Highlights of Max Planck Institute for the Physics of Complex Systems https://www.pks.mpg.de/ here are the highlights of Max Planck Institute for the Physics of Complex Systems en_GB Max Planck Institute for the Physics of Complex Systems Tue, 06 Dec 2022 07:22:22 +0100 Tue, 06 Dec 2022 07:22:22 +0100 TYPO3 EXT:news news-718 Mon, 28 Nov 2022 22:00:00 +0100 Scaling Description of Creep Flow in Amorphous Solids https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.208001 Amorphous solids, which include colloidal glasses, dense emulsions, foams, and granular materials, are ubiquitous and important in both engineering and industry. When subjected to a suddenly imposed stress, they can exhibit a transient flow known as creep during which the flow rate decays as a power law over time. This power law is characterized by a quantity called the creep exponent. If the stress inducing the creep flow is low, the material eventually stops moving. But if this stress is sufficiently high, the power-law decay can be followed by sudden fluidization. Together with colleagues from École polytechnique fédérale de Lausanne (EPFL) and Université Paris-Saclay, Marko Popović of the Max Planck Institute for Physics of Complex Systems developed a theory of creep flow that can predict both the creep exponent and the time at which sudden fluidization occurs, as well as the temperature dependence of these two quantities. These predictions have been tested in numerical simulations and are consistent with previously published experimental observations. The key ingredient of the proposed theory is the new concept of a transient yield stress, which reflects the dynamics of the maximal stress that the material could sustain without flowing while it undergoes creep flow. Remarkably, the scaling of the creep exponent and the time of fluidization then follow from generic properties of the transient yield stress for both athermal and thermal systems. The success of the transient yield stress concept opens new exciting questions: What is the origin of the transient yield stress and what controls its dynamics? Can the concept of a transient yield stress be employed to describe other characteristic behaviours associated with the yielding of amorphous solids, such as shear banding instabilities? Marko Popović, et al., Phys. Rev. Lett. 129, 208001 (2022), Editors' Suggestion Selected for a Synopsis in Physics Publication Highlights news-715 Tue, 18 Oct 2022 22:00:00 +0200 Fragmented Cooper Pair Condensation in Striped Superconductors https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.177001 The mechanism behind high-temperature superconductors has long been a great mystery to physicists. Even though the fundamental physical equations of interacting electrons in these materials are well-known, their solution has proved challenging. Whether or not superconductivity or the so-called "stripe order", where the density of electrons forms regular waves called "stripes", is realized has been an open question and these two states of matter have been considered in competition to one another. This study now shows that stripe order and superconductivity can, in fact, get along with one another quite well. By performing exact numerical simulations on a minimal model for cuprate superconductors, the author demonstrates that there exist states of matter with exactly one superconducting condensate per stripe. Since there are multiple stripes in the systems, there are also multiple condensates, a phenomenon called "fragmentation". The physical picture proposed in this study agrees well with experimental observations and demonstrates the predictive power of modern numerical techniques to study quantum many-body systems. A. Wietek, Phys. Rev. Lett. 129, 177001 (2022) Publication Highlights news-713 Thu, 29 Sep 2022 11:04:00 +0200 Call for Distinguished PKS Postdoctoral Fellowship 2023 now open! https://www.pks.mpg.de/fileadmin/user_upload/MPIPKS/Contact/Work_with_us/BMO-28026090-MPI-Physik-komplexer-Systeme_3_.pdf Application deadline: 17 November 2022. Distinguished PKS postdoctoral fellows appear personally along with the departments and groups on the main research page of the institute and are expected to have at least one year of postdoctoral experience at an institution other than the one at which their PhD was awarded. Applications for this fellowship directly after completion of the PhD might be considered in exceptional cases. Please click on the link- button to see the full advertisement!  

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Institute's News
news-712 Tue, 20 Sep 2022 22:00:00 +0200 Responsive switching between subpopulations can stabilise microbial communities https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.033224 The different microbial species in complex ecological communities like the human microbiome often have different subpopulations called phenotypes, between which they can switch stochastically or in response to environmental cues, such as toxins released by competitors or antibiotics. Pierre Haas of the Max Planck Institute for the Physics of Complex Systems and the Max Planck Institute of Molecular Cell Biology and Genetics and collaborators at the University of Cambridge have analysed the ecological implications of such responsive switching. They combined a statistical analysis of many-species systems, a numerical study of a minimal two-species model, and analytical results for still simpler mathematical models. While responsive switching to a rare phenotype is destabilising on average, they could show that responsive switching to a rare "attack" phenotype is stabilising on average. A similar "attack" subpopulation was recently observed experimentally, which underlines the importance of responsive switching for ecological stability. P. A. Haas, M. A. Gutierrez, N. M. Oliveira, and R. E. Goldstein, Phys. Rev. Research 4, 033224 (2022) Publication Highlights news-710 Fri, 02 Sep 2022 22:00:00 +0200 The rise to royalty; how paper wasps balance specialization and plasticity https://doi.org/10.1016/j.cels.2022.08.002 Biological systems fascinate scientists across disciplines because of the highly complex structures that emerge from these systems, from cells to organisms and societies. While biological systems fulfil highly specialised tasks despite noisy signals, they can also rapidly break up these structures and perform entirely different tasks when the right signals are present. A new study in Cell Systems published by Adolfo Alsina and Steffen Rulands from MPI-PKS, Wolf Reik from the Babraham Institute in Cambridge and Solenn Patalano from the BBSRC Alexander Fleming in Athens used paper wasps as a paradigmatic example. Paper wasps are social insects that display societal division of labor between workers and a queen. While this division of labor remains stable for the entire lifetime of the queen, when the queen is removed from the nest or dies the remaining workers can rapidly change their behavior and establish a new queen. Due to this behavior the paper wasps serve an experimental testing ground to study biological plasticity. Rulands and colleagues carried out a unique set of experiments in Panama where they removed the queen from paper wasp nests and then followed the reorganization process back to the intact society simultaneously on different scales of biological organization: from time-resolved profiling of brains using multi-omics of the brains to colony-level video recordings. Using theory, they showed that by balancing antagonistic molecular and colony-level processes these societies are able to distinguish between different kinds of perturbations affecting the nest: intrinsic perturbations, such as molecular noise, affect insects independently of each other and these perturbations are actively suppressed by the society. By contrast, extrinsic perturbations affect the entire society and the society reacts plasticly. Given the above, the authors conclude that by employing a self-organised multi-scale mechanism Polistes manages to overcome the seeming paradox between specialisation and plasticity. S. Patalano et al., Cell Systems 13, 1–12 (2022) Publication Highlights news-709 Thu, 01 Sep 2022 14:00:00 +0200 New Research Group: Nonequilibrium Quantum Dynamics https://www.pks.mpg.de/nqd The research in our new group "Nonequlibrium Quantum Dynamics" lies at the intersection of many-body dynamics, quantum simulation, quantum control, and applications of machine learning in physics. It is headed by Marin Bukov, who joins MPI-PKS from the University of Sofia. Marin and his coworkers are interested in problems of both fundamental nature and immediate applications. They develop approximate analytical methods, and design numerical techniques in order to investigate different problems in quantum dynamics, and collaborate with theory groups and experimental labs to test the theoretical predictions against experiment. Welcome to the institute, Marin!  

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Institute's News
news-708 Tue, 02 Aug 2022 22:00:00 +0200 The full spectrum of a quantum many-body system in one shot https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.066401 Quantum excited states underpin new states of matter, support biological processes such as vision, and determine opto-electronic properties of photovoltaic devices. Yet, while ground-state properties can be determined by rather accurate computational methods, there remains a need for theoretical and computational developments to target excited states efficiently. Inspired by the duplication of the Hilbert space used to study black-hole entanglement and the electronic pairing of conventional superconductivity, researchers from the Max Planck Institute for the Physics of Complex Systems and their collaborators from Munich and Modena have developed a new scheme to compute the full spectrum of a quantum many-body Hamiltonian, rather than only its ground or lowest-excited states. An important feature of their proposed scheme is that these spectra can be computed in a one-shot calculation. The scheme thus provides a novel variational platform to excited-state physics. It is also suitable for efficient implementation on quantum computers, so has the potential to enable unprecedented calculations of excited-state processes of quantum many-body systems. C. L. Benavides-Riveros et al., Phys. Rev. Lett. 129, 066401 (2022), Editors' Suggestion Publication Highlights news-707 Mon, 04 Jul 2022 22:00:00 +0200 Cells sense their way together https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.148101 Much like animals can trace odors, cells also move toward certain chemicals. In fact, cells often do this in groups, which can be up to millions of individuals strong. But how do these cell populations manage to move together as a cohesive unit while following chemical cues? New work by Ricard Alert of the Max Planck Institute for the Physics of Complex Systems and collaborators shows that the answer lies in limitations in the ability of cells to sense chemicals at high concentrations. Thus, the work bridges scales by connecting the sensing of tiny molecules by individual cells to the shape and motion of an entire cell population, which can be centimeters or even larger in size. The work is important because it reveals a potentially general principle: Sensing—a distinguishing feature of living systems—governs the ability of cells to migrate in groups. This principle could operate in many other examples of collective migration, as cells and other living creatures can sense and follow a variety of stimuli, such as electric fields, temperature, and light intensity. Finally, the new results open a tantalizing question for future work: Has evolution pushed the sensing limitations of cells to ensure that they can follow chemical cues as a cohesive group? (Image credit: Mariona Esquerda Ciutat.) R. Alert, A. Martínez-Calvo, and S. S. Datta, Phys. Rev. Lett. 128, 148101 (2022) Publication Highlights news-705 Wed, 22 Jun 2022 22:00:00 +0200 Anomalous dynamics and equilibration in the classical Heisenberg chain https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.L100403 The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Researchers at the Max Planck Institute for the Physics of Complex Systems studied one of the simplest classical interacting lattice models, the nearest-neighbour Heisenberg chain, with temperature as tuning parameter. Their numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where they observe strong evidence either of spin superdiffusion or an extremely slow crossover to diffusion. At low temperatures in the ferromagnet, they observe an extremely long-lived regime of remarkably clean Kardar-Parisi-Zhang (KPZ) scaling (see figure). The anomalous behaviour also governs the equilibration after a quench, and, remarkably, is apparent even at very high temperatures. A. J. McRoberts, T. Bilitewski, M. Haque, and R. Moessner, Phys. Rev. B 105, L100403 (2022) Publication Highlights news-704 Tue, 14 Jun 2022 22:00:00 +0200 Non-Markovian Quantum State Diffusion: Matrix-product-state approach to the hierarchy of pure states https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.L030202 An important but challenging task is to treat mesoscopic systems that are coupled to a complex environment at finite temperature. Alexander Eisfeld of the Max Planck Institute for the Physics of Complex Systems and his collaborators have derived a stochastic hierarchy of matrix product states (HOMPS) for non-Markovian dynamics, which is numerically exact and efficient. In this way the exponential complexity of the problem can be reduced to scale polynomially with the number of particles and modes of the environment. An additional feature caused by the stochastic noise is that individual trajectories stay well localized. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment. X. Gao, J. Ren, A. Eisfeld, and Z. Shuai, Phys. Rev. A 105, L030202 (2022) Publication Highlights news-703 Mon, 13 Jun 2022 18:00:00 +0200 New Research Group: Dynamics of quantum information https://www.pks.mpg.de/research/divisions-and-groups A warm welcome to Pieter Claeys! Coming to our institute from the University of Cambridge, Pieter establishes the research group "Dynamics of quantum information". The group’s research lies at the interface of condensed matter physics and quantum information, using a variety of theoretical and numerical approaches to study the dynamics of quantum many-body systems. Research topics include the dynamics of entanglement, quantum chaos and thermalization, unitary circuit models, and general aspects of non-equilibrium quantum dynamics. The group will also focus on bridging recent advances in the dynamics of quantum systems and quantum computation.  

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Institute's News
news-702 Tue, 07 Jun 2022 11:49:47 +0200 "Physik-Preis Dresden 2022" awarded to Professor Tomaž Prosen On May 24, 2022, Prof. Tomaž Prosen from the University of Ljubljana in Slovenia received the "Physik-Preis Dresden" (Dresden Physics Prize), jointly awarded by the TU Dresden and the Max Planck Institute for the Physics of Complex Systems (MPI-PKS). The theoretical physicist receives the award for his outstanding work on quantum mechanical many-body systems, nonequilibrium statistical physics, quantum information, classical chaos and quantum chaos. Tomaž Prosen has authored over 200 publications on this broad range of topics, which have over 7000 citations and are recognized in expert circles worldwide. In 2016, he received a prestigious ERC Advanced Grant. The award ceremony took place at a festive colloquium in the Recknagel Building of the TU Dresden, preceded by a reception. Prof. Carsten Timm, Dean of the Faculty of Physics, gave the welcome address, and Prof. Roderich Moessner of MPI-PKS delivered the laudation. The Physik-Preis Dresden was endowed in 2015 by Dresden physicist Prof. Peter Fulde, the founding director of the MPI-PKS. The prize winners are determined by a joint commission of the TU Dresden and the MPI-PKS. In addition to the central criterion of scientific excellence, it is particularly important for the decision that the work of the award winners is of special significance for the cooperation between the two DRESDEN-concept partners MPI-PKS and TU Dresden and that their connection has been further strengthened in the long term. The 2022 awardee, Prof. Tomaž Prosen, has a wide range of connections to the professorships at the Institute for Theoretical Physics at TU Dresden and at MPI-PKS due to his broad scientific orientation. On May 24, 2022, Prof. Tomaž Prosen from the University of Ljubljana in Slovenia received the "Physik-Preis Dresden" (Dresden Physics Prize), jointly awarded by the TU Dresden and the Max Planck Institute for the Physics of Complex Systems (MPI-PKS). The theoretical physicist receives the award for his outstanding work on quantum mechanical many-body systems, nonequilibrium statistical physics, quantum information, classical chaos and quantum chaos.

Tomaž Prosen has authored over 200 publications on this broad range of topics, which have over 7000 citations and are recognized in expert circles worldwide. In 2016, he received a prestigious ERC Advanced Grant. The award ceremony took place at a festive colloquium in the Recknagel Building of the TU Dresden, preceded by a reception. Prof. Carsten Timm, Dean of the Faculty of Physics, gave the welcome address, and Prof. Roderich Moessner of MPI-PKS delivered the laudation.

The Physik-Preis Dresden was endowed in 2015 by Dresden physicist Prof. Peter Fulde, the founding director of the MPI-PKS. The prize winners are determined by a joint commission of the TU Dresden and the MPI-PKS. In addition to the central criterion of scientific excellence, it is particularly important for the decision that the work of the award winners is of special significance for the cooperation between the two DRESDEN-concept partners MPI-PKS and TU Dresden and that their connection has been further strengthened in the long term. The 2022 awardee, Prof. Tomaž Prosen, has a wide range of connections to the professorships at the Institute for Theoretical Physics at TU Dresden and at MPI-PKS due to his broad scientific orientation.

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Awards and Honors
news-700 Wed, 25 May 2022 11:00:00 +0200 Left-right symmetry of zebrafish embryos requires surface tension https://www.nature.com/articles/s41586-022-04646-9 Bilateral symmetry of the vertebrate musculoskeletal system is necessary for proper function and its defects are associated with debilitating conditions, such as scoliosis. In a collaboration with biologists from the École polytechnique fédérale de Lausanne (EPFL) in Switzerland, Marko Popović of the Max Planck Institute for Physics of Complex Systems has studied the early stage of body segmentation using zebrafish as a model organism. They discovered that biochemical signalling and transcriptional processes that drive segmentation are not sufficient to explain the precision and symmetry of tissue shapes and sizes. However, they found that surface tension forces of the newly formed segments are a crucial component of the mechanism that is responsible for recovery and maintenance of the symmetric body plan. This discovery highlights the importance of physical interactions for precise and robust development of living beings. S. R. Naganthan, M. Popovic, and A. C. Oates, Nature 605, 516-521 (2022) Publication Highlights news-698 Thu, 05 May 2022 18:00:00 +0200 New Research Group: Transport and flows in complex environments https://www.pks.mpg.de/tfce We cordially welcome Christina Kurzthaler at the institute! Christina joins MPI-PKS from Princeton University and establishes the research group "Transport and flows in complex environments“. The group aims to unravel physical phenomena arising in soft and active matter, with emphasis on the role of transport and flows for biological systems and microfluidics. Its research topics range from the hydrodynamics of swimming bacteria and their interactions with their environments to the statistical physics of active transport in porous materials to the motion of colloidal suspensions in microfluidic settings. While the group's work is theoretical, it seeks to establish collaborations with experimentalists of the Dresden research community.  

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Institute's News
news-697 Mon, 18 Apr 2022 11:00:00 +0200 Novel quantum phases of droplets https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.103201 Attractive forces are ubiquitous in nature: they glue very different objects ranging from atomic nuclei, droplets of water, to stars, galaxies, and black holes. Peter Karpov and Francesco Piazza of the Max Planck Institute for the Physics of Complex Systems have now demonstrated that highly tuneable attractive interactions can be engineered artificially using optical cavities, leading to various novel phases of quantum droplets of ultracold atoms. Upon tuning the cavity-mediated interactions it is possible to switch between superfluid droplets and incompressible water-like droplets, as well as to realise crystalline and even more exotic supersolid droplets combining superfluid and solid properties. P. Karpov and F. Piazza, Phys. Rev. Lett. 128, 103201 (2022) Publication Highlights news-696 Wed, 30 Mar 2022 11:00:00 +0200 Molecular Assembly Lines in Active Droplets https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.108102 A fundamental question in biology is how complexes of several molecules can assemble reliably. Tyler Harmon and Frank Jülicher of the Max Planck Institute for the Physics of Complex Systems have now shown that a molecular assembly line can be self-organized by active droplets where it can form spontaneously. This assembly line arranges different assembly steps spatially so that a specific order of assembly is achieved and incorrect assembly is suppressed. They have shown how assembly bands are positioned and controlled and discuss the rate and fidelity of assembly as compared to other assembly scenarios. T. S. Harmon and F. Jülicher, Phys. Rev. Lett. 128, 108102 (2022) Publication Highlights news-695 Thu, 17 Mar 2022 12:05:00 +0100 Funding to understand emergent physical properties of chromatin using synthetic nuclei https://erc.europa.eu/news/erc-2021-consolidator-grants-results ERC Consolidator Grant for Jan Brugués Today, the European Research Council (ERC) announced the winners of its latest  Consolidator Grant competition for ambitious mid-career researchers. Jan Brugués, research group leader both at the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG) and the Max Planck Institute for the Physics of Complex Systems (MPI-PKS) is one of the 313 laureates who were awarded the 2022 ERC Consolidator Grants. The funding is part of the EU’s Horizon Europe programme, and the winners will receive in total 632 million Euros to tackle big scientific questions. In total, 2,652 applicants submitted proposals and 12% of them will receive the funding. Male and female applicants were equally successful in winning the grants. The future grantees will carry out their projects at universities and research centers across 24 EU Member States and associated countries. This new round of grants will create an estimated 1,900 jobs for postdoctoral fellows, PhD students and other staff at 189 host institutions. Jan receives the grant for his project “Understanding emergent physical properties of chromatin using synthetic nuclei.” The main goal of this project is to resolve how the physics of molecular-scale activities result in the material properties of chromatin and how those contribute to chromatin organization and function. Jan Brugués explains: “With my project, I hope to provide a physical description of the material state of chromatin across different scales and contribute to reveal the basic physical principles that govern nuclear organization and function.” Congratulations Jan!  

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Awards and Honors
news-694 Wed, 16 Mar 2022 11:00:00 +0100 Dirac Magnons, Nodal Lines, and Nodal Plane in Elemental Gadolinium https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.097201 The exploration of band topology in crystalline solids has been at the forefront of condensed matter physics for many years in efforts tying together theoretical physics, materials science and powerful spectroscopic techniques. One relatively new avenue is the exploration of band topology in the spin wave, or magnon, excitations of magnetic materials. Spin wave topology is connected to novel magnetic transport properties, little explored symmetries and surface magnetism and offers a new platform to study interactions. One of the main current directions is to find new materials with topologically interesting band structures and this new study does exactly this by establishing the existence of Dirac nodal lines and a nodal plane in the magnons of elemental gadolinium. Gadolinium is a hexagonal closed packed magnetic metal in which, at around room temperature, the magnetic moments order into a simple ferromagnetic structure. In this new study, a team of experimentalists at Oakridge National Lab in the US together with theory collaborators explored the magnetic excitations of gadolinium in the ordered phase in unprecedented detail using inelastic neutron scattering. They found that gadolinium hosts Dirac magnons in the form of nodal lines extending along the zone corners. The existence of the nodal lines can be seen to arise from the presence of combined spin rotation and crystalline symmetries providing a first experimental example of the importance of such symmetries for band topology. In the vicinity of the nodal lines, the neutron scattering intensity can be seen to wind around the lines from strong to weak and in antiphase between the two bands (as shown in the figure). This intensity signature is a robust prediction connected to the nontrivial topology of these points. From the existence of the nodal lines one may infer the existence of magnon surface states $-$ a challenging target for future experiments. Furthermore, the nonsymmorphic crystal symmetries together with spin rotation enforce the presence of a degenerate plane of magnon excitations. Just as the nodal lines exhibit winding of the neutron intensity in their vicinity, the nodal plane is linked to a sharp flip in the intensity on paths crossing through the plane. Both the nodal plane and the intensity jump are clearly observed in the data. Phys. Rev. Lett. 128, 097201 (2022) Publication Highlights news-693 Mon, 07 Mar 2022 11:04:00 +0100 Emergency Fellowships for Scientists in Ukraine https://www.pks.mpg.de/work-with-us We offer Emergency Fellowships to researchers at all career stages in Ukraine. Applications are considered continuously.  

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Institute's News
news-692 Mon, 14 Feb 2022 17:00:00 +0100 Flowing by gelating - gelation enables the correct architecture of the mitotic spindle. https://www.nature.com/articles/s41567-021-01467-x In the cell, the mitotic spindle is a structure that forms during cell division and segregates the chromosomes into the two future daughter cells. Spindles are made of dynamic filaments called microtubules that are continuously transported towards the two opposite poles of the spindle by molecular motors. However, scientists still do not understand how these poleward flows are generated and how they lead to spindle self-organization. Researchers in the group led by Jan Brugués at the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG), the Max Planck Institute for the Physics of Complex Systems (MPI-PKS) and the Center for Systems Biology Dresden (CSBD), worked together with Frank Jülicher’s research group at the MPI-PKS to understand how such poleward flows are generated in spindles. In 2018, the Brugués lab was able to show that the size of spindles is controlled by microtubule branching: In the vicinity of DNA, new microtubules branch off from mother microtubules like branches in a tree. However, such a branching process naturally leads to microtubules branching outwards from chromosomes, whereas in real spindles they branch inwards to interact with chromosomes during segregation. In the current study, published in the journal Nature Physics, the scientists combined in vitro experiments with physical models to show that the poleward flows together with a gelation process driven by motor crosslinking, allows for the correct microtubule inward branching observed in spindles. Benjamin Dalton an author in the study, explains, “The spindle is a highly dynamic structure where its building blocks are constantly created, transported and destroyed within seconds. Still, the spindle can survive for as long as an hour and the microtubule flows are remarkably constant throughout the structure. It’s difficult to reconcile these things.” David Oriola, another author in the study explains, “By tracking the movement of single microtubules using fluorescent microscopy, we found that the spindle did not behave as a simple fluid, but rather as a gel.” Combining large-scale simulations with experimental data, the researchers found that gelation is necessary for the generation of the poleward flows, and in turn, such flows are in charge of organizing the microtubule network such that microtubules point inwards rather than outwards. Dalton et al.: A gelation transition enables the self-organization of bipolar metaphase spindles. Nature Physics, 10 February 2022, doi: 10.1038/s41567-021-01467-x Publication Highlights