The response of oscillatory systems to external perturbations is crucial for emergent properties such as synchronisation and phase locking and can be quantified in a phase response curve (PRC). In individual, oscillating yeast cells, we characterised experimentally the phase response of glycolytic oscillations for external acetaldehyde pulses and followed the transduction of the perturbation through the system. Subsequently, we analysed the control of the relevant system components in a detailed mechanistic model. The observed responses are interpreted in terms of the functional coupling and regulation in the reaction network. We find that our model quantitatively predicts the phase-dependent phase shift observed in the experimental data. The phase shift is in agreement with an adaptation leading to synchronisation with an external signal. Our model analysis establishes that phosphofructokinase plays a key role in the phase shift dynamics as shown in the PRC and adaptation time to external perturbations. Specific mechanism-based interventions, made possible through such analyses of detailed models, can improve upon standard trial and error methods, e.g. melatonin supplementation to overcome jet-lag, which are error-prone, specifically, since the effects are phase dependent and dose dependent. The models by Gustavsson and Goldbeter discussed in the text can be obtained from the JWS Online simulation database: (https://jjj.bio.vu.nl/models/ gustavsson5 and https://jjj.bio.vu.nl/models/goldbeter1).