Controlling interactions between cellulose-based materials and membranes of living cells is critical in medicine and biotechnology in, for example, wound dressing, tissue engineering, hemodialysis membranes, and drug transport. Cellulose acetylation is a widely used approach to tuning those interactions. Surprisingly, however, detailed interactions of acetylated cellulose and membranes have thus far not been characterized. Using atomistic molecular dynamics (MD) simulations, we show that the key to such control is hydrogen bonds: by tuning the number of hydrogen bonds between tissue (cell membranes) and cellulose, binding can be controlled in a precise manner. We demonstrate that the acetylation of each hydroxymethyl group reduces the free energy of cellulose-membrane binding by an order of magnitude as compared to that of pristine cellulose. Remarkably, this acetylation-induced weakening does not occur gradually and is characterized by a sharp threshold in the degree of substitution, beyond which the microscopic character of lipid-cellulose interactions changes drastically. When the degree of substitution does not exceed 0.125, the cellulose-lipid interactions are mainly driven by hydrogen bonding between cellulose's hydroxyl groups and phosphate groups of lipid molecules. This results in the tight binding of a cellulose crystal and a lipid bilayer. Larger degrees of substitution (here, 0.25 and 0.5) prevent hydrogen bonding, leading to rather weak and unstable cellulose-bilayer binding. In this case, the lipid-cellulose binding is controlled by the interactions of lipid choline groups with hydroxyl(hydroxymethyl) groups and carbonyl groups of acetyl moieties of acetylated cellulose.