Scale invariance in biological systems
Creators: name: Škatarić, Maja
Publisher: name: No Publisher Supplied
Year: 2014

description: In this dissertation we will discuss various techniques related to modeling and identification problems arising in complex biological networks, and demonstrate how control theory approaches can be used to validate mathematical models coming from exhaustive computational experiments or noisy experimental data. The methodology based on systematic exploration of the basic dynamic processes, feedback control loops, and signal processing mechanisms in complex networks or their parts provides powerful  tools for guiding the reverse-engineering of networks, and allows one to design artificial  systems that are capable of achieving various objectives.  Adaptation is an essential property of many cellular systems and it means that  the measured variables return to their basal levels after a transient response to a step  increase in stimulus. By definition, neither the concepts of perfect nor approximate  adaptation address the characteristics of the transient signaling which occurs prior  to a return to steady state, which are physiologically relevant. It has been recently  observed that some adapting systems, ranging from bacterial chemotaxis pathways  to signal transduction mechanisms in eukaryotes exhibit an additional feature: scale  invariance, meaning that transient behavior remains approximately the same when the  background signal level is scaled. Recent interest in scale-invariance was triggered by a  pair of papers published in 2009, in which scale-invariant behavior was experimentally  observed in several highly conserved eukaryotic signaling pathways that play roles in  embryonic patterning, stem cell homeostasis, cell division, and other central processes,  and their misregulation results in diseases including several types of cancer.  In this thesis we will review the biological phenomena of adaptation and scale invariance,  and present the relevant mathematical results for several classes of systems  that exhibit these properties. We will use a model from the literature which describes  the class of enzyme networks, to prove the impossibility of perfect scale invariance,  and develop the mechanism which gives rise to an approximate scale invariance. We  will demonstrate results on a biological example of soil-living amoeba Dictyostelium  discoideum. Additionally, it has been often remarked in the literature that certain  systems whose output variables respond at a faster time scale than internal components,  give rise to an approximate scale-invariant behavior. We will state a fundamental limitation  of such a mechanism, showing that there is a minimal error that cannot be  overcome, no matter how large the separation of time scales is. We will highlight the  extensions and challenges in analyzing adaptation and scale-invariance in a stochastic  setting.  Finally, we will discuss the development of tools for the identification of time-varying  parameters in nonhomogeneous Poisson processes, in applications where discrete measurements  such as "spikes" or "tumbles" are observed from the behavior of free swimming  bacteria in response to the nutrient (input) signals. The objective is to estimate  the underlying rate of a nonhomogeneous Poisson process that describes these events,  which can then be used to analyze transient behaviors of various species and postulate  a plausible model. This work has been motivated by the novel experimental methods  for assaying various chemotactic bacteria based on microfluidics devices, with the goal  to analyze scale invariance property and model the behavior of different species using  various inputs (nutrients).