Dynamics of Tonic Spiking and Bursting States in Pacemaker Neurons in the Pre-Bötzinger Complex

Muhammad Abdulla

Authors:  Muhammad Abdulla, Jonathan Rubin, Ryan Phillips

Faculty Mentor: Dr. Jonathan Rubin

College:  College of Liberal Arts and Sciences


This research investigates the mechanisms underlying neuronal bursting. Neurons have been modeled as relatively simple dynamical systems for decades. However, neuronal “bursting,” periodic behavior characterized by periods of high frequency spiking alternating with periods of quiescence, is quite complex, and can’t be modeled as simply as other behaviors. Multiple parameters, operating on different time scales, i.e. one parameter having significantly faster dynamics than the other, are necessary to model this behavior. (Ermentrout, 2010) In the past, different biological factors, including positive feedback currents (Butera, 1999), dynamic ion concentrations (Barreto, 2010), and different experimental conditions (Bacak, 2016), have been incorporated into mathematical models to capture various aspects of neuronal bursting. This paper proposes a mathematical model that includes both dynamic ion concentrations and positive feedback via persistent sodium currents, to model neuronal bursting under physiological conditions. Bifurcation analysis of this autonomous dynamical system offers insights into the mathematical mechanisms underlying biologically observed solutions, in which neuronal activity gradually evolves from sparse tonic spiking to full bursting, as well as other activity patterns emerging as neurons transition into the bursting state.

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7 Responses
  1. Hey Muhammad, this was a very interesting presentation! Although the subject of quantitative neuronal modeling is very technical, you made the information easy to digest! Great job!

  2. Sophia Paulitz

    This was a really interesting presentation! It is especially relevant now with the respiratory illness covid-19 being so prevalent. As someone not very familiar with this topic, I was a little lost on the methodology. Did your study involve research participants? What did your day-to-day research look like? Again, awesome job!

    1. Muhammad Abdulla

      Hey Sophia, thanks for the question! My specific research project focused on building a more accurate mathematical model of “bursting behavior” using systems of ordinary differential equations. Most of the data used to construct this model was actually just taken from previous models within the field. However, in order to test whether our model was any better than other models, we did have to compare them via some kind of physiological data. In our case, we simply referred back to neuronal data from other papers in the field of neuroscience.

      As far as the day to day research, I spent a lot of time reading up on the mathematical explanations of different phenomena in previous models. Once I began to get a firmer grasp on the mathematics, I started trying to create my own model. Then most of the day was spent messing around with model parameters in order to understand what effect they have on the system, followed by justifying these effects with mathematical explanations. Once we completed the model, I began performing numerous tests to check the robustness of tuneability of the model. Finally, I began using a lot of programming (specifically MATLAB) to analyze different behaviors within the model, and explain the mathematical mechanisms through which these behaviors happen.

  3. Julia

    Hey Muhammed! I found your presentation interesting and very relevant to what is currently happening today with COVID-19 and its impact on our respiratory system. It was very easy to follow your presentation. Great job!

  4. Nik Mirsaderov

    Hey Muhammad,

    I found your research very interesting! It is inspiring how deep you dive into the human brain and relate it to current world issues, such as COVID-19. I also enjoy your use of previous research, even back from the 1900’s, as a foundation of your own. Very cool!

  5. Rusini Perera

    Hi Muhammad!

    Great presentation! I have a few quick questions for you. How did you figure out what additional neural regulators the new model needed? Also, do you think there is room for more neural regulators to be added to the model?