Model: ENZMEM, two enzymes in vesicle

1. TABLE OF CONTENTS

Parameters

Output Variables

Diagram

Equations

Model demonstrations with parameter sets

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

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.

7.4. 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.


Copyright © 2000, National Simulation Resource, University of Washington.

Contact garyr@bioeng.washington.edu with comments, questions, or critiques.