Figure 1. Principle of thermal noise imaging.

(a) The trapping volume is subdivided into voxels (10 nm side length) to calculate the position histogram. (b) Isosurface (red) of equal voxel occupancy. The heat map of the cut-open section indicates the occupancy of each voxel. (c) If a filament (green circle) is introduced into the optical trap, parts of the trap become inaccessible. The excluded volume depends on the filament and particle radius. (d) Isosurface of equal voxel occupancy for an optical trap intersected by a microtubule confined by rigid supports on both ends (see inset in f). Both isosurfaces are drawn for an occupancy of 2 counts. (e) Two-dimensional projection of the position histogram along the filament axis. (f) Two-dimensional logarithmic relative occupancy (LRO, see main text) calculated from the position histogram shown in e. The LRO is a measure for the interaction energy between the probe and the imaged filament. Voxels that the probe can never visit (excluded volume) have an interaction energy of infinity (dark blue). The hatched area indicates the space inaccessible to the particle due to the confinement by the optical trap. The inset indicates our assay: a microtubule (green) is spanned over a carbon grid (grey) and is imaged by a probe particle (orange) confined by weak optical tweezers (red). (g) Two-dimensional LRO for a probe particle interacting with a microtubule immobilized on one end, while the other end is free to laterally fluctuate driven by thermal forces (see inset). The LRO shown was acquired ∼2.8 μm from the microtubule's fixed end. The filament's thermal motion allows the probe to visit voxels that were previously inaccessible (e,f), and the excluded volume disappears. (h) The radial profile (see Methods) of the static microtubule's LRO (solid line) reveals the extent of the excluded volume, which is made up of all voxels that were inaccessible to the diffusion of the probe. The increase in interaction energy between probe and filament for separations shorter than 150 nm is due to an interplay of electrostatic and steric forces and the thermal motion of the filament. The region of uncertainty indicates the standard deviation of 33 independent recordings of the same filament. The radial LRO for the fluctuating microtubule (dashed line) penetrates into the previously excluded volume. Its diminished slope is a result of the much broader spatial probability density of the fluctuating microtubule. Scale bars, 200 nm.