Structured States of Disordered Proteins from Genomic Sequences.

Protein flexibility ranges from simple hinge movements to functional disorder. Around half of all human proteins contain apparently disordered regions with little 3D or functional information, and many of these proteins are associated with disease. Building on the evolutionary couplings approach previously successful in predicting 3D states of ordered proteins and RNA, we developed a method to predict the potential for ordered states for all apparently disordered proteins with sufficiently rich evolutionary information. The approach is highly accurate (79%) for residue interactions as tested in more than 60 known disordered regions captured in a bound or specific condition. Assessing the potential for structure of more than 1,000 apparently disordered regions of human proteins reveals a continuum of structural order with at least 50% with clear propensity for three- or two-dimensional states. Co-evolutionary constraints reveal hitherto unseen structures of functional importance in apparently disordered proteins.

Functional Atlas of Primary miRNA Maturation by the Microprocessor.

Primary microRNAs (miRNAs) are the precursors of miRNAs that modulate the expression of most mRNAs in humans. They fold up into a hairpin structure that is cleaved at its base by an enzyme complex known as the Microprocessor (Drosha/DGCR8). While many of the molecular details are known, a complete understanding of what features distinguish primary miRNA from hairpin structures in other transcripts is still lacking. We develop a massively parallel functional assay termed Dro-seq (Drosha sequencing) that enables testing of hundreds of known primary miRNA substrates and thousands of single-nucleotide variants. We find an additional feature of primary miRNAs, called Shannon entropy, describing the structural ensemble important for processing. In a deep mutagenesis experiment, we observe particular apical loop U bases, likely recognized by DGCR8, are important for efficient processing. These findings build on existing knowledge about primary miRNA maturation by the Microprocessor and further explore the substrate RNA sequence-structure relationship.

Branching topology of the human embryo transcriptome revealed by Entropy Sort Feature Weighting.

Analysis of single cell transcriptomics (scRNA-seq) data is typically performed after subsetting to highly variable genes (HVGs). Here, we show that Entropy Sorting provides an alternative mathematical framework for feature selection. On synthetic datasets, continuous Entropy Sort Feature Weighting (cESFW) outperforms HVG selection in distinguishing cell-state-specific genes. We apply cESFW to six merged scRNA-seq datasets spanning human early embryo development. Without smoothing or augmenting the raw counts matrices, cESFW generates a high-resolution embedding displaying coherent developmental progression from eight-cell to post-implantation stages and delineating 15 distinct cell states. The embedding highlights sequential lineage decisions during blastocyst development, while unsupervised clustering identifies branch point populations obscured in previous analyses. The first branching region, where morula cells become specified for inner cell mass or trophectoderm, includes cells previously asserted to lack a developmental trajectory. We quantify the relatedness of different pluripotent stem cell cultures to distinct embryo cell types and identify marker genes of naïve and primed pluripotency. Finally, by revealing genes with dynamic lineage-specific expression, we provide markers for staging progression from morula to blastocyst.

Quantifying chemical short-range order in metallic alloys.

Metallic alloys often form phases-known as solid solutions-in which chemical elements are spread out on the same crystal lattice in an almost random manner. The tendency of certain chemical motifs to be more common than others is known as chemical short-range order (SRO), and it has received substantial consideration in alloys with multiple chemical elements present in large concentrations due to their extreme configurational complexity (e.g., high-entropy alloys). SRO renders solid solutions "slightly less random than completely random," which is a physically intuitive picture, but not easily quantifiable due to the sheer number of possible chemical motifs and their subtle spatial distribution on the lattice. Here, we present a multiscale method to predict and quantify the SRO state of an alloy with atomic resolution, incorporating machine learning techniques to bridge the gap between electronic-structure calculations and the characteristic length scale of SRO. The result is an approach capable of predicting SRO length scale in agreement with experimental measurements while comprehensively correlating SRO with fundamental quantities such as local lattice distortions. This work advances the quantitative understanding of solid-solution phases, paving the way for the rigorous incorporation of SRO length scales into predictive mechanical and thermodynamic models.

Causal connectivity measures for pulse-output network reconstruction: Analysis and applications.

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

Indications of flat bands driving the δ to α volume collapse of plutonium.

On cooling from the melt, plutonium (Pu) undergoes a series of structural transformations accompanied by a ≈ 28% reduction in volume from its δ phase to its α phase at low temperatures. While Pu's partially filled 5f-electron shells are known to be involved, their precise role in the transformations has remained unclear. By using calorimetry measurements on α-Pu and gallium-stabilized δ-Pu combined with resonant ultrasound and X-ray scattering data to account for the anomalously large softening of the lattice with temperature, we show here that the difference in electronic entropy between the α and δ phases dominates over the difference in phonon entropy. Rather than finding an electronic specific heat characteristic of broad f-electron bands in α-Pu, as might be expected to occur within a Kondo collapsed phase in analogy with cerium, we find it to be indicative of flatter subbands. An important role played by Pu's 5f electrons in the formation of its larger unit cell α phase comprising inequivalent lattice sites and varying bond lengths is therefore suggested.

Milestoning estimators of dissipation in systems observed at a coarse resolution.

Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.

Maximum entropy determination of mammalian proteome dynamics.

Full understanding of proteostasis and energy utilization in cells will require knowledge of the fraction of cell proteins being degraded with different half-lives and their rates of synthesis. We therefore developed a method to determine such information that combines mathematical analysis of protein degradation kinetics obtained in pulse-chase experiments with Bayesian data fitting using the maximum entropy principle. This approach will enable rapid analyses of whole-cell protein dynamics in different cell types, physiological states, and neurodegenerative disease. Using it, we obtained surprising insights about protein stabilities in cultured cells normally and upon activation of proteolysis by mTOR inhibition and increasing cAMP or cGMP. It revealed that >90% of protein content in dividing mammalian cell lines is long-lived, with half-lives of 24 to 200 h, and therefore comprises much of the proteins in daughter cells. The well-studied short-lived proteins (half-lives < 10 h) together comprise <2% of cell protein mass, but surprisingly account for 10 to 20% of measurable newly synthesized protein mass. Evolution thus appears to have minimized intracellular proteolysis except to rapidly eliminate misfolded and regulatory proteins.

Intrinsic tensile ductility in strain hardening multiprincipal element metallic glass.

Traditional metallic glasses (MGs), based on one or two principal elements, are notoriously known for their lack of tensile ductility at room temperature. Here, we developed a multiprincipal element MG (MPEMG), which exhibits a gigapascal yield strength, significant strain hardening that almost doubles its yield strength, and 2% uniform tensile ductility at room temperature. These remarkable properties stem from the heterogeneous amorphous structure of our MPEMG, which is composed of atoms with significant size mismatch but similar atomic fractions. In sharp contrast to traditional MGs, shear banding in our glass triggers local elemental segregation and subsequent ordering, which transforms shear softening to hardening, hence resulting in shear-band self-halting and extensive plastic flows. Our findings reveal a promising pathway to design stronger, more ductile glasses that can be applied in a wide range of technological fields.

High-entropy engineering with regulated defect structure and electron interaction tuning active sites for trifunctional electrocatalysis.

High-entropy alloy nanoparticles (HEANs) possessing regulated defect structure and electron interaction exhibit a guideline for constructing multifunctional catalysts. However, the microstructure-activity relationship between active sites of HEANs for multifunctional electrocatalysts is rarely reported. In this work, HEANs distributed on multi-walled carbon nanotubes (HEAN/CNT) are prepared by Joule heating as an example to explain the mechanism of trifunctional electrocatalysis for oxygen reduction, oxygen evolution, and hydrogen evolution reaction. HEAN/CNT excels with unmatched stability, maintaining a 0.8V voltage window for 220 h in zinc-air batteries. Even after 20 h of water electrolysis, its performance remains undiminished, highlighting exceptional endurance and reliability. Moreover, the intrinsic characteristics of the defect structure and electron interaction for HEAN/CNT are investigated in detail. The electrocatalytic mechanism of trifunctional electrocatalysis of HEAN/CNT under different conditions is identified by in situ monitoring and theoretical calculation. Meanwhile, the electron interaction and adaptive regulation of active sites in the trifunctional electrocatalysis of HEANs were further verified by density functional theory. These findings could provide unique ideas for designing inexpensive multifunctional high-entropy electrocatalysts.

Structural and physical basis for the elasticity of elastin.

Elastin function is to endow vertebrate tissues with elasticity so that they can adapt to local mechanical constraints. The hydrophobicity and insolubility of the mature elastin polymer have hampered studies of its molecular organisation and structure-elasticity relationships. Nevertheless, a growing number of studies from a broad range of disciplines have provided invaluable insights, and several structural models of elastin have been proposed. However, many questions remain regarding how the primary sequence of elastin (and the soluble precursor tropoelastin) governs the molecular structure, its organisation into a polymeric network, and the mechanical properties of the resulting material. The elasticity of elastin is known to be largely entropic in origin, a property that is understood to arise from both its disordered molecular structure and its hydrophobic character. Despite a high degree of hydrophobicity, elastin does not form compact, water-excluding domains and remains highly disordered. However, elastin contains both stable and labile secondary structure elements. Current models of elastin structure and function are drawn from data collected on tropoelastin and on elastin-like peptides (ELPs) but at the tissue level, elasticity is only achieved after polymerisation of the mature elastin. In tissues, the reticulation of tropoelastin chains in water defines the polymer elastin that bears elasticity. Similarly, ELPs require polymerisation to become elastic. There is considerable interest in elastin especially in the biomaterials and cosmetic fields where ELPs are widely used. This review aims to provide an up-to-date survey of/perspective on current knowledge about the interplay between elastin structure, solvation, and entropic elasticity.

Multiscale chromatin dynamics and high entropy in plant iPSC ancestors.

Plant protoplasts provide starting material for of inducing pluripotent cell masses that are competent for tissue regeneration in vitro, analogous to animal induced pluripotent stem cells (iPSCs). Dedifferentiation is associated with large-scale chromatin reorganisation and massive transcriptome reprogramming, characterised by stochastic gene expression. How this cellular variability reflects on chromatin organisation in individual cells and what factors influence chromatin transitions during culturing are largely unknown. Here, we used high-throughput imaging and a custom supervised image analysis protocol extracting over 100 chromatin features of cultured protoplasts. The analysis revealed rapid, multiscale dynamics of chromatin patterns with a trajectory that strongly depended on nutrient availability. Decreased abundance in H1 (linker histones) is hallmark of chromatin transitions. We measured a high heterogeneity of chromatin patterns indicating intrinsic entropy as a hallmark of the initial cultures. We further measured an entropy decline over time, and an antagonistic influence by external and intrinsic factors, such as phytohormones and epigenetic modifiers, respectively. Collectively, our study benchmarks an approach to understand the variability and evolution of chromatin patterns underlying plant cell reprogramming in vitro.

Evidence implicating sequential commitment of the founder lineages in the human blastocyst by order of hypoblast gene activation.

Successful human pregnancy depends upon rapid establishment of three founder lineages: the trophectoderm, epiblast and hypoblast, which together form the blastocyst. Each plays an essential role in preparing the embryo for implantation and subsequent development. Several models have been proposed to define the lineage segregation. One suggests that all lineages specify simultaneously; another favours the differentiation of the trophectoderm before separation of the epiblast and hypoblast, either via differentiation of the hypoblast from the established epiblast, or production of both tissues from the inner cell mass precursor. To begin to resolve this discrepancy and thereby understand the sequential process for production of viable human embryos, we investigated the expression order of genes associated with emergence of hypoblast. Based upon published data and immunofluorescence analysis for candidate genes, we present a basic blueprint for human hypoblast differentiation, lending support to the proposed model of sequential segregation of the founder lineages of the human blastocyst. The first characterised marker, specific initially to the early inner cell mass, and subsequently identifying presumptive hypoblast, is PDGFRA, followed by SOX17, FOXA2 and GATA4 in sequence as the hypoblast becomes committed.

Ion entropy and accurate entropy-based FDR estimation in metabolomics.

Accurate metabolite annotation and false discovery rate (FDR) control remain challenging in large-scale metabolomics. Recent progress leveraging proteomics experiences and interdisciplinary inspirations has provided valuable insights. While target-decoy strategies have been introduced, generating reliable decoy libraries is difficult due to metabolite complexity. Moreover, continuous bioinformatics innovation is imperative to improve the utilization of expanding spectral resources while reducing false annotations. Here, we introduce the concept of ion entropy for metabolomics and propose two entropy-based decoy generation approaches. Assessment of public databases validates ion entropy as an effective metric to quantify ion information in massive metabolomics datasets. Our entropy-based decoy strategies outperform current representative methods in metabolomics and achieve superior FDR estimation accuracy. Analysis of 46 public datasets provides instructive recommendations for practical application.

Detecting tipping points of complex diseases by network information entropy.

The progression of complex diseases often involves abrupt and non-linear changes characterized by sudden shifts that trigger critical transformations. Identifying these critical states or tipping points is crucial for understanding disease progression and developing effective interventions. To address this challenge, we have developed a model-free method named Network Information Entropy of Edges (NIEE). Leveraging dynamic network biomarkers, sample-specific networks, and information entropy theories, NIEE can detect critical states or tipping points in diverse data types, including bulk, single-sample expression data. By applying NIEE to real disease datasets, we successfully identified critical predisease stages and tipping points before disease onset. Our findings underscore NIEE's potential to enhance comprehension of complex disease development.

A step toward precision gerontology: Lifespan effects of calorie and protein restriction are consistent with predicted impacts on entropy generation.

Understanding aging is a key biological goal. Precision gerontology aims to predict how long individuals will live under different treatment scenarios. Calorie and protein restriction (CR and PR) extend lifespan in many species. Using data from C57BL/6 male mice under graded CR or PR, we introduce a computational thermodynamic model for entropy generation, which predicted the impact of the manipulations on lifespan. Daily entropy generation decreased significantly with increasing CR level, but not PR. Our predictions indicated the lifespan of CR mice should increase by 13 to 56% with 10 to 40% CR, relative to ad libitum-fed animals. This prediction was broadly consistent with the empirical observation of the lifespan impacts of CR in rodents. Modeling entropy fluxes may be a future strategy to identify antiaging interventions.

On cheap entropy-sparsified regression learning.

Regression learning is one of the long-standing problems in statistics, machine learning, and deep learning (DL). We show that writing this problem as a probabilistic expectation over (unknown) feature probabilities - thus increasing the number of unknown parameters and seemingly making the problem more complex-actually leads to its simplification, and allows incorporating the physical principle of entropy maximization. It helps decompose a very general setting of this learning problem (including discretization, feature selection, and learning multiple piece-wise linear regressions) into an iterative sequence of simple substeps, which are either analytically solvable or cheaply computable through an efficient second-order numerical solver with a sublinear cost scaling. This leads to the computationally cheap and robust non-DL second-order Sparse Probabilistic Approximation for Regression Task Analysis (SPARTAn) algorithm, that can be efficiently applied to problems with millions of feature dimensions on a commodity laptop, when the state-of-the-art learning tools would require supercomputers. SPARTAn is compared to a range of commonly used regression learning tools on synthetic problems and on the prediction of the El Niño Southern Oscillation, the dominant interannual mode of tropical climate variability. The obtained SPARTAn learners provide more predictive, sparse, and physically explainable data descriptions, clearly discerning the important role of ocean temperature variability at the thermocline in the equatorial Pacific. SPARTAn provides an easily interpretable description of the timescales by which these thermocline temperature features evolve and eventually express at the surface, thereby enabling enhanced predictability of the key drivers of the interannual climate.

Entropy-based early detection of critical transitions in spatial vegetation fields.

In semiarid regions, vegetated ecosystems can display abrupt and unexpected changes, i.e., transitions to different states, due to drifting or time-varying parameters, with severe consequences for the ecosystem and the communities depending on it. Despite intensive research, the early identification of an approaching critical point from observations is still an open challenge. Many data analysis techniques have been proposed, but their performance depends on the system and on the characteristics of the observed data (the resolution, the level of noise, the existence of unobserved variables, etc.). Here, we propose an entropy-based approach to identify an upcoming transition in spatiotemporal data. We apply this approach to observational vegetation data and simulations from two models of vegetation dynamics to infer the arrival of an abrupt shift to an arid state. We show that the permutation entropy (PE) computed from the probabilities of two-dimensional ordinal patterns may provide an early warning indicator of an approaching tipping point, as it may display a maximum (or minimum) before decreasing (or increasing) as the transition approaches. Like other spatial early warning indicators, the spatial permutation entropy does not need a time series of the system dynamics, and it is suited for spatially extended systems evolving on long time scales, like vegetation plots. We quantify its performance and show that, depending on the system and data, the performance can be better, similar or worse than the spatial correlation. Hence, we propose the spatial PE as an additional indicator to try to anticipate regime shifts in vegetated ecosystems.

Quantum entropy and central limit theorem.

We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to the von Neumann entropy, demonstrating a "maximal entropy principle in DV systems." We obtain a series of inequalities for quantum entropies and for Fisher information based on convolution, giving a "second law of thermodynamics for quantum convolutions." We show that the convolution of two stabilizer states is a stabilizer state. We establish a central limit theorem, based on iterating the convolution of a zero-mean quantum state, and show this converges to its MS. The rate of convergence is characterized by the "magic gap," which we define in terms of the support of the characteristic function of the state. We elaborate on two examples: the DV beam splitter and the DV amplifier.

Exceptional enhancement of mechanical properties in high-entropy alloys via thermodynamically guided local chemical ordering.

Understanding the local chemical ordering propensity in random solid solutions, and tailoring its strength, can guide the design and discovery of complex, paradigm-shifting multicomponent alloys. First, we present a simple thermodynamic framework, based solely on binary enthalpies of mixing, to select optimal alloying elements to control the nature and extent of chemical ordering in high-entropy alloys (HEAs). Next, we couple high-resolution electron microscopy, atom probe tomography, hybrid Monte-Carlo, special quasirandom structures, and density functional theory calculations to demonstrate how controlled additions of Al and Ti and subsequent annealing drive chemical ordering in nearly random equiatomic face-centered cubic CoFeNi solid solution. We establish that short-range ordered domains, the precursors of long-range ordered precipitates, inform mechanical properties. Specifically, a progressively increasing local order boosts the tensile yield strengths of the parent CoFeNi alloy by a factor of four while also substantially improving ductility, which breaks the so-called strength-ductility paradox. Finally, we validate the generality of our approach by predicting and demonstrating that controlled additions of Al, which has large negative enthalpies of mixing with the constituent elements of another nearly random body-centered cubic refractory NbTaTi HEA, also introduces chemical ordering and enhances mechanical properties.