BACKGROUND:

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In-vitro and in-vivo recordings of single cortical neurons show highly heterogeneous responses, presenting predominant activity such as spiking or bursting. Sometimes, traces with continuous spikes show tiny inter-spike fluctuations, which, even if they persist after post-processing phases, are predominantly classified as noise. Unlike this hypothesis, these traces unveil a third type of evolution, known as mixed-mode oscillations (MMOs). As the name suggests, these temporal series contain oscillations with different amplitudes, where sequences of small fluctuations separate consecutive or single action potentials.

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My research investigates MMOs in single and network of neurons, focusing on the biological mechanisms involved in their control and how they modulate relevant features recruited during neuronal communication.

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METHODOLOGY:

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MMOs are analytically investigated in applied mathematics, which classify them depending on their generation mechanism. Concerning single-cell models of spiking neurons, the most common type of MMOs is the one based on folded nodes. This structure acts locally, unveiling its fragility. Despite being a weakness, it highlights the complexity of controlling this phenomenon and why experimental recordings are poorly classified as MMOs.

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An obvious question is: “How can we classify an experimental recording of MMOs-type instead of noisy temporal evolution?”. Neuronal ODE models are a valuable tool to provide an answer. Simulations and mathematical analyses help to investigate the necessary conditions to activate MMOs. Additionally, in-silico drug administration offers you some ideas on how specific features embedded in the model influence these evolutions.

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These investigations require tools to analyse ODE systems. I use XPPAUT, MATLAB, and Python as complementary software. Usually, the first allows you to compute one- or two-parameter bifurcation diagrams. Instead, MATLAB and Python give you the freedom to implement complex routines, integrating and controlling results coming from other programs.

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RESULTS:

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During the first year of my PhD, I jointly worked with my supervisor on explaining how cAMP alters the activity of cortical neurons, transforming spiking into MMOs, as experimentally observed. We found that, after astrocyte-induced cAMP increase, both M and HCN currents strengthen. These alterations modify the neuron's evolution, which starts to separate consecutive action potentials through sets of small amplitude oscillations, as depicted in Figure 1.

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Figure 1. Comparison between control and high intracellular cAMP levels. The increase in cAMP concentration converts spiking into MMOs through M and HCN currents.

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FUTURE WORK:

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In this work, to assess the dynamics of the 5D model, we reduced it to three dimensions, considering the two super-slow variables as parameters set to their average values. The 3D model offered us insights regarding the simplified dynamics, providing some preliminary explanation of the 5D behaviour but evolving with an altered number of small and large amplitude oscillations. These differences raise some interesting mathematical questions regarding how the dynamics of the two approximated super-slow variables influence MMOs. On the other hand, I’m interested in understanding how the dynamics of astrocytes intervene during these tiny oscillations and which colorful dynamics can arise when cortical neurons organize in small networks presenting this type of evolution!

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FUNDED BY:

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CONTACT: