A cell has a total receptor concentration, $R_T.$ When a ligand, with concentration $L,$ is added,

irreversible receptor$-$ligand bonds are formed according to the following reaction scheme:

$R+LkB,$ where $R,L,$ and $B$ are the concentrations of free $($unbound$)$ receptors, free

ligands, and bound receptors on the surface of the cell, respectively. Bound receptors are also

internalized $($removed from the surface$)$ at a rate proportional $($internalization rate constant, $k_{\text{i}\text{n}\text{t}})$ to

the surface concentration of bound receptors.

a$)$ Write the differential equation for the surface concentration of free and bound receptors in

terms of the B$,$ L$,$ R$,k$ and $k_{\text{i}\text{n}\text{t}\text{.}}.$

b$)$ In many cases, ligand is present in concentrations much greater than the receptor concentration

such that the concentration of ligand may be treated as a constant. Assuming a constant ligand

concentration, $L,$ solve for the bond concentration as a function of time with the initial condition

that there are no bonds $(B_{{?}_{?}}(0)=0)$ and the initial surface receptor concentration is $R_0.$ Sketch a

graph of the solution $($B vs$.$ time; use your own example values for the constants$).$ You need to

come up with your own values for the constants; these values have to be realistic $($e$.$g$.,$ using $0$

or negative concentrations would not be appropriate$).$

PLEASE USE MATLAB CODE TO SOLVE THIS USING SYMBOLIC MATH