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Theory Manual Version 3.6
 Subsection 2.9.1: Perfect Osmometer Up Section 2.9: Equilibrium Swelling Subsection 2.9.3: Donnan Equilibrium Swelling 

2.9.2 Cell Growth

The growth of cells requires the active uptake of soluble mass to provide the building blocks for various intracellular structures, such as the cytoskeleton or chromosomes, and growth contributes to the osmolarity of the intracellular space. The resulting mechano-chemical gradient drives solvent into the cell as well, contributing to its volumetric growth.
Cell growth may be modeled using the “perfect osmometer” framework by simply increasing the mass of the intracellular solid matrix and membrane-impermeant solute. This is achieved by using eq.(2.9.1-1) to model the osmotic pressure and allowing the parameters and (normally constant) to increase over time as a result of growth. Since cell growth is often accompanied by cell division, and since daughter cells typically achieve the same solid and solute content as their parent, it may be convenient to assume that and increase proportionally, though this is not an obligatory relationship. To ensure that the initial configuration is a stress-free reference configuration, let in the initial state prior to growth.
 Subsection 2.9.1: Perfect Osmometer Up Section 2.9: Equilibrium Swelling Subsection 2.9.3: Donnan Equilibrium Swelling