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Face of Tobias Ambjörnsson. Photo.

Tobias Ambjörnsson

Senior lecturer

Face of Tobias Ambjörnsson. Photo.

Stochasticity in Biophysical Systems: Searching, Aging, and Spreading


  • Lloyd Sanders

Summary, in English

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.


  • Computational Biology and Biological Physics

Publishing year




Document type



Department of Astronomy and Theoretical Physics, Lund University


  • Biophysics


  • Anomalous diffusion
  • Single-file
  • Markov process
  • Epidemiology
  • First Passage Time




  • Tobias Ambjörnsson


  • ISBN: 978-91-7473-815-5

Defence date

21 February 2014

Defence time


Defence place



  • Bernhard Mehlig (Professor)