Computational biochemistry is what I'm currently pursuing, but I'm pretty new to the field so take everything I say with a grain of salt: Biochemistry is a really really
really tricky problem, for a couple reasons:
1. Biology has a very nasty habit of not cleanly abstracting. It's not like we can treat every protein as a "diffuse mass" without losing a ton of important interactions. This is unlike something like CFD where you can treat a mass of water molecules with certain constants. Think of something like cancer: a small mutation to a DNA strand can cascade into a tumor. You have to deal with the mutation happening at an atomic level while scaling to a whole organism (yes I know there's models that can approximate this, but they can't capture all the interactions).
2. This brings us to modelling at the atomic level. To model a system of atoms with the Schrödinger equation, it naively scales O(6^n) per particle. Note that means every nucleus and electron, so if you have say 10 carbon atoms and 22 hydrogen you're already at 10^127 operations. We can cut corners a bit and end up with something like CCSD which scales O(n^7), or cut more corners and scale O(n^3) for DFT. DFT is pretty much the last method where bond forming and breaking is modelled, so after more corner cutting you lose losing reactions, which are important for understanding why something is happening. Most protein folding simulations (moreso prior to alphafold) run a very crude approximation that models atoms as balls on springs (things like AMBER and CHARMM), which obviously can't handle reactions.
3. If this wasn't bad enough, you also can only move through time at about 1 femtosecond (10^-15), so it takes a ton of simulation steps to get even a nanosecond in. Forget millisecond or second lengths where things start to happen.
So, while the math of the physics exists, computationally it's practically intractible. There's some exciting work with something called Machine Learning Interatomic Potentials (MLIP) which approximate DFT using a neural network which are about 1000x faster than DFT, and iirc scale much more linearly (look at things like MACE and orbmol if you're curious). So we're making progress, but we've gone from so ridiculously impossible to pretty much impossible for large systems.
I have a couple ideas about developing custom microchips to make this faster, which is why I'm pursuing this, but there's still a massive way to go!
1. Biology has a very nasty habit of not cleanly abstracting. It's not like we can treat every protein as a "diffuse mass" without losing a ton of important interactions. This is unlike something like CFD where you can treat a mass of water molecules with certain constants. Think of something like cancer: a small mutation to a DNA strand can cascade into a tumor. You have to deal with the mutation happening at an atomic level while scaling to a whole organism (yes I know there's models that can approximate this, but they can't capture all the interactions).
2. This brings us to modelling at the atomic level. To model a system of atoms with the Schrödinger equation, it naively scales O(6^n) per particle. Note that means every nucleus and electron, so if you have say 10 carbon atoms and 22 hydrogen you're already at 10^127 operations. We can cut corners a bit and end up with something like CCSD which scales O(n^7), or cut more corners and scale O(n^3) for DFT. DFT is pretty much the last method where bond forming and breaking is modelled, so after more corner cutting you lose losing reactions, which are important for understanding why something is happening. Most protein folding simulations (moreso prior to alphafold) run a very crude approximation that models atoms as balls on springs (things like AMBER and CHARMM), which obviously can't handle reactions.
3. If this wasn't bad enough, you also can only move through time at about 1 femtosecond (10^-15), so it takes a ton of simulation steps to get even a nanosecond in. Forget millisecond or second lengths where things start to happen.
So, while the math of the physics exists, computationally it's practically intractible. There's some exciting work with something called Machine Learning Interatomic Potentials (MLIP) which approximate DFT using a neural network which are about 1000x faster than DFT, and iirc scale much more linearly (look at things like MACE and orbmol if you're curious). So we're making progress, but we've gone from so ridiculously impossible to pretty much impossible for large systems.
I have a couple ideas about developing custom microchips to make this faster, which is why I'm pursuing this, but there's still a massive way to go!