Learning protein dynamics from quantum fragments

Ab initio characterization of protein molecular dynamics with AI²BMD

Tong Wang et al. • Nature 635, 1019–1027 (2024)

Reusable quantum-trained fragments connect atomic forces to protein motion.

Sean Florez • CSCI 7000 • September 28, 2026

Approach · Protein to local unit

From a whole protein to fragment energies and forces

Aminopeptidase N ribbon representation from Wang et al. 2024 Fig. 2a

REPRESENTATIVE CAPPED UNIT

Representative capped protein unit from Wang et al. 2024 Fig. 1

Coordinates
atom types + (x, y, z)

Define
local units

ViSNet

Differentiate

Whole protein

Aminopeptidase N

Unit energy

E(r)

Force contributions

F_i=−∂E∂r_i

All unit terms + remaining interactions → update the whole protein

Atomic coordinates define each local environment. Combined forces update the protein’s motion.

Approach

Reusable fragments make quantum training data tractable

Offline

During simulation

Fragment conformations

DFT labels

Trained potentials

Protein fragments

Predicted energies and forces

Atomic motion

repeat each step

A fixed vocabulary of local units supports evaluation across many protein sequences.

Method · Fragmentation

Overlapping fragments reconstruct protein energy

E_protein≈ΣE_unitsCapped units−ΣE_overlapsAce–Nme overlap+E_{remaining interactions}Coulomb + LJ

20 capped amino-acid units + 1 shared Ace–Nme unit

Subtracting the shared contribution corrects double counting; additional interactions connect separate regions.

Training data · What is a conformation?

Different conformations teach the model how energy changes

A conformation is one 3D arrangement of the same bonded atoms.

C

N

Cα

C

Conformation A

twist

C

N

Cα

C

Conformation B

twist

C

N

Cα

C

Conformation C

Rotating the N–Cα bond (ϕ) changes shape, energy and forces.

ϕ

ψ

Each geometry

DFT → E, F

Angle grid

Short quantum trajectories

Energy + atomic forces

20

amino-acid units

×

5,184

starting conformations per unit (72 × 72)*

×

200^†

snapshots per start

=

20,736,000

+

144,000

Ace–Nme (72 × 2,000)

=

20.88M

labelled examples

80% train ≈ 16.7M
10% validation · 10% test

*Two backbone angles at 5° intervals, per non-proline unit. Grid and conformations are schematic.

†Derived: 1,036,800 per unit ÷ 5,184 = 200.

Angles vary continuously. These examples sample the space of possible shapes.

Method · Learned potential

ViSNet learns energy and geometry-consistent forces

Atomic numbers + coordinates

Geometric message passing

Energy

F=−∂E∂r

Forces follow the negative energy gradient.

Rotation-aware representations and energy-derived forces encode useful physical structure.

Rotate the input

Energy unchanged

Forces rotate with the atoms

Method · Hybrid system

AI²BMD combines learned terms with classical interactions

Overlapping units

1

2

3

Protein backbone · schematic

1

Local overlapping units

ViSNet terms + overlap correction

2

Remaining protein interactions

Coulomb + Lennard-Jones terms

3

Solvent and coupling

AMOEBA polarizable force field

Reported simulation results describe this combined system.

Evidence · Error against DFT

Protein benchmarks show lower error against DFT

5 smaller proteins: whole-protein DFT reference

AI²BMD mean energy MAE

0.038

kcal mol⁻¹ atom⁻¹

Mean force MAE

1.974

AI²BMD

8.094

MM

kcal mol⁻¹ Å⁻¹

4 larger proteins use a fragmented DFT reference. Nine proteins, 175–13,728 atoms; 200 configurations each.

Evidence · Runtime

Energy evaluation is much faster than DFT

Trp-cage, 281 atoms

0.072 sAI²BMD

21 minDFT

Reported system: NVIDIA A6000 + 32 CPU cores

Measured · DFT, first four proteins

Extrapolated · DFT, last five proteins

Large-protein DFT timings are extrapolated.

These measurements concern energy evaluation; full solvated trajectories add further work.

Evidence · Experiment

NMR observables test sampled conformations against experiment

Backbone-angle samples

Predicted J couplings

NMR comparison

Pearson correlation

0.924AI²BMD

0.543MM

J couplings (Hz)

χ² error (dimensionless)

A measured observable checks one physical consequence of the simulated ensemble.

Evidence · Trajectories

Short chignolin trajectories capture folding and unfolding

Chignolin10 residues60 starting structuresTrajectories up to 10 ns

Starts unfolded

Starts folded

Plotted curves · Relative potential-energy error over time, against a QM protein + AMOEBA solvent reference

Selected trajectories show transitions between folded and unfolded conformations.

Evidence · Thermodynamics

Energy re-evaluation improves selected thermodynamic estimates

Classical sampling

AI²BMD energy evaluation

Thermodynamic estimates

Unfolding enthalpy ΔH (kcal mol⁻¹)

	AI²BMD	MM	Experiment
Barnase	116.5	110.4	118.7
CI2	73.0	57.1	78.4

Assessment

Accuracy depends on chemistry, sampling and the reference model

Reference

Learned DFT targets + fragmentation + hybrid interactions

Demonstrated: Force MAE 1.974 (AI²BMD) and 8.094 (MM) kcal mol⁻¹ Å⁻¹ against whole-protein DFT
Condition for reuse: Agreement measures fidelity to this reference system

?

Chemistry

A defined vocabulary of protein units

Demonstrated: 20 amino-acid units plus Ace–Nme cover the proteins tested
Condition for reuse: Ligands, nonstandard residues, charge states or reactions need new validation

Sampling

Ensembles must cover states relevant to the observable

Demonstrated: Chignolin folding and unfolding in trajectories up to 10 ns
Condition for reuse: Converged ensembles for each property of interest

Each new application needs validation at these three levels.

Takeaways

Reusable learned physics still needs experimental checks

Offline

During simulation

Fragment conformations

DFT labels

Trained potentials

Protein fragments

Predicted energies and forces

Atomic motion

repeat each step

1

2

3

1

Reuse

Train local units, compose larger systems

2

Physical structure

Geometry and energy-derived forces

3

Evaluation

Reference errors, trajectories and experimental observables

My takeaway: trustworthy reuse depends on the full model-and-sampling system.

Thank you

Questions?

Ab initio characterization of protein molecular dynamics with AI²BMD

Tong Wang et al. • Nature 635, 1019–1027 (2024)

Sean Florez • CSCI 7000

Offline

During simulation

Fragment conformations

DFT labels

Trained potentials

Protein fragments

Predicted energies and forces

Atomic motion

repeat each step

Backup B1 · Fragmentation and hybrid

Fragment and solvent contributions form the hybrid potential

1

Units

E_units=ΣE_dipeptide−ΣE_Ace–Nme

2

Protein

E_protein=E_units+E_{remaining Coulomb}+E_{remaining LJ}

3

Total system

E_total=E_protein+E_AMOEBA,all−E_{AMOEBA,protein}

AMOEBA

Coulomb + LJ

ViSNet units

Subtract overlapping/internal contributions to avoid double counting.

Backup B2 · Network

Training combines energy and force supervision

Separate ViSNet potential for each of 21 unit types
6 hidden layers • 128-dimensional embeddings
5 Å cutoff • maximum 32 neighbours
Energy / force loss weights: 0.05 / 0.95
Random per-unit train / validation / test split: 80 / 10 / 10

Backup B3 · NMR

Backbone angles determine predicted NMR couplings

J(ϕ)=7.09 cos²(ϕ−60°)−1.42 cos(ϕ−60°)+1.55

−180°

−90°

0°

90°

180°

0

2

4

6

8

10

ϕ

J (Hz)

Curve plotted from the equation above

Average J over sampled backbone conformations.

J is measured in Hz; ϕ is a backbone dihedral angle.

Correlation and χ² errors provide complementary views of agreement.

Backup B4 · Thermodynamics

Thermodynamic comparisons depend on ensembles and targets

Barnase

CI2

ΔC_p (kcal mol⁻¹ K⁻¹)

	AI²BMD	MM	Experiment
Barnase	1.4	1.0	1.4
CI2	0.7	0.5	0.8

WW-domain T_m

	AI²BMD	MM	Experiment
WW domain	359.06 K	353.69 K	371 ± 2 K

WW-domain improvement leaves about 12 K discrepancy.

Backup B5 · Runtime and scope

Runtime and chemical coverage define practical use

Energy timing

Fig. 2f

Solvated per-step timing

Extended Data Table 1

Demonstrated chemistry

Protein-unit vocabulary and specified interactions

New chemistry and rare events require additional validation.

Backup B6 · References

Sources and reading

Paper and code

Wang et al. (2024). Ab initio characterization of protein molecular dynamics with AI²BMD. Nature 635, 1019–1027.

DOI: 10.1038/s41586-024-08127-z

Author Correction (2025). DOI: 10.1038/s41586-024-08556-w

Authors' code and data: github.com/microsoft/AI2BMD

Figures in this deck

Fig. 1pages 1 · 2 · 3

Fig. 2pages 2 · 8 · 9

Fig. 3pages 10 · 18

Fig. 4pages 11

Fig. 5pages 12 · 19

Extended Data Fig. 1pages 6 · 17 · 23

Extended Data Fig. 7pages 4 · 16

Extended Data Table 1pages 20

Supplementary

Supplementary slides

23 ViSNet architecture: graph, embedding, message-passing layers, output

Backups B1 to B6 are pages 16 to 21.

Supplementary S1 · ViSNet architecture

ViSNet is a message-passing graph network over nearby atoms

i

j

5 Å

Atom i

Neighbours j send messages

Beyond 5 Å: no edge to i

Schematic. Grey lines: edges between other atoms.

1

Graph. Atoms are nodes. Edges join atoms within 5 Å, at most 32 neighbours per atom. Each unit has 12 to 36 atoms.

2

Embedding. Atomic numbers and 3D coordinates give h⁰
_i and f⁰
_ij, 128 dimensions each, and v⁰
_i = 0. Higher-order spherical harmonics expand the coordinates.

3

ViSNet block × N. One message-passing layer, shown at right. Messages from neighbours j are summed at atom i; the update block then refreshes h_i, f_ij and v_i using angle and dihedral terms (RGC). The paper reports 6 hidden layers.

4

Output. The output block gives one energy Ê. Forces F = −∂Ê/∂r are its gradient with respect to the input coordinates. One model for each of the 21 unit types.

Symbols in the figure and steps

i, jtarget atom and neighbour (source) atom

Åångström, 0.1 nm

llayer index; layer 0 is the embedding output

Nnumber of stacked ViSNet blocks

h^l
_i, h^l
_jscalar features of atoms i and j

f^l
_ijscalar features of edge i–j

v^l
_i, v^l
_jvector features of atoms i and j

0zero vector, the starting value of v_i

r_ijrelative position of atoms i and j

φ^s
_m, φ^v
_mlearned scalar and vector message functions

m^l
_ijscalar message from atom j to atom i

Σ_jsum over the neighbours j of atom i

m^l
_i, m^l
_isummed scalar and vector messages

φ^s
_un, φ^v
_unlearned update functions for atom features

φ^s
_uelearned update function for edge features

RGCruntime geometry calculation

RGC-Angledot product v_i · v_i, angle information at atom i

RGC-Dihedralv_i · v_j after removing parts along r_ij

Δh^l+1
_i, Δv^l+1
_i, Δf^l+1
_ijupdates for layer l + 1

Ê, Fpredicted energy and forces

∂Ê/∂rgradient of Ê with respect to atom coordinates r