The longer cells stay in particular phases of the cell cycle, the longer it will take these cell populations to increase. However, the above qualitative description has very little predictive value, unless it can be codified mathematically. A quantitative relation that defines the population doubling time (T d) as a function of the time eukaryotic cells spend in specific cell cycle phases would be instrumental for estimating rates of cell proliferation and for evaluating introduced perturbations. Here, we show that in human cells, the length of the G1 phase (T G1) regressed on T d with a slope of 0.75, while in the yeast Saccharomyces cerevisiae, the slope was slightly smaller, at 0.60. On the other hand, cell size was not strongly associated with T d or T G1 in cell cultures that were proliferating at different rates. Furthermore, we show that levels of the yeast G1 cyclin Cln3p were positively associated with rates of cell proliferation over a broad range, at least in part through translational control mediated by a short upstream ORF (uORF) in the CLN3 transcript. Cln3p was also necessary for the proper scaling between T G1 and T d. In contrast, yeast lacking the Whi5p transcriptional repressor maintained the scaling between T G1 and T d. These data reveal fundamental scaling relationships between the duration of eukaryotic cell cycle phases and rates of cell proliferation, point to the necessary role of Cln3p in these relationships in yeast, and provide a mechanistic basis linking Cln3p levels to proliferation rates and the scaling of G1 with doubling time.

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The land use allocation problem is an important issue for a sustainable development. Land use optimization can have a profound influence on the provisions of interconnected elements that strongly rely on the same land resources, such as food, energy, and water. However, a major challenge in land use optimization arises from the multiple stakeholders and their differing, and often conflicting, objectives. Industries, agricultural producers and developers are mainly concerned with profits and costs, while government agents are concerned with a host of economic, environmental and sustainability factors. In this work, we developed a hierarchical FEW-N approach to tackle the problem of land use optimization and facilitate decision making to decrease the competition for resources and significantly contribute to the sustainable development of the land. We formulate the problem as a Stackelberg duopoly game, a sequential game with two players – a leader and a follower (Stackelberg, 2011). The government agents are treated as the leader (with the objective to minimize the competition between the FEW-N), and the agricultural producers and land developers as the followers (with the objective to maximize their profit). This formulation results into a bi-level mixed-integer programming problem that is solved using a novel bi-level optimization algorithm through ARGONAUT. ARGONAUT is a hybrid optimization framework which is tailored to solve high- dimensional constrained grey-box optimization problems via connecting surrogate model identification and deterministic global optimization. Results show that our data-driven approach allows us to provide feasible solutions to complex bi-level problems, which are essentially very difficult to solve deterministically.

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