Shapeshifting proteins.

November 6, 2010:

Imagine a blob of plasticine of some colour. Mould it into whatever shape you like and it still is a blob of plasticine of the same colour, just a different shape. Put this plasticine on a plate and play with it. With a leap of imagination, consider this plasticine blob as a protein! Some proteins can be very flexible, and they are a literal chain of chemicals folded into a blob, thus the analogy with a plasticine blob.

Some of the proteins I am playing with these days are distributed in the kinds of shapes they can take as shown in the figure below. Proteins are very small, so instead of the naked eye observing the shape, as can indeed be done with a plasticine blob, some tricks become necessary. One of these tricks is understanding the shapes by shining X rays in a certain way on these tiny blobs. When X rays pass through them (let’s imagine the plasticine blob to be translucent for this purpose), they scatter, and we let them scatter on a plate, and then observe the scattered light. The nature of this scattering of light (more intense at some parts on the plate and less at others), tells us something about the shape of the tiny blob.

In the figure below are shown such observations. The shapes can be distinguished more in the middle region of the figure, which can be considered as the area on the plate where the X rays scatter at a certain angle, as denoted in the figure. This angle at the left extreme is zero. This left extreme in the graph is associated with the scattered light being observed at the centre of the plate – imagine a ray of light passing through the blob of  plasticine, going straight through and hitting a place on the other side of the blob at the centre of a plate. As we go right on the graph along the scattering angle axis, it simply suggests the observation being made further away from the centre of the plate.

Shape distribution detail.

These are shape shifting proteins. The same protein can take many different shapes, which in this case is 1000. For the left extreme, the figure shows a ribbon like thing that connects the 1000 shapes. This is just to show how the observed light varies with the protein when observed at that angle on the plate. Not a lot I would say, as compared to ribbons as we go right. As an analogy, we can see this as how jittered the ribbon would look if placed on top of 1000 plasticine blobs on, say, the left extreme side of these blobs, when the blobs are put one next to the other in a straight line. Since the blobs are different, they may have weird protrusions and intrusions and what not that an imaginative mind can mould them into. Apparently, the left most side has little imagination going for it. However, there is a lot of imagination going on as we go right and place another ribbon on top of all the blobs (see how ruffled up it is!). These ribbons continue to be ruffled up until, at some point along the blobs, the imagination runs out again!

In the next few weeks, I am not going to be more imaginative with moulding the blobs, but will surely do something with them.

November 7, 2010:

Just to go a little deeper into the manner in which the blobs vary when X rays pass through them and the intensities observed at various distance from the centre of the plate, we get the following figure:

Distribution at various scattering angles.

The right most bell shaped curve corresponds to the distribution of light at the centre of the plate (0.0 scattering angle) as it passes through all the 1000 blobs. The bars that the curve tries to approximately cover or fit, correspond to the number of blobs resulting in an intensity of the passed light to be in the region specified by the width of each bar. The bars in the middle are higher than the bars on the ends of the bell shape, suggesting that more blobs let X rays pass through and hit the plate with intensities within the regions specified by the width of the bars (an idea of this region can be had by looking at the bottom axis). Similarly, other bell shaped curves correspond to the distribution of light passing through the 1000 blobs at various distances from the centre of the plate (left most curve – 0.09 scattering angle – being the farthest).

The bells corresponding to the scattering angles 0.02 and 0.03 are much wider than the others. These correspond to the ribbons in the middle of the earlier figure for these scattering angles. The ribbons are more ruffled up accordingly.

November 22, 2010:

Of all the shapes above, let us take a subset of shapes together, assuming it to be a subset of shapes our protein can be in, and that it cannot be in any other shape outside of this subset. This means our actual protein may not actually be able to take up all the shapes described above, but instead shift into only the shapes within the subset. In reality, this is what a shapeshifting protein does. It can only shift into certain shapes out of the many shapes possible. This is the ensemble of shapes that characterise a shapeshifting protein. But there is yet another game that this shapeshifting protein plays. It does not tell us which exactly which shapes it can shift into. How deceptive eih? Well, it does what it does in accordance with nature. But, it is important for medicine research to understand what shapes it can take it seems. We thus need to discover these shapes. How?

The following figure depicts an ensemble of shapes with a few more details which I will talk about soon. For now, the size of the ensemble is N. K is the number of scattering angles at which the measurement of the scattered light was carried out. Each bar in the figure is just a pictorial representation of these K measurements for each shape in the ensemble. The horizontal bar is a pictorial representation of the fact that we need to do something with the values that it hides behind it i.e. it shows the values of all the shapes in the ensemble for one of the K scattering angle measurements. We are eventually going to take an average of these values and do something with this average.

Ensemble of shapes.

November 23, 2010:

What is it that we want to do with shapeshifting proteins?

As mentioned above, we want to discover the ensemble of shapes a shapeshifting protein can mould itself into.

Today I have had the first encouraging experiment with this identification process, or so it seems right now.

Following figures show what I want, and what I achieve. If the red bars in both the figures were to match perfectly, that would mean the discovery of the shapes to be perfect! Of course, there is work to be done as this is not the case. But, the red bars in the two figures are not that far apart, hence it is all encouraging.

Target to achieve.

Discovered ensemble of shapes.