Can Protein Folding be Computed?

Protein folding is a spontaneous process where a given unique string of amino acids folds itself in a solvent (water) into a macromolecule of unique 3d geometry, guided by 

• formation of hydrogen bonds
• hydrophobic interactions
• van der Waals forces. 

Modern physics in the form of quantum mechanics comes with the message that protein folding as a form of molecular dynamics can be described by a Schrödinger Equation SE modeling a collection of atomic kernels held together by a collection of electrons. 

Computing solutions over time of SE starting with a given string would then produce a simulation of the folding process allowing the folded protein to be predicted from given string, and so also reversely a string to be predicted from given folded geometry. This would be immensely helpful for understanding of biological processes and drug design. 

But there is big problem with such a grand scheme: Computational solution of SE is impossible because the work grows exponentially with the number of electrons and so is beyond the capacity of thinkable computers already for 10 electrons, while the true number may be 100.000.  The reason is that SE involves $3N$ spatial dimensions for $N$ electrons. 

Modern physics/chemistry thus has nothing to deliver as concerns computational protein folding, which is illustrated by the fact that the 2014 Nobel Prize in Chemistry was awarded to Artificial Intelligence AI for protein folding trained on large experimental data sets without use of SE theory. 

Instead of letting AI take over completely, let us give human intelligence another chance and ask if maybe there is some other mathematical model than SE that can describe the folding?

And yes, there is a candidate in the form of a different atomic model named Real Quantum Mechanics RealQM in the spirit of Schrödinger as system of non-overlapping electronic charge densities in 3d space geared Coulombic interaction, for which the computational work grows linearly with the number of electrons. 

So there we are: It may be that protein folding is computable by RealQM. The computational process proceeds in time where for a given configuration of atom kernels and electronic charge distributions in 3d, a new configuration is computed from Coulombic interactions through electric potentials, with work scaling with  number of electrons. 

RealQM connects to ad hoc simplified versions SE based on Electron Orbitals or Density Functional Theory, but RealQM is fundamentally different since it is based on a new single principle of non-overlapping charge densities in a parameter-free model. 

You find laptop computations with RealQM for atoms and molecules on RealQM and on this blog under tags RealQM and Real Quantum Chemistry including computer codes essentially consisting of three lines for update of kernel positions, charge densities and potentials.  

Who will do the first RealQM simulation of protein folding?

Recall that the crisis of modern physics is the result of not delivering anything new, in particular nothing for protein folding. We have identified the non-computability of SE as the big trouble. But this is just one aspect of the basic troubling aspect of SE namely that it is a non-physical model for which no convincing physical interpretation has been found despite intense efforts by thousands of highly intelligent physicists ever since the formulation of SE was made 100 years ago. 

The attractive aspect of SE is that it is quick to formulate, allowing physicists to speak with loud voice about wave functions denoted by $\Psi$ as solutions to SE, while covering up that they are uncomputable and lack physical meaning. 

The result is that today the foundation of quantum mechanics is no longer a topic of study at physics departments, and is only pursued by some isolated enthusiast philosophers at philosophy departments. This is clearly not an optimal situation. 

There is no reason for atomic physics models to lack physical meaning nor computability.