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 $$\phi_s > 0$$ 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: $$\phi_s,\phi_r$$
 * same solution for flux $$\phi_s$$ 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 $$\phi_s > 0$$ 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 $$K_{eff}$$ 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