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TD3B: Transition-Directed Discrete Diffusion for Allosteric Binder Generation

Hanqun Cao, Aastha Pal, Sophia Tang, Yinuo Zhang, Jingjie Zhang, Pheng Ann Heng, Pranam Chatterjee

arXiv:2605.09810v1q-bio.BMcs.LG

TL;DR

Existing binder-design methods optimize static structures and do not systematically control directional, non-reversible effects such as agonism versus antagonism. TD3B generates sequence-based binders with specified transition directionality, producing selective directional behavior and success rates of 61% and 100% for forward and backward transitions, respectively.

  • Problem

    Most binder-design methods optimize static structures or equilibrium interfaces and lack mechanisms to represent non-reversible transition directionality or distinguish agonist from antagonist behavior.

  • Method

    TD3B models binder-mediated allostery with sequence-conditioned transition operators and direction-guided discrete diffusion fine-tuning for agonist or antagonist generation.

  • Results

    TD3B produces binders that selectively bias agonistic transitions while minimally affecting reverse transitions, with success rates of 61% and 100% for forward and backward transitions, respectively.

  • Takeaways & Limitations

    The framework supports computational generation of protein-binding peptides with controlled agonist or antagonist behavior when functional directionality is important.

  • Takeaways & Limitations

    Mechanistic conclusions about activation rely on static AlphaFold3-predicted complexes and require molecular-dynamics simulations and experimental mutagenesis for definitive validation.

Abstract

from arXiv · show

Protein function is often controlled by ligands that bias the direction of state transitions, such as agonists and antagonists, rather than stabilizing a single conformation. This is especially important for clinically relevant G protein-coupled receptors (GPCRs), where therapeutic efficacy depends on functional directionality. Structure-based design methods optimize binding to static conformations and cannot represent non-reversible, directional effects or systematically distinguish agonist from antagonist behavior. To address this gap, we introduce Transition-Directed Discrete Diffusion for Allosteric Binder Design (TD3B), a sequence-based generative framework that designs binders with specified agonist or antagonist behavior via a directional transition control objective. TD3B combines a target-aware Direction Oracle, a soft binding-affinity gate, and amortized fine-tuning of a pre-trained discrete diffusion model, enabling targeted agonist and antagonist generation decoupled from binding affinity and unattainable by equilibrium-based or inference-only guidance baselines. The code and checkpoints are available at https://huggingface.co/ChatterjeeLab/TD3B.

1 Introduction

Allosteric function often depends on biasing non-reversible transitions between protein states, whereas prevailing binder-design methods target static or equilibrium binding. TD3B addresses this gap with transition-directed modeling, directional guidance, and empirical selectivity beyond static baselines.

  • Motivation: Agonists trigger shifts toward active states, whereas antagonists stabilize inactive states without inducing structural changes.The figure contrasts agonist-induced activation with antagonist-mediated blocking of signal activation.
  • Motivation: Biological function often depends on biasing activation–deactivation transition directions rather than stabilizing a single conformation.This directional behavior is especially relevant to agonists and antagonists, but contemporary binder-design algorithms generally do not represent it.
  • Method: TD3B models binder action with sequence-conditioned transition operators over protein macrostates, explicitly representing non-reversible, antisymmetric state changes.Its directional supervision biases generation toward binders that promote or suppress specified state transitions.
  • Method: TD3B combines a target-aware Direction Oracle, a soft affinity gate, and tree-search amortized fine-tuning of a pre-trained masked discrete diffusion language model.Importance-weighted denoising and a contrastive loss enforce directional separation in representation space.
  • Results: Contrastive direction-based fine-tuning produces binders that selectively bias agonistic transitions while minimally affecting reverse transitions, beyond static and inference-only baselines.The approach captures functional behaviors that post-hoc filtering cannot achieve.

2 Related Works

Related work spans classical allosteric theory and screening, computational prediction of allosteric sites and pathways, de novo protein design, and guided or reinforcement-learning-based discrete diffusion. These approaches establish foundations for allosteric binder generation and property-directed sampling.

  • Allosteric design: Classical allosteric theory began with the MWC concerted-transition and KNF sequential-induced-fit models, while early discovery depended on serendipitous screening hits.Subsequent computational methods predicted allosteric sites, hotspots, and communication pathways.
  • Allosteric design: De novo allosteric design progressed from Rosetta-based side-chain networks to modular rigid-body coupling strategies using RFDiffusion and ProteinMPNN.These strategies enabled peptide-responsive ring architectures and effector-induced cage disassembly; related work also includes structure-based GPCR design and Chemical Language Model approaches.
  • Diffusion guidance: Discrete diffusion models provide unsupervised generative frameworks for modeling distributions over discrete spaces, with conditional generation supporting efficient sample exploration.The cited work includes Austin et al. (2021), Lou et al., Sahoo et al. (2024), and Shi et al. (2024).
  • Diffusion guidance: Guided-generation methods steer diffusion sampling toward desired properties through classifier gradients, including training-free Classifier Guidance, Sequential Monte Carlo, and Classifier-Free Guidance.The passage contrasts these guidance approaches with limitations motivating more sophisticated conditional-generation methods.
  • Reinforcement learning: Reinforcement-learning methods address guidance limitations by learning more sophisticated conditional distributions through environment interaction, using policy gradients or tree search.DRAKES and GLID2E update policies via reward signals, while PepTune and TR2-D2 explore multi-condition and multi-objective sampling.

3 Preliminaries

This section introduces masked discrete diffusion language models as the sequence-generation backbone and describes amortized objective-guided fine-tuning for biasing generation toward high-scoring binders. The formulation represents arbitrary sequence-based binders and preserves a pretrained model’s learned sequence prior while incorporating external objectives.

  • Sequence formulation: The formulation represents binders as length-L sequences y over a finite alphabet A, with target proteins denoted by x.It applies to arbitrary sequence-based binders, using peptides as a concrete instantiation.
  • Masked discrete diffusion: MDLMs generate discrete sequences by progressively masking and denoising tokens, learning reverse token distributions conditioned on unmasked context and diffusion time.After training, sampling iteratively denoises from a fully masked input, capturing sequence-space combinatorial structure independently of downstream tasks.
  • Objective-guided fine-tuning: Objective-guided design biases a pretrained unconditional distribution pθ0(y) toward sequences with high external objective S(y) while preserving its structural prior.Amortized fine-tuning learns a parameterization approximating a reward-tilted target distribution, with α controlling deviation from pθ0.
  • Objective-guided fine-tuning: Amortized fine-tuning optimizes weighted denoising cross-entropy using trajectory-level importance weights to correct proposal-sampling mismatch.The procedure internalizes S into the sampling distribution, reduces reliance on inference-time search, and updates denoising conditionals without changing diffusion or corruption schedules.

4 Problem Formulation

TD3B formulates allosteric binder design as amortized, objective-guided sequence generation that targets directional protein-state transitions. Its formulation combines coarse-grained transition modeling, direction supervision, affinity-gated rewards, and amortized diffusion fine-tuning.

  • 4.1 Protein Macrostates and Coarse-Grained State Shifts: TD3B models functionally distinct protein configurations as macrostates governed by a continuous-time Markov chain, without requiring atomistic trajectories or detailed kinetic models.The coarse-grained abstraction captures state-to-state transition behavior directly.
  • 4.2 Sequence-Conditioned Transition Operators: Binder sequences perturb transition rates through an asymmetric, sequence-conditioned generator, with no assumed symmetry, reversibility, or detailed balance.The resulting dynamics lack a scalar energy-gradient representation.
  • 4.3 Directional Asymmetry: Directional asymmetry measures net transition bias between ordered macrostates, while the design objective requires only coarse directional information rather than observable rates or the full generator.Consistent signs of Δij(y) define directional allosteric effects for selected transitions.
  • 4.4 Data and Directional Supervision: Functional supervision encodes agonist or antagonist direction as d(y) ∈ {+1, −1} with confidence weights, excluding negative nonbinding labels from directional supervision.Full agonists receive confidence 1, partial agonists κpart, antagonists 1, and negative examples 0.
  • 4.5 Direction Oracle: The Direction Oracle fϕ predicts transition-bias direction from target-protein and binder representations produced by pre-trained encoders and fused through a learned gating mechanism.The oracle is trained with a weighted binary classification loss.
  • 4.6 Contrastive Directional Representation: A margin-based contrastive loss separates MDLM representations of binding sequences with matching versus opposing directional labels, while excluding nonbinding samples.Positive and negative pairs require nonzero confidence weights.
  • 4.7 Incorporating Target Binding Affinity via Gating: Affinity acts as a soft gate that rewards sequences predicted both to bind the target and to match the requested direction, rather than maximizing binding strength.The target and direction condition the reward during fine-tuning while the generative backbone remains target-agnostic architecturally.
  • 4.8 Amortized Fine-Tuning Objective: Amortized fine-tuning reweights masked-token denoising on tree-search replay-buffer samples so high-reward binders matching the desired direction contribute more gradient signal, while regularization preserves the prior.Nonbinders with κ(y) = 0 contribute no gradient; the design task prioritizes transition direction without regressing kinetic rates or stabilizing endpoint states.

5 Results

TD3B is evaluated as a sequence-conditioned framework for generating binders with non-reversible, direction-specific behavior. Results indicate that it combines reliable direction prediction, affinity control, targeted transition bias, and candidate generation for GPCR applications.

  • Evaluation goals: The evaluation tests whether TD3B induces non-reversible transitions, controls direction independently of affinity, and targets specified agonist or antagonist behavior.These experiments are designed to assess capabilities inaccessible to equilibrium- and structure-centric design methods.
  • Direction Oracle: The Direction Oracle achieves strong classification performance across accuracy, precision, recall, and F1 score, supporting reliable guidance across targets and sequence lengths.The reported metrics evaluate the Oracle’s discriminative capability and its ability to identify binder directionality.
  • Affinity and direction: TD3B-generated samples achieve higher predicted normalized affinity than RFDiffusion designs, demonstrating the effectiveness of gated-reward fine-tuning.Binding affinity is treated as a prerequisite for characterizing agonists and antagonists.
  • Affinity and direction: Compared with the unconditioned generator, TD3B produces higher-confidence distributions across both directions and enables explicit agonist-versus-antagonist transition control.The pre-trained model is predominantly agonist-biased, has low confidence, and lacks directional control.
  • Directional generation: TD3B achieves the highest gated reward, while fine-tuning methods improve affinity and directional balance beyond training-free guidance approaches.Weighted sampling and contrastive loss extend TR2-D2 by exploiting high-potential samples and separating directional distributions in latent space.
  • Ablation analysis: Both Lctr and Lreg are necessary: removing Lctr collapses directional separation, whereas removing Lreg increases agonist bias and destabilizes antagonist accuracy.The KL term preserves distributional capacity for reaching the antagonist mode, which is farther from the pre-trained prior.
  • Targeted control: TD3B selectively biases specified transitions while maintaining high affinity, and its de novo binders outperform length-matched wild-type references across directions.Success requires both superior predicted affinity to wild-type and correct Direction Oracle classification.

6 Discussion

TD3B formulates allosteric binder design as control over sequence-conditioned transition operators rather than optimization toward static states or equilibrium energies. It explicitly models directional asymmetry and non-reversibility to capture functional effects that structure-centric design algorithms and predictive dynamics models fail to address.

  • Framework: TD3B introduces a generative framework for allosteric binder design based on sequence-conditioned transition operators.The framework replaces optimization toward static states or equilibrium energies with transition-operator control.
  • Directional control: The framework makes directional asymmetry an explicit modeling target for allosteric binder design.
  • Directional control: TD3B also makes non-reversibility explicit to capture functional effects missed by structure-centric design algorithms and predictive dynamics models.

Impact Statement … A.4 Weighted Denoising Cross-Entropy Fits a Target Distribution

The paper presents TD3B as a framework for generating protein-binding peptides with controlled agonist or antagonist behavior, supported by theoretical guarantees linking directional scoring, exponential tilting, and weighted denoising training. The appendix formalizes these guarantees, including oracle optimality and fitting a tilted target distribution.

  • Impact Statement: TD3B generates protein-binding peptides with controlled agonist or antagonist behavior, aiming to support therapeutic discovery where functional directionality is critical.The approach separates binding from functional effect to reduce late-stage failures from unintended signaling outcomes.
  • A Theoretical Proofs: The theoretical appendix establishes guarantees for exponential tilting, Direction Oracle optimality, weighted denoising cross-entropy, oracle approximation error, and zero contrastive loss.These results are presented as basic guarantees for TD3B.
  • A.1 Notation and Setup: The setup uses a finite sequence space Y, a base distribution p0, a score S with temperature α > 0, and a direction oracle weighted by confidence and directional labels.For direction design, the score is S(y; d⋆) = d⋆fϕ(y) for d⋆∈{+1, −1}.
  • A.2 Exponential Tilting as KL-Regularized Improvement: The unique maximizer of expected score minus α KL(q∥p0) is the exponentially tilted distribution.As α →∞, the tilted distribution approaches p0 in total variation; as α →0+, it concentrates on score maximizers within p0’s support.
  • A.3 Population Optimality of the Direction Oracle: A population-optimal weighted logistic Direction Oracle estimates a weighted log-odds function, making directional exponential tilting principled.The weighting can down-weight partial agonists and exclude non-binders.
  • A.4 Weighted Denoising Cross-Entropy Fits a Target Distribution: Weighted risk under r equals unweighted risk under the normalized reweighted distribution π when the weights have finite positive expectation.This lemma provides the distributional basis for interpreting weighted denoising objectives.
  • A.4 Weighted Denoising Cross-Entropy Fits a Target Distribution: At population optimum, WDCE denoisers recover the true conditional distribution under the target distribution π for each time and masked position.The result follows because cross-entropy is uniquely minimized by matching the true conditional.
  • A.4 Weighted Denoising Cross-Entropy Fits a Target Distribution: With proposal r = p0 and reward-based weights, the reweighted distribution equals the tilted distribution p⋆, so WDCE becomes standard MDLM training under that target.This connection holds in the population limit.

A.5 Stability of Tilting Under Oracle Approximation Error · A.6 A Separability Consequence of Zero Contrastive Loss

A.5 establishes that bounded oracle score error yields controlled divergence between the corresponding tilted distributions at the same temperature. A.6 shows that zero margin-contrastive loss collapses each class to a prototype and guarantees linear separability with margin at least m0/2.

  • A.5 Stability of Tilting Under Oracle Approximation Error: Theorem A.4 considers an ideal score S⋆ and an approximation S whose error is bounded, establishing robustness of the resulting tilting.The corresponding tilted distributions use the same base distribution p0 and temperature α > 0.
  • A.5 Stability of Tilting Under Oracle Approximation Error: The ideal and approximate tilted distributions are constructed from the same p0 and temperature α > 0.They differ only through the ideal score S⋆ versus the approximate score S.
  • A.5 Stability of Tilting Under Oracle Approximation Error: The normalizer ratio is controlled because exp(δ/α) lies in [exp(−ε/α), exp(ε/α)].This interval follows from the bounded score error after exponentiating the scaled error.
  • A.5 Stability of Tilting Under Oracle Approximation Error: KL(ep∥p⋆) ≤ 2ε/α, with the reverse KL bound obtained symmetrically by exchanging S and S⋆.The bound follows by taking expectation under ep; Pinsker’s inequality then supplies the total-variation bound.
  • A.6 A Separability Consequence of Zero Contrastive Loss: Zero margin-contrastive loss forces all embeddings within each class to be identical, defining two class prototypes u+ and u−.This conclusion follows because the within-class squared-distance terms must vanish when Lctr = 0.
  • A.6 A Separability Consequence of Zero Contrastive Loss: For zero loss, the prototypes satisfy ∥u+ −u−∥2 ≥m0 because the cross-class hinge terms are zero.The labeled samples have di ∈ {+1, −1}, and each embedding equals its class prototype.
  • A.6 A Separability Consequence of Zero Contrastive Loss: The two classes are linearly separable by a hyperplane with geometric margin at least m0/2.The margin is at least ∥u+ −u−∥2/2, which is at least m0/2.

B Implementation and Dataset Details … B.3 Affinity Sources and Structural Inputs for Baselines

The paper specifies training procedures for the Direction Oracle and TD3B fine-tuning, and defines experimentally grounded affinity references and structural inputs for baseline evaluation.

  • B.1 Direction Oracle Training: The Direction Oracle is trained for 20 epochs with AdamW, a 10^-5 learning rate, batch size 16, and cross-entropy loss.Training uses the full training split without validation and evaluates only on an independent held-out set.
  • B.1 Direction Oracle Training: Pre-trained encoders remain frozen while projection, attention, and classifier-head modules are optimized.Optimized components include projection layers, self-attention, cross-attention, and a two-layer MLP classifier head.
  • B.2 TD3B Finetuning: TD3B tree-search sampling uses 20 iterations, 24 children per node, 4 targets per iteration, and 32 buffered candidates per target.The procedure is trajectory-aware and maintains a replay buffer of 2000 samples with FIFO replacement.
  • B.2 TD3B Finetuning: TD3B fine-tuning uses batch size 4, four-step gradient accumulation, a 5 × 10^-5 learning rate, and 4 WDCE replicates per sample.The KL regularization coefficient λreg is set to 0.5.
  • B.3 Affinity Sources and Structural Inputs for Baselines: Evaluation ground-truth affinities come from SKEMPI 2.0 experimentally measured dissociation constants converted to binding free energy changes ∆∆G.These measurements provide an independent experimental reference distinct from the pre-trained PepLand-based affinity predictor.
  • B.3 Affinity Sources and Structural Inputs for Baselines: RFDiffusion baseline inputs are experimentally determined, PDB-deposited structures with validated agonist or antagonist activity for each target.Using resolved structures avoids confounding comparisons with potential conformational biases from upstream structure prediction.

B.4 Data Leakage Analysis … C.2 Per-Target Performance Breakdown

Leakage checks found no exact peptide–target overlap and no transferred pair-level binding information from PepLand. Additional-target and per-target analyses show TD3B can distinguish TAAR1 agonist and antagonist binding modes, while antagonist direction accuracy remains intact despite some agonist failures.

  • B.4 Data Leakage Analysis: TD3B’s leakage analysis compared 130 training and 88 test bidirectional pairs against 2,110 PepLand entries using exact peptide, target, and pair-level checks.The analysis addressed whether an externally pretrained affinity predictor could artificially inflate generalization.
  • B.4 Data Leakage Analysis: The sole approximate peptide match, P50984 at 87.5% identity, involved different targets across datasets and therefore transferred no pair-level binding information.The peptide was paired with P30532/P32297 in the authors’ data and Q8WSF8 in PepLand.
  • B.4 Data Leakage Analysis: The authors conclude that TD3B’s apparent generalization is not attributable to leakage through the affinity predictor.This conclusion follows from conditioning the predictor on both target and binder.
  • C.1 Case Studies on Additional Protein Targets: TD3B was additionally applied to TAAR1, a neuromodulatory GPCR linked to schizophrenia for which both agonists and antagonists are pharmacologically relevant.The study evaluated whether generated agonists and antagonists exhibit distinct binding modes.
  • C.1 Case Studies on Additional Protein Targets: Figure C1 evaluates a known TAAR1 agonist alongside TD3B-designed agonist and antagonist complexes.The reference agonist is T1AM bound to TAAR1 in PDB 8JLN.
  • C.2 Per-Target Performance Breakdown: Per-target evaluation used 3-seed gated-reward and direction-accuracy measurements, with cross-seed variance of ±0.03 on aggregated gated reward.The reported variance indicates stable training across seeds.
  • C.2 Per-Target Performance Breakdown: Agonist direction accuracy DA(d⋆= + 1) = 0 on 3/10 targets, whereas antagonist direction accuracy DA(d⋆= −1) = 1.00 remains intact.Residual per-target variance is concentrated on targets where agonist generation fails, consistent with the reported agonist/antagonist asymmetry.

C.3 Ablation Studies … Algorithm 2 Sampling Directional Allosteric Binders

TD3B’s training-time innovations improve gated reward over TR2-D2, while Algorithm 2 adds inference-time weighted resampling to bias generated binders toward a desired direction. Algorithms 1 and 2 combine direction-oracle scoring, weighted replay-buffer fine-tuning, and categorical resampling.

  • C.3 Ablation Studies: 26.5% improvement in gated reward over TR2-D2 came from TD3B’s training-time changes alone without resampling, reaching 4.25 vs. 3.36.The comparison used a 3-seed evaluation and reported p=0.0078 with Welch’s t-test.
  • C.3 Ablation Studies: Table 6 decomposes TD3B’s training-time innovations from inference-time weighted resampling by applying the same resampling procedure to TR2-D2.The two axes are gated reward, contrastive loss, and KL-regularized fine-tuning during training, plus weighted resampling during inference.
  • Algorithm 1 Direction-Only Amortized Fine-Tuning of an MDLM: Algorithm 1 initializes a pre-trained MDLM, a directional dataset, a direction oracle, and an empty replay buffer before iterative fine-tuning.Its hyperparameters include learning rate η, temperature α, contrastive weight λ_ctr, and KL weight λ_reg.
  • Algorithm 1 Direction-Only Amortized Fine-Tuning of an MDLM: Algorithm 1 computes direction labels and weights, updates the oracle using L_dir, and populates the replay buffer with direction-aligned candidate samples.Candidate importance weights are proportional to exp(S(ỹ_k)/α), where S(ỹ_k) is the oracle-based direction score.
  • Algorithm 1 Direction-Only Amortized Fine-Tuning of an MDLM: Algorithm 1 fine-tunes the MDLM with weighted direction-conditioned and contrastive objectives plus KL regularization, returning a fine-tuned generator and oracle.The regularization term is L_reg(θ) = KL(p_θ∥p_θ0).
  • Algorithm 2 Sampling Directional Allosteric Binders: Algorithm 2 samples M candidate binders independently from the fine-tuned MDLM and scores each using the desired direction and the fine-tuned oracle.For candidate y_m, the score is S(y_m) = d⋆·f_ϕ⋆(y_m).
  • Algorithm 2 Sampling Directional Allosteric Binders: Algorithm 2 assigns weights proportional to exp(S(y_m)), resamples categorically, and returns a directionally biased binder.The desired direction d⋆ is either +1 or −1.
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