Analysis of development of direction selectivity in retinotectum by a neural circuit model with spike timing-dependent plasticity

A Hybrid CMOS-Memristor Spiking Neural Network Supporting Multiple Learning Rules

Artificial intelligence (AI) is changing the way computing is performed to cope with real-world, ill-defined tasks for which traditional algorithms fail. AI requires significant memory access, thus running into the von Neumann bottleneck when implemented in standard computing platforms. In this respect, low-latency energy-efficient in-memory computing can be achieved by exploiting emerging memristive devices, given their ability to emulate synaptic plasticity, which provides a path to design large-scale brain-inspired spiking neural networks (SNNs). Several plasticity rules have been described in the brain and their coexistence in the same network largely expands the computational capabilities of a given circuit. In this work, starting from the electrical characterization and modeling of the memristor device, we propose a neuro-synaptic architecture that co-integrates in a unique platform with a single type of synaptic device to implement two distinct learning rules, namely, the spike-timing-dependent plasticity (STDP) and the Bienenstock-Cooper-Munro (BCM). This architecture, by exploiting the aforementioned learning rules, successfully addressed two different tasks of unsupervised learning.

An Algorithm Based on a Cable-Nernst Planck Model Predicting Synaptic Activity throughout the Dendritic Arbor with Micron Specificity

Recent technological advances have enabled the recording of neurons in intact circuits with a high spatial and temporal resolution, creating the need for modeling with the same precision. In particular, the development of ultra-fast two-photon microscopy combined with fluorescence-based genetically-encoded Ca²⁺-indicators allows capture of full-dendritic arbor and somatic responses associated with synaptic input and action potential output. The complexity of dendritic arbor structures and distributed patterns of activity over time results in the generation of incredibly rich 4D datasets that are challenging to analyze (Sakaki et al. in Frontiers in Neural Circuits 14:33, 2020). Interpreting neural activity from fluorescence-based Ca²⁺ biosensors is challenging due to non-linear interactions between several factors influencing intracellular calcium ion concentration and its binding to sensors, including the ionic dynamics driven by diffusion, electrical gradients and voltage-gated conductances. To investigate those dynamics, we designed a model based on a Cable-like equation coupled to the Nernst-Planck equations for ionic fluxes in electrolytes. We employ this model to simulate signal propagation and ionic electrodiffusion across a dendritic arbor. Using these simulation results, we then designed an algorithm to detect synapses from Ca²⁺ imaging datasets. We finally apply this algorithm to experimental Ca²⁺-indicator datasets from neurons expressing jGCaMP7s (Dana et al. in Nature Methods 16:649-657, 2019), using full-dendritic arbor sampling in vivo in the Xenopus laevis optic tectum using fast random-access two-photon microscopy. Our model reproduces the dynamics of visual stimulus-evoked jGCaMP7s-mediated calcium signals observed experimentally, and the resulting algorithm allows prediction of the location of synapses across the dendritic arbor. Our study provides a way to predict synaptic activity and location on dendritic arbors, from fluorescence data in the full dendritic arbor of a neuron recorded in the intact and awake developing vertebrate brain.

Activity-dependent Organization of Topographic Neural Circuits

Sensory information in the brain is organized into spatial representations, including retinotopic, somatotopic, and tonotopic maps, as well as ocular dominance columns. The spatial representation of sensory inputs is thought to be a fundamental organizational principle that is important for information processing. Topographic maps are plastic throughout an animal's life, reflecting changes in development and aging of brain circuitry, changes in the periphery and sensory input, and changes in circuitry, for instance in response to experience and learning. Here, we review mechanisms underlying the role of activity in the development, stability and plasticity of topographic maps, focusing on recent work suggesting that the spatial information in the visual field, and the resulting spatiotemporal patterns of activity, provide instructive cues that organize visual projections.

Rhythmogenesis evolves as a consequence of long-term plasticity of inhibitory synapses

Brain rhythms are widely believed to reflect numerous cognitive processes. Changes in rhythmicity have been associated with pathological states. However, the mechanism underlying these rhythms remains unknown. Here, we present a theoretical analysis of the evolvement of rhythm generating capabilities in neuronal circuits. We tested the hypothesis that brain rhythms can be acquired via an intrinsic unsupervised learning process of activity dependent plasticity. Specifically, we focused on spike timing dependent plasticity (STDP) of inhibitory synapses. We detail how rhythmicity can develop via STDP under certain conditions that serve as a natural prediction of the hypothesis. We show how global features of the STDP rule govern and stabilize the resultant rhythmic activity. Finally, we demonstrate how rhythmicity is retained even in the face of synaptic variability. This study suggests a role for inhibitory plasticity that is beyond homeostatic processes.

Small-Volume Effect Enables Robust, Sensitive, and Efficient Information Transfer in the Spine

Why is the spine of a neuron so small that it can contain only small numbers of molecules and reactions inevitably become stochastic? We previously showed that, despite such noisy conditions, the spine exhibits robust, sensitive, and efficient features of information transfer using the probability of Ca²⁺ increase; however, the mechanisms are unknown. In this study, we show that the small volume effect enables robust, sensitive, and efficient information transfer in the spine volume, but not in the cell volume. In the spine volume, the intrinsic noise in reactions becomes larger than the extrinsic noise of input, resulting in robust information transfer despite input fluctuation. In the spine volume, stochasticity makes the Ca²⁺ increase occur with a lower intensity of input, causing higher sensitivity to lower intensity of input. The volume-dependency of information transfer increases its efficiency in the spine volume. Thus, we propose that the small-volume effect is the functional reason why the spine has to be so small.

Cortical amplification models of experience-dependent development of selective columns and response sparsification

The development of direction-selective cortical columns requires visual experience, but the neural circuits and plasticity mechanisms that are responsible for this developmental transition are unknown. To gain insight into the mechanisms that could underlie experience-dependent increases in selectivity, we explored families of cortical amplifier models that enhance weakly biased feedforward signals. Here we focused exclusively on possible contributions of cortico-cortical connections and took feedforward input to be constant. We modeled pairs of interconnected columns that received equal and oppositely biased inputs. In a single-element model of cortical columns, we found two ways that cortical columns could receive biased feedforward input and exhibit strong but unselective responses to stimuli: 1) within-column recurrent excitatory connections could be strong enough to amplify both strong and weak feedforward input, or 2) columns that received differently biased inputs could have strong excitatory cross-connections that destroy selectivity. A Hebbian plasticity rule combined with simulated experience with stimuli weakened these strong cross-connections across cortical columns, allowing the individual columns to respond selectively to their biased inputs. In a model that included both excitatory and inhibitory neurons in each column, an additional means of obtaining selectivity through the cortical circuit was uncovered: cross-column suppression of inhibition-stabilized networks. When each column operated as an inhibition-stabilized network, cross-column excitation onto inhibitory neurons forced competition between the columns but in a manner that did not involve strong null-direction inhibition, consistent with experimental measurements of direction selectivity in visual cortex. Experimental predictions of these possible contributions of cortical circuits are discussed.NEW & NOTEWORTHY Sensory circuits are initially constructed via mechanisms that are independent of sensory experience, but later refinement requires experience. We constructed models of how circuits that receive biased feedforward inputs can be initially unselective and then be modified by experience and plasticity so that the resulting circuit exhibits increased selectivity. We propose that neighboring cortical columns may initially exhibit coupling that is too strong for selectivity. Experience-dependent mechanisms decrease this coupling so individual columns can exhibit selectivity.

Visual Stimulus Speed Does Not Influence the Rapid Emergence of Direction Selectivity in Ferret Visual Cortex

Sensory experience is necessary for the development of some receptive field properties of neurons in primary sensory cortical areas. However, it remains unclear whether the parameters of an individual animal's experience play an instructive role and influence the tuning parameters of cortical sensory neurons as selectivity emerges, or rather whether experience merely permits the completion of processes that are fully seeded at the onset of experience. Here we have examined whether the speed of visual stimuli that are presented to visually naive ferrets can influence the parameters of speed tuning and direction selectivity in cortical neurons. Visual experience is necessary for the development of direction selectivity in carnivores. If, during development, cortical neurons had the flexibility to choose from among different inputs with a range of spatial positions and temporal delays, then correlation-based plasticity mechanisms could instruct the precise spatiotemporal selectivity that underlies speed tuning and direction selectivity, and the parameters of an individual animal's experience would influence the tuning that emerges. Alternatively, the tuning parameters of these neurons may already be established at the onset of visual experience, and experience may merely permit the expression of this tuning. We found that providing different groups of animals with either slow (12.5 deg/s) or fast (50 deg/s) visual stimuli resulted in emergence of direction selectivity, but that speed tuning and direction selectivity were similar in the two groups. These results are more consistent with a permissive role for experience in the development of direction selectivity.SIGNIFICANCE STATEMENT The proper development of brain circuits and neural response properties depends on both nature (factors independent of experience) and nurture (factors dependent on experience). In this study, we examined whether the quality of visual experience of an individual animal influences the development of basic sensory detectors in primary visual cortex. We found that, although visual experience is required for the development of direction selectivity, tuning for stimulus speed could not be altered by specific experience with slow or fast stimuli. These results suggest that the tuning parameters for direction selectivity are specified independently of an animal's sensory experience, and that a range of experiences can promote the proper mature expression of direction selectivity in primary visual cortex.

Optogenetic spatial and temporal control of cortical circuits on a columnar scale

Many circuits in the mammalian brain are organized in a topographic or columnar manner. These circuits could be activated-in ways that reveal circuit function or restore function after disease-by an artificial stimulation system that is capable of independently driving local groups of neurons. Here we present a simple custom microscope called ProjectorScope 1 that incorporates off-the-shelf parts and a liquid crystal display (LCD) projector to stimulate surface brain regions that express channelrhodopsin-2 (ChR2). In principle, local optogenetic stimulation of the brain surface with optical projection systems might not produce local activation of a highly interconnected network like the cortex, because of potential stimulation of axons of passage or extended dendritic trees. However, here we demonstrate that the combination of virally mediated ChR2 expression levels and the light intensity of ProjectorScope 1 is capable of producing local spatial activation with a resolution of ∼200-300 μm. We use the system to examine the role of cortical activity in the experience-dependent emergence of motion selectivity in immature ferret visual cortex. We find that optogenetic cortical activation alone-without visual stimulation-is sufficient to produce increases in motion selectivity, suggesting the presence of a sharpening mechanism that does not require precise spatiotemporal activation of the visual system. These results demonstrate that optogenetic stimulation can sculpt the developing brain.

Refinement and Pattern Formation in Neural Circuits by the Interaction of Traveling Waves with Spike-Timing Dependent Plasticity

Traveling waves in the developing brain are a prominent source of highly correlated spiking activity that may instruct the refinement of neural circuits. A candidate mechanism for mediating such refinement is spike-timing dependent plasticity (STDP), which translates correlated activity patterns into changes in synaptic strength. To assess the potential of these phenomena to build useful structure in developing neural circuits, we examined the interaction of wave activity with STDP rules in simple, biologically plausible models of spiking neurons. We derive an expression for the synaptic strength dynamics showing that, by mapping the time dependence of STDP into spatial interactions, traveling waves can build periodic synaptic connectivity patterns into feedforward circuits with a broad class of experimentally observed STDP rules. The spatial scale of the connectivity patterns increases with wave speed and STDP time constants. We verify these results with simulations and demonstrate their robustness to likely sources of noise. We show how this pattern formation ability, which is analogous to solutions of reaction-diffusion systems that have been widely applied to biological pattern formation, can be harnessed to instruct the refinement of postsynaptic receptive fields. Our results hold for rich, complex wave patterns in two dimensions and over several orders of magnitude in wave speeds and STDP time constants, and they provide predictions that can be tested under existing experimental paradigms. Our model generalizes across brain areas and STDP rules, allowing broad application to the ubiquitous occurrence of traveling waves and to wave-like activity patterns induced by moving stimuli.

In several areas of the developing brain, waves of electrical activity trace out distinct patterns across the nervous tissue. These waves are intricately involved in developmental processes that set up the structural connections of the adult brain, but it is unclear what role the wave patterns play. Here, we examine how the strength of connections in these brain areas may change by a process called spike-timing dependent plasticity, which is sensitive to the precise times at which individual neurons become electrically active. We use mathematical models and simulations to show that interactions between waves and plasticity build highly structured patterns into the connections. The results of our model are analogous to many cases of biological pattern formation seen, for example, in zebra stripes, leopard spots and seashells. An important connectivity pattern we consider is the receptive field, which determines to a large extent the specific function of a neuron. We demonstrate how pattern formation can refine the shape of a receptive field and therefore the specificity of a neuron, and explore several ways in which pattern formation may be disrupted, providing clues regarding pathologies in receptive field development. Our theory makes several predictions that may be tested using existing experimental paradigms.

A proto-architecture for innate directionally selective visual maps

Self-organizing artificial neural networks are a popular tool for studying visual system development, in particular the cortical feature maps present in real systems that represent properties such as ocular dominance (OD), orientation-selectivity (OR) and direction selectivity (DS). They are also potentially useful in artificial systems, for example robotics, where the ability to extract and learn features from the environment in an unsupervised way is important. In this computational study we explore a DS map that is already latent in a simple artificial network. This latent selectivity arises purely from the cortical architecture without any explicit coding for DS and prior to any self-organising process facilitated by spontaneous activity or training. We find DS maps with local patchy regions that exhibit features similar to maps derived experimentally and from previous modeling studies. We explore the consequences of changes to the afferent and lateral connectivity to establish the key features of this proto-architecture that support DS.

Emerging feed-forward inhibition allows the robust formation of direction selectivity in the developing ferret visual cortex

The computation of direction selectivity requires that a cell respond to joint spatial and temporal characteristics of the stimulus that cannot be separated into independent components. Direction selectivity in ferret visual cortex is not present at the time of eye opening but instead develops in the days and weeks following eye opening in a process that requires visual experience with moving stimuli. Classic Hebbian or spike timing-dependent modification of excitatory feed-forward synaptic inputs is unable to produce direction-selective cells from unselective or weakly directionally biased initial conditions because inputs eventually grow so strong that they can independently drive cortical neurons, violating the joint spatial-temporal activation requirement. Furthermore, without some form of synaptic competition, cells cannot develop direction selectivity in response to training with bidirectional stimulation, as cells in ferret visual cortex do. We show that imposing a maximum lateral geniculate nucleus (LGN)-to-cortex synaptic weight allows neurons to develop direction-selective responses that maintain the requirement for joint spatial and temporal activation. We demonstrate that a novel form of inhibitory plasticity, postsynaptic activity-dependent long-term potentiation of inhibition (POSD-LTPi), which operates in the developing cortex at the time of eye opening, can provide synaptic competition and enables robust development of direction-selective receptive fields with unidirectional or bidirectional stimulation. We propose a general model of the development of spatiotemporal receptive fields that consists of two phases: an experience-independent establishment of initial biases, followed by an experience-dependent amplification or modification of these biases via correlation-based plasticity of excitatory inputs that compete against gradually increasing feed-forward inhibition.

A common framework of signal processing in the induction of cerebellar LTD and cortical STDP

Cerebellar long-term depression (LTD) and cortical spike-timing-dependent synaptic plasticity (STDP) are two well-known and well-characterized types of synaptic plasticity. Induction of both types of synaptic plasticity depends on the spike timing, pairing frequency, and pairing numbers of two different sources of spiking. This implies that the induction of synaptic plasticity may share common frameworks in terms of signal processing regardless of the different signaling pathways involved in the two types of synaptic plasticity. Here we propose that both types share common frameworks of signal processing for spike-timing, pairing-frequency, and pairing-numbers detection. We developed system models of both types of synaptic plasticity and analyzed signal processing in the induction of synaptic plasticity. We found that both systems have upstream subsystems for spike-timing detection and downstream subsystems for pairing-frequency and pairing-numbers detection. The upstream systems used multiplication of signals from the feedback filters and nonlinear functions for spike-timing detection. The downstream subsystems used temporal filters with longer time constants for pairing-frequency detection and nonlinear switch-like functions for pairing-numbers detection, indicating that the downstream subsystems serve as a leaky integrate-and-fire system. Thus, our findings suggest that a common conceptual framework for the induction of synaptic plasticity exists despite the differences in molecular species and pathways.

The spike-timing dependence of plasticity

In spike-timing-dependent plasticity (STDP), the order and precise temporal interval between presynaptic and postsynaptic spikes determine the sign and magnitude of long-term potentiation (LTP) or depression (LTD). STDP is widely utilized in models of circuit-level plasticity, development, and learning. However, spike timing is just one of several factors (including firing rate, synaptic cooperativity, and depolarization) that govern plasticity induction, and its relative importance varies across synapses and activity regimes. This review summarizes this broader view of plasticity, including the forms and cellular mechanisms for the spike-timing dependence of plasticity, and, the evidence that spike timing is an important determinant of plasticity in vivo.