Math Modeling

# Jae Kyoung Kim – Analysis of dynamic data: from molecule to behavior – Mathematical and Computational Methods in Biology Workshop

MBI’s online workshop on Mathematical and Computational Methods in Biology will be running all week! See the schedule here (https://mbi.osu.edu/events/mathematical-and-computational-methods-biology). It is also being live streamed here: https://video.mbi.ohio-state.edu/live.

I really enjoyed this talk by Dr Jae Kyoung Kim of KAIST. In his talk, he discussed the simplification of biological networks to facilitate analysis, and showed that yes, we CAN get valuable inference, even from highly reductive models!

## Simplify and Reduce Network

Dr Kim begins by laying out the logic of simplifying a network. We can simplify very complicated networks by considering the significance of steps that aren’t easily observable. Dr Kim separates these into two broad categories. If a set of hidden steps (hidden in the model, or perhaps experimentally hidden) takes a significant amount of time, we can summarize and replace them using a time delay equation. Alternatively, if they take negligible time, we can simply eliminate them.

In the figure above, Dr Kim shows what his highly simplified model of hypothetical Per2 regulation of p53 looks like. To the right, he shows the experimental observation that Per2 and p53 regulation in the cytoplasm is out of phase, but in the nucleus they are in phase. He asks the question – what kind of regulation would explain these different dynamics?

He uses a Bayesian approach. He creates 3 equations that represent one of 3 regulatory scenarios: positive regulation by Per2; negative regulation by Per2; or no regulation. He then iterates through all the possible regulatory scenarios (represented by the arrows in the previous simplified regulation diagram). The results are summarized in the 3D histgram figure. For every case where the proper phase relationship was observed, the type of regulation is plotted. For each of the 5 regulation types, we get a different distribution of regulations across all the models. This provides some biological inference which was then confirmed experimentally!

Given this information, he was able to create a more complex model of Per2 regulation of p53. You can get more information from the paper below (from which I lifted these figures).

## Existence and Uniqueness of Mathematical Models for Biological Data

Perhaps the coolest part of the talk (for me) was when he discussed his proof that, given a set of dynamic biological data, he can prove that there is a UNIQUE mathematical model (given that a model exists). He walked us through his proof briefly, which was greatly appreciated, as its often hard or impossible to follow during the presentation format. I’m looking forward to reading his papers more in depth.

Part of his lab is also using ODE models for deep learning AI!