Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm

Essentially all biological processes are highly dependent on the nanoscale architecture of the cellular components where these processes take place. Statistical measures, such as the autocorrelation function (ACF) of the three-dimensional (3D) mass-density distribution, are widely used to characterize cellular nanostructure. However, conventional methods of reconstruction of the deterministic 3D mass-density distribution, from which these statistical measures can be calculated, have been inadequate for thick biological structures, such as whole cells, due to the conflict between the need for nanoscale resolution and its inverse relationship with thickness after conventional tomographic reconstruction. To tackle the problem, we have developed a robust method to calculate the ACF of the 3D mass-density distribution without tomography. Assuming the biological mass distribution is isotropic, our method allows for accurate statistical characterization of the 3D mass-density distribution by ACF with two data sets: a single projection image by scanning transmission electron microscopy and a thickness map by atomic force microscopy. Here we present validation of the ACF reconstruction algorithm, as well as its application to calculate the statistics of the 3D distribution of mass-density in a region containing the nucleus of an entire mammalian cell. This method may provide important insights into architectural changes that accompany cellular processes.