6.021/Notes/2006-10-02

Does simple 4-state model explain characteristics of glucose transport?

• Facilitated (faster than diffusion)
  • Enzyme (carrier) binds to solute better than solute dissolves in membrane
• Structure specific
  • Different binding constants K for different solutes
• Passive: flow only down concentration gradient
  • [math]\displaystyle{ \phi_s=(\phi_s)_{max} \frac{K}{(K+c_s^i)(K+c_s^o)}(c_s^i-c_s^o) }[/math]
  • So [math]\displaystyle{ \phi_s \gt 0 }[/math] only if [math]\displaystyle{ c_s^i \gt c_s^o }[/math]
• Transport saturates
  • only finite/fixed number of carrier proteins
  • For low concentrations, predicts Fick's law
  • [math]\displaystyle{ \phi_s=\frac{(\phi_s)_{max}}{K}(c_s^i-c_s^o) }[/math] for small [math]\displaystyle{ c_s^i, c_s^o }[/math]
• Transport can be inhibited
  • can have active transport by addition of another solute
  • for example, adding glucose can change direction of sorbose transport to go against the sorbose gradient
  • 4 state model only deals with 1 solute
  • can extend to 6 state model to deal with 2 solutes
  • 4 inputs: [math]\displaystyle{ c_s^i,c_s^i,c_r^i,c_r^i }[/math] and 2 outputs: [math]\displaystyle{ \phi_s,\phi_r }[/math]
  • same solution for flux [math]\displaystyle{ \phi_s }[/math] as before except instead of K have [math]\displaystyle{ K_{eff}=K_s(1+\frac{c^o_r}{k_r}) }[/math] for inward flux
  • can have a different [math]\displaystyle{ K_{eff}=K_s(1+\frac{c^i_r}{k_r}) }[/math] for outward flux
  • 6 state model is active if [math]\displaystyle{ \phi_s \gt 0 }[/math] when [math]\displaystyle{ c^o_s \ge c_s^i }[/math]
  • This occurs when [math]\displaystyle{ \frac{K_r+c^o_r}{K_r+c^i_r} \gt \frac{c_s^o}{c_s^i} \ge 1 }[/math]
  • This is called secondary active transport where concentration gradient of one solute drives the flux of another solute up concentration gradient.
• Pharmacology (drugs)
  • modify 6 state model with inhibitors
  • competitive inhibitor changes [math]\displaystyle{ K_{eff} }[/math] but does not change the maximum flux
  • non-competitive inhibitor lowers the maximum flux but leaves [math]\displaystyle{ K }[/math] unchanged
• Hormonal control (insulin)
  • Causes more transporters to be delivered to the membrane