The cluster environment can affect galaxy evolution in different ways: via ram pressure stripping or by gravitational perturbations caused by galactic encounters. New IRAM 30m HERA CO(2-1) data of NGC 4501 and NGC 4567/68 are presented. We find an increase in the molecular fraction where the ISM is compressed. The gas is close to self-gravitation in compressed regions. This leads to an increase in gas pressure and a decrease in the ratio between the molecular fraction and total ISM pressure. The overall Kennicutt Schmidt relation based on a pixel-by-pixel analysis at ~1.5 kpc resolution is not significantly modified by compression. However, we detected continuous regions of low molecular star formation efficiencies in the compressed parts of the galactic gas disks. The data suggest that a relation between the molecular star formation efficiency SFE_H2 and gas self-gravitation exists. Both systems show spatial variations in the star formation efficiency with respect to the molecular gas that can be related to environmental compression of the ISM. An analytical model was used to investigate the dependence of SFE_H2 on self-gravitation. The model correctly reproduces the correlations between R_mol/P_tot, SFE_H2, and Toomre Q if different global turbulent velocity dispersions are assumed for the three galaxies. We found that variations in the N_H_2/I_CO conversion factor can mask most of the correlation between SFE_H2 and the Q parameter. Dynamical simulations were used to compare the effects of ram pressure and tidal ISM compression. We conclude that a gravitationally induced ISM compression has the same consequences as ram pressure compression: (i) an increasing gas surface density, (ii) an increasing molecular fraction, and (iii) a decreasing R_mol/P_tot in the compressed region due to the presence of nearly self-gravitating gas. The response of SFE_H2 to compression is more complex.