# 6.021/Notes/2006-09-27

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## Chemical Transport

- Glucose as example
- Transport appears faster than expected from diffusion (Transport is
*facilitated*)- About [math]\displaystyle{ 10^5 }[/math] speedup

- Structure specific
- similar sugars transported very differently

- Transport saturates
- Can be inhibited by other solutes (not independent)
- Drugs can completely block transport
- hormonal control, highly regulated (e.g. insulin)

## Model

- Transport by membrane protein
- binds solute, flips, releases solute on other side
- protein can flip with or without solute
- cannot treat individual solute molecules independently as they are competing for the protein
- flipping is treated as simple first order reversible reaction
- [math]\displaystyle{ R\ \overrightarrow{\leftarrow}\ P }[/math] with a forward rate constant of [math]\displaystyle{ \alpha }[/math] and reverse rate constant of [math]\displaystyle{ \beta }[/math]
- At equilibrium, the relatve concentrations of product P to reactant R will be the association constant [math]\displaystyle{ K_a = \frac{\alpha}{\beta} }[/math]
- the kinetics are exponential with a time constant [math]\displaystyle{ \tau = \frac{1}{\alpha+\beta} }[/math]

- binding reaction
- [math]\displaystyle{ S+E\ \overrightarrow{\leftarrow}\ ES }[/math]
- law of mass action, rate depends on product of concentrations
- Will usually use dissociation constant [math]\displaystyle{ K=\frac{1}{K_a} }[/math] (units concentration)
- total enzyme [math]\displaystyle{ C_{ET}=C_E+C_{ES} }[/math] is constant
- Michaelis-Menten (hyperbolic) kinetics of form [math]\displaystyle{ y=\frac{a}{a+x} }[/math]
- when drawn on doubly reciprocal coordinates, get straight line