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Register a new userGeneralized cable formalism to calculate the magnetic field of single neurons and neuronal populations
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Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magneto-encephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here, we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multi-scale mean-field theory where the neuron is considered in interaction with a mean extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.
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Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.
The ongoing activity of neurons generates a spatially- and time-varying field of extracellular voltage ($V_e$). This $V_e$ field reflects population-level neural activity, but does it modulate neural dynamics and the function of neural circuits? We provide a cable theory framework to study how a bundle of model neurons generates $V_e$ and how this $V_e$ feeds back and influences membrane potential ($V_m$). We find that these ephaptic interactions are small but not negligible. The model neural population can generate $V_e$ with millivolt-scale amplitude and this $V_e$ perturbs the $V_m$ of nearby cables and effectively increases their electrotonic length. After using passive cable theory to systematically study ephaptic coupling, we explore a test case: the medial superior olive (MSO) in the auditory brainstem. The MSO is a possible locus of ephaptic interactions: sounds evoke large $V_e$ in vivo in this nucleus (millivolt-scale). The $V_e$ response is thought to be generated by MSO neurons that perform a known neuronal computation with submillisecond temporal precision (coincidence detection to encode sound source location). Using a biophysically-based model of MSO neurons, we find millivolt-scale ephaptic interactions consistent with the passive cable theory results. These subtle membrane potential perturbations induce changes in spike initiation threshold, spike time synchrony, and time difference sensitivity. These results suggest that ephaptic coupling may influence MSO function.
Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can potentially address a range of theoretical problems and provide a straightforward explanation for our cognition. However, this idea is merely a hypothesis with many questions unsolved. In this paper, I will bring up a new framework to defend the idea of neuronal representations. The strategy is from micro- to macro-level. Specifically, in the micro-level, I first propose that our brain prefers and preserves more active neurons. Yet as total chance of discharge, neurons must take strategies to fire more strongly and frequently. Then I describe how they take synaptic plasticity, inhibition, and synchronization as their strategies and demonstrate how the execution of these strategies during turn them into specialized neurons that selectively but strongly respond to familiar entities. In the macro-level, I further discuss how these specialized neurons underlie various cognitive functions and phenomena. Significantly, this paper, through defending neuronal representation, introduces a novel way to understand the relationship between brain and cognition.
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal description of neurons with adaptation. We derive an integral equation with colored noise that governs the stochastic dynamics of the population activity in response to time-dependent stimulation and calculate the spectral density in the asynchronous state. We show that systems of coupled populations with adaptation can generate a frequency band in which sensory information is preferentially encoded. The theory is applicable to fully as well as randomly connected networks, and to leaky integrate-and-fire as well as to generalized spiking neurons with adaptation on multiple time scales.
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50 -- 2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics like finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly simulate a model of a local cortical microcircuit consisting of eight neuron types. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.
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