Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial

Topological edge modes are excitations that are localized at the materials’ edges and yet are characterized by a topological invariant defined in the bulk. Such bulk–edge correspondence has enabled the creation of robust electronic, electromagnetic, and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter, and geophysical flows. Recently, the advent of non-Hermitian topological systems—wherein energy is not conserved—has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Hermitian systems have been introduced. However, whether such phases can be experimentally observed, and what their properties are, have remained open questions. Here, we identify and observe a form of bulk–edge correspondence for a particular non-Hermitian topological phase. We find that a change in the bulk non-Hermitian topological invariant leads to a change of topological edge-mode localization together with peculiar purely non-Hermitian properties. Using a quantum-to-classical analogy, we create a mechanical metamaterial with nonreciprocal interactions, in which we observe experimentally the predicted bulk–edge correspondence, demonstrating its robustness. Our results open avenues for the field of non-Hermitian topology and for manipulating waves in unprecedented fashions.

The inclusion of non-Hermitian features in topological insulators has recently seen an explosion of activity. Exciting developments include tunable wave guides that are robust to disorder (1–3), structure-free systems (4, 5), and topological lasers and pumping (6–10). In these systems, active components are introduced to typically 1) break time-reversal symmetry to create topological insulators with unidirectional edge modes (1–5) and 2) pump topologically protected edge modes, thus harnessing Hermitian topology in non-Hermitian settings (6–9, 11). In parallel, extensive theoretical efforts have generalized the concept of a topological insulator to truly non-Hermitian phases that cannot be realized in Hermitian materials (12–14). However, such non-Hermitian topology and its bulk–edge correspondence remain a matter of intense debate. On the one hand, it has been argued that the usual bulk–edge correspondence breaks down in non-Hermitian settings, while on the other hand, new topological invariants specific to non-Hermitian systems have been proposed to capture particular properties of their edge modes (15–20).Here, focusing on a non-Hermitian version of the Su–Schrieffer–Heeger (SSH) model (15–17, 21) with an odd number of sites (Fig. 1A), we find that a change in the bulk non-Hermitian topological invariant is accompanied by a localization change in the zero-energy edge modes. This finding suggests the existence of a bulk–edge correspondence for this type of truly non-Hermitian topology. We further construct a mechanical analogue of the non-Hermitian quantum model (Fig. 1B) and create a mechanical metamaterial (Fig. 1C) in which we observe the predicted correspondence between the non-Hermitian topological invariant and the topological edge mode. In particular, we report that the edge mode in the non-Hermitian topological phase has a peculiar nature, as it is localized on the rigid rather than the floppy side of the mechanical metamaterial.Open in a separate windowFig. 1.Quantum-to-classical mapping of a chain with non-Hermitian topology. (A) An SSH chain with two sublattices, A (in red) and B (in blue), augmented with nonreciprocal variations in the hopping amplitudes (indicated by ±ε). (B) The nonreciprocal classical analog of the augmented SSH chain, in which the classical masses (in red) correspond to the A sites in the quantum model, while the nonreciprocal springs (in blue) are analogous to the B sites. (C) Picture of the mechanical metamaterial realizing the nonreciprocal classical analogue of the augmented SSH model.     

Stable metal anodes enabled by a labile organic molecule bonded to a reduced graphene oxide aerogel

Metallic anodes (lithium, sodium, and zinc) are attractive for rechargeable battery technologies but are plagued by an unfavorable metal–electrolyte interface that leads to nonuniform metal deposition and an unstable solid–electrolyte interphase (SEI). Here we report the use of electrochemically labile molecules to regulate the electrochemical interface and guide even lithium deposition and a stable SEI. The molecule, benzenesulfonyl fluoride, was bonded to the surface of a reduced graphene oxide aerogel. During metal deposition, this labile molecule not only generates a metal-coordinating benzenesulfonate anion that guides homogeneous metal deposition but also contributes lithium fluoride to the SEI to improve Li surface passivation. Consequently, high-efficiency lithium deposition with a low nucleation overpotential was achieved at a high current density of 6.0 mA cm⁻². A Li|LiCoO₂ cell had a capacity retention of 85.3% after 400 cycles, and the cell also tolerated low-temperature (−10 °C) operation without additional capacity fading. This strategy was applied to sodium and zinc anodes as well.

Rechargeable batteries based on metal anodes including lithium (Li), sodium (Na), and zinc (Zn) show great promise in achieving high energy density (1–3). Unfortunately, the electrochemical interface of the metal anodes is not favorable for metal deposition. Metal nucleation is inhomogeneous at the surface, leading to the growth of metal dendrites (4–7) and the formation of an unstable solid–electrolyte interphase (SEI) that is incapable of protecting metals from the side reactions with the electrolyte (8–12).Substantial efforts have been devoted to stabilizing the interface of metal anodes, especially for Li metal. These include the design of artificial protective layers (13–17), alternative electrolytes (18–24), and sacrificial additives (25–30) to stabilize the metal–electrolyte interface, the development of mechanically robust coatings (31–34) to block Li dendrite growth, and the use of structured scaffolds to host dendrite-free Li deposition by reducing local current densities (35–43). However, the performance of metal anodes remains poor under high-current or low-temperature conditions. This is because the inhomogeneous Li nucleation and unstable SEI problems have not been well addressed, and these problems at the interface are even exacerbated under critical operating conditions, especially high-current densities and low temperatures (5, 6, 44).Toward this end, we report a simple molecular approach for regulating the electrochemical interface of metal anodes, which enables even Li deposition and stable SEI formation in a conventional electrolyte. This was realized by bonding a labile organic molecule, benzenesulfonyl fluoride (BSF), to a reduced graphene oxide (rGO) aerogel surface as the Li anode host (Fig. 1A). During Li deposition, BSF molecules electrochemically decompose at the interface and generate benzenesulfonate anions bonded to the rGO aerogel (Fig. 1B). The conjugated anions have a strong binding affinity for Li, serving as lithiophilic sites on the rGO surface to synergistically induce homogeneous Li nucleation of Li on the rGO surface. At the same time, BSF molecules contribute LiF to the SEI layer, which facilitates Li surface passivation (Fig. 1C). As a result, high-efficiency (99.2%) Li deposition was achieved at a Li deposition amount of 6.0 mAh cm⁻² and a current density of 6.0 mA cm⁻²; the barrier to Li nucleation was markedly reduced, as evidenced by the low nucleation overpotentials at high-current density (6.0 mA cm⁻²) or at a low temperature (−10 °C). A 400-cycle life with a capacity retention of 83.6% was achieved for a Li|LiCoO₂ (LCO) cell in a conventional carbonate electrolyte. Moreover, with the organic molecule-tuned interface, the Li|LCO cell can be stably cycled at a low operating temperature (−10 °C). This approach was applied to Na and Zn metal anodes as well.Open in a separate windowFig. 1.Illustration of a stable interface for Li deposition using a labile organic molecule, benzenesulfonyl fluoride (BSF). (A) Covalently bonded BSF on the rGO aerogel surface. (B) In situ generation of a lithiophilic conjugated anion (benzenesulfonate) and LiF on the surface during Li deposition. (C) Li nucleation preferentially occurs at the conjugated anion sites owing to the strong Li binding affinity, which leads to uniform Li deposition. In addition, the LiF that is formed is in the SEI layer and passivates the Li surface.     

Trapping a cross-linked lysine–tryptophan radical in the catalytic cycle of the radical SAM enzyme SuiB

The radical S-adenosylmethionine (rSAM) enzyme SuiB catalyzes the formation of an unusual carbon–carbon bond between the sidechains of lysine (Lys) and tryptophan (Trp) in the biosynthesis of a ribosomal peptide natural product. Prior work on SuiB has suggested that the Lys–Trp cross-link is formed via radical electrophilic aromatic substitution (rEAS), in which an auxiliary [4Fe-4S] cluster (AuxI), bound in the SPASM domain of SuiB, carries out an essential oxidation reaction during turnover. Despite the prevalence of auxiliary clusters in over 165,000 rSAM enzymes, direct evidence for their catalytic role has not been reported. Here, we have used electron paramagnetic resonance (EPR) spectroscopy to dissect the SuiB mechanism. Our studies reveal substrate-dependent redox potential tuning of the AuxI cluster, constraining it to the oxidized [4Fe-4S]²⁺ state, which is active in catalysis. We further report the trapping and characterization of an unprecedented cross-linked Lys–Trp radical (Lys–Trp•) in addition to the organometallic Ω intermediate, providing compelling support for the proposed rEAS mechanism. Finally, we observe oxidation of the Lys–Trp• intermediate by the redox-tuned [4Fe-4S]²⁺ AuxI cluster by EPR spectroscopy. Our findings provide direct evidence for a role of a SPASM domain auxiliary cluster and consolidate rEAS as a mechanistic paradigm for rSAM enzyme-catalyzed carbon–carbon bond-forming reactions.

The radical S-adenosylmethionine (rSAM) enzyme superfamily is the largest known in nature, with over 570,000 annotated and predominantly uncharacterized members spanning all domains of life (1–4). The uniting feature of rSAM enzymes is a [4Fe-4S] cluster, usually bound by a CX₃CX₂C motif that catalyzes reductive cleavage of SAM to form L-Met and a strongly oxidizing 5′-deoxyadenosyl radical (5′-dA•) (5–7). Recent studies on a suite of rSAM enzymes have revealed the presence of a previously unknown organometallic intermediate in this process, termed Ω, in which the 5′-C of 5′-dA• is bound to the unique iron of the [4Fe-4S] cluster (Fig. 1A) (8, 9). Homolysis of the Fe–C bond ultimately liberates 5′-dA•, which abstracts a hydrogen atom from substrate to initiate a profoundly diverse set of chemical reactions in both primary and secondary metabolism, including DNA, cofactor, vitamin, and antibiotic biosynthesis (5, 10–13).Open in a separate windowFig. 1.(A) Accepted scheme for radical initiation in rSAM enzymes. (B) X-ray crystal structure of SuiB (PDB ID: 5V1T). The RS domain, SPASM domain, and RiPP recognition element are rendered blue, green, and pink, respectively. [4Fe-4S] clusters are shown as spheres with the distances separating them indicated. (C) Lys–Trp cross-link formation (20) catalyzed by SuiB. The carbon–carbon bond installed by SuiB is shown in red. (D and E) Previously proposed EAS (D) and rEAS (E) mechanisms for SuiB-catalyzed Lys–Trp cross-link formation.Of the 570,000 rSAM enzyme superfamily members, over a quarter (∼165,000 genes from the Enzyme Function Initiative-Enzyme Similarity Tool) possess C-terminal extensions, called SPASM and twitch domains, which bind auxiliary Fe-S clusters (4, 14–19). The SPASM domain typically binds two auxiliary Fe-S clusters and is named after the rSAM enzymes involved in the synthesis of subtilosin, pyrroloquinoline quinone, anaerobic sulfatase, and mycofactocin. The twitch domain is a truncated SPASM domain and only binds one auxiliary cluster (15). Despite the wide prevalence of these domains and the characterization of several different SPASM/twitch rSAM enzymes by spectroscopic and structural studies, direct evidence for their catalytic function(s) has remained elusive.We previously performed functional and structural characterization on the SPASM rSAM enzyme SuiB (Fig. 1B), which is involved in the biosynthesis of a ribosomal peptide natural product in human and mammalian microbiome streptococci (14, 20–22). SuiB introduces an unusual carbon–carbon bond onto its substrate peptide, SuiA, between the sidechains of Lys2 and Trp6 (Fig. 1C). The mechanism for this transformation is of broader relevance, as a number of enzymes, such as RrrB, PqqE, and MqnC (2, 23, 24), are known to join unactivated aliphatic and aromatic carbons to generate sp³-sp² cross-links. A general mechanistic paradigm for this class of transformations is not yet available. For SuiB, two pathways have been proposed (20), one through a typical electrophilic aromatic substitution (EAS) mechanism, which is involved in other enzyme-catalyzed indole modifications, such as indole prenylation or flavin adenine dinucleotide (FAD)-enzyme-dependent indole chlorination (25–27). In this pathway, the 5′-dA• generates an alkyl radical, which upon a second one-electron oxidation, creates an α,β-unsaturated amide electrophile with which the indole sidechain reacts via Michael addition (Fig. 1D). Lanthionine cross-links observed in diverse lanthipeptides are built by this general scheme, though via heterolytic chemistry, with Cys acting as the nucleophile (28, 29). Alternatively, a radical electrophilic aromatic substitution (rEAS) reaction has been proposed, wherein the alkyl radical, formed by 5′-dA•, would react with the indole sidechain to generate a radical σ complex, a cross-linked Lys–Trp radical (Lys–Trp•), which upon oxidation and rearomatization would yield product (Fig. 1E). In both mechanisms, AuxI is proposed as an oxidant. Although this role for an rSAM auxiliary cluster has been previously suggested (30, 31), it has yet to be directly demonstrated experimentally. Mechanistic studies have favored the rEAS pathway (20); however, intermediates in the reaction of SuiB and enzymes that catalyze similar reactions have not yet been detected (15).In the current work, we sought to differentiate between the proposed mechanisms by trapping intermediates in the catalytic cycle of SuiB and characterizing them using electron paramagnetic resonance (EPR) spectroscopy. We report observation of three transient reaction intermediates, most importantly the sought-after Lys–Trp•, which is fundamentally different from previously characterized Trp radicals, as it is cross-linked and carries an indole tetrahedral center. We also provide evidence for AuxI as the oxidant of the Lys–Trp• intermediate as well as insights into redox potential changes of Fe-S clusters in SuiB that accompany SuiA binding. Together, our findings support the rEAS pathway for formation of the sp³-sp² cross-link and carry important implications for other enzymes that catalyze related transformations.     

A source for awareness-dependent figure–ground segregation in human prefrontal cortex

Figure–ground modulation, i.e., the enhancement of neuronal responses evoked by the figure relative to the background, has three complementary components: edge modulation (boundary detection), center modulation (region filling), and background modulation (background suppression). However, the neuronal mechanisms mediating these three modulations and how they depend on awareness remain unclear. For each modulation, we compared both the cueing effect produced in a Posner paradigm and fMRI blood oxygen-level dependent (BOLD) signal in primary visual cortex (V1) evoked by visible relative to invisible orientation-defined figures. We found that edge modulation was independent of awareness, whereas both center and background modulations were strongly modulated by awareness, with greater modulations in the visible than the invisible condition. Effective-connectivity analysis further showed that the awareness-dependent region-filling and background-suppression processes in V1 were not derived through intracortical interactions within V1, but rather by feedback from the frontal eye field (FEF) and dorsolateral prefrontal cortex (DLPFC), respectively. These results indicate a source for an awareness-dependent figure–ground segregation in human prefrontal cortex.

Figure–ground segregation is a fundamental process by which the visual system segments images into figures and background (1, 2). Previous neurophysiological and brain imaging studies of figure–ground segregation have shown neuronal responses are enhanced in the region perceived to be the figure and suppressed in the region perceived to be the background, an effect known as figure–ground modulation (1, 3–9). Figure–ground modulation plays a key role in identifying and localizing visual objects (7) and capturing focused attention (10). Remarkably, evidence from numerous neurophysiological (5, 11–16), psychophysical (17, 18), and brain imaging (19, 20) studies, as well as computational models (2, 17, 21) have suggested that figure–ground modulation relies on three complementary processes: boundary detection (i.e., edge modulation), region filling (i.e., center modulation), and background suppression (i.e., background modulation). During figure–ground segregation, boundary detection is the process that detects feature discontinuities that signal boundaries between the figures and background, while region filling is the process that groups figural regions with the same (or similar) features together (17), and the background suppression is the process that inhibits homogeneous features in the background (5, 22, 23). However, little is known how these three processes depend on awareness.A number of previous studies have supported an early feedforward processing phase for the boundary-detection and later feedback-processing phases for both region filling and background suppression in figure–ground modulation (2, 5, 21). These findings thus suggest that boundary detection is independent of awareness, whereas both region filling and background suppression are strongly modulated by awareness (12). Specifically, boundary detection is thought to be achieved through iso-feature inhibition (2, 21, 24, 25) within early visual areas, as early as the primary visual cortex (V1) (9, 14, 26–30), in which neurons preferring the same or similar features are more likely to suppress each other via lateral connections (31). The region-filling process, however, requires iso-feature excitation in which neurons representing the similar features enhance each other’s activity. In contrast to several studies suggesting the existence of the region-filling process within V1 (1, 9), most previous studies indicate that the region-filling process arises from feedback projections to V1 from a higher cortical area(s) (11, 12, 14, 15, 20, 32). Similarly, several neurophysiological studies have suggested that the background-suppression process may also be derived by feedback to V1 from a higher cortical area(s); it is the later processing phase in which neural activity elicited by the background is suppressed by the preceding segregated figures (5, 22, 23). However, it remains unknown which and how the top-down feedback from a higher cortical area(s) drive the region-filling and background-suppression processes in V1 that enhances the response of neurons tuned to the same feature and suppresses the neural activity elicited by the background, respectively. Also, it is unknown whether and how these feedback processes interact with awareness.Furthermore, another unclear but related issue is how boundary detection and region filling in figure–ground segregation attract focused attention. In fact, it is well known that successful segregation of a figure, as defined by an orientation contrast (Fig. 1A) from the background, leads to pop-out, which automatically attracts bottom-up attention to this salient figure location (10, 21, 25). However, it is not known whether there are different neural mechanisms by which the boundary detection and region filling attract our focused attention and whether the attentional attraction triggered by these two processes interacts with awareness.Open in a separate windowFig. 1.Stimuli, psychophysical protocol, and data. (A) Two sample orientation-defined figures presented in the upper visual field (Left: large figure; Right: small figure). The orientation contrasts between the figure bars and the background bars was 60° (the yellow dot indicates the fixation point). (B) Large (Left) and small (Right) grating probes, with the same diameter as the large and small figures, respectively. (C) Low- (Left) and high- (Right) luminance mask stimuli used in the visible and invisible conditions, respectively. (D) Psychophysical protocol. A figure–ground stimulus was presented for 50 ms, followed by a 100-ms mask and another 50-ms fixation interval. Then a large or small grating probe, with the same diameter as the large figure and small figure, respectively, was randomly presented for 50 ms with equal probability and presented randomly at either the figure location (valid cue condition) or its contralateral counterpart (invalid cue condition) with equal probability. The grating probe was orientated at 45° or 135° away from the vertical. Subjects were asked to press one of two buttons as rapidly and correctly as possible to indicate the orientation of the grating probe (45° or 135°). The psychophysical cueing effect for the large (E) and small (F) figures and the large and small gratings in both visible and invisible conditions. Each cueing effect was quantified as the difference between the reaction time of the probe task performance in the invalid cue condition and that in the valid cue condition. Error bars denote 1 SEM calculated across subjects and colored dots denote the data from each subject.To address these questions, we used a modified version of the Posner paradigm (33, 34) to measure the spatial cueing effect induced by figure boundary (edge modulation) or figure center (center modulation) of the large figure (Fig. 1 A, Left), and by the whole small figure or its surround background (background modulation, Fig. 1 A, Right). Blood oxygen level-dependent (BOLD) signals evoked by the figure boundary and figure center of the large figure, as well as the whole small figure and its surround background were also measured. Using a backward masking paradigm (10) with low- or high-luminance masks to render the whole figure–ground stimulus visible or invisible (confirmed by a two-alternative forced choice [2AFC]) to subjects, respectively, we examined how figure–ground segregation interacts with awareness. We also performed interregional correlation and effective connectivity analyses to examine the neural mechanisms of this potential interaction.     

Paleocene latitude of the Kohistan–Ladakh arc indicates multistage India–Eurasia collision

We report paleomagnetic data showing that an intraoceanic Trans-Tethyan subduction zone existed south of the Eurasian continent and north of the Indian subcontinent until at least Paleocene time. This system was active between 66 and 62 Ma at a paleolatitude of 8.1 ± 5.6 °N, placing it 600–2,300 km south of the contemporaneous Eurasian margin. The first ophiolite obductions onto the northern Indian margin also occurred at this time, demonstrating that collision was a multistage process involving at least two subduction systems. Collisional events began with collision of India and the Trans-Tethyan subduction zone in Late Cretaceous to Early Paleocene time, followed by the collision of India (plus Trans-Tethyan ophiolites) with Eurasia in mid-Eocene time. These data constrain the total postcollisional convergence across the India–Eurasia convergent zone to 1,350–2,150 km and limit the north–south extent of northwestern Greater India to <900 km. These results have broad implications for how collisional processes may affect plate reconfigurations, global climate, and biodiversity.

Classically, the India–Eurasia collision has been considered to be a single-stage event that occurred at 50–55 million years ago (Ma) (1, 2). However, plate reconstructions show thousands of kilometers of separation between India and Eurasia at the inferred time of collision (3, 4). Accordingly, the northern extent of Greater India was thought to have protruded up to 2,000 km relative to present-day India (5, 6) (Fig. 1). Others have suggested that the India–Eurasia collision was a multistage process that involved an east–west trending Trans-Tethyan subduction zone (TTSZ) situated south of the Eurasian margin (7–9) (Fig. 1). Jagoutz et al. (9) concluded that collision between India and the TTSZ occurred at 50–55 Ma, and the final continental collision occurred between the TTSZ and Eurasia at 40 Ma (9, 10). This model reconciles the amount of convergence between India and Eurasia with the observed shortening across the India–Eurasia collision system with the addition of the Kshiroda oceanic plate. Additionally, the presence of two subduction systems can explain the rapid India–Eurasia convergence rates (up to 16 mm a⁻¹) that existed between 135 and 50 Ma (9), as well as variations in global climate in the Cenozoic (11).Open in a separate windowFig. 1.The first panel is an overview map of tectonic structure of the Karakoram–Himalaya–Tibet orogenic system. Blue represents India, red represents Eurasia, and the Kohistan–Ladakh arc (KLA) is shown in gray. The different shades of blue highlight the deformed margin of the Indian plate that has been uplifted to form the Himalayan belt, and the zones of darker red within the Eurasian plate highlight the Eurasian continental arc batholith. Thick black lines denote the suture zones which separate Indian and Eurasian terranes. The tectonic summary panels illustrate the two conflicting collision models and their differing predictions of the location of the Kohistan–Ladakh arc. India is shown in blue, Eurasia is shown in red, and the other nearby continents are shown in gray. Active plate boundaries are shown with black lines, and recently extinct boundaries are shown with gray lines. Subduction zones are shown with triangular tick marks.While the existence of the TTSZ in the Cretaceous is not disputed, the two conflicting collision models make distinct predictions about its paleolatitude in Late Cretaceous to Paleocene time; these can be tested using paleomagnetism. In the single-stage collision model, the TTSZ amalgamated with the Eurasian margin prior to ∼80 Ma (12) at a latitude of ≥20 °N (13, 14). In contrast, in the multistage model, the TTSZ remained near the equator at ≤10 °N, significantly south of Eurasia, until collision with India (9) (Fig. 1).No undisputed paleomagnetic constraints on the location of the TTSZ are available in the central Himalaya (15–17). Westerweel et al. (18) showed that the Burma Terrane, in the eastern Himalaya, was part of the TTSZ and was located near the equator at ∼95 Ma, but they do not constrain the location of the TTSZ in the time period between 50 and 80 Ma, which is required to test the two collision hypotheses. In the western Himalaya, India and Eurasia are separated by the Bela, Khost, and Muslimbagh ophiolites and the 60,000 km² intraoceanic Kohistan Ladakh arc (19, 20) (Fig. 1). These were obducted onto India in the Late Cretaceous to Early Paleocene (19), prior to the closure of the Eocene to Oligocene Katawaz sedimentary basin (20) (Fig. 1). The Kohistan–Ladakh arc contacts the Eurasian Karakoram terrane in the north along the Shyok suture and the Indian plate in the south along the Indus suture (21) (Fig. 1). Previous paleomagnetic studies suggest that the Kohistan–Ladakh arc formed as part of the TTSZ near the equator in the early Cretaceous but provide no information on its location after 80 Ma (22–25). While pioneering, these studies lack robust age constraints, do not appropriately average paleosecular variation of the geodynamo, and do not demonstrate that the measured magnetizations have not been reset during a subsequent metamorphic episode.     

Intolerance of uncertainty modulates brain-to-brain synchrony during politically polarized perception

Political partisans see the world through an ideologically biased lens. What drives political polarization? Although it has been posited that polarization arises because of an inability to tolerate uncertainty and a need to hold predictable beliefs about the world, evidence for this hypothesis remains elusive. We examined the relationship between uncertainty tolerance and political polarization using a combination of brain-to-brain synchrony and intersubject representational similarity analysis, which measured committed liberals’ and conservatives’ (n = 44) subjective interpretation of naturalistic political video material. Shared ideology between participants increased neural synchrony throughout the brain during a polarizing political debate filled with provocative language but not during a neutrally worded news clip on polarized topics or a nonpolitical documentary. During the political debate, neural synchrony in mentalizing and valuation networks was modulated by one’s aversion to uncertainty: Uncertainty-intolerant individuals experienced greater brain-to-brain synchrony with politically like-minded peers and lower synchrony with political opponents—an effect observed for liberals and conservatives alike. Moreover, the greater the neural synchrony between committed partisans, the more likely that two individuals formed similar, polarized attitudes about the debate. These results suggest that uncertainty attitudes gate the shared neural processing of political narratives, thereby fueling polarized attitude formation about hot-button issues.

Countries around the world are experiencing the strain of growing political polarization (1–5). Opposing partisans come to see the world through different eyes. Where one sees the freedom to choose, another sees murder; where one sees the right to protest, another sees violent conduct (6–8). Such a polarized perception of reality hampers bipartisan cooperation and can even undermine the basic principles of democracy (8, 9).How does polarization arise? One popular theory posits that a need to have certain, structured, and stable beliefs about the world drives people toward political extremes (10–13). Rather than seeing the world in nuanced shades of gray, cognitively rigid individuals perceive information in black and white, painting the world in categorical and predictable terms (14)—a view that dovetails with the immutable taxonomy of political ideologues (15–19). The rigid mind is characterized by a trait-like tendency to find unpredictable and uncertain events aversive and threatening (14, 20, 21) and has long been theorized to play an outsized role in shaping polarized perceptions (22–26). Although recent work suggests that uncertainty can impact the evaluation of political candidates (27) and policy positions (28, 29) and is a major factor contributing to political conservatism (30, 31), the link between uncertainty and political polarization remains unclear. Here, we examine whether individual differences in intolerance of uncertainty (IUS) (20, 21) shape how naturalistic political information is processed in the brain at the time of perception. We test the hypothesis that uncertainty-intolerant individuals interpret polarizing political information through an ideologically biased, subjective “lens” that produces clear-cut judgments of the issue at hand (20, 32). We further examine whether the neural fingerprint of these uncertainty-driven polarized perceptions—that is, increased brain-to-brain synchrony between like-minded partisans—predicts the formation of polarized attitudes.We combine two techniques to measure polarized perceptions of political information. First, intersubject correlation [ISC (33)] provides a direct measure of the similarity in subjective interpretations of naturalistic social stimuli (e.g., video narratives) among participants (34, 35). This technique capitalizes on the neural processes triggered by incoming auditory and visual information. If two individuals exhibit similar neural profiles when processing the same incoming information (e.g., synchronized blood oxygen level-dependent [BOLD] responses in functional MRI [fMRI]), they likely have a shared perception and understanding of that information (36–40). Given that ISC offers an established metric to gauge whether individuals are processing information in a similar way, we can use it to test whether two individuals who share the same political ideology also have similar subjective perceptions of political information, which circumvents issues with demand characteristics and explicit self-report (41). Second, to make neural synchrony analyses sensitive to more subtle differences along the ideological continuum than simple left–right groupings and to test for interactive effects between ideology and intolerance to uncertainty, we combine ISC with intersubject representational similarity analysis [IS-RSA (42–44)]. This versatile approach enables us to leverage continuous individual differences and test whether uncertainty attitudes exacerbate the processing of political information in the brain to fuel polarized political attitude formation.Using a combination of targeted online and field recruiting (n = 360), we invited 22 liberals and 22 conservatives to participate in a study on political cognition (Fig. 1A). While undergoing fMRI, participants viewed three types of videos: a neutrally worded news segment on a politically charged topic (abortion; taken from Public Broadcasting Service [PBS] News), an inflammatory debate segment (police brutality and immigration; taken from the 2016 Cable News Network [CNN] Vice-Presidential debate), and a nonpolitical nature video (taken from British Broadcasting Corporation [BBC] Earth; Fig. 1B). Neural data analysis consisted of time locking the fMRI BOLD signal to the onset of the videos and computing voxel-wise time course correlations between each possible pairing of subjects across the entire participant pool, resulting in a “neural synchrony” measurement that indexes shared subjective interpretations of dynamic, naturalistic stimuli (35, 45, 46). We first analyzed behavioral responses to the videos to test whether ideology, IUS, or both predicted similarities in attitude formation about the presented political videos. Next, we analyzed variation in neural synchrony across participant dyads using IS-RSA (Fig. 1D) to test three interrelated hypotheses: 1) shared ideology between subjects will predict brain-to-brain synchrony during the perception of political stimuli, 2) IUS will modulate this neural synchrony in committed partisans, and 3) increasing neural synchrony will predict the subsequent expression of shared polarized attitudes about the political stimuli.Open in a separate windowFig. 1.(A) Participants underwent fMRI and behavioral testing as part of a larger study on political cognition. (B) Participants viewed three videos in a fixed order while undergoing fMRI. (C) Participants were clearly divided on political ideology. (D) Analytical approach. We tested for variation in neural synchrony as a function of ideology and IUS. The statistical map slice is taken from Fig. 2C.     

Photosynthesis tunes quantum-mechanical mixing of electronic and vibrational states to steer exciton energy transfer

Photosynthetic species evolved to protect their light-harvesting apparatus from photoxidative damage driven by intracellular redox conditions or environmental conditions. The Fenna–Matthews–Olson (FMO) pigment–protein complex from green sulfur bacteria exhibits redox-dependent quenching behavior partially due to two internal cysteine residues. Here, we show evidence that a photosynthetic complex exploits the quantum mechanics of vibronic mixing to activate an oxidative photoprotective mechanism. We use two-dimensional electronic spectroscopy (2DES) to capture energy transfer dynamics in wild-type and cysteine-deficient FMO mutant proteins under both reducing and oxidizing conditions. Under reducing conditions, we find equal energy transfer through the exciton 4–1 and 4–2-1 pathways because the exciton 4–1 energy gap is vibronically coupled with a bacteriochlorophyll-a vibrational mode. Under oxidizing conditions, however, the resonance of the exciton 4–1 energy gap is detuned from the vibrational mode, causing excitons to preferentially steer through the indirect 4–2-1 pathway to increase the likelihood of exciton quenching. We use a Redfield model to show that the complex achieves this effect by tuning the site III energy via the redox state of its internal cysteine residues. This result shows how pigment–protein complexes exploit the quantum mechanics of vibronic coupling to steer energy transfer.

Photosynthetic organisms convert solar photons into chemical energy by taking advantage of the quantum mechanical nature of their molecular systems and the chemistry of their environment (1–4). Antenna complexes, composed of one or more pigment–protein complexes, facilitate the first steps in the photosynthesis process: They absorb photons and determine which proportion of excitations to move to reaction centers, where charge separation occurs (4). In oxic environments, excitations can generate highly reactive singlet oxygen species. These pigment–protein complexes can quench excess excitations in these environments with molecular moieties such as quinones and cysteine residues (1, 5–7).The Fenna–Matthews–Olson (FMO) complex, a trimer of pigment–protein complexes found in the green sulfur bacterium Chlorobaculum tepidum (8), has emerged as a model system to study the photophysical properties of photosynthetic antenna complexes (9–19). Each subunit in the FMO complex contains eight bacteriochlorophyll-a site molecules (Protein Data Bank, ID code: 3ENI) that are coupled to form a basis of eight partially delocalized excited states called excitons (Fig. 1) (20–23). Previous experiments on FMO have observed the presence of long-lived coherences in nonlinear spectroscopic signals at both cryogenic and physiological temperatures (11, 13). The coherent signals are thought to arise from some combination of electronic (24–26), vibrational (16–18), and vibronic (27) coherences in the system (28–30). One previous study reported that the coherent signals in FMO remain unchanged upon mutagenesis of the protein, suggesting that the signals are ground state vibrational coherences (17). Others discuss the role of vibronic coupling, where electronic and nuclear degrees of freedom become coupled (29). Other dimeric model systems have demonstrated the regimes in which these vibronically coupled states produce coherent or incoherent transport and vibronic coherences (31–33). Recent spectroscopic data has suggested that vibronic coupling plays a role in driving efficient energy transfer through photosynthetic complexes (27, 31, 33, 34), but to date there is no direct experimental evidence suggesting that biological systems use vibronic coupling as part of their biological function.Open in a separate windowFig. 1.(Left) Numbered sites and sidechains of cysteines C353 and C49 in the FMO pigment–protein complex (PDB ID code: 3ENI) (20). (Right) Site densities for excitons 4, 2, and 1 in reducing conditions with the energy transfer branching ratios for the WT oxidized and reduced protein. The saturation of pigments in each exciton denotes the relative contribution number to the exciton. The C353 residue is located near excitons 4 and 2, which have most electron density along one side of the complex, and other redox-active residues such as the Trp/Tyr chain. C353 and C49 surround site III, which contains the majority of exciton 1 density. Excitons 2 and 4 are generally delocalized over sites IV, V, and VII.It has been shown that redox conditions affect excited state properties in pigment-protein complexes, yet little is known about the underlying microscopic mechanisms for these effects (1, 9). Many commonly studied light-harvesting complexes—including the FMO complex (20), light-harvesting complex 2 (LH2) (35), the PC645 phycobiliprotein (36), and the cyanobacterial antenna complex isiA (37)—contain redox-active cysteine residues in close proximity to their chromophores. As the natural low light environment of C. tepidum does not necessitate photoprotective responses to light quantity and quality, its primary photoprotective mechanism concerns its response to oxidative stress. C. tepidum is an obligate anaerobe, but the presence of many active anoxygenic genes such as sodB for superoxide dismutase and roo for rubredoxin oxygen oxidoreductase (38) suggests that it is frequently exposed to molecular oxygen (7, 39). Using time-resolved fluorescence measurements, Orf et al. demonstrated that two cysteine residues in the FMO complex, C49 and C353, quench excitons under oxidizing conditions (1), which could protect the excitation from generating reactive oxygen species (7, 40–42). In two-dimensional electronic spectroscopy (2DES) experiments, Allodi et al. showed that redox conditions in both the wild-type and C49A/C353A double-mutant proteins affect the ultrafast dynamics through the FMO complex (9, 43). The recent discovery that many proteins across the evolutionary landscape possess chains of tryptophan and tyrosine residues provides evidence that these redox-active residues may link the internal protein behavior with the chemistry of the surrounding environment (41, 43).In this paper, we present data showing that pigment–protein complexes tune the vibronic coupling of their chromophores and that the absence of this vibronic coupling activates an oxidative photoprotective mechanism. We use 2DES to show that a pair of cysteine residues in FMO, C49 and C353, can steer excitations toward quenching sites in oxic environments. The measured reaction rate constants demonstrate unusual nonmonotonic behavior. We then use a Redfield model to determine how the exciton energy transfer (EET) time constants arise from changing chlorophyll site energies and their system-bath couplings (44, 45). The analysis reveals that the cysteine residues tune the resonance between exciton 4–1 energy gap and an intramolecular chlorophyll vibration in reducing conditions to induce vibronic coupling and detune the resonance in oxidizing conditions. This redox-dependent modulation of the vibronic coupling steers excitations through different pathways in the complex to change the likelihood that they interact with exciton quenchers.     

Structure,self-assembly,and properties of a truncated reflectin variant

Naturally occurring and recombinant protein-based materials are frequently employed for the study of fundamental biological processes and are often leveraged for applications in areas as diverse as electronics, optics, bioengineering, medicine, and even fashion. Within this context, unique structural proteins known as reflectins have recently attracted substantial attention due to their key roles in the fascinating color-changing capabilities of cephalopods and their technological potential as biophotonic and bioelectronic materials. However, progress toward understanding reflectins has been hindered by their atypical aromatic and charged residue-enriched sequences, extreme sensitivities to subtle changes in environmental conditions, and well-known propensities for aggregation. Herein, we elucidate the structure of a reflectin variant at the molecular level, demonstrate a straightforward mechanical agitation-based methodology for controlling this variant’s hierarchical assembly, and establish a direct correlation between the protein’s structural characteristics and intrinsic optical properties. Altogether, our findings address multiple challenges associated with the development of reflectins as materials, furnish molecular-level insight into the mechanistic underpinnings of cephalopod skin cells’ color-changing functionalities, and may inform new research directions across biochemistry, cellular biology, bioengineering, and optics.

Materials from naturally occurring and recombinant proteins are frequently employed for the study of fundamental biological processes and leveraged for applications in fields as diverse as electronics, optics, bioengineering, medicine, and fashion (1–13). Such broad utility is enabled by the numerous advantageous characteristics of protein-based materials, which include sequence modularity, controllable self-assembly, stimuli-responsiveness, straightforward processability, inherent biological compatibility, and customizable functionality (1–13). Within this context, unique structural proteins known as reflectins have recently attracted substantial attention because of their key roles in the fascinating color-changing capabilities of cephalopods, such as the squid shown in Fig. 1A, and have furthermore demonstrated their utility for unconventional biophotonic and bioelectronic technologies (11–40). For example, in vivo, Bragg stack-like ultrastructures from reflectin-based high refractive index lamellae (membrane-enclosed platelets) are responsible for the angle-dependent narrowband reflectance (iridescence) of squid iridophores, as shown in Fig. 1B (15–20). Analogously, folded membranes containing distributed reflectin-based particle arrangements within sheath cells lead to the mechanically actuated iridescence of squid chromatophore organs, as shown in Fig. 1C (15, 16, 21, 22). Moreover, in vitro, films processed from squid reflectins not only exhibit proton conductivities on par with some state-of-the-art artificial materials (23–27) but also support the growth of murine and human neural stem cells (28, 29). Additionally, morphologically variable coatings assembled from different reflectin isoforms can enable the functionality of chemically and electrically actuated color-changing devices, dynamic near-infrared camouflage platforms, and stimuli-responsive photonic architectures (27, 30–34). When considered together, these discoveries and demonstrations constitute compelling motivation for the continued exploration of reflectins as model biomaterials.Open in a separate windowFig. 1.(A) A camera image of a D. pealeii squid for which the skin contains light-reflecting cells called iridophores (bright spots) and pigmented organs called chromatophores (colored spots). Image credit: Roger T. Hanlon (photographer). (B) An illustration of an iridophore (Left), which shows internal Bragg stack-like ultrastructures from reflectin-based lamellae (i.e., membrane-enclosed platelets) (Inset). (C) An illustration of a chromatophore organ (Left), which shows arrangements of reflectin-based particles within the sheath cells (Inset). (D) The logo of the 28-residue-long N-terminal motif (RMN), which depicts the constituent amino acids (Upper) and their predicted secondary structures (Lower). (E) The logo of the 28-residue-long internal motif (RMI), which depicts the constituent amino acids (Upper) and their predicted secondary structures (Lower). (F) The logo of the 21-residue-long C-terminal motif (RMC), which depicts the constituent amino acids (Upper) and their predicted secondary structures (Lower). (G) The amino acid sequence of full-length D. pealeii reflectin A1, which contains a single RMN motif (gray oval) and five RMI motifs (orange ovals). (H) An illustration of the selection of the prototypical truncated reflectin variant (denoted as RfA1TV) from full-length D. pealeii reflectin A1.Given reflectins’ demonstrated significance from both fundamental biology and applications perspectives, some research effort has been devoted to resolving their three-dimensional (3D) structures (30, 31, 35–39). For example, fibers drawn from full-length Euprymna scolopes reflectin 1a and films processed from truncated E. scolopes reflectin 1a were shown to possess secondary structural elements (i.e., α-helices or β-sheets) (30, 31). In addition, precipitated nanoparticles and drop-cast films from full-length Doryteuthis pealeii reflectin A1 have exhibited β-character, which was seemingly associated with their conserved motifs (35, 36). Moreover, nanoparticles assembled from both full-length and truncated Sepia officinalis reflectin 2 variants have demonstrated signatures consistent with β-sheet or α-helical secondary structure, albeit in the presence of surfactants (38). However, such studies were made exceedingly challenging by reflectins’ atypical primary sequences enriched in aromatic and charged residues, documented extreme sensitivities to subtle changes in environmental conditions, and well-known propensities for poorly controlled aggregation (12, 14, 15, 30–32, 34–39). Consequently, the reported efforts have all suffered from multiple drawbacks, including the need for organic solvents or denaturants, the evaluation of only polydisperse or aggregated (rather than monomeric) proteins, a lack of consensus among different experimental techniques, inadequate resolution that precluded molecular-level insight, imperfect agreement between computational predictions and experimental observations, and/or the absence of conclusive correlations between structure and optical functionality. As such, there has emerged an exciting opportunity for investigating reflectins’ molecular structures, which remain poorly understood and the subject of some debate.Herein, we elucidate the structure of a reflectin variant at the molecular level, demonstrate a robust methodology for controlling this variant’s hierarchical assembly, and establish a direct correlation between its structural characteristics and optical properties. We first rationally select a prototypical reflectin variant expected to recapitulate the behavior of its parent protein by using a bioinformatics-guided approach. We next map the conformational and energetic landscape accessible to our selected protein by means of all-atom molecular dynamics (MD) simulations. We in turn produce our truncated reflectin variant with and without isotopic labeling, develop solution conditions that maintain the protein in a monomeric state, and characterize the variant’s size and shape with small-angle X-ray scattering (SAXS). We subsequently resolve our protein’s dynamic secondary and tertiary structures and evaluate its backbone conformational fluctuations with NMR spectroscopy. Finally, we demonstrate a straightforward mechanical agitation-based approach to controlling our truncated reflectin variant’s secondary structure, hierarchical self-assembly, and bulk refractive index distribution. Overall, our findings address multiple challenges associated with the development of reflectins as materials, furnish molecular-level insight into the mechanistic underpinnings of cephalopod skin cells’ color-changing functionalities, and appear poised to inform new directions across biochemistry, cellular biology, bioengineering, and optics.     

Widespread occurrence of the droplet state of proteins in the human proteome

A wide range of proteins have been reported to condensate into a dense liquid phase, forming a reversible droplet state. Failure in the control of the droplet state can lead to the formation of the more stable amyloid state, which is often disease-related. These observations prompt the question of how many proteins can undergo liquid–liquid phase separation. Here, in order to address this problem, we discuss the biophysical principles underlying the droplet state of proteins by analyzing current evidence for droplet-driver and droplet-client proteins. Based on the concept that the droplet state is stabilized by the large conformational entropy associated with nonspecific side-chain interactions, we develop the FuzDrop method to predict droplet-promoting regions and proteins, which can spontaneously phase separate. We use this approach to carry out a proteome-level study to rank proteins according to their propensity to form the droplet state, spontaneously or via partner interactions. Our results lead to the conclusion that the droplet state could be, at least transiently, accessible to most proteins under conditions found in the cellular environment.

It has been recently observed that proteins can self-assemble through a liquid–liquid phase separation (LLPS) process into a dense liquid phase, while maintaining at least in part their functional native states (1–4). These liquid-like assemblies of complex compositions are often referred to as biomolecular condensates or membraneless organelles (1–4). Here, we refer to these dynamic and reversible condensates as droplets, in order to distinguish them from irreversible amyloids. Droplets can concentrate cellular components to perform efficiently a variety of different functions, with an increasing number of biological roles being discovered (1–4).In this work, we investigate whether liquid–liquid phase separation can be expected to be a proteome-wide phenomenon. In this view, the condensation of proteins from the native state to the amyloid state may quite generally proceed through an intermediate dense liquid phase, which is typically metastable (5) (Fig. 1). Different proteins may have different propensities to remain in this metastable phase, depending in particular on the free energy barrier between the droplet and amyloid states (Fig. 1). This type of liquid–liquid phase separation is indeed typical of condensation phenomena (1, 6), and sometimes is referred to as the Ostwald step rule (7). One may think that for most proteins the free energy barrier between the droplet and fibrillar states is low, and therefore the droplet state cannot be readily observed (Fig. 1). Indeed, this state may be difficult to detect due to a variety of reasons, including because experimental methods to probe its formation, in particular high-throughput ones, are still under development (8). Furthermore, our current understanding of the interactions that stabilize the metastable dense liquid phase is still incomplete.Open in a separate windowFig. 1.Liquid–liquid phase separation could be expected to be a proteome-wide phenomenon. Proteins that undergo condensation convert from the native state to the amyloid state through a dense liquid state (the droplet state). The stability of these different states (the minima in the free energy), as well as the conversion rates between them (the barriers in the free energy), is different for different proteins. For most proteins under cellular conditions, the native and droplet states could be expected to be metastable (56), being kinetically trapped by a free energy barrier (ΔG) between the droplet and fibrillar states. Proteins that can be observed in the droplet state tend to have a high free energy barrier (LLPS; green) while the other ones tend to have a low free energy barrier compared with the thermal energy (non-LLPS; orange). For certain proteins the droplet state is functional, and it is stabilized by extrinsic factors, such as RNA and posttranslational modifications.Native and amyloid states are stabilized by specific interactions including hydrogen bonds, ionic interactions, and van der Waals contacts typical of ordered states and enthalpic in nature (9, 10). By contrast, in droplets, transient short-range aromatic cation–π and π–π, dipole–dipole, and electrostatic and hydrophobic interactions have been observed, providing low-specificity, weak-affinity contacts characteristic of disordered states (11–16). These observations have led to a series of prediction methods (11, 13, 17–19), which focused on specific side-chain interactions. The redundancy and multivalency of the interacting elements (20) suggest that conformational entropy is a driving force of the condensation (21), also including main-chain contributions. Indeed, proteins exhibiting many binding configurations with a specific partner are often capable of forming droplets (22).Here, we exploit the observation that many proteins exhibit high conformational entropy upon binding, which can be predicted from their amino acid sequences (23). Based on this result, we develop the FuzDrop method to predict the droplet-promoting propensity of proteins and their droplet-promoting profiles based on the conformational entropy of their free states and the binding entropy. Using this method, we identify a list of “droplet-driving” proteins, which are predicted to undergo spontaneous liquid–liquid phase separation under physiological conditions, and estimate that they comprise about 40% of the human proteome. In addition, we also predict that about 80% of the proteins are “droplet clients,” characterized by short droplet-promoting regions in their sequences, which facilitate condensation via interactions with suitable partners. Taken together, our results indicate that protein phase separation is a proteome-wide phenomenon.     

A solution to a sex ratio puzzle in Melittobia wasps

The puzzling sex ratio behavior of Melittobia wasps has long posed one of the greatest questions in the field of sex allocation. Laboratory experiments have found that, in contrast to the predictions of theory and the behavior of numerous other organisms, Melittobia females do not produce fewer female-biased offspring sex ratios when more females lay eggs on a patch. We solve this puzzle by showing that, in nature, females of Melittobia australica have a sophisticated sex ratio behavior, in which their strategy also depends on whether they have dispersed from the patch where they emerged. When females have not dispersed, they lay eggs with close relatives, which keeps local mate competition high even with multiple females, and therefore, they are selected to produce consistently female-biased sex ratios. Laboratory experiments mimic these conditions. In contrast, when females disperse, they interact with nonrelatives, and thus adjust their sex ratio depending on the number of females laying eggs. Consequently, females appear to use dispersal status as an indirect cue of relatedness and whether they should adjust their sex ratio in response to the number of females laying eggs on the patch.

Sex allocation has produced many of the greatest success stories in the study of social behaviors (1–4). Time and time again, relatively simple theory has explained variation in how individuals allocate resources to male and female reproduction. Hamilton’s local mate competition (LMC) theory predicts that when n diploid females lay eggs on a patch and the offspring mate before the females disperse, the evolutionary stable proportion of male offspring (sex ratio) is (n − 1)/2n (Fig. 1) (5). A female-biased sex ratio is favored to reduce competition between sons (brothers) for mates and to provide more mates (daughters) for those sons (6–8). Consistent with this prediction, females of >40 species produce female-biased sex ratios and reduce this female bias when multiple females lay eggs on the same patch (higher n; Fig. 1) (9). The fit of data to theory is so good that the sex ratio under LMC has been exploited as a “model trait” to study the factors that can constrain “perfect adaptation” (4, 10–13).Open in a separate windowFig. 1.LMC. The sex ratio (proportion of sons) is plotted versus the number of females laying eggs on a patch. The bright green dashed line shows the LMC theory prediction for the haplodiploid species (5, 39). A more female-biased sex ratio is favored in haplodiploids because inbreeding increases the relative relatedness of mothers to their daughters (7, 32). Females of many species adjust their offspring sex ratio as predicted by theory, such as the parasitoid Nasonia vitripennis (green diamonds) (82). In contrast, the females of several Melittobia species, such as M. australica, continue to produce extremely female-biased sex ratios, irrespective of the number of females laying eggs on a patch (blue squares) (15).In stark contrast, the sex ratio behavior of Melittobia wasps has long been seen as one of the greatest problems for the field of sex allocation (3, 4, 14–21). The life cycle of Melittobia wasps matches the assumptions of Hamilton’s LMC theory (5, 15, 19, 21). Females lay eggs in the larvae or pupae of solitary wasps and bees, and then after emergence, female offspring mate with the short-winged males, who do not disperse. However, laboratory experiments on four Melittobia species have found that females lay extremely female-biased sex ratios (1 to 5% males) and that these extremely female-biased sex ratios change little with increasing number of females laying eggs on a patch (higher n; Fig. 1) (15, 17–20, 22). A number of hypotheses to explain this lack of sex ratio adjustment have been investigated and rejected, including sex ratio distorters, sex differential mortality, asymmetrical male competition, and reciprocal cooperation (15–18, 20, 22–26).We tested whether Melittobia’s unusual sex ratio behavior can be explained by females being related to the other females laying eggs on the same patch. After mating, some females disperse to find new patches, while some may stay at the natal patch to lay eggs on previously unexploited hosts (Fig. 2). If females do not disperse, they can be related to the other females laying eggs on the same host (27–31). If females laying eggs on a host are related, this increases the extent to which relatives are competing for mates and so can favor an even more female-biased sex ratio (28, 32–35). Although most parasitoid species appear unable to directly assess relatedness, dispersal behavior could provide an indirect cue of whether females are with close relatives (36–38). Consequently, we predict that when females do not disperse and so are more likely to be with closer relatives, they should maintain extremely female-biased sex ratios, even when multiple females lay eggs on a patch (28, 35).Open in a separate windowFig. 2.Host nest and dispersal manners of Melittobia. (A) Photograph of the prepupae of the leaf-cutter bee C. sculpturalis nested in a bamboo cane and (B) a diagram showing two ways that Melittobia females find new hosts. The mothers of C. sculpturalis build nursing nests with pine resin consisting of individual cells in which their offspring develop. If Melittobia wasps parasitize a host in a cell, female offspring that mate with males inside the cell find a different host on the same patch (bamboo cane) or disperse by flying to other patches.We tested whether the sex ratio of Melittobia australica can be explained by dispersal status in a natural population. We examined how the sex ratio produced by females varies with the number of females laying eggs on a patch and whether or not they have dispersed before laying eggs. To match our data to the predictions of theory, we developed a mathematical model tailored to the unique population structure of Melittobia, where dispersal can be a cue of relatedness. We then conducted a laboratory experiment to test whether Melittobia females are able to directly access the relatedness to other females and adjust their sex ratio behavior accordingly. Our results suggest that females are adjusting their sex ratio in response to both the number of females laying eggs on a patch and their relatedness to the other females. However, relatedness is assessed indirectly by whether or not they have dispersed. Consequently, the solution to the puzzling behavior reflects a more-refined sex ratio strategy.     

From the Cover: Evidence from South Africa for a protracted end-Permian extinction on land

Earth’s largest biotic crisis occurred during the Permo–Triassic Transition (PTT). On land, this event witnessed a turnover from synapsid- to archosauromorph-dominated assemblages and a restructuring of terrestrial ecosystems. However, understanding extinction patterns has been limited by a lack of high-precision fossil occurrence data to resolve events on submillion-year timescales. We analyzed a unique database of 588 fossil tetrapod specimens from South Africa’s Karoo Basin, spanning ∼4 My, and 13 stratigraphic bin intervals averaging 300,000 y each. Using sample-standardized methods, we characterized faunal assemblage dynamics during the PTT. High regional extinction rates occurred through a protracted interval of ∼1 Ma, initially co-occurring with low origination rates. This resulted in declining diversity up to the acme of extinction near the Daptocephalus–Lystrosaurus declivis Assemblage Zone boundary. Regional origination rates increased abruptly above this boundary, co-occurring with high extinction rates to drive rapid turnover and an assemblage of short-lived species symptomatic of ecosystem instability. The “disaster taxon” Lystrosaurus shows a long-term trend of increasing abundance initiated in the latest Permian. Lystrosaurus comprised 54% of all specimens by the onset of mass extinction and 70% in the extinction aftermath. This early Lystrosaurus abundance suggests its expansion was facilitated by environmental changes rather than by ecological opportunity following the extinctions of other species as commonly assumed for disaster taxa. Our findings conservatively place the Karoo extinction interval closer in time, but not coeval with, the more rapid marine event and reveal key differences between the PTT extinctions on land and in the oceans.

Mass extinctions are major perturbations of the biosphere resulting from a wide range of different causes including glaciations and sea level fall (1), large igneous provinces (2), and bolide impacts (3, 4). These events caused permanent changes to Earth’s ecosystems, altering the evolutionary trajectory of life (5). However, links between the broad causal factors of mass extinctions and the biological and ecological disturbances that lead to species extinctions have been difficult to characterize. This is because ecological disturbances unfold on timescales much shorter than the typical resolution of paleontological studies (6), particularly in the terrestrial record (6–8). Coarse-resolution studies have demonstrated key mass extinction phenomena including high extinction rates and lineage turnover (7, 9), changes in species richness (10), ecosystem instability (11), and the occurrence of disaster taxa (12). However, finer time resolutions are central to determining the association and relative timings of these effects, their potential causal factors, and their interrelationships. Achieving these goals represents a key advance in understanding the ecological mechanisms of mass extinctions.The end-Permian mass extinction (ca. 251.9 Ma) was Earth’s largest biotic crisis as measured by taxon last occurrences (13–15). Large outpourings from Siberian Trap volcanism (2) are the likely trigger of calamitous climatic changes, including a runaway greenhouse effect and ocean acidification, which had profound consequences for life on land and in the oceans (16–18). An estimated 81% of marine species (19) and 89% of tetrapod genera became extinct as established Permian ecosystems gave way to those of the Triassic. In the ocean, this included the complete extinction of reef-forming tabulate and rugose corals (20, 21) and significant losses in previously diverse ammonoid, brachiopod, and crinoid families (22). On land, many nonmammalian synapsids became extinct (16), and the glossopterid-dominated floras of Gondwana also disappeared (23). Stratigraphic sequences document a global “coral gap” and “coal gap” (24, 25), suggesting reef and forest ecosystems were rare or absent for up to 5 My after the event (26). Continuous fossil-bearing deposits documenting patterns of turnover across the Permian–Triassic transition (PTT) on land (27) and in the oceans (28) are geographically widespread (29, 30), including marine and continental successions that are known from China (31, 32) and India (33). Continental successions are known from Russia (34), Australia (35), Antarctica (36), and South Africa’s Karoo Basin (Fig. 1 and 37–40), the latter providing arguably the most densely sampled and taxonomically scrutinized (41–43) continental record of the PTT. The main extinction has been proposed to occur at the boundary between two biostratigraphic zones with distinctive faunal assemblages, the Daptocephalus and Lystrosaurus declivis assemblage zones (Fig. 1), which marks the traditional placement of the Permian–Triassic geologic boundary [(37) but see ref. 44]. Considerable research has attempted to understand the anatomy of the PTT in South Africa (38, 39, 45–52) and to place it in the context of biodiversity changes across southern Gondwana (53, 54) and globally (29, 31, 32, 44, 47, 55).Open in a separate windowFig. 1.Map of South Africa depicting the distribution of the four tetrapod fossil assemblage zones (Cistecephalus, Daptocephalus, Lystrosaurus declivis, Cynognathus) and our two study sites where fossils were collected in this study (sites A and B). Regional lithostratigraphy and biostratigraphy within the study interval are shown alongside isotope dilution–thermal ionization mass spectrometry dates retrieved by Rubidge et al., Botha et al., and Gastaldo et al. (37, 44, 80). The traditional (dashed red line) and associated PTB hypotheses for the Karoo Basin (37, 44) are also shown. Although traditionally associated with the PTB, the Daptocephalus–Lystrosaurus declivis Assemblage Zone boundary is defined by first appearances of co-occurring tetrapod assemblages, so its position relative to the three PTB hypotheses is unchanged. The Ripplemead member (*) has yet to be formalized by the South African Committee for Stratigraphy.Decades of research have demonstrated the richness of South Africa’s Karoo Basin fossil record, resulting in hundreds of stratigraphically well-documented tetrapod fossils across the PTT (37, 39, 56). This wealth of data has been used qualitatively to identify three extinction phases and an apparent early postextinction recovery phase (39, 45, 51). Furthermore, studies of Karoo community structure and function have elucidated the potential role of the extinction and subsequent recovery in breaking the incumbency of previously dominant clades, including synapsids (11, 57). Nevertheless, understanding patterns of faunal turnover and recovery during the PTT has been limited by the scarcity of quantitative investigations. Previous quantitative studies used coarsely sampled data (i.e., assemblage zone scale, 2 to 3 Ma time intervals) to identify low species richness immediately after the main extinction, potentially associated with multiple “boom and bust” cycles of primary productivity based on δ¹³C variation during the first 5 My of the Triassic (41, 58). However, many details of faunal dynamics in this interval remain unknown. Here, we investigate the dynamics of this major tetrapod extinction at an unprecedented time resolution (on the order of hundreds of thousands of years), using sample-standardized methods to quantify multiple aspects of regional change across the Cistecephalus, Daptocephalus, and Lystrosaurus declivis assemblage zones.     

Increasing risk of another Cape Town “Day Zero” drought in the 21st century

Three consecutive dry winters (2015–2017) in southwestern South Africa (SSA) resulted in the Cape Town “Day Zero” drought in early 2018. The contribution of anthropogenic global warming to this prolonged rainfall deficit has previously been evaluated through observations and climate models. However, model adequacy and insufficient horizontal resolution make it difficult to precisely quantify the changing likelihood of extreme droughts, given the small regional scale. Here, we use a high-resolution large ensemble to estimate the contribution of anthropogenic climate change to the probability of occurrence of multiyear SSA rainfall deficits in past and future decades. We find that anthropogenic climate change increased the likelihood of the 2015–2017 rainfall deficit by a factor of five to six. The probability of such an event will increase from 0.7 to 25% by the year 2100 under an intermediate-emission scenario (Shared Socioeconomic Pathway 2-4.5 [SSP2-4.5]) and to 80% under a high-emission scenario (SSP5-8.5). These results highlight the strong sensitivity of the drought risk in SSA to future anthropogenic emissions.

The Day Zero Cape Town drought was one of the worst water crises ever experienced in a metropolitan area (1, 2). Droughts are a regular occurrence in southwestern South Africa (SSA), having occurred during the late 1920s, early 1970s, and, more recently, during 2003–2004 (Fig. 1 A and B). However, the extended winter (April to September [AMJJAS]) 3-y rainfall deficit (Fig. 1 A and B; SI Appendix, Fig. S1) which drove the 2015–2017 Cape Town drought (2–8) was exceptional over the last century (4, 9). Storage in reservoirs supplying water to 3.7 million people in the Cape Town metropolitan area dropped to about 20% of capacity in May 2018. As a consequence, strict water-usage restrictions were implemented to delay water levels reaching 13.5%, the level at which much of the city’s municipal supply would have been disconnected (7), a scenario referred to as “Day Zero” by the municipal water authorities (7). Above-average winter rain over the rest of the 2018 austral winter allowed Cape Town to avoid the Day Zero scenario.Open in a separate windowFig. 1.(A) Mean 2015–2017 AMJJAS rainfall anomaly relative to 1921–1970. The dashed (continuous) line denotes negative anomalies beyond 1 (1.5) SD. (B) Time series of the observed (GPCC, blue; CRU, red) 3-y running mean AMJJAS WRI (Materials and Methods) from 1901 to 2017. The 2015–2017 mean is record-breaking over the period 1901–2017. (C–E) Mean 1921–1970 AMJJAS rainfall (millimeters per month) in observations (GPCC) (C), SPEAR_MED (D), and SPEAR_LO (E). The red lines encircle the area receiving at least 65% of the total annual rainfall during AMJJAS used to define WRI. (F) Monthly WRI in observations and models. Comparison of SPEAR_MED with SPEAR_LO shows how an enhanced resolution is key to capture finer-scale regional details of winter rainfall in the relatively small SSA Mediterranean region.While poor water-management practices and infrastructure deficiencies worsened the crisis (10, 11), the 2015–2017 rainfall deficit was the main driver of the drought (5). To facilitate the improvement of water-management practices and the infrastructure necessary to make the system more resilient, it is critical to first determine how likely a meteorological drought like the one in 2015–2017 might be in the coming decades. Increased aridity is expected in most of southern Africa (12–14) as a consequence of the Hadley Cell poleward expansion (4, 15–18) and southward shift of the Southern Hemisphere jet stream (19). Second, the risk of more extreme droughts should be quantified to understand the potential for emerging risks that could make a Day Zero event in Cape Town unavoidable.Previous work (5) has suggested that the Day Zero drought may have been made 1.4 to 6.4 times more likely over the last century due to +1 K of global warming, with the risk expected to scale linearly with one additional degree of warming. Such estimates make use of statistical models of the probability distribution’s tail (e.g., the generalized extreme value) applied to observations and previous-generation [i.e., as those participating to the Coupled Model Intercomparison Project Phase 3 (CMIP3) (20) and 5 (21)] climate models. CMIP3 and CMIP5 models have been shown to have a systematically biased position of the Southern Hemisphere jet stream toward the Equator, due to insufficient horizontal resolution (19). This produces a large uncertainty in model projections of jet-stream shifts (22, 23), thus hindering realistic projections of Southern Hemisphere climate change. Furthermore, for hydroclimatic variables, a statistical extrapolation of the probability distribution’s tail might have inherent limitations in providing precise estimates of the event probability of future extreme events, although its precision profits from the use of large ensembles (24, 25).Large ensembles of comprehensive climate models provide thousands of years of data that allow direct construction of the underlying probability distribution of hydroclimatic extremes without relying on a hypothesized statistical model of extremes (25, 26). South African winter rains have high interannual and decadal variability due to El Niño–Southern Oscillation (27), the Southern Annular Mode (28), and interdecadal variability (29). A multidecade to multicentury record may be required to detect the emergence of statistically significant trends in regional precipitation extremes. A large ensemble is, thus, a powerful method to isolate, at the decadal timescale, internal natural variability (e.g., SI Appendix, Fig. S2) from the forced signal (30–32).     

Developmental influence on evolutionary rates and the origin of placental mammal tooth complexity

Development has often been viewed as a constraining force on morphological adaptation, but its precise influence, especially on evolutionary rates, is poorly understood. Placental mammals provide a classic example of adaptive radiation, but the debate around rate and drivers of early placental evolution remains contentious. A hallmark of early dental evolution in many placental lineages was a transition from a triangular upper molar to a more complex upper molar with a rectangular cusp pattern better specialized for crushing. To examine how development influenced this transition, we simulated dental evolution on “landscapes” built from different parameters of a computational model of tooth morphogenesis. Among the parameters examined, we find that increases in the number of enamel knots, the developmental precursors of the tooth cusps, were primarily influenced by increased self-regulation of the molecular activator (activation), whereas the pattern of knots resulted from changes in both activation and biases in tooth bud growth. In simulations, increased activation facilitated accelerated evolutionary increases in knot number, creating a lateral knot arrangement that evolved at least ten times on placental upper molars. Relatively small increases in activation, superimposed on an ancestral tritubercular molar growth pattern, could recreate key changes leading to a rectangular upper molar cusp pattern. Tinkering with tooth bud geometry varied the way cusps initiated along the posterolingual molar margin, suggesting that small spatial variations in ancestral molar growth may have influenced how placental lineages acquired a hypocone cusp. We suggest that development could have enabled relatively fast higher-level divergence of the placental molar dentition.

Whether developmental processes bias or constrain morphological adaptation is a long-standing question in evolutionary biology (1–4). Many of the distinctive features of a species derive from pattern formation processes that establish the position and number of anatomical structures (5). If developmental processes like pattern formation are biased toward generating only particular kinds of variation, adaptive radiations may often be directed along developmental–genetic “lines of least resistance” (2, 4, 6, 7). Generally, the evolutionary consequences of this developmental bias have been considered largely in terms of how it might influence the pattern of character evolution (e.g., refs. 1, 2, 8–10). But development could also influence evolutionary rates by controlling how much variation is accessible to natural selection in a given generation (11).For mammals, the dentition is often the only morphological system linking living and extinct species (12). Correspondingly, tooth morphology plays a crucial role in elucidating evolutionary relationships, time calibrating phylogenetic trees, and reconstructing adaptive responses to past environmental change (e.g., refs. 13–15). One of the most pervasive features of dental evolution among mammals is an increase in the complexity of the tooth occlusal surface, primarily through the addition of new tooth cusps (16, 17). These increases in tooth complexity are functionally and ecologically significant because they enable more efficient mechanical breakdown of lower-quality foods like plant leaves (18).Placental mammals are the most diverse extant mammalian group, comprising more than 6,000 living species spread across 19 extant orders, and this taxonomic diversity is reflected in their range of tooth shapes and dietary ecologies (12). Many extant placental orders, especially those with omnivorous or herbivorous ecologies (e.g., artiodactyls, proboscideans, rodents, and primates), convergently evolved a rectangular upper molar cusp pattern from a placental ancestor with a more triangular cusp pattern (19–21). This resulted from separate additions in each lineage of a novel posterolingual cusp, the "hypocone'''' [sensu (19)], to the tritubercular upper molar (Fig. 1), either through modification of a posterolingual cingulum (“true” hypocone) or another posterolingual structure, like a metaconule (pseudohypocone) (19). The fossil record suggests that many of the basic steps in the origin of this rectangular cusp pattern occurred during an enigmatic early diversification window associated with the divergence and early radiation of several placental orders (20, 21; Fig. 1). However, there remains debate about the rate and pattern of early placental divergence (22–24). On the one hand, most molecular phylogenies suggest that higher-level placental divergence occurred largely during the Late Cretaceous (25, 26), whereas other molecular phylogenies and paleontological analyses suggest more rapid divergence near the Cretaceous–Paleogene (K–Pg) boundary (21, 24, 27–29). Most studies agree that ecological opportunity created in the aftermath of the K–Pg extinction probably played an important role in ecomorphological diversification within the placental orders (30, 31). But exactly how early placentals acquired the innovations needed to capitalize on ecological opportunity remains unclear. Dental innovations, especially those which facilitated increases in tooth complexity, may have been important because they would have promoted expansion into plant-based dietary ecologies left largely vacant after the K–Pg extinction event (32).Open in a separate windowFig. 1.Placental mammal lineages separately evolved complex upper molar teeth with a rectangular cusp pattern composed of two lateral pairs of cusps from a common ancestor with a simpler, triangular cusp pattern. Many early relatives of the extant placental orders, such as Eritherium, possessed a hypocone cusp and a more rectangular primary cusp pattern. Examples of complex upper molars are the following: Proboscidea, the gomphothere Anancus; Rodentia, the wood mouse Apodemus; and Artiodactyla, the suid Nyanzachoerus.Mammalian tooth cusps form primarily during the “cap” and “bell” stage of dental development, when signaling centers called enamel knots establish the future sites of cusp formation within the inner dental epithelium (33, 34). The enamel knots secrete molecules that promote proliferation and changes in cell–cell adhesion, which facilitates invagination of the dental epithelium into an underlying layer of mesenchymal cells (34, 35). Although a range of genes are involved in tooth cusp patterning (36–38), the basic dynamics can be effectively modeled using reaction–diffusion models with just three diffusible morphogens: an activator, an inhibitor, and a growth factor (39–41). Candidate activator genes in mammalian tooth development include Bmp4, Activin A, Fgf20, and Wnt genes, whereas potential inhibitors include Shh and Sostdc, and Fgf4 and Bmp2 have been hypothesized to act as growth factors (38, 40–43). In computer models of tooth development, activator molecules up-regulated in the underlying mesenchyme stimulate differentiation of overlying epithelium into nondividing enamel knot cells. These in turn secrete molecules that inhibit further differentiation of epithelium into knot cells, while also promoting cell proliferation that creates the topographic relief of the cusp (40). Although many molecular, cellular, and physical processes have the potential to influence cusp formation, and thereby tooth complexity (35, 37), parameters that control the strength and conductance of the activator and inhibitor signals, the core components of the reaction–diffusion cusp patterning mechanism (39, 40) are likely to be especially important.Here, we integrate a previous computer model of tooth morphogenesis called ToothMaker (41), with simulations of trait evolution and data from the fossil record (Fig. 2), to examine the developmental origins of tooth complexity in placental mammals. Specifically, we ask the following: 1) What developmental processes can influence how many cusps form? 2) How might these developmental processes influence the evolution of tooth cusp number, especially rates? And 3) what developmental changes may have been important in the origins of the fourth upper molar cusp, the hypocone, in placental mammal evolution?Open in a separate windowFig. 2.Workflow for simulations of tooth complexity evolution. (A) Tooth shape is varied for five signaling and growth parameters in ToothMaker. (B) From an ancestral state, each parameter is varied in 2.5% increments up to a maximum of ± 50% of the ancestral state. (C) Tooth complexity and enamel knot (EK) pattern were quantified for each parameter combination. Tooth complexity was measured using cusp number/EK number and OPC. ToothMaker and placental upper second molars were classified into categories based on EK/cusp pattern. (D) The parameter space was populated with pattern and tooth complexity datums to build a developmental landscape. (E) Tooth complexity evolution was simulated on each developmental landscape. (F) Resulting diversity and pattern of tooth complexity was compared with placental mammal molar diversity.     

Geometrical manipulation of complex supramolecular tessellations by hierarchical assembly of amphiphilic platinum(II) complexes

Here we report complex supramolecular tessellations achieved by the directed self-assembly of amphiphilic platinum(II) complexes. Despite the twofold symmetry, these geometrically simple molecules exhibit complicated structural hierarchy in a columnar manner. A possible key to such an order increase is the topological transition into circular trimers, which are noncovalently interlocked by metal···metal and π–π interactions, thereby allowing for cofacial stacking in a prismatic assembly. Another key to success is to use the immiscibility of the tailored hydrophobic and hydrophilic sidechains. Their phase separation leads to the formation of columnar crystalline nanostructures homogeneously oriented on the substrate, featuring an unusual geometry analogous to a rhombitrihexagonal Archimedean tiling. Furthermore, symmetry lowering of regular motifs by design results in an orthorhombic lattice obtained by the coassembly of two different platinum(II) amphiphiles. These findings illustrate the potentials of supramolecular engineering in creating complex self-assembled architectures of soft materials.

Tessellation in two dimensions (2D) is a very old topic in geometry on how one or more shapes can be periodically arranged to fill a Euclidean plane without any gaps. Tessellation principles have been extensively applied in decorative art since the early times. In natural sciences, there has been a growing attention on creating ordered structures with increasingly complex architectures inspired by semi-regular Archimedean tilings (ATs) and quasicrystalline textures on account of their intriguing physical properties (1–5) and biological functions (6). Recent advances in this regard have been achieved in various fields of supramolecular science, including the programmable self-assembly of DNA molecules (7), coordination-driven assembly (8–10), supramolecular interfacial engineering (11–13), crystallization of organic polygons (14, 15), colloidal particle superlattices (16), and other soft-matter systems (17–20). Moreover, tessellation in 2D can overcome the topological frustration to generate complex semi- or non-regular patterns by using geometrically simple motifs. As exemplified by the self-templating assembly of spherical soft microparticles (21), a vast array of 2D micropatterns encoding non-regular tilings, such as rectangular, rhomboidal, hexagonal, and herringbone superlattices were obtained by layer-by-layer strategy at a liquid–liquid interface. Tessellation principles have also been extended to the self-assembly of giant molecules in three dimensions (3D). Superlattices with high space-group symmetry (Im3¯m, Pm3¯n, and P4₂/mnm) were reported in dendrimers and dendritic polymers by Percec and coworkers (22–24). Recently, Cheng and coworkers identified the highly ordered Frank–Kasper phases obtained from giant amphiphiles containing molecular nanoparticles (25–28). Despite such advancements made in the field of soft matter, an understanding of how structural ordering in supramolecular materials is influenced by the geometric factors of its constituent molecules has so far remained elusive.In light of these developments and the desire to explore the supramolecular systems, square-planar platinum(II) (Pt^II) polypyridine complexes may serve as an ideal candidate for model studies not only because of their intriguing spectroscopic and luminescence properties (29, 30), but also because of their propensity to form supramolecular polymers or oligomers via noncovalent Pt···Pt and π–π interactions (31–39). Although rod-shaped and lamellar structures are the most commonly observed in the self-assembly of planar Pt^II complexes (34–39), 2D-ordered nanostructures, such as the hexagonally packed columns (31, 40) and honeycomb-like networks (41–43), were recently first demonstrated by us.Herein, we report a serendipitous discovery of a C_2h-symmetric Pt^II amphiphile (Fig. 1A) that can hierarchically self-assemble into a 3D-ordered nanostructure with hexagonal geometry. Interestingly, this structurally anisotropic molecule possibly undergoes topological transition and interlocks to form its circular trimer by noncovalent Pt···Pt and π–π interactions (Fig. 1B). The resultant triangular motif is architecturally stabilized and preorganized for one-dimensional (1D) prismatic assembly (Fig. 1C). Together with the phase separation of the tailored hydrophobic and hydrophilic sidechains, an unusual and unique 3D hexagonal lattice is formed (Fig. 1D), in which the Pt centers adopt a rare rhombitrihexagonal AT-like order. Finally, the nanoarchitecture develops in a hierarchical manner on the substrate due to the homogeneous nucleation (Fig. 1E).Open in a separate windowFig. 1.Hierarchical self-assembly of Pt^II amphiphile into hexagonal ordering. (A) Space-filling (CPK) model of a C_2h-symmetric Pt^II amphiphile (1). All of the hydrogen atoms and counterions are omitted for clarity. (B) CPK representations of possible models of regular triangular, tetragonal, pentagonal, and hexagonal motifs formed with Pt···Pt and π–π stacking. These motifs possess a hydrophilic core (red) with various diameters wrapped by a hydrophobic shell comprising long alkyl chains (gray). (C) CPK representation of a 1D prismatic structure consisting of circular trimers with long-range Pt···Pt and π–π stacking. (D) CPK representation of a 3D columnar lattice constructed by the prismatic assemblies adopting a rare rhombitrihexagonal AT-like order. With the assistance of the phase separation, the hydrophobic domain serves as a discrete column associated with six prismatic neighbors. (E) Schematic representation of the nanoarchitecture with homogeneous orientation.     

Bistability in the redox chemistry of sediments and oceans

For most of Earth’s history, the ocean’s interior was pervasively anoxic and showed occasional shifts in ocean redox chemistry between iron-buffered and sulfide-buffered states. These redox transitions are most often explained by large changes in external inputs, such as a strongly altered delivery of iron and sulfate to the ocean, or major shifts in marine productivity. Here, we propose that redox shifts can also arise from small perturbations that are amplified by nonlinear positive feedbacks within the internal iron and sulfur cycling of the ocean. Combining observational evidence with biogeochemical modeling, we show that both sedimentary and aquatic systems display intrinsic iron–sulfur bistability, which is tightly linked to the formation of reduced iron–sulfide minerals. The possibility of tipping points in the redox state of sediments and oceans, which allow large and nonreversible geochemical shifts to arise from relatively small changes in organic carbon input, has important implications for the interpretation of the geological rock record and the causes and consequences of major evolutionary transitions in the history of Earth’s biosphere.

The modern oceans are pervasively oxygenated, with anoxia being restricted to oxygen minimum zones and a few poorly ventilated basins such as the Black Sea (1). In contrast, during the Precambrian and early Phanerozoic Eon, the ocean interior is thought to have been pervasively anoxic (Fig. 1). Reconstruction of the redox evolution of the deep ocean is challenging prior to the Cretaceous due to a lack of rock records that can be unambiguously attributed to deposition in deep-sea environments. Still, redox reconstructions of intermediate water depths are available from a number of localities in the Precambrian and early Phanerozoic Eon, and these data suggest that oceanic basins—or at least subbasins—have alternated spatially and temporally between predominant iron-rich (ferruginous) and sulfide-rich (euxinic) conditions (2–9) (Fig. 1B). Recent evidence also suggests that periodic basin-scale transitions between ferruginous and euxinic conditions occurred during the “oceanic anoxic events” during the predominantly oxygenated Mesozoic (10, 11) (Fig. 1B). These two contrasting redox states imply a very different chemical environment for marine life, as any shift between them also entails a critical change in the concentrations of limiting elements (such as phosphorus, iron, and molybdenum) that sustain marine productivity and energy flow through the ocean biosphere (12–15).Open in a separate windowFig. 1.The evolving redox chemistry of the oceans against the backdrop of atmospheric oxygenation. (A) The estimates of the partial pressure of atmospheric oxygen (pO₂) relative to the PAL (43). The upward arrows during the Archaean denote possible transient episodes of ocean-atmosphere oxygenation just prior to the “Great Oxidation Event” (GOE). (B) The first-order features of evolving redox in surface, middepth, and deep ocean. The pattern of surface ocean oxygenation displayed is based on isotopic data (44, 45) and equilibration with atmospheric pO_2. Note, however, that surface ocean oxygenation was likely spatially variable (46). The records for intermediate (middepth) settings are after ref. 7, supplemented with observations from refs. 2, 4–6, 8, 10. The insets in B schematically depict reported oscillations between ferruginous and sulfidic conditions during the late Archean (47) (Left) and during the Cretaceous Thermal Maximum (11) (Right). The redox conditions in the deep ocean are tentative. Although a “background” state of ferruginous conditions for the deep ocean is consistent with available data from the sedimentary record, existing empirical constraints are not of sufficiently high fidelity to rule out pervasively euxinic deposition in the deep ocean for certain periods during the Precambrian. The question mark denotes the uncertain (potentially oxic) deep ocean redox state during the Lomagundi interval.Transitions between ferruginous and euxinic states on a basin-to-global scale require a switch in the dominant redox chemistry. One mechanism to achieve this is via a shift in the relative rates at which iron and sulfate are delivered to the ocean, with higher iron inputs favoring the prevalence of ferruginous conditions (16, 17). As a result, observed shifts in the redox state of the ocean interior are interpreted as reflecting major state changes in the Earth system, such as an increase in atmospheric oxygen (16), periods with strongly elevated volcanism (2), sea-level changes that modify the extent of the global depositional shelf area (9), or intervals of enhanced Fe or S weathering due to continental breakup (3, 18). An alternative mechanism is that changes in nutrient supply and nutrient availability in the ocean can increase the export of organic matter from the surface to the subsurface ocean. More organic carbon export then leads to increased microbial respiration, stimulating the production of sulfide via sulfate reduction and essentially titrating ferrous iron from the water column as pyrite (18). As a result, switches between ferruginous and euxinic states have been linked to the relative supply or production of ferrous iron and free sulfide, causing transitions at the Fe:S ratio of 1:2, the stoichiometric ratio of pyrite (17, 19).Here, we present a theoretical analysis of redox shifts in anoxic biogeochemical systems of both the ocean interior and marine sediments. Both these systems display aqueous chemistries that can switch between ferrous-iron–dominated and free-sulfide–dominated states. In this analysis, we focus on the question of whether large shifts in the redox state also necessarily require large perturbations to boundary conditions.Paleoredox reconstructions often adopt an implicitly linear perspective in their interpretation of the rock record, whereby small changes in external inputs will only cause small shifts, while large shifts in redox chemistry—such as switches between ferruginous and euxinic deep waters—necessitate major changes in external inputs. Here, in contrast, we demonstrate not only that natural anoxic systems may be subject to critical thresholds—so-called “tipping points”—but that alternative stable states exist with a hysteresis barrier to reversibility. Our analysis reveals that the redox chemistry of anoxic systems shows nonlinear dynamics, characterized by both strong resilience (large changes in the supply of iron oxides or organic carbon must not necessarily induce a shift in redox chemistry) as well as dramatic shifts near the tipping points. As a result, large and abrupt redox changes may occur in response to small and gradual changes in external forcing, without any significant change in Fe or S input fluxes. The existence of redox tipping points in the ocean interior could have important implications for the interpretation of Earth’s evolution.     

Mechanosensitive remodeling of the bacterial flagellar motor is independent of direction of rotation

Motility is important for the survival and dispersal of many bacteria, and it often plays a role during infections. Regulation of bacterial motility by chemical stimuli is well studied, but recent work has added a new dimension to the problem of motility control. The bidirectional flagellar motor of the bacterium Escherichia coli recruits or releases torque-generating units (stator units) in response to changes in load. Here, we show that this mechanosensitive remodeling of the flagellar motor is independent of direction of rotation. Remodeling rate constants in clockwise rotating motors and in counterclockwise rotating motors, measured previously, fall on the same curve if plotted against torque. Increased torque decreases the off rate of stator units from the motor, thereby increasing the number of active stator units at steady state. A simple mathematical model based on observed dynamics provides quantitative insight into the underlying molecular interactions. The torque-dependent remodeling mechanism represents a robust strategy to quickly regulate output (torque) in response to changes in demand (load).

Many bacteria swim through aqueous environments to acquire resources, to disperse progeny, and to infect hosts (1, 2). The rotation of flagella (3, 4), powered by the bidirectional flagellar motor (5–7), drives motility in many bacteria. In Escherichia coli, the flagellar motor consists of over 20 different proteins that self-assemble at the cell wall in varying copy numbers (8–10). Motor structure (Fig. 1A) includes a rotor embedded in the inner cell membrane, a drive shaft, and a flexible hook that transmits torque to the filament (10, 11). The cytoplasmic ring (C ring), which contains copies of the proteins FliG, FliM, and FliN, is mounted on the cytoplasmic face of the rotor and is responsible for directional switching of the motor (12). The rotor is driven by up to 11 ion-powered MotA5B2 stator units (13–16) that surround the rotor and generate torque. MotA engages FliG, whereas MotB is mounted on the rigid framework of the peptidoglycan cell wall (17–20). Motor-bound units exchange with a pool of unbound units in the inner membrane (10, 21).Open in a separate windowFig. 1.Bacterial flagellar motor’s structure and its T-S curve. (A) Schematic representation of the flagellar motor of Gram-negative bacteria. The rotor consists of the MS ring (M for membranous and S for supramembranous) embedded in the inner membrane (IM) and the C ring embedded in the cytoplasm. Stator units (MotA–MotB complexes) that span the inner membrane bind to the peptidoglycan (PG) layer and apply torque on the C ring. The torque is transmitted via a rod (driveshaft) and a flexible hook (universal joint) to the flagellar filament. L and P rings (L for lipopolysaccharide and P for peptidoglycan) are embedded in the outer membrane (OM) and the peptidoglycan, respectively, and act as bushings. Inset shows the outline of an E. coli cell with a square demarcating the region that is represented in detail. (B) T-S curve of the CCW (solid orange) and CW (dashed blue) rotating flagellar motors compared in this study. Data are from refs. 31 and 58. See Materials and Methods for details.Motor function is regulated by inputs from the environment. Detection of specific ligands by chemoreceptors drives a two-component signaling cascade that controls the direction of rotation of the motor (22–24). Upon binding the response regulator CheY-P, the C ring undergoes a concerted conformational change that reverses motor rotation from counterclockwise (CCW) to clockwise (CW), as viewed from outside the cell. This change in the direction of rotation is the basis of run-and-tumble motility in E. coli (CCW = run, CW = tumble). Changes in viscous load trigger remodeling of the stator (25–27), whereby, at high loads, the number of motor-bound stator units increases, and vice versa. Dynamics of stator remodeling have only been quantified in CCW rotating motors, using electrorotation (28) and magnetic tweezers (29, 30). The observed dynamics were rationalized using the CCW torque–speed (T-S) relationship (Fig. 1B) (28). CCW and CW rotating motors have different T-S relationships (Fig. 1B), likely due to differences in stator–rotor interactions (31–33). How the differences in T-S relationship affect stator remodeling in CW motors is unknown. Additionally, the molecular mechanisms underlying the load-dependent remodeling phenomenon remain poorly understood.Here, we use electrorotation to study the dynamics of load-dependent stator remodeling in CW rotating motors. We find that, just like CCW motors, CW rotating flagellar motors release their stator units when the motor torque is low, and recruit stator units when the torque increases again. The rates of stator unit release and recruitment in CW and CCW motors collapse onto a single curve when plotted against torque, despite their dissimilar T-S relationships. The collapse of remodeling data suggests a universal model for torque dependence in the mechanically regulated remodeling of the bacterial flagellar motor. Our in vivo measurements of stator assembly dynamics advance the understanding of a large protein complex with multiple parts.