Universiti Putra Malaysia

Question

Asked 23 December 2021

# How to calculate initial velocity of an enzyme from RFU vs time graph?

Hi everyone, I have been trying to calculate the K

_{m }value of a recombinant HCV NS3/4A protease using a FRET substrate, the cleavage of which can be detected at 500 nm using excitation wavelength of 355 nm. I have a RFU vs. time graph of different concentration of the substrate (attached). Next, I am calculating the initial rate which is the slope of the linear initial part of the progress curve, with the ultimate goal to plot the 1/[S] vs. 1/[V] graph and calculate the K_{m }from the Lineweaver-Burk equation. However, if I calculate the slope from this graph for the time range between 0-10 minutes which is the initial linear part, the intercept for the 1/[S] vs. 1/[V] graph is negative but K_{m }value can not be negative. I was wondering if anyone can guide me on how to calculate the initial velocity correctly from the graph I have? Thank you so much!## Most recent answer

I plotted your data (extracted using webplot, Rohatgi) using graphPad and obtained values very close to what you got, for single y data. Normally I usually plot replicated data, side by side column or enter Mean. SD and N. replicated data usually gives narrower 95%CI data

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## All Answers (14)

University of Zaragoza

I would say that the linear region of the traces is shorter: from 0 to 5 minutes, or even less than 5 minutes.

You should not use the Lineweaver-Buri representation. That is outdated procedure, for several reasons.

You should plot v

_{0}(initial slope) as a function of [S] (substrate concentration) and analyze the data with the Michaelis-Menten model:v

_{0}= k_{cat}[E]_{T}[S] / (K_{m}+ [S])Knowing [E]

_{T}(enzyme concentration) you will estimate k_{cat}(catalytic rate constant or turnover number) and K_{m}(Michaelis constant).1 Recommendation

Stanford University

Thank you so much Adrian Velazquez-Campoy for responding to my question. I have calculated the initial slope for the first 4 minutes and plotted the values as as a function of substrate concentration. However, I don't think the data is fitting well (attached). I am using 40 nM commercial NS3/4A per reaction. Can you please suggest what changes I should add into my experimental design for a better fit? Thank you so much.

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It's actually not a bad Michaelis plot, just a little noisy. You need to go to higher substrate concentrations to get to the point where the rate slows down more, indicating that a near-saturating concentration has been reached. Then fit the data as Adrian Velazquez-Campoy recommended to get the Km. You will need a computer program that does nonlinear regression analysis.

You will get a tighter fit if you do multiple replicates for each concentration, and also if you space the concentrations out evenly, instead of doubling them. You don't need those substrate concentrations at the low end, which are lower than the enzyme concentration and therefore should not be used in any case.

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Stanford University

Adam B Shapiro Thank you so much for taking time to go through my data and for sharing the suggestions. I have just started to work on enzyme kinetic assays and your points were very helpful. I am thinking about repeating the assay with final substrate concentration 0.5-10 uM with 10-12 data points evenly spaced in the range. For this assay, I had two replicates for each concentration and then calculated the average slope. I can add more replicates to each concentration. For the nonlinear regression analysis, I was using GraphPad Prism. I will share the results once I repeat the assay this week to confirm.

Universiti Putra Malaysia

follow Dr Adrian and Dr Shapiro's advice. The curve does not appear to reach Vmax (Fig.1 ).

Equally spaced substrate concentration- 0, 0.05, 0.2, 0.8, 3, 6, 10, 20 and 30 uM should do the trick as the Km is approx 4.7 uM, see

Do triplicate to get narrower confidence intervals, (Fig. 2) simulation

Get more data at the climbing stage (<4 min), maybe every 30 sec, as this is the region you calculate initial velocity (Fig. 3).

Use nonlinear regression software- GraphPad for e.g. as it has an inbuilt MM curve.

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National Institute for Biotechnology and Genetic Engineering

Dear Antara

I am also doing the Fret assay using dengue protease to calculate the kinetic parameters and facing the similar kind of issue in calculating Km. when you done with your experiments please share with us. Thanks

In order to calculate the value of k

_{cat}, you will need to convert RFU to micromolar. This can be done by allowing the reaction to go to completion at various substrate concentrations, which can be achieved by using a fairly high enzyme concentration. The change in RFU from the completed reaction to the same substrate concentration without the enzyme is plotted against the substrate concentration. The result is a standard curve, and the slope of the line (assuming it is linear) is the conversion factor from RFU to micromolar.1 Recommendation

Stanford University

Hi everyone, thank you so much for your suggestions. I have repeated the experiment following the points highlighted and wanted to discuss my results. As my previous curve did not approach V

_{max}, I used substrate concentrations- 0, 0.5, 0.8, 1.7, 3, 6, 10, 20 and 30 uM in technical replicates and removed the substrate concentrations which are lower than the enzyme concentration. I got readings every 30 seconds this time and calculated the slope for the first 3.5 minutes and used GraphPad's non-linear regression M-M plot function. However, the confidence interval is not very narrow and I am getting a K_{m}value of 14.82 (data and calculation attached).The substrate (https://www.anaspec.com/en/catalog/hcv-protease-fret-substrate-ret-s1~12bb469d-1b8c-4b64-9225-444b666c3c26) should have a high K

_{cat/}K_{m}value and I still can not be sure the K_{m}value I am getting is correct. If anyone can share their insights that would be very helpful.I suggest that the first thing you do is look carefully at each of the triplicate progress curves during the first 3.5 min, to make sure the quality of each is satisfactory, and remove as outliers any which have poor data quality data, such as large spikes or high noise. Next, instead of using the same time frame for every curve, check each one for the length of time the progress curve is linear, and measure the slope only over that time period, which is likely to be shorter at lower substrate concentrations. These data quality procedures may tighten up your Km estimate somewhat, although I would say it's already pretty good. Finally, you can repeat the whole measurement a few more times to allow you to calculate the overall average and standard deviation of the Km measurement.

Another approach, which is complementary to the standard initial rate analysis, is progress curve analysis. In this method, the whole progress curve, not just the initial rate part, is used. The data are fit by nonlinear regression to the integrated form of the Michaelis-Menten equation to get estimates of Km and Vmax. You have to make an assumption that there is no product inhibition. In my experience, this method, if applied globally to the whole set of progress curves collected at different substrate concentrations, will agree with the initial rate method within a factor of 2.

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University of Zaragoza

Another issue is the use of confidence intervals for estimating the uncertainty of estimated parameters.

Confidence intervals are the best option, compared to symmetric parametric errors, but too often the 95% statistical significance can be too stringent. The 68% confidence interval corresponds more or less one standard deviation width from the nominal value, while the 95% confidence interval corresponds to two standard deviations width. As Adam B Shapiro said, the plot is fairly good, but using the CI95 results in an unwanted large uncertainty in Km and kcat/Km. The CI68 will result in smaller uncertainty.

Why using CI95 or CI68? It is an arbitrary decision; historical reasons may favor CI95, but practical reasons may favor CI68.

Private Person

If your data are noisy, you can evaluate them with the "direct plot" of Eisenthal and Cornish-Bowden (DOI:10.1042/bj1390721, DOI:10.1042/bj1390715). Being non-parametric, this method is more stable against outliers than a non-linear regression, it is also simple and doesn't even require a computer, only some graph paper. I have published a fully worked-out example in my "Fundamentals" (DOI:10.1007/978-3-319-19920-7_6).

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Universiti Putra Malaysia

Quote

"Another approach, which is complementary to the standard initial rate analysis, is progress curve analysis. In this method, the whole progress curve, not just the initial rate part, is used. The data are fit by nonlinear regression to the integrated form of the Michaelis-Menten equation to get estimates of Km and Vmax. You have to make an assumption that there is no product inhibition. In my experience, this method, if applied globally to the whole set of progress curves collected at different substrate concentrations, will agree with the initial rate method within a factor of 2." from Adam B Shapiro

This should address the universal issue in manual assignment of initial rates "linear tangent line"

minute 1:30

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Dhofar University

Dear Dr Antara Chakravarty . I agree with Dr Adam B Shapiro .

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Universiti Putra Malaysia

I plotted your data (extracted using webplot, Rohatgi) using graphPad and obtained values very close to what you got, for single y data. Normally I usually plot replicated data, side by side column or enter Mean. SD and N. replicated data usually gives narrower 95%CI data

2 Recommendations

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