Chapter 4 – Making Light Work Harder in Biology  137

σ by a factor of √2, i.e., 9.4 nm. To determine if a protein is localized into a droplet

would ideally require us to track it in the droplet at least over a distance greater

than its 2D localization precision, so the minimum droplet size by this logic that

we could observe this would have a diameter of ~14 nm. We are told that the pro­

tein plus PAmCherry tag has an effective diameter of 2–​3 nm, so very roughly say

that a dimer has an effective diameter of more like ~5 nm. The maximum number

of dimers nd that could be present in the droplet would involve tight-​packing of

the dimers, so estimate that under this condition nd multiplied by the volume

of one dimer then equals the total volume of one droplet. Assuming spherical

volumes:

nd × 4π.5³/​3 =​ 4π.14³/​3 ∴ nd =​ (14/​5)³ ≈ 22, or 11 dimers, so although not at

the very first stages in the nucleation process of droplet formation (i.e., two

dimer interacting together presumably), is still at a relatively early formation

stage beyond this.

c

The initial straight line indicates Brownian diffusion whose diffusion coeffi­

cient is proportional to the gradient. The decrease in gradient could indicate a

decrease in mobility toward the edges of the droplet, so some subdiffusive or

anomalous diffusion behavior, but with the presence of a plateau more likely

indicates that diffusion is confined and the plateau is the boundary of the con­

finement (i.e., the edge of the droplet). An increase in tracks detected in the

droplet indicates that more proteins are likely to be present inside the droplet.

A decrease in the plateau height indicates a smaller effective confinement

diameter. So, the concentration of protein inside the droplet will increase. This

molecular crowding could potentially result in an increase in viscosity for the

diffusion of any given protein in the droplet, thus explain the smaller observed

initial gradient.

4.5  LIGHT MICROSCOPY OF DEEP OR THICK SAMPLES

Although much insight can be gained from light microscopy investigations in vitro, and on

single cells or thin multicellular samples, ultimately certain biological questions can only be

addressed inside thicker tissues, for example, to explore specific features of human biology.

The biophysical challenges to deep tissue light microscopy are the attenuation of the optical

signal combined with an increase in background noise as it passes through multiple layers

of cells in a tissue and the optical inhomogeneity of deep tissues distorting the optical wave

front of light.

Some nonlinear optics methods have proved particularly useful for minimizing the back­

ground noise. Nonlinear optics involve properties of light in a given optical medium for which

the dielectric polarization vector has a nonlinear dependence on the electric field vector of

the incident light, typically observed at high light intensities comparable to interatomic elec­

tric fields (~10⁸ V m⁻¹) requiring pulsed laser sources.

4.5.1  DECONVOLUTION ANALYSIS

For a hypothetically homogeneous thick tissue sample, the final image obtained from

fluorescence microscopy is the convolution of the spatial localization function of all of the

fluorophores in the sample (in essence, approximating each fluorophore as a point source

using a delta function at its specific location in the sample) with the 3D PSF of the imaging

system. Therefore, to recover the true position of all fluorophores requires the reverse pro­

cess of deconvolution of the final image. The way this is performed in practice is to generate