Mapping of the forces on biomolecules in cell membranes has spurred the development of effective labels, e.g. organic fluorophores and nanoparticles, to track trajectories of single biomolecules. Standard methods use particular statistics, namely the mean square displacement, to analyze the underlying dynamics. Here, we introduce general inference methods to fully exploit information in the experimental trajectories, providing sharp estimates of the forces and the diffusion coefficients in membrane microdomains. Rapid and reliable convergence of the inference scheme is demonstrated on trajectories generated numerically. The method is then applied to infer forces and potentials acting on the receptor of the $epsilon$-toxin labeled by lanthanide-ion nanoparticles. Our scheme is applicable to any labeled biomolecule and results show show its general relevance for membrane compartmentation.
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