Mathematical Foundations of Neuroscience

Cortical spike trains are highly irregular both during ongoing, spontaneous activity and when driven at high firing rates. There is uncertainty about the source of this irregularity, ranging from intrinsic noise sources in neurons to collective effects in large-scale cortical networks. Cortical interneurons display highly irregular spike times (coefficient of variation of the interspike intervals >1) in response to dc-current injection in vitro. This is in marked contrast to cortical pyramidal cells, which spike highly irregularly in vivo, but regularly in vitro. We show with in vitro recordings and computational models that this is due to the fast activation kinetics of interneuronal K + currents. This explanation holds over a wide parameter range and with Gaussian white, power-law, and OrnsteinUhlenbeck noise. The intrinsically irregular spiking of interneurons could contribute to the irregularity of the cortical network.inhibitory interneuron | bistability | neural noise | fluctuations | cortex W hen spike trains of cortical pyramidal neurons are recorded in vivo from the cortices of awake or sleeping cats (1-3) or awake monkeys (4), the interspike intervals (ISIs) are highly variable, with coefficients of variation (CV ISI = ISI SD/ISI mean) >1. However, when the main cortical excitatory (pyramidal) neurons are depolarized in vitro by injection of constant current to above firing threshold, their spike trains are substantially more regular (CV ISI <0.5). The irregularity of pyramidal neuron firing in vivo arises from the intense, ongoing, temporally correlated synaptic activity that bombards cortical neurons (1, 2, 5-7). The lower in vitro irregularity can be raised to in vivo levels by using fluctuating current injection (8), hyperosmolar solution (9), and a neuromodulatory mixture (10, 11).Computational models of irregular neuronal firing typically include network synaptic activity represented by stochastic aggregate processes. Fluctuating inputs have been represented by Brownian motion (12) or an Ornstein-Uhlenbeck process (8) in both single-and multicompartmental neuronal models (5). These are externally induced fluctuations and do not mechanistically explain the variety of irregular discharge patterns observed in cortical interneurons. In this study we combined in vitro recordings and computational models of cortical interneurons to show how neuronal conductances interact with the stochastic input to produce the variety of observed neuronal phenotypes. ResultsRecordings from Cortical Inhibitory Interneurons. Cortical GABAergic interneurons have a range of functions including the gating (13) and entrainment (14) of neuronal firing, dendritic integration (15), synaptic plasticity (16), and the generation of network oscillations (10, 11). There are several morphologically and physiologically distinct classes of interneurons (17).In contrast to pyramidal neurons, a constant current injected into mouse visual cortex layer 2/3 interneurons in vitro frequently produced a spike train with a CV ISI that substant...

show abstract

“…This high sensitivity to noise is also indicative of the vicinity of the system to a bifurcation (26).…”

Section: Resultsmentioning

confidence: 93%

Origin of intrinsic irregular firing in cortical interneurons

Stiefel

Englitz

Sejnowski

2013

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…The modeling of neuronal networks is critical for understanding almost all cognitive and behavioral phenomenon in neuroscience [37][38][39]. There have been hundreds of network models proposed in the computational neuroscience literature, with varying levels of complexity, architectural configurations and capabilities.…”

Section: Discussionmentioning

confidence: 99%

“…Our modeling efforts are based upon firing rate models of networks of neurons [37][38][39] and a recent innovation of the FORCE learning protocol [1]. The FORCE model is particularly relevant as it is one of the few biophysically inspired models to address plasticity effects and network control for producing robust output patterns associated with behaviors.…”

Section: Discussionmentioning

confidence: 99%

“…The modeling of neuronal networks is one of the most vibrant fields of computational neuroscience [37][38][39]. In our simulations we use the FORCE learning protocol [1].…”

Section: Methodsmentioning

confidence: 99%

“…Over the past few decades, computational neuroscience efforts have developed a host of models for modeling individual neurons as well as network architectures [37][38][39]. Here, we will consider the network temporal dynamics using a firing rate model.…”

Section: Network Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Cognitive and behavioral deficits arising from neurodegeneration and traumatic brain injury: a model for the underlying role of focal axonal swellings in neuronal networks with plasticity

Rudy¹,

Maia²,

Kutz³

2016

J Integr Syst Neurosci

View full text Add to dashboard Cite

Neurodegenerative diseases and traumatic brain injury, whose hallmark features are the presence of focal axonal swellings (FAS), are leading causes of cognitive dysfunction. By leveraging biophysical observations of FAS statistics, we develop a theoretical model of functional neural network activity driven by adaptive changes from plasticity. Based upon the FORCE model of Sussillo and Abbott [1], our innovations highlight the role of plasticity in overcoming injuries and degeneration of neurons in a network architecture. We provide a quantitative measure, on a network level, of cognitive deficits arising from injury. We demonstrate that plasticity is capable of overcoming mild injuries while failing to compensate for more severe injuries. Such injuries are characterized by their underlying effect on spike trains propagating through the neurons in a network architecture. Specifically, spike trains can be filtered in firing rate, or blocked under more severe FAS. The level of injury dictates the FORCE model's ability to produce a desired output functionality (and associated behavior) and allows for quantitative metrics for accessing cognitive and behavioral deficits. Thus a direct link between FAS in neural networks and compromised functional response can be established. The theoretical framework developed is a promising computational framework for providing a deeper understanding of the cognitive deficits arising in, for instance, Alzheimer's, Parkinson's, Multiple-Sclerosis, and TBI.

show abstract

Repetitive Action Potential Firing

Knowlton

Baxter²,

Byrne³

et al. 2020

Encyclopedia of Life Sciences

View full text Add to dashboard Cite

The biophysical basis of repetitive action potential firing can be understood in terms of the opposing positive and negative feedback processes that generate the repetitive activity. The relative timescales of these processes, which can include ion channel activation and inactivation as well as ion accumulation within a cell, are key factors in the generation of repetitive single‐spike firing, intrinsic burst firing and repetitive activity resulting from network interactions. Bifurcation theory, in concert with the steady state current–voltage relationship, explains why the onset of repetitive firing can be gradual or abrupt and accounts for different excitability types and distinct types of bistability. Moreover, bifurcation theory allows for the classification of different mechanisms underlying rhythmic bursting. Key Concepts A branch of mathematics called bifurcation theory can explain initiation of repetitive firing without reference to the specific ionic currents involved. Two major bifurcations can underlie the initiation of repetitive firing. Initiation of repetitive firing is gradual if the underlying bifurcation is a saddle‐node on an invariant circle (SNIC). A SNIC requires that the steady state IV curve intersect the zero current axis in three places. Initiation of repetitive firing is abrupt at a threshold frequency if due to a Hopf bifurcation. Most rhythmic bursting can be classified as square wave, parabolic, or elliptical, depending upon the bifurcations that initiate and terminate spiking. Rhythmic bursting requires at least one slow process, and parabolic bursting requires two. Repetitive firing can also arise via network mechanisms, in addition to the intrinsic ones described above.

show abstract

Mathematical Foundations of Neuroscience

Cited by 1,142 publications

References 8 publications

Origin of intrinsic irregular firing in cortical interneurons

Origin of intrinsic irregular firing in cortical interneurons

Cognitive and behavioral deficits arising from neurodegeneration and traumatic brain injury: a model for the underlying role of focal axonal swellings in neuronal networks with plasticity

Repetitive Action Potential Firing

Contact Info

Product

Resources

About