RealQM vs DFT for Protein Folding

Why density-functional theory cannot dynamically simulate folding — and why RealQM can. Part of the RealQM program.

Message. Protein folding is a dynamical process — a chain moving from an extended state to its native fold over microseconds, in a system of 10³–10⁵ atoms. DFT cannot follow this trajectory (its cost scales as N³ in electrons and it is locked to femtosecond steps — off by ~10⁹–10¹²). RealQM can: its cost is set by a fixed spatial grid (200³–1000³), independent of atom count, and it uses large-step (Brownian) dynamics on the GPU. Biases may be used to guide folding — that helps RealQM and does nothing for DFT.

1. The problem: folding is dynamics, at scale

Folding is not a single energy minimisation; it is a time-evolution — the chain threads through a funnel of conformations from extended to native. The relevant facts:

Timescale: ~microseconds to milliseconds (small fast-folders ~μs; most proteins ms).
Size: ~10³ atoms for a small protein, 10⁴–10⁵ atoms with explicit solvent (~10⁵ electrons).
What's needed: follow the whole trajectory, not just score a static structure.

Any quantum method that hopes to fold must therefore run many time steps on a large system. This is exactly where the two methods diverge.

2. Why DFT cannot

Density-functional theory is the standard quantum method for matter, but its cost structure disqualifies it from folding dynamics:

O(N³) in electrons. Each self-consistent solve scales as the cube of the electron number N (orthogonalisation / diagonalisation). Doubling the system is 8× the cost; a solvated protein (~10⁵ e) is ~10⁶× a ~1,000-atom benchmark.
Femtosecond time steps. Ab-initio MD is locked to ~1 fs by nuclear vibrations, so 1 μs = 10⁹ steps, each requiring a full electronic solve.
The bottom line. For ~5 μs of a solvated protein: 5×10⁹ steps × ~10⁶ core-seconds/step ≈ 10¹³ core-hours ≈ ~1,000+ years on a million-core machine — for a single trajectory.

In practice DFT-AIMD reaches only ~100 ps for ~1,000 atoms. Folding needs ~10⁶× longer and ~30× larger (× N³ = 10⁴× per step) — a combined ~10⁹–10¹² beyond feasibility. This is a wall, not a hardware wait: Moore's law would need decades of doublings to touch it. And biases do not help DFT — restraints reduce how many steps you need to sample, but the disqualifying cost is per step (the N³ electronic solve), which every step still pays.

3. Why RealQM can

RealQM is quantum mechanics as real-space continuum mechanics on a grid. Its cost structure is completely different:

Cost set by the grid, not by N. All atoms share one fixed spatial grid; per-step cost scales with the number of grid cells (multigrid), independent of the atom count. A 200³ grid handles ~1,000 atoms; a 1000³ grid handles ~100,000 atoms — at the same per-cell cost. Adding atoms to a grid does not blow up the cost the way N³ does.
Large-step (Brownian) dynamics. RealQM can run overdamped / Brownian dynamics rather than fs-locked Newtonian AIMD, taking far larger effective steps and reaching folding timescales in orders of magnitude fewer steps.
GPU-native. The real-space grid maps directly onto GPU hardware (the simulations run in WebGPU in a browser).
Demonstrated. Folding trajectories already run in the program — chignolin, crambin, GB1, a solvated α-helix, a coiled coil — the chain visibly moving toward structure.
Biases permitted. As in classical MD (native-contact biasing, restraints, enhanced sampling), biases may guide the fold where the bare energy surface is too flat. This helps RealQM and, again, does nothing for DFT.

4. Side by side

	DFT (ab-initio MD)	RealQM
cost per step	O(N³) in electrons — grows fast	O(grid cells) — fixed by resolution, independent of N
capacity	~1,000 atoms in practice	200³ → ~1,000 atoms; 1000³ → ~100,000 atoms
time stepping	fs-locked (AIMD) → 10⁹ steps/μs	Brownian / large-step → far fewer
reach today	~100 ps / ~1,000 atoms	full folding trajectories (GPU)
cost of ~5 μs fold	~10¹³ core-hours (~millennia)	days–weeks on GPUs
biases	don't help (per-step wall remains)	permitted, help guide the fold
verdict	impossible	feasible

The gap between the two verdicts is a factor of roughly 10⁶–10¹⁰ in compute — the difference between "not in any foreseeable machine" and "runs on a GPU cluster."

5. Honest status

Beyond the capability gap, RealQM has a real advantage on the physics of the dynamics that should be stated plainly: it computes the forces on the atoms directly from the electron charge potentials — the actual Coulomb forces that drive the motion — rather than as gradients of an energy surface, as in the standard energy-first approach. Dynamics is force; RealQM supplies force physically and directly. On this basis RealQM is stronger, not weaker — the force computation is a strength, not a weak point.

The one genuinely open question is quantitative fidelity of the folded state — whether the physical force field carries the chain to the correct native structure across the whole funnel, and how far biases (native-contact restraints, enhanced sampling — standard tools in classical MD) are used. That is ordinary validation, not a defect of the method: the physical, charge-based forces are a reason for confidence, and biases help RealQM while doing nothing for DFT, which remains disqualified by cost.

In one line. DFT is O(N³) in electrons and fs-locked, so a microsecond fold of a solvated protein is ~10¹³ core-hours (millennia) — impossible; RealQM's cost is set by a fixed 200³–1000³ grid (1,000–100,000 atoms) with large-step GPU dynamics, so it can actually run the trajectory — biased if needed, which helps RealQM and not DFT.

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