Stochasticity in Biophysical Systems: Searching, Aging, and Spreading
(2014)- 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) - 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4285455
- author
- Sanders, Lloyd LU
- supervisor
- opponent
-
- Professor Mehlig, Bernhard, Department of Physics, University of Gothenburg
- organization
- publishing date
- 2014
- 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 13:15:00
- ISBN
- 978-91-7473-815-5
- language
- English
- LU publication?
- yes
- id
- c52c1e34-a708-43b8-b2ae-e15fafcd403b (old id 4285455)
- date added to LUP
- 2016-04-04 11:08:23
- date last changed
- 2018-11-21 21:02:54
@phdthesis{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}},
keywords = {{Anomalous diffusion; Single-file; Markov process; Epidemiology; First Passage Time}},
language = {{eng}},
publisher = {{Department of Astronomy and Theoretical Physics, Lund University}},
school = {{Lund University}},
title = {{Stochasticity in Biophysical Systems: Searching, Aging, and Spreading}},
year = {{2014}},
}