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Autonomous artificial intelligence discovers mechanisms of molecular self-organization in virtual experiments

Hendrik Jung, Roberto Covino, A Arjun, Peter G. Bolhuis, Gerhard Hummer

arXiv:2105.06673v1physics.chem-phphysics.bio-phphysics.comp-ph

TL;DR

Rare molecular self-organization events are costly to simulate and difficult to reduce to quantitative mechanisms. The paper presents an AI agent that learns to sample transition paths while building mechanistic models, then uses symbolic regression to make them interpretable. Across ion pairing, gas-hydrate formation, and membrane-protein assembly, it identifies solvent roles, a temperature-dependent nucleation switch, and competing assembly pathways.

Abstract

from arXiv · show

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Understanding the physical mechanisms that govern the formation of molecular complexes and crystals is key to controlling the assembly of nanomachines and new materials. We present an artificial intelligence (AI) agent that uses deep reinforcement learning and transition path theory to discover the mechanism of molecular self-organization phenomena from computer simulations. The agent adaptively learns how to sample complex molecular events and, on the fly, constructs quantitative mechanistic models. By using the mechanistic understanding for AI-driven sampling, the agent closes the learning cycle and overcomes time-scale gaps of many orders of magnitude. Symbolic regression condenses the mechanism into a human-interpretable form. Applied to ion association in solution, gas-hydrate crystal formation, and membrane-protein assembly, the AI agent identifies the many-body solvent motions governing the assembly process, discovers the variables of classical nucleation theory, and reveals competing assembly pathways. The mechanistic descriptions produced by the agent are predictive and transferable to close thermodynamic states and similar systems. Autonomous AI sampling has the power to discover assembly and reaction mechanisms from materials science to biology.

INTRODUCTION

Molecular self-organization is difficult to model because rare transitions occur amid high-dimensional molecular motion, making both transition-path sampling and mechanism extraction challenging. The proposed agent learns a committor model while sampling transition paths, then uses symbolic regression to express the mechanism compactly.

INTRODUCTION

  • Rare self-organization events are difficult to study because systems spend most of their time in metastable states and reorganize during infrequent, rapid transitions.Molecular dynamics is computationally costly, and mechanism learning requires sampling transition paths that capture the reorganization.Source: INTRODUCTION · p. 1
  • The agent simultaneously builds quantitative mechanistic models, validates them on the fly, and uses them to accelerate sampling by orders of magnitude compared with regular molecular dynamics.Source: INTRODUCTION · p. 1

Reinforcement learning of molecular mechanisms

  • The transition path ensemble captures the reorganization at highest resolution, while the committor gives the probability of reaching a state first and predicts trajectory fate.Source: Reinforcement learning of molecular… · pp. 1–2
  • Because the committor determines the probability of sampling a transition path, learning it helps guide path sampling and vice versa.The agent repeatedly shoots trajectories and retrains its committor model only when observed path counts poorly match predictions, improving sampling near transition states.Source: Reinforcement learning of molecular… · p. 2
  • The agent learns the committor with a neural network and uses symbolic regression to distill the learned mechanism into compact, human-interpretable expressions.Sensitivity analysis selects a smaller set of input coordinates for symbolic regression.Source: Reinforcement learning of molecular… · p. 2

AI discovers many-body solvent coordinate in ion

The agent identifies solvent rearrangement as central to ion-pair assembly and distills a solvent-aware model. For methane clathrates, it finds that nucleation predictors shift with temperature, revealing different growth mechanisms.

assembly

  • Inner-shell water near Li+ must open space for incoming Cl−, making solvent rearrangement critical to ion-pair assembly.The most important solvent feature, x12, quantifies oxygen anisotropy 0.25 nm from Li+.Source: assembly · p. 2, Figure 1 · p. 3
  • The distance-only ion-pair model works only at large separations, while q1(rLiCl, x8, x9, x12) is accurate across all distances.The more complex model incorporates the most critical solvent coordinates.Source: Figure 1 · p. 3, assembly · p. 4
  • A committor trained on a single LiCl pair correctly predicts sampled committors for 724 configurations from 1M LiCl solution.The test system is similar but not identical to the training system.Source: Figure 1 · p. 3, assembly · p. 4

for gas-hydrate crystal formation

  • For methane clathrates, temperature is the most critical trajectory factor, followed by surface-water count and the count of 51262 cages.The learned committor was validated on 160 independent configurations and satisfactorily interpolated and extrapolated to unsampled temperatures.Source: for gas-hydrate crystal formation · p. 4, Figure 2 · p. 4
  • Surface-water count and 51262-cage count are classical nucleation variables: they parameterize nucleus size, while temperature sets critical size, barrier height, and rate.The cage count refers to cages with 12 pentagons and two hexagons.Source: for gas-hydrate crystal formation · pp. 4–5
  • The clathrate mechanism switches with temperature: nucleus size alone determines low-temperature growth, while 51262 cages gain importance at higher temperatures.The model identifies amorphous growth at low temperatures and crystalline growth at higher temperatures.Source: Figure 2 · p. 4, for gas-hydrate crystal formation · p. 5

AI reveals competing pathways for membrane-protein complex assembly

The agent samples Mga2 dimer dissociation at scale and reduces its learned committor to two interhelical contacts. Clustering the transition paths reveals two competing assembly routes.

AI reveals competing pathways for membrane-protein complex assembly

  • Nearly 4,000 Mga2 dissociation events were sampled in 20 days on a parallel supercomputer.The approach is naturally parallelizable, and one agent can run virtual experiments on multiple copies of the physical model.Source: AI reveals competing pathways for… · pp. 5–6
  • Committor predictions were accurate across the transition region in validation against 548 configurations not used for training.Configurations were described using inter-residue contacts along the helices and hand-tailored lipid-organization features.Source: AI reveals competing pathways for… · p. 6
  • A committor expressed through two amino-acid contacts supports clustering transition paths into two competing Mga2 assembly pathways.The pathways differ in the order of assembly events; helix-dimer geometry alone predicts assembly progress, with lipid organization implicitly encoded.Source: AI reveals competing pathways for… · p. 6

METHODS

The committor is modeled from shooting outcomes by maximizing their likelihood, while transition path sampling generates paths through two-way shooting. Shooting-point selection is biased toward the estimated transition-state ensemble but retains exploration of alternatives.

function

  • Shooting outcomes define a likelihood used to fit a neural-network committor, with sigmoid or softmax activations constraining probabilities and their normalization.The training loss is the negative log-likelihood.Source: function · p. 6

Training points from transition path sampling

  • Two-way shooting selects a point on the current path, launches trajectories with random Maxwell-Boltzmann velocities in opposite time directions, and accepts a new path according to the shooting-point selection probabilities.A continuous path is formed when the trial trajectories reach different states; rejected paths are repeated.Source: Training points from transition path… · p. 6
  • Shooting points are selected with a Lorentzian centered on the estimated transition-state ensemble, balancing efficient path production with exploration of alternative channels.For two states, the transition-state ensemble corresponds to pB(x) = 1/2, or q(x) = 0.Source: Training points from transition path… · p. 6

Real-time validation of committor model prediction

The model estimates the expected number of transition paths from recent shooting outcomes and compares that estimate with the observed count. Learning is triggered by disagreement and scaled or withheld according to an efficiency factor.

Real-time validation of committor model prediction

committor

The method identifies influential committor inputs by permuting coordinates and measuring the resulting loss change, then uses the most relevant inputs for symbolic regression. The regression seeks compact expressions that approximate the full committor while penalizing complexity.

committor

  • A coordinate is considered relevant when randomly permuting its values across at least 100 training sets produces a large average increase in loss.The perturbed losses are compared with the reference loss on the unperturbed training set.Source: committor · p. 7
  • Symbolic regression uses the most relevant inputs to generate compact mathematical expressions that approximate the full committor.Source: committor · p. 7
  • A genetic algorithm selects and optimizes candidate expressions using likelihood plus a complexity penalty based on the number of mathematical operations.The penalty is intended to keep expressions simple and avoid over-fitting.Source: committor · p. 7

Assembly of LiCl in water

The LiCl-in-water study tests ion-pair assembly in single-pair and 1 M systems, representing solvent environments with symmetry functions. The simulations use a shared force field and water model, while the neural network filters inputs before symbolic regression.

Assembly of LiCl in water

  • The study examines lithium chloride association in water with either one ion pair or a 1 M concentration, using Joung–Cheatham parameters and TIP3P water.The 1 M box contains 37 lithium and 37 chloride ions with 2,104 water molecules; the single-pair box contains 370 water molecules.Source: Assembly of LiCl in water · p. 7
  • The input representation uses the interionic distance for the solute and symmetry functions for solvent structure, including radial density and angular distribution around solute atoms.The symmetry functions incorporate physical symmetries and are scaled approximately to [0, 1].Source: Assembly of LiCl in water · pp. 7–8
  • A five-block residual network progressively reduces hidden units from 221 to 10, and five relevant coordinates are selected for symbolic regression.Training follows every third TPS step for one epoch, with learning rate lr = αeff10^-3 when lr ≥ 10^-4.Source: Assembly of LiCl in water · p. 8

Nucleation of methane clathrates

The methane-hydrate simulations use specified water and methane models and sample assembly at four temperatures. The committor model is trained on structural features and temperature, with selected coordinates passed to symbolic regression.

Nucleation of methane clathrates

  • The simulations used TIP4P/Ice water and united-atom Lennard-Jones methane, with 2 fs integration and NPT conditions.Long-range interactions used Particle Mesh Ewald; shooting simulations covered 270, 275, 280, and 285 K.Source: Nucleation of methane clathrates · p. 8
  • Committor validation used 6–18 trajectory shots per configuration, while disassembled and assembled states were defined by mutually coordinated guest numbers.The state definitions followed Ref.19.Source: Nucleation of methane clathrates · p. 8
  • Twenty-four features described nucleus size, crystallinity, structure, and composition, with temperature also supplied to the neural network and symbolic regression.The network was trained across temperatures, and the three most relevant coordinates were used for symbolic regression.Source: Nucleation of methane clathrates · p. 8

Mga2 transmembrane dimer assembly in lipid

The Mga2 assembly study represents two helices with interhelical and lipid-organization features and samples transition paths through automated, distributed TPS. Its input analysis identifies distinct contact patterns near the unbound state as important to committor prediction.

Mga2 transmembrane dimer assembly in lipid

  • The assembly representation combines 28 interhelical backbone distances, contact and center-of-mass measures, and hand-tailored lipid-organization features.The assembled state requires at least 130 interhelical contacts; the disassembled state has helix-center separation of at least 3 nm.Source: membrane · pp. 8–9
  • Five hundred independent TPS chains ran in parallel, with committor-model updates after rounds two and six before 14 further sampling rounds.The shooting-point selection, TPS setup, and network training were automated.Source: membrane · p. 9
  • Near the unbound state, interhelical contacts tracing an approximate helical pattern matter, while total contact count alone does not yield an accurate committor expression.The contact-only expressions were assessed against validation committor data not used during optimization.Source: membrane · p. 9
  • Trajectory similarity was assessed by dynamic time warping after projection onto contacts 9 and 22, with path-density plots weighted by paths rather than configurations.Repeated visits to a histogram cell within one path counted only once.Source: membrane · p. 9

CONCLUDING REMARKS: BEYOND MOLECULAR SELF-ORGANIZATION

The authors argue that AI-driven sampling can extend beyond molecular dynamics by treating the simulation engine as a replaceable black box. They present autonomous sampling, model validation, and symbolic AI as support for scientific discovery across molecular systems.

CONCLUDING REMARKS: BEYOND MOLECULAR SELF-ORGANIZATION

  • The sampling approach can use dynamics that are reversible or not, with the engine treated as a black box and the statistical model and machine-learning technology tailored to the problem.The authors describe the approach as adaptable to many-body dynamics with a notion of likely fate.Source: CONCLUDING REMARKS: BEYOND MOLECULAR… · p. 9
  • Simpler regression schemes can replace neural networks when trajectory-sampling costs severely limit training-data volume.Source: CONCLUDING REMARKS: BEYOND MOLECULAR… · p. 9
  • AI-driven mechanism discovery can integrate advances in force-field learning, sampling, and molecular representation with symbolic AI.The authors state that autonomous sampling and model validation combined with symbolic AI can support scientific discovery.Source: CONCLUDING REMARKS: BEYOND MOLECULAR… · p. 9

Normalization of symmetry functions

The supplied passages describe symmetry functions for representing solvent configurations and report related input-importance and symbolic-regression materials. They also identify methane-hydrate model checks across temperatures.

Normalization of symmetry functions

  • G2 symmetry functions count solvent atoms in a probing volume, and the expected atom count is related to the probed volume and solvent number density.The passage also gives an approximation condition for small η and rcut > rs.Source: Normalization of symmetry functions · p. 12
  • G5 functions include an angular term and count solvent-atom pairs on opposite sides of a central solute atom, using an approximation guaranteed to be non-negative.The text notes that the direct pair-count expression can become negative when the expected atom count is below one.Source: Normalization of symmetry functions · p. 12
  • The lithium-chloride input-relevance table lists ten coordinates in decreasing order of importance, while its feature table describes solvent symmetry-function parameter choices.The listed G5 functions use ten parameter combinations per rs value and a 1 nm cutoff.Source: Normalization of symmetry functions · p. 12
  • For Mga2 symbolic regression, coordinate pairs containing ncontacts are omitted from the reported combinations because of their low predictive power.The table covers two-coordinate combinations drawn from the seven most relevant inputs.Source: Normalization of symmetry functions · p. 14
  • The methane-hydrate committor models are evaluated for interpolation at 280 K and extrapolation beyond the training temperatures.The figure caption specifies training on three of four available temperatures for each test.Source: Normalization of symmetry functions · p. 15
  • Mga2 input-importance bars average 50 analyses, show one standard deviation, and compare all training points with the subset near the unbound state.The subset is defined by ncontacts < 0.01, and importance values are normalized to the largest value in each set.Source: Normalization of symmetry functions · p. 15
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