Evaluation of origin of driving force for loop formation in a chromatin fiber

Abstract Chromosome condensation results from the formation of consecutive chromatin loops in which excluded volume interactions lead to chromosome stiffness. Formation of chromatin loops requires energy, but the source of such energy remains controversial. Here, we quantified the energy balance during chromatin loop formation by calculating the free energies of unlooped and looped chromatins using a lattice model of polymer chains. We tested two hypothetical energy sources: thermal fluctuation and ATP hydrolysis. We evaluated the free energy difference of the chain loop model without accounting for excluded volume interactions (phantom loop model), and integrated those interactions by employing the mean-field theory (interacting loop model), where we introduced the parameter of excluded volume interaction within a single loop v ex . Using our strategy, we confirmed that loop-growth efficiency calculated by the phantom loop model is too high to explain the experimental data. Comparing loop-growth efficiencies for each energy source, and using the interacting loop model, we found that excluded volume interaction is essential for chromatin’s resistance to looping, regardless of the energy source. We predict that the quantitative measurement of v ex determines which energy source is more plausible. Author summary Before mitosis, the chromatin fibers of eukaryotic cells fold into consecutive loop structures and condense into rod-like chromosomes. Chromosome stiffness results from the interaction of the excluded volume between chromatin loops. The driving force of loop formation and growth is still controversial, despite the many efforts undertaken to clarify it. Two possible origins can be considered: the energy provided by thermal fluctuations or the energy gained from ATP hydrolysis. To discuss the validity of each, we constructed a theoretical model of chromatin loop formation that includes excluded volume interactions. Using this model, we calculated the free energy difference before and after chromatin loop formation, which corresponds to the energy that fuels chromatin looping. By comparing the results for each energy source, we conclude that the spatial distribution of chromatin loops should be relatively wide, given the large excluded volume interaction within a single loop, irrespective of which energy source is valid. Moreover, our results imply that intra-loop interactions are key to determine the driving force of chromatin loop formation.