How it Works
The simulation shows a plant cell expanding under internal turgor pressure. The Lockhart equation governs the irreversible volumetric expansion rate. When turgor P exceeds yield threshold Y, the wall yields and the cell grows. The cell is drawn as a rounded rectangle whose dimensions update each frame based on the computed growth rate.
Cellulose microfibrils are visualized as oriented bands on the cell wall. In anisotropic mode, transversely oriented microfibrils restrict lateral expansion, forcing the cell to elongate axially. The turgor pressure is maintained by a dynamic water influx balanced against wall stretching.
Water influx: dP/dt = L·(Ψs - P) - φ·(P - Y) · E
where L = hydraulic conductivity, Ψs = osmotic pressure
E = elastic modulus of cell wall (~10–100 MPa)
Wall stress σ = P·r / (2t) [thin-shell hoop stress]
Frequently Asked Questions
What is turgor pressure?
Turgor pressure is the hydrostatic pressure exerted by the cell contents against the cell wall. Water enters the cell by osmosis, creating internal pressure that makes plant tissues firm and drives cell expansion.
What is the Lockhart equation?
The Lockhart equation dV/dt = φ·V·(P - Y) describes cell volume expansion rate, where φ is wall extensibility (MPa⁻¹·s⁻¹), P is turgor pressure (MPa), and Y is the yield threshold below which no irreversible expansion occurs.
What is cell wall extensibility?
Cell wall extensibility (φ) quantifies how easily the wall yields to turgor pressure. It is regulated by wall-loosening proteins like expansins, which disrupt hydrogen bonds between cell wall polysaccharides to allow creep.
What are expansins?
Expansins are cell-wall-loosening proteins that disrupt non-covalent bonds between cellulose microfibrils and matrix polysaccharides. They increase wall extensibility, allowing turgor-driven expansion without enzymatic cell wall degradation.
What is the yield threshold (Y) in the Lockhart model?
The yield threshold Y is the minimum turgor pressure required to produce irreversible (plastic) cell wall deformation. When P < Y, only elastic (reversible) expansion occurs; when P > Y, the cell grows irreversibly.
How does the cell maintain water potential equilibrium?
Water moves across membranes from high to low water potential (Ψ = Ψs + Ψp). When the cell expands, turgor decreases and osmotic potential becomes less negative, until equilibrium with the apoplast is reached.
What role does the cell wall play in plant growth?
The cell wall constrains and directs cell expansion. The orientation of cellulose microfibrils determines the axis of growth: transversely oriented microfibrils restrict lateral expansion and promote elongation along the cell axis.
How does acid growth theory relate to expansins?
Acid growth theory proposes that auxin stimulates H⁺-ATPase pumps, acidifying the cell wall. Expansins are most active at low pH, so auxin-induced acidification activates expansins, increasing extensibility and promoting cell elongation.
What happens to turgor pressure during wilting?
During water stress, the cell loses water by osmosis, reducing turgor pressure toward zero. When P drops below Y, growth stops. Severe loss of turgor causes plasmolysis, where the plasma membrane detaches from the cell wall.
How is cellulose synthesized in plant cell walls?
Cellulose synthase complexes (rosettes) in the plasma membrane polymerize UDP-glucose into cellulose chains and extrude them into the wall. The complexes move along cortical microtubule tracks, determining microfibril orientation.