Question

# How to calculate the log2 fold change?

I have 3 groups. 1. Control 2. Disease 3. Treatment. I want to lookup the gene expression btw these groups, compared with control (whether is upregulated or downregulated).
I did real-time qPCR and have ct values. I calculated ∆Ct = Ct[Target]-Ct[Housekeeping] ... and ∆∆Ct = (∆Exp.)-(∆Control) and got the -∆∆Ct log-fold-change. It looks all the values are almost same and not much different between the groups.
My questions are,
1. What I did was right?
2.If I plot a graph what should I mention in y-axis?
3. Is there any other better way to calculate the gene expression results better?
4.How to calculate log2 fold change and does it helps to see the results more clearer?
p.s I have attached the .xls file for your reference.

1st Apr, 2018
Amal Hassan
Egyptian Atomic Energy Authority
Fold change is a measure describing how much a quantity changes going from an initial to a final value. For example, an initial value of 30 and a final value of 60 corresponds to a fold change of 2 (or equivalently, a change to 2 times), or in common terms, a one-fold increase. Fold change is calculated simply as the ratio of the difference between final value and the initial value over the original value. Thus, if the initial value is A and final value is B, the fold change is (B - A)/A or equivalently B/A - 1. As another example, a change from 80 to 20 would be a fold change of -0.75, while a change from 20 to 80 would be a fold change of 3 (a change of 3 to 4 times the original).
Fold change is often used in analysis of gene expression data in micro array and RNA-Seq experiments, for measuring change in the expression level of a gene. A disadvantage to and serious risk of using fold change in this setting is that it is biased  and may miss deferentially expressed genes with large differences (B-A) but small ratios (A/B), leading to a high miss rate at high intensities.
Let's say there are 50 read counts in control and 100 read counts in treatment for gene A. This means gene A is expressing twice in treatment as compared to control (100 divided by 50 =2) or fold change is 2. This works well for over expressed genes as the number directly corresponds to how many times a gene is over-expressed. But when it is other way round (i.e, treatment 50, control 100), the value of fold change will be 0.5 (all under expressed genes will have values between 0 to 1, while over expressed genes will have values from 1 to infinity). To make this leveled, we use log2 for expressing the fold change. I.e, log2 of 2 is 1 and log2 of 0.5 is -1.
159 Recommendations

7th Nov, 2017
Rajesh Parsanathan
looks you calculated Fold change 2^(ΔΔCT )
If you want to calculate log2 fold change, use the same take log base 2.
I added log 2 fold change calculation in your excel sheet data and graph.
30 Recommendations All looks good to me !! I cant really add to that
Hello i would like to share an article with you ...you just need to follow simle examples given in this article...
Regards
3 Recommendations
Thank you all for the answers...!!!
1 Recommendation
1st Apr, 2018
Amal Hassan
Egyptian Atomic Energy Authority
Fold change is a measure describing how much a quantity changes going from an initial to a final value. For example, an initial value of 30 and a final value of 60 corresponds to a fold change of 2 (or equivalently, a change to 2 times), or in common terms, a one-fold increase. Fold change is calculated simply as the ratio of the difference between final value and the initial value over the original value. Thus, if the initial value is A and final value is B, the fold change is (B - A)/A or equivalently B/A - 1. As another example, a change from 80 to 20 would be a fold change of -0.75, while a change from 20 to 80 would be a fold change of 3 (a change of 3 to 4 times the original).
Fold change is often used in analysis of gene expression data in micro array and RNA-Seq experiments, for measuring change in the expression level of a gene. A disadvantage to and serious risk of using fold change in this setting is that it is biased  and may miss deferentially expressed genes with large differences (B-A) but small ratios (A/B), leading to a high miss rate at high intensities.
Let's say there are 50 read counts in control and 100 read counts in treatment for gene A. This means gene A is expressing twice in treatment as compared to control (100 divided by 50 =2) or fold change is 2. This works well for over expressed genes as the number directly corresponds to how many times a gene is over-expressed. But when it is other way round (i.e, treatment 50, control 100), the value of fold change will be 0.5 (all under expressed genes will have values between 0 to 1, while over expressed genes will have values from 1 to infinity). To make this leveled, we use log2 for expressing the fold change. I.e, log2 of 2 is 1 and log2 of 0.5 is -1.
159 Recommendations
Thank you Dr.Amal Hassan.
A very detailed explanation with example. Easy for understanding.
Thanks again...!!!
1 Recommendation
24th May, 2018
Franco Harald Falcone
Justus-Liebig-Universität Gießen
I am not sure how the answer of my previous colleague relates to the question asked, but one important issue to consider is the choice of an apropriate reference gene, or best if validated using a second reference gene. RT-qPCR certainly has its drawbacks, and may be replaced by newer technologies such as droplet digital PCR in the future, but in my opinion not as 'notorious' if planned carefully, as my colleague seems to make it. Technology has moved on since 1990.
4 Recommendations
Thanks Dr.Franco Harald Falcone for your suggestion.
Yes, I am using 3 reference genes for normalization (Validated).
I agree with your point, I will try the droplet digital PCR.
1 Recommendation
Statistical measures of differential expression
Let xij and yij denote the log2 expression levels of gene i in replicate j in the control and treatment, respectively. We define the ordinary two-sample t-statistic as Ti = xi· − yi· si (2.1) where si is the standard deviation of the replicates for gene i. The modified t-statistic is defined as T 0 i = xi· − yi· si + so (2.2) where so is a constant chosen to minimize the coefficient of variation of T 0 i . In our analysis, we chose so and computed the modified t-statistic using Significance Analysis of Microarrays (Tusher et al. 2001). There are two definitions of fold-change in the literature. The standard definition of the fold-change for gene i is (e.g. Tusher et al. 2001) F Ci = x 0 i· /y 0 i· (2.3) where x 0 ij and y 0 ij are the raw expression levels of gene i in replicate j in the control and treatment, respectively. On the other hand, in Guo et al. (2006) and Choe et al. (2005), the fold-change for gene i is defined as F Ci = xi· − yi· (2.4) We will refer to these versions of fold-change as FCratio and FCdif ference, respectively. It is worth noting that as so in the denominator of the modified t-statistic is increased, the resulting gene ordering approaches that obtained using FCdif ference.
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Amal Hassan In my case I have 3 conditions: my control condition and two diferent treatment conditions, in one of both I have a gene upregulated and in the other, the same gene is downregulated. I have a doubt, when a gene is downregulated you do the log2 but only for the downregulated values? or all of them? (up and downregulated).
Thanks
Laura, you would still use log2 for all of the values. That way, a gene that is upregulated relative to the control will have a positive log2 fold change value, and a gene that is downregulated relative to the control will have a negative log2 fold change value.
2 Recommendations
fold change = (group1 - group2)/min(group1,group2).
4 Recommendations
29th Dec, 2019
Shahdat Hossain
National Institute of Biotechnology
Log2 aids in calculating fold change, and measure the up-regulated vs down-regulated genes between samples. Usually, Log2 measured data more close to the biologically-detectable changes.
5 Recommendations
21st Jul, 2020
Kazuya Oikawa
I found this link helpful for understanding how fold changes log2 transformation works.
20th Aug, 2020
Md. Nazim Uddin
Bangladesh Council of Scientific and Industrial Research
you may use NetworkAnalyst software for differential expression analysis
20th Aug, 2020
Md. Nazim Uddin
Bangladesh Council of Scientific and Industrial Research
Md. Nazim Uddin <you may use NetworkAnalyst software for differential expression analysis, https://www.networkanalyst.ca/ > Thank you for your sharing, so can you please share more about the basic steps for that network analysis, which will be more helpful for a beginner
Thanks a lot
Looking forward,
21st Jan, 2021
Md. Nazim Uddin
Bangladesh Council of Scientific and Industrial Research