# Causes and Consequences of Stochastic Gene Expression | Summary and Q&A

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July 28, 2015
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MIT OpenCourseWare
Causes and Consequences of Stochastic Gene Expression

## TL;DR

The model of gene expression in bacteria can be described by a simple model, where the number of mRNA and proteins are determined by rates of synthesis and degradation. The distributions of mRNA and proteins follow Poisson and geometric distributions, respectively.

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### Q: What is the unit of time in the gene expression model?

The unit of time is not explicitly defined in the model and is typically given in units involving seconds, minutes, or hours, depending on the degradation rates of mRNA and protein.

### Q: How is the mean number of mRNA per cell calculated?

The mean number of mRNA per cell is calculated by dividing the synthesis rate of mRNA by the degradation rate of mRNA. This represents the average number of mRNA molecules present in a cell.

### Q: What is the distribution of mRNA and protein in the cell?

The distribution of mRNA in the cell follows a Poisson distribution, while the distribution of protein follows a geometric distribution. These distributions capture the probabilistic behavior of gene expression.

### Q: How does the number of proteins produced per mRNA vary?

The number of proteins produced per mRNA follows a geometric distribution, where the probability of producing a specific number of proteins decreases exponentially as the number increases. The mean number of proteins produced per mRNA is given by the synthesis rate divided by the degradation rate.

## Summary & Key Takeaways

• The goal of the model is to analyze the deterministic and stochastic behavior of gene expression, by understanding the distribution of mRNA and protein in a cell.

• The simple model accurately describes gene expression in bacteria, with the mRNA distribution following a Poisson distribution and the protein distribution following a geometric distribution.

• The mean number of mRNA per cell cycle and the number of proteins per mRNA are calculated using the rates of synthesis and degradation.

• The number of bursts of mRNA per cell cycle is also calculated, which is equivalent to the number of proteins produced per mRNA.