Binding affinity and equilibrium dissociation constant Kd
Lower Ka values = Greater affinity Lower Kd values = Greater affinity as essentially opposites, I would have expected opposing relationships. The smaller the KD value, the greater the binding affinity of the ligand for its target . In addition, binding affinity between a ligand and its target molecule may be. Receptors determine the quantitative relationship between dose or concentration of the A drug with a low Kd value has a high Ka value and therefore high.
A liquid containing the ligand is flowed over the binding surface.
KD value: a quantitative measurement of antibody affinity
The detection system consists of a light beam that passes through a prism on top of the glass layer. The light is totally reflected but another component of the wave called an evanescent wave, passes into the gold layer, where it can excite the Au electrons. If the correct wavelength and angle is chosen, a resonant wave of excited electrons plasmon resonance is produced at the gold surface, decreasing the total intensity of the reflected wave.
The angle of the SPR is sensitive to the layers attached to the gold. Binding and dissociation of ligand is sufficient to change the SPR angle, as seen in the figure below. Science,pg animation: Yet some enzymes require Cu. Free copper ions must be present in the cell to allow binding to appropriate sites in proteins. How are these competing concerns regulated in the cell?
The total Cu concentration in E. Cells have evolved many mechanisms to control and deliver Cu ions. Copper ions can be delivered to target proteins by copper chaperones analogs of the chaperone proteins which guide protein folding.
One particular gene that is up-regulated is copA. In the assay, purified CueR was added to a gene construct containing the promoter a section of DNA immediately upstream of a gene start site where RNA polymerase binds for copA. You solved problems such as this involving linked equilibrium if you have taken analytical chemistry.
Now assume that the volume of the contents of an E. Coli cell is 1. A recent review by Waldron and Robinson illustrates how. The cell has many mechanisms of restricting specific binding sites so metals are able to get to the right proteins. In addition, the natural order of stability for transition metals complexes must be considered in understanding metal affinities.
The trend parallels the size of the cation going from largest to smallest: For example, cyanobacterium has a high demand for copper and manganese.
Manganese is allowed to bind first and then the protein is folded and manganese becomes trapped inside the protein. Metal transporters help regulate how many ions of each metal are in the cell. Metal sensors are under the control of these metal transporters, regulating gene expression. By restricting the concentrations of the competing metals, weaker metal-binding sites remain available Metal sensors can also help to regulate what protein some metals use based on what is available.
Certain enzymes bind specific metals that cause preferential conformational changes. Hence, if a metal comes along that binds more tightly but is not preferred by the enzyme, it will not trigger the enzyme because it binds in a different manner A7. Molecular Basis of High Affinity Interactions What differentiates high and low affinity binding at the molecular level?
Do high affinity interactions have lots of intramolecular H-bonds, salt bridges, van der Waals interactions, or are hydrophobic interactions most important? Recently, the crystal structures of a variety of antibody-protein complexes were determined in order to study the basis of affinity maturation of antibody molecules. It is well know that antibodies elicited on exposure to a foreign molecule antigen are initially of lower affinity than antibodies released later in the immune response.
Clones of antibody-producing cells with higher affinity are selected through binding and clonal expansion of these cells. Investigators studied the crystal structure of 4 different antibodies which bound to the same site epitope on the protein antigen lysozyme. Increased affinity was correlated with increased buried apolar surface area and not with increased numbers of H bonds or salt bridges.
An extremely, extremely high value for Ka. What does that say about Kb for the conjugate base? The conjugate base here is the chloride anion.
If Ka is very large then Kb must be very small for this to be equal to Kw. Kb is extremely small here, so a very small value for Kb. This mathematically describes what we talked about earlier the stronger the acid the weaker the conjugate base.
HCl is a very strong acid, so it has a very, very high value for Ka. And the conjugate base is the chloride anion, and it must have a very, very, very low value for Kb which means it's an extremely weak base. This is mathematically how to think about that relationship. Next let's look at a problem where we're calculating one of those values. Methylamine is a weak base, and the Kb for methylamine is 3. We're talking about a conjugate acid-base pair.
There's one proton difference between those.
Therefore we can use our equation, Ka times Kb is equal to Kw. We can plug in Kb here. Now we have Ka times 3. Let's do the math and solve for Ka. We need to divide that by 3.
Ka is equal to 2. That's our answer, 2.
Let's go a little further. Let's take our equation here, Ka times Kb is equal to Kw. Let's take the log of both sides. That would be the log of Ka times Kb is equal to the log of Kw. If we take the negative of everything, let's go ahead and do that, the negative of everything, negative log of Ka.
I'll put that in parenthesis, plus the negative log of Kb is equal to the negative log of Kw. The negative log of Ka, we know that this is equal to the pKa. The negative log of Ka was our definition for our pKa, and the negative log of Kb was our definition for pKb.
Dissociation constant - Wikipedia
That would give you The negative log of 1. Now we have something else that we can work with, so let me go ahead and box this right here. Let's take the Ka value that we just found.
Let's find the pKa. The pKa would be equal to the negative log of 2. Let's do that on our calculator here. Let's get some room. The negative log of 2. We have to round that. These are our two significant figures because we have two significant figures here. Let's go back up to our problem here, so that's the pKa for the methylammonium ion. Let's say you're given the pKa for the methylammonium ion and asked for the pKb for methylamine.
What is the pKb for methylamine? All we have to do is plug in to our equation. Let's go ahead and write that in here. When we solve for the pKb that would give us 3. So the pKb is equal to 3. We could double-check that. Let's go back up here and we could double-check that, because if we took the negative log of this number that's what we should get. Let's take the negative log of 3.
That's what we just calculated down here. The pKb is equal to 3. That's the relationship between Ka and Kb, and you can also talk about the relationship between pKa and pKb.