Question

Specific DNA Binding by Regulatory Proteins A typical bacterial repressor protein discriminates between its specific DNA-binding site (operator) and nonspecific DNA by a factor of \(10^{4}\) to \(10^{6}\). About 10 molecules of repressor per cell are sufficient to ensure a high level of repression. Assume that a very similar repressor existed in a human cell, with a similar specificity for its binding site. How many copies of the repressor would a human cell require to elicit a level of repression similar to that in the bacterial cell? (Hint: The \(E\). coli genome contains about \(4.6\) million bp; the human haploid genome has about \(3.2\) billion bp.)

Short answer

Approximately 6960 repressor molecules are needed for a human cell.

Step-by-step solution

Understand the problem

We are comparing the number of repressor molecules needed in a human cell to achieve a similar level of repression as in a bacterial cell, given the difference in genome size and specificity of binding.

Calculate the genome size ratio

Calculate the ratio of the human genome size to the E. coli genome size. The E. coli genome is approximately 4.6 million base pairs, and the human genome is about 3.2 billion base pairs. Therefore, the ratio is \( \frac{3.2 \times 10^9}{4.6 \times 10^6} \approx 696 \).

Determine the number of repressor molecules needed

Since the human genome is 696 times larger, the number of repressor molecules needed would be 696 times the number needed for bacteria to achieve equivalent repression. Since 10 molecules are needed for bacteria, for humans it would be \( 10 \times 696 = 6960 \) molecules.

Consider specificity

Depending on the specificity factor, which is between \(10^4\) to \(10^6\), we adjust the number of repressors. Since specificity relates to the ability to discern between specific and nonspecific sites, our initial calculation assumes maximum specificity, so no additional adjustment is necessary.

Key concepts

Regulatory Proteins

Regulatory proteins are essential components in the cellular machinery of both prokaryotic and eukaryotic organisms. These proteins perform a crucial role in modulating the expression of genes, which means they can either turn a gene on or off.
They are not constantly attached to the DNA but interact with it selectively and temporarily. For instance, some bind only when certain signals are present, indicating that a gene product is needed. These interactions are specific, meaning that a regulatory protein recognizes a particular DNA sequence, such as an operator in the case of bacterial cells.

Regulatory proteins can function in different ways:

• As activators, which increase the rate of transcription.
• As repressors, which decrease the rate of transcription.
• They can also work by modifying the chromatin structure, making DNA more or less accessible for transcription.

Repressor Molecules

Repressor molecules are a type of regulatory protein that specifically function to suppress gene expression. They do this by binding to specific DNA sequences known as operators, located near or on the promoters of the genes they regulate.
When the repressor molecule binds to the operator, it blocks the action of RNA polymerase, the enzyme responsible for transcribing DNA into RNA. This effectively "turns off" the gene.

In bacterial cells, repressors are very efficient:

• It requires only a few molecules, about 10 repressor proteins, to achieve significant gene repression for a bacterial genome.
• This is because bacterial genomes are generally smaller and simpler, allowing fewer repressors to effectively control gene expression.

In more complex organisms, like human cells, this process needs adjustments due to larger genome sizes.

Gene Repression

Gene repression is a critical part of gene regulation, ensuring that genes are expressed only when needed. The mechanism of repression involves preventing the transcription machinery from accessing the genetic code, usually through the action of repressor proteins.
Repressors identify their target DNA sequences, often within the promoter region or operator. Upon binding, they physically obstruct the RNA polymerase, stopping transcription.

Key aspects of gene repression include:

• Specificity: The ability to distinguish target sequences from non-targets. This usually involves high specificity, where binding can be between a factor of about \(10^4\) to \(10^6\).
• Efficiency: Minimizing cellular energy costs by producing only the necessary gene products.
• Flexibility: Allows cells to respond to environmental changes rapidly by altering gene expression patterns.

Genome Size Comparison

The size of an organism's genome can significantly impact how gene regulation machinery needs to function. Smaller genomes, like those in bacteria, require fewer regulatory molecules to effectively manage gene expression due to their compact nature.
In contrast, the human genome is vastly larger, over 600 times the size of the bacterial genome. Humans have approximately 3.2 billion base pairs as compared to about 4.6 million in _E. coli_. This size difference requires adaptations in the number of regulatory proteins, such as repressor molecules.

To achieve a comparable level of gene repression seen in _E. coli_ within a human cell:

• The number of repressor molecules needed is scaled according to the genome size. If 10 repressors are sufficient for _E. coli_, humans would need roughly 6960 repressor molecules, considering their genome is 696 times larger.
• Despite this increase in complexity, the principles of regulatory protein function remain consistent across different organisms.

Understanding these differences helps explain why complex organisms like humans require more intricate systems for gene regulation.