Model: ENZMEM, two enzymes in vesicle

1. TABLE OF CONTENTS

2. IMPORTANT !!! To run a demonstration, enter "xhost +nsr.bioeng.washington.edu" in one of your windows to allow the demonstration program to open windows on your machine !!!

3. Parameters

ENZMEM is parameterized as follows.

Table 1. ENZMEM Parameters
Parameter	Description	Units
Stotal	Total amount of substrate	molar (M)
E1total	Total amount of enzyme #1	molar (M)
E2total	Total amount of enzyme #2	molar (M)
PSSin	Permeability-surface area product (PS) for S transported from outside of membrane to inside of membrane	liter/sec
PSSout	PS for S transport from inside of membrane to outside of membrane	liter/sec
PSP1out	PS for P1 from outside of membrane to inside of membrane	liter/sec
PSP1out	PS for P1 from inside membrane to outside of membrane	liter/sec
PSP2in	PS for P2 from outside of membrane to inside of membrane	liter/sec
PSP2out	PS for P2 from inside of membrane to outside of membrane	liter/sec
k+1 E1	forward rate constant for enzyme 1- substrate binding, also called kf	1/(M*sec)
k-1 E1	backward rate constant for enzyme 1- substrate complex dissociation, also called kr	1/sec
k+2 E1	forward rate constant for product 1 formation from enzyme 1-substrate complex, also called kcat	1/sec
k-2 E1	backward rate constant for enzyme 1- substrate complex formation from enzyme 1 and product 1	1/(M*sec)
k+1 E2	forward rate constant for enzyme 2- substrate binding	1/(M*sec)
k-1 E2	backward rate constant for enzyme 2- substrate complex dissociation	1/sec
k+2 E2	forward rate constant for product 2 formation from enzyme 2-substrate complex, also called kcat2	1/sec
k-2 E2	backward rate constant for enzyme 2- substrate complex formation from enzyme 2 and product 2	1/(M*sec)
Vol Vesicle	also called Volves	liter
Vol Outside	also called Vout	liter
Vmax1	`k+2 E1'*E1total	M/sec
Km1	also called Km (`k+2 E1'+'k-1 E1')/`k+1 E1'	M
Vmax2	`k+2 E2'*E2total	M/sec
Km2	(`k+2 E2'+'k-1 E2')/`k+1 E2'	M
(alpha)	`k+2 E1'E1total/( (PSSin/ Vol_Enzyme)Km1) Utilization of substrate by enzyme relative to transport	none
(beta)	`k+2 E2'E1total/( (PSSin/ Vol_Enzyme)Km2) Utilization of substrate by enzyme relative to transport	none
(kappa)	ratio Km1/Km2	none
(rho)	ratio of Vmax2/Vmax1	none

Access to all input variables is via clicking the "INPUT" button on the main model page or by selecting "Inputs" under the "Parameters" menu.

4. Output Variables

Output variables are given by:

Table 2. ENZMEM Output Variables
Parameter	Description	Units
Sout	Substrate outside the membrane	molar (M)
S	Substrate inside the membrane	molar (M)
E1	Free enzyme #1	molar (M)
SE1	Substrate-Enzyme #1 complex	molar (M)
E2	Free enzyme #2	molar (M)
SE2	Substrate-Enzyme #2 complex	molar (M)
P1	Product 1 (from SE1) inside membrane	molar (M)
P2	Product 2 (from SE2) inside membrane	molar (M)
P1out	Product 1 outside membrane	molar (M)
P2out	Product 2 outside membrane	molar (M)
fr sat x	fractional saturation, x=SE1/E1total, averaged over the time step	none
Hill coefficient	slope of the logarithms of x/(1-x) (ordinate) vs. Sout/Km1 (abscissa) Plot vs. fr sat x	none

To plot results, select "Plot Area 1" from the Results menu. Place the cursor in an unused box under Y-parameters and press the right mouse button to bring up a list of plottable parameters.

5. Diagram

6. Equations

7. Model demonstrations with parameter sets

The user should inspect the input parameters and the output curves. Output curves can be found under the Results button under Plot Area 1 and Plot Area 2.

The following parameter sets are can be demonstrated by clicking on them:

7.1. Figure 2, Panels 1 and 2 : Figure2.panel_1_2.par

Run the model. The time dependent model shows curves which reflect the algebraic curves. Under Results, Plot Area 1 shows curves which reflect Panel 1, and Plot Area 2 reflect Panel 2. Note that only partial curves are calculated as the full range of the algebraic parameter space is not reflected in the time-dependent solutions.

7.2. Figure 2, Panels 1 and 3: Figure2.panel_1_3.par

Run the model. The time dependent model shows curves which reflect the algebraic curves. Under Results, Plot Area 1 shows curves which reflect Panel 1, and Plot Area 2 reflect Panel 3. Note that only partial curves are calculated as the full range of the algebraic parameter space is not reflected in the time-dependent solutions.

7.3. Figure 3, Panels 1 and 2: Figure2.panel_1_2.par

7.4. Figure 3, Panels 1 and 3: Figure3.panel_1_3.par

Run the model. The time dependent model shows curves which reflect the algebraic curves. Plot Area 1 shows curves which reflect Panel 1, and Plot Area 2 reflect Panel 3. Note that only partial curves are calculated as the full range of the algebraic parameter space is not reflected in the time-dependent solutions.

7.5. Rapid transport through membrane with single enzyme: progress.par

Run the model. Under Results, find Plot Area 1.