# Generalized Rayleigh-Plesset Theory for Cell Size Maintenance in Viruses and Bacteria

## TL;DR

This paper introduces a hydrodynamic model inspired by bubble stability to explain how the mechanical properties of bacterial and viral shells regulate their sizes, highlighting the role of shell elasticity and turgor pressure.

## Contribution

It presents a novel theoretical framework linking shell elasticity and turgor pressure to organism size regulation in bacteria and viruses.

## Key findings

- Shell rigidity and turgor pressure control organism sizes.
- A dimensionless compliance parameter predicts size based on elastic modulus and pressure.
- Experimental data show correlation between shell elasticity and size.

## Abstract

The envelopes covering bacterial cytoplasm possess remarkable elastic properties. They are rigid enough to resist large pressures while being flexible enough to adapt to growth under environmental constraints. Similarly, the virus shells play an important role in their functions. However, the effects of mechanical properties of the outer shell in controlling and maintaining the sizes of bacteria or viruses are unknown. Here, we present a hydrodynamic "bubbles with shell" model, motivated by the study of bubble stability in fluids, to demonstrate that shell rigidity and turgor pressure control the sizes of bacteria and viruses. A dimensionless compliance parameter, expressed in terms of the elastic modulus of the shell, its thickness and the turgor pressure, determines membrane response to deformation and the size of the organisms. By analyzing experiment data, we show that bacterial and viral sizes correlate with shell elasticity, which plays a critical role in regulating size.