jonelle from stavanger

Q: Double reciprocal plot

Dear all,

 

I am trying to make a double reciprocal plot (Lineweaver Burk) for a study in enzyme activity.  I saw the plot done on Excel but am not able to find

a similar solution in Numbers.  I tried using the Forecast function and also tried putting an estimate of values in my columns to get my trend bar to reach

into the negative numbers.  No luck for far.  How do I get the trend line to cross the Y axis??  I just don't know the technical steps to make the chart.

 

I am using Numbers 3.6.1. and have a MacBook Pro from 2012.

 

Thanks for your help.

 

Kind regards,

Jonelle

 

2000px-Lineweaver-Burke_plot.svg.png

iPod touch, iOS 5.0.1

Posted on Feb 29, 2016 1:37 PM

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Q: Double reciprocal plot

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  • by Wayne Contello,

    Wayne Contello Wayne Contello Feb 29, 2016 2:59 PM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Feb 29, 2016 2:59 PM in response to jonelle from stavanger

    Maybe this will help you?

    Screen Shot 2016-02-29 at 4.52.21 PM.png

     

    you can map everything into simple X and Y then get the best fit line with a linear equation

     

    Screen Shot 2016-02-29 at 4.59.28 PM.png

  • by jonelle from stavanger,

    jonelle from stavanger jonelle from stavanger Mar 1, 2016 9:26 AM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 1, 2016 9:26 AM in response to Wayne Contello

    Hi Wayne,

     

    I was so happy to receive your message - and be reminded that I have a trusty linear equation to work with.  Thank you for that! 

    I am still having problems however.  I thought that I needed -1/Km in order to calculate Km?  As you see by my graph, I am not able to

    cross the y-axis.  When I use the regression line equation, I don't get calculated values of 1/v like my experimental data. 

     

    What am I overseeing??

     

    Best regards,

    Jonelle

     

    LineweaverBurk.jpg

  • by Wayne Contello,Helpful

    Wayne Contello Wayne Contello Mar 1, 2016 10:33 AM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Mar 1, 2016 10:33 AM in response to jonelle from stavanger

    since you have M and B from the regression you have the expression for the line:

     

    y = 0.0004x + 1.9596

     

    you can rearrange this equation and solve for X when Y is zero.

     

     

    said another way, -1/Km is defined as the "X value" when the "Y value" is zero

     

     

    I'm leaving the last part out so you can try to make the "leap" to the solution on your own.

  • by jonelle from stavanger,

    jonelle from stavanger jonelle from stavanger Mar 1, 2016 9:43 AM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 1, 2016 9:43 AM in response to Wayne Contello

    Wayne,

     

    Thank you.  And yet I thought x was 1/S concentration??

     

    Jonelle

  • by Wayne Contello,Helpful

    Wayne Contello Wayne Contello Mar 1, 2016 10:33 AM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Mar 1, 2016 10:33 AM in response to jonelle from stavanger

    I highlighted the corresponding parts of the linear equation in an earlier post.  rearrange the parts using "X" and "Y", then substitute with the corresponding parts

  • by jonelle from stavanger,Solvedanswer

    jonelle from stavanger jonelle from stavanger Mar 1, 2016 10:05 AM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 1, 2016 10:05 AM in response to Wayne Contello

    Wayne,

     

    I have made progress thank you.  I am using a reference line for the Y-axis.  Is this the only way to address this issue?

     

    I appreciate your help! 

     

    J.

     

    Untitled.jpg

  • by Wayne Contello,

    Wayne Contello Wayne Contello Mar 1, 2016 11:21 AM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Mar 1, 2016 11:21 AM in response to jonelle from stavanger
    Is this the only way to address this issue?

     

     

    No.  it is not the only way, nor, in my opinion, is it the preferred way.

     

    you can calculate the value of x where y is 0 for almost any linear equation by doing the following:

     

    y = mx + b

     

    we are interested in the x value when y is zero, so...

     

    y = 0

     

    0 = mx + b

     

    subtract b from each side:

     

    -b = mx + b - b

     

    so

     

    -b = mx

     

    now divide not sides by m

     

    -b/m = x

     

    so

     

    x = -b/m

    in the chart you presented, the linear equation is:

    y = 0.0004x + 1.8913

     

    x = -1.8913/0.0004 = -4728.25

     

    x is the same thing as 1/S

     

    so 1/S = -4728.25

     

    m is  Km/Vmax

    so Km/Vmax = 0.0004

     

    b is 1/Vmax

     

    so 1/Vmax = 1.8913

     

    finally, since you have the linear equation you can create a new column in the data where you have you data.  In that column you enter the linear equation using the same X values and plot the Y values FOR ANY X value you like including negative x values.  In this way you can "extend" or extrapolate the data set beyond the range for which you captured data

  • by jonelle from stavanger,

    jonelle from stavanger jonelle from stavanger Mar 1, 2016 12:52 PM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 1, 2016 12:52 PM in response to Wayne Contello

    Wayne,

     

    I understand you are saying that the x value calculated when y = 0 is now the value of 1/S.  I am confused because I have experimental data already with these 1/S values.  Also, earlier you wrote:

     

    said another way, -1/Km is defined as the "X value" when the "Y value" is zero


    When I read this, I placed the value calculated (-4899) in my 1/S column and this was how I extended my line out to the negative x-axis.  I suppose I was being creative.  And then the equation on the regression line changed....to what you were calculating up above.


    I am sorry but am not able to follow the last paragraph - even though I am trying to stay calm.  This is my small data set.  Please show me what you mean if you have time. 


    J.


    ExpB.jpg

  • by Wayne Contello,

    Wayne Contello Wayne Contello Mar 1, 2016 1:19 PM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Mar 1, 2016 1:19 PM in response to jonelle from stavanger

    Screen Shot 2016-03-01 at 3.08.32 PM.png

     

    If you extrapolate the best fit line for the  data you took to the left, the line will intersect the X axis when y is 0.

     

    F2=INDEX(LINEST(C4:C8,B4:B8,1,0), 1)

    this is shorthand for... select cell F2, then type (or copy and paste from here) the formula:

    =INDEX(LINEST(C4:C8,B4:B8,1,0), 1)

     

    F3=INDEX(LINEST(C4:C8,B4:B8,1,0), 2)

     

    D4=B4×$F$2+$F$3

    select cell D4, copy

    select cells D4 thru D13, paste

    enter additional X values as shown

     

    the X-intercept is calculated in cell B12

    B12=−F3÷F2

     

     

     

    Screen Shot 2016-03-01 at 3.19.27 PM.png

  • by jonelle from stavanger,

    jonelle from stavanger jonelle from stavanger Mar 1, 2016 2:27 PM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 1, 2016 2:27 PM in response to Wayne Contello

    Hi Wayne,

     

    You have the patience of a saint, as my grandmother used to say.  Thank you!  And yet I wasn't able to replicate what you did.  I kept getting an error in syntax message even when I copied the formula directly.  Never mind.  I think I better let it rest for today.

     

    And yet!  I see where you wrote that the line that intersects the x axis (when y = 0). This is what you earlier called -1/Km.  At least I can calculate that manually now so you have taught me something.

     

    Have a nice day.

     

    Jonelle

  • by Wayne Contello,

    Wayne Contello Wayne Contello Mar 1, 2016 2:52 PM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Mar 1, 2016 2:52 PM in response to jonelle from stavanger

    you are in a country that uses the comma as the decimal separator, so you should use the semicolon (I used the comma) in the formulas:

     

     

    In the US (where I reside) I use US English and we use the period as the decimal point.  The formula here is, for example:

    F2=INDEX(LINEST(C4:C8,B4:B8,1,0), 1)


    Where you are it seems you use the comma as the decimal, so you will have to use the semicolon link this to delimit function arguments:

    F2=INDEX(LINEST(C4:C8;B4:B8;1;0); 1)

  • by jonelle from stavanger,

    jonelle from stavanger jonelle from stavanger Mar 2, 2016 12:42 PM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 2, 2016 12:42 PM in response to Wayne Contello

    Wayne,

     

    I made the corrections to my formula (regarding the comma) as you suggested and everything worked out fine.  I do have two math questions:

     

    1) With my data set, the linear equation was y = 0.0004x + 1.9596.  When y = 0 and I solve for x, I get -4899.  When I use the formula you wrote on the Numbers sheet -b/m = intercept on the x axis (-1/Km), I still get -4899.  I don't understand then how you got -535.6557 in cell B12.

     

    2) I noticed that the intercept (b) in the linear equation changes value when we extrapolate new values.  I have tried several different values of x as you suggested.  But then, how does one trust the value of the x intercept?  Or is it understood that it just an estimate??

     

    Thanks again.

    Jonelle

  • by Wayne Contello,

    Wayne Contello Wayne Contello Mar 2, 2016 1:13 PM in response to jonelle from stavanger
    Level 6 (18,972 points)
    iWork
    Mar 2, 2016 1:13 PM in response to jonelle from stavanger

    1) I got 5353.65 (5350,65 for you)

    2) since the slope and intercept (coefficients) for the equation are derived from sampled data, they will vary depending on the data.  Based on the best fit line coefficients, you can estimate the  x intercept

  • by jonelle from stavanger,

    jonelle from stavanger jonelle from stavanger Mar 2, 2016 1:38 PM in response to Wayne Contello
    Level 1 (15 points)
    iWork
    Mar 2, 2016 1:38 PM in response to Wayne Contello

    Wayne!  I also get 5350,65 when I use all the significant figures that you pasted into cell F2. However Numbers only gave me 4 significant figures when I ticked off the box for Show Equation.  Have you formatted Numbers differently than the default - and how did you do it?  Lastly, do you know of any books on the market for Numbers?  I am spending more time on my charts (and my math) than reading about enzymes...

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