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An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of evolution with equal probability in absence of feedback signals, and complex functional structure emerges from quantitative accumulation of adaptive-symmetries breaking in response to feedback signals. One finding is that when a DNN is hierarchically large, sufficient adaptive-symmetries exist to enable convergence to global minima in DNN optimization., 4 pages, 2 figures; the article version can be found at https://doi.org/10.5281/zenodo.5814820.

Background: The scientific understanding of complex systems and deep neural networks (DNNs) are among the unsolved important problems of science; and DNNs are evidently complex systems. Meanwhile, conservative symmetry arguably is the most important concept of physics, and P.W. Anderson, Nobel Laureate in physics, speculated that increasingly sophisticated broken symmetry in many-body systems correlates with increasing complexity and functional specialization. Furthermore, in complex systems such as DNA molecules, different nucleotide sequences consist of different weak bonds with similar free energy; and energy fluctuations would break the symmetries that conserve the free energy of the nucleotide sequences, which selected by the environment would lead to organisms with different phenotypes. Purpose: When the molecule is very large, we might speculate that statistically the system poses in a state that would be of equal probability to transit to a large number of adjacent possible states; that is, an adaptive symmetry whose breaking is selected by the feedback signals from the environment. In physics, quantitative changes would accumulate into qualitative revolution where previous paradoxical behaviors are reconciled under a new paradigm of higher dimensionality (e.g., wave-particle duality in quantum physics). This emergence of adaptive symmetry and complexity might be speculated as accumulation of sophistication and quantity of conservative symmetries that lead to a paradigm shift, which might clarify the behaviors of DNNs. Results: In this work, theoretically and experimentally, we characterize the optimization process of a DNN system as an extended symmetry-breaking process where novel examples are informational perturbations to the system that breaks adaptive symmetries. One particular finding is that a hierarchically large DNN would have a large reservoir of adaptive symmetries, and when the information capacity of the reservoir exceeds the complexity of the dataset, the system could absorb all perturbations of the examples and self-organize into a functional structure of zero training errors measured by a certain surrogate risk. In this diachronically extended process, complexity emerges from quantitative accumulation of adaptive-symmetries breaking. Method: More specifically, this process is characterized by a statistical-mechanical model that could be appreciated as a generalization of statistics physics to the DNN organized complex system, and characterizes regularities in higher dimensionality. The model consists of three constitutes that could be appreciated as the counterparts of Boltzmann distribution, Ising model, and conservative symmetry, respectively: (1) a stochastic definition/interpretation of DNNs that is a multilayer probabilistic graphical model, (2) a formalism of circuits that perform biological computation, (3) a circuit symmetry from which self-similarity between the microscopic and the macroscopic adaptability manifests. The model is analyzed with a method referred as the statistical assembly method that analyzes the coarse-grained behaviors (over a symmetry group) of the heterogeneous hierarchical many-body interaction in DNNs. Conclusion: Overall, this characterization suggests a physical-biological-complex scientific understanding to the optimization power of DNNs., 25 pages, 8 figures; A letter version can be find at https://doi.org/10.5281/zenodo.5814935; update references to letter version in v2.

A large number of post-translational modifications (PTMs) in proteins are buried in the unassigned mass spectrometric (MS) spectra in shot-gun proteomics datasets. Because the modified peptide fragments are low in abundance relative to the corresponding non-modified versions, it is critical to develop tools that allow facile evaluation of assignment of PTMs based on the MS/MS spectra. Such tools would preferably have the ability to allow comparison of fragment ion spectra and retention time between the modified and unmodified peptide pairs or group. Herein, we describe MMS2plot, an R package for visualizing peptide-spectrum matches (PSMs) for multiple peptides. MMS2plot features a batch mode and generates the output images in vector graphics file format that facilitate evaluation and publication of the PSM assignment. We expect MMS2plot to play an important role in PTM discovery from large-scale proteomics datasets generated by LC (liquid chromatography)-MS/MS. The MMS2plot package is freely available at https://github.com/lileir/MMS2plot under the GPL-3 license.

The Src Homology-3 (SH3) domains are ubiquitous protein modules that mediate important intracellular protein interactions via binding to short proline-rich consensus motifs in their target proteins. The affinity and specificity of such core SH3 - ligand contacts are typically modest, but additional binding interfaces can give rise to stronger and more specific SH3-mediated interactions. To understand how commonly such robust SH3 interactions occur in the human protein interactome, and to identify these in an unbiased manner we have expressed 324 predicted human SH3 ligands as full-length proteins in mammalian cells, and screened for their preferred SH3 partners using a phage display-based approach. This discovery platform contains an essentially complete repertoire of the ∼300 human SH3 domains, and involves an inherent binding threshold that ensures selective identification of only SH3 interactions with relatively high affinity. Such strong and selective SH3 partners could be identified for only 19 of these 324 predicted ligand proteins, suggesting that the majority of human SH3 interactions are relatively weak, and thereby have capacity for only modest inherent selectivity. The panel of exceptionally robust SH3 interactions identified here provides a rich source of leads and hypotheses for further studies. However, a truly comprehensive characterization of the human SH3 interactome will require novel high-throughput methods based on function instead of absolute binding affinity.

Figure S2. (Arg)9-GST SH2 TrM could effectively capture diverse pY proteins in A375 and A375/DDP cells. Levels of pY proteins from A375(a) and A375/DDP(b) cells stimulated with or without EGF (100 ng/ml) were assessed with Anti-pY antibody. The whole cell lysates were incubated with (Arg)9-GST, (Arg)9-GST SH2 Wt or (Arg)9-GST SH2 TrM for 12 h at 4 °C and purified by an appropriate amount of glutathione agarose. Data shown are representative of three independent experiments. (PPTX 107 kb)

Figure S7. The toxicity effect of (Arg)9-GST SH2 TrM on PBMCs. (Arg)9-GST-SH2 TrM protein resulted in some toxicity effect on PBMCs according to the CCK-8 data, but the effect was moderate as (Arg)9-GST-SH2 TrM protein only specifically recognizing and binding to pY residue, which is low abundance in PBMCs. Cells were treated with different GST-fused proteins at different concentrations (a) (0.5, 1, 2, 4 and 8 μM) for various time (b) (1,2,4 and 8 h) and cell viability was measured by CCK-8 assay (n = 3, *P

Figure S1. Construction, expression and purification of GST fusion proteins. (a) DNA gel electrophoresis image showing the molecular weights of the DNA fragment of SH2 TrM and pGEX-4Â T3-(Arg)9-SH2 TrM plasmid. (b) SDS-PAGE Coomassie blue-staining image displaying the expression and purification of (Arg)9-GST, (Arg)9-GST SH2 Wt and (Arg)9-GST SH2 TrM in E.coli. Data shown are representative of three independent experiments. (PPTX 163 kb)

Table S1. The amino acid sequences of constructs (N-C). (PDF 323 kb)

Figure S6. The penetration and toxicity effects of (Arg)9-GST SH2 TrM on PBMCs. (a) The level of pY proteins was very low in PBMCs compared with B16F10 cells. (b) (Arg)9-GST-SH2 TrM protein could enter into PBMCs, but could not efficiently be enriched by pY proteins in these non-cancerous cells, thus the green signal was observed to be weak. All images shown are representative of at least three independent experiments. (PPTX 329 kb)

Figure S4. (Arg)9-GST SH2 TrM inhibited the proliferation of A375/DDP cells. Effects of GST, GST SH2 Wt, GST SH2 TrM, (Arg)9-GST, (Arg)9-GST SH2 Wt and (Arg)9-GST SH2 TrM on the proliferation of A375/DDP cells. Cells were treated with different GST-fused proteins at different concentrations (a) (0.5, 1, 2, 4 and 8 μM) for various time (b) (1,2,4 and 8 h) and cell viability was measured by MTT assay (n = 3, *P

Table S2. Sequence of primers. (PDF 69 kb)

Figure S3. (Arg)9-GST SH2 TrM inhibited the proliferation of A375 cells. Effects of GST, GST SH2 Wt, GST SH2 TrM, (Arg)9-GST, (Arg)9-GST SH2 Wt and (Arg)9-GST SH2 TrM on the proliferation of A375 cells. Cells were treated with different GST-fused proteins at different concentrations (a) (0.5,1, 2, 4 and 8 μM) for various time (b) (1,2,4 and 8 h) and cell viability was measured by MTT assay (n = 3, *P

The human proteome contains a plethora of short linear motifs (SLiMs) that serve as binding interfaces for modular protein domains. Such interactions are crucial for signaling and other cellular processes, but are difficult to detect because of their low to moderate affinities. Here we developed a dedicated approach, proteomic peptide-phage display (ProP-PD), to identify domain-SLiM interactions. Specifically, we generated phage libraries containing all human and viral C-terminal peptides using custom oligonucleotide microarrays. With these libraries we screened the nine PSD-95/ Dlg/ZO-1 (PDZ) domains of human Densin-180, Erbin, Scribble, and Disks large homolog 1 for peptide ligands. We identified several known and putative interactions potentially relevant to cellular signaling pathways and confirmed interactions between fulllength Scribble and the target proteins β-PIX, plakophilin-4, and guanylate cyclase soluble subunit a-2 using colocalization and coimmunoprecipitation experiments. The affinities of recombinant Scribble PDZ domains and the synthetic peptides representing the C termini of these proteins were in the 1- to 40-μM range. Furthermore, we identified several well-established host-virus protein- protein interactions, and confirmed that PDZ domains of Scribble interact with the C terminus of Tax-1 of human T-cell leukemia virus with micromolar affinity. Previously unknown putative viral protein ligands for the PDZ domains of Scribble and Erbin were also identified. Thus, we demonstrate that our ProP-PD libraries are useful tools for probing PDZ domain interactions. The method can be extended to interrogate all potential eukaryotic, bacterial, and viral SLiMs and we suggest it will be a highly valuable approach for studying cellular and pathogen-host protein-protein interactions.

A distinct feature of hepatocellular carcinoma (HCC) is the tendency of tumor cells to disperse throughout the liver. Nck family adaptor proteins function to couple tyrosine phosphorylation signals to regulate actin cytoskeletal reorganization that leads to cell motility. In order to explore the role of Nck in HCC development, we performed GST pull-down assay using the SH2 domain of Nck1 as bait. The resulting precipitates were separated by 2-DE. Mass spectrometry analysis revealed a group of Nck1 SH2 domain-binding proteins that were differentially expressed in HCC. One of these proteins, dermcidin (DCD), and its interaction with Nck1, was further validated in vitro. GST pull-down assay revealed that Nck1 SH2 domain binds to the phosphotyrosine residue at position 20 (Y20) of the DCD. Pervandate treatment significantly enhanced the interaction between DCD and Nck1. Moreover, we demonstrated that forced expression of DCD could activate Rac1 and Cdc42 and promoted cell migration. Taken together, these data suggest a role of DCD in tumor metastasis. © 2011 Elsevier B.V.

Epithelial to mesenchymal transition (EMT) is a critical event in embryogenesis and plays a fundamental role in cancer progression and metastasis1. Numb has been shown to play an important role in the proper functions of Par protein complex and in cell-cell junctions, both of which are associated with EMT. However, the role of Numb in EMT has not been fully elucidated. Recently, we showed that Numb is capable of binding to both Par3 and E-cadherin. Intriguingly, the interaction of Numb with E-cadherin or the Par protein complex is dynamically regulated by tyrosine phosphorylation induced by HGF or Src. Knockdown of Numb by shRNA in MDCK cells led to an lateral to apical translocation of E-cadherin and β-catenin, active F-actin polymerization, mis-localization of Par3 and aPKC, a decrease in cell-cell adhesion, and an increase in cell migration and proliferation. These data suggest a diverse role for Numb in regulating cell-cell adhesion, polarity and migration during EMT.