Myelin influences axonal conduction delays which determine the timing of signal transmission. Recent experimental findings have challenged the conventional notion of uniform myelination along single axons, unveiling a wide spectrum of myelin patterns that exhibit important variations from one axon to another. 

We developed a system of partial differential equations based on the cable theory that captures the dynamics of membrane potential along axons with heterogeneous myelination profiles. We found highly variable conduction delays which have additional implications in demyelination.

Talidou, A. & Lefebvre, J. Influence of myelination patterns on axonal conduction and susceptibility to demyelination.

The term activity-dependent myelination (ADM) refers to a dynamic process in which myelin changes as a function of neural activity. At a network level, the speed and timing of signal transmission between neurons are pivotal factors influencing information processing. An optimal neural communication relies on the precise conduction delays along each axon within a network. Myelin, given its dynamic nature, plays a crucial role in achieving and maintaining these optimal conduction delays. 

We built a system of nonlinear stochastic delay differential equations that models the membrane potential of each neuron within a network of independently spiking neurons to explore the implications of ADM on firing activity and information transmission in the brain. A key finding revealed that ADM can induce changes in axonal conduction delays, effectively equalizing conduction velocities across axons of varying lengths. 

Talidou, A., Frankland, P.W., Mabbott, D. &  Lefebvre, J. Homeostatic coordination and up-regulation of neural activity by activity-dependent myelination. Nature Comput Sci 2, 665-676 (2022).

Within the hippocampus, a brain area involved in memory, two predominant oscillatory patterns emerge: theta and gamma rhythms. Theta rhythms are relatively slow (3-12 Hz), whereas gamma rhythms are faster (20-100 Hz). Since theta rhythms are slower than gamma, multiple gamma cycles can occur during a single theta cycle. Recent experimental research indicates that theta and gamma rhythms are coupled together, in a manner that gamma consistently begin at the same relative position within theta. This phenomenon is believed to facilitate memory encoding in the hippocampus.

We constructed a system of functional differential equations representing the mean firing rates of four cell types: pyramidal (PYR), bistratified (BiC), parvalbumin (PV)-expressing, and cholecystokinin (CCK)-expressing basket cells. This system allows us to specify the origin of theta and gamma rhythms and provides a fruitful environment for exploring the cell-type connections that lead to theta-gamma coupling.

Sengupta S.*, Talidou. A*, Lefebvre J., Skinner F. K. Cell-type specific contributions to theta-gamma rhythms in the hippocampus.   * These authors contributed equally.