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Chomchai D, Leda M, Golding A, von Dassow G, Bement WM, Goryachev AB. Testing models of cell cortex wave generation by Rho GTPases. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.04.29.591685. [PMID: 38746143 PMCID: PMC11092441 DOI: 10.1101/2024.04.29.591685] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2024]
Abstract
The Rho GTPases pattern the cell cortex in a variety of fundamental cell-morphogenetic processes including division, wound repair, and locomotion. It has recently become apparent that this patterning arises from the ability of the Rho GTPases to self-organize into static and migrating spots, contractile pulses, and propagating waves in cells from yeasts to mammals 1 . These self-organizing Rho GTPase patterns have been explained by a variety of theoretical models which require multiple interacting positive and negative feedback loops. However, it is often difficult, if not impossible, to discriminate between different models simply because the available experimental data do not simultaneously capture the dynamics of multiple molecular concentrations and biomechanical variables at fine spatial and temporal resolution. Specifically, most studies typically provide either the total Rho GTPase signal or the Rho GTPase activity as reported by various sensors, but not both. Therefore, it remains largely unknown how membrane accumulation of Rho GTPases (i.e., Rho membrane enrichment) is related to Rho activity. Here we dissect the dynamics of RhoA by simultaneously imaging both total RhoA and active RhoA in the regime of acute cortical excitability 2 , characterized by pronounced waves of Rho activity and F-actin polymerization 3-5 . We find that within nascent waves, accumulation of active RhoA precedes that of total RhoA, and we exploit this finding to distinguish between two popular theoretical models previously used to explain propagating cortical Rho waves.
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Wang X, Jiang J, Chen J, Asilehan Z, Tang W, Peng C, Zhang R. Moiré effect enables versatile design of topological defects in nematic liquid crystals. Nat Commun 2024; 15:1655. [PMID: 38409234 PMCID: PMC10897219 DOI: 10.1038/s41467-024-45529-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 01/24/2024] [Indexed: 02/28/2024] Open
Abstract
Recent advances in surface-patterning techniques of liquid crystals have enabled the precise creation of topological defects, which promise a variety of emergent applications. However, the manipulation and application of these defects remain limited. Here, we harness the moiré effect to engineer topological defects in patterned nematic liquid crystal cells. Specifically, we combine simulation and experiment to examine a nematic cell confined between two substrates of periodic surface anchoring patterns; by rotating one surface against the other, we observe a rich variety of highly tunable, novel topological defects. These defects are shown to guide the three-dimensional self-assembly of colloids, which can conversely impact defects by preventing the self-annihilation of loop-defects through jamming. Finally, we demonstrate that certain nematic moiré cells can engender arbitrary shapes represented by defect regions. As such, the proposed simple twist method enables the design and tuning of mesoscopic structures in liquid crystals, facilitating applications including defect-directed self-assembly, material transport, micro-reactors, photonic devices, and anti-counterfeiting materials.
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Affiliation(s)
- Xinyu Wang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - Jinghua Jiang
- Department of Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Juan Chen
- Department of Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- Department of Physics and Materials Science, The University of Memphis, Memphis, TN, 38152, USA
| | - Zhawure Asilehan
- Department of Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Wentao Tang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - Chenhui Peng
- Department of Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China.
| | - Rui Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
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Three-dimensional chiral morphodynamics of chemomechanical active shells. Proc Natl Acad Sci U S A 2022; 119:e2206159119. [PMID: 36442097 PMCID: PMC9894169 DOI: 10.1073/pnas.2206159119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.
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Miller PW, Fortunato D, Muratov C, Greengard L, Shvartsman S. Forced and spontaneous symmetry breaking in cell polarization. NATURE COMPUTATIONAL SCIENCE 2022; 2:504-511. [PMID: 37309402 PMCID: PMC10260237 DOI: 10.1038/s43588-022-00295-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 07/12/2022] [Indexed: 06/14/2023]
Abstract
How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.
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Affiliation(s)
- Pearson W. Miller
- Center for Computational Biology, Flatiron Institute, New York, NY, USA
- These authors contributed equally: Pearson W. Miller, Daniel Fortunato
| | - Daniel Fortunato
- Center for Computational Mathematics, Flatiron Institute, New York, NY, USA
- These authors contributed equally: Pearson W. Miller, Daniel Fortunato
| | - Cyrill Muratov
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA
- Dipartimento di Matematica, Università di Pisa, Pisa, Italy
| | - Leslie Greengard
- Center for Computational Mathematics, Flatiron Institute, New York, NY, USA
- Courant Institute, New York University, New York, NY, USA
| | - Stanislav Shvartsman
- Center for Computational Biology, Flatiron Institute, New York, NY, USA
- Courant Institute, New York University, New York, NY, USA
- Department of Molecular Biology, Princeton University, Princeton, NJ, USA
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
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Lebert J, Ravi N, Fenton FH, Christoph J. Rotor Localization and Phase Mapping of Cardiac Excitation Waves Using Deep Neural Networks. Front Physiol 2022; 12:782176. [PMID: 34975536 PMCID: PMC8718715 DOI: 10.3389/fphys.2021.782176] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 11/11/2021] [Indexed: 11/15/2022] Open
Abstract
The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting.
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Affiliation(s)
- Jan Lebert
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States
| | - Namita Ravi
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States.,Yale School of Medicine, Yale University, New Haven, CT, United States
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Jan Christoph
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, CA, United States
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