Landscape and flux reveal a new global view and physical quantification of mammalian cell cycle

Abstract

Cell cycles, essential for biological function, have been investigated extensively. However, enabling a global understanding and defining a physical quantification of the stability and function of the cell cycle remains challenging. Based upon a mammalian cell cycle gene network, we uncovered the underlying Mexican hat landscape of the cell cycle. We found the emergence of three local basins of attraction and two major potential barriers along the cell cycle trajectory. The three local basins of attraction characterize the G1, S/G2, and M phases. The barriers characterize the G1 and S/G2 checkpoints, respectively, of the cell cycle, thus providing an explanation of the checkpoint mechanism for the cell cycle from the physical perspective. We found that the progression of a cell cycle is determined by two driving forces: curl flux for acceleration and potential barriers for deceleration along the cycle path. Therefore, the cell cycle can be promoted (suppressed), either by enhancing (suppressing) the flux (representing the energy input) or by lowering (increasing) the barrier along the cell cycle path. We found that both the entropy production rate and energy per cell cycle increase as the growth factor increases. This reflects that cell growth and division are driven by energy or nutrition supply. More energy input increases flux and decreases barrier along the cell cycle path, leading to faster oscillations. We also identified certain key genes and regulations for stability and progression of the cell cycle. Some of these findings were evidenced from experiments whereas others lead to predictions and potential anticancer strategies.cell cycle phases | cell cycle checkpoints | landscape | flux T he cell cycle is a series of events that take place in a cell leading to its replication and division. Studying the cell cycle process is essential for understanding cell growth, proliferation, development, and death (1-4). Cell cycle comprises several distinct phases: G1 phase (resting), S phase (synthesis), G2 phase (interphase), and M phase (mitosis). Activation of each phase is dependent on the proper progression and completion of the previous one, which can be monitored by cell cycle checkpoints. It is now believed that all proliferation, differentiation, and cell death processes are controlled by the underlying gene regulatory networks (5), which often involve many complex feedback loops (6). The complexity of the large regulatory networks for the cell cycle makes it difficult to understand the global natures and connections between the underlying network and the cell cycle process. Furthermore, in the cell, the intrinsic fluctuations from the finite number of molecules and extrinsic fluctuations from dynamical and inhomogeneous environments (7, 8) coexist. Therefore, stochastic approaches are often required to explore the nature of the underlying network of chemical reaction soups (9-14). The challenge is how to understand the global picture and physical principles for the stability and function of the cell cycle ...

Division time-based amplifiers for stochastic gene expression

“…30,50 We have shown that the mRNA number is distinctly larger in the case of random division than in the case of constant division, implying that the efficiency is higher in the former case than in the latter case. 30,50 We have shown that the MFPT is shorter in the case of random division than in the case of constant division, and that the MFPT in the case of slow switching is nearly as large as that in the case of fast switching (Fig. 4 Another constraint is in the ability that a gene responds quickly to external stimuli.…”

“…5,6 While quantitative time-lapse fluorescence microscopy allows for tracing the real-time expression of genes in individual cells, [7][8][9] there is considerable interest in theoretically understanding how different molecular mechanisms of gene expression affect variations in mRNA and protein abundances across a population of genetically identical cells. When cellular energy and growth factors are enough, cell growth and division are all periodic events [27][28][29][30] (traditionally, cell division means that a cell begins to divide when its volume reaches twice the original volume, so this kind of division is actually a volume-based division. [17][18][19][20][21][22][23][24][25][26] Cell growth and division are ubiquitous in natural systems.…”

Quantifying the Landscape for Development and Cancer from a Core Cancer Stem Cell Circuit

“…., X n represent the concentration or number of molecules of species), we expect to have n-coupled differential equations, which are hard to solve analytically. Applying a self-consistent mean field approach (14,(32)(33)(34)(35), we split the probability into the products of individual ones: P X 1 ; X 2 ; . .…”

Parameter asymmetry and time‐scale separation in core genetic commitment circuits

“…Therefore, it is not only continuous nonlinear dynamics that is relevant, but it is also stochasticity induced by the paucity of some key molecular regulator(s) in the system. Thus, the notion of stochastic potential is of paramount importance (see Wang et al [13][14][15][16][17][18][19][20][21][22][23]). The role of energy in the establishment and maintenance of living systems at steady-states far from equilibrium is related, but is not addressed here (see Qian et al [24][25][26][27][28][29]).…”