# Background thought

Titin and TTN

Titin is the largest protein in the human genome with 33423 amino acids. Titin is coded by the gene TTN that must be at least $3 \cdot 33423 \approx 100kb$ long. Looking at NCBI entry for the gene TTN indicate that TTN is actually about 240kb long.

Transcription rate

The average transcription rate (Ref.) is around 1.5kb per minute. It therefore takes about $\frac{240k}{1.5k * 60}$ 2.5 hours to transcribe TTN in mRNA. This mRNA then need to be spliced before being available for being translated. Per consequence, I don't think it is possible for translation to happen in the same time as transcription but might well be wrong.

Translation rate

The translation rate is about 8.4 amino acids per second (Ref.). It therefore takes about $\frac{ 33423} { 8.4 \cdot 3600} \approx 1$ hour to translate the protein. Sure, several ribosome can translate the mRNA in the same time but it still remain that it takes 1 hour to synthesize at least one protein.

Transcription + Translation rate

Assuming translation does not occur in the same time as transcription, the total time to create the first protein of titin is about 3.5 hours.

Half-life

The half-life of a typical human protein is 6.9 hours (Ref.). Intuitively I would expect a negative correlation between mRNA size and mRNA half-life.

Half-life and Transcription + Translation rate

Because the time to produce the first protein is about half the half life, it means that a quarter of every single mRNA that is being produced would never give rise to even a single protein because it would degrade before either before or after translation has started.

It sounds like an important cost and would be surprised if a gene or a protein could be any longer.

# Question

Is there evidence of selection against long proteins and long genes?

Are there proteins that are much longer than Titin in other species?

Do I exaggerate the cost it represents, either by not considering that an average rate (such as transcription rate) is not representative of the actual rate for typically long gene/protein or by assuming that it is costly to create tons of mRNAs that won't never be translated?

• You are forgetting that there would be a lot of ribosomes on a single mRNA. Also, there could be multiple RNA polymerases transcribing the gene. – WYSIWYG May 18 '16 at 18:47
• Sure. It still remain that it take 3.5 hours to synthetize the very first protein and I'd expect it to fail 25% of the time. – Remi.b May 18 '16 at 18:58
• Let's say it does take 3.5 h to make a single protein from the point when transcription is initiated. However, titin is a structural protein and is not some kind of protein that has to quickly respond to stimuli. Once the protein reaches steady state then it is just continuously made. Imagine a transcription event that started at time t which culminates in the protein production at t+3.5h. Let's say there is another transcription event that started at t+0.1h which will end up making protein at t+3.6h. You are getting a protein molecule at every 0.1h. Do you get my point? – WYSIWYG May 19 '16 at 4:25
• Similarly, there are multiple ribosomes on the mRNA. If it takes 1h for a single ribosome to traverse through the ORF and let's say there are multiple ribosomes on the mRNA placed 0.1h away (convert that to #codons), you'll end up getting a protein molecule from a mRNA molecule every 0.1h. – WYSIWYG May 19 '16 at 4:28
• I think I get this point. I understand that it is feasible to produce proteins at a constant desired rate. It still remain that plenty of mRNA will degrade without being of any use and that plenty of mRNA will degrade during the translation, leaving half synthesize protein that are of no use either. All of this represent a cost that is much more important for a long gene and long protein than for a short gene and short protein. Thanks for your help! – Remi.b May 19 '16 at 6:13

Is there evidence of selection against long proteins and long genes?

I am not aware of any such evidence and cursory googling did not reveal studies that researched a correlation between gene selection and gene size. However, the larger a gene, the larger the probability of a deleterious mutation within said gene so I expect that there is some limit to the size genes can reach and be stable through evolution.

Are there proteins that are much longer than Titin in other species?

Do I exaggerate the cost it represents, either by not considering that an average rate (such as transcription rate) is not representative of the actual rate for typically long gene/protein or by assuming that it is costly to create tons of mRNAs that won't never be translated?

I really like how you estimated the time cost of producing titin. However, as you already suspect, I believe that you have several flaws in your assumptions.

First of all, the stability of mRNA and proteins varies a lot and depends strongly on their sequences. The half life of proteins can vary from minutes to Years. The Titin protein has a half life of ~70 h.

Similarly, mRNA stability varies from minutes to > 12h. Especially household and structural genes were identified to have mRNAs with long half lifes.

Both protein and mRNA stability is not simply governed by random decay but rather by tightly regulated degradation. For proteins, an example is ubiquitinylation which is a process where certain amino acid sequences are recognized and cause the protein to be ubiquitinylated which in turn triggers the degradation via the proteasome. For mRNA, the secondary structure is crucial since certain loop structures can be recognized by RNAses. Thus average protein/mRNA lifetimes do not help to estimate the actual turnover of a specific protein.

• +1 Thanks for your answer, that was very helpful. In addition to confirming what I suspected might go wrong with my quick estiamtions, I especially realized that a random negative exponential decay is not a good model for mRNA decay. I appreciate that you make reference to the mutation (which is of $e^{-uL}$, where $u$ is the mutation rate per base-pair and $L$ the size of a gene in infinite population) as it is likely a much more important factor that the one I brought about in my quick estimations. Thanks – Remi.b May 19 '16 at 14:58
• I'd expect that genes with the larger probability of a deleterious mutation would be under the stronger evolutionary pressure. Paper genome.cshlp.org/content/24/9/1497.full states that "Longer genes are less likely to produce duplicates and more likely to exhibit alternative splicing". – Maxim Kuleshov May 19 '16 at 15:47

Related to your questions: one thing that is known is that older genes, meaning genes that appear earlier in evolution are longer than new genes. Also new genes evolve faster than old ones. So new genes are usually short and tend to get larger with time.

Inverse Relationship Between Evolutionary Rate and Age of Mammalian Genes