# Using schematic models to understand the microscopic basis for inverted solubility in $\gamma$D-crystallin

## TL;DR

This study investigates the microscopic mechanisms behind inverted solubility in human γD-crystallin, finding that hydrophobicity changes are unlikely the cause and that temperature-dependent interactions require fine-tuning to produce solubility inversion.

## Contribution

The paper combines experimental surface hydrophobicity measurements with schematic modeling to assess the role of hydrophobic effects and temperature-dependent interactions in inverted protein solubility.

## Key findings

- Hydrophobicity does not significantly increase with mutation.
- Hydrophobic effects alone may not explain solubility inversion.
- Temperature-dependent interactions have minimal impact on critical properties.

## Abstract

Inverted solubility--a crystal melting upon cooling--is observed in a handful of proteins, such as carbomonoxy hemoglobin and $\gamma$D-crystallin. In human $\gamma$D-crystallin, the phenomenon is associated with the mutation of the 23$^\mathrm{rd}$ residue, a proline, to a threonine, serine or valine. One proposed microscopic mechanism for this effect entails an increase in hydrophobicity upon mutagenesis. Recent crystal structures of a double mutant that includes the P23T mutation allows for a more careful investigation of this proposal. Here, we first measure the surface hydrophobicity of various mutant structures of this protein and determine that it does not discernibly increase upon the mutating the 23$^\mathrm{rd}$ residue. We then investigate the solubility inversion regime with a schematic patchy particle model that includes one of three models for temperature-dependent patch energies: two of the hydrophobic effect, and a more generic description. We conclude that while solubility inversion due to the hydrophobic effect may be possible, microscopic evidence to support it in $\gamma$D-crystallin is weak. More generally, we find that solubility inversion requires a fine balance between patch strengths and the temperature-dependent contribution, which may explain why inverted solubility is not commonly observed in proteins. In any event, we also find that the temperature-dependent interaction has only a negligible impact on the critical properties of the $\gamma$D-crystallin, in line with previous experimental observations.