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I used matrix math as a hand wavey example of how one might purely numerically describe the angles in a structure. What don't we understand? We know the forces

by alar44 5y ago

I used matrix math as a hand wavey example of how one might purely numerically describe the angles in a structure. What don't we understand? We know the forces of all the atoms that act on each other, what is the mystery at this point other than calculating it is hard?

dekhn 5y ago
"We know the forces of all the atoms that act on each other, what is the mystery at this point other than calculating it is hard?" might be true, but it's computationally intractable and even if you did find a way around it you'd just learn that your force field was inaccurate, or that proteins don't actually fold to their energy minimum. Not just hard, but NP-hard. In fact, the "protein folding problem is NP hard" is misleading; in fact, the "static protein structure problem" is NP hard, and protein folding is "harder" than that (it's a superproblem of static structure prediction). The way to describe angles for a protein is this: you use degrees or radians to describe the torsion angles of the backbone (2 torsions per amino acid, 360 possible positions per torsion, times the number of backbone atoms in the protein). Treat side chains with rotamers, that's already a solved problem. However, you can't compute self-collisions in angle space you need to embed the protein structure in cartesian coordinates, which is how they are normally represented (as a graph representing the bond topology, and an N*3 array of positions).
- alar44 5y ago
  Right, my point is that it's as solved as it can really be as far as human understanding is concerned. There are too many variables at play to have any sort of elegant solution like Ohm's law or calculating an orbit. The best we can do is find different/more efficient/novel methods to calculate it. Am I wrong?
  - dekhn 5y ago
    The problem is ill-posed, not that we lack a solution.
    - alar44 5y ago
      Can you elaborate on why it's ill-posed?
      - majewsky 5y ago
        When you say: > it's as solved as it can really be as far as human understanding is concerned You handwave away several interesting parts of the problem without providing real justification for why that would be necessary or acceptable. It's like saying "politicians are made up of atoms, and since we know how atoms interact, our understanding of politics is reasonably complete".
      - dekhn 5y ago
        proteins don't fold to their energy minimum, they typically "collapse" to an intermediate state and then sample many different states (kinetically), rather than adopting the absolute thermodynamic minimum. In many proteins, the structure snapshot doesn't even correspond to a functionally active protein. The "protein folding problem is NP-hard is an entirely inaccurate view of the biophysics of folding", and if solved, would not address any useful question about folding. What DeepMind solved was a far simpler problem: reproduce the structures that get produced by some experimental method. That's a well posed problem but ultimately a less interesting one, even if it's immediately "useful".

by alar44 5y ago

dekhn 5y ago

"We know the forces of all the atoms that act on each other, what is the mystery at this point other than calculating it is hard?" might be true, but it's computationally intractable and even if you did find a way around it you'd just learn that your force field was inaccurate, or that proteins don't actually fold to their energy minimum. Not just hard, but NP-hard. In fact, the "protein folding problem is NP hard" is misleading; in fact, the "static protein structure problem" is NP hard, and protein folding is "harder" than that (it's a superproblem of static structure prediction). The way to describe angles for a protein is this: you use degrees or radians to describe the torsion angles of the backbone (2 torsions per amino acid, 360 possible positions per torsion, times the number of backbone atoms in the protein). Treat side chains with rotamers, that's already a solved problem. However, you can't compute self-collisions in angle space you need to embed the protein structure in cartesian coordinates, which is how they are normally represented (as a graph representing the bond topology, and an N*3 array of positions).

alar44 5y ago
Right, my point is that it's as solved as it can really be as far as human understanding is concerned. There are too many variables at play to have any sort of elegant solution like Ohm's law or calculating an orbit. The best we can do is find different/more efficient/novel methods to calculate it. Am I wrong?
- dekhn 5y ago
  The problem is ill-posed, not that we lack a solution.
  - alar44 5y ago
    Can you elaborate on why it's ill-posed?
    - majewsky 5y ago
      When you say: > it's as solved as it can really be as far as human understanding is concerned You handwave away several interesting parts of the problem without providing real justification for why that would be necessary or acceptable. It's like saying "politicians are made up of atoms, and since we know how atoms interact, our understanding of politics is reasonably complete".
    - dekhn 5y ago
      proteins don't fold to their energy minimum, they typically "collapse" to an intermediate state and then sample many different states (kinetically), rather than adopting the absolute thermodynamic minimum. In many proteins, the structure snapshot doesn't even correspond to a functionally active protein. The "protein folding problem is NP-hard is an entirely inaccurate view of the biophysics of folding", and if solved, would not address any useful question about folding. What DeepMind solved was a far simpler problem: reproduce the structures that get produced by some experimental method. That's a well posed problem but ultimately a less interesting one, even if it's immediately "useful".