1
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Chew YH, Spill F. Discretised Flux Balance Analysis for Reaction-Diffusion Simulation of Single-Cell Metabolism. Bull Math Biol 2024; 86:39. [PMID: 38448618 DOI: 10.1007/s11538-024-01264-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Accepted: 01/29/2024] [Indexed: 03/08/2024]
Abstract
Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur. Conventional flux balance analysis (FBA), a method based on linear programming that is commonly used to model metabolism, implicitly assumes that all enzymatic reactions are not diffusion-limited though that may not always be the case. In this work, we have developed a spatial method that implements FBA on a grid-based system, to enable the exploration of diffusion effects on metabolism. Specifically, the method discretises a living cell into a two-dimensional grid, represents the metabolic reactions in each grid element as well as the diffusion of metabolites to and from neighbouring elements, and simulates the system as a single linear programming problem. We varied the number of rows and columns in the grid to simulate different cell shapes, and the method was able to capture diffusion effects at different shapes. We then used the method to simulate heterogeneous enzyme distribution, which suggested a theoretical effect on variability at the population level. We propose the use of this method, and its future extensions, to explore how spatiotemporal organisation of sub-cellular compartments and the molecules within could affect cell behaviour.
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Affiliation(s)
- Yin Hoon Chew
- School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, England, UK.
| | - Fabian Spill
- School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, England, UK
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2
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Kohyama S, Frohn BP, Babl L, Schwille P. Machine learning-aided design and screening of an emergent protein function in synthetic cells. Nat Commun 2024; 15:2010. [PMID: 38443351 PMCID: PMC10914801 DOI: 10.1038/s41467-024-46203-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Accepted: 02/16/2024] [Indexed: 03/07/2024] Open
Abstract
Recently, utilization of Machine Learning (ML) has led to astonishing progress in computational protein design, bringing into reach the targeted engineering of proteins for industrial and biomedical applications. However, the design of proteins for emergent functions of core relevance to cells, such as the ability to spatiotemporally self-organize and thereby structure the cellular space, is still extremely challenging. While on the generative side conditional generative models and multi-state design are on the rise, for emergent functions there is a lack of tailored screening methods as typically needed in a protein design project, both computational and experimental. Here we describe a proof-of-principle of how such screening, in silico and in vitro, can be achieved for ML-generated variants of a protein that forms intracellular spatiotemporal patterns. For computational screening we use a structure-based divide-and-conquer approach to find the most promising candidates, while for the subsequent in vitro screening we use synthetic cell-mimics as established by Bottom-Up Synthetic Biology. We then show that the best screened candidate can indeed completely substitute the wildtype gene in Escherichia coli. These results raise great hopes for the next level of synthetic biology, where ML-designed synthetic proteins will be used to engineer cellular functions.
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Affiliation(s)
- Shunshi Kohyama
- Dept. Cellular and Molecular Biophysics, Max Planck Institute of Biochemistry, Martinsried, D-82152, Germany
| | - Béla P Frohn
- Dept. Cellular and Molecular Biophysics, Max Planck Institute of Biochemistry, Martinsried, D-82152, Germany
| | - Leon Babl
- Dept. Cellular and Molecular Biophysics, Max Planck Institute of Biochemistry, Martinsried, D-82152, Germany
| | - Petra Schwille
- Dept. Cellular and Molecular Biophysics, Max Planck Institute of Biochemistry, Martinsried, D-82152, Germany.
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3
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Glazenburg MM, Hettema NM, Laan L, Remy O, Laloux G, Brunet T, Chen X, Tee YH, Wen W, Rizvi MS, Jolly MK, Riddell M. Perspectives on polarity - exploring biological asymmetry across scales. J Cell Sci 2024; 137:jcs261987. [PMID: 38441500 DOI: 10.1242/jcs.261987] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/07/2024] Open
Abstract
In this Perspective, Journal of Cell Science invited researchers working on cell and tissue polarity to share their thoughts on unique, emerging or open questions relating to their field. The goal of this article is to feature 'voices' from scientists around the world and at various career stages, to bring attention to innovative and thought-provoking topics of interest to the cell biology community. These voices discuss intriguing questions that consider polarity across scales, evolution, development and disease. What can yeast and protists tell us about the evolution of cell and tissue polarity in animals? How are cell fate and development influenced by emerging dynamics in cell polarity? What can we learn from atypical and extreme polarity systems? How can we arrive at a more unified biophysical understanding of polarity? Taken together, these pieces demonstrate the broad relevance of the fascinating phenomenon of cell polarization to diverse fundamental biological questions.
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Affiliation(s)
- Marieke Margaretha Glazenburg
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, 2629 HZ, The Netherlands
| | - Nynke Marije Hettema
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, 2629 HZ, The Netherlands
| | - Liedewij Laan
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, 2629 HZ, The Netherlands
| | - Ophélie Remy
- Institut de Duve, UCLouvain, 75 avenue Hippocrate, 1200 Brussels, Belgium
| | - Géraldine Laloux
- Institut de Duve, UCLouvain, 75 avenue Hippocrate, 1200 Brussels, Belgium
| | - Thibaut Brunet
- Institut Pasteur, Université Paris-Cité, CNRS UMR 3691, Evolutionary Cell Biology and Evolution of Morphogenesis Unit, 25-28 rue du docteur Roux, 75015 Paris, France
| | - Xin Chen
- Howard Hughes Medical Institute and Department of Biology, Johns Hopkins University, Levi Hall 137, 3400 North Charles Street, Baltimore, MD 21218-2685, USA
| | - Yee Han Tee
- Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore
| | - Wenyu Wen
- Department of Neurosurgery, Huashan Hospital, State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institutes of Biomedical Sciences, School of Basic Medical Sciences, Fudan University, Shanghai 200032, China
| | - Mohd Suhail Rizvi
- Department of Biomedical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502284, India
| | - Mohit Kumar Jolly
- Department of Bioengineering, Indian Institute of Science, Bangalore 560012, India
| | - Meghan Riddell
- Department of Physiology and Department of Obstetrics and Gynecology, University of Alberta, Edmonton, AB, T6G 2S2, Canada
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4
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Rombouts J, Elliott J, Erzberger A. Forceful patterning: theoretical principles of mechanochemical pattern formation. EMBO Rep 2023; 24:e57739. [PMID: 37916772 DOI: 10.15252/embr.202357739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Revised: 09/21/2023] [Accepted: 09/27/2023] [Indexed: 11/03/2023] Open
Abstract
Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.
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Affiliation(s)
- Jan Rombouts
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Developmental Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
| | - Jenna Elliott
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Anna Erzberger
- Cell Biology and Biophysics Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
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5
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Weyer H, Brauns F, Frey E. Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory. Phys Rev E 2023; 108:064202. [PMID: 38243507 DOI: 10.1103/physreve.108.064202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 08/29/2023] [Indexed: 01/21/2024]
Abstract
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.
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Affiliation(s)
- Henrik Weyer
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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6
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Brauns F, Iñigo de la Cruz L, Daalman WKG, de Bruin I, Halatek J, Laan L, Frey E. Redundancy and the role of protein copy numbers in the cell polarization machinery of budding yeast. Nat Commun 2023; 14:6504. [PMID: 37845215 PMCID: PMC10579396 DOI: 10.1038/s41467-023-42100-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2022] [Accepted: 09/26/2023] [Indexed: 10/18/2023] Open
Abstract
How can a self-organized cellular function evolve, adapt to perturbations, and acquire new sub-functions? To make progress in answering these basic questions of evolutionary cell biology, we analyze, as a concrete example, the cell polarity machinery of Saccharomyces cerevisiae. This cellular module exhibits an intriguing resilience: it remains operational under genetic perturbations and recovers quickly and reproducibly from the deletion of one of its key components. Using a combination of modeling, conceptual theory, and experiments, we propose that multiple, redundant self-organization mechanisms coexist within the protein network underlying cell polarization and are responsible for the module's resilience and adaptability. Based on our mechanistic understanding of polarity establishment, we hypothesize that scaffold proteins, by introducing new connections in the existing network, can increase the redundancy of mechanisms and thus increase the evolvability of other network components. Moreover, our work gives a perspective on how a complex, redundant cellular module might have evolved from a more rudimental ancestral form.
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Affiliation(s)
- Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Leila Iñigo de la Cruz
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Werner K-G Daalman
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Ilse de Bruin
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands
| | - Jacob Halatek
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Liedewij Laan
- Department of Bionanoscience, Kavli Institute of Nanoscience Delft, Delft University of Technology, Delft, the Netherlands.
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany.
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539, Munich, Germany.
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7
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Xie Q, On Lee S, Vissamsetti N, Guo S, Johnson ME, Fried SD. Secretion-Catalyzed Assembly of Protein Biomaterials on a Bacterial Membrane Surface. Angew Chem Int Ed Engl 2023; 62:e202305178. [PMID: 37469298 DOI: 10.1002/anie.202305178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Revised: 06/28/2023] [Accepted: 07/18/2023] [Indexed: 07/21/2023]
Abstract
Protein-based biomaterials have played a key role in tissue engineering, and additional exciting applications as self-healing materials and sustainable polymers are emerging. Over the past few decades, recombinant expression and production of various fibrous proteins from microbes have been demonstrated; however, the resulting proteins typically must then be purified and processed by humans to form usable fibers and materials. Here, we show that the Gram-positive bacterium Bacillus subtilis can be programmed to secrete silk through its translocon via an orthogonal signal peptide/peptidase pair. Surprisingly, we discover that this translocation mechanism drives the silk proteins to assemble into fibers spontaneously on the cell surface, in a process we call secretion-catalyzed assembly (SCA). Secreted silk fibers form self-healing hydrogels with minimal processing. Alternatively, the fibers retained on the membrane provide a facile route to create engineered living materials from Bacillus cells. This work provides a blueprint to achieve autonomous assembly of protein biomaterials in useful morphologies directly from microbial factories.
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Affiliation(s)
- Qi Xie
- Department of Chemistry, Johns Hopkins University, 21218, Baltimore, MD, USA
| | - Sea On Lee
- Department of Chemistry, Johns Hopkins University, 21218, Baltimore, MD, USA
| | - Nitya Vissamsetti
- Department of Chemistry, Johns Hopkins University, 21218, Baltimore, MD, USA
| | - Sikao Guo
- T. C. Jenkins Department of Biophysics, Johns Hopkins University, 21218, Baltimore, MD, USA
| | - Margaret E Johnson
- T. C. Jenkins Department of Biophysics, Johns Hopkins University, 21218, Baltimore, MD, USA
| | - Stephen D Fried
- Department of Chemistry, Johns Hopkins University, 21218, Baltimore, MD, USA
- T. C. Jenkins Department of Biophysics, Johns Hopkins University, 21218, Baltimore, MD, USA
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8
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Piras A, Floris E, Dall'Asta L, Gamba A. Sorting of multiple molecular species on cell membranes. Phys Rev E 2023; 108:024401. [PMID: 37723769 DOI: 10.1103/physreve.108.024401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 06/05/2023] [Indexed: 09/20/2023]
Abstract
Eukaryotic cells maintain their inner order by a hectic process of sorting and distillation of molecular factors taking place on their lipid membranes. A similar sorting process is implied in the assembly and budding of enveloped viruses. To understand the properties of this molecular sorting process, we have recently proposed a physical model [Zamparo et al., Phys. Rev. Lett. 126, 088101 (2021)]10.1103/PhysRevLett.126.088101, based on (1) the phase separation of a single, initially dispersed molecular species into spatially localized sorting domains on the lipid membrane and (2) domain-induced membrane bending leading to the nucleation of submicrometric lipid vesicles, naturally enriched in the molecules of the engulfed sorting domain. The analysis of the model showed the existence of an optimal region of parameter space where sorting is most efficient. Here the model is extended to account for the simultaneous distillation of a pool of distinct molecular species. We find that the mean time spent by sorted molecules on the membrane increases with the heterogeneity of the pool (i.e., the number of distinct molecular species sorted) according to a simple scaling law, and that a large number of distinct molecular species can in principle be sorted in parallel on cell membranes without significantly interfering with each other. Moreover, sorting is found to be most efficient when the distinct molecular species have comparable homotypic affinities. We also consider how valence (i.e., the average number of interacting neighbors of a molecule in a sorting domain) affects the sorting process, finding that higher-valence molecules can be sorted with greater efficiency than lower-valence molecules.
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Affiliation(s)
- Andrea Piras
- Candiolo Cancer Institute, FPO-IRCCS, Strada Provinciale 142, km 3.95, 10060 Candiolo, Italy
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
- Italian Institute for Genomic Medicine (IIGM), Strada Provinciale 142, km 3.95, 10060 Candiolo, Italy
- Department of Oncology, University of Turin, 10060 Candiolo, Italy
| | - Elisa Floris
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - Luca Dall'Asta
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
- Italian Institute for Genomic Medicine (IIGM), Strada Provinciale 142, km 3.95, 10060 Candiolo, Italy
- Collegio Carlo Alberto, Piazza Arbarello 8, 10122, Torino, Italy
| | - Andrea Gamba
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
- Italian Institute for Genomic Medicine (IIGM), Strada Provinciale 142, km 3.95, 10060 Candiolo, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
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9
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Beta C, Edelstein-Keshet L, Gov N, Yochelis A. From actin waves to mechanism and back: How theory aids biological understanding. eLife 2023; 12:e87181. [PMID: 37428017 DOI: 10.7554/elife.87181] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/01/2023] [Indexed: 07/11/2023] Open
Abstract
Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.
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Affiliation(s)
- Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | | | - Nir Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Arik Yochelis
- Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva, Israel
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10
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Carreira LAM, Szadkowski D, Lometto S, Hochberg GKA, Søgaard-Andersen L. Molecular basis and design principles of switchable front-rear polarity and directional migration in Myxococcus xanthus. Nat Commun 2023; 14:4056. [PMID: 37422455 PMCID: PMC10329633 DOI: 10.1038/s41467-023-39773-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 06/28/2023] [Indexed: 07/10/2023] Open
Abstract
During cell migration, front-rear polarity is spatiotemporally regulated; however, the underlying design of regulatory interactions varies. In rod-shaped Myxococcus xanthus cells, a spatial toggle switch dynamically regulates front-rear polarity. The polarity module establishes front-rear polarity by guaranteeing front pole-localization of the small GTPase MglA. Conversely, the Frz chemosensory system, by acting on the polarity module, causes polarity inversions. MglA localization depends on the RomR/RomX GEF and MglB/RomY GAP complexes that localize asymmetrically to the poles by unknown mechanisms. Here, we show that RomR and the MglB and MglC roadblock domain proteins generate a positive feedback by forming a RomR/MglC/MglB complex, thereby establishing the rear pole with high GAP activity that is non-permissive to MglA. MglA at the front engages in negative feedback that breaks the RomR/MglC/MglB positive feedback allosterically, thus ensuring low GAP activity at this pole. These findings unravel the design principles of a system for switchable front-rear polarity.
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Affiliation(s)
| | - Dobromir Szadkowski
- Department of Ecophysiology, Max Planck Institute for Terrestrial Microbiology, 35043, Marburg, Germany
| | - Stefano Lometto
- Evolutionary Biochemistry Group, Max Planck Institute for Terrestrial Microbiology, 35043, Marburg, Germany
- Department of Chemistry and Center for Synthetic Microbiology, Philipps University, 35043, Marburg, Germany
| | - Georg K A Hochberg
- Evolutionary Biochemistry Group, Max Planck Institute for Terrestrial Microbiology, 35043, Marburg, Germany
- Department of Chemistry and Center for Synthetic Microbiology, Philipps University, 35043, Marburg, Germany
| | - Lotte Søgaard-Andersen
- Department of Ecophysiology, Max Planck Institute for Terrestrial Microbiology, 35043, Marburg, Germany.
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11
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Würthner L, Goychuk A, Frey E. Geometry-induced patterns through mechanochemical coupling. Phys Rev E 2023; 108:014404. [PMID: 37583206 DOI: 10.1103/physreve.108.014404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Accepted: 05/15/2023] [Indexed: 08/17/2023]
Abstract
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.
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Affiliation(s)
- Laeschkir Würthner
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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12
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Hladyshau S, Stoop JP, Kamada K, Nie S, Tsygankov D. Spatiotemporal Coordination of Rac1 and Cdc42 at the Whole Cell Level during Cell Ruffling. Cells 2023; 12:1638. [PMID: 37371108 DOI: 10.3390/cells12121638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Revised: 06/06/2023] [Accepted: 06/09/2023] [Indexed: 06/29/2023] Open
Abstract
Rho-GTPases are central regulators within a complex signaling network that controls cytoskeletal organization and cell movement. The network includes multiple GTPases, such as the most studied Rac1, Cdc42, and RhoA, along with their numerous effectors that provide mutual regulation through feedback loops. Here we investigate the temporal and spatial relationship between Rac1 and Cdc42 during membrane ruffling, using a simulation model that couples GTPase signaling with cell morphodynamics and captures the GTPase behavior observed with FRET-based biosensors. We show that membrane velocity is regulated by the kinetic rate of GTPase activation rather than the concentration of active GTPase. Our model captures both uniform and polarized ruffling. We also show that cell-type specific time delays between Rac1 and Cdc42 activation can be reproduced with a single signaling motif, in which the delay is controlled by feedback from Cdc42 to Rac1. The resolution of our simulation output matches those of time-lapsed recordings of cell dynamics and GTPase activity. Our data-driven modeling approach allows us to validate simulation results with quantitative precision using the same pipeline for the analysis of simulated and experimental data.
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Affiliation(s)
- Siarhei Hladyshau
- School of Biology, Georgia Institute of Technology, Atlanta, GA 30332, USA
- Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA
| | - Jorik P Stoop
- Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA
| | - Kosei Kamada
- Faculty of Medicine, The University of Tokyo, Tokyo 113-8654, Japan
| | - Shuyi Nie
- School of Biology, Georgia Institute of Technology, Atlanta, GA 30332, USA
| | - Denis Tsygankov
- Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30332, USA
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13
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Bressloff PC. Close encounters of the sticky kind: Brownian motion at absorbing boundaries. Phys Rev E 2023; 107:064121. [PMID: 37464709 DOI: 10.1103/physreve.107.064121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 05/26/2023] [Indexed: 07/20/2023]
Abstract
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time. In this paper we develop a class of encounter-based models that deal with absorption at sticky boundaries. Sticky boundaries occur in a diverse range of applications, including cell biology, colloidal physics, finance, and human crowd dynamics. They also naturally arise in active matter, where confined active particles tend to spontaneously accumulate at boundaries even in the absence of any particle-particle interactions. We begin by constructing a one-dimensional encounter-based model of sticky Brownian motion (BM), which is based on the zero-range limit of nonsticky BM with a short-range attractive potential well near the origin. In this limit, the boundary-contact time is given by the amount of time (occupation time) that the particle spends at the origin. We calculate the joint probability density or propagator for the particle position and the occupation time, and then identify an absorption event as the first time that the occupation time crosses a randomly generated threshold. We illustrate the theory by considering diffusion in a finite interval with a partially absorbing sticky boundary at one end. We show how various quantities, such as the mean first passage time (MFPT) for single-particle absorption and the relaxation to steady state at the multiparticle level, depend on moments of the random threshold distribution. Finally, we determine how sticky BM can be obtained by taking a particular diffusion limit of a sticky run-and-tumble particle (RTP).
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
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14
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Goychuk A, Kannan D, Chakraborty AK, Kardar M. Polymer folding through active processes recreates features of genome organization. Proc Natl Acad Sci U S A 2023; 120:e2221726120. [PMID: 37155885 PMCID: PMC10194017 DOI: 10.1073/pnas.2221726120] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 04/02/2023] [Indexed: 05/10/2023] Open
Abstract
From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.
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Affiliation(s)
- Andriy Goychuk
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Deepti Kannan
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Arup K. Chakraborty
- Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139
- Ragon Institute of Massachusetts General Hospital, Massachusetts Institute of Technology and Harvard University, Cambridge, MA02139
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
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15
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Frohoff-Hülsmann T, Thiele U, Pismen LM. Non-reciprocity induces resonances in a two-field Cahn-Hilliard model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220087. [PMID: 36842986 DOI: 10.1098/rsta.2022.0087] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
We consider a non-reciprocally coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour and suppression of coarsening. After introducing the model, we first review the linear stability of steady uniform states and show that all instability thresholds are identical to the ones for a corresponding two-species reaction-diffusion system. Next, we consider a specific interaction of linear modes-a 'Hopf-Turing' resonance-and derive the corresponding amplitude equations using a weakly nonlinear approach. We discuss the weakly nonlinear results and finally compare them with fully nonlinear simulations for a specific conserved amended FitzHugh-Nagumo system. We conclude with a discussion of the limitations of the employed weakly nonlinear approach. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
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Affiliation(s)
- Tobias Frohoff-Hülsmann
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, Münster 48149, Germany
| | - Len M Pismen
- Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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16
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Pelz M, Ward MJ. The emergence of spatial patterns for compartmental reaction kinetics coupled by two bulk diffusing species with comparable diffusivities. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220089. [PMID: 36842990 DOI: 10.1098/rsta.2022.0089] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a central problem in many chemical and biological systems. From a mathematical viewpoint, one key challenge with this theory for two component systems is that stable spatial patterns can typically only occur from a spatially uniform state when a slowly diffusing 'activator' species reacts with a much faster diffusing 'inhibitor' species. However, from a modelling perspective, this large diffusivity ratio requirement for pattern formation is often unrealistic in biological settings since different molecules tend to diffuse with similar rates in extracellular spaces. As a result, one key long-standing question is how to robustly obtain pattern formation in the biologically realistic case where the time scales for diffusion of the interacting species are comparable. For a coupled one-dimensional bulk-compartment theoretical model, we investigate the emergence of spatial patterns for the scenario where two bulk diffusing species with comparable diffusivities are coupled to nonlinear reactions that occur only in localized 'compartments', such as on the boundaries of a one-dimensional domain. The exchange between the bulk medium and the spatially localized compartments is modelled by a Robin boundary condition with certain binding rates. As regulated by these binding rates, we show for various specific nonlinearities that our one-dimensional coupled PDE-ODE model admits symmetry-breaking bifurcations, leading to linearly stable asymmetric steady-state patterns, even when the bulk diffusing species have equal diffusivities. Depending on the form of the nonlinear kinetics, oscillatory instabilities can also be triggered. Moreover, the analysis is extended to treat a periodic chain of compartments. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
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Affiliation(s)
- Merlin Pelz
- Department of Mathematics, UBC, Vancouver, British Columbia, Canada
| | - Michael J Ward
- Department of Mathematics, UBC, Vancouver, British Columbia, Canada
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17
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Hladyshau S, Stoop JP, Kamada K, Nie S, Tsygankov DV. Spatiotemporal coordination of Rac1 and Cdc42 at the whole cell level during cell ruffling. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.03.31.535147. [PMID: 37034645 PMCID: PMC10081307 DOI: 10.1101/2023.03.31.535147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Rho-GTPases are central regulators within a complex signaling network that controls the cytoskeletal organization and cell movement. This network includes multiple GTPases, such as the most studied Rac1, Cdc42, and RhoA, and their numerous effectors that provide mutual regulation and feedback loops. Here we investigate the temporal and spatial relationship between Rac1 and Cdc42 during membrane ruffling using a simulation model which couples GTPase signaling with cell morphodynamics to capture the GTPase behavior observed with FRET-based biosensors. We show that membrane velocity is regulated by the kinetic rate of GTPase activation rather than the concentration of active GTPase. Our model captures both uniform and polarized ruffling. We also show that cell-type specific time delays between Rac1 and Cdc42 activation can be reproduced with a single signaling motif, in which the delay is controlled by feedback from Cdc42 to Rac1. The resolution of our simulation output matches those of the time-lapsed recordings of cell dynamics and GTPase activity. This approach allows us to validate simulation results with quantitative precision using the same pipeline for the analysis of simulated and experimental data.
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18
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Demarchi L, Goychuk A, Maryshev I, Frey E. Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence. PHYSICAL REVIEW LETTERS 2023; 130:128401. [PMID: 37027840 DOI: 10.1103/physrevlett.130.128401] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 02/03/2023] [Indexed: 06/19/2023]
Abstract
Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.
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Affiliation(s)
- Leonardo Demarchi
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Ivan Maryshev
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 München, Germany
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19
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Nampoothiri S. Preferential localization of a single spot in reaction-diffusion systems on non-spherical surfaces. SOFT MATTER 2023; 19:1977-1986. [PMID: 36847585 DOI: 10.1039/d2sm01287a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The present work systematically examines the effect of breaking the rotational symmetry of a surface on the spot positioning in reaction-diffusion (RD) systems. In particular, we study analytically and numerically the steady-state positioning of a single spot in RD systems on a prolate and an oblate ellipsoid. We adapt perturbative techniques to perform a linear stability analysis of the RD system on both ellipsoids. Furthermore, the spot positionings in the steady states of non-linear RD equations are obtained numerically on both ellipsoids. Our analysis suggests that preferential spot positioning can be observed on non-spherical surfaces. The present work may provide useful insights into the role of cell geometry on various symmetry-breaking mechanisms in cellular processes.
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Affiliation(s)
- Sankaran Nampoothiri
- Department of Physics, Gandhi Institute of Technology and Management (GITAM) University, Bengaluru, India.
- Dipartimento di Fisica e Astronomia G. Galilei - DFA, Sezione INFN, Universit di Padova, Via Marzolo 8, 35131 Padova, PD, Italy
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Hesaraghatta Hobli, Bengaluru North, 560089, India
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20
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Directing Min protein patterns with advective bulk flow. Nat Commun 2023; 14:450. [PMID: 36707506 PMCID: PMC9883515 DOI: 10.1038/s41467-023-35997-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 01/10/2023] [Indexed: 01/29/2023] Open
Abstract
The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concentration ratios, upstream propagation for large ratios, but multistability of both propagation directions in between. Whereas downstream propagation can be described by a minimal model that disregards MinE conformational switching, upstream propagation can be reproduced by a reduced switch model, where increased MinD bulk concentrations on the upstream side promote protein attachment. Our study demonstrates that a differential flow, where bulk flow advects protein concentrations in the bulk, but not on the surface, can control surface-pattern propagation. This suggests that flow can be used to probe molecular features and to constrain mathematical models for pattern-forming systems.
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21
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Glazenburg MM, Laan L. Complexity and self-organization in the evolution of cell polarization. J Cell Sci 2023; 136:jcs259639. [PMID: 36691920 DOI: 10.1242/jcs.259639] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
Cellular life exhibits order and complexity, which typically increase over the course of evolution. Cell polarization is a well-studied example of an ordering process that breaks the internal symmetry of a cell by establishing a preferential axis. Like many cellular processes, polarization is driven by self-organization, meaning that the macroscopic pattern emerges as a consequence of microscopic molecular interactions at the biophysical level. However, the role of self-organization in the evolution of complex protein networks remains obscure. In this Review, we provide an overview of the evolution of polarization as a self-organizing process, focusing on the model species Saccharomyces cerevisiae and its fungal relatives. Moreover, we use this model system to discuss how self-organization might relate to evolutionary change, offering a shift in perspective on evolution at the microscopic scale.
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Affiliation(s)
- Marieke M Glazenburg
- Department of Bionanoscience, Kavli Institute of Nanoscience, Faculty of Applied Sciences, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Liedewij Laan
- Department of Bionanoscience, Kavli Institute of Nanoscience, Faculty of Applied Sciences, Delft University of Technology, 2629 HZ Delft, The Netherlands
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22
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Lang CF, Munro EM. Oligomerization of peripheral membrane proteins provides tunable control of cell surface polarity. Biophys J 2022; 121:4543-4559. [PMID: 36815706 PMCID: PMC9750853 DOI: 10.1016/j.bpj.2022.10.035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Revised: 08/31/2022] [Accepted: 10/24/2022] [Indexed: 11/02/2022] Open
Abstract
Asymmetric distributions of peripheral membrane proteins define cell polarity across all kingdoms of life. Non-linear positive feedback on membrane binding is essential to amplify and stabilize these asymmetries, but how specific molecular sources of non-linearity shape polarization dynamics remains poorly understood. Here we show that the ability to oligomerize, which is common to many peripheral membrane proteins, can play a profound role in shaping polarization dynamics in simple feedback circuits. We show that size-dependent binding avidity and mobility of membrane-bound oligomers endow polarity circuits with several key properties. Size-dependent membrane binding avidity confers a form of positive feedback on the accumulation of oligomer subunits. Although insufficient by itself, this sharply reduces the amount of additional feedback required for spontaneous emergence and stable maintenance of polarized states. Size-dependent oligomer mobility makes symmetry breaking and stable polarity more robust with respect to variation in subunit diffusivities and cell sizes, and slows the approach to a final stable spatial distribution, allowing cells to "remember" polarity boundaries imposed by transient external cues. Together, these findings reveal how oligomerization of peripheral membrane proteins can provide powerful and highly tunable sources of non-linear feedback in biochemical circuits that govern cell surface polarity. Given its prevalence and widespread involvement in cell polarity, we speculate that self-oligomerization may have provided an accessible path to evolving simple polarity circuits.
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Affiliation(s)
- Charles F Lang
- Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, Illinois; Committee on Genetics, Genomics, and Systems Biology, University of Chicago, Chicago, Illinois
| | - Edwin M Munro
- Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, Illinois; Committee on Genetics, Genomics, and Systems Biology, University of Chicago, Chicago, Illinois.
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23
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Striebel M, Brauns F, Frey E. Length Regulation Drives Self-Organization in Filament-Motor Mixtures. PHYSICAL REVIEW LETTERS 2022; 129:238102. [PMID: 36563230 DOI: 10.1103/physrevlett.129.238102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 10/10/2022] [Indexed: 06/17/2023]
Abstract
Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament clusters despite the absence of mechanical interactions between filaments. Even though the orientation of individual remains fixed, collective filament orientation emerges in the clusters, aligned orthogonal to their interfaces.
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Affiliation(s)
- Moritz Striebel
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 Munich, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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24
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Tsai MC, Spendier K. RBL-2H3 Mast Cell Receptor Dynamics in the Immunological Synapse. BIOPHYSICA 2022; 2:428-439. [PMID: 37654558 PMCID: PMC10470655 DOI: 10.3390/biophysica2040038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
The RBL-2H3 mast cell immunological synapse dynamics is often simulated with reaction-diffusion and Fokker-Planck equations. The equations focus on how the cell synapse captures receptors following an immune response, where the receptor capture at the immunological site appears to be a delayed process. This article investigates the physical nature and mathematics behind such time-dependent delays. Using signal processing methods, convolution and cross-correlation-type delay capture simulations give a χ -squared range of 22 to 60, in good agreement with experimental results. The cell polarization event is offered as a possible explanation for these capture delays, where polarizing rates measure how fast the cell polarization event occurs. In the case of RBL-2H3 mast cells, polarization appears to be associated with cytoskeletal rearrangement; thus, both cytoskeletal and diffusional components are considered. From these simulations, a maximum polarizing rate ranging from 0.0057 s-2 to 0.031 s-2 is obtained. These results indicate that RBL-2H3 mast cells possess both temporal and spatial memory, and cell polarization is possibly linked to a Turing-type pattern formation.
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Affiliation(s)
- Ming Chih Tsai
- Department of Physics and Energy Science, University of Colorado Colorado Springs, Colorado Springs, CO 80918, USA
- BioFrontiers Center, University of Colorado Colorado Springs, Colorado Springs, CO 80918, USA
| | - Kathrin Spendier
- BioFrontiers Center, University of Colorado Colorado Springs, Colorado Springs, CO 80918, USA
- Quantinuum, Broomfield, CO 80021, USA
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25
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Loose M, Auer A, Brognara G, Budiman HR, Kowalski L, Matijević I. In vitro
reconstitution of small
GTPase
regulation. FEBS Lett 2022; 597:762-777. [PMID: 36448231 DOI: 10.1002/1873-3468.14540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Revised: 10/27/2022] [Accepted: 11/07/2022] [Indexed: 12/05/2022]
Abstract
Small GTPases play essential roles in the organization of eukaryotic cells. In recent years, it has become clear that their intracellular functions result from intricate biochemical networks of the GTPase and their regulators that dynamically bind to a membrane surface. Due to the inherent complexities of their interactions, however, revealing the underlying mechanisms of action is often difficult to achieve from in vivo studies. This review summarizes in vitro reconstitution approaches developed to obtain a better mechanistic understanding of how small GTPase activities are regulated in space and time.
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Affiliation(s)
- Martin Loose
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | - Albert Auer
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | - Gabriel Brognara
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | | | - Lukasz Kowalski
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
| | - Ivana Matijević
- Institute of Science and Technology Austria (ISTA) Klosterneuburg Austria
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26
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Moldenhawer T, Moreno E, Schindler D, Flemming S, Holschneider M, Huisinga W, Alonso S, Beta C. Spontaneous transitions between amoeboid and keratocyte-like modes of migration. Front Cell Dev Biol 2022; 10:898351. [PMID: 36247011 PMCID: PMC9563996 DOI: 10.3389/fcell.2022.898351] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 07/18/2022] [Indexed: 01/17/2023] Open
Abstract
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.
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Affiliation(s)
- Ted Moldenhawer
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | - Eduardo Moreno
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Daniel Schindler
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Sven Flemming
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
| | | | - Wilhelm Huisinga
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Sergio Alonso
- Department of Physics, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- *Correspondence: Carsten Beta,
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27
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Nguindjel ADC, de Visser PJ, Winkens M, Korevaar PA. Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics. Phys Chem Chem Phys 2022; 24:23980-24001. [PMID: 36172850 DOI: 10.1039/d2cp02542f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.
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Affiliation(s)
| | - Pieter J de Visser
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands.
| | - Mitch Winkens
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands.
| | - Peter A Korevaar
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands.
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28
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Abstract
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information about the patterns at small scales. Here, we present a semiphenomenological approach which exploits mass conservation in pattern formation, and enables reconstruction of information about patterns from the large-scale dynamics. The basic idea is to partition the domain into distinct regions (coarse grain) and determine instantaneous dispersion relations in each region, which ultimately inform about local pattern-forming instabilities. We illustrate our approach by studying the Min system, a paradigmatic model for protein pattern formation. By performing simulations, we first show that the Min system produces multiscale patterns in a spatially heterogeneous geometry. This prediction is confirmed experimentally by in vitro reconstitution of the Min system. Using a recently developed theoretical framework for mass-conserving reaction-diffusion systems, we show that the spatiotemporal evolution of the total protein densities on large scales reliably predicts the pattern-forming dynamics. Our approach provides an alternative and versatile theoretical framework for complex systems where analytical coarse-graining methods are not applicable, and can, in principle, be applied to a wide range of systems with an underlying conservation law.
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29
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Wagner AM, Eto H, Joseph A, Kohyama S, Haraszti T, Zamora RA, Vorobii M, Giannotti MI, Schwille P, Rodriguez-Emmenegger C. Dendrimersome Synthetic Cells Harbor Cell Division Machinery of Bacteria. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2202364. [PMID: 35579491 DOI: 10.1002/adma.202202364] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 04/11/2022] [Indexed: 06/15/2023]
Abstract
The integration of active cell machinery with synthetic building blocks is the bridge toward developing synthetic cells with biological functions and beyond. Self-replication is one of the most important tasks of living systems, and various complex machineries exist to execute it. In Escherichia coli, a contractile division ring is positioned to mid-cell by concentration oscillations of self-organizing proteins (MinCDE), where it severs membrane and cell wall. So far, the reconstitution of any cell division machinery has exclusively been tied to liposomes. Here, the reconstitution of a rudimentary bacterial divisome in fully synthetic bicomponent dendrimersomes is shown. By tuning the membrane composition, the interaction of biological machinery with synthetic membranes can be tailored to reproduce its dynamic behavior. This constitutes an important breakthrough in the assembly of synthetic cells with biological elements, as tuning of membrane-divisome interactions is the key to engineering emergent biological behavior from the bottom-up.
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Affiliation(s)
- Anna M Wagner
- DWI-Leibniz Institute for Interactive Materials, Forckenbeckstraße 50, 52074, Aachen, Germany
- Institute of Technical and Macromolecular Chemistry, RWTH Aachen University, Worringerweg 2, 52074, Aachen, Germany
| | - Hiromune Eto
- Max Planck Institute of Biochemistry, Department of Cellular and Molecular Biophysics, Am Klopferspitz 18, 82152, Martinsried, Germany
| | - Anton Joseph
- DWI-Leibniz Institute for Interactive Materials, Forckenbeckstraße 50, 52074, Aachen, Germany
- Institute of Technical and Macromolecular Chemistry, RWTH Aachen University, Worringerweg 2, 52074, Aachen, Germany
| | - Shunshi Kohyama
- Max Planck Institute of Biochemistry, Department of Cellular and Molecular Biophysics, Am Klopferspitz 18, 82152, Martinsried, Germany
| | - Tamás Haraszti
- DWI-Leibniz Institute for Interactive Materials, Forckenbeckstraße 50, 52074, Aachen, Germany
| | - Ricardo A Zamora
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST), Carrer de Baldiri Reixac 10-12, Barcelona, 08028, Spain
- Network Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Madrid, 28029, Spain
| | - Mariia Vorobii
- DWI-Leibniz Institute for Interactive Materials, Forckenbeckstraße 50, 52074, Aachen, Germany
| | - Marina I Giannotti
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST), Carrer de Baldiri Reixac 10-12, Barcelona, 08028, Spain
- Network Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Madrid, 28029, Spain
- University of Barcelona, Department of Materials Science and Physical Chemistry, Martí i Franquès 10, Barcelona, 08028, Spain
| | - Petra Schwille
- Max Planck Institute of Biochemistry, Department of Cellular and Molecular Biophysics, Am Klopferspitz 18, 82152, Martinsried, Germany
| | - Cesar Rodriguez-Emmenegger
- DWI-Leibniz Institute for Interactive Materials, Forckenbeckstraße 50, 52074, Aachen, Germany
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology (BIST), Carrer de Baldiri Reixac 10-12, Barcelona, 08028, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, Barcelona, 08010, Spain
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30
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Datta A, Ghosh S, Kondev J. How to assemble a scale-invariant gradient. eLife 2022; 11:71365. [PMID: 35311649 PMCID: PMC8986316 DOI: 10.7554/elife.71365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 03/20/2022] [Indexed: 11/17/2022] Open
Abstract
Intracellular protein gradients serve a variety of functions, such as the establishment of cell polarity or to provide positional information for gene expression in developing embryos. Given that cell size in a population can vary considerably, for the protein gradients to work properly they often have to be scaled to the size of the cell. Here, we examine a model of protein gradient formation within a cell that relies on cytoplasmic diffusion and cortical transport of proteins toward a cell pole. We show that the shape of the protein gradient is determined solely by the cell geometry. Furthermore, we show that the length scale over which the protein concentration in the gradient varies is determined by the linear dimensions of the cell, independent of the diffusion constant or the transport speed. This gradient provides scale-invariant positional information within a cell, which can be used for assembly of intracellular structures whose size is scaled to the linear dimensions of the cell, such as the cytokinetic ring and actin cables in budding yeast cells.
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Affiliation(s)
- Arnab Datta
- Department of Physics, Brandeis University, Waltham, United States
| | - Sagnik Ghosh
- Department of Physics, Brandeis University, Waltham, United States
| | - Jane Kondev
- Department of Physics, Brandeis University, Waltham, United States
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31
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Abstract
Accurate decoding of spatial chemical landscapes is critical for many cell functions. Eukaryotic cells decode local chemical gradients to orient growth or movement in productive directions. Recent work on yeast model systems, whose gradient sensing pathways display much less complexity than those in animal cells, has suggested new paradigms for how these very small cells successfully exploit information in noisy and dynamic pheromone gradients to identify their mates. Pheromone receptors regulate a polarity circuit centered on the conserved Rho-family GTPase, Cdc42. The polarity circuit contains both positive and negative feedback pathways, allowing spontaneous symmetry breaking and also polarity site disassembly and relocation. Cdc42 orients the actin cytoskeleton, leading to focused vesicle traffic that promotes movement of the polarity site and also reshapes the cortical distribution of receptors at the cell surface. In this article, we review the advances from work on yeasts and compare them with the excitable signaling pathways that have been revealed in chemotactic animal cells. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Debraj Ghose
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, North Carolina, USA;
| | - Timothy Elston
- Department of Pharmacology, University of North Carolina at Chapel Hill, North Carolina, USA
| | - Daniel Lew
- Department of Pharmacology and Cancer Biology, Duke University Medical Center, Durham, North Carolina, USA;
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32
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Sundaram M, Steiner E, Gordon DM. Rainfall, neighbors, and foraging: The dynamics of a population of red harvester ant colonies 1988‐2019. ECOL MONOGR 2022. [DOI: 10.1002/ecm.1503] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
| | - Erik Steiner
- Center for Spatial and Textual Analysis Stanford University Stanford CA
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33
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Krause AL, Gaffney EA, Maini PK, Klika V. Modern perspectives on near-equilibrium analysis of Turing systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200268. [PMID: 34743603 PMCID: PMC8580451 DOI: 10.1098/rsta.2020.0268] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/18/2021] [Indexed: 05/02/2023]
Abstract
In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
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Affiliation(s)
- Andrew L. Krause
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
- Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Rd, Durham DH1 3LE, UK
| | - Eamonn A. Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Philip K. Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Václav Klika
- Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova, 13, 12000 Praha, Czech Republic
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34
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Konow C, Dolnik M, Epstein IR. Insights from chemical systems into Turing-type morphogenesis. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200269. [PMID: 34743602 DOI: 10.1098/rsta.2020.0269] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction-diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237, 37-72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction-diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
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Affiliation(s)
- C Konow
- Department of Chemistry, Brandeis University, Waltham, MA 02453, USA
| | - M Dolnik
- Department of Chemistry, Brandeis University, Waltham, MA 02453, USA
| | - I R Epstein
- Department of Chemistry, Brandeis University, Waltham, MA 02453, USA
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35
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Abstract
Spatial organisation through localisation/compartmentalisation of species is a ubiquitous but poorly understood feature of cellular biomolecular networks. Current technologies in systems and synthetic biology (spatial proteomics, imaging, synthetic compartmentalisation) necessitate a systematic approach to elucidating the interplay of networks and spatial organisation. We develop a systems framework towards this end and focus on the effect of spatial localisation of network components revealing its multiple facets: (i) As a key distinct regulator of network behaviour, and an enabler of new network capabilities (ii) As a potent new regulator of pattern formation and self-organisation (iii) As an often hidden factor impacting inference of temporal networks from data (iv) As an engineering tool for rewiring networks and network/circuit design. These insights, transparently arising from the most basic considerations of networks and spatial organisation, have broad relevance in natural and engineered biology and in related areas such as cell-free systems, systems chemistry and bionanotechnology. Complex biomolecular networks are fundamental to the functioning of living systems, both at the cellular level and beyond. In this paper, the authors develop a systems framework to elucidate the interplay of networks and the spatial localisation of network components.
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36
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Sigismund S, Lanzetti L, Scita G, Di Fiore PP. Endocytosis in the context-dependent regulation of individual and collective cell properties. Nat Rev Mol Cell Biol 2021; 22:625-643. [PMID: 34075221 DOI: 10.1038/s41580-021-00375-5] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/22/2021] [Indexed: 02/07/2023]
Abstract
Endocytosis allows cells to transport particles and molecules across the plasma membrane. In addition, it is involved in the termination of signalling through receptor downmodulation and degradation. This traditional outlook has been substantially modified in recent years by discoveries that endocytosis and subsequent trafficking routes have a profound impact on the positive regulation and propagation of signals, being key for the spatiotemporal regulation of signal transmission in cells. Accordingly, endocytosis and membrane trafficking regulate virtually every aspect of cell physiology and are frequently subverted in pathological conditions. Two key aspects of endocytic control over signalling are coming into focus: context-dependency and long-range effects. First, endocytic-regulated outputs are not stereotyped but heavily dependent on the cell-specific regulation of endocytic networks. Second, endocytic regulation has an impact not only on individual cells but also on the behaviour of cellular collectives. Herein, we will discuss recent advancements in these areas, highlighting how endocytic trafficking impacts complex cell properties, including cell polarity and collective cell migration, and the relevance of these mechanisms to disease, in particular cancer.
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Affiliation(s)
- Sara Sigismund
- IEO, European Institute of Oncology IRCCS, Milan, Italy.,Department of Oncology and Haemato-Oncology, Università degli Studi di Milano, Milan, Italy
| | - Letizia Lanzetti
- Department of Oncology, University of Torino Medical School, Torino, Italy.,Candiolo Cancer Institute, FPO - IRCCS, Candiolo, Torino, Italy
| | - Giorgio Scita
- Department of Oncology and Haemato-Oncology, Università degli Studi di Milano, Milan, Italy.,IFOM, the FIRC Institute of Molecular Oncology, Milan, Italy
| | - Pier Paolo Di Fiore
- IEO, European Institute of Oncology IRCCS, Milan, Italy. .,Department of Oncology and Haemato-Oncology, Università degli Studi di Milano, Milan, Italy.
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37
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Bulk-surface coupling identifies the mechanistic connection between Min-protein patterns in vivo and in vitro. Nat Commun 2021; 12:3312. [PMID: 34083526 PMCID: PMC8175580 DOI: 10.1038/s41467-021-23412-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 04/21/2021] [Indexed: 11/08/2022] Open
Abstract
Self-organisation of Min proteins is responsible for the spatial control of cell division in Escherichia coli, and has been studied both in vivo and in vitro. Intriguingly, the protein patterns observed in these settings differ qualitatively and quantitatively. This puzzling dichotomy has not been resolved to date. Using reconstituted proteins in laterally wide microchambers with a well-controlled height, we experimentally show that the Min protein dynamics on the membrane crucially depend on the micro chamber height due to bulk concentration gradients orthogonal to the membrane. A theoretical analysis shows that in vitro patterns at low microchamber height are driven by the same lateral oscillation mode as pole-to-pole oscillations in vivo. At larger microchamber height, additional vertical oscillation modes set in, marking the transition to a qualitatively different in vitro regime. Our work reveals the qualitatively different mechanisms of mass transport that govern Min protein-patterns for different bulk heights and thus shows that Min patterns in cells are governed by a different mechanism than those in vitro.
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38
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Hsieh TS, Lopez VA, Black MH, Osinski A, Pawłowski K, Tomchick DR, Liou J, Tagliabracci VS. Dynamic remodeling of host membranes by self-organizing bacterial effectors. Science 2021; 372:935-941. [PMID: 33927055 PMCID: PMC8543759 DOI: 10.1126/science.aay8118] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 02/17/2021] [Accepted: 04/14/2021] [Indexed: 01/09/2023]
Abstract
During infection, intracellular bacterial pathogens translocate a variety of effectors into host cells that modify host membrane trafficking for their benefit. We found a self-organizing system consisting of a bacterial phosphoinositide kinase and its opposing phosphatase that formed spatiotemporal patterns, including traveling waves, to remodel host cellular membranes. The Legionella effector MavQ, a phosphatidylinositol (PI) 3-kinase, was targeted to the endoplasmic reticulum (ER). MavQ and the Legionella PI 3-phosphatase SidP, even in the absence of other bacterial components, drove rapid PI 3-phosphate turnover on the ER and spontaneously formed traveling waves that spread along ER subdomains inducing vesicle and tubule budding. Thus, bacteria can exploit a self-organizing membrane-targeting mechanism to hijack host cellular structures for survival.
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Affiliation(s)
- Ting-Sung Hsieh
- Department of Molecular Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Victor A Lopez
- Department of Molecular Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Miles H Black
- Department of Molecular Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Adam Osinski
- Department of Molecular Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Krzysztof Pawłowski
- Department of Molecular Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
- Department of Biochemistry and Microbiology, Institute of Biology, Warsaw University of Life Sciences, Warsaw 02-776, Poland
| | - Diana R Tomchick
- Department of Biophysics, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
- Department of Biochemistry, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Jen Liou
- Department of Physiology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Vincent S Tagliabracci
- Department of Molecular Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA.
- Harold C. Simmons Comprehensive Cancer Center, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
- Hamon Center for Regenerative Science and Medicine, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
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39
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Mishra B, Johnson ME. Speed limits of protein assembly with reversible membrane localization. J Chem Phys 2021; 154:194101. [PMID: 34240891 PMCID: PMC8131109 DOI: 10.1063/5.0045867] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 04/26/2021] [Indexed: 12/15/2022] Open
Abstract
Protein assembly is often studied in a three-dimensional solution, but a significant fraction of binding events involve proteins that can reversibly bind and diffuse along a two-dimensional surface. In a recent study, we quantified how proteins can exploit the reduced dimensionality of the membrane to trigger complex formation. Here, we derive a single expression for the characteristic timescale of this multi-step assembly process, where the change in dimensionality renders rates and concentrations effectively time-dependent. We find that proteins can accelerate dimer formation due to an increase in relative concentration, driving more frequent collisions, which often win out over slow-downs due to diffusion. Our model contains two protein populations that dimerize with one another and use a distinct site to bind membrane lipids, creating a complex reaction network. However, by identifying two major rate-limiting pathways to reach an equilibrium steady-state, we derive an excellent approximation for the mean first passage time when lipids are in abundant supply. Our theory highlights how the "sticking rate" or effective adsorption coefficient of the membrane is central in controlling timescales. We also derive a corrected localization rate to quantify how the geometry of the system and diffusion can reduce rates of membrane localization. We validate and test our results using kinetic and particle-based reaction-diffusion simulations. Our results establish how the speed of key assembly steps can shift by orders-of-magnitude when membrane localization is possible, which is critical to understanding mechanisms used in cells.
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Affiliation(s)
- Bhavya Mishra
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, Maryland 21218, USA
| | - Margaret E. Johnson
- TC Jenkins Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, Maryland 21218, USA
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40
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Chiou JG, Moran KD, Lew DJ. How cells determine the number of polarity sites. eLife 2021; 10:e58768. [PMID: 33899733 PMCID: PMC8116050 DOI: 10.7554/elife.58768] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2020] [Accepted: 04/23/2021] [Indexed: 12/15/2022] Open
Abstract
The diversity of cell morphologies arises, in part, through regulation of cell polarity by Rho-family GTPases. A poorly understood but fundamental question concerns the regulatory mechanisms by which different cells generate different numbers of polarity sites. Mass-conserved activator-substrate (MCAS) models that describe polarity circuits develop multiple initial polarity sites, but then those sites engage in competition, leaving a single winner. Theoretical analyses predicted that competition would slow dramatically as GTPase concentrations at different polarity sites increase toward a 'saturation point', allowing polarity sites to coexist. Here, we test this prediction using budding yeast cells, and confirm that increasing the amount of key polarity proteins results in multiple polarity sites and simultaneous budding. Further, we elucidate a novel design principle whereby cells can switch from competition to equalization among polarity sites. These findings provide insight into how cells with diverse morphologies may determine the number of polarity sites.
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Affiliation(s)
- Jian-geng Chiou
- Department of Pharmacology and Cancer Biology, Duke University Medical CenterDurhamUnited States
| | - Kyle D Moran
- Department of Pharmacology and Cancer Biology, Duke University Medical CenterDurhamUnited States
| | - Daniel J Lew
- Department of Pharmacology and Cancer Biology, Duke University Medical CenterDurhamUnited States
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41
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Abstract
The molecular mechanisms that help to place the division septum in bacteria is of fundamental importance to ensure cell proliferation and maintenance of cell shape and size. The Min protein system, found in many rod-shaped bacteria, is thought to play a major role in division site selection. Division site selection is a vital process to ensure generation of viable offspring. In many rod-shaped bacteria, a dynamic protein system, termed the Min system, acts as a central regulator of division site placement. The Min system is best studied in Escherichia coli, where it shows a remarkable oscillation from pole to pole with a time-averaged density minimum at midcell. Several components of the Min system are conserved in the Gram-positive model organism Bacillus subtilis. However, in B. subtilis, it is commonly believed that the system forms a stationary bipolar gradient from the cell poles to midcell. Here, we show that the Min system of B. subtilis localizes dynamically to active sites of division, often organized in clusters. We provide physical modeling using measured diffusion constants that describe the observed enrichment of the Min system at the septum. Mathematical modeling suggests that the observed localization pattern of Min proteins corresponds to a dynamic equilibrium state. Our data provide evidence for the importance of ongoing septation for the Min dynamics, consistent with a major role of the Min system in controlling active division sites but not cell pole areas.
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42
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Fu M, Franquelim HG, Kretschmer S, Schwille P. Non‐Equilibrium Large‐Scale Membrane Transformations Driven by MinDE Biochemical Reaction Cycles. Angew Chem Int Ed Engl 2021. [DOI: 10.1002/ange.202015184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Meifang Fu
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
| | - Henri G. Franquelim
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
| | - Simon Kretschmer
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
- Department of Bioengineering and Therapeutic Science University of California San Francisco San Francisco CA USA
| | - Petra Schwille
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
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43
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Fu M, Franquelim HG, Kretschmer S, Schwille P. Non-Equilibrium Large-Scale Membrane Transformations Driven by MinDE Biochemical Reaction Cycles. Angew Chem Int Ed Engl 2021; 60:6496-6502. [PMID: 33285025 PMCID: PMC7986748 DOI: 10.1002/anie.202015184] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Indexed: 12/11/2022]
Abstract
The MinDE proteins from E. coli have received great attention as a paradigmatic biological pattern-forming system. Recently, it has surfaced that these proteins do not only generate oscillating concentration gradients driven by ATP hydrolysis, but that they can reversibly deform giant vesicles. In order to explore the potential of Min proteins to actually perform mechanical work, we introduce a new model membrane system, flat vesicle stacks on top of a supported lipid bilayer. MinDE oscillations can repeatedly deform these flat vesicles into tubules and promote progressive membrane spreading through membrane adhesion. Dependent on membrane and buffer compositions, Min oscillations further induce robust bud formation. Altogether, we demonstrate that under specific conditions, MinDE self-organization can result in work performed on biomimetic systems and achieve a straightforward mechanochemical coupling between the MinDE biochemical reaction cycle and membrane transformation.
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Affiliation(s)
- Meifang Fu
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
| | - Henri G. Franquelim
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
| | - Simon Kretschmer
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
- Department of Bioengineering and Therapeutic ScienceUniversity of California San FranciscoSan FranciscoCAUSA
| | - Petra Schwille
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
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44
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Bressloff PC. Multi-spike solutions of a hybrid reaction–transport model. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2020.0829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Simulations of classical pattern-forming reaction–diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady state consisting of a spatially repeating pattern of localized spikes. In activator–inhibitor systems such as the two-component Gierer–Meinhardt (GM) model, one can consider the singular limit
D
a
≪
D
h
, where
D
a
and
D
h
are the diffusivities of the activator and inhibitor, respectively. Asymptotic analysis can then be used to analyse the existence and linear stability of multi-spike solutions. In this paper, we analyse multi-spike solutions in a hybrid reaction–transport model, consisting of a slowly diffusing activator and an actively transported inhibitor that switches at a rate
α
between right-moving and left-moving velocity states. Such a model was recently introduced to account for the formation and homeostatic regulation of synaptic puncta during larval development in
Caenorhabditis elegans
. We exploit the fact that the hybrid model can be mapped onto the classical GM model in the fast switching limit
α
→ ∞, which establishes the existence of multi-spike solutions. Linearization about the multi-spike solution yields a non-local eigenvalue problem that is used to investigate stability of the multi-spike solution by combining analytical results for
α
→ ∞ with a graphical construction for finite
α
.
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Affiliation(s)
- P. C. Bressloff
- Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
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45
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Zamparo M, Valdembri D, Serini G, Kolokolov IV, Lebedev VV, Dall'Asta L, Gamba A. Optimality in Self-Organized Molecular Sorting. PHYSICAL REVIEW LETTERS 2021; 126:088101. [PMID: 33709726 DOI: 10.1103/physrevlett.126.088101] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Accepted: 01/25/2021] [Indexed: 06/12/2023]
Abstract
We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle nucleation. Its implications are studied by means of a phenomenological theory describing the diffusion of molecules toward multiple sorting centers that grow due to molecule absorption and are extracted when they reach a sufficiently large size. The predictions of the theory are compared with numerical simulations of a lattice-gas realization of the model and with experimental observations. The efficiency of the distillation process is found to be optimal for intermediate aggregation rates, where the density of sorted molecules is minimal and the process obeys simple scaling laws. Quantitative measures of endocytic sorting performed in primary endothelial cells are compatible with the hypothesis that these optimal conditions are realized in living cells.
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Affiliation(s)
- Marco Zamparo
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- Italian Institute for Genomic Medicine c/o Candiolo Cancer Institute, Fondazione del Piemonte per l'Oncologia (FPO), Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Candiolo, 10060 Torino, Italy
| | - Donatella Valdembri
- Department of Oncology, University of Torino School of Medicine, Candiolo, 10060 Torino, Italy
- Candiolo Cancer Institute, Fondazione del Piemonte per l'Oncologia (FPO), Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Candiolo, 10060 Torino, Italy
| | - Guido Serini
- Department of Oncology, University of Torino School of Medicine, Candiolo, 10060 Torino, Italy
- Candiolo Cancer Institute, Fondazione del Piemonte per l'Oncologia (FPO), Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Candiolo, 10060 Torino, Italy
| | - Igor V Kolokolov
- L.D. Landau Institute for Theoretical Physics, 142432, Moscow Region, Chernogolovka, Ak. Semenova, 1-A, Russia
- National Research University Higher School of Economics, 101000, Myasnitskaya 20, Moscow, Russia
| | - Vladimir V Lebedev
- L.D. Landau Institute for Theoretical Physics, 142432, Moscow Region, Chernogolovka, Ak. Semenova, 1-A, Russia
- National Research University Higher School of Economics, 101000, Myasnitskaya 20, Moscow, Russia
| | - Luca Dall'Asta
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- Italian Institute for Genomic Medicine c/o Candiolo Cancer Institute, Fondazione del Piemonte per l'Oncologia (FPO), Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Candiolo, 10060 Torino, Italy
- Collegio Carlo Alberto, Piazza Arbarello 8, 10122 Torino, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Italy
| | - Andrea Gamba
- Institute of Condensed Matter Physics and Complex Systems, Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- Italian Institute for Genomic Medicine c/o Candiolo Cancer Institute, Fondazione del Piemonte per l'Oncologia (FPO), Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS), Candiolo, 10060 Torino, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Italy
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Subramanian S, Murray SM. Pattern selection in reaction diffusion systems. Phys Rev E 2021; 103:012215. [PMID: 33601645 DOI: 10.1103/physreve.103.012215] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 01/07/2021] [Indexed: 11/07/2022]
Abstract
Turing's theory of pattern formation has been used to describe the formation of self-organized periodic patterns in many biological, chemical, and physical systems. However, the use of such models is hindered by our inability to predict, in general, which pattern is obtained from a given set of model parameters. While much is known near the onset of the spatial instability, the mechanisms underlying pattern selection and dynamics away from onset are much less understood. Here, we provide physical insight into the dynamics of these systems. We find that peaks in a Turing pattern behave as point sinks, the dynamics of which is determined by the diffusive fluxes into them. As a result, peaks move toward a periodic steady-state configuration that minimizes the mass of the diffusive species. We also show that the preferred number of peaks at the final steady state is such that this mass is minimized. Our work presents mass minimization as a potential general principle for understanding pattern formation in reaction diffusion systems far from onset.
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Affiliation(s)
| | - Seán M Murray
- Max Planck Institute for Terrestrial Microbiology, 35043 Marburg, Germany
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Chu L, Liang Z, Mukhina MV, Fisher JK, Hutchinson JW, Kleckner NE. One-dimensional spatial patterning along mitotic chromosomes: A mechanical basis for macroscopic morphogenesis. Proc Natl Acad Sci U S A 2020; 117:26749-26755. [PMID: 33051295 PMCID: PMC7604413 DOI: 10.1073/pnas.2013709117] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
Spatial patterns are ubiquitous in both physical and biological systems. We have recently discovered that mitotic chromosomes sequentially acquire two interesting morphological patterns along their structural axes [L. Chu et al., Mol. Cell, 10.1016/j.molcel.2020.07.002 (2020)]. First, axes of closely conjoined sister chromosomes acquire regular undulations comprising nearly planar arrays of sequential half-helices of similar size and alternating handedness, accompanied by periodic kinks. This pattern, which persists through all later stages, provides a case of the geometric form known as a "perversion." Next, as sister chromosomes become distinct parallel units, their individual axes become linked by bridges, which are themselves miniature axes. These bridges are dramatically evenly spaced. Together, these effects comprise a unique instance of spatial patterning in a subcellular biological system. We present evidence that axis undulations and bridge arrays arise by a single continuous mechanically promoted progression, driven by stress within the chromosome axes. We further suggest that, after sister individualization, this same stress also promotes chromosome compaction by rendering the axes susceptible to the requisite molecular remodeling. Thus, by this scenario, the continuous presence of mechanical stress within the chromosome axes could potentially underlie the entire morphogenetic chromosomal program. Direct analogies with meiotic chromosomes suggest that the same effects could underlie interactions between homologous chromosomes as required for gametogenesis. Possible mechanical bases for generation of axis stress and resultant deformations are discussed. Together, these findings provide a perspective on the macroscopic changes of organized chromosomes.
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Affiliation(s)
- Lingluo Chu
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138
| | - Zhangyi Liang
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138
| | - Maria V Mukhina
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138
| | | | - John W Hutchinson
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138
| | - Nancy E Kleckner
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138;
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Krause AL, Klika V, Halatek J, Grant PK, Woolley TE, Dalchau N, Gaffney EA. Turing Patterning in Stratified Domains. Bull Math Biol 2020; 82:136. [PMID: 33057872 PMCID: PMC7561598 DOI: 10.1007/s11538-020-00809-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 09/18/2020] [Indexed: 01/06/2023]
Abstract
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction-diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of a spatially homogeneous equilibrium analogous to the classical conditions for a Turing instability in the simplest nontrivial setting where one domain has a standard reaction-diffusion system, and the other permits only diffusion. Due to the transverse coupling between these two regions, standard techniques for computing eigenfunctions of the Laplacian cannot be applied, and so we propose an alternative method to compute the dispersion relation directly. We compare instability conditions with full numerical simulations to demonstrate impacts of the geometry and coupling parameters on patterning, and explore various experimentally relevant asymptotic regimes. In the regime where the first domain is suitably thin, we recover a simple modulation of the standard Turing conditions, and find that often the broad impact of the diffusion-only domain is to reduce the ability of the system to form patterns. We also demonstrate complex impacts of this coupling on pattern formation. For instance, we exhibit non-monotonicity of pattern-forming instabilities with respect to geometric and coupling parameters, and highlight an instability from a nontrivial interaction between kinetics in one domain and diffusion in the other. These results are valuable for informing design choices in applications such as synthetic engineering of Turing patterns, but also for understanding the role of stratified media in modulating pattern-forming processes in developmental biology and beyond.
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Affiliation(s)
- Andrew L Krause
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
| | - Václav Klika
- Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Prague, Czech Republic
| | - Jacob Halatek
- Microsoft Research, 21 Station Rd, Cambridge, CB1 2FB, UK
| | - Paul K Grant
- Microsoft Research, 21 Station Rd, Cambridge, CB1 2FB, UK
| | - Thomas E Woolley
- Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK
| | - Neil Dalchau
- Microsoft Research, 21 Station Rd, Cambridge, CB1 2FB, UK
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
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Goryachev AB, Leda M. Compete or Coexist? Why the Same Mechanisms of Symmetry Breaking Can Yield Distinct Outcomes. Cells 2020; 9:E2011. [PMID: 32882972 PMCID: PMC7563139 DOI: 10.3390/cells9092011] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 08/27/2020] [Accepted: 08/28/2020] [Indexed: 12/22/2022] Open
Abstract
Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of dense protein clusters. Thus, a cluster of active GTPase Cdc42 marks the site of nascent bud in the baker's yeast. An important biological question is which mechanisms control the number of pattern maxima (spots) and, thus, the number of nascent cellular structures. Distinct flavors of theoretical models seem to suggest different predictions. While the classical Turing scenario leads to an array of stably coexisting multiple structures, mass-conserved models predict formation of a single spot that emerges via the greedy competition between the pattern maxima for the common molecular resources. Both the outcome and the kinetics of this competition are of significant biological importance but remained poorly explored. Recent theoretical analyses largely addressed these questions, but their results have not yet been fully appreciated by the broad biological community. Keeping mathematical apparatus and jargon to the minimum, we review the main conclusions of these analyses with their biological implications in mind. Focusing on the specific example of pattern formation by small GTPases, we speculate on the features of the patterning mechanisms that bypass competition and favor formation of multiple coexisting structures and contrast them with those of the mechanisms that harness competition to form unique cellular structures.
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Affiliation(s)
- Andrew B. Goryachev
- SynthSys, Centre for Synthetic and Systems Biology, Institute for Cell Biology, University of Edinburgh, Edinburg EH9 3BD, UK;
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50
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Khalili B, Lovelace HD, Rutkowski DM, Holz D, Vavylonis D. Fission Yeast Polarization: Modeling Cdc42 Oscillations, Symmetry Breaking, and Zones of Activation and Inhibition. Cells 2020; 9:E1769. [PMID: 32722101 PMCID: PMC7464287 DOI: 10.3390/cells9081769] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Revised: 07/22/2020] [Accepted: 07/23/2020] [Indexed: 12/24/2022] Open
Abstract
Cells polarize for growth, motion, or mating through regulation of membrane-bound small GTPases between active GTP-bound and inactive GDP-bound forms. Activators (GEFs, GTP exchange factors) and inhibitors (GAPs, GTPase activating proteins) provide positive and negative feedbacks. We show that a reaction-diffusion model on a curved surface accounts for key features of polarization of model organism fission yeast. The model implements Cdc42 membrane diffusion using measured values for diffusion coefficients and dissociation rates and assumes a limiting GEF pool (proteins Gef1 and Scd1), as in prior models for budding yeast. The model includes two types of GAPs, one representing tip-localized GAPs, such as Rga3; and one representing side-localized GAPs, such as Rga4 and Rga6, that we assume switch between fast and slow diffusing states. After adjustment of unknown rate constants, the model reproduces active Cdc42 zones at cell tips and the pattern of GEF and GAP localization at cell tips and sides. The model reproduces observed tip-to-tip oscillations with periods of the order of several minutes, as well as asymmetric to symmetric oscillations transitions (corresponding to NETO "new end take off"), assuming the limiting GEF amount increases with cell size.
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Affiliation(s)
- Bita Khalili
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA; (B.K.); (H.D.L.); (D.M.R.); (D.H.)
| | - Hailey D. Lovelace
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA; (B.K.); (H.D.L.); (D.M.R.); (D.H.)
- Department of Physics and Astronomy, Clemson University, Clemson, SC 29631, USA
| | - David M. Rutkowski
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA; (B.K.); (H.D.L.); (D.M.R.); (D.H.)
| | - Danielle Holz
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA; (B.K.); (H.D.L.); (D.M.R.); (D.H.)
| | - Dimitrios Vavylonis
- Department of Physics, Lehigh University, Bethlehem, PA 18015, USA; (B.K.); (H.D.L.); (D.M.R.); (D.H.)
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