The correlations between star formation rate (SFR), stellar mass (M), and gas-phase metallicity (12+log(O/H)) for star-forming (SF) galaxies, known as global scaling relations or fundamental relations, have been studied during the last decades to understand the evolution of galaxies. However, the origin of these correlations and their scatter, which may also be related to their morphology or environment, is still a subject of debate. In this work, we establish fundamental relations, for the first time, in isolated systems in the local universe (with 0.005<=z<=0.080), which can give insight into the underlying physics of star-formation. We use a sample of isolated galaxies to explore whether star formation is regulated by smooth secular processes. In addition, galaxies in physically bound isolated pairs and isolated triplets may also interact with each other, where interaction itself may enhance/regulate star-formation and the distribution of gas and metals within galaxies. We compared our results with a sample of star-forming galaxies in the SDSS. We found that, on average, at a fixed stellar mass, the SIG SF galaxies have lower SFR values than Main Sequence (MS) SF galaxies in the SDSS and central galaxies in the SIP and SIT. On average, SIG galaxies have higher 12+log(O/H) values than galaxies in the SIP, SIT, and comparison sample. When distinguishing between central and satellite galaxies in the SIP and SIT, centrals and SIG galaxies present similar values (~8.55) while satellites have values close to M33 (~8.4). Using the D_n_(4000) parameter as a proxy of the age of the stellar populations we found that, on average, SIG and central galaxies have higher D_n_(4000) values than satellites and comparison galaxies. Based on our results for isolated galaxies, we propose a ground level nurture free SFR-M and 12+log(O/H)-SFR-M relations for SF galaxies in the local Universe.