Date of Award

11-28-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Science

First Advisor

Xiaoshen Wang

Abstract

Using fission yeast cell cycle as an example, we uncovered that the non-equilibrium network dynamics and global properties are determined by two essential features: the potential landscape and the flux landscape. While potential landscape quantifies the probabilities of different states forming hills and valleys, the flux landscape quantifies the probability fluxes of different loops flowing through states. These two landscapes can be quantified through the decomposition of the dynamics into the detailed balance preserving part and detailed balance breaking non-equilibrium part. While the funneled potential landscape is often crucial for the stability of the single attractor networks, we have uncovered that the argument can be extended to the stabilities of the oscillations states by including them in the same line basin of attraction. However, the stabilities of the oscillation states cannot guarantee the stable direction flows. We have uncovered that the funneled flux landscape is crucial for the emergence and maintenance of the stable limit cycle oscillation flow. This provides a new interpretation of the origin for the limit cycle oscillations: There are many cycles and loops existed flowing through the state space and forming the flux landscapes, each cycle with a probability flux going through the loop. The limit cycle oscillation only emerges when one specific loop stands out and carries much more probability flux than the rest of the others. This happens when the non linearity of the inherent dynamical systems increases. We explore how robustness ratio (RR) quantifying the degrees of the funneling of the underlying potential and flux landscapes. We state that these two landscapes complement each other and are both essential for the stability of the fission yeast cell cycle. The flux is directly related to the speed of the cell cycle. This will allow us to identify the key factors and structure elements of the networks in determining the stability, speed and robustness of the fission yeast cell cycle oscillations. Regulating the cell cycle speed is crucial for designing the prevention and curing strategy of cancer.

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