Caldas, I. L. | Search bioRxiv

bioRxiv2023

The Role of Potassium and Calcium Currents in the Bistable Firing Transition

AO_SCPLOWBSTRACTC_SCPLOWHealthy brains display a wide range of firing patterns, from synchronized oscillations during slowwave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking cells (RS) with frequency adaptation and do not exhibit bursts in current-clamp experiments (in vitro). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings (gsyn) and external current inputs (I). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold (IL) and low-threshold (IT) ion channels play a role in increasing and decreasing the parameter conditions (gsyn and I) in which bistable dynamics occur, respectively. For high values of IL conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance IT increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.

neuroscience↗

bioRxiv2023

Analytical solutions for the short-term plasticity

Synaptic dynamics plays a key role in neuronal communication. Due to its high-dimensionality, the main fundamental mechanisms triggering different synaptic dynamics and its relation with the neurotransmitters release regimes (facilitation, biphasic, and depression) are still elusive. For a general set of parameters, and by means of an approximated solution for a set of differential equations associated with a synaptic model, we obtain a discrete map that provides analytical solutions that shed light into the dynamics of synapses. Assuming that the presynaptic neuron perturbing the neuron whose synapse is being modelled is spiking periodically, we derive the stable equilibria and the maximal values for the release regimes as a function of the percentage of neurotransmitter released and the mean frequency of the presynaptic spiking neuron. Assuming that the presynaptic neuron is spiking stochastically following a Poisson distribution, we demonstrate that the equations for the time average of the trajectory are the same as the map under the periodic presynaptic stimulus, admitting the same equilibrium points. Thus, the synapses under stochastic presynaptic spikes, emulating the spiking behaviour produced by a complex neural network, wander around the equilibrium points of the synapses under periodic stimulus, which can be fully analytically calculated. Author summaryBased on the model proposed by Tsodyks et al., we obtained a map approximation to study analytically the dynamics of short-term synaptic plasticity. We identified the synaptic regimes named facilitation, depression, and biphasic in the parameters space, and determined the maximal and equilibrium points of active neurotransmitters for presynaptic neurons spiking periodically and stochastically following a Poisson process. Besides that, we verify that the time average of the variables for the synaptic dynamics driven by presynaptic neurons spiking following a Poisson distribution presents the equilibrium points obtained for the synaptic driven by periodic presynaptic neurons, spiking with a frequency that is the mean frequency of the Poisson distribution. These results shed analytical light into the understanding of synaptic dynamics.

neuroscience↗