Using optical tweezers combined with image analysis we
investigate motility of single proteins in membranes and of
organelles inside  living cellular organisms, one key issue
being that the organisms are kept alive and healthy. Studies
of two different biological systems will be presented: By
specifically attaching a bead to a single protein, the
lambda-receptor, which is a porin in the outer membrane of
E. coli bacteria, we revealed its nanoscale diffusional
motion and proposed a model that allows for extraction of
the characteristic physical parameters including the
diffusion constant. Surprisingly, the observed mobility is
caused not only by thermal motion but in addition by an
active motion associated with the metabolism of the
organism. Connected to this, we show that antibiotics and
antimicrobial peptides have a pronounced effect on single
protein motility. The second biological system presented
will be an S. pombe yeast cell, where the diffusion patterns
of naturally occurring lipid granules have been uncovered
using optical trapping and single particle tracking; the
granules perform anomalous diffusion, with subdiffusion
being most predominant at short time-lags, and the
biological functions giving motility footprints at longer
time-lags. The diffusional properties inside living yeast
cells change during the cell cycle, and a novel maximal
excursion method shows that the physical origin of the
observed motility is probably fractional Brownian motion.