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Deinum EE, Jacobs B. Rho of Plants patterning: linking mathematical models and molecular diversity. JOURNAL OF EXPERIMENTAL BOTANY 2024; 75:1274-1288. [PMID: 37962515 PMCID: PMC10901209 DOI: 10.1093/jxb/erad447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 11/08/2023] [Indexed: 11/15/2023]
Abstract
ROPs (Rho of Plants) are plant specific small GTPases involved in many membrane patterning processes and play important roles in the establishment and communication of cell polarity. These small GTPases can produce a wide variety of patterns, ranging from a single cluster in tip-growing root hairs and pollen tubes to an oriented stripe pattern controlling protoxylem cell wall deposition. For an understanding of what controls these various patterns, models are indispensable. Consequently, many modelling studies on small GTPase patterning exist, often focusing on yeast or animal cells. Multiple patterns occurring in plants, however, require the stable co-existence of multiple active ROP clusters, which does not occur with the most common yeast/animal models. The possibility of such patterns critically depends on the precise model formulation. Additionally, different small GTPases are usually treated interchangeably in models, even though plants possess two types of ROPs with distinct molecular properties, one of which is unique to plants. Furthermore, the shape and even the type of ROP patterns may be affected by the cortical cytoskeleton, and cortex composition and anisotropy differ dramatically between plants and animals. Here, we review insights into ROP patterning from modelling efforts across kingdoms, as well as some outstanding questions arising from these models and recent experimental findings.
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Affiliation(s)
- Eva E Deinum
- Mathematical and Statistical Methods (Biometris), Plant Science Group, Wageningen University, 6708 PB Wageningen, The Netherlands
| | - Bas Jacobs
- Mathematical and Statistical Methods (Biometris), Plant Science Group, Wageningen University, 6708 PB Wageningen, The Netherlands
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Borgqvist JG, Gerlee P, Lundholm C. Turing pattern formation on the sphere is robust to the removal of a hole. J Math Biol 2024; 88:23. [PMID: 38296874 PMCID: PMC10830788 DOI: 10.1007/s00285-023-02034-z] [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: 01/17/2023] [Revised: 11/17/2023] [Accepted: 12/03/2023] [Indexed: 02/02/2024]
Abstract
The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit diffusion-driven pattern formation, thus providing a mechanism for bud formation. However, it is not known how the accumulation of bud scars on the cell membrane affect the ability of the Schnakenberg system to form patterns. We have approached this problem by modelling a bud scar on the cell membrane with a hole on the sphere. We have studied how the spectrum of the Laplace-Beltrami operator, which determines the resulting pattern, is affected by the size of the hole, and by numerically solving the Schnakenberg system on a sphere with a hole using the finite element method. Both theoretical predictions and numerical solutions show that pattern formation is robust to the introduction of a bud scar of considerable size, which lends credence to the hypothesis that bud formation is driven by diffusion-driven instability.
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Affiliation(s)
- Johannes G Borgqvist
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building Radcliffe Observatory Quarter (550) Woodstock Road, Oxford, Oxfordshire, OX2 6GG, UK.
| | - Philip Gerlee
- Mathematical Sciences, University of Gothenburg, Chalmers tvärgata 3, 412 96, Gothenburg, Västra Götaland, Sweden
- Mathematical Sciences, Chalmers University of Technology, Chalmers tvärgata 3, 412 96, Gothenburg, Västra Götaland, Sweden
| | - Carl Lundholm
- Department of Mathematics and Mathematical Statistics, Umeå University, MIT Building, 3rd Floor Linneaus Väg, 907 36, Umeå, Västerbotten, Sweden
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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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Guan K, Curtis ER, Lew DJ, Elston TC. Particle-based simulations reveal two positive feedback loops allow relocation and stabilization of the polarity site during yeast mating. PLoS Comput Biol 2023; 19:e1011523. [PMID: 37782676 PMCID: PMC10569529 DOI: 10.1371/journal.pcbi.1011523] [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: 05/04/2023] [Revised: 10/12/2023] [Accepted: 09/17/2023] [Indexed: 10/04/2023] Open
Abstract
Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site is often not oriented towards the eventual mating partner, and cells relocate the polarity site in an indecisive manner before developing a stable orientation. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior and moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are unlikely to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Surprisingly, inclusion of a second pathway that promotes polarity site orientation generated relocating polarity sites with properties similar to those observed experimentally. This pathway forms a second positive feedback loop involving the recruitment of receptors to the cell membrane and couples polarity establishment to gradient sensing. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.
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Affiliation(s)
- Kaiyun Guan
- Curriculum in Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Erin R. Curtis
- Department of Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Daniel J. Lew
- Department of Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Timothy C. Elston
- Department of Pharmacology and Computational Medicine Program, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
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Microtubule nucleation complex behavior is critical for cortical array homogeneity and xylem wall patterning. Proc Natl Acad Sci U S A 2022; 119:e2203900119. [PMID: 36475944 PMCID: PMC9897462 DOI: 10.1073/pnas.2203900119] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Plant cell walls are versatile materials that can adopt a wide range of mechanical properties through controlled deposition of cellulose fibrils. Wall integrity requires a sufficiently homogeneous fibril distribution to cope effectively with wall stresses. Additionally, specific conditions, such as the negative pressure in water transporting xylem vessels, may require more complex wall patterns, e.g., bands in protoxylem. The orientation and patterning of cellulose fibrils are guided by dynamic cortical microtubules. New microtubules are predominantly nucleated from parent microtubules causing positive feedback on local microtubule density with the potential to yield highly inhomogeneous patterns. Inhomogeneity indeed appears in all current cortical array simulations that include microtubule-based nucleation, suggesting that plant cells must possess an as-yet unknown balancing mechanism to prevent it. Here, in a combined simulation and experimental approach, we show that a limited local recruitment of nucleation complexes to microtubules can counter the positive feedback, whereas local tubulin depletion cannot. We observe that nucleation complexes preferentially appear at the plasma membrane near microtubules. By incorporating our experimental findings in stochastic simulations, we find that the spatial behavior of nucleation complexes delicately balances the positive feedback, such that differences in local microtubule dynamics-as in developing protoxylem-can quickly turn a homogeneous array into a banded one. Our results provide insight into how the plant cytoskeleton has evolved to meet diverse mechanical requirements and greatly increase the predictive power of computational cell biology studies.
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González B, Cullen PJ. Regulation of Cdc42 protein turnover modulates the filamentous growth MAPK pathway. J Cell Biol 2022; 221:213675. [PMID: 36350310 PMCID: PMC9811999 DOI: 10.1083/jcb.202112100] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Revised: 05/25/2022] [Accepted: 09/19/2022] [Indexed: 11/11/2022] Open
Abstract
Rho GTPases are central regulators of cell polarity and signaling. How Rho GTPases are directed to function in certain settings remains unclear. Here, we show the protein levels of the yeast Rho GTPase Cdc42p are regulated, which impacts a subset of its biological functions. Specifically, the active conformation of Cdc42p was ubiquitinated by the NEDD4 ubiquitin ligase Rsp5p and HSP40/HSP70 chaperones and turned over in the proteasome. A GTP-locked (Q61L) turnover-defective (TD) version, Cdc42pQ61L+TD, hyperactivated the MAPK pathway that regulates filamentous growth (fMAPK). Cdc42pQ61L+TD did not influence the activity of the mating pathway, which shares components with the fMAPK pathway. The fMAPK pathway adaptor, Bem4p, stabilized Cdc42p levels, which resulted in elevated fMAPK pathway signaling. Our results identify Cdc42p turnover regulation as being critical for the regulation of a MAPK pathway. The control of Rho GTPase levels by stabilization and turnover may be a general feature of signaling pathway regulation, which can result in the execution of a specific developmental program.
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Affiliation(s)
- Beatriz González
- Department of Biological Sciences, State University of New York at Buffalo, Buffalo, NY
| | - Paul J. Cullen
- Department of Biological Sciences, State University of New York at Buffalo, Buffalo, NY,Correspondence to Paul J. Cullen:
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Herron JC, Hu S, Liu B, Watanabe T, Hahn KM, Elston TC. Spatial models of pattern formation during phagocytosis. PLoS Comput Biol 2022; 18:e1010092. [PMID: 36190993 PMCID: PMC9560619 DOI: 10.1371/journal.pcbi.1010092] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Revised: 10/13/2022] [Accepted: 09/22/2022] [Indexed: 11/17/2022] Open
Abstract
Phagocytosis, the biological process in which cells ingest large particles such as bacteria, is a key component of the innate immune response. Fcγ receptor (FcγR)-mediated phagocytosis is initiated when these receptors are activated after binding immunoglobulin G (IgG). Receptor activation initiates a signaling cascade that leads to the formation of the phagocytic cup and culminates with ingestion of the foreign particle. In the experimental system termed "frustrated phagocytosis", cells attempt to internalize micropatterned disks of IgG. Cells that engage in frustrated phagocytosis form "rosettes" of actin-enriched structures called podosomes around the IgG disk. The mechanism that generates the rosette pattern is unknown. We present data that supports the involvement of Cdc42, a member of the Rho family of GTPases, in pattern formation. Cdc42 acts downstream of receptor activation, upstream of actin polymerization, and is known to play a role in polarity establishment. Reaction-diffusion models for GTPase spatiotemporal dynamics exist. We demonstrate how the addition of negative feedback and minor changes to these models can generate the experimentally observed rosette pattern of podosomes. We show that this pattern formation can occur through two general mechanisms. In the first mechanism, an intermediate species forms a ring of high activity around the IgG disk, which then promotes rosette organization. The second mechanism does not require initial ring formation but relies on spatial gradients of intermediate chemical species that are selectively activated over the IgG patch. Finally, we analyze the models to suggest experiments to test their validity.
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Affiliation(s)
- John Cody Herron
- Curriculum in Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
- Computational Medicine Program, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Shiqiong Hu
- Department of Pharmacology, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Bei Liu
- Department of Pharmacology, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Takashi Watanabe
- Department of Pharmacology, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Klaus M. Hahn
- Computational Medicine Program, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
- Department of Pharmacology, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
| | - Timothy C. Elston
- Curriculum in Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
- Computational Medicine Program, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
- Department of Pharmacology, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America
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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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Peng Y, Zhang D, Qiu Y, Xiao Z, Ji Y, Li W, Xia Y, Wang Y, Guo H. Growth asymmetry precedes differential auxin response during apical hook initiation in Arabidopsis. JOURNAL OF INTEGRATIVE PLANT BIOLOGY 2022; 64:5-22. [PMID: 34786851 DOI: 10.1111/jipb.13190] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 11/15/2021] [Indexed: 06/13/2023]
Abstract
The development of a hook-like structure at the apical part of the soil-emerging organs has fascinated botanists for centuries, but how it is initiated remains unclear. Here, we demonstrate with high-throughput infrared imaging and 2-D clinostat treatment that, when gravity-induced root bending is absent, apical hook formation still takes place. In such scenarios, hook formation begins with a de novo growth asymmetry at the apical part of a straightly elongating hypocotyl. Remarkably, such de novo asymmetric growth, but not the following hook enlargement, precedes the establishment of a detectable auxin response asymmetry, and is largely independent of auxin biosynthesis, transport and signaling. Moreover, we found that functional cortical microtubule array is essential for the following enlargement of hook curvature. When microtubule array was disrupted by oryzalin, the polar localization of PIN proteins and the formation of an auxin maximum became impaired at the to-be-hook region. Taken together, we propose a more comprehensive model for apical hook initiation, in which the microtubule-dependent polar localization of PINs may mediate the instruction of growth asymmetry that is either stochastically taking place, induced by gravitropic response, or both, to generate a significant auxin gradient that drives the full development of the apical hook.
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Affiliation(s)
- Yang Peng
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Faculty of Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, 999077, China
| | - Dan Zhang
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Yuping Qiu
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Zhina Xiao
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Yusi Ji
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Microlens Technologies, Beijing, 100086, China
| | - Wenyang Li
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Yiji Xia
- Department of Biology, Faculty of Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, 999077, China
| | - Yichuan Wang
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Hongwei Guo
- Department of Biology, Institute of Plant and Food Science, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
- Department of Biology, Key Laboratory of Molecular Design for Plant Cell Factory of Guangdong Higher Education Institutes, School of Life Sciences, Southern University of Science and Technology, Shenzhen, 518055, China
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