Criticality in optimal organelle biogenesis

Among the hallmarks of the eukaryotic cell is its organization into organelles. In order to tailor organelle biogenesis to the needs of the cell, the cell can regulate the size and number of many of its organelles. Organelle biogenesis, however, is fundamentally constrained by the limited available pool of resources available to the cell to synthesize its organelles. What principles dictate how much of the cell’s limited resources are devoted to increasing the number versus the size of a given organelle? This question can be cast in terms of the NP-hard mixed integer nonlinear optimization. Here we propose a model of resource allocation to organelle number and size and use the tools of MINLOP to solve for optimal organelle number and size subject to the constraint of having only a limited pool of resources to build organelles from. We find that the solutions to the constrained optimization fall into two regimes separated by a critical point, suggesting that cells face an unexpectedly sharp tradeoff between organelle number and size in resource-limited contexts. The existence of this critical point is consistent with observations that cells grow larger numbers of small organelles as opposed to simply reducing each organelle’s size when faced with a constraining pool of resources.