Generative design of intrinsically disordered protein regions with IDiom

Intrinsically disordered protein regions are ubiquitous across all kingdoms of life. These structurally heterogeneous regions play central roles in cellular processes such as transcriptional regulation, cellular signaling, and subcellular organization, yet they have remained largely inac- cessible to rational design. Structure-based generative methods are not applicable to proteins that lack a stable fold, and existing sequence-based approaches for disordered regions rely on sampling methods that do not capture the evolutionary statistics of natural disordered regions. Here, we introduce IDiom, an autoregressive protein language model trained on 37 million in- trinsically disordered region sequences curated from the AlphaFold Database. Trained using a fill-in-the-middle data augmentation, IDiom generates disordered region sequences conditioned on their surrounding structured context, as well as fully disordered proteins without any con- text. The model generates diverse sequences that recapitulate biologically relevant sequence features of natural disordered regions, and we demonstrate that post-training via reinforcement learning with a subcellular localization reward model produces sequences with features which are consistent with known sequence determinants of compartment-specific localization. These

establish IDiom as a general platform for the generative design of intrinsically disordered proteins and regions.

Intrinsically disordered protein regions are ubiquitous across all kingdoms of life. The functional relevance of intrinsically disordered regions (IDRs) has become increasingly clear recently, in spite of the classical dogma of protein biology that structure implies function [ 1]. While IDRs do not adopt well-defined folds, these sequences can act as flexible linkers [2], multivalent signaling hubs †These authors contributed equally. Code is available on GitHub. Data is available on HuggingFace. ∗Correspondence: [email protected], [email protected] 1 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [3], and drivers of biomolecular condensate formation [4, 5, 6], playing crucial roles in biological processes such as transcriptional regulation, chromatin organization, and subcellular organization [1, 7]. Rational design of IDRs would unlock new functional controls in bioengineering, including tunable condensate phase behavior, precise regulation of cell signaling, and targeted protein lo- calization [8]. While much of the recent progress in protein design has been driven by accurate structure prediction [9, 10] and diffusion-based generative models [11, 12, 13], direct application of these approaches to IDRs is untenable due to their lack of a stable folded structure. Sequence-based generative models have also been extensively explored recently for applications in protein design. Transformer-based [14] protein language models (PLMs) have been trained on corpora of full length protein sequences from databases such as the UniProt Reference Clusters and the Big Fantastic Database. These models learn rich evolutionary statistics over amino acid se- quences and have enabled the design of novel proteins and functional variants [ 15, 16, 17, 18, 19, 20]. Nevertheless, the design of intrinsically disordered regions with existing PLMs is not straight- forward: since structured domains outnumber intrinsically disordered regions in the sequence databases on which current PLMs are trained, the generative prior is largely biased towards folded domains [ 15]. Alternative sequence-based approaches to IDR design have attempted to use sampling-based methods to construct IDRs from compositional rules or simple statistical mod- els [ 21, 22, 23, 24]. However, these approaches cannot be conditioned on any surrounding sequence context of generated IDRs, and they do not capture the evolutionary statistics which emerge from training on large corpora of natural protein sequences. Here, we address this gap by training a 122M parameter autoregressive, decoder-only protein language model called IDiom using a dataset of 37 million intrinsically disordered regions curated from the AlphaFold Database (Figure 1a) [25, 26]. We apply a fill-in-the-middle transformation to the training data [27, 28] to enable the model to generate IDR spans conditioned on their surrounding context, a capability essential for the design of disordered regions [8]. Training on this dataset of disordered sequences allows IDiom to learn a generative prior over the sequence statistics of natural disordered regions, and we demonstrate that the model generates diverse sequences that recapitulate the compositions, patterning, and motifs of natural intrinsically disordered regions. We further show that IDiom learns in-context: given the flanking sequence context of a specific protein, the model generates disordered spans whose sequence features are more appropriate for that context than unprompted generations. Finally, we demonstrate that IDiom can be post- trained using reinforcement learning, and we apply this to design disordered sequences with targeted subcellular localization [ 23]. Together, these results establish IDiom as a general platform for the generative design of intrinsically disordered proteins and regions.

Protein language modeling for intrinsically disordered proteins and regions To curate a dataset of intrinsically disordered region (IDR) sequences for model training, we first use AlphaFold2 (AF2) predicted structures from the AlphaFold Database (AFDB) [ 26] to identify IDRs of proteins. We use low AF2 predicted local distance difference test (pLDDT) values as a predictor of disorder, as this has been demonstrated to correlate strongly with experimental measurements of disorder [ 29, 30, 31]. To curate these IDRs from the database, we first cluster AFDB sequences at 90% sequence identity before applying a windowed pLDDT-based threshold to identify IDRs [ 32], with proteins containing multiple IDRs contributing multiple records to the dataset. Finally, we discard IDRs shorter than 30 residues, IDRs which reside in proteins whose full 2 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint 37M pLDDT-based IDRs from the AlphaFold Database Fill-in-the-middle transformation IDP data augmentation MEDS..LVAVEED..KGPSSVED..KSLME..VASV..SLVE..PS VEED..KGPS P(ai | a<i) M..AS..LED[ ] or MSTSN[ ] GeneratePretrain Reward(MSTSN..) Post-train Predict IDiom Wild-type NPM1 SYFA prompt generated IDR Unprompted generated IDP MSTSNLNLTDDN..FAPLAARPGTRS MRANRR..PAELTPITLM..EQFKGVL a b c d e g f Fig. 1: Data curation, training, and generative modeling of intrinsically disordered regions (IDRs) and proteins (IDPs) using IDiom. (a) Schematic depicting data preparation, pre-training, sequence generation, and post-training of IDiom. (b) Distribution of the sequence locations of 37M IDRs curated from the AlphaFold Database (AFDB), as well as the locations of experimentally validated DisProt IDRs. (c) AlphaFold2 (AF2)-predicted structures, amino acid sequences, and plots of predicted local distance difference test (pLDDT) values of an example IDR curated from AFDB (NPM1, upper), an IDR generated by IDiom using SYF A as the prompt (middle), and an unprompted generated IDP (lower). Blue and green regions correspond to the N-terminal and C-terminal flanking context around the IDR, which is orange. (d) Distribution of maximum sequence identities of unprompted generated IDPs and DisProt-prompt generated IDRs relative to the 37M IDRs of the training set, calculated using MMseqs2. (e) Distribution of sequence lengths of unprompted generated IDPs, DisProt-prompt generated IDRs, natural DisProt IDRs, and training set IDRs. (f) Relative enrichment of amino acid compositions of unprompted generated IDPs, DisProt- prompt generated IDRs, natural DisProt IDRs, and training set IDRs. The horizontal dashed line is the

composition of folded CATH domain sequences. (g) (Upper): AF2 prediction pLDDTs of generated unprompted IDPs, natural DisProt IDRs removed from their surrounding context (DisProt IDPs), training set IDRs removed from their surrounding context (train IDPs), and CATH domains. (Lower): AF2 prediction pLDDTs of DisProt-prompt generated IDRs, natural DisProt IDRs within their context, training set IDRs within their context, and CATH domains. length is greater than 512 residues, and proteins whose entire length is low-pLDDT. This process yields a dataset of 37M IDRs and their positions within their associated full length proteins (see

for more details). Figure 1c (upper) depicts an example low-pLDDT IDR, in orange, extracted by this process for the human protein NPM1 (UniProt: P06748). We use two baselines to validate our data curation strategy. First, we use 1,017 experimentally validated IDRs from the DisProt database as a ground-truth dataset of IDRs [ 33]. Second, we 3 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint use 1,000 randomly chosen sequences from the Class, Architecture, Topology, and Homologous superfamily (CATH) database clustered at 60% identity (S60) as a ground-truth dataset of protein domains with well-defined folded structures [34]. Using secondary structure content calculations, we show that this method extracts IDRs with substantially lower secondary structural content compared to CATH sequences (Figure S1). We note that our analysis shows that AF2 assigns high secondary structural content (with low confidence) to a fraction of the extracted IDRs, although this effect is also reflected in the set of DisProt IDRs. We additionally run orthogonal disorder predictions on a subset of the dataset and further validate that the curated sequences score similarly to DisProt sequences on these metrics (Figures S2, S3). Intrinsically disordered regions are naturally located at various locations within a protein se- quence, with approximately 45% of the AFDB-curated IDRs located at the N-terminus, 29% at the C-terminus, and 26% in between other regions of the protein; similar percentages are observed for experimentally validated IDRs from the DisProt set (Figure 1b). To enable IDiom to infill sequences of intrinsically disordered regions at arbitrary locations within a protein, we employ a fill-in-the-middle data transformation [ 27, 28]. In this approach, we prepend the special token to residues in the N-terminal flanking context before the IDR, the token to residues in the C-terminal context after the IDR, and the token to residues of the IDR span itself. Then, we transform the sequence by relocating and the IDR span to the end of the entire sequence, thus allowing the standard causal language modeling objective to generate IDR spans conditioned on any preceding N-terminal and succeeding C-terminal flanking context (see Figure 1a). In addition, to enable the generation of intrinsically disordered proteins (IDPs) with no surrounding context, we augment the dataset by creating records in which take each curated IDR and delete their N- and C-terminal flanking context, enabling unconditioned generation. The final dataset comprises 74M sequences in total (37M IDRs and 37M IDPs), which we use to pre-train IDiom. Additional details of the data augmentation, model architecture, and training procedure are provided in the

section. IDiom generates diverse disordered regions and proteins To characterize the pre-trained model, we first generate two sets of sequences: 100,000 unprompted IDPs (referred to as generated IDPs), and a set of context-prompted IDRs in which 100 IDRs are generated for each of 1,017 experimentally validated IDRs from the DisProt set, using the IDR flanking contexts as prompts (referred to as generated IDRs). Representative examples of a DisProt context-prompted IDR and an unprompted IDP are shown in Figure 1c (middle) and 1c (lower), respectively. We find that across multiple metrics, IDiom generates sequences that closely resemble natural DisProt IDRs while remaining diverse and distinct from the training data. The distribution of maximum sequence identities to training set IDRs peaks broadly around 60%, indicating that most generated sequences are substantially dissimilar to any sequence seen during training (Figure 1d). Generated IDR and IDP lengths are also consistent with those of both the training set and DisProt IDRs, with most sequences below 100 residues long and a tail extending to approximately 300 residues long (Figure 1e). To analyze the compositional biases of the IDRs and IDPs, we compute the amino acid enrich- ment of training, generated, and DisProt sequences relative to a baseline composition of the folded CATH domains (Figure 1f). Consistent with established compositional biases of disordered regions [35, 36], generated sequences are strongly enriched in proline and serine, and depleted in order- promoting aliphatics such as leucine, isoleucine, and valine, as well as the aromatics phenylalanine, tryptophan, and tyrosine. The trends for training and generated sequences closely match natural 4 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint DisProt IDRs across most amino acids, with the closest agreement observed for IDRs generated with the DisProt flanking contexts as prompts. We note that the discrepancies with DisProt in the generated compositions of cysteine and charged residues (glutamic acid, lysine, and aspartic acid), may be attributed to the small size and selection bias of the DisProt dataset. We next assess the extent to which the generated sequences are disordered by predicting their structures using ColabFold [37]; the resulting pLDDT distributions are shown in Figure 1g. We run the structure predictions in two settings. In the first, we compare the unprompted generated IDPs to DisProt and training IDRs which are provided to ColabFold as standalone sequences, without their flanking context (i.e. as IDPs). In this setting, the pLDDT for a given sequence is averaged across the entire IDP, generated or extracted (Figure 1g (upper)). In the second, we compare the DisProt-prompt generated IDRs to the full protein DisProt and training sequences. In this setting, we provide the full generated, training, or DisProt sequence to ColabFold, and the pLDDT is only averaged across the IDR span (Figure 1g (lower)). Across both settings, generated sequences exhibit pLDDT distributions that closely mirror those of DisProt as well as the training set, confirming that IDiom is able to generate sequences which are predicted to be disordered to the same extent as natural IDRs. We note that the pLDDTs of IDPs in isolation are higher than for IDRs within their flanking context, which may be due to dataset biases in the AF2 training data. We additionally calculate secondary structure metrics and conduct orthogonal disorder predictions on these generated sequences, and we find that the metrics compare similarly to DisProt IDRs (Figures S1–S3). Generated sequences capture the residue patterning of natural disordered re- gions IDRs exhibit sequence patterning features that differ substantially from those of folded domains, including characteristic charge distributions, hydrophobic residue patterning, and low-complexity compositions [ 38, 36, 39]. Figure 2a shows representative generated sequences which illustrate canonical IDR features such as Q/N-rich low-complexity regions [ 40], polyampholyte charge block patterning [41], prion-like aromatic/glycine patterning [4], and proline enrichment [35]. To quantify how well IDiom recapitulates these properties, we computed the distributions of several sequence- level metrics for the generated, training, and DisProt disordered sequences, as well as the folded CATH domain sequences (Figure 2b-e). Electrostatic interactions strongly influence the conformational behavior of IDRs, and both the overall charge content and its linear patterning are closely linked to physical properties and biological function [42, 43, 41, 39]. The fraction of charged residues (FCR, Figure 2b) distinguishes strongly charged polyampholytes from weakly charged sequences. We find that the generated and natural IDRs and IDPs span a wider range of FCR values than folded CATH domains, reflecting the heterogeneity of natural IDRs, which range from highly charged sequences in which electrostatic repulsion drives disorder, to weakly charged low-complexity sequences [44]. To characterize charge patterning, we calculate the linear charge patterning parameter κ, which quantifies the deviation of a given sequence from a maximally charge segregated permutation of the same sequence [ 44]. κ ≈ 0 indicates well-mixed opposite charges and κ ≈ 1 indicates segregation into blocks of the same charge, and we plot the distributions of these values in Figure 2c. Consistent with prior work linking charge segregation in IDRs to intermolecular interactions and phase behavior [41, 45], natural IDRs from the training and DisProt sets exhibit a tail toward high κ values relative to CATH domains, a feature that IDiom reproduces with its generated sequences. We next examined hydrophobic patterning using the sequence hydropathy decoration (SHD) metric, which quantifies the spatial clustering of hydrophobic residues along the chain [46]. Gen- 5 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint erated sequences exhibit substantially lower SHD values than folded CATH domains (Figure 2d), consistent with the reduced hydrophobic clustering in disordered regions that prevents hydrophobic collapse [ 46]. This trend closely matches natural DisProt and training set IDRs, and it contrasts with folded CATH domains, which exhibit higher SHD values, reflecting the locally concentrated hydrophobic residues required to stabilize buried protein cores [47]. Finally, we assessed sequence complexity using the SEG algorithm, which computes the average compositional entropy over a sliding window [ 48]. IDRs frequently contain low-complexity segments [49], and natural DisProt and training set IDRs show lower complexity than folded CATH domains. Generated IDRs and IDPs closely reproduce this shift, with the complexities of generated sequences matching the DisProt distribution well (Figure 2e). All together, these results demonstrate that IDiom has learned the sequence grammar of disordered regions across multiple metrics, and that generated sequences closely recapitulate the sequence patterning features of natural IDRs. Charge patterning Aromatic patterning Low complexity Compositional biases ed b c a Fig. 2: IDiom generates intrinsically disordered regions and proteins which capture the se- quence patterning features of natural sequences. (a) Example IDPs (upper row) and IDRs (lower row) generated using IDiom which exhibit canonical sequence features of intrinsically disordered regions, including low complexity regions, charge blockiness, aromatic patterning, and compositional biases. Greyed- out residues correspond to the flanking context of the IDR. (b)–(e) Distributions of various sequence metrics for generated IDPs and IDRs, training set IDRs, DisProt IDRs, and folded CATH domains. Right subplots: Normalized Wasserstein-1 (W 1) distance between the distributions of DisProt IDRs and all other distribu- tions. (b) Fraction of charged residues (FCR). (c) Charge patterning κ parameter. (d) Sequence hydropathy decoration (SHD). (e) Sequence complexity quantified by the SEG algorithm. 6 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Conditioned generation recapitulates context-specific IDR sequence features The previous analysis demonstrates that IDiom can generate sequences with patterning features and biophysical properties which are similar to natural IDRs. To quantify the agreement between generated and natural IDRs, we compute the normalized Wasserstein-1 distance ( W1) [50] between the distributions of each sequence metric and the DisProt reference distribution (right subplots of Figure 2b-e). Across most metrics, W1 distances for generated sequences are low relative to folded CATH domains, confirming that IDiom produces sequences that are statistically much closer to natural IDRs than to folded proteins. We find that in Figure 2b, the shift in mean values for generated and training sequences relative to DisProt leads to relatively larger W1 values compared to the other metrics we consider, but we note that the shift relative to the training data likely

from the relatively small set of IDRs in DisProt. We also note that the shape of the broad distribution of FCR values for generated and training sequences matches that of DisProt more closely than the narrower CATH distribution. Furthermore, W1 distances for DisProt context- prompted IDRs are consistently lower than for unprompted IDPs across all metrics, demonstrating that conditioning on flanking sequence context shifts IDiom’s generations toward the sequence features of the natural IDRs that reside inside those contexts. b ca Fig. 3: Conditioned generation and in-context learning enables generation of disordered regions which capture biologically relevant sequence features. (a) Distribution of sequence identities between the wild-type (WT) NPM1 IDR and sequences generated with the NPM1 IDR’s flanking context as the prompt. Generated sequences with identities greater than 0.9 are filtered out. (b) Distribution of κ values for the WT NPM1 IDR (black vertical dashed line), IDRs generated with the NPM1 context as prompt (blue), randomly scrambled versions of the generated IDRs (orange), and DisProt IDRs (green). (c) Plots of the net charge per residue along the sequence. The WT NPM1 IDR is in the upper row, and three representative generated IDRs are below. The sequence identities relative to the WT, κ values, and the amino acid sequences themselves are printed within the plots. To further illustrate the model’s ability to learn via this in-context conditioning, we consider the human protein NPM1 (UniProt: P06748) as a case study. NPM1 has an IDR (residues 119–242) which drives nucleolar phase separation through charge block patterning that mediates interactions with itself [ 41] as well as binding partners such as SURF6 [51]. Using the flanking regions around this IDR as the prompt (green and blue domains in Figure 1c (upper)), we generated 100,000 IDRs and filtered out any with sequence identity > 90% to the wild-type (WT) NPM1 IDR (Figure 3a). 7 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Figure 3b shows the distribution of κ values for NPM1-prompted generations, randomly scrambled versions of those sequences, and the dataset of DisProt IDRs. We find that the κ distribution of NPM1-prompted generations is peaked near the WT NPM1 value, and is substantially shifted toward higher charge segregation than either randomly scrambled sequences or generic DisProt IDRs, indicating that the model has learned to generate sequences with substantial charge block patterning, when conditioned on the NPM1 flanking contexts. Figure 3c shows linear plots of net charge per residue (NCPR) for the WT NPM1 IDR and representative generated sequences with high κ values but low sequence identity to the WT IDR. These plots illustrate that IDiom generates sequences with alternating blocks of positive and neg- ative charge which closely mirror the architecture of the WT IDR, despite sharing little sequence identity with it. Together, these results demonstrate that IDiom is able to use flanking context to reproduce the biologically relevant sequence features of a given IDR, and that the model is able to generate diverse sequences that preserve the key sequence features that underlie biological function. Sequence optimization using reinforcement learning Our results demonstrate that IDiom has learned a strong generative prior over IDR sequence space, and that the model produces diverse and biologically realistic sequences. This naturally positions the pre-trained model as a starting point for sequence design: post-training IDiom with external rewards allows us to steer generation towards sequences that score well on specified objectives while remaining IDR-like. Unlike supervised fine-tuning on labeled datasets, post-training via reinforce- ment learning allows us to optimize arbitrary reward functions such as computational predictors and reward models trained on experimental data. Reinforcement learning can additionally incor- porate explicit regularization to control sequence diversity, length, and deviation from the base model [52, 53, 54]. As a design target, we focus on subcellular localization, as the ability to engineer protein lo- calization could enable both targeted delivery of therapeutics and modulation of synthetic con- densates [55, 56]. As the reward model, we use ProtGPS, a neural network trained with ESM2 embeddings to predict the probability of a given protein sequence localizing to each of twelve specific subcellular compartments [ 23, 16]. Here, we post-train IDiom to optimize localization to four compartments: the nucleolus, chromosomes/chromatin, P-bodies, and stress granules. These compartments were chosen because they are known to be enriched in proteins with IDR-specific se- quence features, including charge segregation, RNA-interacting motifs, nuclear localization signals, and post-translational modification sites, thus providing a clear test of whether RL post-training can induce the generation of biologically relevant sequence features. We optimize IDiom using the reinforcement learning algorithm Group Relative Policy Opti- mization (GRPO) [57, 58], and we generate unprompted IDPs in all post-training runs (overview in Figure 4a). To prevent reward hacking and to maintain sequence diversity, we incorporate three forms of regularization: a Kullback-Liebler (KL) divergence penalty DKL to prevent excess diver- gence of the post-trained model from the pre-trained base model, a quadratic penalty around a target Shannon entropy of H = 2 .7 nats to prevent diversity collapse, and a quadratic penalty around a target sequence length of 100 residues. Figure 4b shows training curves for the ProtGPS reward, DKL, and mean sequence length versus post-training optimizer steps. The ProtGPS reward increases steadily across all four compartments, the mean sequence lengths converge to the target value, and DKL remains below 0.4 throughout training, confirming that post-training successfully optimizes the reward without diverging substantially from the pre-trained base distribution. Figure 4c shows the distributions of AlphaFold2 pLDDT values for sequences generated from each post-trained checkpoint, alongside the pLDDT distribution of the full length proteins used to 8 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint MGPGS[ ] Generate RL Loss Post-train IDR PLM ProtGPS score Target length Target Shannon entropy KL Divergence penalty a b c Fig. 4: Post-training IDiom with reinforcement learning enables the generation of sequences aligned with an external reward model. (a) Schematic depicting the reinforcement learning process for post-training IDiom. ProtGPS is a reward model which returns a score between 0 and 1 indicating the probability of a given sequence localizing to a chosen subcellular compartment. Quadratic penalties are applied to sequences which deviate from the target ProtGPS score, target length, and target Shannon entropy, and a penalty is applied for an increased Kullback-Liebler (KL) divergence of the post-trained model from the pre-trained base model. These metrics are combined in a reinforcement learning loss which is used to update the IDiom policy. (b) Training curves depicting the ProtGPS score for a given compartment, magnitude of the KL-divergence, DKL , and the average generated sequence length, as a function of post-training optimizer steps. (c) Distribution of AlphaFold2 pLDDTs of sequences generated from IDiom checkpoints after 1500 post-training optimizer steps, as well as pLDDTs of the original sequences used to train the ProtGPS reward model. train the ProtGPS predictor. The ProtGPS training sequences have a wide distribution of pLDDTs, with a substantial fraction of high-pLDDT residues, reflecting the fact that ProtGPS was trained on full length proteins containing both folded domains and disordered regions. However, sequences generated by the post-trained IDiom models maintain low pLDDT values, comparable to those of natural IDRs, demonstrating that the KL regularization successfully prevents the model from drifting towards the sequence features of folded proteins in the ProtGPS training set. This further confirms that post-training steers generation towards the desired compartment localization while preserving the disordered nature of generated sequences. Post-trained models generate sequences with compartment-specific features After post-training with the ProtGPS reward, we generate 10,000 sequences from each localization- optimized checkpoint and analyze their amino acid compositions. Sequences targeting specific subcellular compartments are expected to have compositional biases that reflect their local bio- chemical environments, and we find that post-trained generations exhibit biologically interpretable compositional shifts relative to both base model generations and DisProt IDRs (Figure 5). Nucleolar-targeting sequences are enriched in lysine and arginine, consistent with the prevalence of positively charged nuclear localization signals and the charge-rich low-complexity regions found in nucleolar proteins [ 59, 60]. Sequences targeting the chromosomes are enriched in serine and threonine, consistent with the high density of phosphorylation sites characteristic of chromatin- 9 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint asso ciating proteins, which are heavily regulated by post-translational modification [61, 62]. The generated P-body targeting sequences are glycine-rich and basic (lysine- and arginine-rich), con- sistent with the RNA-binding motifs and arginine-glycine rich regions present in proteins that associate with RNA granules [ 63, 64]. Finally, stress granule-targeting sequences are similarly glycine-rich, consistent with the low-complexity, RNA-interacting motifs expected in stress granule associating proteins [65]. Representative sequences generated from each checkpoint are also shown in Figure 5, with specific sequence features such as nuclear localization signals, post-translational modification sites, and RNA-binding motifs underlined, illustrating that the global compositional shifts accompanied by the generation of specific local sequence features. a b c d Fig. 5: Post-trained IDiom models generate sequences which reproduce the amino acid composi- tional biases known to drive subcellular localization. Amino acid composition of sequences generated after post-training IDiom to optimize the ProtGPS localization score for the (a) nucleolus, (b) chromosome, (c) P-bodies, and (d) stress granules. Underneath each plot is one representative generated sequence for each compartment, with sequence features such as nuclear localization signals, post-translational modifica- tion sites, and RNA-binding motifs underlined. To further characterize the sequence features learned during post-training, we analyze the compartment-specific generations for sequence patterning and sequence-specific motifs. Charge segregation, quantified by κ, varies across compartments (Figure 6a), with nucleolus-targeting sequences showing elevated κ relative to all other sequences; this observation is consistent with the prevalence of charge-block architectures in nucleolar-associating IDRs [ 66]. In contrast, se- quences targeting stress granules and P-bodies show reduced κ relative to baselines, consistent with the weakly charged nature of stress granule proteins [67] and the aromaticity-driven nature of P-body condensate formation [4]. In addition, we find that sequences targeting the nucleolus and chromosomes are enriched in nuclear localization signals (NLSs), as is expected for these nu- clear compartments [ 68]. We scan generated sequences for a curated set of NLS patterns from the Eukaryotic Linear Motif (ELM) Resource [69] (patterns are provided in the Supplementary Infor- mation), and we find that a substantially higher fraction of nucleolus- and chromosome-targeting sequences contain at least one NLS compared to sequences targeting cytoplasmic compartments (Figure 6b). Chromosome-associating proteins are heavily regulated through post-translational modifications (PTMs), and we probe whether chromosome-targeting sequences are correspondingly enriched in 10 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Nuclear Non-nuclear Reference Nuclear Non-nuclear Reference Nuclear Non-nuclear Reference a b e c d Fig. 6: Proteins generated from post-trained IDiom models recapitulate specific sequences fea- tures which are characteristic of each target cellular compartment. (a) Box plot of the distribution of κ charge patterning values for sequences generated from IDiom checkpoints optimized for localization to the four labeled ProtGPS compartments. The horizontal orange line and band indicates the mean and stan- dard deviation of κ for sequences generated from the base pre-trained model. The green line indicates the mean κ value of natural DisProt IDRs. (b) Plot of the percentage of generated sequences which contain at least one nuclear localization signal from the Eukaryotic Linear Motif (ELM) Resource. (c) Plot of the per- centage of generated sequences which contain the RNA-interaction sequence motifs indicated in the legend. (≥ 1) indicates the presence of at least one motif within a given sequence. (≥ 2) indicates the presence of at least two motifs within 30 residues of one another within a given sequence. (d) Plot of the average number of unique post-translational modification (PTM) motifs from the ELM Resource per sequence for sequences generated from various model checkpoints or the DisProt IDRs. (e) Plot of the ratio of the number of counts of all PTM motifs from the ELM Resource (MOD) appearing in a generated sequence or DisProt IDRs, normalized to the counts within sequences generated by the base model. PTM motifs [70]. We scan generated sequences for all 40 PTM motif classes from the ELM Re- source (ELM Identifiers beginning with the MOD prefix). Chromosome-targeting sequences show a pronounced increase in MOD-motif density, with over 10 putative unique PTM sites per sequence on average, compared to approximately 5-7 sites per sequence for other compartments (Figure 6c). In Figure 6d we quantify enrichment as the ratio of motif counts in post-trained generations rel- ative to the base model, finding that the enriched motifs span multiple kinase families, including AGC-class sites ( MOD_PKA_1, MOD_PKB_1, MOD_PK_1), PIK/PIKK-associated phosphorylation sites (MOD_PIK_1, MOD_PIK_2-3, MOD_PIKK_1), acidophilic CK2 motifs (MOD_CK2_1), and proline-directed CDK-class motifs (MOD_CDK_SPK_2). This broad enrichment across kinase families is consistent with PTM-driven regulatory control being a crucial role of chromatin-interacting proteins [61, 62], and it demonstrates that post-training with a localization reward is sufficient to induce the generation of these specific sequence features. P-bodies and stress granules are RNA-rich condensates with central roles in mRNA regula- tion and decay [ 71], and we find that post-trained sequences targeting these compartments are enriched in short RNA-interaction motifs including RG/RGG tracts, F/YGG motifs, and SYG 11 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint motifs (Figure 6e). RG/RGG-rich regions are widely implicated in RNA binding and recruitment to ribonucleoprotein assemblies [63, 64], while F/YGG [ 72, 73] and SYG [ 74, 75] motifs provide aromatic sticker elements that mediate π-π and cation- π interactions which drive phase separation in low-complexity IDRs. The emergence of these motifs through post-training indicates that opti- mizing for RNA granule localization is also sufficient to induce the generation of RNA-interaction sequence grammars. Altogether, these results demonstrate that RL post-training using the ProtGPS predictor as a reward model is able to teach IDiom the global amino acid compositions, sequence patterning, and specific motifs which are necessary for compartment-specific localization. Each of the changes we identify is biologically interpretable and consistent with the known sequence determinants of local- ization to or interaction with the corresponding compartment, and these features emerge without any explicit supervision. This indicates that the post-training of IDiom to optimize the Prot- GPS score alone is sufficient to learn the necessary compartment-specific sequence grammars for subcellular localization of IDRs.

IDiom demonstrates that a protein language model trained exclusively on intrinsically disordered region sequences can faithfully capture the highly contextual evolutionary statistics of natural IDRs. The pre-trained model generates diverse sequences that recapitulate the compositional bi- ases, charge patterning, hydrophobic decoration, and low-complexity features of natural disordered regions. Crucially, the model is able to generate highly plausible disordered sequences while remain- ing substantially dissimilar to the training examples. Furthermore, IDiom learns in-context and is able to generate IDRs conditioned on flanking sequence context that are more similar to the natural IDRs that exist within that flanking context, as demonstrated by the DisProt context-prompted IDRs and the NPM1 case study. Beyond generation from the base pre-trained model, we demonstrate that IDiom can be post- trained using reinforcement learning to optimize arbitrary external reward functions. While here we demonstrate this using ProtGPS as the reward signal for subcellular localization, the post-training approach is general. IDiom can be combined with any objective, such as sequence-based predictors of conformational ensembles [76], intermolecular interactions [45], phase behavior [77], as well as machine-learned predictors of experimentally characterized biological function such as transcrip- tional activity [ 78, 79] or direct binding affinity [80]. Post-training can also be applied directly to experimental data, using approaches such as direct preference optimization [54, 81] or energy rank alignment [82, 83]. Such approaches would enable iterative optimization of the generative model as new experimental measurements become available. Due to the often modular nature of IDRs, a designed IDR could be inserted or appended to a full length protein to tune localization, phase behavior, or signaling properties without redesigning the folded domains. Additionally, the preva- lence of short IDRs in our training data (Figure 1e) also makes IDiom well-suited for the design of disordered peptides for therapeutic applications. Finally, IDiom offers interesting opportunities for shrinking proteins containing functional IDRs, an important objective in protein delivery [ 84]. IDiom can also enable the automated discovery of evolutionarily and biologically important sequence features within IDRs. In the examples with the ProtGPS reward model, we manually identified sequence features to analyze in the post-trained sequences. Future work applying tech- niques such as feature learning with sparse autoencoders [85] would enable automatic identification of prominent sequence features learned by IDiom. While prior work has studied the features learned by protein language models trained on full length sequences, intrinsically disordered regions are 12 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint p oorly resolved in those learned feature spaces [ 86]. In contrast, sparse autoencoders trained on IDiom representations would be free from folded domain features, allowing for more precise iden- tification of sequence grammars that underlie intrinsically disordered regions. When applied to post-trained models, this approach could further reveal the function-specific features that underlie biological function, such as subcellular localization. Intrinsically disordered regions play central roles in cellular processes such as gene regula- tion, subcellular compartmentalization, and signaling, yet they have remained largely inaccessible to rational design. IDiom provides a generative framework for disordered sequence design that can be steered towards specific functional objectives through post-training. Combined with high- throughput experimental assays and machine learned reward models trained on experimental data, this platform offers a path toward the systematic design and engineering of intrinsically disordered proteins and regions, opening new avenues in synthetic biology, targeted therapeutics, and the design of programmable condensates.

Data Curation We curate our dataset of intrinsically disordered regions from the AlphaFold Database (AFDB), version 4. First, we use MMseqs2 to cluster the 214M AFDB sequences at 90% identity and 80% coverage (other MMseqs2 parameters below). Next, we follow the method of [ 32] to determine the sequences and locations of pLDDT-based IDRs within the MMseqs2 cluster representative proteins. In this method, we first apply a 15 residue-wide averaging filter to the pLDDT values. Next, we mark residues with pLDDT > 80 as folded, pLDDT < 70 as disordered, and 70 < pLDDT < 80 as gap regions. Folded and disordered regions with a length shorter than ten residues are reclassified as gaps. If a gap region is flanked by two disordered regions, or if it is N- or C-terminal and is adjacent to a disordered region, we relabel it as disordered. All other gap regions are relabeled as folded. Each record within the dataset corresponds to a different IDR, and any given protein may yield ≥ 1 IDR. IDRs which are located in proteins whose full length is greater than 512 residues, IDRs shorter than 30 residues long, and sequences whose entire length is low-pLDDT are discarded. This curation process yields 37M IDRs and their associated N- and C-terminal flanking contexts. Sequence Clustering and Percent Identity Characterization We use MMseqs2 to cluster sequences in the AlphaFold Database at 90% identity and 80% coverage. MMseqs2 was run using the following command: mmseqs linclust --min-seq-id 0.9 --cov-mode 0 -c 0.8 --cluster-mode 2. We also use MMseqs2 to identify the sequence identity of generated sequences with respect to the training set. Specifically, we compare generated IDR and IDP sequences against the 37M AFDB training set IDRs without their surrounding context. MMseqs2 was run with the following command to search the generated sequences against the AFDB training set IDRs: mmseqs search --max-seqs 1 -e 1e3 --min-seq-id 0.0 -c 0.0. For each generated sequence, this command returns the sequence identity of the closest match in the training set, which is plotted in Figure 1. T okenization We tokenize protein sequences using a simple alphabet in which each amino acid is rep- resented by a single token. We introduce the tokens , , and to denote the N-terminal flanking context of an IDR, the C-terminal flanking context, and the IDR span itself, respectively. We additionally add the standard beginning-of-sequence and end-of-sequence tokens to all sequences, and we pad all sequences to the maximum length of 512 tokens using the token. The total size of the alphabet we use is 27 tokens (20 amino acids, , , and , and , , , and . Data Augmentations To process the curated AFDB IDRs for model pre-training, we transform the protein sequences into a fill-in-the-middle format. We prepend the token to any N-terminal context of the IDR, prepend to the IDR itself, and prepend to any C-terminal context of the IDR. We then rearrange the sequence in the order . An example sequence is MEDS..HLVASVED..RKSLVEED..KGPS. 13 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint W e augment the data with intrinsically disordered proteins by duplicating the set of IDRs and re- moving their N- and C-terminal flanking contexts. An example sequence from this data augmentation is VEED..KGPS. In all, this produces 74M sequences for training (37M IDRs and 37M IDPs). Model Architecture IDiom is a 12-layer decoder-only Transformer with 14 attention heads and a hidden dimension of dmodel = 896 . The model employs pre-LayerNorm and utilizes the SwiGLU non-linearity [ 87] in all feedforward networks. The feedforward network expansion ratio is 8/3, resulting in a total of 122M trainable parameters. Positional information is encoded using Rotary Position Embeddings (RoPE) [ 88]. The model processes sequences with a maximum length of 512 tokens, and shorter sequences are padded to this length. Multi-head attention is computed using Flash Attention [89]. Pre-training We pre-train IDiom on the aforementioned 74M sequences. The data are randomly split into 99% training, 0.5% validation, and 0.5% test sets. All sequences are padded or truncated to a fixed length of 512 tokens. The model is trained autoregressively using next-token prediction. Training is performed using the AdamW optimizer with a learning rate of 4.0×10−4 and no weight decay. The learning rate schedule uses a linear warmup over the first 3,000 steps, followed by cosine annealing decay to a minimum of 4.0×10−5 (10% the initial learning rate) over 250,000 total training steps. The global batch size is 1,024 (Distributed Data Parallel training with 128 sequences per GPU across 8 NVIDIA H100 GPUs), with no gradient accumulation. We use a cross-entropy loss while ignoring contributions from pad or mask tokens. Training is performed in mixed precision (fp32/bfloat16) and no gradient clipping is applied. Model validation is performed every 25,000 training steps on the validation set, and training is run for 250,000 optimizer steps. The training and validation curves are presented in the Supplementary Information. Sequence Generation We generate IDR sequences from IDiom using autoregressive decoding. At each position t in the sequence, we compute the model logits zt and convert them to a probability distribution via p(xt|x<t) = softmax(zt/T ), then sample the next token from this full categorical distribution over the vocabulary. We use a fixed sampling temperature of T = 1.0 for all generations Sequence generation supports both prompted and unprompted modes. For prompted generation, the N- and C-terminal flanking contexts are provided as the prompt in fill-in-the-middle format: , and the model generates the IDR span autoregressively following the token. For unprompted generation of fully disordered proteins, the prompt consists of only the three special tokens without any flanking context: , and the model generates the disordered sequence. In both cases, generation terminates upon sampling the token or upon reaching the maximum sequence length of 512 tokens. Post-training We fine-tuned IDiom using Group Relative Policy Optimization (GRPO) with the De- coupled Advantage Policy Optimization (DAPO) modification. During GRPO training, for each batch of sequence prompts, the model generates multiple completions per prompt (group size = 8). Rewards are computed for each generated sequence using a reward function that combines three rewards: 1. A quadratic reward around a target ProtGPS score of 0.9 for the desired target compartment, 2. A quadratic reward around a target sequence length of Ltarget = 100 residues, and 3. A quadratic reward around a target sequence Shannon entropy of Htarget = 2.7 nats to prevent diversity collapse. Within each group, advantages are computed as normalized relative rewards: Ai = ri−¯rg σg , where ¯rg and σg are the group-wise mean and standard deviation. The GRPO loss combines a clipped policy gra- dient term (PPO-style clipping with ϵclip = 0 .2) weighted by advantages, and a KL-divergence penalty LKL = βKLDKL(pref||pcurrent) with strength βKL = 0.02. The total loss is optimized per-token on generated completions only (any prompt tokens are masked). Post-training is performed with a learning rate of 5×10−6, the AdamW optimizer, and a global batch size of 8, for 1,500 optimizer steps. Post-training was performed separately for all 12 target cellular compartments in ProtGPS, although we only analyze the sequences generated from checkpoints trained for localization to the nucleolus, chromosomes, P-bodies, and stress granules. 14 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Structure Prediction We use Colabfold [37] to perform AlphaFold2 structure predictions on generated sequences and determine the predicted local distance difference test (pLDDT) values. Sequence Analysis We use the Sparrow package [ 90] to calculate sequence-level metrics such as charge patterning κ, sequence hydropathy decoration, sequence complexity (SEG), and fraction of charged residues. Short linear motif (SLIM) analysis is performed with a regular expression search using the SLIM regular expressions from the Eukaryotic Linear Motif Resource [ 69]. The specific regular expressions are presented in the Supplementary Information Visualization Protein structure visualization is performed with PyMOL [91]. Data and Code A vailability The code used for model pre-training, sequence generation, and post- training is available on Github: Code (https://github.com/rotskoff-group/idiom). The pre-training datasets and pre- and post-trained model checkpoints are available on Hugging Face: Datasets (https://huggingface.co/datasets/jxliu2/idiom-datasets) Models (https://huggingface.co/jxliu2/idiom) . Information regarding these artifacts is provided in the Supplementary Information.

J.X.L. acknowledges support from the National Institute of Health T32 award num- ber T32HL094274. S.I. acknowledges support from the National Science Foundation Graduate Research Fellowship Program and the Shoucheng Zhang Graduate Fellowship. F.H. acknowledges support from the Stanford Center for Molecular Analysis and Design Fellowship. Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health un- der award number 1R35GM159834-01 (G.M.R.) and 5R35GM130332 (A.R.D.). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors acknowledge the use of the Stanford Sherlock compute cluster, and the authors acknowledge insightful discussions with Prof. Mikko Haataja. Competing Interests G.M.R. holds equity in and is a paid consultant for Topos Bio and holds equity in Azulene Labs.

[1] Alex S. Holehouse and Birthe B. Kragelund. The molecular basis for cellular function of intrinsically disordered protein regions. Nature Reviews Molecular Cell Biology , 25(3):187–211, March 2024. [2] Nicolás S. González-Foutel, Juliana Glavina, Wade M. Borcherds, Matías Safranchik, Susana Barrera- Vilarmau, Amin Sagar, Alejandro Estaña, Amelie Barozet, Nicolás A. Garrone, Gregorio Fernandez- Ballester, Clara Blanes-Mira, Ignacio E. Sánchez, Gonzalo de Prat-Gay, Juan Cortés, Pau Bernadó, Rohit V. Pappu, Alex S. Holehouse, Gary W. Daughdrill, and Lucía B. Chemes. Conformational buffering underlies functional selection in intrinsically disordered protein regions. Nature Structural & Molecular Biology, 29(8):781–790, August 2022. [3] Peter E. Wright and H. Jane Dyson. Intrinsically disordered proteins in cellular signalling and regulation. Nature Reviews Molecular Cell Biology , 16(1):18–29, January 2015. [4] Erik W. Martin, Alex S. Holehouse, Ivan Peran, Mina Farag, J. Jeremias Incicco, Anne Bremer, Christy R. Grace, Andrea Soranno, Rohit V. Pappu, and Tanja Mittag. Valence and patterning of aromatic residues determine the phase behavior of prion-like domains. Science, 367(6478):694–699, February 2020. [5] Shana Elbaum-Garfinkle, Younghoon Kim, Krzysztof Szczepaniak, Carlos Chih-Hsiung Chen, Chris- tian R. Eckmann, Sua Myong, and Clifford P. Brangwynne. The disordered P granule protein LAF-1 drives phase separation into droplets with tunable viscosity and dynamics. Proceedings of the National Academy of Sciences , 112(23):7189–7194, June 2015. 15 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [6] Ming-T zo Wei, Shana Elbaum-Garfinkle, Alex S. Holehouse, Carlos Chih-Hsiung Chen, Marina Feric, Craig B. Arnold, Rodney D. Priestley, Rohit V. Pappu, and Clifford P. Brangwynne. Phase behaviour of disordered proteins underlying low density and high permeability of liquid organelles. Nature Chemistry, 9(11):1118–1125, November 2017. [7] Salman F. Banani, Hyun O. Lee, Anthony A. Hyman, and Michael K. Rosen. Biomolecular condensates: organizers of cellular biochemistry. Nature Reviews Molecular Cell Biology , 18(5):285–298, May 2017. [8] Giulio Tesei, Francesco Pesce, and Kresten Lindorff-Larsen. Computational design of intrinsically dis- ordered proteins. Current Opinion in Structural Biology , 96:103210, February 2026. [9] John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Žídek, Anna Potapenko, Alex Bridgland, Clemens Meyer, Simon A. A. Kohl, Andrew J. Ballard, Andrew Cowie, Bernardino Romera-Paredes, Stanislav Nikolov, Rishub Jain, Jonas Adler, Trevor Back, Stig Petersen, David Reiman, Ellen Clancy, Michal Zielinski, Martin Steinegger, Michalina Pacholska, Tamas Berghammer, Sebastian Bodenstein, David Silver, Oriol Vinyals, Andrew W. Senior, Koray Kavukcuoglu, Pushmeet Kohli, and Demis Hassabis. Highly accurate protein structure prediction with AlphaFold. Nature, 596(7873):583–589, August 2021. [10] Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneberger, Lindsay Willmore, Andrew J. Ballard, Joshua Bambrick, Sebastian W. Bodenstein, David A. Evans, Chia-Chun Hung, Michael O’Neill, David Reiman, Kathryn Tunyasuvunakool, Zachary Wu, Akvilė Žemgulytė, Eirini Arvaniti, Charles Beattie, Ottavia Bertolli, Alex Bridgland, Alexey Cherepanov, Miles Congreve, Alexander I. Cowen-Rivers, Andrew Cowie, Michael Figurnov, Fabian B. Fuchs, Hannah Gladman, Rishub Jain, Yousuf A. Khan, Caroline M. R. Low, Kuba Perlin, Anna Potapenko, Pascal Savy, Sukhdeep Singh, Adrian Stecula, Ashok Thillaisundaram, Catherine Tong, Sergei Yakneen, Ellen D. Zhong, Michal Zielinski, Augustin Žídek, Victor Bapst, Pushmeet Kohli, Max Jaderberg, Demis Hassabis, and John M. Jumper. Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature, 630(8016):493–500, June 2024. [11] Joseph L. Watson, David Juergens, Nathaniel R. Bennett, Brian L. Trippe, Jason Yim, Helen E. Eisenach, Woody Ahern, Andrew J. Borst, Robert J. Ragotte, Lukas F. Milles, Basile I. M. Wicky, Nikita Hanikel, Samuel J. Pellock, Alexis Courbet, William Sheffler, Jue Wang, Preetham Venkatesh, Isaac Sappington, Susana Vázquez Torres, Anna Lauko, Valentin De Bortoli, Emile Mathieu, Sergey Ovchinnikov, Regina Barzilay, Tommi S. Jaakkola, Frank DiMaio, Minkyung Baek, and David Baker. De novo design of protein structure and function with RFdiffusion. Nature, 620(7976):1089–1100, August 2023. [12] Alexander E. Chu, Jinho Kim, Lucy Cheng, Gina El Nesr, Minkai Xu, Richard W. Shuai, and Po- Ssu Huang. An all-atom protein generative model. Proceedings of the National Academy of Sciences, 121(27):e2311500121, July 2024. [13] Martin Pacesa, Lennart Nickel, Christian Schellhaas, Joseph Schmidt, Ekaterina Pyatova, Lucas Kissling, Patrick Barendse, Jagrity Choudhury, Srajan Kapoor, Ana Alcaraz-Serna, Yehlin Cho, Kourosh H. Ghamary, Laura Vinué, Brahm J. Yachnin, Andrew M. Wollacott, Stephen Buckley, Adrie H. Westphal, Simon Lindhoud, Sandrine Georgeon, Casper A. Goverde, Georgios N. Hatzopou- los, Pierre Gönczy, Yannick D. Muller, Gerald Schwank, Daan C. Swarts, Alex J. Vecchio, Bernard L. Schneider, Sergey Ovchinnikov, and Bruno E. Correia. One-shot design of functional protein binders with BindCraft. Nature, 646(8084):483–492, October 2025. [14] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. Attention is All you Need. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017. [15] Noelia Ferruz, Steffen Schmidt, and Birte Höcker. ProtGPT2 is a deep unsupervised language model for protein design. Nature Communications, 13(1):4348, July 2022. 16 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [16] Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Nikita Smetanin, Robert Verkuil, Ori Kabeli, Yaniv Shmueli, Allan dos Santos Costa, Maryam Fazel-Zarandi, Tom Sercu, Sal- vatore Candido, and Alexander Rives. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science, 379(6637):1123–1130, March 2023. [17] Thomas Hayes, Roshan Rao, Halil Akin, Nicholas J. Sofroniew, Deniz Oktay, Zeming Lin, Robert Verkuil, Vincent Q. Tran, Jonathan Deaton, Marius Wiggert, Rohil Badkundri, Irhum Shafkat, Jun Gong, Alexander Derry, Raul S. Molina, Neil Thomas, Yousuf A. Khan, Chetan Mishra, Carolyn Kim, Liam J. Bartie, Matthew Nemeth, Patrick D. Hsu, Tom Sercu, Salvatore Candido, and Alexander Rives. Simulating 500 million years of evolution with a language model. Science, 387(6736):850–858, February 2025. [18] Ali Madani, Ben Krause, Eric R. Greene, Subu Subramanian, Benjamin P. Mohr, James M. Holton, Jose Luis Olmos, Caiming Xiong, Zachary Z. Sun, Richard Socher, James S. Fraser, and Nikhil Naik. Large language models generate functional protein sequences across diverse families. Nature Biotech- nology, 41(8):1099–1106, August 2023. [19] Erik Nijkamp, Jeffrey A. Ruffolo, Eli N. Weinstein, Nikhil Naik, and Ali Madani. ProGen2: Exploring the boundaries of protein language models. Cell Systems , 14(11):968–978.e3, November 2023. [20] Aadyot Bhatnagar, Sarthak Jain, Joel Beazer, Samuel C Curran, Alexander M Hoffnagle, Kyle S Ching, Michael Martyn, Stephen Nayfach, Jeffrey A Ruffolo, and Ali Madani. Scaling Unlocks Broader Generation and Deeper Functional Understanding of Proteins. NeurIPS, 2025. [21] Francesco Pesce, Anne Bremer, Giulio Tesei, Jesse B. Hopkins, Christy R. Grace, Tanja Mittag, and Kresten Lindorff-Larsen. Design of intrinsically disordered protein variants with diverse structural properties. Science Advances, 10(35):eadm9926, August 2024. [22] Ryan Krueger, Michael P. Brenner, and Krishna Shrinivas. Generalized design of sequence-ensemble- function relationships for intrinsically disordered proteins, October 2024. Pages: 2024.10.10.617695 Section: New Results. [23] Henry R. Kilgore, Itamar Chinn, Peter G. Mikhael, Ilan Mitnikov, Catherine Van Dongen, Guy Zyl- berberg, Lena Afeyan, Salman F. Banani, Susana Wilson-Hawken, Tong Ihn Lee, Regina Barzilay, and Richard A. Young. Protein codes promote selective subcellular compartmentalization. Science, 387(6738):1095–1101, March 2025. [24] Kara Hunter, Trevor Brandt, Karina Guadalupe, Kavindu Chathuranga Kolamunna, Jeffrey M. Lot- thammer, Nora M. Shamoon, Brooke Nicholson, Lea Day, Alec Martinez, Alex S. Holehouse, Shahar Sukenik, and Ryan J. Emenecker. Rational design of disordered proteins for systematic sequence-to- function investigation, February 2026. ISSN: 2692-8205 Pages: 2023.10.29.564547 Section: New Results. [25] Mihaly Varadi, Stephen Anyango, Mandar Deshpande, Sreenath Nair, Cindy Natassia, Galabina Yor- danova, David Yuan, Oana Stroe, Gemma Wood, Agata Laydon, Augustin Žídek, Tim Green, Kathryn Tunyasuvunakool, Stig Petersen, John Jumper, Ellen Clancy, Richard Green, Ankur Vora, Mira Lutfi, Michael Figurnov, Andrew Cowie, Nicole Hobbs, Pushmeet Kohli, Gerard Kleywegt, Ewan Birney, Demis Hassabis, and Sameer Velankar. AlphaFold Protein Structure Database: massively expanding the structural coverage of protein-sequence space with high-accuracy models. Nucleic Acids Research , 50(D1):D439–D444, January 2022. [26] Mihaly Varadi, Damian Bertoni, Paulyna Magana, Urmila Paramval, Ivanna Pidruchna, Malarvizhi Radhakrishnan, Maxim Tsenkov, Sreenath Nair, Milot Mirdita, Jingi Yeo, Oleg Kovalevskiy, Kathryn Tunyasuvunakool, Agata Laydon, Augustin Žídek, Hamish Tomlinson, Dhavanthi Hariharan, Josh Abrahamson, Tim Green, John Jumper, Ewan Birney, Martin Steinegger, Demis Hassabis, and Sameer Velankar. AlphaFold Protein Structure Database in 2024: providing structure coverage for over 214 million protein sequences. Nucleic Acids Research , 52(D1):D368–D375, January 2024. [27] Mohammad Bavarian, Heewoo Jun, Nikolas Tezak, John Schulman, Christine McLeavey, Jerry Tworek, and Mark Chen. Efficient Training of Language Models to Fill in the Middle, July 2022. arXiv:2207.14255 [cs]. 17 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [28] Ra ymond Li, Loubna Ben Allal, Yangtian Zi, Niklas Muennighoff, Denis Kocetkov, Chenghao Mou, Marc Marone, Christopher Akiki, Jia Li, Jenny Chim, Qian Liu, Evgenii Zheltonozhskii, Terry Yue Zhuo, Thomas Wang, Olivier Dehaene, Mishig Davaadorj, Joel Lamy-Poirier, João Monteiro, Oleh Shliazhko, Nicolas Gontier, Nicholas Meade, Armel Zebaze, Ming-Ho Yee, Logesh Kumar Umapathi, Jian Zhu, Benjamin Lipkin, Muhtasham Oblokulov, Zhiruo Wang, Rudra Murthy, Jason Stillerman, Siva Sankalp Patel, Dmitry Abulkhanov, Marco Zocca, Manan Dey, Zhihan Zhang, Nour Fahmy, Ur- vashi Bhattacharyya, Wenhao Yu, Swayam Singh, Sasha Luccioni, Paulo Villegas, Maxim Kunakov, Fedor Zhdanov, Manuel Romero, Tony Lee, Nadav Timor, Jennifer Ding, Claire Schlesinger, Hailey Schoelkopf, Jan Ebert, Tri Dao, Mayank Mishra, Alex Gu, Jennifer Robinson, Carolyn Jane Ander- son, Brendan Dolan-Gavitt, Danish Contractor, Siva Reddy, Daniel Fried, Dzmitry Bahdanau, Yacine Jernite, Carlos Muñoz Ferrandis, Sean Hughes, Thomas Wolf, Arjun Guha, Leandro von Werra, and Harm de Vries. StarCoder: may the source be with you!, December 2023. arXiv:2305.06161 [cs]. [29] Kiersten M. Ruff and Rohit V. Pappu. AlphaFold and Implications for Intrinsically Disordered Proteins. Journal of Molecular Biology , 433(20):167208, October 2021. [30] Carter J. Wilson, Wing-Yiu Choy, and Mikko Karttunen. AlphaFold2: A Role for Disordered Pro- tein/Region Prediction? International Journal of Molecular Sciences , 23(9):4591, January 2022. [31] Bi Zhao, Sina Ghadermarzi, and Lukasz Kurgan. Comparative evaluation of AlphaFold2 and disorder predictors for prediction of intrinsic disorder, disorder content and fully disordered proteins. Computa- tional and Structural Biotechnology Journal, 21:3248–3258, January 2023. [32] Giulio Tesei, Anna Ida Trolle, Nicolas Jonsson, Johannes Betz, Frederik E. Knudsen, Francesco Pesce, Kristoffer E. Johansson, and Kresten Lindorff-Larsen. Conformational ensembles of the human intrin- sically disordered proteome. Nature, 626(8000):897–904, February 2024. [33] Maria Victoria Nugnes, Kamel Eddine Adel Bouhraoua, Mehdi Zoubiri, Rita Pancsa, Erzsébet Fichó, DisProt Consortium, Peter Tompa, Damiano Piovesan, Silvio C E Tosatto, and Maria Cristina As- promonte. DisProt in 2026: enhancing intrinsically disordered proteins accessibility, deposition, and annotation. Nucleic Acids Research , 54(D1):D383–D392, January 2026. [34] Vaishali P Waman, Nicola Bordin, Andy Lau, Shaun Kandathil, Jude Wells, David Miller, Sameer Velankar, David T Jones, Ian Sillitoe, and Christine Orengo. CATH v4.4: major expansion of CATH by experimental and predicted structural data. Nucleic Acids Research, 53(D1):D348–D355, January 2025. [35] Francois-Xavier Theillet, Lajos Kalmar, Peter Tompa, Kyou-Hoon Han, Philipp Selenko, A. Keith Dunker, Gary W. Daughdrill, and Vladimir N. Uversky. The alphabet of intrinsic disorder: I. Act like a Pro: On the abundance and roles of proline residues in intrinsically disordered proteins. Intrinsically Disordered Proteins, 1(1):e24360, 2013. [36] Kiersten M. Ruff, Matthew R. King, Alexander W. Ying, Vicky Liu, A vnika Pant, Whitney E. Lieber- man, Min Kyung Shinn, Xiaolei Su, Cigall Kadoch, and Rohit V. Pappu. Molecular grammars of predicted intrinsically disordered regions that span the human proteome. Cell, 189(1):323–342.e17, January 2026. [37] Milot Mirdita, Konstantin Schütze, Yoshitaka Moriwaki, Lim Heo, Sergey Ovchinnikov, and Martin Steinegger. ColabFold: making protein folding accessible to all. Nature Methods, 19(6):679–682, June 2022. [38] Iris Langstein-Skora, Andrea Schmid, Frauke Huth, Drin Shabani, Lorenz Spechtenhauser, Mariia Likhodeeva, Franziska Kunert, Felix J. Metzner, Ryan J. Emenecker, Mary O. Richardson, Wasim Aftab, Maximilian J. Götz, Sarah K. Payer, Niccoló Pietrantoni, Valentina Valka, Sakthi K. Ravichan- dran, Till Bartke, Karl-Peter Hopfner, Ulrich Gerland, Philipp Korber, and Alex S. Holehouse. Sequence and chemical specificity define the functional landscape of intrinsically disordered regions. Nature Cell Biology, 28(2):323–337, February 2026. [39] Rahul K Das, Kiersten M Ruff, and Rohit V Pappu. Relating sequence encoded information to form and function of intrinsically disordered proteins. Current Opinion in Structural Biology , 32:102–112, June 2015. 18 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [40] Robin van der Lee, Marija Buljan, Benjamin Lang, Robert J. Weatheritt, Gary W. Daughdrill, A. Keith Dunker, Monika Fuxreiter, Julian Gough, Joerg Gsponer, David T. Jones, Philip M. Kim, Richard W. Kriwacki, Christopher J. Oldfield, Rohit V. Pappu, Peter Tompa, Vladimir N. Uversky, Peter E. Wright, and M. Madan Babu. Classification of Intrinsically Disordered Regions and Proteins. Chemical Reviews, 114(13):6589–6631, July 2014. [41] Diana M. Mitrea, Jaclyn A. Cika, Christopher B. Stanley, Amanda Nourse, Paulo L. Onuchic, Priya R. Banerjee, Aaron H. Phillips, Cheon-Gil Park, Ashok A. Deniz, and Richard W. Kriwacki. Self-interaction of NPM1 modulates multiple mechanisms of liquid–liquid phase separation. Nature Communications, 9(1):842, February 2018. [42] Malisa Vittoria Mantonico, Federica De Leo, Giacomo Quilici, Liam Sean Colley, Francesco De Marchis, Massimo Crippa, Rosanna Mezzapelle, Tim Schulte, Chiara Zucchelli, Chiara Pastorello, Camilla Car- meno, Francesca Caprioglio, Stefano Ricagno, Gabriele Giachin, Michela Ghitti, Marco Emilio Bianchi, and Giovanna Musco. The acidic intrinsically disordered region of the inflammatory mediator HMGB1 mediates fuzzy interactions with CXCL12. Nature Communications, 15(1):1201, February 2024. [43] Yi-Hsuan Lin, Jacob P Brady, Julie D Forman-Kay, and Hue Sun Chan. Charge pattern matching as a ‘fuzzy’ mode of molecular recognition for the functional phase separations of intrinsically disordered proteins. New Journal of Physics, 19(11):115003, November 2017. [44] Rahul K. Das and Rohit V. Pappu. Conformations of intrinsically disordered proteins are influenced by linear sequence distributions of oppositely charged residues. Proceedings of the National Academy of Sciences, 110(33):13392–13397, August 2013. [45] Garrett M. Ginell, Ryan J. Emenecker, Jeffrey M. Lotthammer, Alex T. Keeley, Stephen P. Plassmeyer, Nicholas Razo, Emery T. Usher, Jaqueline F. Pelham, and Alex S. Holehouse. Sequence-based prediction of intermolecular interactions driven by disordered regions. Science, 388(6749):eadq8381, May 2025. [46] Wenwei Zheng, Gregory Dignon, Matthew Brown, Young C. Kim, and Jeetain Mittal. Hydropathy Pat- terning Complements Charge Patterning to Describe Conformational Preferences of Disordered Proteins. The Journal of Physical Chemistry Letters , 11(9):3408–3415, May 2020. [47] H. Jane Dyson, Peter E. Wright, and Harold A. Scheraga. The role of hydrophobic interactions in initia- tion and propagation of protein folding. Proceedings of the National Academy of Sciences, 103(35):13057– 13061, August 2006. [48] John C. Wootton and Scott Federhen. Statistics of local complexity in amino acid sequences and sequence databases. Computers & Chemistry , 17(2):149–163, June 1993. [49] Pedro Romero, Zoran Obradovic, Xiaohong Li, Ethan C. Garner, Celeste J. Brown, and A. Keith Dunker. Sequence complexity of disordered protein. Proteins: Structure, Function, and Bioinformatics, 42(1):38–48, 2001. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/1097- 0134%2820010101%2942%3A1%3C38%3A%3AAID-PROT50%3E3.0.CO%3B2-3. [50] Victor M. Panaretos and Yoav Zemel. Statistical Aspects of Wasserstein Distances. Annual Review of Statistics and Its Application , 6(Volume 6, 2019):405–431, March 2019. [51] Mylene C. Ferrolino, Diana M. Mitrea, J. Robert Michael, and Richard W. Kriwacki. Compositional adaptability in NPM1-SURF6 scaffolding networks enabled by dynamic switching of phase separation mechanisms. Nature Communications, 9(1):5064, November 2018. [52] Long Ouyang, Jeff Wu, Xu Jiang, Diogo Almeida, Carroll L Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, John Schulman, Jacob Hilton, Fraser Kelton, Luke Miller, Maddie Simens, Amanda Askell, Peter Welinder, Paul Christiano, Jan Leike, and Ryan Lowe. Training language models to follow instructions with human feedback. NeurIPS, 2022. [53] Noelia Ferruz and Birte Höcker. Controllable protein design with language models. Nature Machine Intelligence, 4(6):521–532, June 2022. 19 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [54] Junhao Xiong, Hunter Nisonoff, Maria Lukarska, Ishan Gaur, Luke M. Oltrogge, David F. Savage, and Jennifer Listgarten. Guide your favorite protein sequence generative model, July 2025. arXiv:2505.04823 [cs]. [55] Christine S. C. Ng, Aofei Liu, Bianxiao Cui, and Steven M. Banik. Targeted protein relocalization via protein transport coupling. Nature, 633(8031):941–951, September 2024. [56] Yifan Dai, Lingchong You, and Ashutosh Chilkoti. Engineering synthetic biomolecular condensates. Nature Reviews Bioengineering , pages 1–15, April 2023. [57] Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Peiyi Wang, Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, Xiaokang Zhang, Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chong Ruan, Damai Dai, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangbo Hao, Guanting Chen, Guowei Li, H. Zhang, Hanwei Xu, Honghui Ding, Huazuo Gao, Hui Qu, Hui Li, Jianzhong Guo, Jiashi Li, Jingchang Chen, Jingyang Yuan, Jinhao Tu, Junjie Qiu, Junlong Li, J. L. Cai, Jiaqi Ni, Jian Liang, Jin Chen, Kai Dong, Kai Hu, Kaichao You, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Liang Zhao, Litong Wang, Liyue Zhang, Lei Xu, Leyi Xia, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Mingxu Zhou, Meng Li, Miaojun Wang, Mingming Li, Ning Tian, Panpan Huang, Peng Zhang, Qiancheng Wang, Qinyu Chen, Qiushi Du, Ruiqi Ge, Ruisong Zhang, Ruizhe Pan, Runji Wang, R. J. Chen, R. L. Jin, Ruyi Chen, Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shengfeng Ye, Shiyu Wang, Shuiping Yu, Shunfeng Zhou, Shuting Pan, S. S. Li, Shuang Zhou, Shaoqing Wu, Tao Yun, Tian Pei, Tianyu Sun, T. Wang, Wangding Zeng, Wen Liu, Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang, W. L. Xiao, Wei An, Xiaodong Liu, Xiaohan Wang, Xiaokang Chen, Xiaotao Nie, Xin Cheng, Xin Liu, Xin Xie, Xingchao Liu, Xinyu Yang, Xinyuan Li, Xuecheng Su, Xuheng Lin, X. Q. Li, Xiangyue Jin, Xiaojin Shen, Xiaosha Chen, Xiaowen Sun, Xiaoxiang Wang, Xinnan Song, Xinyi Zhou, Xianzu Wang, Xinxia Shan, Y. K. Li, Y. Q. Wang, Y. X. Wei, Yang Zhang, Yanhong Xu, Yao Li, Yao Zhao, Yaofeng Sun, Yaohui Wang, Yi Yu, Yichao Zhang, Yifan Shi, Yiliang Xiong, Ying He, Yishi Piao, Yisong Wang, Yixuan Tan, Yiyang Ma, Yiyuan Liu, Yongqiang Guo, Yuan Ou, Yuduan Wang, Yue Gong, Yuheng Zou, Yujia He, Yunfan Xiong, Yuxiang Luo, Yuxiang You, Yuxuan Liu, Yuyang Zhou, Y. X. Zhu, Yanping Huang, Yaohui Li, Yi Zheng, Yuchen Zhu, Yunxian Ma, Ying Tang, Yukun Zha, Yuting Yan, Z. Z. Ren, Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, Zhenda Xie, Zhengyan Zhang, Zhewen Hao, Zhicheng Ma, Zhigang Yan, Zhiyu Wu, Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li, Ziwei Xie, Ziyang Song, Zizheng Pan, Zhen Huang, Zhipeng Xu, Zhongyu Zhang, and Zhen Zhang. DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning. Nature, 645(8081):633–638, September 2025. [58] Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin. Understanding R1-Zero-Like Training: A Critical Perspective, March 2025. arXiv:2503.20783 [cs] version: 1. [59] Yana R. Musinova, Eugenia Y. Kananykhina, Daria M. Potashnikova, Olga M. Lisitsyna, and Eugene V. Sheval. A charge-dependent mechanism is responsible for the dynamic accumulation of proteins inside nucleoli. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research , 1853(1):101–110, January 2015. [60] Robert M Martin, Gohar Ter-A vetisyan, Henry D Herce, Anne K Ludwig, Gisela Lättig-Tünnemann, and M Cristina Cardoso. Principles of protein targeting to the nucleolus. Nucleus, 6(4):314–325, August 2015. [61] Sean D Taverna, Haitao Li, Alexander J Ruthenburg, C David Allis, and Dinshaw J Patel. How chromatin-binding modules interpret histone modifications: lessons from professional pocket pickers. Nature structural & molecular biology , 14(11):1025–1040, November 2007. [62] Andrew J. Bannister and Tony Kouzarides. Regulation of chromatin by histone modifications. Cell Research, 21(3):381–395, March 2011. [63] Mashiat N. Chowdhury and Hong Jin. The RGG motif proteins: Interac- tions, functions, and regulations. WIREs RNA, 14(1):e1748, 2023. _eprint: https://wires.onlinelibrary.wiley.com/doi/pdf/10.1002/wrna.1748. 20 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [64] P alaniraja Thandapani, Timothy R. O’Connor, Timothy L. Bailey, and Stéphane Richard. Defining the RGG/RG Motif. Molecular Cell, 50(5):613–623, June 2013. [65] Sean R. Millar, Jie Qi Huang, Karl J. Schreiber, Yi-Cheng Tsai, Jiyun Won, Jianping Zhang, Alan M. Moses, and Ji-Young Youn. A New Phase of Networking: The Molecular Composition and Regulatory Dynamics of Mammalian Stress Granules. Chemical Reviews, 123(14):9036–9064, July 2023. [66] Tamami Miyagi, Rio Yamazaki, Koji Ueda, Satoshi Narumi, Yuhei Hayamizu, Hiroshi Uji-i, Masahiko Kuroda, and Kohsuke Kanekura. The Patterning and Proportion of Charged Residues in the Arginine- Rich Mixed-Charge Domain Determine the Membrane-Less Organelle Targeted by the Protein. Inter- national Journal of Molecular Sciences , 23(14):7658, January 2022. [67] Amandine Molliex, Jamshid Temirov, Jihun Lee, Maura Coughlin, Anderson P. Kanagaraj, Hong Joo Kim, Tanja Mittag, and J. Paul Taylor. Phase Separation by Low Complexity Domains Promotes Stress Granule Assembly and Drives Pathological Fibrillization. Cell, 163(1):123–133, September 2015. [68] Marc Ba¨uerle, Detlef Doenecke, and Werner Albig. The Requirement of H1 Histones for a Het- erodimeric Nuclear Import Receptor*. Journal of Biological Chemistry, 277(36):32480–32489, Septem- ber 2002. [69] Manjeet Kumar, Sushama Michael, Jesús Alvarado-Valverde, András Zeke, Tamas Lazar, Juliana Glav- ina, Eszter Nagy-Kanta, Juan Mac Donagh, Zsofia E Kalman, Stefano Pascarelli, Nicolas Palopoli, László Dobson, Carmen Florencia Suarez, Kim Van Roey, Izabella Krystkowiak, Juan Esteban Griffin, Anurag Nagpal, Rajesh Bhardwaj, Francesca Diella, Bálint Mészáros, Kellie Dean, Norman E Davey, Rita Pancsa, Lucía B Chemes, and Toby J Gibson. ELM—the Eukaryotic Linear Motif resource—2024 update. Nucleic Acids Research , 52(D1):D442–D455, January 2024. [70] Vikas Pejaver, Wei-Lun Hsu, Fuxiao Xin, A. Keith Dunker, Vladimir N. Uversky, and Pre- drag Radivojac. The structural and functional signatures of proteins that undergo multiple events of post-translational modification. Protein Science, 23(8):1077–1093, 2014. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pro.2494. [71] Carolyn J. Decker and Roy Parker. P-Bodies and Stress Granules: Possible Roles in the Control of Translation and mRNA Degradation. Cold Spring Harbor Perspectives in Biology, 4(9):a012286, September 2012. [72] Joris Van Lindt, Tamas Lazar, Donya Pakravan, Manon Demulder, Attila Meszaros, Ludo Van Den Bosch, Dominique Maes, and Peter Tompa. F/YGG-motif is an intrinsically dis- ordered nucleic-acid binding motif. RNA Biology , 19(1):622–635, December 2022. _eprint: https://doi.org/10.1080/15476286.2022.2066336. [73] Lennart Sänger, Julian Bender, Katja Rostowski, Ralph Golbik, Hauke Lilie, Carla Schmidt, Sven-Erik Behrens, and Susann Friedrich. Alternatively spliced isoforms of AUF1 regulate a miRNA–mRNA interaction differentially through their YGG motif. RNA Biology, 18(6):843–853, June 2021. _eprint: https://doi.org/10.1080/15476286.2020.1822637. [74] Annkatrin Bressin, Roman Schulte-Sasse, Davide Figini, Erika C Urdaneta, Benedikt M Beckmann, and Annalisa Marsico. TriPepSVM: de novo prediction of RNA-binding proteins based on short amino acid motifs. Nucleic Acids Research, 47(9):4406–4417, May 2019. [75] Masato Kato, Tina W. Han, Shanhai Xie, Kevin Shi, Xinlin Du, Leeju C. Wu, Hamid Mirzaei, Eliza- beth J. Goldsmith, Jamie Longgood, Jimin Pei, Nick V. Grishin, Douglas E. Frantz, Jay W. Schneider, She Chen, Lin Li, Michael R. Sawaya, David Eisenberg, Robert Tycko, and Steven L. McKnight. Cell- free Formation of RNA Granules: Low Complexity Sequence Domains Form Dynamic Fibers within Hydrogels. Cell, 149(4):753–767, May 2012. [76] Borna Novak, Jeffrey M. Lotthammer, Ryan J. Emenecker, and Alex S. Holehouse. Accurate predictions of disordered protein ensembles with STARLING. Nature, pages 1–11, February 2026. [77] Sören Von Bülow, Giulio Tesei, Fatima Kamal Zaidi, Tanja Mittag, and Kresten Lindorff-Larsen. Predic- tion of phase-separation propensities of disordered proteins from sequence. Proceedings of the National Academy of Sciences , 122(13):e2417920122, April 2025. 21 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint [78] A drian L Sanborn, Benjamin T Yeh, Jordan T Feigerle, Cynthia V Hao, Raphael JL Townshend, Erez Lieberman Aiden, Ron O Dror, and Roger D Kornberg. Simple biochemical features underlie transcriptional activation domain diversity and dynamic, fuzzy binding to Mediator. eLife, 10:e68068, April 2021. [79] Nicole DelRosso, Josh Tycko, Peter Suzuki, Cecelia Andrews, Aradhana, Adi Mukund, Ivan Liongson, Connor Ludwig, Kaitlyn Spees, Polly Fordyce, Michael C. Bassik, and Lacramioara Bintu. Large-scale mapping and mutagenesis of human transcriptional effector domains. Nature, 616(7956):365–372, April 2023. [80] Nicole DelRosso, Peter H. Suzuki, Daniel Griffith, Jeffrey M. Lotthammer, Borna Novak, Selin Kocalar, Maya U. Sheth, Alex S. Holehouse, Lacramioara Bintu, and Polly Fordyce. High-throughput affinity measurements of direct interactions between activation domains and co-activators, August 2024. Pages: 2024.08.19.608698 Section: New Results. [81] Rafael Rafailov, Archit Sharma, Eric Mitchell, Stefano Ermon, Christopher D. Manning, and Chelsea Finn. Direct Preference Optimization: Your Language Model is Secretly a Reward Model, July 2024. arXiv:2305.18290 [cs]. [82] Sebastian Ibarraran, Shriram Chennakesavalu, Frank Hu, and Grant M. Rotskoff. Efficient, Few- shot Directed Evolution with Energy Rank Alignment, February 2026. ISSN: 2692-8205 Pages: 2026.02.03.703561 Section: New Results. [83] Shriram Chennakesavalu, Frank Hu, Sebastian Ibarraran, and Grant M. Rotskoff. Aligning Transformers with Continuous Feedback via Energy Rank Alignment, October 2025. arXiv:2405.12961 [cs]. [84] Ethan Baron, Alan Nawzad Amin, Ruben Weitzman, Simon d’Oelsnitz, Debora Susan Marks, and Andrew Gordon Wilson. Shrinking proteins with diffusion. In The Fourteenth International Conference on Learning Representations , 2026. [85] Hoagy Cunningham, Aidan Ewart, Logan Riggs, Robert Huben, and Lee Sharkey. Sparse Autoencoders Find Highly Interpretable Features in Language Models, October 2023. arXiv:2309.08600 [cs]. [86] Elana Simon and James Zou. InterPLM: discovering interpretable features in protein language models via sparse autoencoders. Nature Methods, 22(10):2107–2117, October 2025. [87] Noam Shazeer. GLU Variants Improve Transformer, February 2020. arXiv:2002.05202 [cs]. [88] Jianlin Su, Yu Lu, Shengfeng Pan, Ahmed Murtadha, Bo Wen, and Yunfeng Liu. RoFormer: Enhanced Transformer with Rotary Position Embedding, November 2023. arXiv:2104.09864 [cs]. [89] Tri Dao, Daniel Y. Fu, Stefano Ermon, Atri Rudra, and Christopher Ré. FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness, June 2022. arXiv:2205.14135 [cs]. [90] Alex S. Holehouse. sparrow: a tool for integrative analysis and prediction from protein sequence data. Zenodo, July 2022. ADS Bibcode: 2022zndo...6891920H. [91] Schrödinger, LLC. The PyMOL Molecular Graphics System, 2025. PyMOL (Version 3.1). [92] Robert T. McGibbon, Kyle A. Beauchamp, Matthew P. Harrigan, Christoph Klein, Jason M. Swails, Carlos X. Hernández, Christian R. Schwantes, Lee-Ping Wang, Thomas J. Lane, and Vijay S. Pande. Mdtraj: A modern open library for the analysis of molecular dynamics trajectories. Biophysical Journal, 109(8):1528 – 1532, 2015. [93] Jeffrey M. Lotthammer, Jorge Hernández-García, Daniel Griffith, Dolf Weijers, Alex S. Holehouse, and Ryan J. Emenecker. Metapredict enables accurate disorder prediction across the Tree of Life, November 2024. Pages: 2024.11.05.622168 Section: New Results. [94] Gábor Erdős, Mátyás Pajkos, and Zsuzsanna Dosztányi. IUPred3: prediction of protein disorder en- hanced with unambiguous experimental annotation and visualization of evolutionary conservation. Nu- cleic Acids Research , 49(W1):W297–W303, July 2021. 22 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Supplemen tary Information Datasets Here we describe the datasets provided on HuggingFace: Datasets (https://huggingface.co/datasets/jxliu2/idiom-datasets) Below, we describe the data files under idr_datasets/training_sequences: • AFDB_IDR_90_reps.fasta contains the 53M cluster representatives after the initial 214M full length AFDB protein sequences are clustered at 90% identity, 80% coverage. • AFDB_IDR_90_alldata.h5 contains 73M IDRs as extracted from the AFDB according to the Tesei logic [32] (see Methods), and after filtering for IDRs belonging to the 53M cluster representatives identified in AFDB_IDR_90_reps.fasta. This HDF5 file contains the following keys: . • AFDB_IDR_90_FIM_512.h5 is created from AFDB_IDR_90_alldata.h5 by filtering out IDRs whose full length sequences are longer than 512 residues. We also find that ∼ 1/3 of records in AFDB_IDR_90_alldata.h5 are fully low-pLDDT sequences, and we filter out those sequences because we find that they are not representative of intrinsically disordered proteins. We only keep sequences with both low- and high-pLDDT regions. We hypothesize that sequences which are fully low-pLDDT are due to AlphaFold2’s poor confidence in sequences which are not similar to those seen during training, rather than because they are fully intrinsically disordered proteins. For the remaining 37M IDRs, we apply the fill-in-the-middle (FIM) transformation as well as IDP data augmentation as mentioned in the Methods, and place those records into AFDB_IDR_90_FIM_512.h5. We note that we represent the , , and tokens with 1, 2, and 3, respectively, in this HDF5 file as well as in the codebase. This is the final file used for the precompute and pre-training steps. • AFDB_IDR_90_FIM_512_full.fasta contains the 37M full length sequences (in correct order, not FIM-transformed) contained in AFDB_IDR_90_FIM_512.h5. The fasta header contains _IDR_X-Y where X and Y are the 1-indexed indices of the start and end (inclusive) of the intrinsically disordered region. • AFDB_IDR_90_FIM_512_idrs.fasta contains only the sequences of the 37M intrinsically dis- ordered regions in AFDB_IDR_90_FIM_512_full.fasta, without their surrounding context. We also provide several datasets of sequences generated by our model under idr_datasets/generated_- sequences. All generated sequences are provided in F ASTA format along with their corresponding autoregressive model log (pickle format). • Generated IDPs: 100,000 unprompted intrinsically disordered proteins. • Generated IDRs: 101,700 intrinsically disordered regions generated using 1,017 DisProt flank- ing contexts prompts (100 generated IDRs per prompt). • Generated NPM1 IDRs: 100,000 sequences generated using the NPM1 flanking context as the prompt (UniProt: P06748). • Generated ProtGPS Sequences: 10,000 IDPs generated from post-trained checkpoints. Post- training was done to optimize ProtGPS localization scores for the four target compartments: chromosome, nucleolus, P-body, and stress granule. 23 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Mo dels Here we describe the model checkpoints and other files provided on HuggingFace: Models (https://huggingface.co/jxliu2/idiom) Below, we describe the directories under idiom/: • base/ contains the checkpoint of our pre-trained base IDiom model, along with its configu- ration files. • post_trained/protgps_reward/ contains the checkpoints of IDiom post-trained via rein- forcement learning using the ProtGPS reward model, one checkpoint per target compart- ment. In this paper, we analyzed results for 4 compartments: the nucleolus, stress granules, P-bodies, and chromosomes. However, post-training runs were conducted for all 12 Prot- GPS compartments (chromosome, nucleolus, nuclear speckle, nuclear pore complex, P-body, PML body, post-synaptic density, stress granule, Cajal body, RNA granule, cell junction, and transcriptional condensate). We leave analysis of the remaining compartments to future work. • protgps/ contains the ProtGPS reward model used during reinforcement learning post- training. • data/ contains auxiliary files used during training and inference. Secondary Structure Metric Analysis Here we present analysis of secondary structure metrics for training, generated, DisProt, and CATH sequences. Secondary structure was assigned per residue using the dictionary of secondary structure of proteins (DSSP) algorithm as implemented in MDTraj [92]. Secondary structure content was then defined as the sum of the mean α-helical and mean β-sheet fractions across all residues. Fig. S1 shows histograms of the average secondary structure content of 100 randomly chosen sequences from the various training, generated, DisProt, and CATH sets of proteins. Train/uni00A0IDRs/uni00A0no/uni00A0context DisProt/uni00A0IDRs/uni00A0no/uni00A0context Gen/uni00A0IDRs/uni00A0no/uni00A0context Gen/uni00A0IDPs CATH 0.00 0.25 0.50 0.75 Secondary/uni00A0structure/uni00A0content 0 1 2 3 4Density (a) Train/uni00A0IDRs/uni00A0w//uni00A0context DisProt/uni00A0IDRs/uni00A0w//uni00A0context Gen/uni00A0IDRs/uni00A0w//uni00A0context CATH 0.00 0.25 0.50 0.75 Secondary/uni00A0structure/uni00A0content 0 2 4 6Density (b) RL/uni00A0chromosome/uni00A0IDPs RL/uni00A0nucleolus/uni00A0IDPs RL/uni00A0p/uni00ADbody/uni00A0IDPs RL/uni00A0stress/uni00A0granule/uni00A0IDPs CATH 0.00 0.25 0.50 0.75 Secondary/uni00A0structure/uni00A0content 0.0 2.5 5.0 7.5 10.0Density (c) Fig. S1: Secondary structure content analysis. Histograms of of the average secondary structure content (α + β) for the AF2-predicted structures of 100 randomly chosen sequences from the following sets of sequences: (a) Secondary structure content of training IDRs, generated IDRs, DisProt IDRs, and CATH sequences, with their structures predicted with surrounding context included. (b) Secondary structure con- tent of training IDPs, generated IDPs, DisProt IDPs, and CATH sequences, with their structures predicted without their surrounding context. (c) Secondary structure content of IDPs generated from post-trained IDiom checkpoints and CATH sequences, with their structures predicted with surrounding context included. 24 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Disorder Predictions Here, we present orthogonal disorder predictions from Metapredict v3 [93] and IUPred3 [ 94]. For both predictors, a higher value represents a higher propensity towards disorder. DisProt/uni00A0IDRs/uni00A0(mean=0.639)CATH/uni00A0(mean=0.145) Gen/uni00A0IDPsGen/uni00A0IDRsTrain/uni00A0IDRs NPM1 Chromosome NucleolusP/uni00ADbody Stress/uni00A0granule 0.0 0.5 1.0Metapredict/uni00A0V3 Fig. S2: Disorder predictions from Metapredict V3 . Higher values correspond to higher propensity towards disorder. The horizontal green and red dashed lines correspond to the predicted Metapredict V3 values for 1,017 DisProt IDRs and 1,000 CATH sequences, respectively. The bars correspond to predicted Metapredict values for 10,000 sequences generated from IDiom for each condition, as well as 10,000 training sequences. The sequences generated from IDiom include unprompted IDPs, DisProt-prompted IDRs, NPM1 IDRs, and IDPs generated after post-training for localization to the chromosomes, nucleolus, P-bodies, and stress granules. DisProt/uni00A0IDRs/uni00A0(mean=0.535)CATH/uni00A0(mean=0.231) Gen/uni00A0IDPsGen/uni00A0IDRsTrain/uni00A0IDRs NPM1 Chromosome NucleolusP/uni00ADbody Stress/uni00A0granule 0.0 0.5 1.0IUPred3 Fig. S3: Disorder predictions from IUPred3 . Higher values correspond to higher propensity towards disorder. The horizontal green and red dashed lines correspond to the predicted IUPred3 values for 1,017 DisProt IDRs and 1,000 CATH sequences, respectively. The bars correspond to predicted IUPred3 values for 10,000 sequences generated from IDiom for each condition, as well as 10,000 training sequences. The sequences generated from IDiom include unprompted IDPs, DisProt-prompted IDRs, NPM1 IDRs, and IDPs generated after post-training for localization to the chromosomes, nucleolus, P-bodies, and stress granules. ESM3 Comparison Here we present comparison plots between sequences generated by IDiom and ESM3, using the same 1,017 DisProt flanking domain prompts. ESM3 sequences are generated using iterative decoding. A total of 1,000 sequences are sampled for each prompt. As ESM3 consists of a bidirectional trans- former architecture, the length of the generated IDRs is fixed at the length of the ground truth IDR. The number of decoding steps, i.e. forward passes until the sequence is fully unmasked, is set 25 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint to be the minimum of 20 and the ground truth IDR length for each prompt. Tokens are sampled with a temperature of 1.0, and all other default inference hyperparameters for ESM3 are used. We find that compared to IDiom, ESM3-generated IDRs are extremely low-complexity sequences, with a peak in the SEG complexity distribution around 0.5 (Figure S4). We show three example ESM3-generated IDRs below, in red: UniProt P48439: MNWLFLVSLVFFCGVSTHPALAHFLDLLLLLLLLLLLLLQLILTAILAAIALLLLLLFLL IVIGILLGLSLGALQLLLLLLLLLLLLSFALQLIFAAILAALLLILLLLLLLIVIGILLS LSFGALQLLILLLILLLWLLTLLLAKQLKLALALILAAILAALILLLLLLLLLLLIVIGI LFGLSLSALQLLLFLLLLLLLLLLVSFALKLKNPISRIIWATLSTFFIICMISAYMFNQI RNTQLAGVGPKGEVMYFLPNEFQHQFAIETQVMVLIYGTLAALVVVLVKGIQFLRSHLYP ETKKAYFIDAILASFCALFIYVFFAALTTVFTIKSPAYPFPLLRLSAPFK UniProt Q9NS23-4: MPCHPPPLPPPPPPPSPPPEEEEEEEEIEEEGEEEEPPASPLPPASPPAPEPVEWETPDL SQAEIEQKIKEYNAQINSNLFMSLNKDGSYTGFIKVQLKLVRPVSVPSSKKPPSLQDARR GPGRGTSVRRRTSFYLPKDAVKHLHVLSRTRAREVIEALLRKFLVVDDPRKFALFERAER HGQVYLRKLLDDEQPLRLRLLAGPSDKALSFVLKENDSGEVNWDAFSMPELHNFLRILQR EEEEHLRQILQKYSYCRQKIQEALHACPLG UniProt Q14011: MASDEGKLFVGGLSFDTNEQSLEQVFSKYGQISEVVVVKDRETQRSRGFGFVTFENIDDA KDAMMAMNGKSVDGRQIRVDQAGKSSDNRGGGGGGGGGRGGGGGGGGGGGGRGGGGGGRG GGGSGGGGGGRGGGGGSGGRGGGGGGGGGGGGGGGGGGGGGRGGGGGGGGRY 0.0 0.2 0.4 0.6 FCR 0 2 4 6 8Density (a) Gen/uni00A0IDPs Gen/uni00A0IDRs DisProt/uni00A0IDRs Train/uni00A0IDRs CATH ESM3/uni00A0IDRs 0.0 0.5 1.0 0 2 4 6 8Density (b) 4 6 8 SHD 0 0 0Density (c) 0.0 0.5 1.0 Sequence/uni00A0Complexity 0 5 10Density (d) Fig. S4: Comparison between ESM3-generated IDRs and IDiom-generated IDRs. (a)–(d) Distri- butions of various sequence metrics for sequences generated from IDiom versus ESM3. Training set IDRs, natural DisProt IDRs, and folded CATH domains are shown as well. (a) Fraction of charged residues (FCR). (b) Charge patterning κ parameter. (c) Sequence hydropathy decoration (SHD). (d) Sequence complexity quantified by the SEG algorithm. 26 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint Short Linear Motifs from the Eukaryotic Linear Motif Resource Here, we list the short linear motifs from the ELM Resource which we scan for, for nuclear local- ization signals (NLSs) as well as for post-translational modification (PTM) sites (ELM Identifier: MOD). Nuclear Localization Signals The regular expressions of the 4 NLSs we consider are: ID P attern (regex) TRG_NLS_Bipartite_1 [KR][KR].{7,15}[D̂E]((K[RK])|(RK))(([D̂E][KR])|([KR][D̂E]))[D̂E] TRG_NLS_MonoCore_2 [D̂E]((K[RK])|(RK))[KRP][KR][D̂E] TRG_NLS_MonoExtC_3 [D̂E]((K[RK])|(RK))(([D̂E][KR])|([KR][D̂E]))(([PKR])|([D̂E][DE])) TRG_NLS_MonoExtN_4 (([PKR].{0,1}[D̂E])|([PKR]))((K[RK])|(RK))(([D̂E][KR])|([KR][D̂E]))[D̂E] T able 1: ELM NLS motifs and their corresponding regex patterns. 27 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint P ost Translational Modification Motifs The regular expressions of the 40 PTM MOD sites we consider are: ID P attern (regex) MOD_AAK1BIKe_LxxQxTG_1 [LIVM][D̂][D̂EHYWF]Q.(T)G MOD_ASX_betaOH_EGF C.([DN]).{4,4}[FY].C.C MOD_CAAXbox (C)[D̂ENQ][LIVMF].$ MOD_CDC14_SPxK_1 (S)P.[KR] MOD_CDK_SPK_2 ...([ST])P[RK] MOD_CDK_SPxK_1 ...([ST])P.[KR] MOD_CDK_SPxxK_3 ...([ST])P..[RK] MOD_CK1_1 S..([ST])... MOD_CK2_1 ...([ST])..E MOD_CMANNOS (W)..W MOD_Cter_Amidation (.)G[RK][RK] MOD_DYRK1A_RPxSP_1 R[PSVA].([ST])P MOD_GlcNHglycan [ED]{0,3}.(S)[GA]. MOD_GSK3_1 ...([ST])...[ST] MOD_LATS_1 H.[KR]..([ST])[P̂] MOD_LOK_YxT_1 [KR][YF][ÎVEDPGAC](T)[LMIVWFY][RKH] MOD_NEK2_1 [FLM][P̂VIED][P̂VID]([ST])[MLIVF][RKH]. MOD_NEK2_2 [FLMW][P̂][P̂]([ST])[P̂DEGAN][RKH]. MOD_N-GLC_1 .(N)[P̂][ST].. MOD_N-GLC_2 (N)[P̂]C MOD_NMyristoyl M̂{0,1}(G)[ÊDRKHPFYW]..[STAGCN][P̂] MOD_OFUCOSY C.{3,5}([ST])C MOD_OGLYCOS C.(S).PC MOD_PIKK_1 ...([ST])Q.. MOD_PK_1 [RK]..(S)[VI].. MOD_PKA_1 [RK][RK].([ST])[P̂].. MOD_PKA_2 .R.([ST])[P̂].. MOD_PKB_1 R.R..([ST])[P̂].. MOD_Plk_1 .[DNE][P̂G][ST](([FYILMVW]..)|([P̂EDGKN][FWYLIVM]).) MOD_Plk_2-3 [DE]..([ST])[EDILMVFWY](([DE].)|(.[DE])) MOD_Plk_4 ..[ÎRFW]([ST])[ILMVFWY][ILMVFWY]. MOD_PRMT_GGRGG_1 GGRGG MOD_ProDKin_1 ...([ST])P.. MOD_SPalmitoyl_2 G(C)M[GS][CL][KP]C MOD_SPalmitoyl_4 M̂{0,1}G(C)..S[AKS] MOD_SUMO_for_1 [VILMAFP](K).E MOD_SUMO_rev_2 [SDE].{0,5}[DE].(K).{0,1}[AIFLMPSTV] MOD_TYR_CSK [TAD][EA].Q(Y)[QE].[GQA][PEDLS] MOD_TYR_DYR ..[RKTC][IVL]Y[TQHS](Y)[IL]QSR MOD_WntLipid [ETA](C)[QERK]..F...RWNC[ST] T able 2: ELM MOD motifs and their corresponding regex patterns. 28 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint T raining Curves Here, we present additional training curves from pre-training as well as post-training. 0 100k 250k Training/uni00A0Steps 2.2 2.4 2.6 2.8Loss Validation Train Fig. S5: Pretraining loss curves. Training and validation losses vs optimizer steps during pre-training. The final training loss is 2.19. The final validation loss is 2.22. 0 500 1000 1500 Training/uni00A0Steps 2.6 2.7Sequence/uni00A0Entropy p/uni00ADbody stress/uni00ADgranule nucleolus chromosome (a) 0 500 1000 1500 Training/uni00A0Steps 40 42 44%ID (b) Fig. S6: Additional post-training curves with the ProtGPS reward model. (a) Shannon entropy vs. training steps (target H = 2.7). (b) %ID within a generated batch vs training steps (no target value). 29 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint