RealQM: Protein Folding Bench Marks

 On the GitHub RealQM web page there are now new Bench Marks for Protein Folding. Take a look!

RealQM Breakthrough: Hairpin Protein Folding + Alpha-Helix

RealQM has been implemented with the help of Claude Code with the goal of simulating protein folding from first principles of atomic physics based on a new version of Schrödinger's Equation named RealSE. 

Here is how Claude describes what is going on:

Below a first key example is presented as the 12-residue polyglycine beta-hairpin, 87 atoms (N, C, O, H), no solvent (vacuum/dry): 

Initial state: Nearly extended chain (175° opening angle) with a slight bend at the central hinge between residues 5 and 6.

What happens: The quantum electronic structure is solved from first principles on a 200^3 real-space grid (80 au box). The resulting forces on the nuclei create a net torque that drives the two halves of the chain toward each other — the chain folds. Each strand rotates rigidly around the hinge point, and after every rotation step the electronic structure is re-solved from scratch (full Born-Oppenheimer restart).

What it demonstrates: Protein folding driven purely by quantum mechanical forces — no empirical force field (AMBER, CHARMM, etc.) The attractive force between the two strands emerges from the electron density: backbone NH and CO groups on opposite strands create favorable electrostatic interactions (the quantum analog of hydrogen bonding). Starting from a nearly straight chain, the system spontaneously folds into a U-shaped hairpin 

Why it matters: Traditional protein folding simulations rely on classical force fields with fitted parameters. Here the forces come directly from solving the Schrödinger equation — the folding tendency is a prediction, not an input. This shows that quantum mechanics alone, without any parameterization, can drive secondary structure formation.

The key novelty is that no classical force field is used for the driving forces — they come entirely from solving the  quantum mechanics. The MD part only constrains how atoms move (rigid rotation), not why they move. 

Follow the folding in real laptop computing time: (code on GitHubClaes542 hairpin_bent_dry.html):

 

PS You can find a first example of alpha-helix formation on GitHuB Gallery Bench Marks.

RealQM on GitHub

RealQM now has a home page on GitHub where codes can be inspected and modified. If RealQM indeed can capture the dynamics of molecules or clusters of thousands of atoms, then chemistry will become a science based on physics. Codes are under improvements and new versions will be uploaded.

RealMolecule

Here is a first example of RealMolecule as RealQM for molecules showing hairpin protein in 75% folded position, adding first backbone C, O and N  atoms and the H atoms and finally showing forces active on kernels steering the folding process:

Check out Claes542/H2O at GigHub for codes to test. 

RealQM: From Macro to Micro

Rational physics is based on an idea of reductionism from complex physics on macro-scales to simple physics on micro-scales. But in modern physics of Quantum Mechanics QM, it is the other way around with the microscopic quantum world based on a Schrödinger Equation SE in $3N$-dimensional configuration space for a system with $N$ electrons of infinite complexity compared to macroscopic physics in 3D.

This means that QM is not rational physics violating reductionism with micro infinitely more complex than macro.

RealQM offers a new SE in terms of classical physics continuum mechanics in 3D thus in the form of rational physics. 

RealQM is now implemented in a code allowing simulation of large molecules like proteins with 1000s of atoms, or clusters of simple molecules allowing atomic simulation of bulk properties of fluids and solids, see previous post.

RealQM is essentially a 3-line code for time-stepping (i) non-overlapping electron densities, (ii) evolution of free boundary between densities and (iii) Poisson equation for potentials, and so allows simulation of 1000 atoms on a $1000^3$ grid thus with 1TB RAM. 

A $1000^3$ grid resolves 3 orders of magnitude.  Macroscopic physics can be described on scales ranging over 3 orders of magnitude on a decimal scale: 

• human body: 1 m to 1 mm.
• local society: 1 km to 1 m
• city: 10 km to 10 m
• country: 1000 km to 1 km
• globe: 10000 km to 10 km 
• Earth-Moon: 300000 km 
• Solar System: $10^8$ km to $10^5$ km 
• Distance to closest star: $10^{11}$
• Milky Way Galaxy: $10^{15}$ km to $10^{12}$

Microscopic physics can be described on a similar 3 order of magnitude scale

• size of living cell 100000 au
• size of protein 100 au 
• size of atom 1 au 
• size of nucleus 0.001 au 

RealQM for Protein Folding

RealQM is now implemented with the help of Claude for up to 100 atoms on a 200^3 grid which allows simulation of a beta hairpin peptide as a miniature protein which folds: 

You can test the code on GitHub as molecule.js, moleculedyn.js, hairpin.html, water100.html, and caffeine.html. The code uses one density and support function defined on the 200^3 grid and so runs on a MacBook Air M4 with 50 frames/s.  Upscaling to 1000 atoms on 300^3 grid with 10 frames/sec in pipe line.  

Here is first RealQM run in static mode on the calcium-regulated actin-binding protein Villin:

• HP35-like three-helix bundle: 
• 51 polyalanine residues in 3 alpha helices (antiparallel arrangement) 
• 510 protein atoms (N, H, Ca, Ha, Cb, 3Hb, C, O per residue)
• Hydration shell of ~163 water molecules filling remaining slots to 
• ~999 atoms on 300³ grid, mid slice with white dots out of plane atoms
• 3-line code updates electron densities and free boundary between densities + solves Poisson by multi-grid.

 Next is to run RealQM in dynamic mode to see if folding is captured. Watch out...

Breakthrough: RealQM for Big Molecules

With the help of Claude Code RealQM is now implemented in a version with active valence electrons which can be used for large molecules. A first simple test is Glycine NH2-CH2-COOH, which is the simplest amino acid with proteins built from 20-300 amino acids.

Below you see RealQM running on a MacBook Air with 100^3 grid in minutes (with up to 5 atoms on 200^3 grid). You can test yourself downloading from Claes542 on GitHub  (C:green, N:blue, O:red, H:white), 

• molecule.js (10-atom support, dynamic grid)
• molecule.html (grid selector)
• glycine.html
• co2.html  nh3.html  h2co.html
• h2o.js h2o.html  run to find binding energy 0.48 Hartree compared to 0.35 observed (no calibration)

This is only a first test. Will add molecule dynamics based on real forces from potentials. Simulation of protein folding appears as a clear possibility. The code is 3-line explicit updating of densities, free boundary and potentials and great speed up awaiting. 

PS1 The valence electrons (H=1, N=3, O=2, C=4) are here homogenized into non-overlapping electron charges of charge 1, 3, 2 and 4 with reduction of potentials representing no self-repulsion, but can be split into charge 1 electrons if needed. Max number of valence electrons appears to be 4. 

PS2 Another case Camphor C10H16O (27 atoms on 100^3 grid):

PS3 Solvated Caffeine C8H10N4O2 + 9H2O  (51 atoms on 100^3 grid)

PS4 Can now run 1000 atoms on 300^3 grid.