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Abstract

Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single
protein molecule averaged over a very long time resembles that of an ensemble. Here, by performing
single-molecule fluorescence resonance energy transfer (smFRET) experiments and molecular dynamics
(MD) simulations of a multi-domain globular protein, cytoplasmic protein-tyrosine phosphatase (SHP2),
we demonstrate that the functional inter-domain motion is observationally non-ergodic over the time
spans 1012 to 107 s and 101 to 102 s. The difference between observational non-ergodicity and simple
non-convergence is discussed. In comparison, a single-strand DNA of similar size behaves ergodically
with an energy landscape resembling a one-dimensional linear chain. The observed non-ergodicity
results from the hierarchical connectivity of the high-dimensional energy landscape of the protein
molecule. As the characteristic time for the protein to conduct its dephosphorylation function is 10 s,
our findings suggest that, due to the non-ergodicity, individual, seemingly identical protein molecules
can be dynamically and functionally different.