Question

Gap junctions and glial cells are currently “hot” subjects of neuroscientific research. Describe the findings that have generated such interest, and explain how they have changed our conception of brain function.

Answer 1

Most of the communication between the neurons in the brain of an adult animal is achieved by means of chemical synapses . In the cortex for example, a typical neuron can get as many as An external file that holds a picture, illustration, etc.and communicate its spike to, other neurons, thus making synaptic transmission a ubiquitous mode of information transfer. Consequently, over the years many successful “synaptic theories” were developed to explain a variety of phenomena, such as the working memory long-term plasticity and memory formation but also pathological conditions such as the schizophrenia and the epilepsies. In particular, one of the widely accepted theories attributes epileptic seizures to the shift of synaptic balance toward excitation in conditions of impaled inhibition or augmented excitation .

Besides chemical synapses, neurons can also form direct electrotonic connections with their peers via electrical synapses, or so called gap junctions. Conceptually, a network of neurons coupled by gap junctions has often been likened to excitable reaction-diffusion (RD) media. In RD systems, a substance (usually chemical) spreads by diffusion from one excitable site to its neighbors where it can be regenerated by a reaction, and the process repeats itself, resulting in the propagation of regenerative waves through the medium . The speed of wave propagation is mostly limited by the characteristic reaction time. In RD neuronal networks, membrane voltage plays the role of a “diffusible chemical” and gap junctions play a role of “diffusion” providing coupling of membrane voltages between neighbor neurons; since the spike width (“reaction time”) is very short (∼ 1 ms) the “voltage wave” can quickly engage neurons that are relatively far apart in space. Indeed, computational modeling studies supported by mathematical analysis suggested that a network of neurons coupled by gap junctions can support collective activity in the form of waves that are generated spontaneously and propagate through the network . The existence of such dynamical state requires the coupling by gap junctions to be sparse and strong .Gap junctions also play an important role in promoting synchronization in networks of inhibitory interneurons, which is believed to be necessary for the generation of collective oscillatory activity in the gamma band .As was first shown by Kepler et al. , resistive coupling can significantly affect the frequency of a neural oscillator in a way that depends on several parameters, such as the strength of coupling (conductance), the state of a neuron to which the given neural oscillator is coupled, and the sub-threshold dynamics of the oscillator. Our observations extend the conclusions of Kepler et al. To networks of noise-driven model neurons with realistic firing properties, and highlight another aspect critical for collective activity – the topological connectivity. We identified a special regime in which strong topological connectivity can dramatically suppress the collective noise-driven activity. This occurred because topologically strong (large number of contacts) but functionally weak (relatively weak individual contacts) electrical connections reduced input resistance of the model neurons and, therefore, enforced fast relaxation of sub-threshold excitation, thus weakening the neuronal responsiveness to external stimulation . However, the primary effect of increase in gap junction connectivity can be described as membrane conductance increase only under assumption that other neurons are far enough from spiking threshold. Since currents escape through gap junction to other neurons, not to the extracellular space, once many neurons are close enough to the spiking threshold, effect of gap junctions reverts and starts to mediate firing rate increase. Thus, in spatially extended networks of resistively coupled neurons driven by fluctuating current, the spatial profile of the current and the connectivity of the network (both its topological and functional aspects) can dramatically affect the emerging collective activity.

The firing rate of model neurons was estimated by computing the number of action potentials generated in a predefined time window, and then normalizing by the window duration.

To characterize the extent to which the abundance of gap junctions in a given neuron can affect the propagation of electrical activity, we used the following procedure: First, for a preset time window T, a spike count of each model neuron in the network was obtained. Then, for each model neuron, we computed the averaged spike count of its topological neighbors, . The “spike number disorder” is then defined as