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.

Animals in Art - Pablo Picasso
Dr. Kim likens simplification of complex biological networks to Picasso’s progressive reductionism of a bull.

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.

Given the different phase relationships between circadian regulator Per2 and p53, a set of possible regulatory relationships exists within a simplified network.

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?

The set of models that were able to recover the phasic relationships observed had different regulation types, which provided biological inference on the network.

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!

The simplification analysis, and following experimental confirmation, allowed Dr Kim et al to develop a more complex model of the Per2 and p53 network.

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).

Paper here.

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.

Paper here.

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

Click here to check out his website.

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