Uses canonical residue templates from experimental A‑RNA (1RNA) and B‑DNA (1BNA) and a lightweight constrained minimizer; orbital/π clouds are qualitative.
Math / Physical Model
We place each residue by repeating an averaged experimental step transform S:
F₀ = local→global frame from PDB residue
Fᵢ = F₀ · Sⁱ
Each frame Fᵢ is a rigid transform (Rᵢ, tᵢ). For any template atom:
x_global = Fᵢ · x_local.
If no scaffold is available, we fall back to an ideal helix:
θᵢ = i·twist, zᵢ = i·rise
rᵢ = (R cosθᵢ, R sinθᵢ, zᵢ)
and build an orthonormal basis (radial, tangent, axis) for Fᵢ.
Relaxation minimizes a constrained energy:
E = Σ k_b (r - r₀)² (bonds)
+ Σ k_θ (d - d₀)² (angles as 1–3 springs)
+ Σ k_φ (1 - cos(φ - φ₀)) (dihedrals)
+ Σ k_rep · max(0, r_cut - r)² (clash repulsion)
+ Σ k_HB (r_HB - r)² (H‑bond distance)
r₀, d₀, φ₀ are taken from the initial scaffolded structure.
We take small gradient steps until RMS‖∇E‖ < tol.
Electron density is visualized as a stochastic point cloud.
π systems (aromatic rings):
- Compute ring centroid c and normal n.
- Sample points uniformly in a disk around c with radius ~ ring size.
- Create two lobes by offsetting along ±n by δ:
p = c + u·r·cosα + v·r·sinα ± n·δ
Lone‑pair / hetero‑atom density (O/N/P):
- Sample points on a spherical shell outside vdW radius:
p = x_atom + n̂·(r_shell + ε)
The density slider multiplies the base counts:
N = density × N₀.
4000
1.0×
Overlap τ highlights bonding by keeping points where neighbors contribute. Absolute ρ uses a physical density cutoff (vdW surface ~0.013 e/ų).
Requires per‑frame resampling
300 K
2.0
1.0×
Math / Model
This page uses a promolecular electron density approximation:
ρ_total(r) = Σ_atoms ρ_atom(|r - R_a|)
Each atomic density is modeled as a Gaussian mixture:
ρ_atom(r) = Σ_i w_i · exp(-α_i r²)
with Σ_i w_i = Z (atomic electron count). We sample electron points from
this distribution to visualize |ψ|²‑like density without running QM.
Polarization (QEq):
We estimate partial charges qᵢ by minimizing
E(q)=Σ χᵢ qᵢ + 1/2 Σ ηᵢ qᵢ² + 1/2 Σ_{i≠j} qᵢ qⱼ / √(Rᵢⱼ²+a²)
with Σ qᵢ = Q_total. Electron density per atom is scaled by Z_eff = Z - qᵢ.
Dynamics (MD / bond rotation):
E = Σ k_b (r-r₀)² + Σ k_θ (d-d₀)²
+ Σ k_φ (1+cos(nφ-δ)) + Σ LJ_rep(r)
+ Σ qᵢqⱼ/√(r²+a²)
Promolecular densities are approximate; for true QM densities, load external cube grids in a future step.