Part number 5. Biochemistry on folding. One fundamental problem
In this article we will look at how to fold one helix into RNA. To understand, you need to read all the previous parts From proteins to RNA , Mat. criteria How to reduce the number of turns the chain? How to evaluate the course of folding of single-stranded RNA? , The limitation of optimizing methods in games with the opponent and without . If earlier everything was going smoothly, then here we will face a serious problem. Can someone tell me how to solve it.
We repeat the pattern of the secondary structure of the ribozyme, which we will collapse.
')
Here we pay attention to the spiral L1. In the previous section, we introduced the objective function for the formation of hydrogen bonds between one pair of nucleotides (let's call it F (xy), where xy is a pair of nucleotides). Here we need to form as many as six: between nucleotides 14-22, 13-23, 12-24, 11-25, 10-26, 9-27. When we form them a chain of RNA will coil into a spiral by itself -> such is the geometric arrangement of the atoms that form hydrogen bonds.
It would seem that we can take and use the following objective function:
Fo = F (14-22) + F (13-23) + F (12-24) + F (11-25) + F (10-26) + F (9-27)
But it turns out that the bonds at the end of the spiral, i.e. between nucleotides 10-26, 9-27 will be formed faster. Why? Well, in general, it is clear, the length of the chain is longer for the ends, there are more opportunities to dock, the probability of finding the necessary turns more quickly.
But how does it get in the way? The fact is, as soon as a hydrogen bond is formed, the atoms come so close that it becomes so difficult for them to find a turn so that, on the contrary, it moves away from each other - the probability of a collision is high. And this is not physics - it is geometry in those restrictions about which I wrote earlier.
So, if connections 10-26, 9-27 were almost formed, then under the condition “do not break up these connections”, and our objective function assumes this, it almost nullifies the possibility to form then links at the beginning of the chain, i.e. between nucleotides 14-22, 13-23.
Of course, this is due to calculations, not to nature. In nature, all is well.
But as the chain rotates. In the game FoldIt - there is such an opportunity - the Rebuild tool (see the video, it will be clearer what we are talking about). It fixes the end of the chain, and begins to rotate the nucleotides. Moreover, if we say, turn the nucleotide 18, then all the nucleotides before it 1-17 remain immobile. But after turning 18 nucleotides, everyone else will change their position further, i.e. 19-61. And what they are farther from the 18th, the more they change the location.
So, if we have formed a bond 9-27, and we want to form a bond 14-22, then this is affected by the turns inside the loop 15, 16, 17, 18, 19, 20, 21 ... let's say the rotation of X in nucleotide strongly reduces the objective function F (14-22), but at the same time it breaks the link 9-27, and the objective function F (9-27) increases greatly. It is clear that with the general objective function Fo we will never make such a turn, which means that we will not be able to move towards the intended goal.
In the game FoldIt there is such an opportunity to freeze nucleotides. And then the Rebuild tool rotates the chain of non-frozen nucleotides only (this is observed in the video above). For example, it can freeze nucleotides 9-27, i.e. where we formed a connection, and rotate inside between points 9 - 27, without shifting them. How he does it? Please tell me.
I came out of this problem by changing the objective function Fo. She is visible on the slide
The idea is very simple - to adjust the compression ratio which pairs of hydrogen bonds need to form at the beginning, and which later. With a coefficient = 1, this function simply turns into a sum as in Fo.
This greatly improves the folding of the helix. But there can still be looping, especially at short distances. Then you have to change the compression ratio, somehow break ties and repeat the process. This is already done manually, and it is impossible to automate.
upd. An important addition is to be found below in the comments with 3 pictures of the folding ribozyme.
We repeat the pattern of the secondary structure of the ribozyme, which we will collapse.
')
Here we pay attention to the spiral L1. In the previous section, we introduced the objective function for the formation of hydrogen bonds between one pair of nucleotides (let's call it F (xy), where xy is a pair of nucleotides). Here we need to form as many as six: between nucleotides 14-22, 13-23, 12-24, 11-25, 10-26, 9-27. When we form them a chain of RNA will coil into a spiral by itself -> such is the geometric arrangement of the atoms that form hydrogen bonds.
It would seem that we can take and use the following objective function:
Fo = F (14-22) + F (13-23) + F (12-24) + F (11-25) + F (10-26) + F (9-27)
But it turns out that the bonds at the end of the spiral, i.e. between nucleotides 10-26, 9-27 will be formed faster. Why? Well, in general, it is clear, the length of the chain is longer for the ends, there are more opportunities to dock, the probability of finding the necessary turns more quickly.
But how does it get in the way? The fact is, as soon as a hydrogen bond is formed, the atoms come so close that it becomes so difficult for them to find a turn so that, on the contrary, it moves away from each other - the probability of a collision is high. And this is not physics - it is geometry in those restrictions about which I wrote earlier.
So, if connections 10-26, 9-27 were almost formed, then under the condition “do not break up these connections”, and our objective function assumes this, it almost nullifies the possibility to form then links at the beginning of the chain, i.e. between nucleotides 14-22, 13-23.
Of course, this is due to calculations, not to nature. In nature, all is well.
But as the chain rotates. In the game FoldIt - there is such an opportunity - the Rebuild tool (see the video, it will be clearer what we are talking about). It fixes the end of the chain, and begins to rotate the nucleotides. Moreover, if we say, turn the nucleotide 18, then all the nucleotides before it 1-17 remain immobile. But after turning 18 nucleotides, everyone else will change their position further, i.e. 19-61. And what they are farther from the 18th, the more they change the location.
So, if we have formed a bond 9-27, and we want to form a bond 14-22, then this is affected by the turns inside the loop 15, 16, 17, 18, 19, 20, 21 ... let's say the rotation of X in nucleotide strongly reduces the objective function F (14-22), but at the same time it breaks the link 9-27, and the objective function F (9-27) increases greatly. It is clear that with the general objective function Fo we will never make such a turn, which means that we will not be able to move towards the intended goal.
In the game FoldIt there is such an opportunity to freeze nucleotides. And then the Rebuild tool rotates the chain of non-frozen nucleotides only (this is observed in the video above). For example, it can freeze nucleotides 9-27, i.e. where we formed a connection, and rotate inside between points 9 - 27, without shifting them. How he does it? Please tell me.
I came out of this problem by changing the objective function Fo. She is visible on the slide
The idea is very simple - to adjust the compression ratio which pairs of hydrogen bonds need to form at the beginning, and which later. With a coefficient = 1, this function simply turns into a sum as in Fo.
This greatly improves the folding of the helix. But there can still be looping, especially at short distances. Then you have to change the compression ratio, somehow break ties and repeat the process. This is already done manually, and it is impossible to automate.
upd. An important addition is to be found below in the comments with 3 pictures of the folding ribozyme.
Source: https://habr.com/ru/post/140641/
All Articles