Question

Fidelity of protein synthesis 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 a typical protein is about 6.25 seconds, while for titin, it is about 625 seconds, which is 100 times longer. The error rate per amino acid addition is 0.01%, thus the fraction of average-sized proteins synthesized without any mistake is around 98%.

Step-by-step solution

Calculate the number of amino acids in a protein

To calculate the number of amino acids in a protein, divide the total mass of the protein by the mass of an individual amino acid. For a typical protein, this would be \(\frac{30000}{120}=250\) and for titin, \(\frac{3 \times 10^{6}}{120}=25,000\).

Calculate the translation time for proteins

To calculate how long it takes for a protein to be synthesized, divide the number of amino acids in the protein by the translation rate. For a typical protein, this is \(\frac{250}{40}\approx6.25\) seconds and for titin, \(\frac{25000}{40}=625\) seconds.

Compare the translation times

Comparing the translation time for a typical protein to that of titin, it can be observed that titin takes approximately 100 times longer to synthesize.

Calculate the error per amino acid

The error rate for a single amino acid addition is given as one error in every 10,000 amino acids. The probability can thus be calculated as \(\frac{1}{10000}=0.0001\) or 0.01%.

Calculate the fraction of error-free proteins

To calculate the fraction of average-sized proteins synthesized without any mistake, raise the probability of success (i.e., no error) of a single amino acid addition to the power equivalent to the number of amino acids in the protein. This results in \((1-0.0001)^{250}\approx0.98\), or 98%.

Key concepts

Translation Rate

The translation rate is a measure of how quickly a ribosome can add amino acids to a growing polypeptide chain during protein synthesis. In eukaryotic cells, a single ribosome synthesizes about 40 amino acids per second. Understanding this rate is critical when estimating how long it will take for a protein to be fully synthesized.

For example, an average-sized protein with a mass of 30,000 Da composed of about 250 amino acids would take approximately 6.25 seconds to synthesize at this rate. This rapid assembly allows cells to respond quickly to changes in their environment by producing the proteins necessary for survival and function. Translation rate is a balance between speed and accuracy; although the ribosome works quickly, it must also ensure that each amino acid is correctly incorporated to maintain protein function.

Ribosome Function

Ribosomes play a critical role in the essential biological process of protein synthesis, acting as the site where genetic information is translated into proteins. They are complex molecular machines composed of ribosomal RNA (rRNA) and proteins, functioning to read messenger RNA (mRNA) sequences and translate them into polypeptide chains.

During translation, ribosomes move along an mRNA strand, match the mRNA codons with the correct transfer RNA (tRNA) molecules, and link the amino acids carried by tRNA into a polypeptide chain. This chain will fold into a functional protein after release from the ribosome. Ribosome's function is highly intricate, requiring not only the precise matching of codons to amino acids but also the correct binding, peptidyl transfer, and movement along the mRNA, all of which contribute to the fidelity of protein synthesis.

Polypeptide Chain

A polypeptide chain is a sequence of amino acids linked together by peptide bonds and is the primary structure of a protein. The specific sequence of amino acids determines the protein's unique structure and function.

The formation of a polypeptide chain is a critical step in protein synthesis, with ribosomes playing a central role in joining amino acids one at a time in the correct order. After synthesis, the polypeptide chain undergoes folding and sometimes chemically modifies before becoming a fully functioning protein. As exemplified by titin, the largest known polypeptide chain, which weighs approximately 3 million Da and contains around 25,000 amino acids, even large proteins are synthesized effectively by the cell's translation machinery.

Amino Acid

Amino acids are the building blocks of proteins. Every amino acid consists of a central carbon atom bonded to an amino group, a carboxyl group, a hydrogen atom, and a variable side chain (R group). There are 20 different standard amino acids, each with unique properties provided by its side chain.

The sequence and nature of the amino acids in a polypeptide chain determine the protein's structure and function. Amino acids are linked by peptide bonds during translation to form proteins, with a typical amino acid weighing approximately 120 Da. The precise addition of amino acids in the correct order is crucial for the synthesis of error-free proteins.

Error Rate in Protein Synthesis

Protein synthesis is a highly accurate process, but errors can occur. The average error rate is about one mistake for every 10,000 amino acids added, which translates to a 0.01% chance of an error in any single addition. Although this error rate may seem small, the accumulation of errors can have significant consequences for protein function.

For an average-sized protein consisting of 250 amino acids, approximately 98% are synthesized without any mistakes. However, the longer the polypeptide chain, the higher the chance that an error will occur during its synthesis. It is the cell's quality control mechanisms, such as proofreading functions by the ribosome and the protein repair systems, that help to maintain such high fidelity in protein synthesis.