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1. Integrated Construction of Multimodal Atlases with Structural Connectomes in the Space of Riemannian Metrics.

   Campbell, Kristen M.; Dai, Haocheng; Su, Zhe; Bauer, Martin; Fletcher, Thomas P.; Joshi, Sarang C. (July 2022, The journal of machine learning for biomedical imaging)

   The structural network of the brain, or structural connectome, can be represented by fiber bundles generated by a variety of tractography methods. While such methods give qualitative insights into brain structure, there is controversy over whether they can provide quantitative information, especially at the population level. In order to enable population-level statistical analysis of the structural connectome, we propose representing a connectome as a Riemannian metric, which is a point on an infinite-dimensional manifold. We equip this manifold with the Ebin metric, a natural metric structure for this space, to get a Riemannian manifold along with its associated geometric properties. We then use this Riemannian framework to apply object-oriented statistical analysis to define an atlas as the Fréchet mean of a population of Riemannian metrics. This formulation ties into the existing framework for diffeomorphic construction of image atlases, allowing us to construct a multimodal atlas by simultaneously integrating complementary white matter structure details from DWMRI and cortical details from T1-weighted MRI. We illustrate our framework with 2D data examples of connectome registration and atlas formation. Finally, we build an example 3D multimodal atlas using T1 images and connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project. 

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2. Topology-Based Lattice Engineering in Condensed Soft Matter

   https://doi.org/10.26434/chemrxiv-2025-r17k1  

   Horvath, Andrew; Woloszyn, Karol; Rizk, Joanna A; Wang, Mindy; Rueb, Joe; Perren, Lara; Jaffe, Mara; Mao, Chengde; Ohayon, Yoel P; Canary, James W; et al (June 2025, ACS)

   In this study, we investigate the topological adaptability and structural resilience of periodic soft matter entanglements using the DNA tensegrity triangle, a foundational motif in structural DNA nanotechnology, as a model system. By simulating the Reidemeister moves from knot theory, which describe a series of “moves” by which the knot equivalence is preserved, we demonstrate that many variants of the tensegrity triangle maintain their lattice geometry, underscoring the motif’s inherent topological robustness. Using granular deformations in a series of closely related motifs, we systematically twist the helices and slide their ends relative to junction crossings to yield 48 distinct crystal structures. Notably, we Identify a novel poke-DX feature (PDX), which introduces rigid crossover configurations with enhanced crystallographic resolution and site-specific metal ion coordination. Further exploration reveals the formation of semi-junctions – a new class of four-arm junctions held together by a single rotatable bond, which feature relaxed torsional strain and altered crossover geometries. These configurations support lattice transformations into tetragonal and distorted rhombohedral forms as well as facilitate topological inversion between left- and right- handed triangles. Altogether, these findings illustrate how controlled topological operations at the molecular level can tune local flexibility and stiffness at key sites to affect long-range lattice geometry. This work positions DNA-based frameworks as a programmable platform for the design of architected materials, topological metamaterials, and nanoscale devices with tunable structural and functional properties. 

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3. Altered topological structure of the brain white matter in maltreated children through topological data analysis

   https://doi.org/10.1162/netn_a_00355  

   Chung, Moo K.; Azizi, Tahmineh; Hanson, Jamie L.; Alexander, Andrew L.; Pollak, Seth D.; Davidson, Richard J. (April 2024, Network Neuroscience)

   Abstract Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging and diffusion tensor imaging. We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children with a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated. 

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4. Biotropic liquid crystal phase transformations in cellulose-producing bacterial communities

   https://doi.org/10.1073/pnas.2200930119  

   Repula, Andrii; Abraham, Eldho; Cherpak, Vladyslav; Smalyukh, Ivan I. (June 2022, Proceedings of the National Academy of Sciences)

   Biological functionality is often enabled by a fascinating variety of physical phenomena that emerge from orientational order of building blocks, a defining property of nematic liquid crystals that is also pervasive in nature. Out-of-equilibrium, “living” analogs of these technological materials are found in biological embodiments ranging from myelin sheath of neurons to extracellular matrices of bacterial biofilms and cuticles of beetles. However, physical underpinnings behind manifestations of orientational order in biological systems often remain unexplored. For example, while nematiclike birefringent domains of biofilms are found in many bacterial systems, the physics behind their formation is rarely known. Here, using cellulose-synthesizing Acetobacter xylinum bacteria, we reveal how biological activity leads to orientational ordering in fluid and gel analogs of these soft matter systems, both in water and on solid agar, with a topological defect found between the domains. Furthermore, the nutrient feeding direction plays a role like that of rubbing of confining surfaces in conventional liquid crystals, turning polydomain organization within the biofilms into a birefringent monocrystal-like order of both the extracellular matrix and the rod-like bacteria within it. We probe evolution of scalar orientational order parameters of cellulose nanofibers and bacteria associated with fluid-gel and isotropic-nematic transformations, showing how highly ordered active nematic fluids and gels evolve with time during biological-activity-driven, disorder-order transformation. With fluid and soft-gel nematics observed in a certain range of biological activity, this mesophase-exhibiting system is dubbed “biotropic,” analogously to thermotropic nematics that exhibit solely orientational order within a temperature range, promising technological and fundamental-science applications. 

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5. Soft matter roadmap

   https://doi.org/10.1088/2515-7639/ad06cc  

   Barrat, Jean-Louis; Del Gado, Emanuela; Egelhaaf, Stefan U; Mao, Xiaoming; Dijkstra, Marjolein; Pine, David J; Kumar, Sanat K; Bishop, Kyle; Gang, Oleg; Obermeyer, Allie; et al (December 2023, Journal of Physics: Materials)

   Soft materials are usually defined as materials made of mesoscopic entities, often self-organised, sensitive to thermal fluctuations and to weak perturbations. Archetypal examples are colloids, polymers, amphiphiles, liquid crystals, foams. The importance of soft materials in everyday commodity products, as well as in technological applications, is enormous, and controlling or improving their properties is the focus of many efforts. From a fundamental perspective, the possibility of manipulating soft material properties, by tuning interactions between constituents and by applying external perturbations, gives rise to an almost unlimited variety in physical properties. Together with the relative ease to observe and characterise them, this renders soft matter systems powerful model systems to investigate statistical physics phenomena, many of them relevant as well to hard condensed matter systems. Understanding the emerging properties from mesoscale constituents still poses enormous challenges, which have stimulated a wealth of new experimental approaches, including the synthesis of new systems with, e.g. tailored self-assembling properties, or novel experimental techniques in imaging, scattering or rheology. Theoretical and numerical methods, and coarse-grained models, have become central to predict physical properties of soft materials, while computational approaches that also use machine learning tools are playing a progressively major role in many investigations. This Roadmap intends to give a broad overview of recent and possible future activities in the field of soft materials, with experts covering various developments and challenges in material synthesis and characterisation, instrumental, simulation and theoretical methods as well as general concepts. 

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