Edge-specific signal propagation on mature chromophore-region 3D mechanism graphs for fluorescent protein quantum-yield prediction Yuchen Xiong1 , Swee Keong Yeap1,∗ and Steven Aw Yoong Kit1,∗ 1 China-ASEAN College of Marine Sciences, Xiamen University Malaysia,
Sepang 43900, Selangor, Malaysia ∗ Correspondence: Swee Keong Yeap, [email protected];
arXiv:2605.06644v1 [cs.LG] 7 May 2026
Steven Aw Yoong Kit, [email protected].
Abstract
physical determinant is not merely which residues are present, but how the mature chromophore is constrained, polarised and shielded by its local three-dimensional environment.
Motivation: Fluorescent protein quantum yield (QY) is controlled by the mature chromophore and its three-dimensional microenvironment, not by sequence identity alone. Generic protein language models and coarse emission-band averages can capture some global trends, but they do not explicitly model how local physical signals act on specific chromophore regions. Results: We present a chromophore-centred mechanism graph algorithm for QY prediction. The method converts each PDB structure into a typed 3D residue graph, applies lightweight mature-state chromophore registration, partitions the chromophore into phenolate, bridge and imidazolinone regions, and propagates physicochemical residue signals through activated contact channels. The resulting representation contains 121 chromophore-centred enrichment features, from which a 52-feature non-identity pool is retained before band-specific ExtraTrees regression. Because each feature is defined by a channel–signal–region tuple, the interpretation is built into the representation rather than added only post hoc. On a 531-protein benchmark, the method achieved the best random cross-validation performance among the primary modelbased baselines (𝑅 = 0.772±0.008, MAE = 0.131±0.002), exceeding Band mean (𝑅 = 0.632), ESM-C (𝑅 = 0.734) and SaProt (𝑅 = 0.731). The method also ranked first on the most stringent random brightscreening task (Bright P@5 = 0.704). Under homology-controlled evaluation, its advantage was clearest in the most remote bucket (< 50% similarity; 𝑅 = 0.697 versus 0.633, 0.575 and 0.408 for Band mean, SaProt and ESM-C, respectively), with the strongest overall bright/dark Top-K screening in that regime. Stable selected features formed interpretable band-specific motifs: GFP-like models emphasised aromatic bridge/imidazolinone and clamp asymmetry terms, Red models emphasised charge and clamp balance, and Far-red models emphasised flexibility-risk and bulky-contact features. Availability and implementation: Source code, processed feature tables and evaluation scripts are available from the first author upon reasonable request. Contact: [email protected]
This creates a mismatch between many predictive baselines and the underlying photophysics. Sequence-similarity methods can perform well when labelled close homologues are available, but they offer little extrapolative or mechanistic value. Generic protein language models (PLMs) encode broad evolutionary and structural information, yet they are not designed around the mature chromophore. Band-level averages capture coarse emission-class differences but ignore within-band microenvironmental variation. A related lesson has emerged from graph-based AI for drug discovery: molecular function is often better predicted when the biochemical environment and interaction context are represented explicitly. Environment-aware graph models for protein–ligand affinity, such as EM-PLA, improve binding-affinity prediction by incorporating biochemical environmental information and non-covalent interaction structure [24]. Interpretable network-medicine models, such as iDPath and GraphSynergy, further show that graph models can be designed not only to predict outcomes but also to expose mechanism paths, pivotal proteins or contribution patterns [25, 26]. These ideas motivate an analogous question in fluorescent-protein engineering: can QY be predicted from a local molecular environment graph around the mature chromophore, while retaining a mechanism-level explanation of which chromophore-region interactions drive brightness or darkness? Here we introduce a structure-derived, environment-aware mechanism graph algorithm built around four design choices. First, the model moves from sequence identity to a typed 3D residue graph. Second, it performs mature-state chromophore registration so downstream features are anchored to the chemically relevant fluorescent core. Third, it partitions the mature chromophore into phenolate, bridge and imidazolinone regions. Fourth, it propagates physicochemical residue signals through robust contact channels to these regions. These steps produce features that are not generic embeddings; they are explicit measurements of how steric locking, hydrophobic packing, chargerelated, hydrogen-bond-capable, aromatic and flexibility-related signals are enriched around functional chromophore regions.
1. Introduction Fluorescent proteins (FPs) are central tools for live-cell imaging, biosensing and protein engineering. Their practical usefulness depends strongly on quantum yield (QY), which measures the efficiency with which absorbed photons are converted into emitted fluorescence. QY is difficult to infer from sequence because the 1
In this sense, the method treats brightness prediction as local molecular-environment reasoning around a functional chemical centre rather than as direct sequence-to-property regression. We evaluate the method against three primary model-based baselines: Band mean, ESM-C and SaProt. The method improves random-CV regression, remains competitive across intermediate homology regimes and becomes strongest in the most difficult remote-homology evaluation. More importantly, its selected features reveal coherent chromophore-region mechanisms that are inaccessible to the baseline models and align with known photophysical themes such as chromophore rigidification, electrostatic tuning and torsional-relaxation suppression. The resulting interpretation is intrinsic to the representation: selected features correspond to concrete channel–signal–region paths, rather than to post-hoc explanations attached after prediction.
feature anchor to the mature CRO state and supports region definition, but it is not intended as a quantum-chemical simulation of chromophore formation. 2.3 Algorithmic novelty The proposed method is not a generic residue-level featurisation followed by regression. Its novelty lies in making the functional chemical centre of the protein explicit. First, all structural measurements are anchored to a mature-state chromophore reference rather than to arbitrary sequence positions. Second, the chromophore is decomposed into phenolate, bridge and imidazolinone regions, so the model can distinguish electrostatic stabilisation of the phenolate from bridge rigidity or imidazolinone packing. Third, residue properties are propagated as channel–signal–region tuples: the activated channel defines the physical contact path, the seed signal defines the physicochemical quantity being transmitted, and the target region defines where that signal acts on the chromophore. Fourth, direct residue-identity shortcuts are removed before model fitting, forcing the predictor to rely on transferable local-environment descriptors rather than memorising amino-acid labels. This design makes the selected features mechanistic by construction: a feature such as a charge-related signal reaching the phenolate region through a steric-lock path has a direct physical interpretation before any post-hoc explanation is applied.
2. Materials and methods 2.1 Dataset and evaluation design The benchmark contained 531 fluorescent proteins with measured QY and emission maxima curated from FPbase. Input structures were taken from the Protein Data Bank when available and otherwise generated using OpenFold3-predicted models [17, 18, 19]. Proteins were assigned to three emission bands: GFP-like (500–560 nm), Red (580–610 nm) and Far-red (≥ 610 nm). These bands were used for stratified modelling because different chromophore classes can have distinct QY determinants. Two evaluation protocols were used. Random evaluation used five seeds and five folds per seed, with out-of-fold predictions pooled for regression metrics. Homology-controlled evaluation reported performance in three increasingly difficult similarity buckets: 70–85%, 50–70% and < 50%, defined from sequencesimilarity searches computed with MMseqs2 [23]. Bright and dark Top-K metrics used training-fold thresholds only, so the held-out fold did not influence the definition of bright or dark candidates. The primary baselines were Band mean, ESM-C and SaProt [20, 21]. A nearest-neighbour retrieval baseline was not used as a primary comparator because it is a database lookup strategy rather than a transferable model of QY determinants, and it can obscure the intended comparison between generic representations and chromophore-centred mechanism features.
2.4 Mathematical formulation For protein 𝑖, the predictor is a composition of graph construction, state transformation, propagation and regression: A : (PDB𝑖 , em𝑖 ) ↦→ 𝑦ˆ 𝑖 ,
(1)
where PDB𝑖 is the input structure, em𝑖 is the emission maximum and 𝑦ˆ 𝑖 is predicted QY. Typed 3D mechanism graph. The structure is converted into a typed residue graph 𝐺 𝑖 = (𝑉𝑖 , {𝐸 𝑖( 𝜏 ) } 𝜏 ∈ Tcand , 𝑋𝑖 , 𝑊𝑖 ),
(2)
where 𝑉𝑖 = {𝑣 1 , . . . , 𝑣 𝑛𝑖 } is the residue-node set, 𝑋𝑖 ∈ R𝑛𝑖 × 𝑝 stores physicochemical attributes, 𝐸 𝑖( 𝜏 ) is the edge set for candidate interaction type 𝜏 and 𝑊𝑖( 𝜏 ) stores edge weights. We distinguish candidate physical edge annotations from the propagation channels used for prediction. The candidate annotation set is Tcand = {spatial, steric, hydrophobic, (3) hbond, electrostatic, aromatic}.
2.2 Algorithm overview The complete algorithm maps a protein structure and emission maximum to a QY prediction through structure parsing, typed graph construction, mature chromophore registration, regional decomposition, edge-specific signal propagation, non-identity feature filtering and band-specific regression (Fig. 1). In this benchmark, the structural inputs include OpenFold3-predicted models, so the activated propagation channels are restricted to geometry-robust steric and hydrophobic contacts. The maturation component is intentionally lightweight: it standardises the
For the OpenFold3-predicted structures used in this benchmark, the activated propagation channels are Ton = {steric, hydrophobic}.
(4)
Thus, an annotated edge records a possible physical relation between residues, whereas an activated channel defines the graph path actually used for signal propagation. 2
Edge-specific propagation on mature chromophore-region 3D mechanism graphs
1. PDB structure residue coordinates local geometry
2. Typed 3D graph
3. Mature CRO state
residue nodes steric / charge / H-bond / aromatic edges
5. Edge-specific propagation
lightweight mature-state registration of X--Tyr--Gly
6. Mechanistic feature pool
19 residuesignals ×2channels×3CROregions = 114 enrichment features
4. CRO regions phenolate bridge imidazolinone
7. Band-specific learning GFP-like / Red / Far-red training-fold feature selection
7 clampdescriptors 52 non-identity edge features
8. Outputs QY regression bright/dark Top-K mechanistic motifs
Typed signals steric
charge
H-bond
aromatic
hydrophob.
clamp
Core algorithmic innovations 1. 3Dmechanismgraphrather than residue identity 2. Mature-state chromophore registration 3. Phenolate / bridge / imidazolinone partition 4. Edge-type-specific signal propagation
Fig. 1: Clean overview of the proposed algorithm. A PDB structure is converted into a typed 3D residue graph, registered to a mature chromophore state, partitioned into functional CRO regions, transformed by edge-specific signal propagation, filtered to remove identity shortcuts and routed to a band-specific predictor.
Mature-state chromophore registration. cursor is represented as
The immature pre-
𝑐 𝑖(0) = triad(𝑋 −Tyr−Gly),
and hydrophobicity. In the present OpenFold3-based implementation, signal propagation is restricted to the two structurally robust channels Ton = {steric, hydrophobic}. Hydrogen-bond, electrostatic and proton-transfer propagation channels are not activated because the input OpenFold3-predicted PDB structures do not provide hydrogen atoms, ordered water networks or sufficiently reliable local electrostatic field geometry. These channels are therefore treated as reserved physical channels that can be reactivated for X-ray structures or MD ensembles. For activated channel 𝜏 ∈ Ton and CRO region 𝑟, residue 𝑢 receives the graph-decay weight
(5)
and the mature chromophore state is obtained by a rule-based transition 𝑐 𝑖(𝑡+1) = R 𝑐 𝑖(𝑡 ) , 𝐺 𝑖 , 𝑐∗𝑖 = 𝑐 𝑖(𝑇 ) = CRO𝑖 . (6) Here R denotes the implemented cyclization, oxidation and dehydration registration rules. In this work, the purpose of R is to define a consistent mature CRO anchor for graph features.
𝐾 𝜏 (𝑢, 𝑟) = exp[−𝜆 𝜏 𝑑 𝜏 (𝑢, 𝑟)] 𝜓 𝜏 (𝑢, 𝑟),
CRO regional decomposition. The mature chromophore is decomposed into disjoint functional regions, phenolate
CRO𝑖 = 𝐶𝑖
bridge ∪¤ 𝐶𝑖 ∪¤ 𝐶𝑖imidazolinone ,
where 𝑑 𝜏 (𝑢, 𝑟) is the typed-graph distance from 𝑢 to region 𝑟, 𝜆 𝜏 is the channel-specific decay term and 𝜓 𝜏 (𝑢, 𝑟) represents edge-compatibility along the mechanism path. The enrichment of seed 𝑎 through channel 𝜏 into region 𝑟 is
(7)
with R CRO = {phenolate, bridge, imidazolinone}. This partition lets the model distinguish phenolate electrostatic stabilisation from bridge rigidity or imidazolinone packing.
Í 𝐹𝑎, 𝜏,𝑟 (𝐺 𝑖 ) = Í
𝑢∈𝑉𝑖 \CRO𝑖 𝑠𝑢𝑎 𝐾 𝜏 (𝑢, 𝑟)
𝑢∈𝑉𝑖 \CRO𝑖 𝐾 𝜏 (𝑢, 𝑟) + 𝜀
.
(10)
With 19 seed signals, two activated propagation channels and three CRO regions, 19 × 2 × 3 = 114 enrichment features are produced. Seven chromophore-clamp descriptors are appended,
Edge-specific signal propagation. Each non-chromophore residue 𝑢 emits a 19-dimensional seed vector 𝑠𝑢 = (𝑠𝑢1 , 𝑠𝑢2 , . . . , 𝑠𝑢,19 ) ∈ R19 ,
(9)
(8)
h 𝜙𝑖 = {𝐹𝑎, 𝜏,𝑟 (𝐺 𝑖 ) : 𝑎 = 1, . . . , 19,
covering steric bulk, flexibility risk, rotatable-bond burden, charge, hydrogen-bond donor/acceptor capacity, aromaticity
i 𝜏 ∈ Ton , 𝑟 ∈ R CRO }, 𝜅𝑖(1) , . . . , 𝜅 𝑖(7) ∈ R121 . 3
(11)
Non-identity feature pool. The final mechanism feature pool is " ! # Ø FnonID = F𝑚 ∪ Fclamp \ Fidentity , (12)
Table 1: Core algorithmic modules and their implementation in the proposed method.
𝑚∈ M
where M includes steric, hydrophobic, charge-related, hydrogen-bond-capable, aromatic and solvent-related seedsignal families. The set Fidentity removes direct residue-identity shortcuts, including is_Tyr, is_Phe and is_His. The implementation retains |FnonID | = 52 features; the 121-to-52 filtering logic is detailed in Table 4.
Module
Implementation detail
Typed 3D graph
Residue nodes with candidate spatial, steric, hydrophobic, hydrogen-bond, electrostatic and aromatic annotations. Rule-based transition from X–Tyr–Gly precursor to a mature-state CRO anchor for downstream geometry. Separate phenolate, bridge and imidazolinone target regions. Channel–signal–region propagation: 19 residue signals are transmitted through two OpenFold3-robust activated channels, steric and hydrophobic, into three CRO regions. 52 edge/clamp-geometry features after removing direct amino-acid identity shortcuts. Training-fold-only feature selection and per-band ExtraTrees regression.
Mature CRO registration CRO partition Signal propagation
Band-specific selection and prediction. Band assignment is deterministic: GFP-like, 𝑏 𝑖 = Red, Far-red,
500 ≤ em𝑖 < 560, 580 ≤ em𝑖 < 610, em𝑖 ≥ 610.
Non-identity pool
(13)
Band model
Within each training fold and band 𝑏, features are ranked by 𝜌 𝑗,𝑏 = corr 𝜙 · 𝑗 , 𝑦 , (14)
Direct residue-identity strings are removed after candidate construction, so aromatic or hydrophobic features are retained only when they represent physicochemical signal classes rather than amino-acid labels. This channel–signal design gives the algorithm a useful inductive bias. A charge-related seed propagated through a steric-lock path to the phenolate region is not treated as equivalent to a rotatable-bond burden propagated through a hydrophobic-contact path to the bridge region, even if both residues are close in Euclidean distance. Instead, the feature name encodes a mechanism tuple,
and the selected set is 𝑆 𝑏 = TopK 𝑗 ∈ FnonID (𝜌 𝑗,𝑏 ),
𝐾 = 25.
(15)
The prediction is routed through the corresponding band model: 𝑦ˆ 𝑖 = 𝑓𝑏𝑖 𝜙𝑖,𝑆𝑏𝑖 , (16) where 𝑓𝑏 is the ExtraTrees regressor for band 𝑏 [5, 22]. Top-K screening. Training-fold quantiles define bright and dark labels,
feature = (channel, seed signal, CRO region),
𝑞 90 = 𝑄 0.90 (𝑦 train ),
𝑞 10 = 𝑄 0.10 (𝑦 train ),
(17)
𝐵𝑖 = I[𝑦 𝑖 ≥ 𝑞 90 ],
𝐷 𝑖 = I[𝑦 𝑖 ≤ 𝑞 10 ].
(18)
which is why the selected features can later be interpreted as concrete mechanistic motifs.
For the 𝐾 largest and smallest predictions, denoted TopK+ ( 𝑦ˆ ) and TopK − ( 𝑦ˆ ), the screening metrics are Bright P@K =
1 𝐾
1 Dark P@K = 𝐾
∑︁
𝐵𝑖 ,
(19)
𝐷𝑖 .
(20)
2.6 Leakage control and distributional diagnostics The random-CV experiment uses out-of-fold prediction throughout. For seed 𝑠, the QY values are first converted into quantile bins, 𝑧 𝑖 = qcut(𝑦 𝑖 , 𝑄), 𝑄 = min(5, ⌊𝑛/5⌋), (22)
𝑖 ∈TopK+ ( 𝑦) ˆ
∑︁
(21)
𝑖 ∈TopK − ( 𝑦) ˆ
and stratified folds are built from 𝑧𝑖 . Feature selection, bandspecific model fitting and bright/dark thresholds are recomputed inside each training fold only. Thus, the held-out fold does not influence the selected feature set, the fitted regressor or the Top-K threshold. We additionally monitor prediction compression,
2.5 Edge-family construction and implementation details The feature construction is not a generic graph featurisation step. It is organised by physically distinct propagation channels and seed-signal families. In the present OpenFold3-based setting, steric and hydrophobic contact channels are activated because their geometric definitions are robust to the absence of hydrogens and explicit solvent. Within these channels, the seed signals still encode bulky contacts, flexibility risk, rotatablebond burden, charge-related side-chain properties, hydrogenbond donor/acceptor capacity, aromaticity and hydrophobicity.
𝐶=
sd( 𝑦ˆ ) , sd(𝑦)
(23)
where values much smaller than one indicate collapse toward the mean. This diagnostic is useful for QY prediction because a model that only predicts mid-range QY may have tolerable MAE but poor value for bright/dark candidate discovery. 4
Table 2: Random-CV regression performance. Means for the proposed method are reported across five seeds; baseline values are averaged across random-seed runs.
Method Band mean ESM-C SaProt Mechanism graph
Random 𝑅 0.632 ± 0.002 0.734 ± 0.005 0.731 ± 0.002 0.772 ± 0.008
Table 3: Pearson correlation under homology-controlled evaluation.
Method Band mean ESM-C SaProt Mechanism graph
Random MAE 0.167 ± 0.000 0.143 ± 0.001 0.146 ± 0.000 0.131 ± 0.002
70–85% 0.643 0.672 0.701 0.756
50–70% 0.830 0.626 0.714 0.824
<50% 0.633 0.408 0.575 0.697
Prediction strength across random and homology-controlled regimes Band mean
ESM-C
SaProt
Mechanism graph
0.830 0.824
0.8
3. Results
0.772 0.734 0.731
0.7
Pearson R
The evaluation was designed to test whether chromophorecentred environment features improve both prediction and mechanism-level interpretation. We therefore report randomCV regression, homology-controlled generalisation, bright/dark Top-K screening and the stability of selected channel–signal– region features.
0.632
strongest under remote homology
0.756 0.701 0.672 0.643
0.714 0.626
0.6
0.697 0.633 0.575
0.5 0.408
0.4 Random
70-85
50-70
<50
Fig. 2: Prediction strength across random and homology-controlled regimes. The mechanism graph model is best under random CV and strongest in the most remote-homology bucket.
3.1 Random-CV QY prediction Under random cross-validation, the mechanism graph model achieved the strongest primary model-based performance (Table 2; Fig. 2). Its mean Pearson correlation was 𝑅 = 0.772±0.008, compared with 𝑅 = 0.734 for ESM-C, 𝑅 = 0.731 for SaProt and 𝑅 = 0.632 for Band mean. It also had the lowest MAE (0.131 ± 0.002), indicating that chromophore-centred mechanism features improve both ranking and absolute regression error. The same pattern appeared in candidate screening. The proposed method ranked first in the most stringent bright-screening setting, with Bright P@5 of 0.704 versus 0.680 for ESM-C, 0.640 for SaProt and 0.160 for Band mean. For Dark P@5, it reached 0.536, exceeding ESM-C (0.507), SaProt (0.453) and Band mean (0.227). At larger K, PLM baselines remained competitive on bright retrieval, but the mechanism graph model stayed in the strongest tier while retaining interpretability.
labelled neighbours. In the < 50% similarity bucket, the proposed method produced the best bright precision at 𝐾 = 10, 15, 20 and 25, and the best dark precision at all tested 𝐾 values from 5 to 25 (Fig. 3). For example, Dark P@10 reached 0.533, compared with 0.400 for Band mean, 0.300 for ESM-C and 0.200 for SaProt. Bright P@15 reached 0.333, compared with 0.133 for Band mean, 0.133 for ESM-C and 0.200 for SaProt. Thus, the method is not only a stronger remote-homology regressor but also a useful screening tool. 3.4 Stable selected features expose band-specific mechanism signatures The feature-stability map is central to the interpretability claim and is therefore retained as a main-text figure (Fig. 4). Each point corresponds to a concrete selected feature, not to a posthoc attribution score. Bubble size indicates how often that feature appeared among the top-10 selected features across five seeds and five folds. The resulting patterns are biologically coherent and consistent with known fluorescent-protein photophysics. GFP-like models repeatedly selected hydrophobic/aromatic and steric/aromatic signals into the bridge and imidazolinone regions, together with clamp asymmetry. This agrees with structural and chromophoremodel studies showing that tight packing, aromatic interactions and restriction of chromophore torsion suppress non-radiative decay in GFP-like scaffolds [9, 10, 11]. Red models repeatedly selected charge signals to phenolate, bridge and imidazolinone regions, as well as rotatable-burden features around the bridge and imidazolinone. This is consistent with studies of red fluorescent proteins in which local electric fields, hydrogen-bond/electrostatic interactions and chromophore planarity control non-radiative relaxation and QY [12, 13]. Far-red models were dominated by flex-risk and bulky-contact features, especially around bridge and imidazolinone regions. This
3.2 Homology-controlled generalisation Homology-controlled evaluation showed the most important behaviour of the algorithm (Table 3; Fig. 2). In the 70–85% bucket, the method reached 𝑅 = 0.756, outperforming Band mean (0.643), ESM-C (0.672) and SaProt (0.701). In the 50–70% bucket, it reached 𝑅 = 0.824, essentially matching Band mean (0.830) while clearly exceeding ESM-C (0.626) and SaProt (0.714). In the most remote bucket (< 50%), it was clearly strongest with 𝑅 = 0.697, compared with 0.633 for Band mean, 0.575 for SaProt and 0.408 for ESM-C. This pattern is important because remote-homology prediction is the regime most relevant to novel FP design. When sequence similarity is low, generic representations degrade more sharply, whereas chromophore-region mechanism features remain comparatively transferable. 3.3 Remote-homology Top-K screening Candidate prioritisation under remote homology is a practical test for FP engineering because novel designs often lack close 5
Top-K retrieval frontiers for bright and dark protein prioritisation Band mean
ESM-C
SaProt
Bright Precision@K
Random CV
Mechanism graph
Remote homology (<50%)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 5
10
5
10
K
20
5
10
15
20
25
20
5
10
15
20
25
K
Dark Precision@K
0.6 0.5 0.4 0.3 0.2 0.1
K K Fig. 3: Top-K retrieval frontiers for bright and dark proteins. Left: random CV. Right: remote-homology bucket (< 50% similarity). The mechanism graph model provides the strongest overall screening behaviour in the remote-homology setting.
matches crystallographic and photophysical work on far-red proteins showing that chromophore isomerization, planarity and steric restriction of torsional relaxation are central to far-red fluorescence [15, 16, 12]. Thus, the stable selected features are not arbitrary correlates: they recover known physical themes in a band-specific manner.
propagation separates the activated physical contact channel from the physicochemical seed signal, so that steric-lock and hydrophobic-contact paths can carry distinct charge-related, hydrogen-bond-capable, aromatic, flexibility-risk and bulkycontact information. Fifth, the non-identity feature pool removes direct amino-acid shortcuts, making the learned inputs closer to transferable physical descriptors than to sequence-family tags. The restored feature-stability map is especially important because it connects the algorithm to interpretable photophysical hypotheses already suggested by structural and spectroscopic studies of fluorescent proteins. GFP-like proteins emphasise aromatic packing into bridge and imidazolinone regions, consistent with chromophore rigidification and suppression of torsional non-radiative decay. Red proteins emphasise charge and rotatable burden around all chromophore regions, consistent with electric-field and chromophore-planarity mechanisms. Far-red proteins emphasise flex-risk and bulky contacts, consistent with the importance of steric restriction and chromophore isomerization in far-red fluorescence. These patterns are not merely decorative explanations after prediction. They are the actual feature families repeatedly selected inside training folds. The maturation component should be interpreted carefully. It is valuable because it gives a consistent mature-CRO anchor for feature extraction, but the current implementation is rulebased and lightweight rather than a detailed chemical kinetics or quantum-chemical simulation. Future work could replace
4. Discussion The proposed algorithm was designed around the idea that QY should be predicted as a local chromophore-environment problem rather than as ordinary sequence-to-property regression. The results support this premise. The method improves randomCV regression over Band mean, ESM-C and SaProt, and its strongest advantage appears under remote-homology evaluation, where labelled neighbours and generic embeddings are less reliable. Several algorithmic details are essential and should not be reduced to ordinary feature engineering. First, the typed 3D graph changes the prediction problem from residue-identity lookup to propagation over physical interaction channels. Second, mature-state chromophore registration gives a consistent chemical anchor for all downstream geometric features. Third, CRO regional decomposition prevents the model from averaging phenolate, bridge and imidazolinone effects into a single undifferentiated neighbourhood descriptor. Fourth, edge-specific 6
Stable selected features reveal band-specific mechanism signatures hydrophobic aromatic bridge
25/25
1/25
rotatable burden bridge
1/25
25/25
steric aromatic bridge
23/25
rotatable burden imidaz.
6/25
clamp asymmetry
23/25
steric charge phenolate
3/25
25/25
6/25
hydrophobic aromatic imidaz.
25/25
3/25
6/25
steric aromatic imidaz.
25/25
2/25 2/25
25/25
4/25 4/25
Feature family (not propagation channel)
7/25
steric charge bridge
25/25
14/25
steric charge imidaz.
25/25
20/25
steric bulky imidaz.
aromatic charge-related steric/flex hydrophobic clamp
22/25
hydrophobic flex-risk phenolate
4/25
25/25
steric flex-risk imidaz.
1/25
25/25
steric flex-risk bridge
4/25
25/25
steric flex-risk phenolate
21/25
25/25
GFP-like
Red
Far-red
Bubble area is proportional to recurrence among top-10 selected features across 5 seeds × 5 folds. Fig. 4: Stable selected features across seeds and folds. Bubble area is proportional to recurrence among top-10 selected features across five seeds and five folds. Colours denote feature families, not propagation channels. The activated propagation channels are steric and hydrophobic; feature families describe the physicochemical seed signal or clamp descriptor carried by those channels. The label clamp asymmetry denotes the local chromophore-clamp asymmetry feature after removing implementation-specific residue numbering.
or augment this step with more explicit chemical-state modelling, learned propagation kernels, uncertainty-aware structural ensembles, or reactivated hydrogen-bond/electrostatic/protontransfer channels when experimental structures or MD trajectories provide hydrogen atoms, ordered water networks and reliable local electrostatic geometry. This conservative description is important: the novelty here is not a complete reaction simulator, but a graph-learning framework that uses a mature chromophore reference state to define region-specific signal propagation. For FP engineering, the main value of the method is the combination of predictive performance, remote-homology transfer and interpretable mechanism signatures. It can prioritise bright candidates, identify likely dark proteins and report which chromophore-region interactions drive the prediction. That combination makes it complementary to generic PLM baselines and well suited to design settings in which mechanistic guidance matters.
7
A. Implementation details of channel–signal–region features A.1 Activated channels and reserved channels The implementation separates candidate physical annotations from activated propagation channels. Candidate annotations can include spatial proximity, steric contact, hydrophobic contact, hydrogen-bond-related geometry, electrostatic relation and aromatic contact. However, the OpenFold3-predicted PDB structures used in this benchmark do not provide hydrogen atoms, explicit water molecules or reliable local electrostatic field geometry. Therefore, only the two geometry-robust contact channels are activated for propagation: Ton = {steric, hydrophobic}. (24) Hydrogen-bond, electrostatic and proton-transfer channels are treated as reserved physical channels. They are not discarded conceptually; rather, they are not activated in the present benchmark because their reliable use would require experimental structures with hydrogens, explicit solvent, protonation-state assignment or MD ensembles. A.2 Seed-signal families Each residue emits physicochemical seed signals, and these signals are grouped into six interpretable families before the non-identity feature pool is constructed: M = {steric, hydrophobic, charge, hbond, aromatic, solvent}. (25) The important distinction is that these are seed-signal families, not necessarily independent propagation channels. For example, a charge-related seed can be propagated through a steric-lock path or through a hydrophobic-contact path, producing different channel–signal–region features. This is why the representation can retain charge-related, hydrogen-bond-capable and aromatic information even though only steric and hydrophobic contact channels are activated in the OpenFold3-based setting. A.3 Feature counting and non-identity filtering The full chromophore-centred representation contains 121 candidate features. These consist of 57 steric-channel enrichment features, 57 hydrophobic-channel enrichment features and seven local chromophore-clamp descriptors: (19 × 3)steric + (19 × 3)hydrophobic + 7clamp = 121.
(26)
Here the factor 19 denotes residue seed signals and the factor 3 denotes the phenolate, bridge and imidazolinone CRO regions. The reduction from 121 to 52 features is performed in two steps. First, the implementation keeps only seed signals assigned to six physicochemical signal families plus the local chromophore-clamp descriptors. This family mapping covers 73 columns: 66family enrichment + 7clamp = 73.
(27)
The remaining 48 enrichment columns are not used because they are either direct residue-identity signals outside the retained families or auxiliary signals not included in the final mechanism pool. Second, direct amino-acid identity shortcuts within the 73-column family pool are removed. These include aromatic-family is_PHE, is_TYR and is_HIS features in both activated channels, and solvent-family is_ALA features in the hydrophobic channel: 73 − 21 = 52.
(28)
The final non-identity pool therefore contains 45 enrichment features and seven clamp descriptors: 52 = 45nonID enrichment + 7clamp .
(29)
Table 4: Composition of the final 52-feature non-identity pool. Each number in parentheses counts the three CRO regions unless otherwise noted. Family
Steric channel
Hydrophobic channel
Steric Hydrophobic Charge-related H-bond-capable Aromatic Solvent-related Clamp
bulky, flex-risk, rotatable-bond burden (9) – charge (3) donor, acceptor (6) aromatic signal (3) – local bridge/phenolate/imidazolinone/asymmetry descriptors (7)
– hydrophobic, bulky contact (6) charge (3) donor, acceptor (6) aromatic signal (3) flex-risk, total contact burden (6) –
Total
Total 9 6 6 12 6 6 7 52
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A.4 Intrinsic interpretation The model interpretation is intrinsic to the representation. Each selected feature is already a mechanism tuple, feature = (channel, seed signal, CRO region),
(30)
rather than an attribution score assigned after model fitting. Thus, stable selected features directly identify which physical signal reaches which chromophore region through which activated contact path. This is the basis for interpreting GFP-like models as aromatic-packing dominated, Red models as charge/rotatable-burden dominated and Far-red models as flex-risk/bulky-contact dominated.
Funding This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.
Acknowledgements The authors thank the maintainers of FPbase and the Protein Data Bank for making fluorescent-protein metadata and structural resources publicly available, and the developers of OpenFold3, MMseqs2, ESM-C, SaProt and scikit-learn for releasing the tools used in this study.
Acknowledgements Funding: This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.
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