The Ribosome Translates Below its Capacity to Ensure Accuracy and Speed

Much of biology is expressed in “informational” language: the famous central dogma of molecular biology, for example, states that information is “stored” in DNA, “transcribed” to RNA, and “translated” to protein during protein synthesis. Such perspectives in biology inspire powerful computing methods such as the artificial neural network, a computational framework loosely inspired by the brain and the basis of some of our most powerful algorithms. Uncovering similar connections between biology and artificial intelligence may enhance the performance of existing algorithms. Conversely, insights from computation could shed light on new theoretical models in biology.

Motivated by these goals, we studied the information-processing abilities of the ribosome, a microscopic biological particle that synthesizes proteins, in our recent paper. Ribosomes are critical components of brain cells, suggesting they play fundamental roles in real neural networks. When a cell wants to produce a certain protein, a two-stage process called translation occurs. First, a gene in DNA is copied over (transcribed) to a molecule called messenger RNA (mRNA), which encodes the gene’s information in a string of symbols called codons. Second, the ribosome “reads” the mRNA molecule by matching each codon to an amino acid—a building block of protein—using a “dictionary” called the genetic code.

In this way, one can view the ribosome as an information transmitter, or channel, which sends the information contained in mRNA codons to a protein destination. Ribosomes translate quickly and accurately, producing several amino acids per second and making errors about once for every 10,000 to 100,000 codons. How is such high speed and accuracy possible? Fortunately, understanding information transmission is a well-studied problem. In any communication system, a message is sent across some kind of medium—a channel—to a receiver. Any channel, whether it be air or an electrical cable, introduces noise into a message. That is to say, a message can become corrupted or “garbled” before reaching the receiver.

In 1948, the mathematician Claude Shannon famously outlined a way one could minimize the degree of corruption in the received message. Specifically, he proved a remarkable theorem saying that as long as one transmits information below a certain threshold—called the capacity—then one can transmit information with as small an error as one likes. This theorem thus places a limit on how fast we can transmit accurately.

With Shannon’s theorem in mind, we modeled the ribosome as an information channel and calculated its capacity. In particular, we modeled the ribosome as a conditional probability distribution giving the probability that a certain amino acid is produced from a given codon. Calculating an exact value for the capacity of even the simplest channels, however, is difficult, often requiring the solution of a nonlinear optimization problem. We worked around this problem by calculating an approximate range for the capacity. More precisely, we calculated by hand upper and lower bounds for the capacity and discovered that it lies between 77-81 codons per second. In addition, to better estimate the ribosome’s capacity, we numerically approximated it using a computer algorithm. Our algorithm computed a capacity value of 81 codons per second, a value that agrees with the upper bound of our pen-and-paper estimate.

We compared these theoretical  results to experimentally determined translation rates. Such rates are well-documented and typically lie between 13-22 codons per second. This range lies far below both the pen-and-paper and numerical estimates of 77-81 and 81 codons per second, respectively. Since the ribosome operates at rates below its theoretical capacity, Shannon’s theorem guarantees a way for the ribosome to translate at the observed high accuracies.

Our model therefore successfully explains the ribosome’s ability to translate quickly and accurately. In fact, considering that our estimates lie so much higher than observed translation rates, one conclusion is that the ribosome could in principle translate even faster without sacrificing any more speed or accuracy! To the best of our knowledge, our work is the first to compare known translation rates to the ribosome’s capacity and supports the informational interpretation within biology.

Some open questions remain, however. Can we obtain a more precise pen-and-paper estimate of the capacity? Moreover, since some organisms possess non-standard genetic codes, can we optimize the capacity using one of these alternative codes? Finally, we anticipate the application of our model to other systems, particularly those that play key information-processing roles in biology, such as enzymes involved in DNA replication and transcription. We hope to face these challenges in future work.

This piece was based on the paper: Daniel A. Inafuku, Kay L. Kirkpatrick, Onyema Osuagwu, Qier An, David A. Brewster, and Mayisha Zeb Nakib. Channel capacity of the ribosome. Phys. Rev. E, 108:044404, Oct 2023 (available on arXiV and Physical Review E).