Transcription Network Basics: Part Two
Activators, repressors, and how to model gene expression
In Part One, we described what transcription factors are and introduced the topic of transcription networks. In short, transcription factors are special proteins that increase or decrease the rate of gene expression, and transcription networks illustrate and explain the complex interactions between transcription factors and genes.
In this segment, we'll look a little deeper at how transcription factors affect gene expression; namely, how they can increase or decrease the transcription rate of a gene. We'll also introduce simple network diagrams to illustrate transcription factor-gene relationships, and finally, look at the mathematical relationships between transcription factors and their corresponding proteins.
In the previous section, we built our way up to the following diagram:
A signal transforms the transcription factor into its active state , which binds to its binding site enabling RNA polymerase to begin transcribing DNA into mRNA, which is translated into the protein .
This diagram describes one type of transcription factor, the activator, which, when bound to DNA, increases the transcription rate of a gene. There's another type, the repressor, that decreases the transcription rate. For repressors, gene expression is on by default; the binding of a repressor turns it off. These simple diagrams illustrate what on and off look like:
We can represent this activating or repressing relationship in network diagrams as well. Activators are denoted by a regular arrow, and repressors are denoted by a blunt-headed arrow:
Mathematical Models
So far, we've talked about transcription factors like they're a switch; they turn genes on or off. In reality, they're more like a valve; they increase or decrease the rate of production of a protein. This may include turning it on or off, but ramping up or ramping down production paints a more accurate picture. The arrows, in effect, don't only signify the positive or negative relationship, but the strength of that relationship as well.
Before we dive into some math, it's important to understand its context: the inner workings of a cell. Cells are a crowded place, stuffed with molecules large and small: proteins, nucleic acids, amino acids, sugars, ATP, and other small molecules, all surrounded by water. Moving inside a cell involves a lot of bumping into one another constantly, like hastily making your way across a crowded nightclub floor.
It is this bumping, however, that enables the molecular interactions that sustain life. Molecular interactions occur at specific orientations: the atoms or molecules connect best at some specific region, like two adjacent puzzle pieces. The crowded environment means two elements will spend more time next to each other, shuffling and bumping, which increases the likelihood of reactions.
"Crowded" and "likelihood" hint towards two features that we can use mathematically: concentration and probability. The higher the concentration of a molecule in a cell, the more there is of it given some volume, and so the higher the chance of the right kind of molecular interaction.
We can use this when we think of interactions with transcription factors. The number of molecules of protein produced per unit of time is dependant on the concentration of in its active form, .
Mathematically, we can write this as as an input function:
It is an increasing function when is an activator and a decreasing function when is a repressor.
One function that realistically represents protein production is the Hill function. Let's look at activators first. The Hill function for an activator is defined as:
where:
- is the activation coefficient; it defines the concentration of , the active form of , needed to significantly activate expression.
- is the maximal promoter activity: the maximum rate of production of , achieved at very high concentrations of (higher probability of binding)
- is the Hill coefficient, determines the steepness of the curve (typically between 1 and 4)
Let's take a look at what this looks like graphically and what that means:
When the curve looks something like this — a quick ascent, and then a gradual tapering off when the concentration gets very high, trending towards .
The Hill function gets saturated at high levels of , so more leads to less and less additional proteins until it levels off at the maximum.
Repressors are the opposite — the function decreases as we increase the concentration of . So, the Hill function for a repressor is defined as:
Let's take a look at what this looks like as well:
When = 1, the Hill function for a repressor gradually reduces as the concentration of increases, starting at the maximal expression, , and going to zero — the opposite of the activator Hill function.
Just like with the activator, however, half maximal expression is found at .
The Real World
The values for and in real-world biology depend on the organism, and don't remain constant either. Evolution can tinker with these numbers through mutations in DNA. For example, a mutation in the transcription factor binding site can strengthen the bonds between the transcription factor and the site, and therefore increase the likelihood of bonding and lower the values of (less concentration is needed for significant gene expression). Shifting around the promoter region within DNA can also change the value of , and mutations in the RNA polymerase binding site can change the value of .
Scientists can also harness this phenomenon to engineer precise biological changes. One remarkable aspect of genes is their modularity; a gene from one organism can be expressed in another. The gene encoding green fluorescent protein (GFP), originally isolated from jellyfish, is a prime example. When introduced into bacteria, the GFP gene is expressed, causing the bacteria to produce the proteins, glowing with small specks of fluoroscent green. This technique has become a staple in biological research for visualizing and quantifying gene expression.
GFP's versatility extends beyond simple expression studies. By pairing the GFP gene with specific regulatory elements, researchers can investigate complex gene regulation mechanisms. For instance, when the GFP gene is placed under the control of a sugar-responsive promoter, the bacteria only fluoresce in the presence of the specific sugar. This elegant system allows scientists to directly observe and measure the activity of regulatory elements in real-time, providing valuable insights into gene regulation dynamics.
In the next part, we'll begin taking a closer look at these dynamics, including how to analyze genes that are regulated by multiple transcription factors, and how to model gene expression as a function of time.
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