Illuminating dendritic function with computational models

Parallel and Recurrent Cascade Models as a Unifying Force for Understanding Sub-cellular Computation

Neurons are very complicated computational devices, incorporating numerous non-linear processes, particularly in their dendrites. Biophysical models capture these processes directly by explicitly modelling physiological variables, such as ion channels, current flow, membrane capacitance, etc. However, another option for capturing the complexities of real neural computation is to use cascade models, which treat individual neurons as a cascade of linear and non-linear operations, akin to a multi-layer artificial neural network. Recent research has shown that cascade models can capture single-cell computation well, but there are still a number of sub-cellular, regenerative dendritic phenomena that they cannot capture, such as the interaction between sodium, calcium, and NMDA spikes in different compartments. Here, we propose that it is possible to capture these additional phenomena using parallel, recurrent cascade models, wherein an individual neuron is modelled as a cascade of parallel linear and non-linear operations that can be connected recurrently, akin to a multi-layer, recurrent, artificial neural network. Given their tractable mathematical structure, we show that neuron models expressed in terms of parallel recurrent cascades can themselves be integrated into multi-layered artificial neural networks and trained to perform complex tasks. We go on to discuss potential implications and uses of these models for artificial intelligence. Overall, we argue that parallel, recurrent cascade models provide an important, unifying tool for capturing single-cell computation and exploring the algorithmic implications of physiological phenomena.

Unique properties of dually innervated dendritic spines in pyramidal neurons of the somatosensory cortex uncovered by 3D correlative light and electron microscopy

Pyramidal neurons (PNs) are covered by thousands of dendritic spines receiving excitatory synaptic inputs. The ultrastructure of dendritic spines shapes signal compartmentalization, but ultrastructural diversity is rarely taken into account in computational models of synaptic integration. Here, we developed a 3D correlative light-electron microscopy (3D-CLEM) approach allowing the analysis of specific populations of synapses in genetically defined neuronal types in intact brain circuits. We used it to reconstruct segments of basal dendrites of layer 2/3 PNs of adult mouse somatosensory cortex and quantify spine ultrastructural diversity. We found that 10% of spines were dually innervated and 38% of inhibitory synapses localized to spines. Using our morphometric data to constrain a model of synaptic signal compartmentalization, we assessed the impact of spinous versus dendritic shaft inhibition. Our results indicate that spinous inhibition is locally more efficient than shaft inhibition and that it can decouple voltage and calcium signaling, potentially impacting synaptic plasticity.

Dendrite enlightenment

Neuronal dendrites acquire complex morphologies during development. These are not just the product of cell-intrinsic developmental programs; rather they are defined in close interaction with the cellular environment. Thus, to understand the molecular cascades that yield appropriate morphologies, it is essential to investigate them in vivo, in the actual complex tissue environment encountered by the differentiating neuron in the developing animal. Particularly, genetic approaches have pointed to factors controlling dendrite differentiation in vivo. These suggest that localized and transient molecular cascades might underlie the formation and stabilization of dendrite branches with neuron type-specific characteristics. Here, I highlight the need for studies of neuronal dendrite differentiation in the animal, the challenges provided by such an approach, and the promising pathways that have recently opened.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

Transcription factor encoding of neuron subtype: Strategies that specify arbor pattern

Dendrite and axon arbors form scaffolds that connect a neuron to its partners; they are patterned to support the specific connectivity and computational requirements of each neuron subtype. Transcription factor networks control the specification of neuron subtypes, and the consequent diversification of their stereotyped arbor patterns during differentiation. We outline how the differentiation trajectories of stereotyped arbors are shaped by hierarchical deployment of precursor cell and postmitotic transcription factors. These transcription factors exert modular control over the dendrite and axon features of a single neuron, create spatial and functional compartmentalization of an arbor, instruct implementation of developmental patterning rules, and exert operational control over the cell biological processes that construct an arbor.

Application of the Mirror Technique for Three-Dimensional Electron Microscopy of Neurochemically Identified GABA-ergic Dendrites

In the nervous system synaptic input arrives chiefly on dendrites and their type and distribution have been assumed pivotal in signal integration. We have developed an immunohistochemistry (IH)-correlated electron microscopy (EM) method – the “mirror” technique – by which synaptic input to entire dendrites of neurochemically identified interneurons (INs) can be mapped due preserving high-fidelity tissue ultrastructure. Hence, this approach allows quantitative assessment of morphometric parameters of synaptic inputs along the whole length of dendrites originating from the parent soma. The method exploits the fact that adjoining sections have truncated or cut cell bodies which appear on the common surfaces in a mirror fashion. In one of the sections the histochemical marker of the GABAergic subtype, calbindin was revealed in cell bodies whereas in the other section the remaining part of the very same cell bodies were subjected to serial section EM to trace and reconstruct the synaptology of entire dendrites. Here, we provide exemplary data on the synaptic coverage of two dendrites belonging to the same calbindin-D_28K immunopositive IN and determine the spatial distribution of asymmetric and symmetric synapses, surface area and volume of the presynaptic boutons, morphometric parameters of synaptic vesicles, and area extent of the active zones.

Activation function dependence of the storage capacity of treelike neural networks

The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions. Though a wide variety of nonlinear activation functions have been proposed for use in artificial neural networks, a detailed understanding of their role in determining the expressive power of a network has not emerged. Here, we study how activation functions affect the storage capacity of treelike two-layer networks. We relate the boundedness or divergence of the capacity in the infinite-width limit to the smoothness of the activation function, elucidating the relationship between previously studied special cases. Our results show that nonlinearity can both increase capacity and decrease the robustness of classification, and provide simple estimates for the capacity of networks with several commonly used activation functions. Furthermore, they generate a hypothesis for the functional benefit of dendritic spikes in branched neurons.

Shedding light on learning and memory: optical interrogation of the synaptic circuitry

In the quest for the physical substrate of learning and memory, a consensus gradually emerges that memory traces are stored in specific neuronal populations and the synaptic circuits that connect them. In this review, we discuss recent progresses in understanding the reorganization of synaptic circuits and neuronal assemblies associated with learning and memory, with an emphasis on optical techniques for in vivo interrogations. We also highlight some open questions on the missing link between synaptic modifications and neuronal coding, and how stable memory persists despite synaptic and neuronal fluctuations.

Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction

Class I ventral posterior dendritic arborisation (c1vpda) proprioceptive sensory neurons respond to contractions in the Drosophila larval body wall during crawling. Their dendritic branches run along the direction of contraction, possibly a functional requirement to maximise membrane curvature during crawling contractions. Although the molecular machinery of dendritic patterning in c1vpda has been extensively studied, the process leading to the precise elaboration of their comb-like shapes remains elusive. Here, to link dendrite shape with its proprioceptive role, we performed long-term, non-invasive, in vivo time-lapse imaging of c1vpda embryonic and larval morphogenesis to reveal a sequence of differentiation stages. We combined computer models and dendritic branch dynamics tracking to propose that distinct sequential phases of stochastic growth and retraction achieve efficient dendritic trees both in terms of wire and function. Our study shows how dendrite growth balances structure-function requirements, shedding new light on general principles of self-organisation in functionally specialised dendrites.

Inhibitory stabilization and cortical computation

Neuronal networks with strong recurrent connectivity provide the brain with a powerful means to perform complex computational tasks. However, high-gain excitatory networks are susceptible to instability, which can lead to runaway activity, as manifested in pathological regimes such as epilepsy. Inhibitory stabilization offers a dynamic, fast and flexible compensatory mechanism to balance otherwise unstable networks, thus enabling the brain to operate in its most efficient regimes. Here we review recent experimental evidence for the presence of such inhibition-stabilized dynamics in the brain and discuss their consequences for cortical computation. We show how the study of inhibition-stabilized networks in the brain has been facilitated by recent advances in the technological toolbox and perturbative techniques, as well as a concomitant development of biologically realistic computational models. By outlining future avenues, we suggest that inhibitory stabilization can offer an exemplary case of how experimental neuroscience can progress in tandem with technology and theory to advance our understanding of the brain.

Predicting brain organization with a computational model: 50-year perspective on lateral inhibition and oscillatory gating by dendrodendritic synapses

The first compartmental computer models of brain neurons using the Rall method predicted novel and unexpected dendrodendritic interactions between mitral and granule cells in the olfactory bulb. We review the models from a 50-year perspective on the work that has challenged, supported, and extended the original proposal that these interactions mediate both lateral inhibition and oscillatory activity, essential steps in the neural basis of olfactory processing and perception. We highlight strategies behind the neurophysiological experiments and the Rall methods that enhance the ability of detailed compartmental modeling to give counterintuitive predictions that lead to deeper insights into neural organization at the synaptic and circuit level. The application of these methods to mechanisms of neurogenesis and plasticity are exciting challenges for the future.