Optimized Energy Dissipation of Minde Oscillator for Symmetric Cell Division

Abstract

Prokaryotic cells often utilize a MinCDE oscillatory system to locate the mid-cell location for symmetric cell division. Several diffusion-reaction based models have been developed to explain the occurrence of the sustainable oscillation of Min proteins from pole to pole, and extensive efforts have been devoted to understanding the patterns of oscillation and the precision of the designated mid-cell location. However, how this highly dissipative yet vital biological oscillation is driven by energy-bearing molecules is left uninvestigated. We address this fundamental question by studying the MinCDE oscillator in Escherichia coli. We assess the oscillator's performance of spatially differentiating mid-cell region from the rest of cell body, and further relate this quantified performance to the amount of dissipated energy as well as the stage of cell growth. Unlike the two adaptive reaction networks (Negative-Feedback-Loop and Feedfoward-Loop) whose performances get monotonically improved upon larger energy input, the MinCDE oscillator shows nonmonotonic performance-to-cost relation that depends on the reaction rates and the cell length. Our analysis further indicated that this oscillator operates optimally at cell length around 4 micro-meters and to achieve the best performance, energy is dissipated unevenly through the reaction pathway with the largest dissipation at immobilizing MinD and hydrolyzing ATP. These results present a novel mode of converting biochemical energy into spatiotemporal information in living systems and suggest that the MinCDE oscillator in prokaryotic cells are highly optimized both functionally and energetically to ensure high fitness under natural selection.