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Register a new userGeneralized cable theory for neurons in complex and heterogeneous media
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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.
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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.
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.
Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the summed activity of all neurons in the population. However, an explicit, tractable model for these interactions is still lacking. Here we build a probabilistic model of population activity that reproduces the firing rate of each cell, the distribution of the population rate, and the linear coupling between them. This model is tractable, meaning that its parameters can be learned in a few seconds on a standard computer even for large population recordings. We inferred our model for a population of 160 neurons in the salamander retina. In this population, single-cell firing rates depended in unexpected ways on the population rate. In particular, some cells had a preferred population rate at which they were most likely to fire. These complex dependencies could not be explained by a linear coupling between the cell and the population rate. We designed a more general, still tractable model that could fully account for these non-linear dependencies. We thus provide a simple and computationally tractable way to learn models that reproduce the dependence of each neuron on the population rate.
We describe a large-scale functional brain model that includes detailed, conductance-based, compartmental models of individual neurons. We call the model BioSpaun, to indicate the increased biological plausibility of these neurons, and because it is a direct extension of the Spaun model cite{Eliasmith2012b}. We demonstrate that including these detailed compartmental models does not adversely affect performance across a variety of tasks, including digit recognition, serial working memory, and counting. We then explore the effects of applying TTX, a sodium channel blocking drug, to the model. We characterize the behavioral changes that result from this molecular level intervention. We believe this is the first demonstration of a large-scale brain model that clearly links low-level molecular interventions and high-level behavior.
Since the early work of Bernard Katz, the process of cellular chemical communication via exocytosis, quantal release, has been considered to be all or none. Recent evidence has shown exocytosis to be partial or subquantal at single-cell model systems, but there is a need to understand this at communicating nerve cells. Partial release allows nerve cells to control the signal at the site of release during individual events, where the smaller the fraction released, the greater the range of regulation. Here we show that the fraction of the vesicular octopamine content released from a living Drosophila larval neuromuscular neuron is very small. The percentage of released molecules was found to be only 4.5% for simple events and 10.7% for complex (i.e., oscillating or flickering) events. This large content, combined with partial release controlled by fluctuations of the fusion pore, offers presynaptic plasticity that can be widely regulated. Two works published in 2010 suggested that the Katz principle, [1] was incorrect for all-or-none release and that only part of the chemical load of vesicles was released during exocytosis, at least as measured as a full spike during amperometry. [2] The combination of electrochemical methods to measure both release and vesicle content in 2015 added a wealth of information to support the concept of partial release in exocytosis. [3] Additionally, this has recently been supported by work with TIRF microscopy showing subquantal release from vesicles in adrenal chromaffin cells and using super-resolution STED microscopy. [4] It appears that the full event generally involves release of only part of the load of chemical messenger in single-cell model systems like adrenal chromaffin and PC12 cells. Is this also true at living neurons in a nervous system and to what extent? To answer this critical question, we quantified the number of octopamine molecules in the neuromuscular neurons of Drosophila larvae by adapting an amperometric technique developed in our
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