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SUMMARY:Agent-based modelling of higher order chemical reactions using Smo
luchowski kinetics
DTSTART;VALUE=DATE-TIME:20180709T094500Z
DTEND;VALUE=DATE-TIME:20180709T100000Z
DTSTAMP;VALUE=DATE-TIME:20241109T193833Z
UID:indico-contribution-384@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: James Cavallo (Monash University)\nChemical reaction
s are traditionally modelled using deterministic methods such as ordinary
differential equations. In biology\, we also consider the effect of diffus
ion upon a reactive system. For small biological systems\, it is necessary
to use stochastic models. In this talk\, we choose to use an agent-based
model commonly known as Smoluchowski kinetics.\n\nIn the Smoluchowski mode
l\, two molecules diffuse in space\, and react when they are within a crit
ical separation distance (Smoluchowski radius). This radius is at a rate p
roportional to the reaction rate constant. Over the last 100 years\, the m
odel has been extended to incorporate reversible reactions by introducing
a second separation distance. \n\nA common problem with Smoluchowski kinet
ics is when modelling rapid enzyme reactions\, where the assumptions used
to model Smoluchowski kinetics break down. Using differential equations\,
these rapid interactions can be easily analysed using a pseudo steady stat
e approximation which effectively results in non-linear reactions. Other m
odels have utilised multiple timescales to model what is called fast-slow
reaction kinetics.\n\nIn this talk\, we theorise that a way to bypass the
fast-slow reaction kinetics problem is to extend the Smoluchowski model to
reversible trimolecular reactions. We develop these kinetics and apply th
em to the canonical Wnt signalling pathway. We model this pathway using tr
aditional Smoluchowski kinetics\, and show how the aforementioned issues c
ome into effect. We then compare this to our trimolecular model and show h
ow the issues disappear.\n\nhttps://conferences.maths.unsw.edu.au/event/2/
contributions/384/
LOCATION:University of Sydney Holme Building/--The Refectory
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/384/
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