Synaptic input sequence discrimination on behavioral timescales mediated by reaction-diffusion chemistry in dendrites

Understanding molecular signaling cascades in neural disease using multi-resolution models

If the genome defines the program for the operations of a cell, signaling networks execute it. These cascades of chemical, cell-biological, structural, and trafficking events span milliseconds (e.g., synaptic release) to potentially a lifetime (e.g., stabilization of dendritic spines). In principle almost every aspect of neuronal function, particularly at the synapse, depends on signaling. Thus dysfunction of these cascades, whether through mutations, local dysregulation, or infection, leads to disease. The sheer complexity of these pathways is matched by the range of diseases and the diversity of their phenotypes. In this review, we discuss how to build computational models, how these models are essential to tackle this complexity, and the benefits of using families of models at different levels of detail to understand signaling in health and disease.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

A computational view of short-term plasticity and its implications for E-I balance

Short-term plasticity (STP) and excitatory-inhibitory balance (EI balance) are both ubiquitous building blocks of brain circuits across the animal kingdom. The synapses involved in EI are also subject to short-term plasticity, and several experimental studies have shown that their effects overlap. Recent computational and theoretical work has begun to highlight the functional implications of the intersection of these motifs. The findings are nuanced: while there are general computational themes, such as pattern tuning, normalization, and gating, much of the richness of these interactions comes from region- and modality specific tuning of STP properties. Together these findings point towards the STP-EI balance combination as being a versatile and highly efficient neural building block for a wide range of pattern-specific responses.

Synthetic Data Resource and Benchmarks for Time Cell Analysis and Detection Algorithms

Hippocampal CA1 cells take part in reliable, time-locked activity sequences in tasks that involve an association between temporally separated stimuli, in a manner that tiles the interval between the stimuli. Such cells have been termed time cells. Here, we adopt a first-principles approach to comparing diverse analysis and detection algorithms for identifying time cells. We generated synthetic activity datasets using calcium signals recorded in vivo from the mouse hippocampus using two-photon (2-P) imaging, as template response waveforms. We assigned known, ground truth values to perturbations applied to perfect activity signals, including noise, calcium event width, timing imprecision, hit trial ratio and background (untuned) activity. We tested a range of published and new algorithms and their variants on this dataset. We find that most algorithms correctly classify over 80% of cells, but have different balances between true and false positives, and different sensitivity to the five categories of perturbation. Reassuringly, most methods are reasonably robust to perturbations, including background activity, and show good concordance in classification of time cells. The same algorithms were also used to analyze and identify time cells in experimental physiology datasets recorded in vivo and most show good concordance.

Representing Stimulus Information in an Energy Metabolism Pathway

We explored a computational model of astrocytic energy metabolism and demonstrated the theoretical plausibility that this type of pathway might be capable of coding information about stimuli in addition to its known functions in cellular energy and carbon budgets. Simulation results indicate that glycogenolytic glycolysis triggered by activation of adrenergic receptors can capture the intensity and duration features of a neuromodulator waveform and can respond in a dose-dependent manner, including non-linear state changes that are analogous to action potentials. We show how this metabolic pathway can translate information about external stimuli to production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or non-linear amplification. The results suggest the operation of a metabolic state-machine from the spatially discontiguous yet interdependent metabolite elements. Such metabolic pathways might be well-positioned to code an additional level of salient information about a cell's environmental demands to impact its function. Our hypothesis has implications for the computational power and energy efficiency of the brain.

HillTau: A fast, compact abstraction for model reduction in biochemical signaling networks

Signaling networks mediate many aspects of cellular function. The conventional, mechanistically motivated approach to modeling such networks is through mass-action chemistry, which maps directly to biological entities and facilitates experimental tests and predictions. However such models are complex, need many parameters, and are computationally costly. Here we introduce the HillTau form for signaling models. HillTau retains the direct mapping to biological observables, but it uses far fewer parameters, and is 100 to over 1000 times faster than ODE-based methods. In the HillTau formalism, the steady-state concentration of signaling molecules is approximated by the Hill equation, and the dynamics by a time-course tau. We demonstrate its use in implementing several biochemical motifs, including association, inhibition, feedforward and feedback inhibition, bistability, oscillations, and a synaptic switch obeying the BCM rule. The major use-cases for HillTau are system abstraction, model reduction, scaffolds for data-driven optimization, and fast approximations to complex cellular signaling.

Chemical signals mediate many computations in cells, from housekeeping functions in all cells to memory and pattern selectivity in neurons. These signals form complex networks of interactions. Computer models are a powerful way to study how such networks behave, but it is hard to get all the chemical details for typical models, and it is slow to run them with standard numerical approaches to chemical kinetics. We introduce HillTau as a simplified way to model complex chemical networks. HillTau models condense multiple reaction steps into single steps defined by a small number of parameters for activation and settling time. As a result the models are simple, easy to find values for, and they run quickly. Remarkably, they fit the full chemical formulations rather well. We illustrate the utility of HillTau for modeling several signaling network functions, and for fitting complicated signaling networks.

A synaptic learning rule for exploiting nonlinear dendritic computation

Information processing in the brain depends on the integration of synaptic input distributed throughout neuronal dendrites. Dendritic integration is a hierarchical process, proposed to be equivalent to integration by a multilayer network, potentially endowing single neurons with substantial computational power. However, whether neurons can learn to harness dendritic properties to realize this potential is unknown. Here, we develop a learning rule from dendritic cable theory and use it to investigate the processing capacity of a detailed pyramidal neuron model. We show that computations using spatial or temporal features of synaptic input patterns can be learned, and even synergistically combined, to solve a canonical nonlinear feature-binding problem. The voltage dependence of the learning rule drives coactive synapses to engage dendritic nonlinearities, whereas spike-timing dependence shapes the time course of subthreshold potentials. Dendritic input-output relationships can therefore be flexibly tuned through synaptic plasticity, allowing optimal implementation of nonlinear functions by single neurons.

Computation, wiring, and plasticity in synaptic clusters

Synaptic clusters on dendrites are extraordinarily compact computational building blocks. They contribute to key local computations through biophysical and biochemical signaling that utilizes convergence in space and time as an organizing principle. However, these computations can only arise in very special contexts. Dendritic cluster computations, their highly organized input connectivity, and the mechanisms for their formation are closely linked, yet these have not been analyzed as parts of a single process. Here, we examine these linkages. The sheer density of axonal and dendritic arborizations means that there are far more potential connections (close enough for a spine to reach an axon) than actual ones. We see how dendritic clusters draw upon electrical, chemical, and mechano-chemical signaling to implement the rules for formation of connections and subsequent computations. Crucially, the same mechanisms that underlie their functions also underlie their formation.

Temporal pattern and synergy influence activity of ERK signaling pathways during L-LTP induction

Long-lasting long-term potentiation (L-LTP) is a cellular mechanism of learning and memory storage. Studies have demonstrated a requirement for extracellular signal-regulated kinase (ERK) activation in L-LTP produced by a diversity of temporal stimulation patterns. Multiple signaling pathways converge to activate ERK, with different pathways being required for different stimulation patterns. To answer whether and how different temporal patterns select different signaling pathways for ERK activation, we developed a computational model of five signaling pathways (including two novel pathways) leading to ERK activation during L-LTP induction. We show that calcium and cAMP work synergistically to activate ERK and that stimuli given with large intertrial intervals activate more ERK than shorter intervals. Furthermore, these pathways contribute to different dynamics of ERK activation. These results suggest that signaling pathways with different temporal sensitivities facilitate ERK activation to diversity of temporal patterns.

Presynaptic endoplasmic reticulum regulates short-term plasticity in hippocampal synapses

Short-term plasticity preserves a brief history of synaptic activity that is communicated to the postsynaptic neuron. This is primarily regulated by a calcium signal initiated by voltage dependent calcium channels in the presynaptic terminal. Imaging studies of CA3-CA1 synapses reveal the presence of another source of calcium, the endoplasmic reticulum (ER) in all presynaptic terminals. However, the precise role of the ER in modifying STP remains unexplored. We performed in-silico experiments in synaptic geometries based on reconstructions of the rat CA3-CA1 synapses to investigate the contribution of ER. Our model predicts that presynaptic ER is critical in generating the observed short-term plasticity profile of CA3-CA1 synapses and allows synapses with low release probability to operate more reliably. Blocking the ER lowers facilitation in a manner similar to what has been previously characterized in animal models of Alzheimer's disease and underscores the important role played by presynaptic stores in normal function.

Somatodendritic consistency check for temporal feature segmentation

The brain identifies potentially salient features within continuous information streams to process hierarchical temporal events. This requires the compression of information streams, for which effective computational principles are yet to be explored. Backpropagating action potentials can induce synaptic plasticity in the dendrites of cortical pyramidal neurons. By analogy with this effect, we model a self-supervising process that increases the similarity between dendritic and somatic activities where the somatic activity is normalized by a running average. We further show that a family of networks composed of the two-compartment neurons performs a surprisingly wide variety of complex unsupervised learning tasks, including chunking of temporal sequences and the source separation of mixed correlated signals. Common methods applicable to these temporal feature analyses were previously unknown. Our results suggest the powerful ability of neural networks with dendrites to analyze temporal features. This simple neuron model may also be potentially useful in neural engineering applications.

The authors propose a learning rule for a neuron model with dendrite. In their model, somatodendritic interaction implements self-supervised learning applicable to a wide range of sequence learning tasks, including spike pattern detection, chunking temporal input and blind source separation.

Geometric principles of second messenger dynamics in dendritic spines

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

The Role of Hierarchical Dynamical Functions in Coding for Episodic Memory and Cognition

Behavioral research in human verbal memory function led to the initial definition of episodic memory and semantic memory. A complete model of the neural mechanisms of episodic memory must include the capacity to encode and mentally reconstruct everything that humans can recall from their experience. This article proposes new model features necessary to address the complexity of episodic memory encoding and recall in the context of broader cognition and the functional properties of neurons that could contribute to this broader scope of memory. Many episodic memory models represent individual snapshots of the world with a sequence of vectors, but a full model must represent complex functions encoding and retrieving the relations between multiple stimulus features across space and time on multiple hierarchical scales. Episodic memory involves not only the space and time of an agent experiencing events within an episode but also features shown in neurophysiological data such as coding of speed, direction, boundaries, and objects. Episodic memory includes not only a spatio-temporal trajectory of a single agent but also segments of spatio-temporal trajectories for other agents and objects encountered in the environment consistent with data on encoding the position and angle of sensory features of objects and boundaries. We will discuss potential interactions of episodic memory circuits in the hippocampus and entorhinal cortex with distributed neocortical circuits that must represent all features of human cognition.

NetPyNE, a tool for data-driven multiscale modeling of brain circuits

Biophysical modeling of neuronal networks helps to integrate and interpret rapidly growing and disparate experimental datasets at multiple scales. The NetPyNE tool (www.netpyne.org) provides both programmatic and graphical interfaces to develop data-driven multiscale network models in NEURON. NetPyNE clearly separates model parameters from implementation code. Users provide specifications at a high level via a standardized declarative language, for example connectivity rules, to create millions of cell-to-cell connections. NetPyNE then enables users to generate the NEURON network, run efficiently parallelized simulations, optimize and explore network parameters through automated batch runs, and use built-in functions for visualization and analysis - connectivity matrices, voltage traces, spike raster plots, local field potentials, and information theoretic measures. NetPyNE also facilitates model sharing by exporting and importing standardized formats (NeuroML and SONATA). NetPyNE is already being used to teach computational neuroscience students and by modelers to investigate brain regions and phenomena.

From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity

Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.

Adenosine A1 Receptor-Mediated Attenuation of Reciprocal Dendro-Dendritic Inhibition in the Mouse Olfactory Bulb

It is well described that A₁ adenosine receptors inhibit synaptic transmission at excitatory synapses in the brain, but the effect of adenosine on reciprocal synapses has not been studied so far. In the olfactory bulb, the majority of synapses are reciprocal dendro-dendritic synapses mediating recurrent inhibition. We studied the effect of A₁ receptor activation on recurrent dendro-dendritic inhibition in mitral cells using whole-cell patch-clamp recordings. Adenosine reduced dendro-dendritic inhibition in wild-type, but not in A₁ receptor knock-out mice. Both NMDA receptor-mediated and AMPA receptor-mediated dendro-dendritic inhibition were attenuated by adenosine, indicating that reciprocal synapses between mitral cells and granule cells as well as parvalbumin interneurons were targeted by A₁ receptors. Adenosine reduced glutamatergic self-excitation and inhibited N-type and P/Q-type calcium currents, but not L-type calcium currents in mitral cells. Attenuated glutamate release, due to A₁ receptor-mediated calcium channel inhibition, resulted in impaired dendro-dendritic inhibition. In behavioral tests we tested the ability of wild-type and A₁ receptor knock-out mice to find a hidden piece of food. Knock-out mice were significantly faster in locating the food. Our results indicate that A₁ adenosine receptors attenuates dendro-dendritic reciprocal inhibition and suggest that they affect odor information processing.

Dendrites, deep learning, and sequences in the hippocampus

The hippocampus places us both in time and space. It does so over remarkably large spans: milliseconds to years, and centimeters to kilometers. This works for sensory representations, for memory, and for behavioral context. How does it fit in such wide ranges of time and space scales, and keep order among the many dimensions of stimulus context? A key organizing principle for a wide sweep of scales and stimulus dimensions is that of order in time, or sequences. Sequences of neuronal activity are ubiquitous in sensory processing, in motor control, in planning actions, and in memory. Against this strong evidence for the phenomenon, there are currently more models than definite experiments about how the brain generates ordered activity. The flip side of sequence generation is discrimination. Discrimination of sequences has been extensively studied at the behavioral, systems, and modeling level, but again physiological mechanisms are fewer. It is against this backdrop that I discuss two recent developments in neural sequence computation, that at face value share little beyond the label "neural." These are dendritic sequence discrimination, and deep learning. One derives from channel physiology and molecular signaling, the other from applied neural network theory - apparently extreme ends of the spectrum of neural circuit detail. I suggest that each of these topics has deep lessons about the possible mechanisms, scales, and capabilities of hippocampal sequence computation.