Mapping transcriptomic vector fields of single cells.

Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. Fully exploiting these data, however, requires kinetic models capable of unveiling governing regulatory functions. Here, we introduce an analytical framework dynamo (https://github.com/aristoteleo/dynamo-release), which infers absolute RNA velocity, reconstructs continuous vector fields that predict cell fates, employs differential geometry to extract underlying regulations, and ultimately predicts optimal reprogramming paths and perturbation outcomes. We highlight dynamo's power to overcome fundamental limitations of conventional splicing-based RNA velocity analyses to enable accurate velocity estimations on a metabolically labeled human hematopoiesis scRNA-seq dataset. Furthermore, differential geometry analyses reveal mechanisms driving early megakaryocyte appearance and elucidate asymmetrical regulation within the PU.1-GATA1 circuit. Leveraging the least-action-path method, dynamo accurately predicts drivers of numerous hematopoietic transitions. Finally, in silico perturbations predict cell-fate diversions induced by gene perturbations. Dynamo, thus, represents an important step in advancing quantitative and predictive theories of cell-state transitions.

Representational geometry of perceptual decisions in the monkey parietal cortex.

Lateral intraparietal (LIP) neurons represent formation of perceptual decisions involving eye movements. In circuit models for these decisions, neural ensembles that encode actions compete to form decisions. Consequently, representation and readout of the decision variables (DVs) are implemented similarly for decisions with identical competing actions, irrespective of input and task context differences. Further, DVs are encoded as partially potentiated action plans through balance of activity of action-selective ensembles. Here, we test those core principles. We show that in a novel face-discrimination task, LIP firing rates decrease with supporting evidence, contrary to conventional motion-discrimination tasks. These opposite response patterns arise from similar mechanisms in which decisions form along curved population-response manifolds misaligned with action representations. These manifolds rotate in state space based on context, indicating distinct optimal readouts for different tasks. We show similar manifolds in lateral and medial prefrontal cortices, suggesting similar representational geometry across decision-making circuits.

The Geometry of Abstraction in the Hippocampus and Prefrontal Cortex.

The curse of dimensionality plagues models of reinforcement learning and decision making. The process of abstraction solves this by constructing variables describing features shared by different instances, reducing dimensionality and enabling generalization in novel situations. Here, we characterized neural representations in monkeys performing a task described by different hidden and explicit variables. Abstraction was defined operationally using the generalization performance of neural decoders across task conditions not used for training, which requires a particular geometry of neural representations. Neural ensembles in prefrontal cortex, hippocampus, and simulated neural networks simultaneously represented multiple variables in a geometry reflecting abstraction but that still allowed a linear classifier to decode a large number of other variables (high shattering dimensionality). Furthermore, this geometry changed in relation to task events and performance. These findings elucidate how the brain and artificial systems represent variables in an abstract format while preserving the advantages conferred by high shattering dimensionality.

Linking Genes to Shape in Plants Using Morphometrics.

A transition from qualitative to quantitative descriptors of morphology has been facilitated through the growing field of morphometrics, representing the conversion of shapes and patterns into numbers. The analysis of plant form at the macromorphological scale using morphometric approaches quantifies what is commonly referred to as a phenotype. Quantitative phenotypic analysis of individuals with contrasting genotypes in turn provides a means to establish links between genes and shapes. The path from a gene to a morphological phenotype is, however, not direct, with instructive information progressing both across multiple scales of biological complexity and through nonintuitive feedback, such as mechanical signals. In this review, we explore morphometric approaches used to perform whole-plant phenotyping and quantitative approaches in capture processes in the mesoscales, which bridge the gaps between genes and shapes in plants. Quantitative frameworks involving both the computational simulation and the discretization of data into networks provide a putative path to predicting emergent shape from underlying genetic programs.

Cardiomyocyte orientation recovery at micrometer scale reveals long-axis fiber continuum in heart walls.

Coordinated cardiomyocyte contraction drives the mammalian heart to beat and circulate blood. No consensus model of cardiomyocyte geometrical arrangement exists, due to the limited spatial resolution of whole heart imaging methods and the piecemeal nature of studies based on histological sections. By combining microscopy and computer vision, we produced the first-ever three-dimensional cardiomyocyte orientation reconstruction across mouse ventricular walls at the micrometer scale, representing a gain of three orders of magnitude in spatial resolution. We recovered a cardiomyocyte arrangement aligned to the long-axis direction of the outer ventricular walls. This cellular network lies in a thin shell and forms a continuum with longitudinally arranged cardiomyocytes in the inner walls, with a complex geometry at the apex. Our reconstruction methods can be applied at fine spatial scales to further understanding of heart wall electrical function and mechanics, and set the stage for the study of micron-scale fiber remodeling in heart disease.

Spontaneous eye movements reflect the representational geometries of conceptual spaces.

Functional neuroimaging studies indicate that the human brain can represent concepts and their relational structure in memory using coding schemes typical of spatial navigation. However, whether we can read out the internal representational geometries of conceptual spaces solely from human behavior remains unclear. Here, we report that the relational structure between concepts in memory might be reflected in spontaneous eye movements during verbal fluency tasks: When we asked participants to randomly generate numbers, their eye movements correlated with distances along the left-to-right one-dimensional geometry of the number space (mental number line), while they scaled with distance along the ring-like two-dimensional geometry of the color space (color wheel) when they randomly generated color names. Moreover, when participants randomly produced animal names, eye movements correlated with low-dimensional similarity in word frequencies. These results suggest that the representational geometries used to internally organize conceptual spaces might be read out from gaze behavior.

A transient radial cortical microtubule array primes cell division in Arabidopsis.

Although the formation of new walls during plant cell division tends to follow maximal tensile stress direction, analyses of individual cells over time reveal a much more variable behavior. The origin of such variability as well as the exact role of interphasic microtubule behavior before cell division have remained mysterious so far. To approach this question, we took advantage of the Arabidopsis stem, where the tensile stress pattern is both highly anisotropic and stable. Although cortical microtubules (CMTs) generally align with maximal tensile stress, we detected a specific time window, ca. 3 h before cell division, where cells form a radial pattern of CMTs. This microtubule array organization preceded preprophase band (PPB) formation, a transient CMT array predicting the position of the future division plane. It was observed under different growth conditions and was not related to cell geometry or polar auxin transport. Interestingly, this cortical radial pattern correlated with the well-documented increase of cytoplasmic microtubule accumulation before cell division. This radial organization was prolonged in cells of the trm678 mutant, where CMTs are unable to form a PPB. Whereas division plane orientation in trm678 is noisier, we found that cell division symmetry was in contrast less variable between daughter cells. We propose that this "radial step" reflects a trade-off in robustness for two essential cell division attributes: symmetry and orientation. This involves a "reset" stage in G2, where an increased cytoplasmic microtubule accumulation transiently disrupts CMT alignment with tissue stress.

Unraveling the mesoscale organization induced by network-driven processes.

Complex systems are characterized by emergent patterns created by the nontrivial interplay between dynamical processes and the networks of interactions on which these processes unfold. Topological or dynamical descriptors alone are not enough to fully embrace this interplay in all its complexity, and many times one has to resort to dynamics-specific approaches that limit a comprehension of general principles. To address this challenge, we employ a metric-that we name Jacobian distance-which captures the spatiotemporal spreading of perturbations, enabling us to uncover the latent geometry inherent in network-driven processes. We compute the Jacobian distance for a broad set of nonlinear dynamical models on synthetic and real-world networks of high interest for applications from biological to ecological and social contexts. We show, analytically and computationally, that the process-driven latent geometry of a complex network is sensitive to both the specific features of the dynamics and the topological properties of the network. This translates into potential mismatches between the functional and the topological mesoscale organization, which we explain by means of the spectrum of the Jacobian matrix. Finally, we demonstrate that the Jacobian distance offers a clear advantage with respect to traditional methods when studying human brain networks. In particular, we show that it outperforms classical network communication models in explaining functional communities from structural data, therefore highlighting its potential in linking structure and function in the brain.

The training process of many deep networks explores the same low-dimensional manifold.

We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks with different architectures follow distinguishable trajectories, but other factors have a minimal influence; larger networks train along a similar manifold as that of smaller networks, just faster; and networks initialized at very different parts of the prediction space converge to the solution along a similar manifold.

Large nonlinear optical magnetoelectric response in a noncentrosymmetric magnetic Weyl semimetal.

Weyl semimetals resulting from either inversion (P) or time-reversal (T) symmetry breaking have been revealed to show the record-breaking large optical response due to intense Berry curvature of Weyl-node pairs. Different classes of Weyl semimetals with both P and T symmetry breaking potentially exhibit optical magnetoelectric (ME) responses, which are essentially distinct from the previously observed optical responses in conventional Weyl semimetals, leading to the versatile functions such as directional dependence for light propagation and gyrotropic effects. However, such optical ME phenomena of (semi)metallic systems have remained elusive so far. Here, we show the large nonlinear optical ME response in noncentrosymmetric magnetic Weyl semimetal PrAlGe, in which the polar structural asymmetry and ferromagnetic ordering break P and T symmetry. We observe the giant second harmonic generation (SHG) arising from the P symmetry breaking in the paramagnetic phase, being comparable to the largest SHG response reported in Weyl semimetal TaAs. In the ferromagnetically ordered phase, it is found that interference between this nonmagnetic SHG and the magnetically induced SHG emerging due to both P and T symmetry breaking results in the magnetic field switching of SHG intensity. Furthermore, such an interference effect critically depends on the light-propagating direction. The corresponding magnetically induced nonlinear susceptibility is significantly larger than the prototypical ME material, manifesting the existence of the strong nonlinear dynamical ME coupling. The present findings establish the unique optical functionality of P- and T-symmetry broken ME topological semimetals.

Exotic self-assembly of hard spheres in a morphometric solvent.

The self-assembly of spheres into geometric structures, under various theoretical conditions, offers valuable insights into complex self-assembly processes in soft systems. Previous studies have utilized pair potentials between spheres to assemble maximum contact clusters in simulations and experiments. The morphometric approach to solvation free energy that we utilize here goes beyond pair potentials; it is a geometry-based theory that incorporates a weighted combination of geometric measures over the solvent accessible surface for solute configurations in a solvent. In this paper, we demonstrate that employing the morphometric model of solvation free energy in simulating the self-assembly of sphere clusters results, under most conditions, in the previously observed maximum contact clusters. Under other conditions, it unveils an assortment of extraordinary sphere configurations, such as double helices and rhombohedra. These exotic structures arise specifically under conditions where the interactions take multibody potentials into account. This investigation establishes a foundation for comprehending the diverse range of geometric forms in self-assembled structures, emphasizing the significance of the morphometric approach in this context.

Theory of topological exciton insulators and condensates in flat Chern bands.

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.

The length and spacing of river tributaries.

River networks are composed of a mainstem and tributaries. These tributaries dissect landscapes, regulate water and habitat availability, and transport sediment and nutrients. Despite the importance of tributaries, we currently lack theory and data describing whether and how tributary length and spacing varies within watersheds, thereby limiting our ability to accurately describe river network geometry. We address this knowledge gap by analyzing 4,696 tributaries across six landscapes with varying climate, tectonic setting, and lithology. Our results show that both tributary length and spacing systematically increase with downstream distance along the mainstem river, following a power-law scaling. This power-law scaling can be modulated by basin shape, with tributaries becoming shorter and, in some cases, more closely spaced as basin elongate. Furthermore, the power-law scaling may break down in cases where river networks have been disturbed by pervasive faulting, raising the possibility that the scaling we observe is not unique to all branching networks, and instead may be universal across undisturbed fluvial networks. These findings can be used to improve predictions of river network geometry and potentially to distinguish fluvial river networks from other branching networks.

Geometry of focal conics in sessile cholesteric droplets.

Focal conic domains are defects characteristic of layered liquid crystal phases. Their association can build flowers where petals are the ellipses of the Dupin cyclides involved in these defects. We report here the observation of focal conic flowers in cholesteric droplets sessile on a glass surface and surrounded by glycerol. The observation of the droplets in different directions helps to solve the three dimensional architecture of the flower. The effects of the droplet size and of the pitch value are also reported.

Subspace partitioning in the human prefrontal cortex resolves cognitive interference.

The human prefrontal cortex (PFC) constitutes the structural basis underlying flexible cognitive control, where mixed-selective neural populations encode multiple task features to guide subsequent behavior. The mechanisms by which the brain simultaneously encodes multiple task-relevant variables while minimizing interference from task-irrelevant features remain unknown. Leveraging intracranial recordings from the human PFC, we first demonstrate that competition between coexisting representations of past and present task variables incurs a behavioral switch cost. Our results reveal that this interference between past and present states in the PFC is resolved through coding partitioning into distinct low-dimensional neural states; thereby strongly attenuating behavioral switch costs. In sum, these findings uncover a fundamental coding mechanism that constitutes a central building block of flexible cognitive control.

Curvature gradient drives polarized tissue flow in the Drosophila embryo.

Tissue flow during morphogenesis is commonly driven by local constriction of cell cortices, which is caused by the activation of actomyosin contractility. This can lead to long-range flows due to tissue viscosity. However, in the absence of cell-intrinsic polarized forces or polarity in forces external to the tissue, these flows must be symmetric and centered around the region of contraction. Polarized tissue flows have been previously demonstrated to arise from the coupling of such contractile flows to points of increased friction or adhesion to external structures. However, we show with experiments and modeling that the onset of polarized tissue flow in early Drosophila morphogenesis occurs independent of adhesion and is instead driven by a geometric coupling of apical actomyosin contractility to tissue curvature. Particularly, the onset of polarized flow is driven by a mismatch between the position of apical myosin activation and the position of peak curvature at the posterior pole of the embryo. Our work demonstrates how genetic and geometric information inherited from the mother interact to create polarized flow during embryo morphogenesis.

A tropical geometric approach to exceptional points.

Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. Tropical geometry is an emerging field of mathematics at the interface between algebraic geometry and polyhedral geometry, with diverse applications to science. Here, we introduce and develop a unified tropical geometric framework to characterize different facets of non-Hermitian systems. We illustrate the versatility of our approach using several examples and demonstrate that it can be used to select from a spectrum of higher-order EPs in gain and loss models, predict the skin effect in the non-Hermitian Su-Schrieffer-Heeger model, and extract universal properties in the presence of disorder in the Hatano-Nelson model. Our work puts forth a framework for studying non-Hermitian physics and unveils a connection of tropical geometry to this field.

GRAS transcription factors regulate cell division planes in moss overriding the default rule.

Plant cells are surrounded by a cell wall and do not migrate, which makes the regulation of cell division orientation crucial for development. Regulatory mechanisms controlling cell division orientation may have contributed to the evolution of body organization in land plants. The GRAS family of transcription factors was transferred horizontally from soil bacteria to an algal common ancestor of land plants. SHORTROOT (SHR) and SCARECROW (SCR) genes in this family regulate formative periclinal cell divisions in the roots of flowering plants, but their roles in nonflowering plants and their evolution have not been studied in relation to body organization. Here, we show that SHR cell autonomously inhibits formative periclinal cell divisions indispensable for leaf vein formation in the moss Physcomitrium patens, and SHR expression is positively and negatively regulated by SCR and the GRAS member LATERAL SUPPRESSOR, respectively. While precursor cells of a leaf vein lacking SHR usually follow the geometry rule of dividing along the division plane with the minimum surface area, SHR overrides this rule and forces cells to divide nonpericlinally. Together, these results imply that these bacterially derived GRAS transcription factors were involved in the establishment of the genetic regulatory networks modulating cell division orientation in the common ancestor of land plants and were later adapted to function in flowering plant and moss lineages for their specific body organizations.

Critical amino acid residues regulating TRPA1 Zn2+ response: A comparative study across species.

Cellular zinc ions (Zn2+) are crucial for signal transduction in various cell types. The transient receptor potential (TRP) ankyrin 1 (TRPA1) channel, known for its sensitivity to intracellular Zn2+ ([Zn2+]i), has been a subject of limited understanding regarding its molecular mechanism. Here, we used metal ion-affinity prediction, three-dimensional structural modeling, and mutagenesis, utilizing data from the Protein Data Bank and AlphaFold database, to elucidate the [Zn2+]i binding domain (IZD) structure composed by specific AAs residues in human (hTRPA1) and chicken TRPA1 (gTRPA1). External Zn2+ induced activation in hTRPA1, while not in gTRPA1. Moreover, external Zn2+ elevated [Zn2+]i specifically in hTRPA1. Notably, both hTRPA1 and gTRPA1 exhibited inherent sensitivity to [Zn2+]i, as evidenced by their activation upon internal Zn2+ application. The critical AAs within IZDs, specifically histidine at 983/984, lysine at 711/717, tyrosine at 714/720, and glutamate at 987/988 in IZD1, and H983/H984, tryptophan at 710/716, E854/E855, and glutamine at 979/980 in IZD2, were identified in hTRPA1/gTRPA1. Furthermore, mutations, such as the substitution of arginine at 919 (R919) to H919, abrogated the response to external Zn2+ in hTRPA1. Among single-nucleotide polymorphisms (SNPs) at Y714 and a triple SNP at R919 in hTRPA1, we revealed that the Zn2+ responses were attenuated in mutants carrying the Y714 and R919 substitution to asparagine and proline, respectively. Overall, this study unveils the intrinsic sensitivity of hTRPA1 and gTRPA1 to [Zn2+]i mediated through IZDs. Furthermore, our findings suggest that specific SNP mutations can alter the responsiveness of hTRPA1 to extracellular and intracellular Zn2+.

GAABind: a geometry-aware attention-based network for accurate protein-ligand binding pose and binding affinity prediction.

Protein-ligand interactions are increasingly profiled at high-throughput, playing a vital role in lead compound discovery and drug optimization. Accurate prediction of binding pose and binding affinity constitutes a pivotal challenge in advancing our computational understanding of protein-ligand interactions. However, inherent limitations still exist, including high computational cost for conformational search sampling in traditional molecular docking tools, and the unsatisfactory molecular representation learning and intermolecular interaction modeling in deep learning-based methods. Here we propose a geometry-aware attention-based deep learning model, GAABind, which effectively predicts the pocket-ligand binding pose and binding affinity within a multi-task learning framework. Specifically, GAABind comprehensively captures the geometric and topological properties of both binding pockets and ligands, and employs expressive molecular representation learning to model intramolecular interactions. Moreover, GAABind proficiently learns the intermolecular many-body interactions and simulates the dynamic conformational adaptations of the ligand during its interaction with the protein through meticulously designed networks. We trained GAABind on the PDBbindv2020 and evaluated it on the CASF2016 dataset; the results indicate that GAABind achieves state-of-the-art performance in binding pose prediction and shows comparable binding affinity prediction performance. Notably, GAABind achieves a success rate of 82.8% in binding pose prediction, and the Pearson correlation between predicted and experimental binding affinities reaches up to 0.803. Additionally, we assessed GAABind's performance on the severe acute respiratory syndrome coronavirus 2 main protease cross-docking dataset. In this evaluation, GAABind demonstrates a notable success rate of 76.5% in binding pose prediction and achieves the highest Pearson correlation coefficient in binding affinity prediction compared with all baseline methods.