The SARS-CoV-2 spike protein contains a functionally important fatty acid (FA) binding site, also found in some other coronaviruses (e.g. SARS-CoV and MERS-CoV), which binds linoleic acid. When occupied by linoleic acid, it reduces infectivity, by 'locking' the spike in a less infectious conformation. Here, we use dynamical-nonequilibrium molecular dynamics (D-NEMD) simulations to compare the response of spike variants to linoleic acid removal. D-NEMD simulations show that the FA site is coupled to other, some distant, functional regions of the protein, e.g. the receptor-binding motif, N-terminal domain, furin cleavage site, and regions surrounding the fusion peptide. D-NEMD simulations also identify the allosteric networks connecting the FA site to the functional regions. Comparison of the response of the wild-type spike with four variants (Alpha, Delta, Delta plus, and Omicron BA.1) shows that the variants differ significantly in their response to linoleic acid removal. The allosteric connections to the FA site on Alpha are generally similar to those on the wild-type protein, with the exception of the receptor-binding motif and the S71-R78 region, which show a weaker link to the FA site. In contrast, Omicron is the most affected variant exhibiting significant differences in the receptor-binding motif, N-terminal domain, V622-L629, and the furin cleavage site. These differences in allosteric modulation may be of functional relevance, potentially affecting transmissibility and virulence. Experimental comparison of the effects of linoleic acid on SARS-CoV-2 variants, including emerging variants, is warranted.