Spurious higher-order correlations from non-linearities in a receptor-ligand model

Multi-body correlations arise frequently in analyses of biological systems, such as antibiotic interactions in cell growth rate, mutational interactions on protein function and ligand interactions in the immune system. In particular, it is common practice to measure the 1st and 2nd-moments of quantities of interest, and fit a maximum-entropy model to the data. We demonstrate that pairwise and higher-order interactions emerge naturally from mismatches between the fitted model and the underlying physical system, as well as ignorance of unmeasured quantities. We study a simple receptor-ligand model and demonstrate that spurious higher-order interactions can arise from simpler interactions combined with non-linearities not accounted for. Our analysis shows how careful accounting for the underlying biology is needed to conclude the existence or absence of complex interactions within the system.