Physics of biological systems PH 419 LECTURE 16: Biological - PowerPoint PPT Presentation

Physics of biological systems – PH 419 LECTURE 16: Biological dynamics and rate equations mithun@phy.iitb.ac.in Office: Physics 303

CELLS ARE IN CONSTANT FLUX Gene expression during cell cycle of caulobacter

The living cytoskeleton

Dynamic instability of microtubules

Dynamic instability of microtubules

Actin polymerization

Actin TREADMILLING

Actin polymerization Kalman Lab, Emory Mechanobio.info Cossart Lab, Institut Pasteur

Actin polymerization

CHEMICAL REACTIONS ➢ Changes in numbers of reacting molecules ➢ Changes in time as well as changes in space ➢ Concentration, c( r ,t) ➢ If species numbers are very small, fluctuations can be as important ➢ Local vs global concentrations

RATE EQUATIONS Assume, no spatial variations 𝑒𝑑 𝑗 𝑒𝑢 = 𝑔 𝑑 𝑘 }, {𝑙 𝑗 = 𝑔 𝑑 1, 𝑑 2, . . . , 𝑑 𝑜 ; 𝑙 1, 𝑙 2, . . . , 𝑙 𝑛

Retinal: Conformational change −𝑢 τ τ = 𝑒𝑑 𝑑 = 𝑑 0 𝑓 1 𝑙 𝑒𝑢 = −𝑙𝑑

The trajectory picture = 1, if 𝑢 < 𝑢 𝑗 σ 𝑗 𝑢 0, otherwise 𝑞 𝑢 Δ𝑢 = 1 −𝑢 τ Δ𝑢 τ 𝑓

Decay and growth 𝐵 → 𝐶

Bimolecular reactions 𝐵 + 𝐶 ⇔ 𝐵𝐶

ION CHANNEL gating 𝑒𝑞 𝑝 = −𝑙 + 𝑞 𝑝 + 𝑙 − 𝑞 𝑑 𝑒𝑢 𝑙 − 𝑙 + 𝑓 − 𝑙 + +𝑙 − 𝑢 𝑞 𝑝 = + 𝑙 + + 𝑙 − 𝑙 + + 𝑙 −

RAPID EQUILIBRIUM

ENZYME KINETICS

Michaelis-menten KINETICS