Jin Wang

The potential and flux landscape for physical and biological nonequilibrium systems

The complex systems are everywhere around us ranging from the physical to the biological objects. These are often open systems with inputs of energy and information from outside. Uncovering the organization principles and physical quantification of the complex non-equilibrium open systems are essential for understanding the global function and stability. This presents us a great challenge. In this talk, we summarized our recent efforts in this direction. We found that the dynamics of the complex nonequilibrium systems can be determined by the two driving forces. One is the gradient of the underlying landscape and the other is from the curl flux in an analogy to the force experienced of an electron moving in the electric and magnetic field. The underlying landscape is linked to the probability distribution of the steady state and provides a global quantification for describing the complex nonequilibrium system. We found that the landscape can be used to quantify the global stability and robustness of the system. The non-zero flux breaks the detailed balance and therefore gives a quantitative measure of how far away the system is from the equilibrium state, reflecting the degree of the energy/material/information input to the system. Our decomposition of the driving forces of the complex nonequilibrium systems into landscape gradient and curl flux establishes the link between the dynamics and the underlying thermodynamic non-equilibrium natures. We further have uncovered the non-equilibrium versions of the optimal kinetic paths, the transition state theory, and the fluctuation-dissipation theorem, which are all deviated from their equilibrium counter-parts. We applied our theory to several physical and biological systems such as cell cycle, stem cell differentiation and reprograming, cancer, neural networks, evolution, ecology and chaos [1]. For cell cycle oscillations, we found the underlying landscape has a Mexican hat ring shape topology. The height of the Mexican hat determines the global stability. The landscape gradient attracts the system down to the oscillation ring. The curl flux is the driving force for coherent oscillation on the ring.  The flux and landscape together determines the global function (such as period and amplitude) of the cell cycle oscillation. The global sensitivity analysis according to the landscape and flux reveals the key genes and regulations controlling the cell cycle, important for anti-cancer strategy.