15: Passive Transport
- Page ID
- 294337
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.
- 15.2: Facilitated Diffusion
- Facilitated diffusion is a type of dimensionality reduction that has been used to describe the motion of transcription factors and regulatory proteins looking for their binding target on DNA.