{"paper_id":"0657918f-e467-463c-9ded-d9def325afc6","body_text":"Generativ\ne design of intrinsically disordered protein regions with\nIDiom\nJason X. Liu 1, Sebastian Ibarraran 2,†, Frank Hu 2,†, Abigail Park 2,†,\nAlexander R. Dunn 1,∗, and Grant M. Rotskoff 2,3,∗\n1Department of Chemical Engineering, Stanford University, Stanford, CA 94305\n2Department of Chemistry, Stanford University, Stanford, CA 94305\n3Institute for Computational and Mathematical Engineering,\nStanford University, Stanford, CA 94305\nApril 9, 2026\nAbstract\nIntrinsically disordered protein regions are ubiquitous across all kingdoms of life. These\nstructurally heterogeneous regions play central roles in cellular processes such as transcriptional\nregulation, cellular signaling, and subcellular organization, yet they have remained largely inac-\ncessible to rational design. Structure-based generative methods are not applicable to proteins\nthat lack a stable fold, and existing sequence-based approaches for disordered regions rely on\nsampling methods that do not capture the evolutionary statistics of natural disordered regions.\nHere, we introduce IDiom, an autoregressive protein language model trained on 37 million in-\ntrinsically disordered region sequences curated from the AlphaFold Database. Trained using a\nfill-in-the-middle data augmentation, IDiom generates disordered region sequences conditioned\non their surrounding structured context, as well as fully disordered proteins without any con-\ntext. The model generates diverse sequences that recapitulate biologically relevant sequence\nfeatures of natural disordered regions, and we demonstrate that post-training via reinforcement\nlearning with a subcellular localization reward model produces sequences with features which\nare consistent with known sequence determinants of compartment-specific localization. These\nresults establish IDiom as a general platform for the generative design of intrinsically disordered\nproteins and regions.\nIntroduction\nIntrinsically disordered protein regions are ubiquitous across all kingdoms of life. The functional\nrelevance of intrinsically disordered regions (IDRs) has become increasingly clear recently, in spite\nof the classical dogma of protein biology that structure implies function [ 1]. While IDRs do not\nadopt well-defined folds, these sequences can act as flexible linkers [2], multivalent signaling hubs\n†These\nauthors contributed equally.\nCode is available on GitHub. Data is available on HuggingFace.\n∗Correspondence: rotskoff@stanford.edu, ardunn@stanford.edu\n1\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\n[3],\nand drivers of biomolecular condensate formation [4, 5, 6], playing crucial roles in biological\nprocesses such as transcriptional regulation, chromatin organization, and subcellular organization\n[1, 7].\nRational design of IDRs would unlock new functional controls in bioengineering, including\ntunable condensate phase behavior, precise regulation of cell signaling, and targeted protein lo-\ncalization [8]. While much of the recent progress in protein design has been driven by accurate\nstructure prediction [9, 10] and diffusion-based generative models [11, 12, 13], direct application of\nthese approaches to IDRs is untenable due to their lack of a stable folded structure.\nSequence-based generative models have also been extensively explored recently for applications\nin protein design. Transformer-based [14] protein language models (PLMs) have been trained on\ncorpora of full length protein sequences from databases such as the UniProt Reference Clusters and\nthe Big Fantastic Database. These models learn rich evolutionary statistics over amino acid se-\nquences and have enabled the design of novel proteins and functional variants [ 15, 16, 17, 18, 19, 20].\nNevertheless, the design of intrinsically disordered regions with existing PLMs is not straight-\nforward: since structured domains outnumber intrinsically disordered regions in the sequence\ndatabases on which current PLMs are trained, the generative prior is largely biased towards\nfolded domains [ 15]. Alternative sequence-based approaches to IDR design have attempted to\nuse sampling-based methods to construct IDRs from compositional rules or simple statistical mod-\nels [ 21, 22, 23, 24]. However, these approaches cannot be conditioned on any surrounding sequence\ncontext of generated IDRs, and they do not capture the evolutionary statistics which emerge from\ntraining on large corpora of natural protein sequences.\nHere, we address this gap by training a 122M parameter autoregressive, decoder-only protein\nlanguage model called IDiom using a dataset of 37 million intrinsically disordered regions curated\nfrom the AlphaFold Database (Figure 1a) [25, 26]. We apply a fill-in-the-middle transformation\nto the training data [27, 28] to enable the model to generate IDR spans conditioned on their\nsurrounding context, a capability essential for the design of disordered regions [8]. Training on this\ndataset of disordered sequences allows IDiom to learn a generative prior over the sequence statistics\nof natural disordered regions, and we demonstrate that the model generates diverse sequences that\nrecapitulate the compositions, patterning, and motifs of natural intrinsically disordered regions.\nWe further show that IDiom learns in-context: given the flanking sequence context of a specific\nprotein, the model generates disordered spans whose sequence features are more appropriate for\nthat context than unprompted generations. Finally, we demonstrate that IDiom can be post-\ntrained using reinforcement learning, and we apply this to design disordered sequences with targeted\nsubcellular localization [ 23]. Together, these results establish IDiom as a general platform for the\ngenerative design of intrinsically disordered proteins and regions.\nResults\nProtein language modeling for intrinsically disordered proteins and regions\nTo curate a dataset of intrinsically disordered region (IDR) sequences for model training, we first\nuse AlphaFold2 (AF2) predicted structures from the AlphaFold Database (AFDB) [ 26] to identify\nIDRs of proteins. We use low AF2 predicted local distance difference test (pLDDT) values as\na predictor of disorder, as this has been demonstrated to correlate strongly with experimental\nmeasurements of disorder [ 29, 30, 31]. To curate these IDRs from the database, we first cluster\nAFDB sequences at 90% sequence identity before applying a windowed pLDDT-based threshold\nto identify IDRs [ 32], with proteins containing multiple IDRs contributing multiple records to the\ndataset. Finally, we discard IDRs shorter than 30 residues, IDRs which reside in proteins whose full\n2\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\n37M pLDDT-based\nIDRs from the\nAlphaFold Database\nFill-in-the-middle\ntransformation\nIDP data\naugmentation\nMEDS..LVAVEED..KGPSSVED..KSL<N>ME..VA<C>SV..SL<I>VE..PS\n<N><C><I>VEED..KGPS\nP(ai | a<i)\n<N>M..A<C>S..L<I>ED[ ]\nor \n<N><C><I>MSTSN[ ]\nGeneratePretrain\nReward(MSTSN..)\nPost-train\nPredict\nIDiom\nWild-type NPM1\nSYFA prompt generated IDR\nUnprompted generated IDP\nMSTSNLNLTDDN..FAPLAARPGTRS\nMRANRR..PAELTPITLM..EQFKGVL\na b c\nd e g\nf\nFig.\n1: Data curation, training, and generative modeling of intrinsically disordered regions\n(IDRs) and proteins (IDPs) using IDiom. (a) Schematic depicting data preparation, pre-training,\nsequence generation, and post-training of IDiom. (b) Distribution of the sequence locations of 37M IDRs\ncurated from the AlphaFold Database (AFDB), as well as the locations of experimentally validated DisProt\nIDRs. (c) AlphaFold2 (AF2)-predicted structures, amino acid sequences, and plots of predicted local distance\ndifference test (pLDDT) values of an example IDR curated from AFDB (NPM1, upper), an IDR generated\nby IDiom using SYF A as the prompt (middle), and an unprompted generated IDP (lower). Blue and green\nregions correspond to the N-terminal and C-terminal flanking context around the IDR, which is orange. (d)\nDistribution of maximum sequence identities of unprompted generated IDPs and DisProt-prompt generated\nIDRs relative to the 37M IDRs of the training set, calculated using MMseqs2. (e) Distribution of sequence\nlengths of unprompted generated IDPs, DisProt-prompt generated IDRs, natural DisProt IDRs, and training\nset IDRs. (f) Relative enrichment of amino acid compositions of unprompted generated IDPs, DisProt-\nprompt generated IDRs, natural DisProt IDRs, and training set IDRs. The horizontal dashed line is the\nreference composition of folded CATH domain sequences. (g) (Upper): AF2 prediction pLDDTs of generated\nunprompted IDPs, natural DisProt IDRs removed from their surrounding context (DisProt IDPs), training\nset IDRs removed from their surrounding context (train IDPs), and CATH domains. (Lower): AF2 prediction\npLDDTs of DisProt-prompt generated IDRs, natural DisProt IDRs within their context, training set IDRs\nwithin their context, and CATH domains.\nlength is greater than 512 residues, and proteins whose entire length is low-pLDDT. This process\nyields a dataset of 37M IDRs and their positions within their associated full length proteins (see\nMethods for more details). Figure 1c (upper) depicts an example low-pLDDT IDR, in orange,\nextracted by this process for the human protein NPM1 (UniProt: P06748).\nWe use two baselines to validate our data curation strategy. First, we use 1,017 experimentally\nvalidated IDRs from the DisProt database as a ground-truth dataset of IDRs [ 33]. Second, we\n3\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nuse\n1,000 randomly chosen sequences from the Class, Architecture, Topology, and Homologous\nsuperfamily (CATH) database clustered at 60% identity (S60) as a ground-truth dataset of protein\ndomains with well-defined folded structures [34]. Using secondary structure content calculations,\nwe show that this method extracts IDRs with substantially lower secondary structural content\ncompared to CATH sequences (Figure S1). We note that our analysis shows that AF2 assigns high\nsecondary structural content (with low confidence) to a fraction of the extracted IDRs, although\nthis effect is also reflected in the set of DisProt IDRs. We additionally run orthogonal disorder\npredictions on a subset of the dataset and further validate that the curated sequences score similarly\nto DisProt sequences on these metrics (Figures S2, S3).\nIntrinsically disordered regions are naturally located at various locations within a protein se-\nquence, with approximately 45% of the AFDB-curated IDRs located at the N-terminus, 29% at\nthe C-terminus, and 26% in between other regions of the protein; similar percentages are observed\nfor experimentally validated IDRs from the DisProt set (Figure 1b). To enable IDiom to infill\nsequences of intrinsically disordered regions at arbitrary locations within a protein, we employ a\nfill-in-the-middle data transformation [ 27, 28]. In this approach, we prepend the special token <N>\nto residues in the N-terminal flanking context before the IDR, the token <C> to residues in the\nC-terminal context after the IDR, and the token <I> to residues of the IDR span itself. Then, we\ntransform the sequence by relocating <I> and the IDR span to the end of the entire sequence, thus\nallowing the standard causal language modeling objective to generate IDR spans conditioned on\nany preceding N-terminal and succeeding C-terminal flanking context (see Figure 1a). In addition,\nto enable the generation of intrinsically disordered proteins (IDPs) with no surrounding context,\nwe augment the dataset by creating records in which take each curated IDR and delete their N-\nand C-terminal flanking context, enabling unconditioned generation. The final dataset comprises\n74M sequences in total (37M IDRs and 37M IDPs), which we use to pre-train IDiom. Additional\ndetails of the data augmentation, model architecture, and training procedure are provided in the\nMethods section.\nIDiom generates diverse disordered regions and proteins\nTo characterize the pre-trained model, we first generate two sets of sequences: 100,000 unprompted\nIDPs (referred to as generated IDPs), and a set of context-prompted IDRs in which 100 IDRs\nare generated for each of 1,017 experimentally validated IDRs from the DisProt set, using the IDR\nflanking contexts as prompts (referred to as generated IDRs). Representative examples of a DisProt\ncontext-prompted IDR and an unprompted IDP are shown in Figure 1c (middle) and 1c (lower),\nrespectively.\nWe find that across multiple metrics, IDiom generates sequences that closely resemble natural\nDisProt IDRs while remaining diverse and distinct from the training data. The distribution of\nmaximum sequence identities to training set IDRs peaks broadly around 60%, indicating that most\ngenerated sequences are substantially dissimilar to any sequence seen during training (Figure 1d).\nGenerated IDR and IDP lengths are also consistent with those of both the training set and DisProt\nIDRs, with most sequences below 100 residues long and a tail extending to approximately 300\nresidues long (Figure 1e).\nTo analyze the compositional biases of the IDRs and IDPs, we compute the amino acid enrich-\nment of training, generated, and DisProt sequences relative to a baseline composition of the folded\nCATH domains (Figure 1f). Consistent with established compositional biases of disordered regions\n[35, 36], generated sequences are strongly enriched in proline and serine, and depleted in order-\npromoting aliphatics such as leucine, isoleucine, and valine, as well as the aromatics phenylalanine,\ntryptophan, and tyrosine. The trends for training and generated sequences closely match natural\n4\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nDisProt\nIDRs across most amino acids, with the closest agreement observed for IDRs generated\nwith the DisProt flanking contexts as prompts. We note that the discrepancies with DisProt in the\ngenerated compositions of cysteine and charged residues (glutamic acid, lysine, and aspartic acid),\nmay be attributed to the small size and selection bias of the DisProt dataset.\nWe next assess the extent to which the generated sequences are disordered by predicting their\nstructures using ColabFold [37]; the resulting pLDDT distributions are shown in Figure 1g. We\nrun the structure predictions in two settings. In the first, we compare the unprompted generated\nIDPs to DisProt and training IDRs which are provided to ColabFold as standalone sequences,\nwithout their flanking context (i.e. as IDPs). In this setting, the pLDDT for a given sequence\nis averaged across the entire IDP, generated or extracted (Figure 1g (upper)). In the second, we\ncompare the DisProt-prompt generated IDRs to the full protein DisProt and training sequences.\nIn this setting, we provide the full generated, training, or DisProt sequence to ColabFold, and the\npLDDT is only averaged across the IDR span (Figure 1g (lower)). Across both settings, generated\nsequences exhibit pLDDT distributions that closely mirror those of DisProt as well as the training\nset, confirming that IDiom is able to generate sequences which are predicted to be disordered to the\nsame extent as natural IDRs. We note that the pLDDTs of IDPs in isolation are higher than for\nIDRs within their flanking context, which may be due to dataset biases in the AF2 training data.\nWe additionally calculate secondary structure metrics and conduct orthogonal disorder predictions\non these generated sequences, and we find that the metrics compare similarly to DisProt IDRs\n(Figures S1–S3).\nGenerated sequences capture the residue patterning of natural disordered re-\ngions\nIDRs exhibit sequence patterning features that differ substantially from those of folded domains,\nincluding characteristic charge distributions, hydrophobic residue patterning, and low-complexity\ncompositions [ 38, 36, 39]. Figure 2a shows representative generated sequences which illustrate\ncanonical IDR features such as Q/N-rich low-complexity regions [ 40], polyampholyte charge block\npatterning [41], prion-like aromatic/glycine patterning [4], and proline enrichment [35]. To quantify\nhow well IDiom recapitulates these properties, we computed the distributions of several sequence-\nlevel metrics for the generated, training, and DisProt disordered sequences, as well as the folded\nCATH domain sequences (Figure 2b-e).\nElectrostatic interactions strongly influence the conformational behavior of IDRs, and both\nthe overall charge content and its linear patterning are closely linked to physical properties and\nbiological function [42, 43, 41, 39]. The fraction of charged residues (FCR, Figure 2b) distinguishes\nstrongly charged polyampholytes from weakly charged sequences. We find that the generated and\nnatural IDRs and IDPs span a wider range of FCR values than folded CATH domains, reflecting\nthe heterogeneity of natural IDRs, which range from highly charged sequences in which electrostatic\nrepulsion drives disorder, to weakly charged low-complexity sequences [44].\nTo characterize charge patterning, we calculate the linear charge patterning parameter κ, which\nquantifies the deviation of a given sequence from a maximally charge segregated permutation of the\nsame sequence [ 44]. κ ≈ 0 indicates well-mixed opposite charges and κ ≈ 1 indicates segregation\ninto blocks of the same charge, and we plot the distributions of these values in Figure 2c. Consistent\nwith prior work linking charge segregation in IDRs to intermolecular interactions and phase behavior\n[41, 45], natural IDRs from the training and DisProt sets exhibit a tail toward high κ values relative\nto CATH domains, a feature that IDiom reproduces with its generated sequences.\nWe next examined hydrophobic patterning using the sequence hydropathy decoration (SHD)\nmetric, which quantifies the spatial clustering of hydrophobic residues along the chain [46]. Gen-\n5\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nerated\nsequences exhibit substantially lower SHD values than folded CATH domains (Figure 2d),\nconsistent with the reduced hydrophobic clustering in disordered regions that prevents hydrophobic\ncollapse [ 46]. This trend closely matches natural DisProt and training set IDRs, and it contrasts\nwith folded CATH domains, which exhibit higher SHD values, reflecting the locally concentrated\nhydrophobic residues required to stabilize buried protein cores [47].\nFinally, we assessed sequence complexity using the SEG algorithm, which computes the average\ncompositional entropy over a sliding window [ 48]. IDRs frequently contain low-complexity segments\n[49], and natural DisProt and training set IDRs show lower complexity than folded CATH domains.\nGenerated IDRs and IDPs closely reproduce this shift, with the complexities of generated sequences\nmatching the DisProt distribution well (Figure 2e). All together, these results demonstrate that\nIDiom has learned the sequence grammar of disordered regions across multiple metrics, and that\ngenerated sequences closely recapitulate the sequence patterning features of natural IDRs.\nCharge patterning\nAromatic patterning\nLow complexity\nCompositional biases\ned\nb c\na\nFig.\n2: IDiom generates intrinsically disordered regions and proteins which capture the se-\nquence patterning features of natural sequences. (a) Example IDPs (upper row) and IDRs (lower\nrow) generated using IDiom which exhibit canonical sequence features of intrinsically disordered regions,\nincluding low complexity regions, charge blockiness, aromatic patterning, and compositional biases. Greyed-\nout residues correspond to the flanking context of the IDR. (b)–(e) Distributions of various sequence metrics\nfor generated IDPs and IDRs, training set IDRs, DisProt IDRs, and folded CATH domains. Right subplots:\nNormalized Wasserstein-1 (W 1) distance between the distributions of DisProt IDRs and all other distribu-\ntions. (b) Fraction of charged residues (FCR). (c) Charge patterning κ parameter. (d) Sequence hydropathy\ndecoration (SHD). (e) Sequence complexity quantified by the SEG algorithm.\n6\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nConditioned\ngeneration recapitulates context-specific IDR sequence features\nThe previous analysis demonstrates that IDiom can generate sequences with patterning features\nand biophysical properties which are similar to natural IDRs. To quantify the agreement between\ngenerated and natural IDRs, we compute the normalized Wasserstein-1 distance ( W1) [50] between\nthe distributions of each sequence metric and the DisProt reference distribution (right subplots of\nFigure 2b-e). Across most metrics, W1 distances for generated sequences are low relative to folded\nCATH domains, confirming that IDiom produces sequences that are statistically much closer to\nnatural IDRs than to folded proteins. We find that in Figure 2b, the shift in mean values for\ngenerated and training sequences relative to DisProt leads to relatively larger W1 values compared\nto the other metrics we consider, but we note that the shift relative to the training data likely\nresults from the relatively small set of IDRs in DisProt. We also note that the shape of the broad\ndistribution of FCR values for generated and training sequences matches that of DisProt more\nclosely than the narrower CATH distribution. Furthermore, W1 distances for DisProt context-\nprompted IDRs are consistently lower than for unprompted IDPs across all metrics, demonstrating\nthat conditioning on flanking sequence context shifts IDiom’s generations toward the sequence\nfeatures of the natural IDRs that reside inside those contexts.\nb\nca\nFig.\n3: Conditioned generation and in-context learning enables generation of disordered regions\nwhich capture biologically relevant sequence features. (a) Distribution of sequence identities between\nthe wild-type (WT) NPM1 IDR and sequences generated with the NPM1 IDR’s flanking context as the\nprompt. Generated sequences with identities greater than 0.9 are filtered out. (b) Distribution of κ values\nfor the WT NPM1 IDR (black vertical dashed line), IDRs generated with the NPM1 context as prompt\n(blue), randomly scrambled versions of the generated IDRs (orange), and DisProt IDRs (green). (c) Plots\nof the net charge per residue along the sequence. The WT NPM1 IDR is in the upper row, and three\nrepresentative generated IDRs are below. The sequence identities relative to the WT, κ values, and the\namino acid sequences themselves are printed within the plots.\nTo further illustrate the model’s ability to learn via this in-context conditioning, we consider the\nhuman protein NPM1 (UniProt: P06748) as a case study. NPM1 has an IDR (residues 119–242)\nwhich drives nucleolar phase separation through charge block patterning that mediates interactions\nwith itself [ 41] as well as binding partners such as SURF6 [51]. Using the flanking regions around\nthis IDR as the prompt (green and blue domains in Figure 1c (upper)), we generated 100,000 IDRs\nand filtered out any with sequence identity > 90% to the wild-type (WT) NPM1 IDR (Figure 3a).\n7\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nFigure 3b\nshows the distribution of κ values for NPM1-prompted generations, randomly scrambled\nversions of those sequences, and the dataset of DisProt IDRs. We find that the κ distribution\nof NPM1-prompted generations is peaked near the WT NPM1 value, and is substantially shifted\ntoward higher charge segregation than either randomly scrambled sequences or generic DisProt\nIDRs, indicating that the model has learned to generate sequences with substantial charge block\npatterning, when conditioned on the NPM1 flanking contexts.\nFigure 3c shows linear plots of net charge per residue (NCPR) for the WT NPM1 IDR and\nrepresentative generated sequences with high κ values but low sequence identity to the WT IDR.\nThese plots illustrate that IDiom generates sequences with alternating blocks of positive and neg-\native charge which closely mirror the architecture of the WT IDR, despite sharing little sequence\nidentity with it. Together, these results demonstrate that IDiom is able to use flanking context to\nreproduce the biologically relevant sequence features of a given IDR, and that the model is able to\ngenerate diverse sequences that preserve the key sequence features that underlie biological function.\nSequence optimization using reinforcement learning\nOur results demonstrate that IDiom has learned a strong generative prior over IDR sequence space,\nand that the model produces diverse and biologically realistic sequences. This naturally positions\nthe pre-trained model as a starting point for sequence design: post-training IDiom with external\nrewards allows us to steer generation towards sequences that score well on specified objectives while\nremaining IDR-like. Unlike supervised fine-tuning on labeled datasets, post-training via reinforce-\nment learning allows us to optimize arbitrary reward functions such as computational predictors\nand reward models trained on experimental data. Reinforcement learning can additionally incor-\nporate explicit regularization to control sequence diversity, length, and deviation from the base\nmodel [52, 53, 54].\nAs a design target, we focus on subcellular localization, as the ability to engineer protein lo-\ncalization could enable both targeted delivery of therapeutics and modulation of synthetic con-\ndensates [55, 56]. As the reward model, we use ProtGPS, a neural network trained with ESM2\nembeddings to predict the probability of a given protein sequence localizing to each of twelve\nspecific subcellular compartments [ 23, 16]. Here, we post-train IDiom to optimize localization to\nfour compartments: the nucleolus, chromosomes/chromatin, P-bodies, and stress granules. These\ncompartments were chosen because they are known to be enriched in proteins with IDR-specific se-\nquence features, including charge segregation, RNA-interacting motifs, nuclear localization signals,\nand post-translational modification sites, thus providing a clear test of whether RL post-training\ncan induce the generation of biologically relevant sequence features.\nWe optimize IDiom using the reinforcement learning algorithm Group Relative Policy Opti-\nmization (GRPO) [57, 58], and we generate unprompted IDPs in all post-training runs (overview\nin Figure 4a). To prevent reward hacking and to maintain sequence diversity, we incorporate three\nforms of regularization: a Kullback-Liebler (KL) divergence penalty DKL to prevent excess diver-\ngence of the post-trained model from the pre-trained base model, a quadratic penalty around a\ntarget Shannon entropy of H = 2 .7 nats to prevent diversity collapse, and a quadratic penalty\naround a target sequence length of 100 residues. Figure 4b shows training curves for the ProtGPS\nreward, DKL, and mean sequence length versus post-training optimizer steps. The ProtGPS reward\nincreases steadily across all four compartments, the mean sequence lengths converge to the target\nvalue, and DKL remains below 0.4 throughout training, confirming that post-training successfully\noptimizes the reward without diverging substantially from the pre-trained base distribution.\nFigure 4c shows the distributions of AlphaFold2 pLDDT values for sequences generated from\neach post-trained checkpoint, alongside the pLDDT distribution of the full length proteins used to\n8\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nMGPGS[ ]\nGenerate\nRL Loss\nPost-train\nIDR PLM\nProtGPS score\nTarget length\nTarget Shannon entropy\nKL Divergence penalty\na b c\nFig.\n4: Post-training IDiom with reinforcement learning enables the generation of sequences\naligned with an external reward model. (a) Schematic depicting the reinforcement learning process\nfor post-training IDiom. ProtGPS is a reward model which returns a score between 0 and 1 indicating\nthe probability of a given sequence localizing to a chosen subcellular compartment. Quadratic penalties are\napplied to sequences which deviate from the target ProtGPS score, target length, and target Shannon entropy,\nand a penalty is applied for an increased Kullback-Liebler (KL) divergence of the post-trained model from the\npre-trained base model. These metrics are combined in a reinforcement learning loss which is used to update\nthe IDiom policy. (b) Training curves depicting the ProtGPS score for a given compartment, magnitude of\nthe KL-divergence, DKL , and the average generated sequence length, as a function of post-training optimizer\nsteps. (c) Distribution of AlphaFold2 pLDDTs of sequences generated from IDiom checkpoints after 1500\npost-training optimizer steps, as well as pLDDTs of the original sequences used to train the ProtGPS reward\nmodel.\ntrain the ProtGPS predictor. The ProtGPS training sequences have a wide distribution of pLDDTs,\nwith a substantial fraction of high-pLDDT residues, reflecting the fact that ProtGPS was trained\non full length proteins containing both folded domains and disordered regions. However, sequences\ngenerated by the post-trained IDiom models maintain low pLDDT values, comparable to those\nof natural IDRs, demonstrating that the KL regularization successfully prevents the model from\ndrifting towards the sequence features of folded proteins in the ProtGPS training set. This further\nconfirms that post-training steers generation towards the desired compartment localization while\npreserving the disordered nature of generated sequences.\nPost-trained models generate sequences with compartment-specific features\nAfter post-training with the ProtGPS reward, we generate 10,000 sequences from each localization-\noptimized checkpoint and analyze their amino acid compositions. Sequences targeting specific\nsubcellular compartments are expected to have compositional biases that reflect their local bio-\nchemical environments, and we find that post-trained generations exhibit biologically interpretable\ncompositional shifts relative to both base model generations and DisProt IDRs (Figure 5).\nNucleolar-targeting sequences are enriched in lysine and arginine, consistent with the prevalence\nof positively charged nuclear localization signals and the charge-rich low-complexity regions found\nin nucleolar proteins [ 59, 60]. Sequences targeting the chromosomes are enriched in serine and\nthreonine, consistent with the high density of phosphorylation sites characteristic of chromatin-\n9\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nasso\nciating proteins, which are heavily regulated by post-translational modification [61, 62]. The\ngenerated P-body targeting sequences are glycine-rich and basic (lysine- and arginine-rich), con-\nsistent with the RNA-binding motifs and arginine-glycine rich regions present in proteins that\nassociate with RNA granules [ 63, 64]. Finally, stress granule-targeting sequences are similarly\nglycine-rich, consistent with the low-complexity, RNA-interacting motifs expected in stress granule\nassociating proteins [65]. Representative sequences generated from each checkpoint are also shown\nin Figure 5, with specific sequence features such as nuclear localization signals, post-translational\nmodification sites, and RNA-binding motifs underlined, illustrating that the global compositional\nshifts accompanied by the generation of specific local sequence features.\na b\nc d\nFig.\n5: Post-trained IDiom models generate sequences which reproduce the amino acid composi-\ntional biases known to drive subcellular localization. Amino acid composition of sequences generated\nafter post-training IDiom to optimize the ProtGPS localization score for the (a) nucleolus, (b) chromosome,\n(c) P-bodies, and (d) stress granules. Underneath each plot is one representative generated sequence for\neach compartment, with sequence features such as nuclear localization signals, post-translational modifica-\ntion sites, and RNA-binding motifs underlined.\nTo further characterize the sequence features learned during post-training, we analyze the\ncompartment-specific generations for sequence patterning and sequence-specific motifs. Charge\nsegregation, quantified by κ, varies across compartments (Figure 6a), with nucleolus-targeting\nsequences showing elevated κ relative to all other sequences; this observation is consistent with\nthe prevalence of charge-block architectures in nucleolar-associating IDRs [ 66]. In contrast, se-\nquences targeting stress granules and P-bodies show reduced κ relative to baselines, consistent\nwith the weakly charged nature of stress granule proteins [67] and the aromaticity-driven nature\nof P-body condensate formation [4]. In addition, we find that sequences targeting the nucleolus\nand chromosomes are enriched in nuclear localization signals (NLSs), as is expected for these nu-\nclear compartments [ 68]. We scan generated sequences for a curated set of NLS patterns from the\nEukaryotic Linear Motif (ELM) Resource [69] (patterns are provided in the Supplementary Infor-\nmation), and we find that a substantially higher fraction of nucleolus- and chromosome-targeting\nsequences contain at least one NLS compared to sequences targeting cytoplasmic compartments\n(Figure 6b).\nChromosome-associating proteins are heavily regulated through post-translational modifications\n(PTMs), and we probe whether chromosome-targeting sequences are correspondingly enriched in\n10\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nNuclear Non-nuclear Reference Nuclear Non-nuclear Reference\nNuclear Non-nuclear Reference\na b e\nc d\nFig.\n6: Proteins generated from post-trained IDiom models recapitulate specific sequences fea-\ntures which are characteristic of each target cellular compartment. (a) Box plot of the distribution\nof κ charge patterning values for sequences generated from IDiom checkpoints optimized for localization to\nthe four labeled ProtGPS compartments. The horizontal orange line and band indicates the mean and stan-\ndard deviation of κ for sequences generated from the base pre-trained model. The green line indicates the\nmean κ value of natural DisProt IDRs. (b) Plot of the percentage of generated sequences which contain at\nleast one nuclear localization signal from the Eukaryotic Linear Motif (ELM) Resource. (c) Plot of the per-\ncentage of generated sequences which contain the RNA-interaction sequence motifs indicated in the legend.\n(≥ 1) indicates the presence of at least one motif within a given sequence. (≥ 2) indicates the presence of at\nleast two motifs within 30 residues of one another within a given sequence. (d) Plot of the average number\nof unique post-translational modification (PTM) motifs from the ELM Resource per sequence for sequences\ngenerated from various model checkpoints or the DisProt IDRs. (e) Plot of the ratio of the number of\ncounts of all PTM motifs from the ELM Resource (MOD) appearing in a generated sequence or DisProt\nIDRs, normalized to the counts within sequences generated by the base model.\nPTM motifs [70]. We scan generated sequences for all 40 PTM motif classes from the ELM Re-\nsource (ELM Identifiers beginning with the MOD prefix). Chromosome-targeting sequences show a\npronounced increase in MOD-motif density, with over 10 putative unique PTM sites per sequence\non average, compared to approximately 5-7 sites per sequence for other compartments (Figure 6c).\nIn Figure 6d we quantify enrichment as the ratio of motif counts in post-trained generations rel-\native to the base model, finding that the enriched motifs span multiple kinase families, including\nAGC-class sites ( MOD_PKA_1, MOD_PKB_1, MOD_PK_1), PIK/PIKK-associated phosphorylation sites\n(MOD_PIK_1, MOD_PIK_2-3, MOD_PIKK_1), acidophilic CK2 motifs (MOD_CK2_1), and proline-directed\nCDK-class motifs (MOD_CDK_SPK_2). This broad enrichment across kinase families is consistent with\nPTM-driven regulatory control being a crucial role of chromatin-interacting proteins [61, 62], and\nit demonstrates that post-training with a localization reward is sufficient to induce the generation\nof these specific sequence features.\nP-bodies and stress granules are RNA-rich condensates with central roles in mRNA regula-\ntion and decay [ 71], and we find that post-trained sequences targeting these compartments are\nenriched in short RNA-interaction motifs including RG/RGG tracts, F/YGG motifs, and SYG\n11\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nmotifs\n(Figure 6e). RG/RGG-rich regions are widely implicated in RNA binding and recruitment\nto ribonucleoprotein assemblies [63, 64], while F/YGG [ 72, 73] and SYG [ 74, 75] motifs provide\naromatic sticker elements that mediate π-π and cation- π interactions which drive phase separation\nin low-complexity IDRs. The emergence of these motifs through post-training indicates that opti-\nmizing for RNA granule localization is also sufficient to induce the generation of RNA-interaction\nsequence grammars.\nAltogether, these results demonstrate that RL post-training using the ProtGPS predictor as a\nreward model is able to teach IDiom the global amino acid compositions, sequence patterning, and\nspecific motifs which are necessary for compartment-specific localization. Each of the changes we\nidentify is biologically interpretable and consistent with the known sequence determinants of local-\nization to or interaction with the corresponding compartment, and these features emerge without\nany explicit supervision. This indicates that the post-training of IDiom to optimize the Prot-\nGPS score alone is sufficient to learn the necessary compartment-specific sequence grammars for\nsubcellular localization of IDRs.\nDiscussion\nIDiom demonstrates that a protein language model trained exclusively on intrinsically disordered\nregion sequences can faithfully capture the highly contextual evolutionary statistics of natural\nIDRs. The pre-trained model generates diverse sequences that recapitulate the compositional bi-\nases, charge patterning, hydrophobic decoration, and low-complexity features of natural disordered\nregions. Crucially, the model is able to generate highly plausible disordered sequences while remain-\ning substantially dissimilar to the training examples. Furthermore, IDiom learns in-context and is\nable to generate IDRs conditioned on flanking sequence context that are more similar to the natural\nIDRs that exist within that flanking context, as demonstrated by the DisProt context-prompted\nIDRs and the NPM1 case study.\nBeyond generation from the base pre-trained model, we demonstrate that IDiom can be post-\ntrained using reinforcement learning to optimize arbitrary external reward functions. While here we\ndemonstrate this using ProtGPS as the reward signal for subcellular localization, the post-training\napproach is general. IDiom can be combined with any objective, such as sequence-based predictors\nof conformational ensembles [76], intermolecular interactions [45], phase behavior [77], as well as\nmachine-learned predictors of experimentally characterized biological function such as transcrip-\ntional activity [ 78, 79] or direct binding affinity [80]. Post-training can also be applied directly to\nexperimental data, using approaches such as direct preference optimization [54, 81] or energy rank\nalignment [82, 83]. Such approaches would enable iterative optimization of the generative model\nas new experimental measurements become available. Due to the often modular nature of IDRs,\na designed IDR could be inserted or appended to a full length protein to tune localization, phase\nbehavior, or signaling properties without redesigning the folded domains. Additionally, the preva-\nlence of short IDRs in our training data (Figure 1e) also makes IDiom well-suited for the design of\ndisordered peptides for therapeutic applications. Finally, IDiom offers interesting opportunities for\nshrinking proteins containing functional IDRs, an important objective in protein delivery [ 84].\nIDiom can also enable the automated discovery of evolutionarily and biologically important\nsequence features within IDRs. In the examples with the ProtGPS reward model, we manually\nidentified sequence features to analyze in the post-trained sequences. Future work applying tech-\nniques such as feature learning with sparse autoencoders [85] would enable automatic identification\nof prominent sequence features learned by IDiom. While prior work has studied the features learned\nby protein language models trained on full length sequences, intrinsically disordered regions are\n12\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\np\noorly resolved in those learned feature spaces [ 86]. In contrast, sparse autoencoders trained on\nIDiom representations would be free from folded domain features, allowing for more precise iden-\ntification of sequence grammars that underlie intrinsically disordered regions. When applied to\npost-trained models, this approach could further reveal the function-specific features that underlie\nbiological function, such as subcellular localization.\nIntrinsically disordered regions play central roles in cellular processes such as gene regula-\ntion, subcellular compartmentalization, and signaling, yet they have remained largely inaccessible\nto rational design. IDiom provides a generative framework for disordered sequence design that\ncan be steered towards specific functional objectives through post-training. Combined with high-\nthroughput experimental assays and machine learned reward models trained on experimental data,\nthis platform offers a path toward the systematic design and engineering of intrinsically disordered\nproteins and regions, opening new avenues in synthetic biology, targeted therapeutics, and the\ndesign of programmable condensates.\nMethods\nData Curation We curate our dataset of intrinsically disordered regions from the AlphaFold Database\n(AFDB), version 4. First, we use MMseqs2 to cluster the 214M AFDB sequences at 90% identity and 80%\ncoverage (other MMseqs2 parameters below). Next, we follow the method of [ 32] to determine the sequences\nand locations of pLDDT-based IDRs within the MMseqs2 cluster representative proteins. In this method, we\nfirst apply a 15 residue-wide averaging filter to the pLDDT values. Next, we mark residues with pLDDT > 80\nas folded, pLDDT < 70 as disordered, and 70 < pLDDT < 80 as gap regions. Folded and disordered regions\nwith a length shorter than ten residues are reclassified as gaps. If a gap region is flanked by two disordered\nregions, or if it is N- or C-terminal and is adjacent to a disordered region, we relabel it as disordered. All\nother gap regions are relabeled as folded. Each record within the dataset corresponds to a different IDR,\nand any given protein may yield ≥ 1 IDR. IDRs which are located in proteins whose full length is greater\nthan 512 residues, IDRs shorter than 30 residues long, and sequences whose entire length is low-pLDDT are\ndiscarded. This curation process yields 37M IDRs and their associated N- and C-terminal flanking contexts.\nSequence Clustering and Percent Identity Characterization We use MMseqs2 to cluster sequences\nin the AlphaFold Database at 90% identity and 80% coverage. MMseqs2 was run using the following\ncommand: mmseqs linclust --min-seq-id 0.9 --cov-mode 0 -c 0.8 --cluster-mode 2.\nWe also use MMseqs2 to identify the sequence identity of generated sequences with respect to the training\nset. Specifically, we compare generated IDR and IDP sequences against the 37M AFDB training set IDRs\nwithout their surrounding context. MMseqs2 was run with the following command to search the generated\nsequences against the AFDB training set IDRs: mmseqs search --max-seqs 1 -e 1e3 --min-seq-id 0.0\n-c 0.0. For each generated sequence, this command returns the sequence identity of the closest match in\nthe training set, which is plotted in Figure 1.\nT okenization We tokenize protein sequences using a simple alphabet in which each amino acid is rep-\nresented by a single token. We introduce the tokens <N>, <C>, and <I> to denote the N-terminal flanking\ncontext of an IDR, the C-terminal flanking context, and the IDR span itself, respectively. We additionally\nadd the standard beginning-of-sequence <bos> and end-of-sequence <eos> tokens to all sequences, and we\npad all sequences to the maximum length of 512 tokens using the <pad> token. The total size of the alphabet\nwe use is 27 tokens (20 amino acids, <N>, <C>, and <I>, and <bos>, <eos>, <pad>, and <mask>.\nData Augmentations To process the curated AFDB IDRs for model pre-training, we transform the\nprotein sequences into a fill-in-the-middle format. We prepend the token <N> to any N-terminal context of\nthe IDR, prepend <I> to the IDR itself, and prepend <C> to any C-terminal context of the IDR. We then\nrearrange the sequence in the order <N><N-terminal context><C><C-terminal context><I><IDR span> .\nAn example sequence is <N>MEDS..HLVA<C>SVED..RKSL<I>VEED..KGPS.\n13\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nW\ne augment the data with intrinsically disordered proteins by duplicating the set of IDRs and re-\nmoving their N- and C-terminal flanking contexts. An example sequence from this data augmentation is\n<N><C><I>VEED..KGPS. In all, this produces 74M sequences for training (37M IDRs and 37M IDPs).\nModel Architecture IDiom is a 12-layer decoder-only Transformer with 14 attention heads and a hidden\ndimension of dmodel = 896 . The model employs pre-LayerNorm and utilizes the SwiGLU non-linearity [ 87]\nin all feedforward networks. The feedforward network expansion ratio is 8/3, resulting in a total of 122M\ntrainable parameters. Positional information is encoded using Rotary Position Embeddings (RoPE) [ 88].\nThe model processes sequences with a maximum length of 512 tokens, and shorter sequences are padded to\nthis length. Multi-head attention is computed using Flash Attention [89].\nPre-training We pre-train IDiom on the aforementioned 74M sequences. The data are randomly split into\n99% training, 0.5% validation, and 0.5% test sets. All sequences are padded or truncated to a fixed length\nof 512 tokens. The model is trained autoregressively using next-token prediction.\nTraining is performed using the AdamW optimizer with a learning rate of 4.0×10−4 and no weight decay.\nThe learning rate schedule uses a linear warmup over the first 3,000 steps, followed by cosine annealing decay\nto a minimum of 4.0×10−5 (10% the initial learning rate) over 250,000 total training steps. The global batch\nsize is 1,024 (Distributed Data Parallel training with 128 sequences per GPU across 8 NVIDIA H100 GPUs),\nwith no gradient accumulation. We use a cross-entropy loss while ignoring contributions from pad or mask\ntokens. Training is performed in mixed precision (fp32/bfloat16) and no gradient clipping is applied. Model\nvalidation is performed every 25,000 training steps on the validation set, and training is run for 250,000\noptimizer steps. The training and validation curves are presented in the Supplementary Information.\nSequence Generation We generate IDR sequences from IDiom using autoregressive decoding. At each\nposition t in the sequence, we compute the model logits zt and convert them to a probability distribution\nvia p(xt|x<t) = softmax(zt/T ), then sample the next token from this full categorical distribution over the\nvocabulary. We use a fixed sampling temperature of T = 1.0 for all generations\nSequence generation supports both prompted and unprompted modes. For prompted generation, the N-\nand C-terminal flanking contexts are provided as the prompt in fill-in-the-middle format: <N><N-terminal\ncontext><C><C-terminal context><I> , and the model generates the IDR span autoregressively following\nthe <I> token. For unprompted generation of fully disordered proteins, the prompt consists of only the three\nspecial tokens without any flanking context: <N><C><I>, and the model generates the disordered sequence. In\nboth cases, generation terminates upon sampling the <eos> token or upon reaching the maximum sequence\nlength of 512 tokens.\nPost-training We fine-tuned IDiom using Group Relative Policy Optimization (GRPO) with the De-\ncoupled Advantage Policy Optimization (DAPO) modification. During GRPO training, for each batch of\nsequence prompts, the model generates multiple completions per prompt (group size = 8). Rewards are\ncomputed for each generated sequence using a reward function that combines three rewards: 1. A quadratic\nreward around a target ProtGPS score of 0.9 for the desired target compartment, 2. A quadratic reward\naround a target sequence length of Ltarget = 100 residues, and 3. A quadratic reward around a target\nsequence Shannon entropy of Htarget = 2.7 nats to prevent diversity collapse.\nWithin each group, advantages are computed as normalized relative rewards: Ai = ri−¯rg\nσg\n,\nwhere ¯rg\nand σg are the group-wise mean and standard deviation. The GRPO loss combines a clipped policy gra-\ndient term (PPO-style clipping with ϵclip = 0 .2) weighted by advantages, and a KL-divergence penalty\nLKL = βKLDKL(pref||pcurrent) with strength βKL = 0.02. The total loss is optimized per-token on generated\ncompletions only (any prompt tokens are masked).\nPost-training is performed with a learning rate of 5×10−6, the AdamW optimizer, and a global batch size\nof 8, for 1,500 optimizer steps. Post-training was performed separately for all 12 target cellular compartments\nin ProtGPS, although we only analyze the sequences generated from checkpoints trained for localization to\nthe nucleolus, chromosomes, P-bodies, and stress granules.\n14\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nStructure\nPrediction We use Colabfold [37] to perform AlphaFold2 structure predictions on generated\nsequences and determine the predicted local distance difference test (pLDDT) values.\nSequence Analysis We use the Sparrow package [ 90] to calculate sequence-level metrics such as charge\npatterning κ, sequence hydropathy decoration, sequence complexity (SEG), and fraction of charged residues.\nShort linear motif (SLIM) analysis is performed with a regular expression search using the SLIM regular\nexpressions from the Eukaryotic Linear Motif Resource [ 69]. The specific regular expressions are presented\nin the Supplementary Information\nVisualization Protein structure visualization is performed with PyMOL [91].\nData and Code A vailability The code used for model pre-training, sequence generation, and post-\ntraining is available on Github: Code (https://github.com/rotskoff-group/idiom).\nThe pre-training datasets and pre- and post-trained model checkpoints are available on Hugging Face:\nDatasets (https://huggingface.co/datasets/jxliu2/idiom-datasets)\nModels (https://huggingface.co/jxliu2/idiom) .\nInformation regarding these artifacts is provided in the Supplementary Information.\nAcknowledgements J.X.L. acknowledges support from the National Institute of Health T32 award num-\nber T32HL094274. S.I. acknowledges support from the National Science Foundation Graduate Research\nFellowship Program and the Shoucheng Zhang Graduate Fellowship. F.H. acknowledges support from the\nStanford Center for Molecular Analysis and Design Fellowship. Research reported in this publication was\nsupported by the National Institute of General Medical Sciences of the National Institutes of Health un-\nder award number 1R35GM159834-01 (G.M.R.) and 5R35GM130332 (A.R.D.). The content is solely the\nresponsibility of the authors and does not necessarily represent the official views of the National Institutes\nof Health. The authors acknowledge the use of the Stanford Sherlock compute cluster, and the authors\nacknowledge insightful discussions with Prof. Mikko Haataja.\nCompeting Interests G.M.R. holds equity in and is a paid consultant for Topos Bio and holds equity in\nAzulene Labs.\nReferences\n[1] Alex S. Holehouse and Birthe B. Kragelund. The molecular basis for cellular function of intrinsically\ndisordered protein regions. Nature Reviews Molecular Cell Biology , 25(3):187–211, March 2024.\n[2] Nicolás S. González-Foutel, Juliana Glavina, Wade M. 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PyMOL (Version 3.1).\n[92] Robert T. McGibbon, Kyle A. Beauchamp, Matthew P. Harrigan, Christoph Klein, Jason M. Swails,\nCarlos X. Hernández, Christian R. Schwantes, Lee-Ping Wang, Thomas J. Lane, and Vijay S. Pande.\nMdtraj: A modern open library for the analysis of molecular dynamics trajectories. Biophysical Journal,\n109(8):1528 – 1532, 2015.\n[93] Jeffrey M. Lotthammer, Jorge Hernández-García, Daniel Griffith, Dolf Weijers, Alex S. Holehouse, and\nRyan J. Emenecker. Metapredict enables accurate disorder prediction across the Tree of Life, November\n2024. Pages: 2024.11.05.622168 Section: New Results.\n[94] Gábor Erdős, Mátyás Pajkos, and Zsuzsanna Dosztányi. IUPred3: prediction of protein disorder en-\nhanced with unambiguous experimental annotation and visualization of evolutionary conservation. Nu-\ncleic Acids Research , 49(W1):W297–W303, July 2021.\n22\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nSupplemen tary Information\nDatasets\nHere we describe the datasets provided on HuggingFace:\nDatasets (https://huggingface.co/datasets/jxliu2/idiom-datasets)\nBelow, we describe the data files under idr_datasets/training_sequences:\n• AFDB_IDR_90_reps.fasta contains the 53M cluster representatives after the initial 214M full\nlength AFDB protein sequences are clustered at 90% identity, 80% coverage.\n• AFDB_IDR_90_alldata.h5 contains 73M IDRs as extracted from the AFDB according to\nthe Tesei logic [32] (see Methods), and after filtering for IDRs belonging to the 53M cluster\nrepresentatives identified in AFDB_IDR_90_reps.fasta. This HDF5 file contains the following\nkeys: <KeysViewHDF5 ['accession_ids', 'full_avg_plddt', 'full_length', 'full_-\nseq', 'idr_end', 'idr_length', 'idr_plddt', 'idr_start', 'idrs']>.\n• AFDB_IDR_90_FIM_512.h5 is created from AFDB_IDR_90_alldata.h5 by filtering out IDRs\nwhose full length sequences are longer than 512 residues. We also find that ∼ 1/3 of records in\nAFDB_IDR_90_alldata.h5 are fully low-pLDDT sequences, and we filter out those sequences\nbecause we find that they are not representative of intrinsically disordered proteins. We only\nkeep sequences with both low- and high-pLDDT regions. We hypothesize that sequences\nwhich are fully low-pLDDT are due to AlphaFold2’s poor confidence in sequences which are\nnot similar to those seen during training, rather than because they are fully intrinsically\ndisordered proteins. For the remaining 37M IDRs, we apply the fill-in-the-middle (FIM)\ntransformation as well as IDP data augmentation as mentioned in the Methods, and place\nthose records into AFDB_IDR_90_FIM_512.h5. We note that we represent the <N>, <C>, and\n<I> tokens with 1, 2, and 3, respectively, in this HDF5 file as well as in the codebase. This\nis the final file used for the precompute and pre-training steps.\n• AFDB_IDR_90_FIM_512_full.fasta contains the 37M full length sequences (in correct order,\nnot FIM-transformed) contained in AFDB_IDR_90_FIM_512.h5. The fasta header contains\n_IDR_X-Y where X and Y are the 1-indexed indices of the start and end (inclusive) of the\nintrinsically disordered region.\n• AFDB_IDR_90_FIM_512_idrs.fasta contains only the sequences of the 37M intrinsically dis-\nordered regions in AFDB_IDR_90_FIM_512_full.fasta, without their surrounding context.\nWe also provide several datasets of sequences generated by our model under idr_datasets/generated_-\nsequences. All generated sequences are provided in F ASTA format along with their corresponding\nautoregressive model log (pickle format).\n• Generated IDPs: 100,000 unprompted intrinsically disordered proteins.\n• Generated IDRs: 101,700 intrinsically disordered regions generated using 1,017 DisProt flank-\ning contexts prompts (100 generated IDRs per prompt).\n• Generated NPM1 IDRs: 100,000 sequences generated using the NPM1 flanking context as\nthe prompt (UniProt: P06748).\n• Generated ProtGPS Sequences: 10,000 IDPs generated from post-trained checkpoints. Post-\ntraining was done to optimize ProtGPS localization scores for the four target compartments:\nchromosome, nucleolus, P-body, and stress granule.\n23\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nMo\ndels\nHere we describe the model checkpoints and other files provided on HuggingFace:\nModels (https://huggingface.co/jxliu2/idiom)\nBelow, we describe the directories under idiom/:\n• base/ contains the checkpoint of our pre-trained base IDiom model, along with its configu-\nration files.\n• post_trained/protgps_reward/ contains the checkpoints of IDiom post-trained via rein-\nforcement learning using the ProtGPS reward model, one checkpoint per target compart-\nment. In this paper, we analyzed results for 4 compartments: the nucleolus, stress granules,\nP-bodies, and chromosomes. However, post-training runs were conducted for all 12 Prot-\nGPS compartments (chromosome, nucleolus, nuclear speckle, nuclear pore complex, P-body,\nPML body, post-synaptic density, stress granule, Cajal body, RNA granule, cell junction,\nand transcriptional condensate). We leave analysis of the remaining compartments to future\nwork.\n• protgps/ contains the ProtGPS reward model used during reinforcement learning post-\ntraining.\n• data/ contains auxiliary files used during training and inference.\nSecondary Structure Metric Analysis\nHere we present analysis of secondary structure metrics for training, generated, DisProt, and CATH\nsequences. Secondary structure was assigned per residue using the dictionary of secondary structure\nof proteins (DSSP) algorithm as implemented in MDTraj [92]. Secondary structure content was\nthen defined as the sum of the mean α-helical and mean β-sheet fractions across all residues. Fig.\nS1 shows histograms of the average secondary structure content of 100 randomly chosen sequences\nfrom the various training, generated, DisProt, and CATH sets of proteins.\nTrain/uni00A0IDRs/uni00A0no/uni00A0context\nDisProt/uni00A0IDRs/uni00A0no/uni00A0context\nGen/uni00A0IDRs/uni00A0no/uni00A0context\nGen/uni00A0IDPs\nCATH\n0.00 0.25 0.50 0.75\nSecondary/uni00A0structure/uni00A0content\n0\n1\n2\n3\n4Density\n(a)\nTrain/uni00A0IDRs/uni00A0w//uni00A0context\nDisProt/uni00A0IDRs/uni00A0w//uni00A0context\nGen/uni00A0IDRs/uni00A0w//uni00A0context\nCATH\n0.00 0.25 0.50 0.75\nSecondary/uni00A0structure/uni00A0content\n0\n2\n4\n6Density (b)\nRL/uni00A0chromosome/uni00A0IDPs\nRL/uni00A0nucleolus/uni00A0IDPs\nRL/uni00A0p/uni00ADbody/uni00A0IDPs\nRL/uni00A0stress/uni00A0granule/uni00A0IDPs\nCATH\n0.00 0.25 0.50 0.75\nSecondary/uni00A0structure/uni00A0content\n0.0\n2.5\n5.0\n7.5\n10.0Density (c)\nFig.\nS1: Secondary structure content analysis. Histograms of of the average secondary structure\ncontent (α + β) for the AF2-predicted structures of 100 randomly chosen sequences from the following sets\nof sequences: (a) Secondary structure content of training IDRs, generated IDRs, DisProt IDRs, and CATH\nsequences, with their structures predicted with surrounding context included. (b) Secondary structure con-\ntent of training IDPs, generated IDPs, DisProt IDPs, and CATH sequences, with their structures predicted\nwithout their surrounding context. (c) Secondary structure content of IDPs generated from post-trained\nIDiom checkpoints and CATH sequences, with their structures predicted with surrounding context included.\n24\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nDisorder\nPredictions\nHere, we present orthogonal disorder predictions from Metapredict v3 [93] and IUPred3 [ 94]. For\nboth predictors, a higher value represents a higher propensity towards disorder.\nDisProt/uni00A0IDRs/uni00A0(mean=0.639)CATH/uni00A0(mean=0.145)\nGen/uni00A0IDPsGen/uni00A0IDRsTrain/uni00A0IDRs\nNPM1\nChromosome\nNucleolusP/uni00ADbody\nStress/uni00A0granule\n0.0\n0.5\n1.0Metapredict/uni00A0V3\nFig.\nS2: Disorder predictions from Metapredict V3 . Higher values correspond to higher propensity\ntowards disorder. The horizontal green and red dashed lines correspond to the predicted Metapredict V3\nvalues for 1,017 DisProt IDRs and 1,000 CATH sequences, respectively. The bars correspond to predicted\nMetapredict values for 10,000 sequences generated from IDiom for each condition, as well as 10,000 training\nsequences. The sequences generated from IDiom include unprompted IDPs, DisProt-prompted IDRs, NPM1\nIDRs, and IDPs generated after post-training for localization to the chromosomes, nucleolus, P-bodies, and\nstress granules.\nDisProt/uni00A0IDRs/uni00A0(mean=0.535)CATH/uni00A0(mean=0.231)\nGen/uni00A0IDPsGen/uni00A0IDRsTrain/uni00A0IDRs\nNPM1\nChromosome\nNucleolusP/uni00ADbody\nStress/uni00A0granule\n0.0\n0.5\n1.0IUPred3\nFig.\nS3: Disorder predictions from IUPred3 . Higher values correspond to higher propensity towards\ndisorder. The horizontal green and red dashed lines correspond to the predicted IUPred3 values for 1,017\nDisProt IDRs and 1,000 CATH sequences, respectively. The bars correspond to predicted IUPred3 values\nfor 10,000 sequences generated from IDiom for each condition, as well as 10,000 training sequences. The\nsequences generated from IDiom include unprompted IDPs, DisProt-prompted IDRs, NPM1 IDRs, and IDPs\ngenerated after post-training for localization to the chromosomes, nucleolus, P-bodies, and stress granules.\nESM3 Comparison\nHere we present comparison plots between sequences generated by IDiom and ESM3, using the same\n1,017 DisProt flanking domain prompts. ESM3 sequences are generated using iterative decoding. A\ntotal of 1,000 sequences are sampled for each prompt. As ESM3 consists of a bidirectional trans-\nformer architecture, the length of the generated IDRs is fixed at the length of the ground truth\nIDR. The number of decoding steps, i.e. forward passes until the sequence is fully unmasked, is set\n25\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nto\nbe the minimum of 20 and the ground truth IDR length for each prompt. Tokens are sampled\nwith a temperature of 1.0, and all other default inference hyperparameters for ESM3 are used.\nWe find that compared to IDiom, ESM3-generated IDRs are extremely low-complexity sequences,\nwith a peak in the SEG complexity distribution around 0.5 (Figure S4). We show three example\nESM3-generated IDRs below, in red:\nUniProt P48439:\nMNWLFLVSLVFFCGVSTHPALAHFLDLLLLLLLLLLLLLQLILTAILAAIALLLLLLFLL\nIVIGILLGLSLGALQLLLLLLLLLLLLSFALQLIFAAILAALLLILLLLLLLIVIGILLS\nLSFGALQLLILLLILLLWLLTLLLAKQLKLALALILAAILAALILLLLLLLLLLLIVIGI\nLFGLSLSALQLLLFLLLLLLLLLLVSFALKLKNPISRIIWATLSTFFIICMISAYMFNQI\nRNTQLAGVGPKGEVMYFLPNEFQHQFAIETQVMVLIYGTLAALVVVLVKGIQFLRSHLYP\nETKKAYFIDAILASFCALFIYVFFAALTTVFTIKSPAYPFPLLRLSAPFK\nUniProt Q9NS23-4:\nMPCHPPPLPPPPPPPSPPPEEEEEEEEIEEEGEEEEPPASPLPPASPPAPEPVEWETPDL\nSQAEIEQKIKEYNAQINSNLFMSLNKDGSYTGFIKVQLKLVRPVSVPSSKKPPSLQDARR\nGPGRGTSVRRRTSFYLPKDAVKHLHVLSRTRAREVIEALLRKFLVVDDPRKFALFERAER\nHGQVYLRKLLDDEQPLRLRLLAGPSDKALSFVLKENDSGEVNWDAFSMPELHNFLRILQR\nEEEEHLRQILQKYSYCRQKIQEALHACPLG\nUniProt Q14011:\nMASDEGKLFVGGLSFDTNEQSLEQVFSKYGQISEVVVVKDRETQRSRGFGFVTFENIDDA\nKDAMMAMNGKSVDGRQIRVDQAGKSSDNRGGGGGGGGGRGGGGGGGGGGGGRGGGGGGRG\nGGGSGGGGGGRGGGGGSGGRGGGGGGGGGGGGGGGGGGGGGRGGGGGGGGRY\n0.0 0.2 0.4 0.6\nFCR\n0\n2\n4\n6\n8Density\n(a)\nGen/uni00A0IDPs\nGen/uni00A0IDRs\nDisProt/uni00A0IDRs\nTrain/uni00A0IDRs\nCATH\nESM3/uni00A0IDRs\n0.0 0.5 1.0\n0\n2\n4\n6\n8Density (b)\n4 6 8\nSHD\n0\n0\n0Density (c)\n0.0 0.5 1.0\nSequence/uni00A0Complexity\n0\n5\n10Density (d)\nFig.\nS4: Comparison between ESM3-generated IDRs and IDiom-generated IDRs. (a)–(d) Distri-\nbutions of various sequence metrics for sequences generated from IDiom versus ESM3. Training set IDRs,\nnatural DisProt IDRs, and folded CATH domains are shown as well. (a) Fraction of charged residues (FCR).\n(b) Charge patterning κ parameter. (c) Sequence hydropathy decoration (SHD). (d) Sequence complexity\nquantified by the SEG algorithm.\n26\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nShort\nLinear Motifs from the Eukaryotic Linear Motif Resource\nHere, we list the short linear motifs from the ELM Resource which we scan for, for nuclear local-\nization signals (NLSs) as well as for post-translational modification (PTM) sites (ELM Identifier:\nMOD).\nNuclear Localization Signals The regular expressions of the 4 NLSs we consider are:\nID P\nattern (regex)\nTRG_NLS_Bipartite_1 [KR][KR].{7,15}[D̂E]((K[RK])|(RK))(([D̂E][KR])|([KR][D̂E]))[D̂E]\nTRG_NLS_MonoCore_2 [D̂E]((K[RK])|(RK))[KRP][KR][D̂E]\nTRG_NLS_MonoExtC_3 [D̂E]((K[RK])|(RK))(([D̂E][KR])|([KR][D̂E]))(([PKR])|([D̂E][DE]))\nTRG_NLS_MonoExtN_4 (([PKR].{0,1}[D̂E])|([PKR]))((K[RK])|(RK))(([D̂E][KR])|([KR][D̂E]))[D̂E]\nT\nable 1: ELM NLS motifs and their corresponding regex patterns.\n27\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nP\nost Translational Modification Motifs The regular expressions of the 40 PTM MOD sites\nwe consider are:\nID P\nattern (regex)\nMOD_AAK1BIKe_LxxQxTG_1 [LIVM][D̂][D̂EHYWF]Q.(T)G\nMOD_ASX_betaOH_EGF C.([DN]).{4,4}[FY].C.C\nMOD_CAAXbox (C)[D̂ENQ][LIVMF].$\nMOD_CDC14_SPxK_1 (S)P.[KR]\nMOD_CDK_SPK_2 ...([ST])P[RK]\nMOD_CDK_SPxK_1 ...([ST])P.[KR]\nMOD_CDK_SPxxK_3 ...([ST])P..[RK]\nMOD_CK1_1 S..([ST])...\nMOD_CK2_1 ...([ST])..E\nMOD_CMANNOS (W)..W\nMOD_Cter_Amidation (.)G[RK][RK]\nMOD_DYRK1A_RPxSP_1 R[PSVA].([ST])P\nMOD_GlcNHglycan [ED]{0,3}.(S)[GA].\nMOD_GSK3_1 ...([ST])...[ST]\nMOD_LATS_1 H.[KR]..([ST])[P̂]\nMOD_LOK_YxT_1 [KR][YF][ÎVEDPGAC](T)[LMIVWFY][RKH]\nMOD_NEK2_1 [FLM][P̂VIED][P̂VID]([ST])[MLIVF][RKH].\nMOD_NEK2_2 [FLMW][P̂][P̂]([ST])[P̂DEGAN][RKH].\nMOD_N-GLC_1 .(N)[P̂][ST]..\nMOD_N-GLC_2 (N)[P̂]C\nMOD_NMyristoyl M̂{0,1}(G)[ÊDRKHPFYW]..[STAGCN][P̂]\nMOD_OFUCOSY C.{3,5}([ST])C\nMOD_OGLYCOS C.(S).PC\nMOD_PIKK_1 ...([ST])Q..\nMOD_PK_1 [RK]..(S)[VI]..\nMOD_PKA_1 [RK][RK].([ST])[P̂]..\nMOD_PKA_2 .R.([ST])[P̂]..\nMOD_PKB_1 R.R..([ST])[P̂]..\nMOD_Plk_1 .[DNE][P̂G][ST](([FYILMVW]..)|([P̂EDGKN][FWYLIVM]).)\nMOD_Plk_2-3 [DE]..([ST])[EDILMVFWY](([DE].)|(.[DE]))\nMOD_Plk_4 ..[ÎRFW]([ST])[ILMVFWY][ILMVFWY].\nMOD_PRMT_GGRGG_1 GGRGG\nMOD_ProDKin_1 ...([ST])P..\nMOD_SPalmitoyl_2 G(C)M[GS][CL][KP]C\nMOD_SPalmitoyl_4 M̂{0,1}G(C)..S[AKS]\nMOD_SUMO_for_1 [VILMAFP](K).E\nMOD_SUMO_rev_2 [SDE].{0,5}[DE].(K).{0,1}[AIFLMPSTV]\nMOD_TYR_CSK [TAD][EA].Q(Y)[QE].[GQA][PEDLS]\nMOD_TYR_DYR ..[RKTC][IVL]Y[TQHS](Y)[IL]QSR\nMOD_WntLipid [ETA](C)[QERK]..F...RWNC[ST]\nT\nable 2: ELM MOD motifs and their corresponding regex patterns.\n28\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint \n\nT\nraining Curves\nHere, we present additional training curves from pre-training as well as post-training.\n0 100k 250k\nTraining/uni00A0Steps\n2.2\n2.4\n2.6\n2.8Loss\nValidation\nTrain\nFig.\nS5: Pretraining loss curves. Training and validation losses vs optimizer steps during pre-training.\nThe final training loss is 2.19. The final validation loss is 2.22.\n0 500 1000 1500\nTraining/uni00A0Steps\n2.6\n2.7Sequence/uni00A0Entropy\np/uni00ADbody\nstress/uni00ADgranule\nnucleolus\nchromosome\n(a)\n0 500 1000 1500\nTraining/uni00A0Steps\n40\n42\n44%ID (b)\nFig.\nS6: Additional post-training curves with the ProtGPS reward model. (a) Shannon entropy\nvs. training steps (target H = 2.7). (b) %ID within a generated batch vs training steps (no target value).\n29\n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted April 11, 2026. ; https://doi.org/10.64898/2026.04.10.717777doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}