Neuronal integration of synaptic input in the fluctuation-driven regime

Differences in the consolidation by spontaneous and evoked ripples in the presence of active dendrites

Ripples are a typical form of neural activity in hippocampal neural networks associated with the replay of episodic memories during sleep as well as sleep-related plasticity and memory consolidation. The emergence of ripples has been observed both dependent as well as independent of input from other brain areas and often coincides with dendritic spikes. Yet, it is unclear how input-evoked and spontaneous ripples as well as dendritic excitability affect plasticity and consolidation. Here, we use mathematical modeling to compare these cases. We find that consolidation as well as the emergence of spontaneous ripples depends on a reliable propagation of activity in feed-forward structures which constitute memory representations. This propagation is facilitated by excitable dendrites, which entail that a few strong synapses are sufficient to trigger neuronal firing. In this situation, stimulation-evoked ripples lead to the potentiation of weak synapses within the feed-forward structure and, thus, to a consolidation of a more general sequence memory. However, spontaneous ripples that occur without stimulation, only consolidate a sparse backbone of the existing strong feed-forward structure. Based on this, we test a recently hypothesized scenario in which the excitability of dendrites is transiently enhanced after learning, and show that such a transient increase can strengthen, restructure and consolidate even weak hippocampal memories, which would be forgotten otherwise. Hence, a transient increase in dendritic excitability would indeed provide a mechanism for stabilizing memories.

On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks

Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory. Our study based on extensive bifurcation analyses thus reveal the functional optimality and criticality of structural and physiological parameters in establishing the baseline operating state of local cortical networks.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons allow signals from the cerebellar cortex to influence the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many PC inputs are thought to converge onto each CbN neuron to suppress its firing. It has been proposed that PCs convey information using a rate code, a synchrony and timing code, or both. The influence of PCs on CbN neuron firing was primarily examined for the combined effects of many PC inputs with comparable strengths, and the influence of individual PC inputs has not been extensively studied. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modeling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, individual PC-CbN synapses are suited to concurrently convey rate codes and generate precisely timed responses in CbN neurons. Either synchronous firing or synchronous pauses of PCs promote CbN neuron firing on rapid time scales for nonuniform inputs, but less effectively than for uniform inputs. This is a secondary consequence of variable input sizes elevating the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. These findings may generalize to other brain regions with highly variable inhibitory synapse sizes.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

Role of interneuron subtypes in controlling trial-by-trial output variability in the neocortex

Trial-by-trial variability is a ubiquitous property of neuronal activity in vivo which shapes the stimulus response. Computational models have revealed how local network structure and feedforward inputs shape the trial-by-trial variability. However, the role of input statistics and different interneuron subtypes in this process is less understood. To address this, we investigate the dynamics of stimulus response in a cortical microcircuit model with one excitatory and three inhibitory interneuron populations (PV, SST, VIP). Our findings demonstrate that the balance of inputs to different neuron populations and input covariances are the primary determinants of output trial-by-trial variability. The effect of input covariances is contingent on the input balances. In general, the network exhibits smaller output trial-by-trial variability in a PV-dominated regime than in an SST-dominated regime. Importantly, our work reveals mechanisms by which output trial-by-trial variability can be controlled in a context, state, and task-dependent manner.

How to incorporate biological insights into network models and why it matters

Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large-scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task-oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance.

It's Time to Go Quantum in Medicine

As the field of medicine grows and expands, new scientific developments hold great promise for improving quality of care, clinical research, and the diagnosis and treatment of diseases. Quantum physics is a promising field that intersects with medicine much more than originally understood. In terms of diagnosing different diseases, incorporating quantum mechanics into the study of medicine can allow for efficient diagnosis before symptoms even arise in a patient. Applying theory-based mathematical structures that describe neuron transmission throughout the brain and mind on a quantum scale can help us to better understand neurological diseases in patients. Quantum theory can even give plausible explanations for subtle DNA changes and even telomere reduction in patients who develop cancer. Utilizing quantum theory in the field of medicine can help in understanding and applying treatments for a multitude of different diseases, such as Alzheimer's disease or diverse types of cancer, and even expand upon efficient and reliable diagnosis in clinical settings. Quantum physics is a pertinent advancing field that may have a significant impact on expanding medical care and treatment in the near future. In this review, the application of quantum physics in medicine is discussed.

Heterogeneity of voltage gated sodium current density between neurons decorrelates spiking and suppresses network synchronization in Scn1b null mouse models

Voltage gated sodium channels (VGSCs) are required for action potential initiation and propagation in mammalian neurons. As with other ion channel families, VGSC density varies between neurons. Importantly, sodium current (INa) density variability is reduced in pyramidal neurons of Scn1b null mice. Scn1b encodes the VGSC β1/ β1B subunits, which regulate channel expression, trafficking, and voltage dependent properties. Here, we investigate how variable INa density in cortical layer 6 and subicular pyramidal neurons affects spike patterning and network synchronization. Constitutive or inducible Scn1b deletion enhances spike timing correlations between pyramidal neurons in response to fluctuating stimuli and impairs spike-triggered average current pattern diversity while preserving spike reliability. Inhibiting INa with a low concentration of tetrodotoxin similarly alters patterning without impairing reliability, with modest effects on firing rate. Computational modeling shows that broad INa density ranges confer a similarly broad spectrum of spike patterning in response to fluctuating synaptic conductances. Network coupling of neurons with high INa density variability displaces the coupling requirements for synchronization and broadens the dynamic range of activity when varying synaptic strength and network topology. Our results show that INa heterogeneity between neurons potently regulates spike pattern diversity and network synchronization, expanding VGSC roles in the nervous system.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons convey signals from the cerebellar cortex to the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many uniform sized PC inputs are thought to converge onto each CbN neuron to suppress or eliminate firing. Leading theories maintain that PCs encode information using either a rate code, or by synchrony and precise timing. Individual PCs are thought to have limited influence on CbN neuron firing. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modelling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, PC-CbN synapses are suited to concurrently convey rate codes, and generate precisely-timed responses in CbN neurons. Variable input sizes also elevate the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. Although this reduces the relative influence of PC synchrony on the firing rate of CbN neurons, synchrony can still have important consequences, because synchronizing even two large inputs can significantly increase CbN neuron firing. These findings may be generalized to other brain regions with highly variable sized synapses.

On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks

Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory.

Noise Enhancement of Neural Information Processing

Cortical neurons in vivo function in highly fluctuating and seemingly noisy conditions, and the understanding of how information is processed in such complex states is still incomplete. In this perspective article, we first overview that an intense "synaptic noise" was measured first in single neurons, and computational models were built based on such measurements. Recent progress in recording techniques has enabled the measurement of highly complex activity in large numbers of neurons in animals and human subjects, and models were also built to account for these complex dynamics. Here, we attempt to link these two cellular and population aspects, where the complexity of network dynamics in awake cortex seems to link to the synaptic noise seen in single cells. We show that noise in single cells, in networks, or structural noise, all participate to enhance responsiveness and boost the propagation of information. We propose that such noisy states are fundamental to providing favorable conditions for information processing at large-scale levels in the brain, and may be involved in sensory perception.

Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants

We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations and computer codes based on combinatorial recursions are included.

Mean-field based framework for forward modeling of LFP and MEG signals

The use of mean-field models to describe the activity of large neuronal populations has become a very powerful tool for large-scale or whole brain simulations. However, the calculation of brain signals from mean-field models, such as the electric and magnetic fields, is still under development. Thus, the emergence of new methods for an accurate and efficient calculation of such brain signals is currently of great relevance. In this paper we propose a novel method to calculate the local field potentials (LFP) and magnetic fields from mean-field models. The calculation of LFP is done via a kernel method based on unitary LFP's (the LFP generated by a single axon) that was recently introduced for spiking-networks simulations and that we adapt here for mean-field models. The calculation of the magnetic field is based on current-dipole and volume-conductor models, where the secondary currents (due to the conducting extracellular medium) are estimated using the LFP calculated via the kernel method and the effects of medium-inhomogeneities are incorporated. We provide an example of the application of our method for the calculation of LFP and MEG under slow-waves of neuronal activity generated by a mean-field model of a network of Adaptive-Exponential Integrate-and-Fire (AdEx) neurons. We validate our method via comparison with results obtained from the corresponding spiking neuronal networks. Finally we provide an example of our method for whole brain simulations performed with The Virtual Brain (TVB), a recently developed tool for large scale simulations of the brain. Our method provides an efficient way of calculating electric and magnetic fields from mean-field models. This method exhibits a great potential for its application in large-scale or whole-brain simulations, where calculations via detailed biological models are not feasible.

A neuronal basis of iconic memory in macaque primary visual cortex

After a briefly presented visual stimulus disappears, observers retain a detailed representation of this stimulus for a short period of time. This sensory storage is called iconic memory. We measured iconic memory in the perception of monkeys and its neuronal correlates in the primary visual cortex (area V1). We determined how many milliseconds extra viewing time iconic memory is worth and how it decays by varying the duration of a brief stimulus and the timing of a mask. The V1 activity that persists after the disappearance of a stimulus predicted accuracy, with a time course resembling the worth and decay of iconic memory. Finally, we examined how iconic memory interacts with attention. A cue presented after the stimulus disappears boosts attentional influences pertaining to a relevant part of the stimulus but only if it appears before iconic memory decayed. Our results relate iconic memory to neuronal activity in early visual cortex.

Spontaneous traveling waves naturally emerge from horizontal fiber time delays and travel through locally asynchronous-irregular states

Studies of sensory-evoked neuronal responses often focus on mean spike rates, with fluctuations treated as internally-generated noise. However, fluctuations of spontaneous activity, often organized as traveling waves, shape stimulus-evoked responses and perceptual sensitivity. The mechanisms underlying these waves are unknown. Further, it is unclear whether waves are consistent with the low rate and weakly correlated “asynchronous-irregular” dynamics observed in cortical recordings. Here, we describe a large-scale computational model with topographically-organized connectivity and conduction delays relevant to biological scales. We find that spontaneous traveling waves are a general property of these networks. The traveling waves that occur in the model are sparse, with only a small fraction of neurons participating in any individual wave. Consequently, they do not induce measurable spike correlations and remain consistent with locally asynchronous irregular states. Further, by modulating local network state, they can shape responses to incoming inputs as observed in vivo.

Spontaneous traveling cortical waves shape neural responses. Using a large-scale computational model, the authors show that transmission delays shape locally asynchronous spiking dynamics into traveling waves without inducing correlations and boost responses to external input, as observed in vivo.

Nonlinear collision between propagating waves in mouse somatosensory cortex

How does cellular organization shape the spatio-temporal patterns of activity in the cortex while processing sensory information? After measuring the propagation of activity in the mouse primary somatosensory cortex (S1) in response to single whisker deflections with Voltage Sensitive Dye (VSD) imaging, we developed a two dimensional model of S1. We designed an inference method to reconstruct model parameters from VSD data, revealing that a spatially heterogeneous organization of synaptic strengths between pyramidal neurons in S1 is likely to be responsible for the heterogeneous spatio-temporal patterns of activity measured experimentally. The model shows that, for strong enough excitatory cortical interactions, whisker deflections generate a propagating wave in S1. Finally, we report that two consecutive stimuli activating different spatial locations in S1 generate two waves which collide sub-linearly, giving rise to a suppressive wave. In the inferred model, the suppressive wave is explained by a lower sensitivity to external perturbations of neural networks during activated states.

Assessment of optogenetically-driven strategies for prosthetic restoration of cortical vision in large-scale neural simulation of V1

The neural encoding of visual features in primary visual cortex (V1) is well understood, with strong correlates to low-level perception, making V1 a strong candidate for vision restoration through neuroprosthetics. However, the functional relevance of neural dynamics evoked through external stimulation directly imposed at the cortical level is poorly understood. Furthermore, protocols for designing cortical stimulation patterns that would induce a naturalistic perception of the encoded stimuli have not yet been established. Here, we demonstrate a proof of concept by solving these issues through a computational model, combining (1) a large-scale spiking neural network model of cat V1 and (2) a virtual prosthetic system transcoding the visual input into tailored light-stimulation patterns which drive in situ the optogenetically modified cortical tissue. Using such virtual experiments, we design a protocol for translating simple Fourier contrasted stimuli (gratings) into activation patterns of the optogenetic matrix stimulator. We then quantify the relationship between spatial configuration of the imposed light pattern and the induced cortical activity. Our simulations in the absence of visual drive (simulated blindness) show that optogenetic stimulation with a spatial resolution as low as 100 [Formula: see text]m, and light intensity as weak as [Formula: see text] photons/s/cm[Formula: see text] is sufficient to evoke activity patterns in V1 close to those evoked by normal vision.

Short-Term Synaptic Plasticity Makes Neurons Sensitive to the Distribution of Presynaptic Population Firing Rates

The ability to discriminate spikes that encode a particular stimulus from spikes produced by background activity is essential for reliable information processing in the brain. We describe how synaptic short-term plasticity (STP) modulates the output of presynaptic populations as a function of the distribution of the spiking activity and find a strong relationship between STP features and sparseness of the population code, which could solve this problem. Furthermore, we show that feedforward excitation followed by inhibition (FF-EI), combined with target-dependent STP, promote substantial increase in the signal gain even for considerable deviations from the optimal conditions, granting robustness to this mechanism. A simulated neuron driven by a spiking FF-EI network is reliably modulated as predicted by a rate analysis and inherits the ability to differentiate sparse signals from dense background activity changes of the same magnitude, even at very low signal-to-noise conditions. We propose that the STP-based distribution discrimination is likely a latent function in several regions such as the cerebellum and the hippocampus.

Feed-forward and noise-tolerant detection of feature homogeneity in spiking networks with a latency code

In studies of the visual system as well as in computer vision, the focus is often on contrast edges. However, the primate visual system contains a large number of cells that are insensitive to spatial contrast and, instead, respond to uniform homogeneous illumination of their visual field. The purpose of this information remains unclear. Here, we propose a mechanism that detects feature homogeneity in visual areas, based on latency coding and spike time coincidence, in a purely feed-forward and therefore rapid manner. We demonstrate how homogeneity information can interact with information on contrast edges to potentially support rapid image segmentation. Furthermore, we analyze how neuronal crosstalk (noise) affects the mechanism's performance. We show that the detrimental effects of crosstalk can be partly mitigated through delayed feed-forward inhibition that shapes bi-phasic post-synaptic events. The delay of the feed-forward inhibition allows effectively controlling the size of the temporal integration window and, thereby, the coincidence threshold. The proposed model is based on single-spike latency codes in a purely feed-forward architecture that supports low-latency processing, making it an attractive scheme of computation in spiking neuronal networks where rapid responses and low spike counts are desired.

Modulation of intercolumnar synchronization by endogenous electric fields in cerebral cortex

Neurons synaptically interacting in a conductive medium generate extracellular endogenous electric fields (EFs) that reciprocally affect membrane potential. Exogenous EFs modulate neuronal activity, and their clinical applications are being profusely explored. However, whether endogenous EFs contribute to network synchronization remains unclear. We analyzed spontaneously generated slow-wave activity in the cerebral cortex network in vitro, which allowed us to distinguish synaptic from nonsynaptic mechanisms of activity propagation and synchronization. Slow oscillations generated EFs that propagated independently of synaptic transmission. We demonstrate that cortical oscillations modulate spontaneous rhythmic activity of neighboring synaptically disconnected cortical columns if layers are aligned. We provide experimental evidence that these EF-mediated effects are compatible with electric dipoles. With a model of interacting dipoles, we reproduce the experimental measurements and predict that endogenous EF-mediated synchronizing effects should be relevant in the brain. Thus, experiments and models suggest that electric-dipole interactions contribute to synchronization of neighboring cortical columns.

On the rate coding response of peripheral sensory neurons

The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge is required. The theoretical expression shows good agreement with spike-frequency adaptation data across different sensory modalities and animal species. The approach permits the discovery of a new neurophysiological equation and shares similarities with statistical physics.

Nonstationary shot noise modeling of neuron membrane potentials by closed-form moments and Gram-Charlier expansions

We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram-Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. This approach extends the results of Brigham and Destexhe (Preprint, 2015a; Phys Rev E 91:062102, 2015b) by the use of exact combinatorial expressions for the moments of multiplicative nonstationary filtered shot noise processes. Our results are confirmed by stochastic simulations and apply to single- and multiple-noise-source models.

Nonlinear stimulus representations in neural circuits with approximate excitatory-inhibitory balance

Balanced excitation and inhibition is widely observed in cortex. How does this balance shape neural computations and stimulus representations? This question is often studied using computational models of neuronal networks in a dynamically balanced state. But balanced network models predict a linear relationship between stimuli and population responses. So how do cortical circuits implement nonlinear representations and computations? We show that every balanced network architecture admits stimuli that break the balanced state and these breaks in balance push the network into a "semi-balanced state" characterized by excess inhibition to some neurons, but an absence of excess excitation. The semi-balanced state produces nonlinear stimulus representations and nonlinear computations, is unavoidable in networks driven by multiple stimuli, is consistent with cortical recordings, and has a direct mathematical relationship to artificial neural networks.

The Spectrum of Asynchronous Dynamics in Spiking Networks as a Model for the Diversity of Non-rhythmic Waking States in the Neocortex

The awake cortex exhibits diverse non-rhythmic network states. However, how these states emerge and how each state impacts network function is unclear. Here, we demonstrate that model networks of spiking neurons with moderate recurrent interactions display a spectrum of non-rhythmic asynchronous dynamics based on the level of afferent excitation, from afferent input-dominated (AD) regimes, characterized by unbalanced synaptic currents and sparse firing, to recurrent input-dominated (RD) regimes, characterized by balanced synaptic currents and dense firing. The model predicted regime-specific relationships between different neural biophysical properties, which were all experimentally validated in the somatosensory cortex (S1) of awake mice. Moreover, AD regimes more precisely encoded spatiotemporal patterns of presynaptic activity, while RD regimes better encoded the strength of afferent inputs. These results provide a theoretical foundation for how recurrent neocortical circuits generate non-rhythmic waking states and how these different states modulate the processing of incoming information.

Portraits of communication in neuronal networks

The brain is organized as a network of highly specialized networks of spiking neurons. To exploit such a modular architecture for computation, the brain has to be able to regulate the flow of spiking activity between these specialized networks. In this Opinion article, we review various prominent mechanisms that may underlie communication between neuronal networks. We show that communication between neuronal networks can be understood as trajectories in a two-dimensional state space, spanned by the properties of the input. Thus, we propose a common framework to understand neuronal communication mediated by seemingly different mechanisms. We also suggest that the nesting of slow (for example, alpha-band and theta-band) oscillations and fast (gamma-band) oscillations can serve as an important control mechanism that allows or prevents spiking signals to be routed between specific networks. We argue that slow oscillations can modulate the time required to establish network resonance or entrainment and, thereby, regulate communication between neuronal networks.

Bridging Single Neuron Dynamics to Global Brain States

Biological neural networks produce information backgrounds of multi-scale spontaneous activity that become more complex in brain states displaying higher capacities for cognition, for instance, attentive awake versus asleep or anesthetized states. Here, we review brain state-dependent mechanisms spanning ion channel currents (microscale) to the dynamics of brain-wide, distributed, transient functional assemblies (macroscale). Not unlike how microscopic interactions between molecules underlie structures formed in macroscopic states of matter, using statistical physics, the dynamics of microscopic neural phenomena can be linked to macroscopic brain dynamics through mesoscopic scales. Beyond spontaneous dynamics, it is observed that stimuli evoke collapses of complexity, most remarkable over high dimensional, asynchronous, irregular background dynamics during consciousness. In contrast, complexity may not be further collapsed beyond synchrony and regularity characteristic of unconscious spontaneous activity. We propose that increased dimensionality of spontaneous dynamics during conscious states supports responsiveness, enhancing neural networks' emergent capacity to robustly encode information over multiple scales.

Direct pathway neurons in mouse dorsolateral striatum in vivo receive stronger synaptic input than indirect pathway neurons

Striatal projection neurons, the medium spiny neurons (MSNs), play a crucial role in various motor and cognitive functions. MSNs express either D1- or D2-type dopamine receptors and initiate the direct-pathway (dMSNs) or indirect pathways (iMSNs) of the basal ganglia, respectively. dMSNs have been shown to receive more inhibition than iMSNs from intrastriatal sources. Based on these findings, computational modeling of the striatal network has predicted that under healthy conditions dMSNs should receive more total input than iMSNs. To test this prediction, we analyzed in vivo whole cell recordings from dMSNs and iMSNs in healthy and dopamine-depleted (6OHDA) anaesthetized mice. By comparing their membrane potential fluctuations, we found that dMSNs exhibited considerably larger membrane potential fluctuations over a wide frequency range. Furthermore, by comparing the spike-triggered average membrane potentials, we found that dMSNs depolarized toward the spike threshold significantly faster than iMSNs did. Together, these findings (in particular the STA analysis) corroborate the theoretical prediction that direct-pathway MSNs receive stronger total input than indirect-pathway neurons. Finally, we found that dopamine-depleted mice exhibited no difference between the membrane potential fluctuations of dMSNs and iMSNs. These data provide new insights into the question of how the lack of dopamine may lead to behavioral deficits associated with Parkinson’s disease.

NEW & NOTEWORTHY The direct and indirect pathways of the basal ganglia originate from the D1- and D2-type dopamine receptor expressing medium spiny neurons (dMSNs and iMSNs). Theoretical results have predicted that dMSNs should receive stronger synaptic input than iMSNs. Using in vivo intracellular membrane potential data, we provide evidence that dMSNs indeed receive stronger input than iMSNs, as has been predicted by the computational model.

ELFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models

The transmembrane ionic currents that underlie changes in a cell's membrane potential give rise to electric fields in the extracellular space. In the context of brain activity, these electric fields form the basis for extracellularly recorded signals, such as multiunit activity, local field potentials and electroencephalograms. Understanding the underlying neuronal dynamics and localizing current sources using these signals is often challenging, and therefore effective computational modeling approaches are critical. Typically, the electric fields from neural activity are modeled in a post-hoc form, i.e., a traditional neuronal model is used to first generate the membrane currents, which in turn are then used to calculate the electric fields. When the conductivity of the extracellular space is high, the electric fields are weak, and therefore treating membrane currents and electric fields separately is justified. However, in brain regions of lower conductivity, extracellular fields can feed back and significantly influence the underlying transmembrane currents and dynamics of nearby neurons—this is often referred to as ephaptic coupling. The closed-loop nature of ephaptic coupling cannot be modeled using the post-hoc approaches implemented by existing software tools; instead, electric fields and neuronal dynamics must be solved simultaneously. To this end, we have developed a generalized modeling toolbox for studying ephaptic coupling in compartmental neuron models: E_LFENN (E_Lectric Field Effects in Neural Networks). In open loop conditions, we validate the separate components of E_LFENN for modeling membrane dynamics and associated field potentials against standard approaches (NEURON and LFPy). Unlike standard approaches however, E_LFENN enables the closed-loop condition to be modeled as well, in that the field potentials can feed back and influence membrane dynamics. As an example closed-loop case, we use E_LFENN to study phase-locking of action potentials generated by a population of axons running parallel in a bundle. Being able to efficiently explore ephaptic coupling from a computational perspective using tools, such as E_LFENN will allow us to better understand the physical basis of electric fields in the brain, as well as the conditions in which these fields may influence neuronal dynamics in general.

Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

To integrate essential anatomical and physiological properties of local cortical circuits and to elucidate mechanistic links between them, we develop a novel circuit model capturing key synaptic connectivity features. We show that the model explains the emergence of a range of connectivity patterns such as rich-club connectivity, and gives rise to a rich repertoire of cortical states. We identify both the anatomical and physiological mechanisms underlying the transition of these cortical states, and show that our model reconciles an otherwise disparate set of key physiological findings on neural activity dynamics. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to diverse neural population correlations as observed recently. Our model thus provides a framework for integrating and explaining a variety of neural connectivity properties and spatiotemporal activity dynamics observed in experimental studies, and provides novel experimentally testable predictions.

Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

Odorant mixtures elicit less variable and faster responses than pure odorants

In natural environments, odors are typically mixtures of several different chemical compounds. However, the implications of mixtures for odor processing have not been fully investigated. We have extended a standard olfactory receptor model to mixtures and found through its mathematical analysis that odorant-evoked activity patterns are more stable across concentrations and first-spike latencies of receptor neurons are shorter for mixtures than for pure odorants. Shorter first-spike latencies arise from the nonlinear dependence of binding rate on odorant concentration, commonly described by the Hill coefficient, while the more stable activity patterns result from the competition between different ligands for receptor sites. These results are consistent with observations from numerical simulations and physiological recordings in the olfactory system of insects. Our results suggest that mixtures allow faster and more reliable olfactory coding, which could be one of the reasons why animals often use mixtures in chemical signaling.

Imbalanced amplification: A mechanism of amplification and suppression from local imbalance of excitation and inhibition in cortical circuits

Understanding the relationship between external stimuli and the spiking activity of cortical populations is a central problem in neuroscience. Dense recurrent connectivity in local cortical circuits can lead to counterintuitive response properties, raising the question of whether there are simple arithmetical rules for relating circuits’ connectivity structure to their response properties. One such arithmetic is provided by the mean field theory of balanced networks, which is derived in a limit where excitatory and inhibitory synaptic currents precisely balance on average. However, balanced network theory is not applicable to some biologically relevant connectivity structures. We show that cortical circuits with such structure are susceptible to an amplification mechanism arising when excitatory-inhibitory balance is broken at the level of local subpopulations, but maintained at a global level. This amplification, which can be quantified by a linear correction to the classical mean field theory of balanced networks, explains several response properties observed in cortical recordings and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.

Understanding how the brain represents and processes stimuli requires a quantitative understanding of how signals propagate through networks of neurons. Developing such an understanding is made difficult by the dense interconnectivity of neurons, especially in the cerebral cortex. One approach to quantifying neural processing in the cortex is derived from observations that excitatory (positive) and inhibitory (negative) interactions between neurons tend to balance each other in many brain areas. This balance is achieved under a class of computational models called “balanced networks.” However, previous approaches to the mathematical analysis of balanced network models is not possible under some biologically relevant connectivity structures. We show that, under these structures, balance between excitation and inhibition is necessarily broken and the resulting imbalance causes some stimulus features to be amplified. This “imbalanced amplification” of stimuli can explain several observations from recordings in mouse somatosensory and visual cortical circuits and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.

Spontaneous Fluctuations in Visual Cortical Responses Influence Population Coding Accuracy

Information processing in the cerebral cortex depends not only on the nature of incoming stimuli, but also on the state of neuronal networks at the time of stimulation. That is, the same stimulus will be processed differently depending on the neuronal context in which it is received. A major factor that could influence neuronal context is the background, or ongoing neuronal activity before stimulation. In visual cortex, ongoing activity is known to play a critical role in the development of local circuits, yet whether it influences the coding of visual features in adult cortex is unclear. Here, we investigate whether and how the information encoded by individual neurons and populations in primary visual cortex (V1) depends on the ongoing activity before stimulus presentation. We report that when individual neurons are in a "low" prestimulus state, they have a higher capacity to discriminate stimulus features, such as orientation, despite their reduction in evoked responses. By measuring the distribution of prestimulus activity across a population of neurons, we found that network discrimination accuracy is improved in the low prestimulus state. Thus, the distribution of ongoing activity states across the network creates an "internal context" that dynamically filters incoming stimuli to modulate the accuracy of sensory coding. The modulation of stimulus coding by ongoing activity state is consistent with recurrent network models in which ongoing activity dynamically controls the balanced background excitation and inhibition to individual neurons.

Assessing the Role of Inhibition in Stabilizing Neocortical Networks Requires Large-Scale Perturbation of the Inhibitory Population

Neurons within cortical microcircuits are interconnected with recurrent excitatory synaptic connections that are thought to amplify signals (Douglas and Martin, 2007), form selective subnetworks (Ko et al., 2011), and aid feature discrimination. Strong inhibition (Haider et al., 2013) counterbalances excitation, enabling sensory features to be sharpened and represented by sparse codes (Willmore et al., 2011). This balance between excitation and inhibition makes it difficult to assess the strength, or gain, of recurrent excitatory connections within cortical networks, which is key to understanding their operational regime and the computations that they perform. Networks that combine an unstable high-gain excitatory population with stabilizing inhibitory feedback are known as inhibition-stabilized networks (ISNs) (Tsodyks et al., 1997). Theoretical studies using reduced network models predict that ISNs produce paradoxical responses to perturbation, but experimental perturbations failed to find evidence for ISNs in cortex (Atallah et al., 2012). Here, we reexamined this question by investigating how cortical network models consisting of many neurons behave after perturbations and found that results obtained from reduced network models fail to predict responses to perturbations in more realistic networks. Our models predict that a large proportion of the inhibitory network must be perturbed to reliably detect an ISN regime robustly in cortex. We propose that wide-field optogenetic suppression of inhibition under promoters targeting a large fraction of inhibitory neurons may provide a perturbation of sufficient strength to reveal the operating regime of cortex. Our results suggest that detailed computational models of optogenetic perturbations are necessary to interpret the results of experimental paradigms.SIGNIFICANCE STATEMENT Many useful computational mechanisms proposed for cortex require local excitatory recurrence to be very strong, such that local inhibitory feedback is necessary to avoid epileptiform runaway activity (an "inhibition-stabilized network" or "ISN" regime). However, recent experimental results suggest that this regime may not exist in cortex. We simulated activity perturbations in cortical networks of increasing realism and found that, to detect ISN-like properties in cortex, large proportions of the inhibitory population must be perturbed. Current experimental methods for inhibitory perturbation are unlikely to satisfy this requirement, implying that existing experimental observations are inconclusive about the computational regime of cortex. Our results suggest that new experimental designs targeting a majority of inhibitory neurons may be able to resolve this question.

Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice layer V pyramidal neurons

In this study, we present a theoretical framework combining experimental characterizations and analytical calculus to capture the firing rate input-output properties of single neurons in the fluctuation-driven regime. Our framework consists of a two-step procedure to treat independently how the dendritic input translates into somatic fluctuation variables, and how the latter determine action potential firing. We use this framework to investigate the functional impact of the heterogeneity in firing responses found experimentally in young mice layer V pyramidal cells. We first design and calibrate in vitro a simplified morphological model of layer V pyramidal neurons with a dendritic tree following Rall's branching rule. Then, we propose an analytical derivation for the membrane potential fluctuations at the soma as a function of the properties of the synaptic input in dendrites. This mathematical description allows us to easily emulate various forms of synaptic input: either balanced, unbalanced, synchronized, purely proximal or purely distal synaptic activity. We find that those different forms of dendritic input activity lead to various impact on the somatic membrane potential fluctuations properties, thus raising the possibility that individual neurons will differentially couple to specific forms of activity as a result of their different firing response. We indeed found such a heterogeneous coupling between synaptic input and firing response for all types of presynaptic activity. This heterogeneity can be explained by different levels of cellular excitability in the case of the balanced, unbalanced, synchronized and purely distal activity. A notable exception appears for proximal dendritic inputs: increasing the input level can either promote firing response in some cells, or suppress it in some other cells whatever their individual excitability. This behavior can be explained by different sensitivities to the speed of the fluctuations, which was previously associated to different levels of sodium channel inactivation and density. Because local network connectivity rather targets proximal dendrites, our results suggest that this aspect of biophysical heterogeneity might be relevant to neocortical processing by controlling how individual neurons couple to local network activity.

Mesoscale Architecture Shapes Initiation and Richness of Spontaneous Network Activity

Spontaneous activity in the absence of external input, including propagating waves of activity, is a robust feature of neuronal networks in vivo and in vitro The neurophysiological and anatomical requirements for initiation and persistence of such activity, however, are poorly understood, as is their role in the function of neuronal networks. Computational network studies indicate that clustered connectivity may foster the generation, maintenance, and richness of spontaneous activity. Since this mesoscale architecture cannot be systematically modified in intact tissue, testing these predictions is impracticable in vivo Here, we investigate how the mesoscale structure shapes spontaneous activity in generic networks of rat cortical neurons in vitro In these networks, neurons spontaneously arrange into local clusters with high neurite density and form fasciculating long-range axons. We modified this structure by modulation of protein kinase C, an enzyme regulating neurite growth and cell migration. Inhibition of protein kinase C reduced neuronal aggregation and fasciculation of axons, i.e., promoted uniform architecture. Conversely, activation of protein kinase C promoted aggregation of neurons into clusters, local connectivity, and bundling of long-range axons. Supporting predictions from theory, clustered networks were more spontaneously active and generated diverse activity patterns. Neurons within clusters received stronger synaptic inputs and displayed increased membrane potential fluctuations. Intensified clustering promoted the initiation of synchronous bursting events but entailed incomplete network recruitment. Moderately clustered networks appear optimal for initiation and propagation of diverse patterns of activity. Our findings support a crucial role of the mesoscale architectures in the regulation of spontaneous activity dynamics.SIGNIFICANCE STATEMENT Computational studies predict richer and persisting spatiotemporal patterns of spontaneous activity in neuronal networks with neuron clustering. To test this, we created networks of varying architecture in vitro Supporting these predictions, the generation and spatiotemporal patterns of propagation were most variable in networks with intermediate clustering and lowest in uniform networks. Grid-like clustering, on the other hand, facilitated spontaneous activity but led to degenerating patterns of propagation. Neurons outside clusters had weaker synaptic input than neurons within clusters, in which increased membrane potential fluctuations facilitated the initiation of synchronized spike activity. Our results thus show that the intermediate level organization of neuronal networks strongly influences the dynamics of their activity.

Fundamental Activity Constraints Lead to Specific Interpretations of the Connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.

Inhibitory suppression of heterogeneously tuned excitation enhances spatial coding in CA1 place cells

Place cells in the CA1 region of the hippocampus express location-specific firing despite receiving a steady barrage of heterogeneously tuned excitatory inputs that should compromise output dynamic range and timing. We examined the role of synaptic inhibition in countering the deleterious effects of off-target excitation. Intracellular recordings in behaving mice demonstrate that bimodal excitation drives place cells, while unimodal excitation drives weaker or no spatial tuning in interneurons. Optogenetic hyperpolarization of interneurons had spatially uniform effects on place cell membrane potential dynamics, substantially reducing spatial selectivity. These data and a computational model suggest that spatially uniform inhibitory conductance enhances rate coding in place cells by suppressing out-of-field excitation and by limiting dendritic amplification. Similarly, we observed that inhibitory suppression of phasic noise generated by out-of-field excitation enhances temporal coding by expanding the range of theta phase precession. Thus, spatially uniform inhibition allows proficient and flexible coding in hippocampal CA1 by suppressing heterogeneously tuned excitation.

Propagation of Collective Temporal Regularity in Noisy Hierarchical Networks

Neuronal communication between different brain areas is achieved in terms of spikes. Consequently, spike-time regularity is closely related to many cognitive tasks and timing precision of neural information processing. A recent experiment on primate parietal cortex reports that spike-time regularity increases consistently from primary sensory to higher cortical regions. This observation conflicts with the influential view that spikes in the neocortex are fundamentally irregular. To uncover the underlying network mechanism, we construct a multilayered feedforward neural information transmission pathway and investigate how spike-time regularity evolves across subsequent layers. Numerical results reveal that despite the obviously irregular spiking patterns in previous several layers, neurons in downstream layers can generate rather regular spikes, which depends on the network topology. In particular, we find that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight, i.e., the optimal topology parameter maximizes the spike-timing regularity. Furthermore, it is demonstrated that synaptic properties, including inhibition, synaptic transient dynamics, and plasticity, have significant impacts on spike-timing regularity propagation. The emergence of the increasingly regular spiking (RS) patterns in higher parietal regions can, thus, be viewed as a natural consequence of spiking activity propagation between different brain areas. Finally, we validate an important function served by increased RS: promoting reliable propagation of spike-rate signals across downstream layers.

Lognormal firing rate distribution reveals prominent fluctuation-driven regime in spinal motor networks

When spinal circuits generate rhythmic movements it is important that the neuronal activity remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we simultaneously record from hundreds of neurons in lumbar spinal circuits of turtles and establish the neuronal fraction that operates within either a 'mean-driven' or a 'fluctuation-driven' regime. Fluctuation-driven neurons have a 'supralinear' input-output curve, which enhances sensitivity, whereas the mean-driven regime reduces sensitivity. We find a rich diversity of firing rates across the neuronal population as reflected in a lognormal distribution and demonstrate that half of the neurons spend at least 50 % of the time in the 'fluctuation-driven' regime regardless of behavior. Because of the disparity in input-output properties for these two regimes, this fraction may reflect a fine trade-off between stability and sensitivity in order to maintain flexibility across behaviors.

Effects of Calcium Spikes in the Layer 5 Pyramidal Neuron on Coincidence Detection and Activity Propagation

The role of dendritic spiking mechanisms in neural processing is so far poorly understood. To investigate the role of calcium spikes in the functional properties of the single neuron and recurrent networks, we investigated a three compartment neuron model of the layer 5 pyramidal neuron with calcium dynamics in the distal compartment. By performing single neuron simulations with noisy synaptic input and occasional large coincident input at either just the distal compartment or at both somatic and distal compartments, we show that the presence of calcium spikes confers a substantial advantage for coincidence detection in the former case and a lesser advantage in the latter. We further show that the experimentally observed critical frequency phenomenon, in which action potentials triggered by stimuli near the soma above a certain frequency trigger a calcium spike at distal dendrites, leading to further somatic depolarization, is not exhibited by a neuron receiving realistically noisy synaptic input, and so is unlikely to be a necessary component of coincidence detection. We next investigate the effect of calcium spikes in propagation of spiking activities in a feed-forward network (FFN) embedded in a balanced recurrent network. The excitatory neurons in the network are again connected to either just the distal, or both somatic and distal compartments. With purely distal connectivity, activity propagation is stable and distinguishable for a large range of recurrent synaptic strengths if the feed-forward connections are sufficiently strong, but propagation does not occur in the absence of calcium spikes. When connections are made to both the somatic and the distal compartments, activity propagation is achieved for neurons with active calcium dynamics at a much smaller number of neurons per pool, compared to a network of passive neurons, but quickly becomes unstable as the strength of recurrent synapses increases. Activity propagation at higher scaling factors can be stabilized by increasing network inhibition or introducing short term depression in the excitatory synapses, but the signal to noise ratio remains low. Our results demonstrate that the interaction of synchrony with dendritic spiking mechanisms can have profound consequences for the dynamics on the single neuron and network level.

Heterogeneous firing rate response of mouse layer V pyramidal neurons in the fluctuation-driven regime

KEY POINTS

We recreated in vitro the fluctuation-driven regime observed at the soma during asynchronous network activity in vivo and we studied the firing rate response as a function of the properties of the membrane potential fluctuations. We provide a simple analytical template that captures the firing response of both pyramidal neurons and various theoretical models. We found a strong heterogeneity in the firing rate response of layer V pyramidal neurons: in particular, individual neurons differ not only in their mean excitability level, but also in their sensitivity to fluctuations. Theoretical modelling suggest that this observed heterogeneity might arise from various expression levels of the following biophysical properties: sodium inactivation, density of sodium channels and spike frequency adaptation.

ABSTRACT

Characterizing the input-output properties of neocortical neurons is of crucial importance for understanding the properties emerging at the network level. In the regime of low-rate irregular firing (such as in the awake state), determining those properties for neocortical cells remains, however, both experimentally and theoretically challenging. Here, we studied this problem using a combination of theoretical modelling and in vitro experiments. We first identified, theoretically, three somatic variables that describe the dynamical state at the soma in this fluctuation-driven regime: the mean, standard deviation and time constant of the membrane potential fluctuations. Next, we characterized the firing rate response of individual layer V pyramidal cells in this three-dimensional space by means of perforated-patch recordings and dynamic clamp in the visual cortex of juvenile mice in vitro. We found that individual neurons strongly differ not only in terms of their excitability, but also, and unexpectedly, in their sensitivities to fluctuations. Finally, using theoretical modelling, we attempted to reproduce these results. The model predicts that heterogeneous levels of biophysical properties such as sodium inactivation, sharpness of sodium activation and spike frequency adaptation account for the observed diversity of firing rate responses. Because the firing rate response will determine population rate dynamics during asynchronous neocortical activity, our results show that cortical populations are functionally strongly inhomogeneous in young mouse visual cortex, which should have important consequences on the strategies of cortical computation at early stages of sensory processing.

Dynamical state of the network determines the efficacy of single neuron properties in shaping the network activity

Spike patterns are among the most common electrophysiological descriptors of neuron types. Surprisingly, it is not clear how the diversity in firing patterns of the neurons in a network affects its activity dynamics. Here, we introduce the state-dependent stochastic bursting neuron model allowing for a change in its firing patterns independent of changes in its input-output firing rate relationship. Using this model, we show that the effect of single neuron spiking on the network dynamics is contingent on the network activity state. While spike bursting can both generate and disrupt oscillations, these patterns are ineffective in large regions of the network state space in changing the network activity qualitatively. Finally, we show that when single-neuron properties are made dependent on the population activity, a hysteresis like dynamics emerges. This novel phenomenon has important implications for determining the network response to time-varying inputs and for the network sensitivity at different operating points.

Push-Pull Receptive Field Organization and Synaptic Depression: Mechanisms for Reliably Encoding Naturalistic Stimuli in V1

Neurons in the primary visual cortex are known for responding vigorously but with high variability to classical stimuli such as drifting bars or gratings. By contrast, natural scenes are encoded more efficiently by sparse and temporal precise spiking responses. We used a conductance-based model of the visual system in higher mammals to investigate how two specific features of the thalamo-cortical pathway, namely push-pull receptive field organization and fast synaptic depression, can contribute to this contextual reshaping of V1 responses. By comparing cortical dynamics evoked respectively by natural vs. artificial stimuli in a comprehensive parametric space analysis, we demonstrate that the reliability and sparseness of the spiking responses during natural vision is not a mere consequence of the increased bandwidth in the sensory input spectrum. Rather, it results from the combined impacts of fast synaptic depression and push-pull inhibition, the later acting for natural scenes as a form of “effective” feed-forward inhibition as demonstrated in other sensory systems. Thus, the combination of feedforward-like inhibition with fast thalamo-cortical synaptic depression by simple cells receiving a direct structured input from thalamus composes a generic computational mechanism for generating a sparse and reliable encoding of natural sensory events.

Burst Firing Enhances Neural Output Correlation

Neurons communicate and transmit information predominantly through spikes. Given that experimentally observed neural spike trains in a variety of brain areas can be highly correlated, it is important to investigate how neurons process correlated inputs. Most previous work in this area studied the problem of correlation transfer analytically by making significant simplifications on neural dynamics. Temporal correlation between inputs that arises from synaptic filtering, for instance, is often ignored when assuming that an input spike can at most generate one output spike. Through numerical simulations of a pair of leaky integrate-and-fire (LIF) neurons receiving correlated inputs, we demonstrate that neurons in the presence of synaptic filtering by slow synapses exhibit strong output correlations. We then show that burst firing plays a central role in enhancing output correlations, which can explain the above-mentioned observation because synaptic filtering induces bursting. The observed changes of correlations are mostly on a long time scale. Our results suggest that other features affecting the prevalence of neural burst firing in biological neurons, e.g., adaptive spiking mechanisms, may play an important role in modulating the overall level of correlations in neural networks.

A Diffusion Approximation and Numerical Methods for Adaptive Neuron Models with Stochastic Inputs

Characterizing the spiking statistics of neurons receiving noisy synaptic input is a central problem in computational neuroscience. Monte Carlo approaches to this problem are computationally expensive and often fail to provide mechanistic insight. Thus, the field has seen the development of mathematical and numerical approaches, often relying on a Fokker-Planck formalism. These approaches force a compromise between biological realism, accuracy and computational efficiency. In this article we develop an extension of existing diffusion approximations to more accurately approximate the response of neurons with adaptation currents and noisy synaptic currents. The implementation refines existing numerical schemes for solving the associated Fokker-Planck equations to improve computationally efficiency and accuracy. Computer code implementing the developed algorithms is made available to the public.

Current injection and receptor-mediated excitation produce similar maximal firing rates in hypoglossal motoneurons

The maximum firing rates of motoneurons (MNs), activated in response to synaptic drive, appear to be much lower than that elicited by current injection. It could be that the decrease in input resistance associated with increased synaptic activity (but not current injection) might blunt overall changes in membrane depolarization and thereby limit spike-frequency output. To test this idea, we recorded, in the same cells, maximal firing responses to current injection and to synaptic activation. We prepared 300 μm medullary slices in neonatal rats that contained hypoglossal MNs and used whole-cell patch-clamp electrophysiology to record their maximum firing rates in response to triangular-ramp current injections and to glutamate receptor-mediated excitation. Brief pressure pulses of high-concentration glutamate led to significant depolarization, high firing rates, and temporary cessation of spiking due to spike inactivation. In the same cells, we applied current clamp protocols that approximated the time course of membrane potential change associated with glutamate application and with peak current levels large enough to cause spike inactivation. Means (SD) of maximum firing rates obtained in response to glutamate application were nearly identical to those obtained in response to ramp current injection [glutamate 47.1 ± 12.0 impulses (imp)/s, current injection 47.5 ± 11.2 imp/s], even though input resistance was 40% less during glutamate application compared with current injection. Therefore, these data suggest that the reduction in input resistance associated with receptor-mediated excitation does not, by itself, limit the maximal firing rate responses in MNs.

The Slow Oscillation in Cortical and Thalamic Networks: Mechanisms and Functions

During even the most quiescent behavioral periods, the cortex and thalamus express rich spontaneous activity in the form of slow (<1 Hz), synchronous network state transitions. Throughout this so-called slow oscillation, cortical and thalamic neurons fluctuate between periods of intense synaptic activity (Up states) and almost complete silence (Down states). The two decades since the original characterization of the slow oscillation in the cortex and thalamus have seen considerable advances in deciphering the cellular and network mechanisms associated with this pervasive phenomenon. There are, nevertheless, many questions regarding the slow oscillation that await more thorough illumination, particularly the mechanisms by which Up states initiate and terminate, the functional role of the rhythmic activity cycles in unconscious or minimally conscious states, and the precise relation between Up states and the activated states associated with waking behavior. Given the substantial advances in multineuronal recording and imaging methods in both in vivo and in vitro preparations, the time is ripe to take stock of our current understanding of the slow oscillation and pave the way for future investigations of its mechanisms and functions. My aim in this Review is to provide a comprehensive account of the mechanisms and functions of the slow oscillation, and to suggest avenues for further exploration.

Characterization of dendritic morphology and neurotransmitter phenotype of thoracic descending propriospinal neurons after complete spinal cord transection and GDNF treatment

After spinal cord injury (SCI), poor regeneration of damaged axons of the central nervous system (CNS) causes limited functional recovery. This limited spontaneous functional recovery has been attributed, to a large extent, to the plasticity of propriospinal neurons, especially the descending propriospinal neurons (dPSNs). Compared with the supraspinal counterparts, dPSNs have displayed significantly greater regenerative capacity, which can be further enhanced by glial cell line-derived neurotrophic factor (GDNF). In the present study, we applied a G-mutated rabies virus (G-Rabies) co-expressing green fluorescence protein (GFP) to reveal Golgi-like dendritic morphology of dPSNs. We also investigated the neurotransmitters expressed by dPSNs after labeling with a retrograde tracer Fluoro-Gold (FG). dPSNs were examined in animals with sham injuries or complete spinal transections with or without GDNF treatment. Bilateral injections of G-Rabies and FG were made into the 2nd lumbar (L2) spinal cord at 3 days prior to a spinal cord transection performed at the 11th thoracic level (T11). The lesion gap was filled with Gelfoam containing either saline or GDNF in the injury groups. Four days post-injury, the rats were sacrificed for analysis. For those animals receiving G-rabies injection, the GFP signal in the T7-9 spinal cord was visualized via 2-photon microscopy. Dendritic morphology from stack images was traced and analyzed using a Neurolucida software. We found that dPSNs in sham injured animals had a predominantly dorsal-ventral distribution of dendrites. Transection injury resulted in alterations in the dendritic distribution with dorsal-ventral retraction and lateral-medial extension. Treatment with GDNF significantly increased the terminal dendritic length of dPSNs. The density of spine-like structures was increased after injury, and treatment with GDNF enhanced this effect. For the group receiving FG injections, immunohistochemistry for glutamate, choline acetyltransferase (ChAT), glycine, and GABA was performed in the T7-9 spinal cord. We show that the majority of FG retrogradely-labeled dPSNs were located in the Rexed Lamina VII. Over 90% of FG-labeled neurons were glutamatergic, with the other three neurotransmitters contributing less than 10% of the total. To our knowledge this is the first report describing the morphologic characteristics of dPSNs and their neurotransmitter expressions, as well as the dendritic response of dPSNs after transection injury and GDNF treatment.