Question

The average mass of proteins in the cell is 30.000 Da, and the average mass of an amino acid is 120 Da. In eukaryotic cells the translation rate for a single ribosome is roughly 40 amino acids per second. (a) The largest known polypeptide chain made by any cell is titin. It is made by muscle cells and has an average weight of \(3 \times 10^{6}\) Da. Estimate the translation time for titin and compare it with that of a typical protein. (b) Protein synthesis is very accurate: for every 10,000 amino acids joined together, only one mistake is made. What is the probability of an error occurring for one amino acid addition? What fraction of average sized proteins are synthesized error free?

Short answer

The translation time for titin is approximately 625 seconds, which is much longer than the 6.25 seconds it takes for the translation of a typical protein. The probability of an error occurring for one amino acid addition is 0.01%, and about 97.75% of average sized proteins are synthesized error free.

Step-by-step solution

Calculate the translation time for titin

First, calculate the number of amino acids in titin by dividing the weight of titin by the weight of one amino acid. That would be, \(3 \times 10^{6}\) Da / 120 Da = 25,000 amino acids. Then this should be divided by the rate of translation, 40 amino acids per second, to find the time it would take to translate titin. \(25,000 amino acids / 40 amino acids per second = 625 seconds.\)

Compare the results

Next, compare this with the translation time for a typical protein. The average weight of a protein is given as 30,000 Da. The number of amino acids in such a protein would be 30,000 Da / 120 Da = 250 amino acids. The translation time would be 250 amino acids / 40 amino acids per second = 6.25 seconds. The translation time for titin is much longer than that of an average protein.

Calculate the probability of an error

It is given that for every 10,000 amino acids joined together, one mistake is made. So the probability of an error occurring for one amino acid addition can be calculated as 1/10,000 = 0.0001 or 0.01%. This is the probability that a single amino acid will be erroneously joined.

Calculate the fraction of error-free proteins

Finally, to calculate the fraction of error-free proteins, it is necessary to consider the probability of a mistake not happening during the synthesis of a complete average-sized protein. Given that such a protein is made up of 250 amino acids, and the probability of a mistake at each joining is 0.0001, the fraction of proteins synthesized without any mistakes will be \(0.9999^{250} \approx 0.9775\), or about 97.75% of average-sized proteins are synthesized error free.

Key concepts

Ribosome Translation Rate

Understanding the rate at which ribosomes translate mRNA into polypeptides is crucial for grasping the efficiency of protein synthesis within cells. The translation rate can be defined as the number of amino acids a ribosome adds to a growing polypeptide chain per unit of time, often measured per second.

In eukaryotic cells, the translation rate is approximately 40 amino acids per second. To put this into perspective, consider an average protein with a molecular weight of 30,000 Daltons (Da), which roughly equates to 250 amino acids. To synthesize this protein, a single ribosome would take approximately 6.25 seconds, performing a remarkably rapid and complex process of decoding mRNA into functional proteins.

This speed, however, can vary based on several factors, including the complexity of the mRNA being translated, the availability of amino acids, and the energy status of the cell. Efficient translation is vital for cell survival, allowing rapid response and adaptation to changing environmental conditions.

Polypeptide Chain

A polypeptide chain is a series of amino acids linked together by peptide bonds, forming the primary structure of a protein. Each protein's unique function is determined by the specific sequence and length of the polypeptide chain that folds into a three-dimensional structure.

The largest polypeptide known, titin, which plays a structural role in muscle cells, has a massive molecular weight of 3 million Da. To synthesize such a colossal polypeptide, a ribosome would take approximately 625 seconds (or just over 10 minutes), highlighting the significant variability in translation time depending on the protein being produced.

A fascinating aspect of polypeptides is how their sequence dictates their folding and ultimately their function. Errors in this sequence can lead to malfunctioning proteins and are often the basis for many diseases, thus emphasizing the importance of accuracy during protein synthesis.

Amino Acid Sequence Accuracy

The accuracy of the amino acid sequence in polypeptides is fundamental to producing functional proteins. During translation, ribosomes must correctly match tRNA molecules carrying amino acids to the codons on mRNA. The step-by-step solution points out that protein synthesis is very accurate, with an error rate of only one incorrect amino acid for every 10,000 added.

When considering a singular amino acid addition, the probability of an error is a mere 0.01%. For an average-sized protein consisting of 250 amino acids, this translates to about 97.75% of proteins being synthesized without any mistakes. Given the intricate nature of protein function, even such a small error rate can have significant biological consequences. Therefore, cells have evolved complex quality control mechanisms, including proofreading activities by the ribosome and post-translation repair processes, to reduce the chances of these potentially detrimental mistakes.