2. 20 points. Consider the network shown below. In this cell, LuxR (which is always expressed) binds to AHL taken up from the environment. The LuxR-AHL complex activates expression of both c and GFP. Production of GFP is repressed by ci, so only a transient amount of fluorescence is produced in response to an AHL signal. (Adapted from Figure 1 of Basu et al. 2004.) Receiver Cell GFP LuxR AHL AHL LuxR-AHL clThe differential equations that describe the system are below, where R is LuxR-AHL, C is Ci, and G is GFP. dR = KA2 (RT - 2R) -KR dt dC a (R K R.) dt 1+ (R/ K ) -bc C dG as (R/ K ,) dt 1+ (R/K R) + (C/Kc) + (R/K R) . (C/Kc ) Parameter values are as follows: k1 = 0.5 min-1 M-3, k2 = 0.02 min-1, RT = 0.5 M, KR = 0.02 M, bc = 0.07 min", ac = 5 M/min, Kc = 0.08 M, be = 0.07 min", and A = 1 M. The value of ac varies as described in part (b) below. a) What type of feedforward loop represents this gene regulatory network? b ) Solve this set of ODEs using MATLAB and plot the concentrations of R, C, and G as a function of time with ac = 0. Initially, all species' concentrations are zero. c) Solve the set of ODEs with the following values of ac: 0, 0.02, 0.05, and 5 M/min. On a figure with four subplots, graph the concentration G as a function of cell generation (bo. time). d) What happens to the shape of the curve as ac increases? Relate this back to our discussion of FFLs in class