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Stochasticity in Biophysical Systems: Searching, Aging, and Spreading

Sanders, Lloyd LU (2014)
Abstract (Swedish)
Popular Abstract in Swedish

Stokastika effekter är av stor betydelse i många biofysiska system. Evolution, djurs

sökande efter föda, spridning av virusinfektioner och stamcellsdifferentiering, är alla

exempel på processer som på ett eller annat sätt är stokastiska till sin natur. Syftet

med denna avhandling är att undersöka de verktyg som ofta används för att kvantifiera

slumpmässighet i naturen och applicera dessa verktyg på ett antal biofysiska system.

I våra artiklar har vi ett starkt fokus på två områden: single–file diffusion (SFD) och

epidemiologi.

I ett SFD-system tillåts partiklar i en endimensionell kanal diffusera men partiklarna

kan inte... (More)
Popular Abstract in Swedish

Stokastika effekter är av stor betydelse i många biofysiska system. Evolution, djurs

sökande efter föda, spridning av virusinfektioner och stamcellsdifferentiering, är alla

exempel på processer som på ett eller annat sätt är stokastiska till sin natur. Syftet

med denna avhandling är att undersöka de verktyg som ofta används för att kvantifiera

slumpmässighet i naturen och applicera dessa verktyg på ett antal biofysiska system.

I våra artiklar har vi ett starkt fokus på två områden: single–file diffusion (SFD) och

epidemiologi.

I ett SFD-system tillåts partiklar i en endimensionell kanal diffusera men partiklarna

kan inte passera varandra; partiklarna behåller med andra ord sin ordning för alla

tider. SFD-processer är av särskild relevans i biologin, till exempel används SFD

ofta som en abstrakt representation av många proteiners rörelse på DNA, vilket

också är motivationen för de två första artiklarna i denna avhandling. I Artikel I

analyserar vi first passage time density (FPTD)1 för en given partikel i homogena

och heterogena SFD-system och hur de länkar till icke-Markovsk Brownsk rörelse.

I Artikel II utökar vi modellen för att tillåta grann-partiklarna att binda till och

lossna från det endimensionella systemet med givna reaktionshastigheter och vi

undersöker hur detta påverkar FPTD. Artikel III liknar den första, men partiklarna

är alla funktionaliserade; deras väntetid mellan hopp tas från en potenslag, inte en

exponentiell sannolikhetsdensitet (som i artikel I och II). Genom ett enkelt argument

analyserar vi dynamiken, samt beskriver en mikroskopisk mekanism för mycket långsam

dynamik i vissa fysikaliska system.

I det andra området, Artikel IV, utforskar vi stokastisk spridning av virus på

metapopulationer. Vi introducerar en störningsteoretisk analysmetod (i ett område

mättat med numeriska metoder) för att kvantifiera spridningen av ett susceptible-

infected-susceptible-virus (SIS; mottaglig-infekterad-mottaglig) på ett nätverk av stora

befolkningar, anslutna via en kopplingsmatris. (Less)
Abstract
The role of stochasticity throughout many biophysical systems is of great importance. From

evolution to foraging, from the spreading of viruses to cell fate, all hinge in one way or

another on inherent stochasticity. The aim of this thesis is to explore the tools often used

to quantify randomness in nature, and employ these tools on a selected range of biophysical

systems (Papers I-IV). In these papers we cover many-bodied systems with keen focus on two

areas: single-file diffusion (SFD), and epidemiology.

In a SFD system particles in a 1D channel are allowed to diffuse but cannot occupy the same

space, thus the particles maintain their order for all time. SFD occurs often in... (More)
The role of stochasticity throughout many biophysical systems is of great importance. From

evolution to foraging, from the spreading of viruses to cell fate, all hinge in one way or

another on inherent stochasticity. The aim of this thesis is to explore the tools often used

to quantify randomness in nature, and employ these tools on a selected range of biophysical

systems (Papers I-IV). In these papers we cover many-bodied systems with keen focus on two

areas: single-file diffusion (SFD), and epidemiology.

In a SFD system particles in a 1D channel are allowed to diffuse but cannot occupy the same

space, thus the particles maintain their order for all time. SFD occurs often in biology, for

example, it is often used as an abstract representation of protein motion on crowded DNA,

the motivation for the first two papers. In Paper I we analyze the first passage time density

(FPTD) of a tracer particle in homogeneous and heterogeneous systems and how they link

to fractional Brownian motion particles (non-Markovian diffusive particles). In Paper II we

extend the model to allow flanking particles of the tracer to enter/leave the 1D channel with

a given rate, and investigate how this affects the FPTD. Paper III is similar to the first,

but the particles are all functionalized: their waiting time between movement is taken from

a power-law density, not an exponential (as in Papers I and II). Through a simple scaling

argument we analyze the tracer dynamics, and seek to provide a mechanism for "aging",

logarithmically slow dynamics seen in certain physical systems.

In the second area, Paper IV, we explore the stochastic spreading of viruses on metapop-

ulations. We provide an analytical method (in an area saturated by numerical techniques)

to model the spread of a susceptible-infected-susceptible virus on a general network of large

populations, connected through a travel rate matrix. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Mehlig, Bernhard, Department of Physics, University of Gothenburg
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Anomalous diffusion, Single-file, Markov process, Epidemiology, First Passage Time
pages
92 pages
publisher
Department of Astronomy and Theoretical Physics, Lund University
defense location
Lundmarkshalen
defense date
2014-02-21 13:15
ISBN
978-91-7473-815-5
language
English
LU publication?
yes
id
c52c1e34-a708-43b8-b2ae-e15fafcd403b (old id 4285455)
date added to LUP
2014-02-10 14:33:07
date last changed
2016-09-19 08:45:08
@misc{c52c1e34-a708-43b8-b2ae-e15fafcd403b,
  abstract     = {The role of stochasticity throughout many biophysical systems is of great importance. From<br/><br>
evolution to foraging, from the spreading of viruses to cell fate, all hinge in one way or<br/><br>
another on inherent stochasticity. The aim of this thesis is to explore the tools often used<br/><br>
to quantify randomness in nature, and employ these tools on a selected range of biophysical<br/><br>
systems (Papers I-IV). In these papers we cover many-bodied systems with keen focus on two<br/><br>
areas: single-file diffusion (SFD), and epidemiology.<br/><br>
In a SFD system particles in a 1D channel are allowed to diffuse but cannot occupy the same<br/><br>
space, thus the particles maintain their order for all time. SFD occurs often in biology, for<br/><br>
example, it is often used as an abstract representation of protein motion on crowded DNA,<br/><br>
the motivation for the first two papers. In Paper I we analyze the first passage time density<br/><br>
(FPTD) of a tracer particle in homogeneous and heterogeneous systems and how they link<br/><br>
to fractional Brownian motion particles (non-Markovian diffusive particles). In Paper II we<br/><br>
extend the model to allow flanking particles of the tracer to enter/leave the 1D channel with<br/><br>
a given rate, and investigate how this affects the FPTD. Paper III is similar to the first,<br/><br>
but the particles are all functionalized: their waiting time between movement is taken from<br/><br>
a power-law density, not an exponential (as in Papers I and II). Through a simple scaling<br/><br>
argument we analyze the tracer dynamics, and seek to provide a mechanism for "aging",<br/><br>
logarithmically slow dynamics seen in certain physical systems.<br/><br>
In the second area, Paper IV, we explore the stochastic spreading of viruses on metapop-<br/><br>
ulations. We provide an analytical method (in an area saturated by numerical techniques)<br/><br>
to model the spread of a susceptible-infected-susceptible virus on a general network of large<br/><br>
populations, connected through a travel rate matrix.},
  author       = {Sanders, Lloyd},
  isbn         = {978-91-7473-815-5},
  keyword      = {Anomalous diffusion,Single-file,Markov process,Epidemiology,First Passage Time},
  language     = {eng},
  pages        = {92},
  publisher    = {ARRAY(0xda66048)},
  title        = {Stochasticity in Biophysical Systems: Searching, Aging, and Spreading},
  year         = {2014},
}