Text S1 Mathematical modeling Our mathematical model ... - PLOS

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Text S1 Mathematical modeling Our mathematical model consists of a system of coupled ordinary differential equations (ODEs) which describe the dynamic concentrations of the phosphotransfer proteins throughout the R. sphaeroides cell. We applied the law of mass action to the phosphotransfer reactions in Table 1 and obtained the following system of non-linear ODEs.

dA2   k1 A2  k 3 A2 PY3  k 3 A2Y3 P  k 4 A2 PY4  k  4 A2Y4 P  k 5 A2 PY6  k 5 A2Y6 P dt (1)  k 6 A2 P B1  k  6 A2 B1P  k 7 A2 P B2  k  7 A2 B2 P dA2 P  k1 A2  k 3 A2 PY3  k 3 A2Y3 P  k 4 A2 PY4  k  4 A2Y4 P  k 5 A2 PY6  k 5 A2Y6 P dt ( 2)  k 6 A2 P B1  k  6 A2 B1P  k 7 A2 P B2  k  7 A2 B2 P dA3   k 2 A3  k8 A3 PY6  k 8 A3Y6 P  k 9 A3 P B2  k 9 A3 B2 P dt dA3 P  k 2 A3  k8 A3 PY6  k 8 A3Y6 P  k 9 A3 P B2  k 9 A3 B2 P dt dY3   k 3 A2 PY3  k 3 A2Y3 P  k10Y3 P dt dY3 P  k 3 A2 PY3  k 3 A2Y3 P  k10Y3 P dt dY4   k 4 A2 PY4  k  4 A2Y4 P  k11Y4 P dt dY4 P  k 4 A2 PY4  k  4 A2Y4 P  k11Y4 P dt dY6   k 5 A2 PY6  k 5 A2Y6 P  k8 A3 PY6  k 8 A3Y6 P  k12Y6 P dt  k15 aY6 P A3  k15 bY6 P A3 P

(3) ( 4) (5) ( 6) (7 ) (8)

(9 )

dY6 P  k 5 A2 PY6  k 5 A2Y6 P  k8 A3 PY6  k 8 A3Y6 P  k12Y6 P dt  k15 aY6 P A3  k15 bY6 P A3 P dB1   k 6 A2 P B1  k 6 A2 B1P  k13 B1P dt dB1P  k 6 A2 P B1  k 6 A2 B1P  k13 B1P dt dB2   k 7 A2 P B2  k  7 A2 B2 P  k 9 A3 P B2  k 9 A3 B2 P  k14 B2 P dt dB2 P  k 7 A2 P B2  k  7 A2 B2 P  k 9 A3 P B2  k 9 A3 B2 P  k14 B2 P dt

(10) (11) (12) (13) (14)

Here Ai=[CheAi], AiP=[CheAiP], Yj=[CheYj], YjP=[CheYjP] , Bk=[CheBk] and YkP=[CheYkP] where i=[2,3], j=[3,4,6] and k=[1,2] with the reaction rates as given in Table S2. In order to close the system of equations we defined a set of initial conditions: Ai (x,0)  Ai 0 , AiP (x,0)  0, Y j (x,0)  Y j 0 , Y jP (x,0)  0, Bk (x,0)  Bk 0 and BkP (x,0)  0

(15)

Here Ai0 is the initial concentration of CheAi, Yj0 the initial concentration of CheYj and Bk0 the initial concentration of CheBk. The model was populated with the experimental data in Table S2 and equations (1)-(14), along with the respective initial conditions in equation (15), were solved using an adaptive time stepping ODE solver in Matlab (ode15s) due to the stiffness of the problem.