15: Passive Transport

Passive transport is often synonymous with diffusion, where thermal energy is the only source of motion.

\[ \langle r(t) \rangle = 0 \qquad \qquad \qquad \langle r^2(t) \rangle^{1/2}=\sqrt{6Dt} \qquad \qquad \qquad r_{rms}\propto \sqrt{t} \nonumber \]

In biological systems, diffusive transport may work on a short scale, but it is not effective for long-range transport. Consider:

\( \langle r^2 \rangle^{1/2} \) for small protein moving in water

~10 nm →10^–7 s

~10 μm → 10^–1 s

Active transport refers to directed motion:

\[ \langle r(t) \rangle = \langle v \rangle t \qquad \qquad \qquad \qquad r \propto t \nonumber \]

This requires an input of energy into the system, however, we must still deal with random thermal fluctuations.

How do you speed up transport?

We will discuss these possibilities:

• Reduce dimensionality: Facilitated diffusion
• Free energy (chemical potential) gradient: Diffusion in a potential
• Directional: Requires input of energy, which drives the switching between two conformational states of the moving particle tied to translation.

---