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Fri, Dec 03, 2021
Colloquium Stability‌ ‌Analysis‌ ‌of‌ ‌Reaction‌ ‌Models‌ ‌for‌ ‌Protein‌ ‌Interaction‌ ‌Networks Lucas M. Stolerman, OSU / Machine Intelligence Lab / Harvard Med. School Host: David Wright Professor Stolerman is joining the Department of Mathematics this spring 2022 as an expert in applications of mathematics to cell biology and related topics. Abstract: This‌ ‌talk‌ ‌will‌ ‌cover‌ ‌two‌ ‌of‌ ‌my‌ ‌recent‌ ‌papers‌ ‌in‌ ‌cell‌ ‌biology,‌ ‌where‌ ‌local‌ ‌stability‌‌
analysis‌ ‌provided‌ ‌insights‌ ‌into‌ ‌protein‌ ‌network‌ ‌dynamics.‌ ‌In‌ ‌the‌ ‌first‌ ‌paper,‌ ‌we‌‌
investigate‌ ‌the‌ ‌pattern‌ ‌formation‌ ‌of‌ ‌a‌ ‌reaction-diffusion‌ ‌model‌ ‌for‌ ‌protein‌ ‌clustering‌‌
in‌ ‌the‌ ‌plasma‌ ‌membrane.‌ ‌We‌ ‌obtain‌ ‌theoretical‌ ‌estimates‌ ‌for‌ ‌diffusion-driven‌‌
instabilities‌ ‌of‌ ‌the‌ ‌protein‌ ‌aggregates‌ ‌based‌ ‌on‌ ‌the‌ ‌Turing‌ ‌mechanism.‌ ‌Our‌ ‌main‌‌
result‌ ‌is‌ ‌a‌ ‌threshold‌ ‌phenomenon:‌ ‌a‌ ‌sufficiently‌ ‌high‌ ‌feedback‌ ‌reaction‌ ‌between‌ ‌the‌‌
membrane‌ ‌and‌ ‌cytosolic‌ ‌proteins‌ ‌promotes‌ ‌the‌ ‌formation‌ ‌of‌ ‌a‌ ‌single-patch‌ ‌spatially‌‌
heterogeneous‌ ‌steady‌ ‌state.‌ ‌In‌ ‌the‌ ‌second‌ ‌paper,‌ ‌we‌ ‌discuss‌ ‌GTPase‌ ‌molecular‌‌
switches‌ ‌and‌ ‌a‌ ‌network‌ ‌between‌ ‌monomeric‌ ‌(m)‌ ‌and‌ ‌trimeric‌ ‌(t)‌ ‌GTPases‌ ‌that‌ ‌have‌‌
been‌ ‌recently‌ ‌found‌ ‌in‌ ‌experiments.‌ ‌We‌ ‌develop‌ ‌a‌ ‌nonlinear‌ ‌ordinary‌ ‌differential‌‌
equation‌ ‌model‌ ‌and‌ ‌provide‌ ‌explicit‌ ‌formulae‌ ‌for‌ ‌the‌ ‌steady‌ ‌states‌ ‌of‌ ‌the‌ ‌system.‌ ‌By‌‌
performing‌ ‌a‌ ‌local‌ ‌stability‌ ‌analysis,‌ ‌we‌ ‌systematically‌ ‌investigate‌ ‌the‌ ‌role‌ ‌of‌ ‌the‌‌
different‌ ‌connections‌ ‌between‌ ‌the‌ ‌GTPase‌ ‌switches.‌ ‌Interestingly,‌ ‌a‌ ‌coupling‌ ‌of‌ ‌the‌‌
active‌ ‌mGTPase‌ ‌to‌ ‌the‌ ‌GEF‌ ‌of‌ ‌the‌ ‌tGTPase‌ ‌is‌ ‌sufficient‌ ‌to‌ ‌provide‌ ‌two‌ ‌locally‌ ‌stable‌‌
states‌ ‌that‌ ‌can‌ ‌be‌ ‌interpretable‌ ‌biologically.‌ ‌When‌ ‌we‌ ‌add‌ ‌a‌ ‌feedback‌ ‌loop‌ ‌to‌ ‌the‌‌
coupled‌ ‌system,‌ ‌two‌ ‌other‌ ‌locally‌ ‌stable‌ ‌states‌ ‌emerge.‌ ‌Our‌ ‌findings‌ ‌reveal‌ ‌that‌‌
coupling‌ ‌these‌ ‌two‌ ‌different‌ ‌GTPase‌ ‌motifs‌ ‌can‌ ‌dramatically‌ ‌change‌ ‌their‌‌
steady-state‌ ‌behaviors‌ ‌and‌ ‌shed‌ ‌light‌ ‌on‌ ‌how‌ ‌such‌ ‌coupling‌ ‌may‌ ‌impact‌ ‌signaling‌‌
mechanisms‌ ‌in‌ ‌eukaryotic‌ ‌cells.
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