Neurodynamics

Na Yu

Toronto Metropolitan University

"Exploring the Roles of Noise and Coupling Strength in the Emergent Dynamics of Clustered Neural Motifs"

Understanding how neural networks process information involves exploring how their structure and external influences shape collective dynamics. Research has shown that neuronal networks are not always randomly connected; instead they are organized into highly clustered motifs that act as fundamental building blocks. These motifs play a critical role in shaping collective dynamics such as synchrony and coherence. In this study, we modeled a neural network composed of six representative types of clustered motifs and examined how key factors, including intrinsic noise, inter-motif connectivity, network size, and coupling strength, affect the emergence of synchrony and coherence at both the motif and network levels. Our results reveal that synchrony is optimized when noise intensity and inter-motif connectivity are at intermediate levels. We also find that network performance is enhanced when the ratio of intra- to inter-motif coupling strength is within a specific range.  These results reveal how the interplay between structure and noise shapes coherent neural dynamics.

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Amin Akhshi

McGill University

"From Chaos to Neural Code: Exploring the Role of Gamma-Frequency Burst Oscillations in Sensory Pyramidal Cells"

Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish fire action potentials in the form of bursts (i.e., repeated clusters of spikes) through a mechanism known as ghostbursting. This mechanism enables ELL pyramidal cells to fire gamma-frequency burst oscillations (20–80 Hz) in response to constant applied current, characterized by progressively increasing spike frequencies within bursts. To efficiently investigate the emergence of these complex burst dynamics, we developed a phenomenological model based on the Hindmarsh-Rose (HR) formalism by incorporating dual adaptation variables and an extracellular noise term representing random excitatory and inhibitory inputs. Using parameter optimization against in vivo recordings, we demonstrated the model reliably reproduced key spiking features of ELL pyramidal cells, including chaotic burst firing patterns comparable to experimental observations. Subsequently, bifurcation analysis confirmed that chaotic burst firing is an intrinsic property of the model, consistent with the behavior of ELL pyramidal cells, while parameter sensitivity analysis revealed that external stochastic input modulates spiking activity, collectively shaping the firing patterns observed in vivo. Finally, to investigate the implications of our model for population coding, we performed network simulations in response to electrocommunication stimuli and found that burst firing significantly enhances synchronization among model neurons receiving common input. In this talk, I will provide an overview of these results.

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Adam Stinchcombe

University of Toronto

"Modelling Insights into Two Behaviour Rhythm Phenomena"

Ultradian behavioural rhythms are highly-flexible oscillations in goal-directed behaviour with periods shorter than a day. They remain mysterious in both their biochemical mechanisms and their functional significance, but are generally believed to be a reflection of neural dynamics. We propose that D2 autoreceptor-dependent dopamine self-regulation in the midbrain-striatal synapses gives rise to ultradian rhythmicity. We express this hypothesis in an ordinary differential equation based mathematical model in a dual-negative feedback-loop structure. Numerical integration and bifurcation analysis shows that the oscillations have a flexible and parameter-sensitive period in agreement with experimental observation. The model also demonstrates the masking-entraining effects of circadian (approximately 24 hour) regulation on ultradian rhythms and the rapid-resetting effect of transient excitation. This reveals the crucial role of circadian-ultradian interaction in consolidating behavioural activity and coordinating the motivation to engage in recurring, albeit not highly predictable events, such as social interactions.

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Richard Bertram

Florida State University

"Dynamic Homeostasis in Relaxation and Bursting Oscillations"

Homeostasis is typically thought of as the invariance of an equilibrium across a range of input values. However, many biological systems oscillate, and dynamic homeostasis refers to the invariance of some feature of the oscillation across a range of input values. In this presentation, we demonstrate that in fast/slow systems, in which the variables can be partitioned into those that change rapidly and those that change slowly, invariance can be produced in the mean value of a slow variable responsible for driving the oscillations. We use fast/slow analysis to explain this form of dynamic homeostasis and consider the effects of noise. The biological relevance lies in the fact that the slow variable driving the relaxation or bursting oscillation is often a quantity, such as the intracellular calcium or ATP concentration, that plays many roles in a cell and for which homeostasis is advantageous to cell behavior or health.

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