ELMAVG

BCHM2972 ELMA Simulation page 1

Simulating the ELMA reaction.

The Mathematics behind the reaction.The ELMA reaction is a pseudo first order reaction. In other words, everything is in vast excess except the glucose. The rate of the reaction is therefore dependent upon the [glucose]. This can be written mathematically as:

-d[S]/dt is proportional to [S] where S (=substrate) is, say, glucose.

Inverting and integrating (and fiddling around) we get…

[S] = Ae-kt………(1).

Now, to find the [S] at the beginning of the reaction, (lets call that [S0]) we find [S] at t = 0 by

substituting into equation (1) [S0] = Ae0 or A (as e0 = 1)

Now the expression looks like this:

[S] = [S0]e-kt ………..(3)

Now also, [P] = [So] – [S]…….(2). where [S0] is the starting substrate concentration.

Therefore [P]/[So] = 1 – [S]/[So]………..(4)

and rearranging equation (3) we get [S]/[S0] = e-kt ………….(5).

So plug equation (5) into equation (4) [P]/[S0] = 1 - e-kt

Now we can solve this equation to find [P] when we know t (time), k (rate constant) and [S0]

Half-life (t½) and rate constant

Half life is the constant of a first order reaction. It is the time it takes for half the starting substrate, S0 to be converted to product. Determine this value using the optimized timecourse you did in the first week. Irrespective of the starting concentration, the half-life, t ½ for a particular reaction is constant (Convince yourself of this by determining t ½ at different [S0] ).

We can also then express k (the rate constant) in terms of the half-life:

The half-life mathematically is when [S]/[S0] = ½.

So equation (4) becomes ½ = e-kt -ln0.5/t ½ = k


Setting up the time course simulation

On the top row of one Excel worksheet set up a series of cells: the Extinction Coefficient; the rate constant, k; the fold-enzyme and the half-life, t½.

(μM-1cm-

1)0.0053

Rate constan

t, k

-0.11552453

[enzyme]

-fold1

Half-life,

t½ (min)

6

Now we have the parameters in place and we are ready to simulate the standard curve.

3. The rate constant cell has the formula =LN(0.5)/Half_life insertedas k = -ln0.5/t ½

1. This number came from the gradient of the standard curve. Take care with units!

(mM-1cm-1)

0.053Rate

constant, k

0.11552453[enzyme]

-fold1

Half-life,t½ (min)

6

[So] (nmol/ml) 0 50 100 150 200 250

Time (min) P/So

0 05 0.438769

10 0.6850215 0.82322320 0.90078725 0.94431930 0.96875

35 0.98246240 0.99015745 0.994476

Absorbance

The [glucose] used in your standard curve

Formula entered:=1-EXP(-$F$1*A5)This is 1 - e-kt

as [P]/[S0] = 1 - e-kt

2.Determine the half life from your timecourse. It is the time at which the absorbance = 1/2 the maximum. It is independent of [S0]Name this cell half_life (see below if you are unsure how to name cells)


The next step involves converting this ratio to absorbances. This is quite easy. Multiply the [P]/[S0] ratio by the [S0] (to get [P]) and the extinction coefficient and you have the absorbances. Use fixed rows, columns or both to allow you to drag the formula across and down the whole table.

You can now plot the graphs; time course and standard curve.

Simulating a change in [enzyme]To set this up simply multiply k (the rate constant) by the [enzyme], expressed as fold change. You are now in the position to change the amount of enzyme you add by adjusting the fold change cell. The effect of the half life of the reaction can also be seen. Here are the graphs if the half life is 6 min and there is 1-fold [enzyme].

(mM-1cm-1)

0.0053Rate

constant, k

0.11552453[enzyme]

-fold1

Half-life,t½ (min)

6

[So] (nmol/ml) 0 50 100 150 200 250

Time (min) P/So

0 0 0 0 0 0 0 05 0.438769 0 0.116274 0.232548 0.348821336 0.465095 0.581369

10 0.68502 0 0.18153 0.36306 0.544590691 0.726121 0.90765115 0.823223 0 0.218154 0.436308 0.654462527 0.872617 1.09077120 0.900787 0 0.238709 0.477417 0.71612601 0.954835 1.19354325 0.944319 0 0.250244 0.500489 0.75073347 1.000978 1.25122230 0.96875 0 0.256719 0.513438 0.77015625 1.026875 1.283594

35 0.982462 0 0.260352 0.520705 0.781056917 1.041409 1.30176240 0.990157 0 0.262392 0.524783 0.787174709 1.049566 1.31195845 0.994476 0 0.263536 0.527072 0.790608204 1.054144 1.31768

Absorbance

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50

Time (min)

Ab

sorb

ance

500

nm

250 M

200 M

150 M

100 M

50 M

y = 0.0053x

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 50 100 150 200 250

[Glucose] (M)

Ab

sorb

ance

500

nm


If the amount of enzyme decreases…If I drop the [enzyme] to 0.1 then the reaction is not completed in the 45 min.

The standard curve is still linear but it does not reach the desired final absorbance. The time course is a fan rather than a series of plateaux. Does this matter if the standard curve is still linear?

Increasing the amount of enzyme…If I add 5 times the enzyme the reaction just reaches the plateau quicker. The standard curve is the same, it is just more expensive as the enzyme is usually the most expensive component of an ELMA. You do finish the reaction quicker, in this case the reaction is all over in 5 min.

Time Course

0

0.1

0.2

0.3

0.4

0.5

0.6

-5 5 15 25 35 45

Time (min)

Abso

rbance

500 n

m

Standard Curve: Glucose

y = 0.0021xR2 = 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250

[glucose] (nmol/ mL)A

bso

rbance

500 n

m

Time Course

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-5 5 15 25 35 45

Time (min)

Abso

rbance

500 n

m


y = 0.0053xR2 = 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250

[glucose] (nmol/ mL)

Abso

rbance

500 n

m


Simulating impurities in the standard glucose.Now let’s try to simulate the effect of an impure standard glucose solution. To do this you will need to add a cell with the % impurity at the top of the spreadsheet with the other parameters. You may like to name this cell. Then you need to apply this %impurity to the [S0] values as this will alter the effective [S0]. This is done by multiplying the [S0] by (100-%impurity)/100 and then making sure the absorbances are calculated from the effective [S0] rather than the [S0]. If you set the impurity at 50 % the graph should look like this:

Note that the effect of an impurity is to lower the final absorbances of all the standards but the time course still plateaus. The standard curve is linear; the gradient is just lower. Can you distinguish between denatured enzyme and impure standard glucose from the standard curve?

Limiting ReagentsA second scenario is when you have a limiting amount of one of the reagents. In the case of the glucose assay this will be the 4-AAP. To set up this simulation you have to be aware of the stoichiometry of the reaction. Two glucose molecules require 1 4-AAP, so the standard curve becomes limited at [4-AAP] < 125 M. At concentrations above 125 M the reaction will proceed, albeit not under truly first order conditions (the reaction rate may be more dependent on the [AAP] than the [glucose]). To simulate this situation you need to use the “IF” statements in Excel. Set up a cell which will have the [AAP] (see the final screen shot). To this cell you can enter any numerical value. Then into another row add your IF statement. We want the IF statement to imply “If the value of [glucose] is less than 2x value of [4AAP], then the ‘usable’ [substrate] will be the same as the actual [substrate], BUT if not (ie if [glucose] is > 2x[4AAP], then assay is limited by [4AAP]…and the usable [S0] = 2x [4AAP]”

IF Statement:IF the [S0] < [AAP]*2 then use [S0]. IF [S0]>[AAP]*2, use [AAP]*2 as the [S0]. While this gives an over-simplified representation of the effect of reagent limitation, it does show the bunch-up nicely. The standard curve becomes very bent!!

Time Course

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-5 5 15 25 35 45

Time (min)

Abso

rbance

500 n

m


y = 0.0026xR2 = 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200 250


Abso

rbance

500 n

m


The additional Excel skills which would make this simulation really work well would be:

Naming cells Macros Protecting your worksheet once you have finished.

I have included a short set of instructions on how to do these 3 tasks at the end of this section.

Record macros for the increase and decrease in [enzyme], the limiting and excess reagent, impurities in the standard glucose, increasing and decreasing the half-life of the reaction, maybe even new chromophores with higher or lower extinction coefficients.

Finally to make the simulation very user-friendly move the graphs up to cover the absorbance calculations. Your users don’t need to see the data, just the graphs!

Time Course

0

0.05

0.1

0.15

0.2

0.25

-5 5 15 25 35 45

Time (min)

Abso

rbance

500 n

m


y = 0.0011xR2 = 0.3923

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200 250


Abso

rbance

500 n

m


Present all the simulations on ONE page: The whole page would look something like this:

Naming cells.

It is sometimes helpful to name cells, rather than absolutely referencing them with $ everywhere. To name a cell, click on the cell insert name define and then give it an informative title. Whenever you click in that cell (to incorporate it into an equation) the cell will appear as its name in the equation and it will be absolutely referenced (ie fixed).

This takes the limiting reagent into account.

% Impurity 0

(mM-1cm-1)0.0053

Rate constant,

k0.11552453

[enzyme]-fold

1Half-life,t½ (min)

6[AAP] (uM)

2500

Effective [S0]

0 50 100 150 200 250

Reagent Limitations

0 50 100 150 200 250

[So] (nmol/ml) 0 50 100 150 200 250

Time (min)P/So

0 0 0 0 0 0 0 05 0.438769 0 0.116274 0.232548 0.348821336 0.465095 0.581369

10 0.68502 0 0.18153 0.36306 0.544590691 0.726121 0.90765115 0.823223 0 0.218154 0.436308 0.654462527 0.872617 1.09077120 0.900787 0 0.238709 0.477417 0.71612601 0.954835 1.19354325 0.944319 0 0.250244 0.500489 0.75073347 1.000978 1.25122230 0.96875 0 0.256719 0.513438 0.77015625 1.026875 1.283594

35 0.982462 0 0.260352 0.520705 0.781056917 1.041409 1.30176240 0.990157 0 0.262392 0.524783 0.787174709 1.049566 1.31195845 0.994476 0 0.263536 0.527072 0.790608204 1.054144 1.31768

Absorbance

Time Course

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-5 5 15 25 35 45

Time (min)

Abso

rbance

500 n

m


y = 0.0053x

R2 = 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250


Abso

rbance

500 n

m

The standard [4-AAP] is 2.5 mM or 2500 mM.

Enter the % impurity here

The effective [S0] is shown here. This takes into account the impurity of the standard glucose.

Move the graphs up to

cover the data.


Recording Macros.

What is a Macro? It is a section of code (written in visual basic), which performs a common task. Don’t panic: you don’t have to know visual basic to do this….I don’t! The Excel program has a built-in process, which can record your task and convert it to visual basic for you. You must ensure that you know EXACTLY what you need to do before recording your macro. It is a good idea to practice the task a couple of times before starting to record. You should also finish the whole spreadsheet before recording macros, as changing things later can upset the macro!

Once you are confident you know what to do go to Tools Macros record new macro. First record a macro to “reset” the graphs at the default position. This is often a great idea when you have many alternative options to try (which you will later). Set the half-life to 6, the [enzyme] to 1, the impurity to 0 and the [4-AAP] to 2500. These are the default conditions. Every time you record a macro, you will need to type in the value for EVERY parameter that may change in other macros (even if it doesn’t change in the particular macro you are recording). Otherwise, that value will not return to the original value after you run a different macro.

Be sure to give your macro a name and assign it a hotkey. Record your hotkeys as you go along. When you have finished the actions click the stop (blue square) in the record box. Make sure you have worked out which cell you want to finish in before recording.

We now want to assign this macro to a button. The buttons are found in the FORMS toolbar (view toolbars forms). Click on the button option and then place the button appropriately somewhere near the graphs. Give the button a name etc. You will be asked which macro you want to assign to the button. Click on the appropriate macro and you are all set. If you want to change the size of your button or edit the text once you have located it and clicked elsewhere, simply right click on the button.

Protecting your worksheet.

When you have completed your tutorial you need to lock all the cells except for the ones your macro (or the user of your spreadsheet) will want to change. You don’t want someone to come in and alter all the other settings. This process is very handy to know how to do in Excel and is actually done in a reverse process. You go into your spreadsheet unlock the cells you need to change then protect the whole sheet. To unlock the relevant cells click on the cells and go to Format cells protection then untick the locked box. Then go to Tools protection protect sheet. It will ask you for a password (not a bad idea). Make sure you write your password down somewhere!

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