We study the motion of quantum dots and individual messenger RNA (mRNA) in the cytoplasm of HeLa cells using single-particle tracking. The trajectories are analyzed in terms of the mean squared displacement and the power spectral density. We observe that the motion resembles an antipersistent random walk, which suggests fractional Brownian motion as a useful model. However, the trajectories alternate between different states due to cellular heterogeneities and interactions with specific partners. Quantum dots randomly switch between different mobility states, which can be dissected using a hidden Markov model. In contrast to the quantum dot trajectories, mRNA dynamics exhibit aging and ergodicity breaking. These complexities are found to be governed by heterogeneous interactions where the residence times in a bound state have a heavy-tailed distribution.