Interactions between tethered layers composed of aggrecan (charged bottle-brush) macromolecules are responsible for the molecular origin of cartilage biomechanical behavior. To elucidate the role of the electrostatic forces in interaction between bottle-brush layers, we have performed molecular dynamics simulations of charged and neutral bottle-brush macromolecules tethered to substrates. In the case of charged bottle-brush layers, the disjoining pressure P between two brush layers in salt-free solutions increases with decreasing distance D between substrates as P proportional to D(-1.8). A stronger dependence of the disjoining pressure P on the surface separation D was observed for neutral bottle-brushes, P proportional to D(-4.6), in the same interval of disjoining pressures. These scaling laws for dependence of disjoining pressure P on distance D are due to bending energy of the bottle-brush macromolecules within compressed brush layers. The weaker distance dependence observed in polyelectrolyte bottle-brushes is due to interaction between counterion clouds surrounding the bottle-brush macromolecules preventing strong brush overlap.