Mathematical Biology Calendar

How Neurons Add Spikes: Slow Rhythms, Geometry, and Bursting Patterns

Speaker: Zahra Aminzare (University of Iowa)

Abstract: Bursting—episodes of rapid spiking separated by quiescent phases—is a common feature of neuronal activity and plays an important role in information processing. In particular, the number and timing of spikes within a burst can encode information and influence downstream responses. 

While the transition from tonic spiking to bursting has been widely studied, the mechanisms by which spikes are added to or removed from a burst remain less understood. In this talk, I examine spike-adding phenomena in neuronal models driven by slow rhythmic inputs, using tools from geometric singular perturbation theory and bifurcation theory. Using periodically forced neuronal models—with the FitzHugh–Nagumo system as a prototypical example and the Morris–Lecar model as a more biologically detailed case—I show how varying the frequency and amplitude of the input leads to transitions from single spikes to complex bursting patterns. Within the bursting regime, the dynamics further organize into a spike-adding structure in parameter space, where the number of spikes per burst changes in a predictable way.

Overall, this work highlights how slow rhythms shape neuronal activity and suggests that spikeadding provides a mechanism by which neural systems regulate information transmission.

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Prof. Zahra Aminzare is also speaking at the DCL Seminar Series on Wed 3pm at B02 CSL: 

Rhythm Generation and Control in Insect Locomotion: A Dynamical Systems Perspective

Abstract: Locomotion in animals emerges from complex interactions between neural control, musculoskeletal dynamics, and environmental forces, and can be viewed as a network of coupled nonlinear systems generating coordinated rhythmic outputs. While stable rhythmic patterns (limit cycles) can be generated intrinsically within neural circuits, feedback plays a critical role in enhancing their stability, robustness to perturbations, and adaptability in locomotion.

In this talk, focusing on locomotion in the stick insect, we first adopt a feedforward perspective to study the mechanisms underlying the generation and control of stepping patterns from the intrinsic dynamics of neural circuits. In particular, we consider a biologically grounded model of central pattern generator (CPG) networks for the metathoracic segment of the middle leg, formulated as an 18-dimensional system of synaptically coupled ordinary differential equations. Using tools from nonlinear dynamical systems, including fast–slow decomposition, we identify mechanisms that give rise to stable, robust, and flexible multi-phase stepping rhythms.

Time permitting, we then incorporate feedback and move to a closed-loop setting, investigating how interactions between neural circuitry and biomechanics shape and stabilize single-leg stepping patterns. These results suggest principles for the design of distributed rhythmic controllers in legged robotic systems