I'm also interested in a different direction for modeling proteins: ab-initio. I am curious if we can get a good-enough simulation of charge density around atoms to simulation folding using electric force models. It seems that chemists are using very computationally-intense models (HF, Kohn-Sham DFT etc) where the wave function (and therefore charge density) is modeled as a product etc. This does not scale well as electron count goes up. And, Valence Bond and Molecular Orbital theories of bonding both seem like not great approximations.
I am suspicious we can come up with reasonable models of charge density for atoms and simple molecules without this complexity, by solving the Schrodinger equation; the relation between psi'', psi, V, and E. And then perhaps interpolating various solved solutions, incorporating ambient water molecules etc. I can, unfortunately, find very little about this approach, but am making progress on a program that will probably go no where, but I still feel is worth building. Incorporating spin is proving tricky. It is possible we need to model using spinors, but I am suspicious there may be shortcuts where we accept Fermi-Dirac statistics as an axiom, without using exchange terms.
Of course, modelling the electron-electron interaction is tough because you need to integrate over 3D space, and there is a feedback loop between psi, charge, V, which then feeds back into psi for the other electrons, and vice versa!
This is fringe, and probably intractable, but... seems worth trying. One of the key challenges is the big challenge with modelling in general: We have differential equations that can verify a solution, but not come up with the solution... This, at least, gives a validation for work on this topic.
Even more fringe, but relevant: I wonder if the rules of quantum mechanics are intrinsically tied to nature's fondness of differential equations, and are key to how nature "solves" them.
It's still unclear to me that using QM to simulate protein folding or enzymatic activity is a worthwhile endeavor. Even highly approximate QM methods don't seem significantly better than classical force fields for recapitulating folding dynamics, and the actual amount of computational effort required would be astronomical. I would recommend against it simply because we know of better, more economical methods, to get at solutions we need.
I don't think DFTs will get better anytime soon. But here's something wild: Maybe it doesn't matter.
Run a DFT simulation of a protein with known structure melting. Time-reverse it. Train some sort of 3d convnet on the deltas at every point in the (wrong) melting curve.
Who cares if the DFT is wrong! The ml model will learn the rules of this fictional universe that uses the wrong rules to get the right thing.
I'm also interested in a different direction for modeling proteins: ab-initio. I am curious if we can get a good-enough simulation of charge density around atoms to simulation folding using electric force models. It seems that chemists are using very computationally-intense models (HF, Kohn-Sham DFT etc) where the wave function (and therefore charge density) is modeled as a product etc. This does not scale well as electron count goes up. And, Valence Bond and Molecular Orbital theories of bonding both seem like not great approximations.
I am suspicious we can come up with reasonable models of charge density for atoms and simple molecules without this complexity, by solving the Schrodinger equation; the relation between psi'', psi, V, and E. And then perhaps interpolating various solved solutions, incorporating ambient water molecules etc. I can, unfortunately, find very little about this approach, but am making progress on a program that will probably go no where, but I still feel is worth building. Incorporating spin is proving tricky. It is possible we need to model using spinors, but I am suspicious there may be shortcuts where we accept Fermi-Dirac statistics as an axiom, without using exchange terms.
Of course, modelling the electron-electron interaction is tough because you need to integrate over 3D space, and there is a feedback loop between psi, charge, V, which then feeds back into psi for the other electrons, and vice versa!
This is fringe, and probably intractable, but... seems worth trying. One of the key challenges is the big challenge with modelling in general: We have differential equations that can verify a solution, but not come up with the solution... This, at least, gives a validation for work on this topic.
Even more fringe, but relevant: I wonder if the rules of quantum mechanics are intrinsically tied to nature's fondness of differential equations, and are key to how nature "solves" them.