# 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
• $\phi_s=(\phi_s)_{max} \frac{K}{(K+c_s^i)(K+c_s^o)}(c_s^i-c_s^o)$
• So φs > 0 only if $c_s^i > c_s^o$
• Transport saturates
• only finite/fixed number of carrier proteins
• For low concentrations, predicts Fick's law
• $\phi_s=\frac{(\phi_s)_{max}}{K}(c_s^i-c_s^o)$ for small $c_s^i, c_s^o$
• 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: $c_s^i,c_s^i,c_r^i,c_r^i$ and 2 outputs: φsr
• same solution for flux φs as before except instead of K have $K_{eff}=K_s(1+\frac{c^o_r}{k_r})$ for inward flux
• can have a different $K_{eff}=K_s(1+\frac{c^i_r}{k_r})$ for outward flux
• 6 state model is active if φs > 0 when $c^o_s \ge c_s^i$
• This occurs when $\frac{K_r+c^o_r}{K_r+c^i_r} > \frac{c_s^o}{c_s^i} \ge 1$
• 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 Keff but does not change the maximum flux
• non-competitive inhibitor lowers the maximum flux but leaves K unchanged
• Hormonal control (insulin)
• Causes more transporters to be delivered to the membrane