A simcell with a water permeable membrane
A simcell with a water permeable membrane represents a simplified cell whose boundary allows water to pass freely while restricting at least some solutes. The dominant consequence is osmosis: a net water flux driven by differences in effective solute concentration across the membrane.
Model assumptions
The phrase “water permeable membrane” is used in biology in two closely related senses: high water permeability (often via aquaporins) and selective permeability that prevents many solutes from crossing on the same time scale. The following assumptions define a concrete simcell model that produces unambiguous predictions.
- Membrane permeability: water passes; the highlighted solutes are effectively impermeant during the observation interval.
- Well-mixed compartments: extracellular fluid and cytosol are uniform in solute concentration (no gradients within each side).
- Temperature stability: thermal conditions are constant, so osmotic driving forces do not drift with time.
- Mechanical response: the membrane can change area/volume within limits, so volume changes reflect net water movement.
Water movement across the membrane
Osmosis is diffusion of water across a selectively permeable membrane, driven by a gradient in water’s chemical potential. In practice, a higher concentration of impermeant solute lowers the “free” water concentration on that side, biasing net water movement toward it. The direction is commonly summarized as “water moves toward higher effective solute concentration,” with “effective” emphasizing solutes that do not cross the membrane on the time scale of interest.
Tonicity and cell volume outcomes
Tonicity describes how an external solution affects cell volume, assuming the membrane is permeable to water and relatively impermeable to key solutes. The same osmolarity can yield different tonicity if different solutes have different membrane permeabilities.
| External condition | Relative effective solute level (outside vs inside) | Net water movement | Volume outcome for the simcell |
|---|---|---|---|
| Hypotonic | Lower outside than inside | Into the cell | Swelling; in animal-like cells, excessive swelling can progress to lysis |
| Isotonic | Approximately equal outside and inside | No net movement (bidirectional exchange persists) | Stable volume |
| Hypertonic | Higher outside than inside | Out of the cell | Shrinking; in animal-like cells, shrinkage is often termed crenation |
Quantitative relationship
A compact approximation for osmotic driving force uses osmotic pressure. For dilute solutions, \(\pi\) can be estimated with the van ’t Hoff form:
\(i\) is the van ’t Hoff factor (effective particle count per formula unit), \(M\) is molarity (mol/L), \(R\) is the gas constant, and \(T\) is absolute temperature (K). A transmembrane imbalance in effective osmolarity produces an approximate pressure difference:
Example at \(T = 298\ \text{K}\): an interior effective osmolarity of \(0.30\ \text{Osm}\) and an exterior of \(0.10\ \text{Osm}\) give
The magnitude highlights why even modest osmolarity differences can drive substantial water movement in biological systems. Actual volume change depends on membrane mechanics, cytoskeletal constraints, and whether the system can relieve pressure (for example, via a rigid cell wall).
Common pitfalls
- Osmolarity vs tonicity: osmolarity counts total particles; tonicity depends on particles that remain effectively separated by the membrane.
- Permeant solutes: a solute that crosses rapidly reduces sustained gradients and can flip a short-term prediction over longer times.
- Plant vs animal response: a cell wall limits expansion; hypotonic surroundings can produce turgor rather than lysis.
- “No net” does not mean “no movement”: isotonic conditions still involve continuous bidirectional water exchange with zero net flux.
Summary statement
In a simcell with a water permeable membrane, sustained volume changes arise when impermeant solutes differ across the membrane, producing net osmosis toward the side with higher effective solute concentration and yielding predictable hypotonic, isotonic, and hypertonic outcomes.