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Jan-Hendrik Schleimer

Publications and source records attributed to Jan-Hendrik Schleimer.

5 recordsLinked to original sources
arXiv2022

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

q-bio.NC↗
arXiv2021

Neural Optimization: Understanding Trade-offs with Pareto Theory

Nervous systems, like any organismal structure, have been shaped by evolutionary processes to increase fitness. The resulting neural 'bauplan' has to account for multiple objectives simultaneously, including computational function as well as additional factors like robustness to environmental changes and energetic limitations. Oftentimes these objectives compete and a quantification of the relative impact of individual optimization targets is non-trivial. Pareto optimality offers a theoretical framework to decipher objectives and trade-offs between them. We, therefore, highlight Pareto theory as a useful tool for the analysis of neurobiological systems, from biophysically-detailed cells to large-scale network structures and behavior. The Pareto approach can help to assess optimality, identify relevant objectives and their respective impact, and formulate testable hypotheses.

q-bio.NC↗
arXiv2020

Firing statistics in the bistable regime of neurons with homoclinic spike generation

Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixpoint and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This study focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle (SNIC) bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential -- a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.

q-bio.NC↗
arXiv2016

Qualitative changes in spike-based neural coding and synchronization at the saddle-node loop bifurcation

Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting state and limit cycle spiking. Prominent qualitative changes in encoding have previously been attributed to a specific switch of such a bifurcation at the Bogdanov-Takens (BT) point. This study unveils another, highly relevant and so far underestimated transition point: the saddle-node loop bifurcation. As we show, this bifurcation turns out to induce even more drastic changes in spike-based coding than the BT transition. This result arises from a direct effect of the saddle-node loop bifurcation on the limit cycle and hence spike dynamics, in contrast to the BT bifurcation, whose immediate influence is exerted upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle-node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails close to optimal coding and synchronization properties in event-based information processing units, such as neurons. The saddle-node loop bifurcation leads to a peak in synchronization range and provides an attractive mechanism for the so far unresolved facilitation of high frequencies in neuronal processing. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators. On the experimental side, our theory applies to optical stimulation of nerve cells, and reveals that these techniques could manipulate a variety of information processing characteristics in nerve cells beyond pure activation.

q-bio.NC↗