arXiv:2412.04172v3 Announce Type: replace Abstract: Neurons rely on two interdependent mechanisms, homeostasis and neuromodulation, to maintain robust and adaptable functionality. Calcium homeostasis stabilizes neuronal activity by adjusting ionic conductances, whereas neuromodulation dynamically modifies ionic properties in response to external signals carried by neuromodulators. Combining these mechanisms in conductance-based models often produces unreliable outcomes, particularly when sharp neuromodulation interferes with calcium-homeostatic tuning. This study explores how a biologically inspired neuromodulation controller can harmonize with calcium homeostasis to ensure reliable neuronal function. Using computational models of stomatogastric ganglion and dopaminergic neurons, we demonstrate that controlled neuromodulation preserves neuronal firing patterns while calcium homeostasis simultaneously maintains target intracellular calcium levels. Unlike sharp neuromodulation, the neuromodulation controller integrates activity-dependent feedback through mechanisms mimicking G-protein-coupled receptor cascades. The interaction between these controllers critically depends on the existence of an intersection in conductance space, representing a balance between target calcium levels and neuromodulated firing patterns. Maximizing neuronal degeneracy enhances the likelihood of such intersections, enabling robust modulation and compensation for channel blockades. We further show that this controller pairing extends to network-level activity, reliably modulating the rhythmic activity of central pattern generators. This study highlights the complementary roles of calcium homeostasis and neuromodulation, proposing a unified control framework for maintaining robust and adaptive neural activity under physiological and pathological conditions.

arXiv:2509.12783v2 Announce Type: replace Abstract: Inferring the biophysical parameters of conductance-based models (CBMs) from experimentally accessible recordings remains a central challenge in computational neuroscience. Spike times are the most widely available data, yet they reveal little about which combinations of ion channel conductances generate the observed activity. This inverse problem is further complicated by neuronal degeneracy, where multiple distinct conductance sets yield similar spiking patterns. We introduce a method that addresses this challenge by combining deep learning with Dynamic Input Conductances (DICs), a theoretical framework that reduces complex CBMs to three interpretable feedback components governing excitability and firing patterns. Our approach first maps spike times to DIC densities at threshold using a neural network that learns a low-dimensional representation of neuronal activity. The predicted DIC values are then used to generate degenerate CBM populations via an iterative compensation algorithm, ensuring compatibility with the intermediate target DICs, and thereby reproducing the corresponding firing patterns, even in high-dimensional models. Applied to two models, this algorithmic pipeline reconstructs spiking and bursting regimes with high accuracy and robustness to variability, including spike trains generated under noisy current injection mimicking physiological stochasticity. It produces diverse degenerate populations within milliseconds on standard hardware, enabling scalable and efficient inference from spike recordings alone. Together, this work positions DICs as a practical and interpretable link between experimentally observed activity and mechanistic models. By enabling fast and scalable reconstruction of degenerate populations directly from spike times, our approach provides a powerful way to investigate how neurons exploit conductance variability to achieve reliable computation.