5.2.3 Receptors\Ligands

1. Purpose

The concept of the receptor-ligand interaction is one of the most basic in all of biology. It is a key element to the functioning of all biological systems. It allows neighboring and distant cells to communicate with each other. One cell may have a receptor in its membrane and when it binds to a matching ligand on a neighboring cell the receptor performs some action. Typically this action is to take an existing protein and modify it in some way to either activate or deactivate it. A good example of this is a tyrosine kinase receptor. When this receptor binds to a ligand it becomes activated and can phosphorylate other proteins and activate them. Those proteins can then go on to perform a number of different functions. So cell A that expressed the ligands on its surface was able to communicate with cell B that had the receptors and cause cell B to alter its behavior. The activated proteins inside B could go on to alter gene expression or modify other proteins. This communication is the basic purpose behind the receptor/ligand interactions.

Receptor Properties
Protein Type: All proteins have this property. It is used to determine the type of protein to load.
Binding ID: All proteins have this property. For GC's it matches up with control sites on genes to determine which genes that it can flip.
Degrade Rate: All proteins have this property. This determines the rate at which this protein is degraded in the cell.
Ke: This parameter is part of the Michealson-Menten equation of enzyme kinetics. It is a constant that relates the concentration of the receptor to Vmax. A higher Ke is equivalent to having many more receptors.
Km: This parameter is part of the Michealson-Menten equation of enzyme kinetics. It is a constant that specifies how much affinity the ligand has for the receptor. A lower value of Km means the ligand releases faster, and thus the reaction is faster. A higher Km means a slower reaction.
Graph Type: This determines which type of graph to use for the expression function of this protein. The expression function determines how much of the expressed protein will be produced.
A: This is one parameter of the expression function and its affect depends on the graph type.
B: This is one parameter of the expression function and its affect depends on the graph type.
C: This is one parameter of the expression function and its affect depends on the graph type.
D: This is one parameter of the expression function and its affect depends on the graph type.
Expressed Protein: This is a complete definition of another protein that will be expressed when this receptor is activated.
Table 1.These are the different properties of a receptor protein that are defined in the digital genes.

Ligand Properties
Protein Type: All proteins have this property. It is used to determine the type of protein to load.
Binding ID: All proteins have this property. For GC's it matches up with control sites on genes to determine which genes that it can flip.
Degrade Rate: All proteins have this property. This determines the rate at which this protein is degraded in the cell.
Diffusion Rate: This property is only found on diffusible ligands. It determines the rate at which this protein diffuses out of the cell.
Table 2.These are the different properties of a ligand protein that are defined in the digital genes.

2. Receptor/Ligand Classes

This emulator breaks receptors and ligands down into two basic classes: membrane bound and cell bound/diffusible. The first class is like that described above. A given cell has receptors in its membrane and neighboring cells have ligands in their membranes. Membrane receptors can only be activated membrane ligands on immediately adjacent neighbors. Membrane ligands within the same cell that has the receptors do not activate each other. Also, there is no concept of positional location between the cells. Each of the neighbors can see exactly the same quantity of membrane receptors/ligands. The other class is cell bound receptors and diffusible ligands. In this class the receptors are inside the cell and can not leave and they will only bind to diffusible ligands. The diffusible ligands on the other hand can diffuse outside of the cell. This allows one cell to communicate over a large range of cells. This is especially useful in setting up concentration gradients.

2. Diffusion

In table 2 you can see that the properties of the ligand are very basic. The diffusible ligand has one extra parameter from the basic protein, and that is the diffusion rate. This works in a very similar manner to the degrade rate of each protein. At each time slice the diffusion rate specifies that a certain percentage of the ligands in a cell will attempt to diffuse out. The diffusion algorithm was made to be very simple while attempting to retain the basics of how real molecules diffuse. It does not use differential equations or mathematical models, just a few simple rules that can be done very quickly at each time step. The point was not to come up with something that duplicated exactly what happens in the real world, just to get something that behaves similarly in as fast a manner as possible. At each time slice the cell determines how much of a given ligand can be diffused out of the cell. It then checks the immediately neighboring cells and tries to determine how much of that total should go into each neighbor. If the concentration in a neighbor is higher than the concentration in the current cell then nothing will diffuse into it from this cell because that would be going up the concentration gradient. Each neighboring cell will get a percentage of the diffusible quantity that is proportional to its current quantity. So if you have neighbor A that has almost none of the ligand and neighbor B that has almost the same quantity as this cell, then the majority of the amount to diffuse will go to A. That is the basics of how diffusion is handled. In some cases you may want a cell bound ligand that mates up with a cell bound receptor. This can be produced by using a diffusible ligand and setting the diffusion rate to be zero so that it can not diffuse outside of the cell.

2. Receptor Expression

Receptors are a bit different from most of the other proteins. The reason is that they actually have a dynamic protein structure embedded within them. In nature receptors typically take proteins or other molecules that are already present in a cell and alter those items in some way so that they behave differently. The receptors in this system are slightly different. They essentially produce proteins. Each receptor has an expressed protein. Whenever a ligand binds to the receptor it causes the receptor to produce more of the expressed protein. This protein can be of any type except another receptor. This is to prevent loops or long chaining where a receptor makes a receptor makes a ... etc. The receptor determines the protein to express exactly like the gene does. It looks first at the protein type and then a protein object of that type loads in the rest of the structure. The receptors were made to work this way in order to increase the processing speed. It slows things down enough trying to find the ligands to bind to the receptor, if you then also had to try and find all of the possible precursor proteins it would be even slower. Also it was felt that this did change the operating of the system enough from that found in nature to cause serious problems. This is an assumption, but so far it seems to be working out okay.

2. Receptor-Ligand Binding

Now that we know that a receptor expresses new protein we are still left with a couple of questions: When does the expression take place and what determines how much is expressed? The when part is easy. Expressed protein is produced whenever there is a quantity of receptors and a quantity of ligands that are of the same class and that have the same binding ID. So whenever there is a membrane receptor in one cell and a membrane ligand in a neighboring cell that match up, or whenever a diffusible ligand and a cell receptor that match up are in the same cell, then it will attempt to express the protein of the receptor. But how much of that protein should be produced? It was simple in transcription. There was 1 gene to N transcription factors, and that quantity was used in the expression function to determine the amount of protein expressed by the gene. But receptors/ligands have a new wrinkle, both receptors and ligands have a quantity. If we were to try and do the exact same thing that was done during transcription using the quantity of ligands it would simply not work correctly. For example, lets suppose that we have a quantity of 1000 ligands and in the first case we have 1 receptor molecule. In the second case we have 1000 ligands and 1000 receptors. Is it fair to say that both cases produce the exact same amount of protein? This amount needs to be based on the quantities of both. Something else that needs to be considered is how well does a ligand bind to a receptor. Perhaps one receptor is really good at binding and releasing the ligands and in one time slice it can do that twice as fast as another receptor can. It should then produce a lot more protein. The questions are related to enzyme kinetics and there is an equation that was discovered that describes this situation. It is called the Michealson-Menten equation of enzyme kinetics, and it can be seen in table 3.

Michealson-Menten Equation of Enzyme Kinetics
Vmax = Ke * [R]

     Vmax * [L]      Ke * [R] * [L]
V = -----------  =   --------------
     Km + [L]          Km + [L]
V: velocity of reaction, or the number of binding occurrences.
Vmax: This is a maximum rate at which the reaction can take place.
[R]: Concentration of receptor.
[L]: Concentration of ligand.
Ke: A constant that relates the concentration of the receptor to Vmax. A higher Ke is equivalent to having many more receptors.
Km: A constant that specifies how much affinity the ligand has for the receptor. A lower value of Km means the ligand releases faster, and thus the reaction is faster. A higher Km means a slower reaction.
Table 3.This table describes the parameters of the Michealson-Menten Equation.

This equation is used to relate the quantity of receptors present, the quantity of ligands present and how well the receptor binds the ligand to determine the value that is then fed into the expression function of the receptor to calculate the quantity of expressed protein. The values Ke and Km are constants that determine the binding affinity of the receptor and they are properties of the receptor defined in its protein structure. However, perhaps I did something wrong with this equation or something because in the form stated it does not behave as excepted. Since the receptor concentration is not found in the denominator this can create an imbalance where the calcuated bound quantity is not really related to the quantity of receptors present. Therefore, I changed the equation that I used slightly to add the quantity of receptors in the denominator as shown below. Sounds a bit complicated, right? Lets go through a simple example.

     Ke * [R] * [L]
V = -----------------
      Km + [L] + [R]

Binding Example Properties
Receptor Properties
Ke: 1.50
Km: 20
Graph Type: Linear
A: 10
B: 100
C: 50
D: 0
Protein Quantities
Receptor Qty: 400
Ligand Qty: 200
Table 4.These are the properties for the binding example.

      Ke * [R] * [L]     1.5 * 400 * 200     120,000
 V = ----------------  = ----------------- = --------- = 200 
      Km + [L] + [R]       20 + 200 + 400      602

Once V is calculated based on the amounts of the receptors and ligands in the cell then the expressed quantity is calculated using the expression function. E = (B/A)*V + C = (100/10)*200 + 50 = 2050. So 2050 units of the expressed protein will be produced in this time slice.

3. Membrane Receptor\Ligand Example

Figure 1. This shows an example membrane receptor in action.

Membrane Receptor\Ligand Results
Video 1. This video demonstrates shows the membrane receptor example.

Figure 1 shows a membrane receptor in cell (2, 2, 0) and a ligand in cell (1, 2, 0). Since these two are neighbors and they have the same binding ID's then they mate up to express another protein in the same cell as the receptor. You can also notice in the graph that as the quantity of receptor and ligand decreases the level of protein expressed also dips. You can also see the production of the expressed protein by looking at the immuno labeling video.

3. Diffusible Receptor\Ligand Examples

Diffusible Example 1
Video 2. This video demonstrates the diffusion of ligands across cells.

Diffusible Example 2
Video 3. This video is another example of the diffusion of ligands.

These first two example videos demonstrate how the ligands can diffuse. In the first one you can see how the degrade rate and diffusion rate work together to limit the spread of the ligand. The ligand will diffuse to a certain point until its degradation rate balances its diffusion rate and it can not spread any further. By altering these values you can alter how far the ligand spreads. The second video demonstrates what happens when the ligand degrades very slowly. It eventually diffuses throughout the entire set of cells.

Diffusible Example 3
Video 4. This video demonstrates the cell receptor, diffusible ligand and gene control working together in a feedback loop to produce a cyclic pattern of gene expression.

Diffusible Example 3 Chromosome
Figure 2. This figure shows the genes involved in producing the third diffusible example.

This example of a diffusible system is much more interesting. When I was working on building for display I was not originally trying to get it to do this. But when I ran it I was surprised at how cool it was and decided to use it instead. This genome uses some simple feedbacks to produce a cyclic pattern of gene expression that looks like the ripples in a pond when a rock is thrown in. The video plays back a little to fast and it is better if you slow it down a bit when watching it. If you look at the chromosome analysis I will explain what is happening. First, gene G_1 is turned on by default and basal produces the cell receptor CR_2 in all cells. All of the other genes are initially off. At this point nothing will happen. However, we inject a special diffusible ligand directly into the center cell. This ligand has a diffusion rate of zero so that it can not effect any cell other than the initial one it is injected into. The ligands and the receptors mate up and produce gene control GC_3. Once this gene control accumulates to a threshold quantity it turns on both genes G_0 and G_2. Gene G_0 begins producing diffusible ligands that mate up with the cell receptor, but these ligands do diffuse out to other cells. Gene G_2 eventually begins producing gene control GC_4. However, the threshold to turn this gene on is much higher than the threshold for gene G_0. This means that G_0 will be pumping out diffusible ligands for a while before G_2 is turned on. So now this center cell is pumping out ligands that are flowing to the neighboring cells and causing the same thing to happen in these neighbor cells. So you can watch in the second pane of the immuno-graph as gene G_0 is switched on. At this point if G_2 was not also on then eventually all cells would have gene G_0 on and would producing DL_1. But as GC_4 builds up in the cell it eventually exceeds the threshold and turns off all of the genes in the system. At this point I thought that it would have a second wave of genes turning off following the first wave of turning on. And this is what happens. However, I did not think about the fact that the neighboring cells were still pumping out diffusible ligands that would re-enter the cells that were turned off. And since the receptors degrade fairly slowly this starts a new cycle of turning the other genes on. Since GC_3 does not turn G_1 back on then eventually the cyclic pattern would fail as all of the receptors degrade away. But until then this system produces a very pretty and surprising pattern. This is good example of how receptors and ligands work and how a simple feedback system can produce surprising results.

4. Receptor/Ligand Overview

Receptors and ligands play a crucial role in this and in all biological systems by allowing cells to communicate with each other. Short range and localized communication is performed by using receptors and ligands embedded into the cell membrane. Long range communication is performed using diffusible ligands that can spread over larger regions. These two systems complement each other and can work together to produce some incredible results. The representation of receptor/ligand interaction used in this system was designed to try and produce the major features found in biological systems, while allowing for very fast processing and simple algorithms.


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