Metabolic pathways expanded before translation functionalities. A dual hourglass recruitment pattern transferred scale-free properties from loop to domain components of the EF network in generative cycles of hierarchical modularity. Modeling the evolutionary emergence of the oldest P-loop and winged-helix domains with AlphFold2 uncovered rapid convergence towards folded structure, suggesting that a folding vocabulary exists in loops for protein fold repurposing and design.The structures and functions of proteins are embedded into the loop scaffolds of structural domains. Their origin and evolution remain mysterious. Here, we use a novel graph-theoretical approach to describe how modular and non-modular loop prototypes combine to form folded structures in protein domain evolution. Phylogenomic data-driven chronologies reoriented a bipartite network of loops and domains (and its projections) into ‘waterfalls’ depicting an evolving ‘elementary functionome’ (EF). Two primordial waves of functional innovation involving founder ‘ And here begins my despair as a writer. All language is a set of symbols whose use among its speakers assumes a shared past. How, then, can I translate into words the limitless Aleph, which my floundering mind can scarcely encompass? …”— Jorge Luis Borges, The Aleph and Other Storieslex continui’ promoted by Leibnitz, requires that structural domains – the structural, functional and evolutionary units of proteins – emerge from earlier structural states. These prior states likely involve a combinatorial origami of dipeptides capable of forming flexible protein loop structures, which led to coevolutionary interactions with nucleic acid cofactors and the rise of genetics1. Prior states may also involve evolutionary stable and functionally relevant loop intermediates capable of giving rise to the enormous diversity of protein domains that exist in nature3. We here explore such scenario of emergence with structural phylogenomics and evolving networks.The protein world is both structured and functionally complex. Its emergence and history merits exploration. The evolutionary principle of spatiotemporal continuity, the ‘supersecondary building blocks made of helix, strand, turn and coil segments that are generally ~ 25 to 30 amino acid residues long, much smaller than the ~ 100 amino acid residues typical of an average compact domain5. Loop structures embody non-regular (aperiodic) loop regions spanning ‘helical’ and ‘sheet’ structural components6, which direct the polypeptide chain in space and are often functionally important. Supersecondary ‘closed loop’ structures collapse into extended flexible or rigid loop-shaped primordial intermediate conformations stabilized by van der Waals locks8. Loop prototypes are ubiquitous structures regarded as modern determinants of molecular function10. While their biophysical properties may constrain their evolution, studies identified evolutionarily conserved loop prototypes that were likely responsible for the early rise of molecular functions in protein evolution. A first group of ‘elementary functional loop’ (EFL) prototypes combine with others to form active sites that bind cofactors and exert molecular functions13. These EFLs were obtained by iterative derivation of sequence profiles from protein coding sequences in complete proteomes using a scoring function that weights profile positions according to their information content10. Distant evolutionary relationships between protein functions of EFLs revealed patterns of motif reuse in archaeal proteins11. A chronology of bipartite networks linked domains to EFLs (and their projections) and showed that the multifunctional α-β-α layered design typical of P-loop and Rossmann-like sandwich structures was primordial14. The networks also showed EFL recruitment events occurring throughout the 3.8 billion years (Gy) history of proteins, suggesting the origin of novel domains is an ongoing process. In contrast with EFLs, a second group of highly repeated non-combinable loop structures present in popular folds indicate remnants of an ancient peptide ‘vocabulary’ that formed folded polypeptides during a primordial RNA-peptide world15. Using machine learning methods, biphasic patterns in probability distributions highlighted high-scoring subdomain-sized fragments that were unified by < 30% sequence similarities. These fragments were aligned into folded loop structures that were 9–39 residue long, embedding helix-turn-helix, helix-hairpin-helix, ribosomal protein, P-loop/dinucleotide-binding β-α-β , and metal ion/iron-sulfur cluster (binding function) motifs. A third general type of supersecondary structural motifs involve widely reused, contiguous, and non-overlapping segments with longer lengths varying from 35 to 200 amino acids17. These so-called ‘themes’ have been used to build networks of domains and motifs linked by motif reuse in domains16, which interestingly increased with decreasing theme length following a power law17. The power law indicates a significantly biased distribution of themes in proteins. All three approaches characterize (1) supersecondary motifs by sequence and/or structure similarities, not necessarily carrying any evolutionary relationship; (2) motif recurrence across proteins driven by biological function; and (3) complex patterns showcasing an interplay of divergent vs. convergent evolution driven by rearrangements, duplications, and divergences. EFLs, loops and themes therefore represent ancient building blocks that are evolutionarily conserved.Loops define a diverse group of 19]. These chronologies showed a gradual evolutionary appearance of domain structures21, an evolving combinatorial rearrangement of domains in proteins22, and gradual accumulation of chemical, biophysical and molecular functions24. For instance, tracing chemical reaction mechanisms operating in metabolic enzymes uncovered a natural history of biocatalysis25. Similarly, tracing the average relative distance of amino acid contacts in the tertiary structure of proteins, a property known as ‘contact order’ that correlates to flexibility, showed that folding speed follows a biphasic pattern of increase and decrease during protein evolution26.We previously reconstructed evolutionary timelines of molecular accretion built with phylogenomic methods from the sequence and structure of thousands of nucleic acid molecules and millions of protein sequences encoded in thousands of genomes  was used to convert relative nd ages of FF domains into geological time in Gy . These projections describe how one set of nodes interlink based on bipartite connections to nodes of the other set: links in the domain projection describe how domains share loops in their structural makeup, while conversely, links in the loop projection describe how loops combine to form structures around active sites in domains. Since loops host molecular functions5, and domains represent bona fide structural, functional and evolutionarily conserved units of proteins28, the time series of EF networks and their projections described how domains recruited molecular functions in protein evolution.The EF network is a bipartite graph with two segregate sets of vertices (nodes), one representing loops (circles) and the other domains (rhomboids) Fig. E. Bipart42. DES tools delineate the growth and behavior of complex networks as a sequence of discrete events, with time flowing from event to event as a step function. Here, we borrow the DES rationale by mapping the growing structure of the undirected and unweighted EF network and its directed weighted projections to evolutionary time intervals  toolsals Fig. E. This i‘non-modular’ (NM) prototypes mapped uniquely to individual domains of a same age belonging to a set of 1965 domains. In contrast, a subset of 1937 ‘modular’ (M) prototypes mapped to more than one domain out of 1442 domains with times of origin spread throughout the timeline, with 2546 mappings. These prototypes acted as modular units of structural, functional and evolutionary significance. They represented the most abundant, widely distributed, and interesting loops of this study. Finally, a small subset of 16 ‘modular’ (contemporaneous) (M’) prototypes involved associations with more than one domain that occurred within individual time events. While we define modules as sets of integrated (coordinated) parts that cooperate to perform a task and interact more extensively with each other than with other parts and modules of a system, we recognize modules by the property of ‘modularity’, the degree to which parts of a system can be separated and rearranged in different contexts.We clustered 88,321 ArchDB loop structures mapped to 3892 domain families of our phylogenomic timeline, filtered at an e-value of < 0.001 to minimize false positives while detecting reliable structural and functional associations at statistically significant levels. This clustering yielded 7078 loop prototypes with 9650 many-to-many mappings to 2447 domains. The 7078 loop prototypes were divided into three subsets according to how they associated with domains across the evolutionary timeline  or the existence of molecular discriminating Maxwell demons that dissipate energy and information45. These views foster molecular systems that are frustrated by ‘messiness’ in the form of stochastic noise, heterogeneity, infidelity, and variation, as nicely exemplified by the existence of intrinsic disorder embedded in the structural makeup of proteins.A Venn diagram of domains mapping to the three groups of prototypes revealed three Venn groups of especial interest, domains mapping to only M loops (313 domains), domains mapping to only NM loops 827), and domains mapping to both M and NM loops (1109)  of 0.0009 [2546/(1442 × 1937)] and a node average degree (links per node) of 1.507 (± 0.018), i.e. loop components had approximately less than 2 interlinks on average. Visual inspection revealed that the network was well clustered. The Visualization of Similarity (VOS) clustering method47 uncovered 889 communities  with a high modularity index of 0.996. The adaptive events of the EF network were made vivid by color coding and arranging the component nodes by age in a top-down bimodal layout that followed the evolutionary timeline of domain structures )] and 0.00048 [1005/(1442 × (1442 − 1))] and total node average degrees of 2.104 (± 0.061) and 1.415 (± 0.067). In other words, ~ 2 domains and ~ 1.5 loops were shared on average, respectively. Both the loop and domain monomodal networks also showed significantly high community structure with 879 and 882 clusters each, and modularity indices of 0.994 and 0.990, respectively. The number of outward (outdegree) and inward (indegree) directed links (arcs) defined nodes as ‘donors’ (sources) or ‘acceptors’ (sinks), respectively. The horizontal and vertical scale of node symbols were made proportional to the weighted outdegree and indegree, respectively. This made the visualization of hubs explicit, e.g., a transition from wide to tall symbols along events indicated source-sink morphing dynamics. Overall, these transitions expressed an expected increase in the probability of co-opting older loops and domains with time, but also a surprisingly continual recruitment process operating among recent molecular forms.The bipartite EF network of Fig. 1442 × 197] and a 1442 × 197] and a P(k) of a node linked to k nodes decays as a power law, P(k) ~ k–γ, and does so without a characteristic scale. These scale-free networks are ubiquitous in biology, and in general have regression exponents γ = 2.1–2.4 with typical heavy-tailed distributions49. For metabolic networks of organisms in all superkingdoms, γ = 2.2 . We tested if the evolving EF network and its projections were scale free by studying their degree distributions along the time series of the growing networks , domains but not of loops during the nd ~ 0.02–0.04 interval, then of loops but not domains during nd ~ 0.04–0.07, and finally of loops but not domains of the EF bipartite network throughout the rest of the timeline  and low values of the KS fit statistic (≤ 0.10) failed to reject a fitted power-law distribution. Fitting the power law distribution produces decay exponent α. Values of α higher than 1 supported assumption of probability of power law fit P(X = x–α) for example for later degree distributions of loop components of the growing EF network. However, the log-likelihoods of the fitted power law gradually deviated towards larger negative values for most network events of the timeline, diminishing the likelihood of power law distributions. Analyses of the growing EF networks therefore reveal remarkable patterns of power law emergence and transfer. While power law behavior was shared between the early-evolved loop component and the domain component of the bipartite network, these ancient components went through two cycles of an exchange of scale-free properties, from domains to loops and then from loops to domains, as molecular functions developed in protein evolution , γ increased through fluctuations evident well before the first ripple occurring ~ 2.4 Gya (mentioned above), reaching a very strong power law scale for the loop portion  and domain portion  of the EF network, with coefficient of determination (R2) of ~ 95% supporting the linear models. Similarly, the loop and domain network projections maintained strong (average γ = 2.270 ± 0.030) and moderate (γ = 1.865 ± 0.038) power law scale, respectively. Thus, the extent of preferential attachment of our recruitment networks is in general more robust than that reported for metabolic networks52. The extraordinary observation of a dual ‘yin-and-yang’-like power law transfer between loop and domain components may be indicative of a continuing global scaling phenomenon in a biphasic emergence of biological modules57, which we now explain.Several statistics could not reject power law connectivity behavior in the most ancient loops and domains very early in evolution , a ratio of triangles (graph cycles of length 3) to connected triads in the network, averaged over all nodes, while ignoring edge directionality and weights53. Since C for the bipartite EF network was not meaningful due to absence of triangles, modular organization was investigated through its projections  and ~ 0.893 (± 0.0025), respectively, significantly higher than ~ 0.6 reported for metabolic networks59. The elevated C of EF network projections suggests integration of modules of loop prototypes and domain structures, which are densely connected, by few sparsely connected links between them. Thus, the EF network has a highly cohesive structure of modules.Networks become modular when their nodes connect to each other within bounds of a community (module)ons Fig. . The domC is its sharp decline with network size N for scale-free models60, as N−0.75, contrary to highly modular networks that are independent of N (e.g.52). For the domain and loop networks, C regressed with N as N–0.00019 and N–0.000033, and with age nd of the networks as nd–0.35 and nd–0.091, respectively , followed by a plateau to ~ 0.73 and ~ 0.88 at nd ~ 0.635, respectively. These patterns matched the power law trends, as indicated by KS fit indegree statistic, which manifested slightly earlier than the corresponding modularity phases and rejected power law behavior in initial phases , before plateauing to ~ 0.06 and ~ 0.1 at nd ~ 0.339, respectively  index partitioned either by age (NGage) and by VOS (NGvos) and the Fast Greedy Community (FGC) index. The NG algorithm calculates the maximum number of shortest paths running through an edge, a property known as ‘edge betweenness’51. The algorithm detects communities (modules) by progressively removing edges with high betweenness in iterative fashion. NGage ranges from –1 to 1, with positive values indicating modular structure within age events, while negative values indicating otherwise. NG partitioned by VOS (NGvos) describes VOS membership cohesiveness47. The FGC detection algorithm uses a hierarchical agglomerative approach of iteratively sampling random links that would increase the modularity of an initial subnetwork linking highly connected nodes in the original network63. Remarkably, the NGvos and FGC indicators measured along the timeline uncovered mirrored patterns of increase in modular cohesiveness and agglomerative structure for all growing networks. Conversely, NGage indicated divergent progress towards age-associativity in the EF network and its projections. All three networks showed age-independent origins with NGage ≤ − 0.3, − 0.25 and − 0.5 until nd ~ 0.034, ~ 0.073 and ~ 0.039, respectively. Loop and domain networks then parsimoniously progressed towards age-associativity with an early rise of NGage to ~ − 0.2 and then to ~ − 0.1 at nd ~ 0.039 and ~ 0.056, respectively, in the EF network, and at nd ~ 0.077 and ~ 0.112, respectively, in the domain projection, before plateauing out to ~ − 0.01 at nd ~ 0.545 in EF and to ~ − 0.006 at nd ~ 0.575 in the domain network. However, the loop projection became aggressively age-associative early in evolution, with an initial increase of NGage from − 0.5 to ~ − 0.07 at nd ~ 0.43 followed by a gradual rise to ~ 0.29 at nd ~ 0.18, before plateauing out to ~ 0.02 at nd ~ 0.528  theory of module emergence proposed by Mittenthal et al.nd = 0) to the present (nd = 1)  along a timeline that spans from the origin of proteins (1) Figs.  and 4. A1) Figs.  and 4. Tnd = [0.3–0.8) and domain acceptors originating at nd = [0.4–1.0]  being acceptors of very old donors or source nodes originating at nd < 0.3. In this respect, sink loops seem to be particularly adaptive, progressively drawing innovation from donors spanning the entire timeline. Box-and-whisker plots of cumulative weighted indegree and outdegree across network chronology . Domain connectivity fluctuated in a mirror fashion but with a slight phase delay (∆nd = 0.02) and with peaks of ~ 1.8, ~ 1.5 and ~ 1.7 loops per domain. These dual hourglass trends suggest a frustrated dynamics of growth in the number of loops making up the active sites of structural domains.Finally, the connectivity of loop and domain components of the EF network gradually evolved from 1 to a global average of 1.77 (± 0.032) loops per domain and 1.31 (± 0.018) domains per loop, respectively  subnetworks of the hubs in the loop and domain projections visually untangled the two recruitment waves  hydrolase domains   sequence motif, which binds to di- and trinucleotides. The EF network confirmed that the ‘p-loop’ wave massively recruited loops during a period of over ~ 2.5 Gy of history, especially using pathways of cysteine-rich loop prototypes. In these strong recruitment pathways, the most ancient domains such as NAD(P)-binding Rossmann-fold domain (c.2.1.2) family and the S-adenosyl-L-methionine-dependent methyltransferase domain (c.66.1.43) family, both of which harbored 3-layered α/β/α structures, and the ancient OB-fold of the nucleic acid-binding protein domains (b.40.4.5 and b.40.4.4) with their closed or partly-opened β-barrel structure, enabled many metabolic and translation functions. In particular, the cysteine-rich metal binding loop of the secondarily connected, downstream DS.HE.3.1.1 prototype formed a Zn2+-metal binding cysteine nest, which enables interactions with nucleic acids in 6 loop-related domains. This wave also included the class II aminoacyl-tRNA synthetases and biotin synthetases (d.104.1.1) and nucleotidyltransferase (d.218.1.5) families with α/β/α-layered and sheet structures, and beta and beta-prime subunits of DNA dependent RNA polymerase (e.29.1.1 and e.29.1.2) and prokaryotic type I DNA topoisomerase (e.10.1.1) families with β-barrel and winged helix-like structures  family structure. Loop DS.HH.1.1.1 was also linked to other downstream prototypes, including DS.EH.4.2.1 and DS.HH.1.1.3  Figs. A, 7A andp-loop wave but part of it merged with the p-loop wave through the sister loop hub, the DS.GH.0.0.1 prototype, and its ancestral hub domain, the N-acetyl transferase (d.108.1.1) family. The a.4.5 superfamily harbors the DNA/RNA-binding 3-helical bundle fold (a.4) structure, which is flanked by a 4-strand β-sheet. This domain exposes crucial elbow structures between the helix-turn-helix (HTH) motifs, harboring the specificity of protein–protein and protein-RNA interactions typical of these enzymes. The winged-helix domain is central to transcription67. The domain provides nucleic acid clamping and flexibility to RNA polymerases and paired structural recognition interfaces of ubiquitin-ligase and condensing complexes.The second wave in turn originated in the ‘winged-helix’ DNA-binding domain a.4.5) superfamily  transporter ATPase domain-like (c.37.1.12), which is part of the P-loop containing nucleoside triphosphate hydrolases fold (c.37) and superfamily (c.37.1) of SCOP. The fold has a 3-layered α/β/α sandwich arrangement with parallel or mixed β-sheets of variable sizes and topologies. The P-loop containing ABC transporter family that is responsible for the transport of a wide range of molecules across membranes  has a central core with a RecA topology that is missing some typical secondary structures of the fold. Modeling the birth of the fold demanded three procedural steps. First, the times of origin of loops were traced onto the 3-dimensional structure of a representative ABC transporter molecule, as we have previously done with proteins37, protein complexes70 or the ribosome71. Second, a time-ordered series of growing molecules was reconstructed by stitching loop sequences together, starting with the most primordial loop (the P-loop) and adding loops sequentially according to their time of origin. Finally, the three-dimensional structures of the growing molecules were modeled directly from their sequences with AlphaFold272, the star of the last biannual structure prediction experiment 73. AlphaFold2 uses a deep leaning algorithm to predict 3-dimensional structure directly from its sequence with levels of accuracy that are within the margin of error of experimental structure determination methods. Calculation of the median ‘global distance test’ (GDT), which measures the similarity of predicted and experimentally acquired structures with known amino acid correspondences, resulted in total scores of well above 90%, indicating global folds and structural details were correct. AlphaFold2 extracts co-evolutionary information in both multiple sequence alignments and structural templates from libraries using an ‘oracle’ that can quickly and iteratively identify which alignment and ‘pair representation’ of structural template data is more informative. This neural network-generated information is then processed by an ‘Evo former’ module to produce increasingly refined deep learning models of both sequence and structure, which converge into the structural prediction. The module uses two attention matrix-based ‘transformer’ architectures to convert the discrete vocabulary of sequence alignments into a continuous ‘embedded’ space of structure capable of training the multiple-layered neural networks. The structural prediction is finally assembled by a ‘structure’ module, which considers a protein as a ‘residue gas’. Each amino acid is modeled as a floating triangle with the three atoms of the backbone, which coalesce into the structure by translations and rotations in space using another attention transformer mechanism and ulterior refinements.Figure Remarkably, the series of predicted structural intermediates converged towards a mixed β-sheet flanked by α-helices making up the ‘binding’ cassette of the primordial RecA-like domain core . This steady pattern of ‘reformation’ follows a cryptic phenomenon illustrated by the appearance of the loop structure 213 (mapping to DS.HE.2.2.4) as a helix-coil region 3.3 Gya (nd = 0.122). This integrated structure was reformed into a fluid beta-hairpin 3.2 Gya (nd = 0.146) when pushed towards the C-terminus by the insertion of loop 80 (DS.EH.2.1.58). Its integration onto the expanding β-sheet however was only stabilized into its final form HE, 3.1 Gya (nd = 0.184), once the insertion of loop 186 (DS.HE.4.2.20) reformed the terminal loop 213 structure placing the terminal β-strand at the C-terminal region of the β-sheet. A similar phenomenon occurred 2.4 Gya (nd = 0.373) following the integration of the first α-helix of the bundle. The incorporation of loop 68 (which mapped to DS.BK.2.1.3) downstream the P-loop structure resulted in the formation of a loop form HE, mimicking the DS.HE.0.1.1 prototype (colored green) that was integrated 400 million years later . This instance of loop reformation from a BK to HE bracing architecture seems to represent an instance of significant structural rearrangement. These types of rearrangement continue throughout the timeline but are particularly striking during the last 50 million years of evolution (nd = 0.991–1.000) when an entire 4-strand β-sheet was formed. Structural alignments of predicted structures against the extant crystallographic entry showed RMSD values increased from 5.367 to 11.658 Å during the initial convergence period, decreasing thereafter to ~ 4–6 Å and then to 0.75 Å at nd = 1.0 , which are relatively far away from each other in the extant sequence and structure. To test if convergence was resilient, we conducted reshuffling experiments based on the 34|80|186|213 loop sequence where we systematically replaced loop 80 in the second position by all possible loops  that would maintain sequence order, and separately loop 213 in the fourth position by the only option, loop 222 (note that loop 186 could not be replaced). We then modeled structures from the reshuffled sequences and compared them to the reference structure using pruned and total RMSD measurements of structural overlaps  binding motif made of a right-handed three helical bundle (HTH) and a small β-sheet holding the ‘wings’67. The typical three α-helices (α) and three β-strands (β) of the wHTH motif follow the canonical order α1-β1-α2-α3-β2-β3 in the polypeptide chain. They are often preceded by an N-terminal α0 helical extension. While helices α2 and α3 are arranged perpendicular to one another, the nucleic acid-recognition helix α3 makes sequence-specific contacts with the major groove of DNA or RNA. The helix forms hydrogen-bond and van der Waals contacts with functional groups on the exposed base pairs and phosphate backbone. Helices α2 and α3 brace the aperiodic loop region of the very ancient DS.HH.3.1.1 prototype, which defines the nucleic acid-binding specificity of the HTH domain. The two loops that hold the ‘wings’ and a flanking β-hairpin are delimited by β2 and β3 and make other nucleic acid contacts, often with the minor groove or the backbone. Protein–nucleic acid interactions are further stabilized by nonspecific contacts between the nucleic acid backbone and residues in α2 and the turn between α2 and α3. The β-hairpin can separate nucleic acid strands in unconventional helicases holding the wHTH domain74.Bacillus subtilis  of mdtR of lis Fig. . The timlis Fig. . This co75, and so is the library of loop prototypes, which has all geometries sampled76, and is considered saturated even for the case of long loops77. These properties not only guarantee an exhaustive phylogenomic exploration of the history of domains and loops but also enable the sequence-to-structure mapping of deep learning methods needed to solve the fold recognition problem in ab initio explorations. Here, we trace the history of growing EF networks and their projections, verifying the existence of two primordial waves of functional innovation in elementary functional loops involving founder ‘p-loop’ and ‘winged-helix’ domain structures14. These waves originally explained recruitment patterns responsible for the origin of modern metabolism66. Our findings support an ongoing and highly modular recruitment of loop prototypes into structural domains. Remarkably, we also reveal an underground recruitment process of non-modular loop structures that are drawn at each time event of the timeline. The origin and evolution of loops and domains appears to have evolved in concert from the beginning of the protein world. Structures unfolded at different rates from diverse families of sequence motifs and in different structural contexts. This falsifies the sequential build-up of loops and domains and molecularly ‘canalized’ immutable structures in favor of a dynamic combinatorial landscape of structural creation. Our exploration also supports the evolving EF network becoming structured in evolution by exhibiting hierarchy, modularity, and a power law-based underlying scale free behavior. Integrated communities of interacting structural parts of domains defined modular classes of molecular functions in biphasic patterns of emergence. Collectively, links encapsulated the growth of an elementary alphabet of loop functions embedded in an alphabet of domain structures.The library of single domain protein structures is essentially complete78. The P-loop prototypes were embedded in a fold made of four tandem β-α repeats with a 3-layered α/β/α sandwich architecture, which much resembled the structural intermediates that appeared 2.7–3.1 Gya in our evolutionary timeline. The study confirmed that short (55-residue) P-loop proteins were catalytically active, supporting the functionality of our early molecular intermediates. Furthermore, construction of 40-residue polypeptides comprising just one P-loop element revealed they acted as helicases capable of separating and exchanging nucleic acid strands79 supporting the early nucleic acid-linked functionality of the P-loop prototype. A further focus on the emergence of the winged-helix domain fold of the second wave also revealed quick convergence towards the three helical bundle and 3-strand β-sheet structures of the fold, which centered around the nucleic acid-binding loop. Remarkably, convergence towards the core structure of the winged-helix fold resembled that of the P-loop transporters. In both cases, a central helix component of a functional loop prototype was packed against a small β-sheet structure to enhance functional roles.To explore the interplay of these two molecular languages, we modeled the evolutionary emergence of folded structure using historical information derived from chronologies and networks and deep learning algorithms of ab initio structural prediction. We first focused on the oldest domain of the timeline, the P-loop domain of ABC transporters. Remarkably, as accretion proceeded in evolution, the fold converged relatively quickly towards its typical core structure. Convergence, which was organized around the nucleotide-binding P-loop prototype, first materialized into a 3-strand β-sheet, then into the 3-layered α/β/α structure, and finally into an extended central β-sheet forming first a 5-strand and then a 6-strand planar structure. Remarkably, a recent phylogenetic-inspired engineering exploration was able to generate small P-loop–containing loop proteins capable of binding a range of phosphate-containing ligands, including RNA and single stranded DNAStructural convergence suggests the presence of a primordial folding vocabulary in loop structures that overrides the stochastic effects of recruitment. This vocabulary is likely driven by structural reformations occurring within a combinatorial (syntactic) landscape of innovation. Our analysis prompts generalizing ab initio structural prediction of molecular intermediates to all domains in an exploration of how semantics (the meaning of functions and structures) determine the pragmatics (context-dependent rules) of molecular communication.36 allowed calculation of geological ages of FFs in Gy. Details of the phylogenomic reconstruction are provided in Supplementary Materials and Methods. Since a loop is embedded in a domain structure and both loops and domains describe functional and structural abstractions, the age of domains can be directly transferred to loop prototypes. Whenever an older domain donates its loop to a younger domain in evolutionary recruitment, the loop can neither be younger than the younger domain nor be older than the older domain. Consequently, we considered two likely schemes of age transfer: (1) the age of a loop is the age of the most ancient associated domain, or (2) the age of a loop is the age of the more recent of the pair of most ancient associated domains. The age of a loop prototype in these schemes is either the age of the first structural scaffold or the age when the loop function is first transferred between structural scaffolds, respectively. Both schemes provided similar age mappings. For that reason, we only present mappings derived using the second more conservative scheme. Since the first loop that appeared in evolution must generate the first domain in order to preserve the ‘lex continui’ principle and a donor loop has to be either older or at least contemporaneous to the acceptor domain, the most ancient loop DS.EH.6.1.1 was assigned a time of origin of 0 according to scheme (1) as an exception because of the absence of any older donor domain.Times of origin (age) of domains, were directly derived from a published phylogenomic tree describing the evolution of structural domains defined at FF level of SCOP classification. A calibrated molecular clock of domain structures27 while mapping domains to loops at e-value < 0.001. This resulted in 88,321 loops structures clustering into 7078 unique loop prototypes that mapped to 2447 domains, with 9650 mappings. Note that each loop structure in ArchDB has one loop prototype annotation in the DS classification system with many-to-many mappings between loops and domains. Out of the set of 7078 loop prototypes, a subset of 5125 only mapped ‘horizontally’ and uniquely to domains of a same age within a subset of 1965 domains. They were reported as ‘non-modular’ (NM) loop prototypes because they failed to be recruited by different domains across the timeline, including those that were contemporaneous. In contrast, a subset of 1937 loop prototypes mapped ‘vertically’ to 1442 domains with times of origin spread throughout the timeline. They were reported as ‘modular’ (M) loops since they acted as modular units of structural, functional, and evolutionary significance. Finally, a subset of 16 loops each mapped ‘horizontally’ to sets of 2 contemporaneous domains, a subset of size 32. We reported these loops as ‘modular’ (contemporaneous) (M’) loops because they involved recruitments occurring within individual time events and representing focal innovations.Loop prototypes were computationally identified by filtering DS-derived loop structures from ArchDB80 and R’s igraph package81. Community-based layouts of the networks were generated using the Visualization of Similarity (VOS) clustering method. Network properties were analyzed with code constructed using graphing packages and tools of R83. A detailed description of data files, partitions and functions used to analyze network data, produce charts and plots, compute power law statistics and modularity indices, and construct waterfall diagrams can be found in the Supplementary Materials and Methods.Networks were visualized and analyzed using PajekP(k) vs. k (probability of having k-neighbors vs. k) and log–log (log of P(k) vs. log of k) mathematical curves, with linear regression models to derive γ of the power law and the determination coefficient (R2). γ is the absolute slope of the log linear model. Higher γ indicate higher levels of preferential attachment. R2 describes the percentage of the data fitting the linear model. High values of both γ and R2 indicate that scale free behavior is strongly supported. Other power law statistics included: (1) KS fit statistic, which compares the fitted distribution with the input degree vector; (2) the KS p-value, with the null hypothesis of data being drawn from the power law distribution63; and (3) the exponent of the fitted power law distribution (α), which assumes P(X = x) is proportional to x–α. Lower KS fit score, larger KS p-value (≥ 0.05), and higher α suggest better fit to power law distribution. The maximum log likelihoods of the fitted parameters were also determined. Reference networks were created using ‘Barabási’ methods84 of R’s igraph package81 to simulate power law and extended age-dependent control models for the corresponding networks.Scale free network behavior was studied using VOS Quality index (VQ), was generated by the Pajek layout algorithm that considers weights of links (edges/arcs) as similarities. Communities were iteratively drawn closer based on similarity and the quality index of the final layout with least crossings and closest clusters was given. VQ is then calculated as ∑i=1àc, j=i+1àc (eij – ai2), where c is the number of communities. eij is the fraction of edges with one node v in community i and the other w in community j, given as ∑vw (Avw/2 m) with 1v ϵ ci, 1w ϵ cj, where m is the sum of weights in the graph and Avw = the weighted value or 0, indicating presence or absence of edge between the nodes v and w, respectively, in the adjacency matrix A of the network. Finally, ai is the fraction of weighted k neighbors that are attached to the nodes of a community i, i.e. ki/2 m 47; (2) The Clustering Ratio (C-ratio) is the ratio of the number of clusters to the size of an inter connected node set; (3) The average Clustering Coefficient (C) describes the mean ratio of triangles to connected triads over all nodes in the simplified (undirected/unweighted) network54 is meaningful only for unimodal graphs62. We also report coefficients of linear regression over C for loop and domain network projections; (4) The Fast Greedy Community (FGC) hierarchical agglomeration algorithm detects community structure with linear run time O(m d logn) ~ O(n log2n), of a network with m edges, n nodes, and depth d of the dendrogram describing its community structure63; and (5 and 6) The Newman-Girvan algorithm index (NG), computed with partitions defined by age (NGage) and VOS clustering (NGvos). NG calculates the modularity of a network based on some classification (partition) to measure how good that classification is in dividing the various node types, indicated by assortative (positive) or disassortative (negative) mixing across modules51. NG equals 1/(2 m)∑ij(Aij − 1/(2 m)kikj*∆), where m is the collective weights in the graph, Aij are weighted entries in the adjacency matrix, ki, kj and ci, cj are the weighted degrees and the components (numeric partitions), respectively, of nodes i and j each, and finally, ∆ is 1 if x = y and 0 otherwise57. VQ, C-ratio, C and FGC each range from 0 to 1, while the NG indices range from − 1 to 1. Higher indices represent strong network modularity at an event. Heatmaps were generated using customized scaled modularity matrices with elements given as (Aij − kikj/(2 m))Mnd, where Aij, ki, kj and m are as defined for NG51, and Mnd is a network’s modularity index at event nd. Dendrograms were calculated as squared Euclidean distance matrices indicating dissimilarities between the cluster means85. The distance (or dissimilarity) matrices were hierarchically clustered with the Ward's minimum variance method aiming at finding compact, spherical clusters86.We studied modularity with six indices: (1) The 72 in ColabFold87. We requested output of 5 ranked models obtained with 3 recycles using PDB70 as template and the multiple sequence alignment (MSA) mode MMseqs2 . The use of PDB70 template did not significantly affect modeling results. Accuracy was measured with pLDDT and the predicted aligned error (PAE). pLDDT provides a per-residue estimate of prediction confidence based on the local Distance Difference Test (lDDT)-Cα metric88. The expected prediction reliability of a given region or molecule follows pLDDT ‘confidence bands’: > 90, models with very high confidence; 90–70, models with confidence, showing good backbone predictions; 70–50; models with low confidence; and < 50, models with very low confidence, generally showing ribbon-like structures. pLDDT < 60 can be considered a reasonably strong predictor of intrinsic disorder. TAE measures confidence in the relative positions of pairs of residues and is a good metric to evaluate the cohesiveness of domains. Structural alignment were carried out using subroutines of the visualization software Chimera89 (available at https://www.rbvi.ucsf.edu/chimera). Frag’r’Us was used to sample protein backbone conformations of loops90.The 3-dimensional structures of evolving molecules were modeled directly from their sequences with the AlphaFold2 pipelineSupplementary Information 1.Supplementary Information 2.Supplementary Information 3.Supplementary Video 1.Supplementary Video 2.Supplementary Video 3.Supplementary Video 4.Supplementary Video 5.Supplementary Video 6.Supplementary Video 7.


The kinase ZAKα acts as the proximal sensor of translational impairment and ribotoxic stress, which results in the activation of the MAP kinases p38 and JNK. Despite recent insights into the functions and binding partners of individual protein domains in ZAKα, the mechanisms by which ZAKα binds ribosomes and becomes activated have remained elusive. Here, we highlight a short, thrice-repeated, and positively charged peptide motif as critical for the ribotoxic stress-sensing function of the Sensor (S) domain of ZAKα. We use this insight to demonstrate that the mutation of the SAM domain uncouples ZAKα activity from ribosome binding. Finally, we use 3D structural comparison to identify and functionally characterize an additional folded domain in ZAKα with structural homology to YEATS domains. These insights allow us to formulate a model for ribosome-templated ZAKα activation based on the re-organization of interactions between modular protein domains. In sum, our work both advances our understanding of the protein domains and 3D architecture of the ZAKα kinase and furthers our understanding of how the ribotoxic stress response is activated. The MAP kinases (MAPK) p38 and JNK are central transducers of cellular stress pathways . In mammSaccharomyces cerevisiae, but clearly present in the genomes of vertebrate species, including fish and mammals. Curiously, only some metazoans, such as Caenorhabditis elegans, have a ZAKα homologue, whereas others such as Drosophila melanogaster do not.For extracellular ligand-mediated MAPK activation, the signaling from upstream MAPKKKs has been largely deduced. However, how the same group of kinases respond to stressful conditions is less understood. An example of this is the Ribotoxic Stress Response (RSR), where the MAPKKK ZAKα is activated by translational impairment and/or dysfunctional ribosomes . MultiplZAKα is a highly modular protein consisting of a number of annotated domains. Of these, crystal structures have determined the folding of the N-terminal kinase, leucine zipper, and SAM domains. Point mutations in the Sterile Alpha Motif (SAM) of ZAKα have been identified as a cause of developmental limb defects in humans and mice . SurprisSome knowledge about the mechanism(s) underlying ZAKα activation has been gleaned in recent years, such as the ability of the kinase to bind directly to ribosomes through dedicated sensor domains  and beco2 cell incubator. Experiments were conducted when the cells reached 70–80% confluency. U2OS ΔZAK cells were generated and described previously [2) was delivered to cells in a BS-02 irradiation chamber equipped with 254 nm bulbs . Cells were subsequently allowed to recover for 1 h prior to harvesting. The chemicals used in this paper were: doxycycline , anisomycin , and Earle’s Balanced Salt Solution (EBSS) . Human osteosarcoma cells  were cultured in Dulbecco’s Modified Eagle’s Medium  supplemented with 10% fetal bovine serum , L-glutamine, 1% penicillin, and streptomycin and cultured at 37 °C in a humidified 5–8% COeviously . To geneFor protein extraction, cells were lysed in EBC lysis buffer  supplemented with protease inhibitors ), phosphatase inhibitors . Constructs were then PCR-cloned into pcDNA4/TO/Strep-HA. U2OS ΔZAK stably expressing ZAKα WT and ZAKα ΔCTD were generated previously . PlasmidPDB text file formats of ZAKα domains were prepared in PyMOL from AF-Q9NYL2-F1 prior to computational distanced-assisted matrix alignment (DALI) analysis. DALI is a server for 3D protein structure comparison ,22, and In previous work, the functionality of the S domain of ZAKα was demonstrated by internal deletion of a region spanning 150 amino acids . Upon anZak KO U2OS (U2OS ΔZAK) cells with doxycycline-inducible versions of ectopic STREP-HA-tagged ZAKα, where all arginines and lysines in these motifs were replaced with alanines, either in a full-length context or with a deletion of the last 27 amino acids of the CTD   . Mutatio A ΔCTD) b. Howeve A ΔCTD) b. This d A ΔCTD) b, which  A ΔCTD) c. As a c A ΔCTD) . This mu A ΔCTD) d, sugges A ΔCTD) . Two of  A ΔCTD) e. Howeve A ΔCTD) e, indicaWe next combined inactivating mutations in the S and CTD domains (R -> A ΔCTD) with a previously described point mutation (W347S) in the SAM domain that confers constitutive activity and mild instability on ZAKα . StrikinDespite recent advances in the search for ZAKα activation mechanism(s) ,20, muchWe next sought to investigate whether this domain bears resemblance to known functional protein domains. A 2D-homology search did not return any hits, and we instead turned to a strategy of 3D-homology searches, looking for proteins with topological similarity. To this end, we subjected the uncharacterized ZAKα domain to pairwise, hierarchical distance-assisted matrix alignment (DALI) against the human AlphaFold database a. The DADALI analysis of the structure of the amino acids 433 to 550 of ZAKα against all human AlphaFold-predicted structure returned seven such hits . Four ofWe next investigated the regional, topological similarities between amino acids 433–550 of ZAKα and the DALI hits in The topological similarity of ZAKα YLD to the SMARCD proteins, however, did not map to the annotated SWIB/MDM2 domains of these proteins a. Multip domains a. Finall domains . Our bioThe outcome of the DALI analysis  promptedZAKα is a ribotoxic stress-sensing kinase by virtue of its direct interaction with ribosomes. Unlike other ribosomal stress-surveying factors , ZAKα binds to elongating as well as stalled and collided ribosomes with apparent similar affinity ,17,20. TThese motifs are likely to form critical contacts with impaired ribosomes, but at present, we have no insight into whether this is based on interaction with rRNA or protein. Given the modular organization of the S domain (there are three redundant repeats) and the lack of an absolute requirement for this domain in the presence of the CTD, we speculate that impaired ribosomes expose a unique surface that is recognized by one RGRYXXR/K in a charge-dependent manner. Future work is required to identify this ribosomal binding surface, for example by cross-linking mass spectrometry or cryo-EM.3D-homology modeling of a predicted folded domain in ZAKα revealed a hitherto ignored structural feature of this kinase. This domain, which we have dubbed the YLD, has a striking similarity to the well-characterized YEATS domain that is found in a number of nuclear proteins  Figure . YEATS dPoint mutation of the ZAKα SAM domain has been linked to mesoaxial polydactyly, hearing loss, and limb development in human patients as well as mouse models . Our preIn conclusion, our work highlights new structural features of the ZAKα kinase, improving our understanding of the mechanism(s) underlying RSR activation by impaired ribosomes. Structural information from ZAKα-bound ribosome complexes will be key to further inform our proposed model.


Data augmentation has been widely used to improve generalization in training deep neural networks. Recent works show that using worst-case transformations or adversarial augmentation strategies can significantly improve accuracy and robustness. However, due to the non-differentiable properties of image transformations, searching algorithms such as reinforcement learning or evolution strategy have to be applied, which are not computationally practical for large-scale problems. In this work, we show that by simply applying consistency training with random data augmentation, state-of-the-art results on domain adaptation (DA) and generalization (DG) can be obtained. To further improve the accuracy and robustness with adversarial examples, we propose a differentiable adversarial data augmentation method based on spatial transformer networks (STNs). The combined adversarial and random-transformation-based method outperforms the state-of-the-art on multiple DA and DG benchmark datasets. Furthermore, the proposed method shows desirable robustness to corruption, which is also validated on commonly used datasets. For modern computer vision applications, we expect a model trained on large-scale datasets to be able to perform uniformly well across various testing scenarios. For example, consider the perception system of a self-driving car; we want it to be able to generalize well across weather conditions and city environments. However, current supervised-learning-based models remain weak when it comes to out-of-distribution generalization . When teDomain adaptation (DA) and domain generalization (DG) are two typical techniques used to address the domain shift problem. DA and DG aim to utilize one or multiple labeled source domains to learn a model that performs well on an unlabeled target domain. The major difference between DA and DG is that DA methods require target data during training, whereas DG methods do not require target data in the training phase. DA can be categorized as supervised, semi-supervised, and unsupervised, depending on the availability of the labels of target data. In this paper, we consider unsupervised DA, which does not require labels of target data. In recent years, many works have been proposed to address either DA or DG problems ,5. In thData augmentation is an effective technique for reducing overfitting and has been widely used in many computer vision tasks to improve the generalization ability  of the mMotivated by the recent success of RandomAugment  on improTo further improve the accuracy and robustness, we consider employing adversarial augmentations to find worst-case transformations. Our interest is in performing adversarial augmentation for DA and/or DG without using searching-based methods. Most image transformations are non-differentiable, except for a subset of geometric transformations. Inspired by the spatial transformer networks (STNs) of , we propCIFAR-10-C [In this work, apart from the cross-domain generalization ability, robustness is also our concern. This is particularly important for real applications when applying a model to unseen domains, which, however, is largely ignored in current DA and DG literature. We evaluate the robustness of our models on FAR-10-C , which i(1)We build a unified framework for domain adaptation and domain generalization based on data augmentation and consistency training.(2)We propose an end-to-end differentiable adversarial data-augmentation strategy with spatial transformer networks to improve accuracy and robustness.(3)We show that our proposed methods outperform state-of-the-art DA and DG methods on multiple object recognition datasets.(4)CIFAR-10-C robustness benchmark.We show that our model is robust to common corruptions and obtained promising results on the Our contributions can be summarized as follows:Modern domain adaption methods usually address domain shifts by learning domain-invariant features. This purpose can be achieved by minimizing a certain measure of domain variance, such as the Maximum Mean Discrepancy (MMD) ,18 and fAnother line of work uses adversarial learning to learn features that are discriminative in source space and at the same time invariant with respect to domain shift ,22,23. IRecently, self-supervised-learning-based domain adaptation was proposed . Self-suSimilar to domain adaptation, existing work usually learns domain-invariant features by minimizing the discrepancy between the given multiple source domains, assuming that the source-domain-invariant feature works well for the unknown target domain. Domain-Invariant Component Analysis (DICA) is proposed in  to learnAdversarial learning has also been applied in DG. In , an MMD-Some work utilizes the low-rank constraint to achieve domain generalization capability, such as ,37,38. MIn ,43, selfData augmentation is a widely used trick in training deep neural networks. In visual learning, early data augmentation usually uses a composition of elementary image transformation, including translation, flipping, rotation, stretching, shearing, and adding noise . RecentlAnother kind of data augmentation method aims at finding the worst-case transformations and utilizing them to improve the robustness of the learned model. In , adversaRecently, consistency training with data augmentation has been used for improving semi-supervised training  and the Most related works focus on either domain adaptation or domain generalization, while in this work, we consider designing a general model to address both of them. Domain adversarial training is a widely used technique for DA and DG, and our work does not follow this mainstream methodology but seeks resolution from the perspective of representation learning, e.g., self-supervised learning , and conIn this section, we present the proposed method for domain adaptation and generalization in detail.In the domain adaptation and generalization problem, we are given a source domain The task of unsupervised domain adaptation is to train a classification model Many works have addressed either domain adaptation or domain generalization. In this work, we propose a unified framework to address both problems. In what follows, we first focus on domain adaptation and introduce the main idea and explain the details of the proposed method. Then, we show how this method can be adapted to domain generalization tasks as well.(1)Given an input image (2)For domain adaptation, we jointly minimize the classification loss with labeled source-domain samples and a divergence metric between the two distributions (3)For domain generalization, the procedure is similar to (2) but without using any target domain samples.Inspired by a recent line of work ,29 in seOur intuition is that, on one hand, minimizing the consistency loss can enforce the model to be insensitive to the noise and improve the generalization ability; on the other hand, the consistency training gradually transmits label information from labeled source domain examples to unlabeled target domain ones, which improves the domain adaptation ability.Shear, Translation, Rotation, and Flip. The second group is the color-enhancing-based image transformations, e.g., Solarize, Contrast, etc., and the last group includes other transformations, e.g., CutOut and SamplePairing. Each type of image transformation has a corresponding magnitude, which indicates the strength of the transformation. The magnitude can be either a continuous or discrete variable. Following [PACS dataset and VisDA dataset and found that The applied random-image transformations are similar to RandAugment . Table 1ollowing , we alsoollowing ,9,10. Foollowing , we do nctice of , we sampFollowing VAT  and UDA The consistency loss for domain adaptation can be written asAs a common underlying assumption in many semi-supervised learning methods, the classifier’s decision boundary should not pass through high-density regions of the marginal data distribution . The conFollowing ,5, we alFor domain generalization, as no target domain data are involved during the training, Equation  can be wLc(θm)=ExEquation :(6)JDG=In this section, we conduct experiments to evaluate the proposed method and compare the results with the state-of-the-art domain adaptation and generalization methods.Our method was evaluated on the following popular domain adaptation and generalization datasets:PACS [PACS  is a staPACS , we evalImageCLEF-DA [eCLEF-DA  is a benOffice-Home [A), Clipart (C), Product (P), and Real-World (R). The Clipart domain is formed with clipart images. The Art domain consists of artistic images in the form of paintings, sketches, ornamentation, etc. The Real-World domain’s images are captured by a regular camera and the Product domain’s images have no background. The total number of images is about 15,500.ice-Home  was usedVLCS [VLCS  was usedVisDA http://ai.bu.edu/visda-2017/ (accessed on 10 May 2020) is a simulation-to-real domain-adaptation dataset that has over 280 K images across 12 classes. The synthetic domain contains renderings of 3D models from different angles and with different lighting conditions, and the real domain contains nature images.To investigate the robustness of the proposed model, we also evaluated it on popular robustness benchmarks, including the following.CIFAR-10.1 [CIFAR-10 with 2000 images and the exact same classes and image dimensionality. Its creation follows the creation process of the original CIFAR-10 paper as closely as possible. The purpose of this dataset is to investigate the distribution shifts present between the two test sets, and the effect on object recognition.FAR-10.1  is a newCIFAR-10-C [CIFAR-10 [FAR-10-C  is a robCIFAR-10  test setWe implemented the proposed method using the PyTorch framework on a single RTX 2080 Ti GPU with 11 GB memory. The Alexnet , Resnet-For training the model, we used an SGD solver with an initial learning rate of We followed the standard protocol for unsupervised domain adaptation ,62, wherDeep All to denote the baseline model trained with all available source-domain examples when all the introduced domain adaptive conditions are disabled. For the compared methods in We compared our proposed method with state-of-the-art DA and DG methods. The descriptions of the compared methods are shown in PACS are reported in RotC is an improved version of Rot, which applies consistency loss with the simplest image rotation transformations [CDAN and CDAN+E and the open source code of [MDD. Our proposed approach outperforms all baseline methods on all transfer tasks. The last column shows the average accuracy on the four tasks. Our proposed approach outperforms state-of-the-art CDAN+E [MDD by The multi-source domain adaptation-results on rmations . We use rmations  to produ code of  to produt CDAN+E  by 4.7 pDeep All, DANN, CDAN, CDAN+E, and MDD, which are denoted by Deep All (Aug), DANN (Aug), CDAN (Aug), CDAN+E (Aug), and MDD (Aug), respectively. From these results, we can see that data augmentation can obtain an improvement of To investigate the improvement from data augmentation, we add the same type of data augmentation as ours on Office-Home dataset are reported in Office-Home dataset, we conducted 12 transfer tasks of four domains in the context of single-source domain adaptation. We achieved state-of-the-art performance on 8 out of 12 transfer tasks. It is noted that although Office-Home and PACS are related in terms of domain types, the number of total categories in Office-Home and PACS are 65 and 7, respectively. From the results, we can see that the proposed method scales when the number of categories changes from 7 to 65. The average accuracy achieved by our proposed method is The results on ImageCLEF-DA dataset are reported in ImageCLEF-DA are of equal size and balanced in each category and are visually more similar, there is little room for improvement in this dataset. Even so, our method still outperforms the comparison methods on four out of six transfer tasks. Our method achieves CDAN+E [RotC [MLADA [The results on the g CDAN+E , RotC [2+E [RotC  and MLADC [MLADA .VisDA as reported in CDAN+E by The proposed method also obtains strong results on RotC is the combination of simple image rotation transformation and consistency loss, without using complex data augmentation, we can better understand how much of the improvement is from the consistency loss. Comparing to Rot, which does not use consistency loss, we can see from the above DA experiments that RotC obtains an improvemnt of about It is important to understand the improvement of the consistency loss. Because the PACS dataset. We compared the performance of our proposed method against several recent domain-generalization methods. We evaluated the method with both Alexnet and Resnet-18 and report the results in WADG by around In the context of multi-source domain generalization, we conducted four transfer tasks on Ours w/o consis. We can see that the model trained with cross-entropy loss obtains similar accuracy to ours with consistency loss. However, the consistency loss is required for DA because of the unlabeled target domain samples. To keep a unified framework for both DA and DG problems, we used consistency loss for DG in this work.As consistency loss is not mandatory for DG, we replaced consistency loss with cross-entropy loss and ran our methods. The results are denoted by JiGen and Deep All with the same type of data augmentation as ours, denoted by JiGen (Aug) and Deep All (Aug). We can see that using pure augmentation, Deep All can obtain an improvement of around JiGen can obtain an improvement of around To investigate the improvement of pure data augmentation without consistency, we ran Office-Home and VLCS datasets for multi-source domain generalization. Compared to PACS, these two datasets are more difficult, and most recent works have only obtained small accuracy gains with respect to the Deep All baselines. The results on Office-Home and VLCS dataset are reported in the Office-Home dataset, and the results tested on the VLCS dataset show that our method achieves the best or close to the best performance on the four tasks, outperforming the recently proposed ones on average. It is noted that our baseline Deep All has relatively higher accuracy than other baselines. This is because we also add data augmentations such as random crop, horizontal flipping, and color jittering when training Deep All models. In this case, it is fairer to compare with the proposed method, which incorporates various data augmentation operations.We also conducted experiments on CIFAR-10.1 and CIFAR-10-C. We trained on the standard CIFAR-10 training set and tested on various corruption datasets, i.e., in a single-source domain-generalization setting. JT and TTT. Following [Apart from domain adaptation and generalization, we are also interested in the robustness of the learned model. In this part, we evaluate the proposed method on robustness benchmarks ollowing , we usedbaseline refers to the plain Resnet model, which is equivalent to Deep All in the DG setting. JT and TTT are the joint training and testing time training in [rnd-all the random image transformation including geometric and color-based transformations, adv-stn the proposed adversarial STN without random image transforms, and adv-stn-color the adversarial STN combined with random color-based transformations.The method denoted by ining in , respectCIFAR-10 testing dataset, where we can see that all the compared methods obtained similar accuracies. On CIFAR10.1, the testing errors of all these methods increase simultaneously, but there is no significant gap between them. On the CIFAR-10-C corruption data sets, the performances of these methods vary a lot. Our proposed methods show improved accuracies compared to the baseline. adv-stn-color shows better performance than its variants and also outperforms JT and TTT. It can also be seen that adv-stn even outperforms rnd-all in most cases, although it only applies geometric transformations, which indicates the effectiveness of the proposed adversarial spatial transformations for improving robustness.On the left is the standard Below, we focus on the PACS DG and DA setting for ablation analyses of the proposed method.rnd-color and rnd-geo are subsets of rnd-all, where rnd-color refers to color-based transformations and rnd-geo refers to geometric transformations. Please see rnd-color obtained the best accuracy, and adv-stn outperformed rnd-geo. The combination of rnd-color + adv-stn also outperformed rnd-color + rnd-geo. However, in this experiment, adv-stn did not further improve rnd-color, which might be due to the limited room for improvement in the baseline method.In this part, we conducted ablation studies on adversarial and random image transformations. adv-stn outperforms rnd-geo. As the baseline accuracy of DG is far from saturated compared to DA, we can see that adv-stn further improved rnd-color and the combination of rnd-color + adv-stn obtained the best accuracy.In the DG experiment, we obtained the similar conclusion that photo, cartoon, and sketch as the source domains and art_painting as the target domain, are reported in In this part, we conducted ablation studies on the hyperparameters setting. The final objective functions of our proposed method for domain adaptation  and domaFrom the figures, we can see that when both Deep All, which does not apply any adaptation.To better understand the learned domain-invariant feature representations, we use t-SNE  to conduFrom the visualization of the embeddings, we can see that the clusters created by our model not only separate the categories but also mix the domains. The visualization from the DG model suggests that our proposed method is able to learn feature representations generalizable to unseen domains. It also implies that the proposed method can effectively learn domain-invariant representation with unlabeled target domain examples.adv-stn are, we plot the transformed examples during training in rnd-all and adv-stn-color, respectively. From the figure, we can see that the proposed adversarial STN does find more difficult image transformations than random augmentation. Training with these adversarial examples greatly improves the generalization ability and robustness of the model.To visually examine what the adversarial spatial transformations learned by In this work, we proposed a unified framework for addressing both domain adaptation and generalization problems. Our domain adaptation and generalization methods are built upon random image transformation and consistency training. This simple strategy can be used to obtain promising DA and DG performance on multiple benchmarks. To further improve its performance, we proposed a novel adversarial spatial transformer network that is differentiable and able to find the worst-case image transformation to improve the generalizability and robustness of the model. Experimental results on multiple object recognition DA and DG benchmarks verified the effectiveness of the proposed methods. Additional experiments tested on CIFAR-10.1 and CIFAR-10-C also validated the robustness of the proposed method.


S-adenosyl methionine (SAM) cofactor binding domain among KMT subfamilies. Therefore, understanding the unique interactions within each KMT–substrate pair can facilitate developing highly specific inhibitors. The FAM86A gene encodes an N-terminal FAM86 domain of unknown function in addition to its C-terminal methyltransferase domain. Here, we used a combination of X-ray crystallography, the AlphaFold algorithms, and experimental biochemistry to identify an essential role of the FAM86 domain in mediating EEF2 methylation by FAM86A. To facilitate our studies, we also generated a selective EEF2K525 methyl antibody. Overall, this is the first report of a biological function for the FAM86 structural domain in any species and an example of a noncatalytic domain participating in protein lysine methylation. The interaction between the FAM86 domain and EEF2 provides a new strategy for developing a specific FAM86A small molecule inhibitor, and our results provide an example in which modeling a protein–protein interaction with AlphaFold expedites experimental biology.FAM86A is a class I lysine methyltransferase (KMT) that generates trimethylation on the eukaryotic translation elongation factor 2 (EEF2) at Lys525. Publicly available data from The Cancer Dependency Map project indicate high dependence of hundreds of human cancer cell lines on FAM86A expression. This classifies FAM86A among numerous other KMTs as potential targets for future anticancer therapies. However, selective inhibition of KMTs by small molecules can be challenging due to high conservation within the  Protein lysine methylation is the addition of one, two, or three methyl moieties to the ε-nitrogen of a lysine side chain, forming mono-, di-, and trimethylated derivatives . Lysine S-adenosylmethionine (SAM), the methyl donor in lysine methylation catalysis  domain (A). Primary amino acid sequence alignment shows the FAM86 and MTase domains of FAM86A are conserved from yeast with 20% and 28% conserved identity, respectively (A). Although the FAM86 domain evolved alongside the MTase domain through the evolutionary tree, there remains no known biological function for the FAM86 domain in any species.It is common for KMTs to encode structural domains in addition to catalytic domains . In bot) domain A. Primarectively A. Althouin silico has the potential to facilitate the process of experimental biology by enabling molecular insights on an accelerated timescale. In this work, we used a combination of X-ray crystallography, the newest AlphaFold algorithms, and experimental biochemistry to characterize the role of the FAM86 domain in EEF2 methylation by FAM86A.AlphaFold is the machine learning algorithm developed by DeepMind to predict protein structures based on primary amino acid sequences . In the in vitro and in human cells. Simulated models of the FAM86A–EEF2 interaction generated by AlphaFold-Multimer suggested the FAM86 domain of FAM86A forms an extensive intermolecular interaction with EEF2. Point mutations within this predicted interface inhibited EEF2 methylation in human cells. Based on these data, we propose that the FAM86 domain of FAM86A confers substrate specificity by orienting EEF2-Lys525 toward the FAM86A active site. Future work may leverage these insights or take similar approaches to develop selective inhibitors of FAM86A and other KMTs.Using the structural data provided by X-ray crystallography and AlphaFold, we determined the FAM86 domain of FAM86A forms a five-helix bundle distinct from the 7βS domain. By testing the catalytic activity of a truncated FAM86A construct lacking the FAM86 domain, we found the FAM86 domain is required for EEF2 methylation S-adenosyl homocysteine (SAH) at 3.3-Å resolution . We were able to trace the entire FAM86A protein, except for the very N terminus (residues 1–5) and a portion of the domain linker between the FAM86 and MTase domains (residues 127–133).Our initial effort in crystallizing wildtype FAM86A failed to generate diffractable crystals. To overcome this challenge, we designed a FAM86A construct harboring a triple mutation for reduction of surface entropy see , which pB and C, . The cryric unit A. We werB and C)  , 28. TheD). Of note, the experimental and predicted models reveal the nearly identical SAM-binding pocket with approximately 14 residues participating in the coordination of the ligand SAH  Nevertheless, the experimental and predicted models show a slight difference in the helical orientations (αe and αf) in the FAM86 domain, as well as the positionings of the SAH-engaging residues W139 and Y251 . AlphaFill did not predict any ligands to interact with the FAM86 domain.We next examined the predicted model of FAM86A’s 3D structure available through the AlphaFold database with ligand transposition provided by AlphaFill . The preFig. 1A). We used the custom antibody to ask whether the FAM86 domain of FAM86A is required for EEF2 methylation. To test this, we cloned a truncated construct of FAM86A (FAM86A(101–330)) lacking the FAM86 domain  and tested its activity on EEF2 by adding back wildtype or truncated FAM86A to KO cells by transfection. While wildtype FAM86A generated EEF2-K525me3, the truncated mutant, which expressed at the same level as wildtype protein, did not . Next, we asked a similar question in vitro by incubating recombinant, purified FAM86A with recombinant, purified EEF2 in the presence of radiolabeled SAM (3H-SAM). Consistent with the result in cells, we found the FAM86 domain is required for EEF2 methylation in vitro . When recombinant, purified FAM86A(101–330) was incubated with whole cell extracts from the FAM86A KO HEK293T cells in vitro, we did not observe activity on any protein, whereas full-length protein methylated a protein the size of EEF2 . From these data we conclude the FAM86 domain is required for EEF2-Lys525 methylation by FAM86A and that EEF2 is the likely main physiologic target of FAM86A.We began our investigation into FAM86A methylation by raising an antibody that is highly selective and specific for EEF2-K525 trimethylation . First, Fig. 2in silico, we queried AlphaFold-Multimer via ColabFold (A). Importantly, EEF2-Lys525 was predicted to occupy a position proximal to the FAM86A active site near the SAM-binding residues that were independently identified by X-ray crystallography and AlphaFill (A). When superimposed with the AlphaFill model, we can visualize the proximity of EEF2-Lys525 to the ligand SAM as if FAM86A, EEF2, and SAM were experimentally cocrystallized (B). In a second interface, an interaction was predicted involving the FAM86 domain and domain IV of EEF2 (A). A close-up view reveals an extensive network of interactions involving FAM86A residues Ile78, Pro88, Asp90, Try93, Glu94, Leu96, Ala97, Leu100, and Met101 as well as EEF2 residues Pro596, Val680, Ala681, Trp685, Gly718, Gly719, Gln720, Ile722, Pro723, and Arg726 (C). Since AlphaFold-Multimer folds proteins with a goal of simulating an interaction, we superimposed the models of FAM86A and EEF2 that were individually predicted by AlphaFold onto the FAM86A–EEF2 complex as a measure of quality control. We found the individual FAM86A model was nearly identical to its conformation in the FAM86A–EEF2 complex, with RMSD of only 0.366 Å over 252 aligned Cα atoms (D). In the case of EEF2, the RMSD was calculated to be 0.733 Å over 642 aligned Cα atoms (E). Most of the variation for EEF2 is caused by rotation of domain IV, a physiologic flexibility known to be crucial for GTP hydrolysis and ribosomal translocation . As shown in Figure 4A, complementation of FAM86A (A97R) in FAM86A KO HEK293T cells failed to rescue EEF2-Lys525 methylation in cells, whereas wildtype FAM86A restored methylation (A). To test whether EEF2(I722R) is a viable substrate for FAM86A, we transfected and immunoprecipitated FLAG-EEF2(I722R) from HEK293T cells endogenously expressing FAM86A. While the input sample shows methylation of endogenous wildtype EEF2 in the I722R sample, the exogenous EEF2 carrying I722R substitution was not methylated (B). Importantly, both FAM86A (A97R) and EEF2(I722R) mutant constructs expressed equally well compared with wildtype in cells and are predicted by AlphaFold to not impact overall protein folding (A and B and C and D). These data suggest that substitutions of FAM86A (A97R) and EEF2(I722R) prevent EEF2-Lys525 methylation through an allosteric mechanism, likely due to inhibition of the interface predicted by AlphaFold-Multimer.To test the AlphaFold-Multimer predicted interaction, we asked if blocking the interaction between the FAM86 domain of FAM86A and domain IV of EEF2 inhibits FAM86A-mediated EEF2-Lys525 methylation. We generated model-guided FAM86A and EEF2 derivatives carrying point mutations in the FAM86 domain and domain IV, respectively. Specifically, FAM86A-Ala97 and EEF2-Ile722 were substituted to arginine to increase the likelihood of disrupting the binding interface while still maintaining the native individual structures of FAM86A and EEF2 , A–D. Ashylation A. To testhylated B. ImportIn vitro, the activity of purified FAM86A (A97R) on purified EEF2 was similar to that of wildtype FAM86A (C). In contrast, purified FAM86A showed reduced activity on purified EEF2(I722R) compared with wildtype EEF2 (D). We postulate that, in a physiological context, the transient nature of the FAM86A and EEF2 interaction becomes sensitive to the modest interference generated by the point mutations. Meanwhile, the simplicity and high stoichiometry of each protein in in vitro reaction mixtures amplify the possibility that any two proteins might interact with one another.e FAM86A C. In conype EEF2 D. We posA and B). FAM86B2 is nearly identical to FAM86A, while FAM86B1 encodes a truncated FAM86 domain resulting from loss of a single exon compared with FAM86A and FAM86B2 (C). Notably, the exon lost in FAM86B1 encodes the homologous helix that forms the interface of FAM86A with EEF2. We tested whether FAM86B1 and FAM86B2 are redundant copies of FAM86A by adding back FAM86B1 and FAM86B2 to FAM86A KO HEK293T cells. However, neither FAM86B1 nor FAM86B2 generates EEF2-K525me3 (D), suggesting that they may have different substrates or not be active enzymes.The implication that the FAM86 domain of FAM86A confers substrate specificity for EEF2 is intriguing on multiple fronts. First, this is an instance in which a noncatalytic domain of a KMT is required for catalysis. Second, the FAM86 domain represents a novel and clinically actionable target for inhibition of FAM86A catalytic activity, which may be relevant given the possible role of the FAM86A–EEF2 methylation axis in cancer biology. Third, there are other FAM86 domain–containing human KMT genes that likely emerged from FAM86A as a common ancestor. While FAM86A exists in yeast, neither of the human genes FAM86B1 or FAM86B2 exists in many lower animals including mice . FAM86B1 FAM86B2 . While t FAM86B2 C. Notabl-K525me3 D, suggesA). However, FAM86B1 is categorized as an essential gene by its DepMap gene effect data (B). This suggests that it could be an active enzyme in human cells and hints at an interesting evolutionary story: by deleting the residues of its FAM86 domain that promote EEF2-Lys525 methylation, FAM86B1 evolved specificity for a different substrate that, like the FAM86A–EEF2 methylation axis, promotes a critical function in human cells. A future iteration of AlphaFold  cells were grown in Dulbecco’s modified Eagle’s medium supplemented with 10% fetal bovine serum and 100 U/ml penicillin/streptomycin. Cells were cultured at 37 °C in a humidified incubator with 5% CO2. Cell lines were authenticated by short tandem repeat profiling and tested negative for mycoplasma .Transient expression was performed using polyethylenimine (PEI) 3 μg per 1 μg of plasmid DNA. For CRISPR-Cas9 knockout of FAM86A, virus particles were produced by cotransfection of 293T cells with the lentiCRISPR v2/puro (Addgene) construct containing the sgRNA sequence AGCACGGCCATCATCTCCTA, pCMV-VSV-G (Addgene), and pCMV-dR8.2 dvpr (Addgene) in a ratio of 5:1:4 by mass. As a control, viruses were prepared in the same manner using the safe-targeting sgRNA sequence GGGCTACTAGGATTCAATCT . The medQ96G04) including all FAM86A mutants, FAM86B1 (Uniprot ID: Q8N7N1), FAM86B2 (Uniprot ID: P0C5J1). For bacterial protein expression and purification, FAM86A and its mutants were cloned into pGEX-6P-1 (Addgene). For protein expression and purification from human cells, EEF2 (Uniprot ID: P13639) and its mutants were cloned into pcDNA3.1(+) (Addgene) including the N-terminal FLAG sequence DYKDDDDK.In addition to plasmids listed for virus production, the following plasmids were cloned and used throughout the study. For transient transfection, the following genes were cloned into pQCXIH-CMV/TO-DEST (Addgene): FAM86A . Dot blot analysis was performed by directly loading peptides of the indicated concentrations onto a Nitrocellulose membrane. A volume of 1 μl was loaded for immunoblots and 5 μl was loaded for Ponceau S staining (Sigma). The following antibodies were used at the indicated dilutions: EEF2-K525me3 (1:1000) , EEF2  , FAM86A (1:500) (Genemed), tubulin (1:4000) , FLAG M2 (1:4000) . Mouse and rabbit secondary antibodies from Jackson Immunoresearch were used at 1:10,000 dilution. Protein bands were visualized using Amersham ECL or Amersham ECL Prime Western Blotting Detection Reagent.in vitro methylation or resuspended in Laemmli buffer for Western blot analysis.Plasmids encoding FLAG-fusion proteins were transfected into 293T cells selected for CRISPR-mediated FAM86A depletion. Whole cell extracts were prepared in lysis buffer containing 50 mM Tris-HCl (pH 7.5), 250 mM NaCl, 0.5% Nonidet P-40, 10% glycerol, and complete protease inhibitor cocktail 48 h after transfection. Equal amounts of whole cell extracts were incubated with equal volumes of anti-FLAG M2 magnetic beads slurry (Sigma) at 4 °C overnight and either eluted with 0.2 mg/ml 3× FLAG peptide (Sigma) for A600) reached 1.0. Protein expression was then induced by addition of 0.13 mM isopropyl β-D-1-thiogalactopyranoside (IPTG), and the cells continued to grow at 16  °C overnight. The cells were harvested and lysed in a buffer containing 50 mM Tris-HCl (pH 8.0), 1 M NaCl, 25 mM Imidazole, 10% glycerol, and 1 mM PMSF. After centrifugation, the fusion protein in the soluble fraction was purified through a nickel column, followed by removal of His6-MBP tag by TEV cleavage, ion-exchange chromatography on a Q HP column , and size-exclusion chromatography on a HiLoad 16/600 Superdex 75 pg column . The purified protein samples were concentrated in 20 mM Tris-HCl (pH 7.5), 100 mM NaCl, 5% glycerol, and 5 mM DTT and stored at −80 °C.For crystallography, the DNA encoding full-length human FAM86A was inserted into an in-house bacterial expression vector, in which the FAM86 gene is preceded by an N-terminal hexa-histidine (His6)-MBP tag and a TEV cleavage site. To overcome the challenge of crystallization, three mutations  were introduced to reduce surface entropy. The expression plasmid was transformed into BL21(DE3) RIL cells. The transformed cells were grown at 37 °C until cell density . Protein expression was induced by 0.1 mM IPTG  in overnight culture at 18 °C. Proteins were purified using Glutathione Sepharose 4B  and eluted in 10 mM reduced glutathione (Sigma). Protein concentrations were measured using Pierce Coomassie Plus Assay, and DTT was added to a concentration of 5 mM.Plasmids encoding GST-fusion proteins were transformed into BL21 The peptide spanning EEF2-Lys525 (VEGL(Kme3)RLAK) was synthesized and purified by high-performance liquid chromatography (>95% purity). Peptides were conjugated to KLH and used as antigen to immunize rabbits. Rabbit protocols, peptide conjugation, immunization, and antiserum production were performed by Abclonal Technology. Antiserum was negatively selected against an identical, unmodified peptide (VEGLKRLAK). Final purification was performed with the immobilized antigenic peptide to select for methyl-specific antibodies. Peptides carrying Kme1 and Kme2 were also synthesized for antibody validation.The first 126 amino acids of FAM86A were cloned into pGEX-6P-1 and purified as a GST-fusion protein. GST-FAM86A(1–126) protein was then used as an antigen to immunize rabbits for polyclonal antibody production at Genemed Biotechnology, Inc. Antiserum was enriched for specific FAM86A antibodies using NHS-activated High Performance columns (Sigma) following manufacturer’s instructions. Briefly, GST-FAM86A(1–126) was immobilized in coupling buffer containing 200 mM NaHCO3 (pH 8.3) and 500 mM NaCl. Antiserum was diluted 10-fold in dilution buffer containing 10 mM Tris-HCl (pH7.5) and injected over the column. Specific antibodies were collected in elution buffer containing 100 mM Glycine (pH 2.5).https://alphafold.ebi.ac.uk) or AlphaFill  as indicated. Combinatorial FAM86A–EEF2 structures were determined by querying the FAM86A and EEF2 primary protein sequences (Uniprot) in ColabFold (https://colab.research.google.com) in 1:1 stoichiometry with default parameters. Rank 1 structures were visualized and analyzed with PyMOL after all ranked structures were examined for overall similarity.Individual structures were downloaded either from AlphaFold , 10% w/v Polyethylene glycol 3350, and 5 mM TCEP using the hanging-drop vapor diffusion method at 12 °C. The crystals appeared overnight and continued to grow for 1 week. The crystals were soaked in the crystallization buffer supplemented with 25% (v/v) glycerol before being flash frozen in liquid nitrogen. X-ray diffraction data were collected on the beamline 24-ID-C at Advanced Photo Source, Argonne National Lab. The datasets were processed with the HKL3000 program . The strhttps://www.ebi.ac.uk/interpro/) for domain structure analysis or protein BLAST (https://blast.ncbi.nlm.nih.gov/Blast.cgi) for alignments.Protein sequences were retrieved under the indicated UniProt IDs and queried using InterPro (In vitro methylation assays were performed as described (S-adenosyl-methionine (New England Biolabs) or 2 mCi of tritiated AdoMet . The reaction mixtures were incubated overnight at 30 °C. Reactions were resolved by SDS-PAGE and either stained with Coomassie or transferred to a PVDF membrane (0.45 μm) for autoradiography.escribed  by combihttps://depmap.org/portal/download/all/) and visualized using R.Gene effect data  were downloaded directly (8FZB). DepMap, AlphaFold, and AlphaFill data are publicly available online for direct download.All data supporting the findings of this study are available within the paper and supporting information or otherwise publicly available for download. The crystal structure of FAM86A–SAH has been submitted to the Protein Data Bank (ID: This article contains O. G. is a co-scientific founder, consultant, and stockholder of EpiCypher, Inc, K36 Therapeutics, Inc, and Alternative Bio, Inc.