrupted by various effects. We quantify the information lost due to these effects for the relatively simple but sufficiently broad class of Markovian model neurons. We find that decoders that model the probability distribution of spike-neuron assignments significantly outperform decoders that use only the most likely spike assignments. We also apply the ideas of the low-rank models from the first section to defining a class of prior distributions over the space of stimuli (or other covariate) which, by conjugacy, preserve the tractability of inference. In the third part, we treat Bayesian methods for the estimation of sparse signals, with application to the locating of synapses in a dendritic tree. We develop a compartmentalized model of the dendritic tree. Building on previous work that applied and generalized ideas of least angle regression to obtain a fast Bayesian solution to the resulting estimation problem, we describe two other approaches to the same problem, one employing a horseshoe prior and the other using various spike-and-slab priors. In the last part, we revisit the low-rank models of the first section and apply them to the problem of inferring orientation selectivity maps from noisy observations of orientation preference. The relevant low-rank model exploits the self-conjugacy of the von Mises distribution on the circle. Because the orientation map model is loopy, we cannot do exact inference on the low-rank model by the forward backward algorithm, but block-wise Gibbs sampling by the forward backward algorithm speeds mixing. We explore another von Mises coupling potential Gibbs sampler that proves to effectively smooth noisily observed orientation maps