Question

Cell cycle and number of ribosomes Read the paper "Ribosome content and the rate of growth of Salmonella typhimurium" by R.E. Ecker and M. Schaechter (Biochim. Biophys. Acta 76,275,1963 ). (a) The authors show that their data can be fit by a simple assumption that the rate of production of soluble protein, \(P\) is proportional to the number of ribosomes. But this leaves out the need for the ribosomes to also make ribosomal protein, in an amount, \(R\). The simplest assumptions are that the total protein production rate, \(\mathrm{d} A / \mathrm{d} t,\) is proportional to the number of ribosomes, and the total amount of non-ribosomal protein (also knows as soluble protein) needed per cell is independent of growth rate. Given these assumptions, how would the ratio \(R / A\), with \(A\) the total protein content, depend on the growth rate? Does this give a maximum growth rate? If so, what is it? (b) With a 3000 s division time for \(E .\) coli, about \(25 \%\) of its protein is ribosomal. Note that the microbe Salmonella typhimurium considered here is very similar to \(E .\) coli. Using these numbers and your results from above, what fraction of the protein would be ribosomal for the highest growth rate studied in the paper? How does this compare to their measured ratio of ribosomes to soluble protein, \(R / P\) at these growth rates? How does the predicted \(R / P\) at high growth rates change if you now assume that \(\mathrm{d} P / \mathrm{d} t\) is proportional to \(R\) as they did in the paper? (c) Another factor that needs to be taken into account is the decay of proteins. If all proteins decayed at the same rate, \(\gamma\) how would this modify your results from (a)? How does the predicted functional from of R/A versus growth rate change? Explain why the data rule out \(\gamma\) being too large and hence infer a rough lower bound for the lifetime, \(1 / \gamma,\) of "average" proteins.

Short answer

The ratio R/A would increase with an increase in the growth rate and a maximum occurs when the derivative of A with respect to growth rate equals zero. For the highest growth rate, the fraction of ribosomal protein would also be at its highest. Including protein decay modifies the model by introducing a decay factor, \(\gamma\), and a larger \(\gamma\) value, which implies a shorter lifetime, does not match the observed data.

Step-by-step solution

Understand Relation between R, A and growth rate

From the problem, we know that the rate of protein production (P) is proportional to the number of ribosomes, and the total amount of non-ribosomal protein needed per cell is independent of growth rate. However, the ribosomes also produce an amount of ribosomal protein (R). It's also given that the total protein production rate \(\mathrm{d} A / \mathrm{d} t\) is proportional to the number of ribosomes. This means the production of total protein (A), that includes both ribosomal (R) and soluble protein (P), is proportional to the number of ribosomes which in turn are proportional to the growth rate. Therefore, as the growth rate increases, the total protein produced also increases and so does the ribosomal protein.

Calculate maximum growth rate

To find the maximum growth rate, we need to determine when \(\mathrm{d} A / \mathrm{d} t\) is at its maximum. Since A is proportional to the growth rate, we can set the derivative of A with respect to the growth rate equal to zero and solve for the growth rate. This will be the maximum growth rate.

Interpret the ratio, R/A at highest growth rate

The ratio R/A represents the proportion of ribosomal protein to the total protein in the cell. At the highest growth rate, this ratio would be at its maximum because more ribosomes would be needed to sustain the high protein production.

Relation of R/P with growth rate

By assuming that \(\mathrm{d} P / \mathrm{d} t\) is proportional to R, we're inferring that the rate of soluble protein production is tied to the amount of ribosomal protein. Thus, as the growth rate increases, the rate of soluble protein production must increase, which would alter the protein makeup of the cell and the ratio R/P would increase.

Modification due to protein decay

\(\gamma\) represents the rate of protein decay. If proteins decay at a constant rate, then the results from the previous steps would be times \(\gamma\). A lower bound of the lifetime of proteins can be determined by setting \(\gamma\) to be a maximum reasonable value. For a larger \(\gamma\) which corresponds to a shorter lifetime of proteins, the model would not match the observed data, ruling out such a possibility.

Key concepts

Ribosome Content

Ribosomes are essential components of cells, responsible for synthesizing proteins. These structures function as the site of translation in the cell's protein production process. The more ribosomes a cell contains, the higher its capacity for protein production. In the given exercise, ribosome content is critical because it directly relates to the rate at which proteins are produced. This means that as the cell divides and grows, its ribosome content influences how much protein it can generate, thereby affecting its growth rate and overall size.

The balance between ribosomal protein and non-ribosomal protein is maintained to ensure that sufficient ribosomes are available without overproducing. As the cell grows, ribosomes help maintain this balance by generating the proteins necessary for cellular functions. An interesting result from studies like the one in the original exercise is understanding how ribosome content scales with the growth rate, indicating a biological optimization where ribosomal content is tuned to meet the cell's growth demands.

Protein Production

Protein production in cells is a fundamental process that relies heavily on ribosomes. The production of proteins can be visualized as a dynamic integration where messenger RNA (mRNA) is translated into proteins by ribosomes. In the exercise, the rate of protein production is not only proportional to the number of ribosomes but also needs to account for the synthesis of ribosomal proteins themselves.

Therefore, to maintain a steady protein production rate that supports cell growth, there is a continuous need for ribosomes to produce both soluble proteins and ribosomal proteins. This dual role means that ribosomes are actively involved in increasing their own numbers, a process which becomes pivotal as the cell grows faster. The interplay between ribosomal protein production and soluble protein synthesis is delicate, and the cell must manage its resources efficiently to optimize growth without overheating its metabolic capacities.

Growth Rate Dependence

The growth rate of a cell is deeply intertwined with its protein production capacity. As cells grow, they consume resources and scale their ribosomal content to match their protein production demands. In the case of organisms like Salmonella and E. coli, this relationship is particularly evident, as highlighted in the exercise.

For these fast-growing organisms, the maximum growth rate is achieved when protein production cannot be further scaled due to biological limits such as ribosomal saturation or resource constraints. During rapid growth phases, the balance of ribosomal vs non-ribosomal proteins shifts dynamically to favor increased protein synthesis. This dependency means that as the growth rate increases, so does the demand for ribosomal proteins, creating a scenario where the cell must also ensure efficient degradation and recycling of proteins to sustain a high growth environment.

Understanding this concept could help predict cell behavior, particularly in varying nutrient environments, aiding in bioengineering and medical research.

Ribosomal Protein Decay

Protein decay is an aspect that can complicate the picture of protein production and cellular growth. In the process of protein decay, proteins lose their functionality over time and must be broken down and recycled. Within the context of the exercise, the decay rate, denoted by \(\gamma\), plays a significant role. If protein decay is too rapid, it counteracts the effects of protein synthesis, thereby affecting the overall protein availability for the cell’s growth.

A high decay rate would necessitate increased ribosomal production to compensate for lost proteins, potentially straining cellular resources. If \(\gamma\) is too large, the model predictions would not align with experimental observations, helping to set a lower bound for protein lifetimes (\(1/\gamma\)). Efficient recycling mechanisms allow cells to reuse amino acids, aiding in maintaining the delicate balance required for optimal protein production.
Managing protein decay is crucial, especially in cells experiencing rapid growth, as it impacts their ability to sustain long-term viability and adaptability in fluctuating environments. Thus, grasping the nuances of ribosomal protein decay provides insights into cellular resilience and efficiency.