  Single-molecule experiments provide insight into the motion (conformational
dynamics) of individual protein molecules. Usually, a well-defined but
coarse-grained intramolecular coordinate is measured and subsequently analysed
with the help of Hidden Markov Models (HMMs) to deduce the kinetics of protein
conformational changes. Such approaches rely on the assumption that the
microscopic dynamics of the protein evolve according to a Markov-jump process
on some network. However, the manifestation and extent of memory in the
dynamics of the observable strongly depends on the chosen underlying Markov
model, which is generally not known and therefore can lead to
misinterpretations. Here, we combine extensive single-molecule plasmon ruler
experiments on the heat shock protein Hsp90, computer simulations, and theory
to infer and quantify memory in a model-free fashion. Our analysis is based on
the bare definition of non-Markovian behaviour and does not require any
underlying model. In the case of Hsp90 probed by a plasmon ruler, the Markov
assumption is found to be clearly and conclusively violated on timescales up to
roughly 50 s, which corresponds roughly to $\sim$50% of the inferred
correlation time of the signal. The extent of memory is striking and reaches
biologically relevant timescales. This implies that memory effects penetrate
even the slowest observed motions. We provide clear and reproducible guidelines
on how to test for the presence and duration of memory in experimental
single-molecule data.
