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Gannon A, Quaife B, Young YN. Hydrodynamics of a multicomponent vesicle under strong confinement. SOFT MATTER 2024; 20:599-608. [PMID: 38131477 DOI: 10.1039/d3sm01087b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2023]
Abstract
We numerically investigate the hydrodynamics and membrane dynamics of a multicomponent vesicle in two strongly confined geometries. This serves as a simplified model for red blood cells undergoing large deformations while traversing narrow constrictions. We propose a new parameterization for the bending modulus that remains positive for all lipid phase parameter values. For a multicomponent vesicle passing through a stenosis, we establish connections between various properties: lipid phase coarsening, size and flow profile of the lubrication layers, excess pressure, and the tank-treading velocity of the membrane. For a multicomponent vesicle passing through a contracting channel, we find that the lipid always phase separates so that the vesicle is stiffer in the front as it passes through the constriction. For both cases of confinement we find that lipid coarsening is arrested under strong confinement, and resumes at a high rate upon relief from extreme confinement. The results may be useful for efficient sorting lipid domains using microfluidic flows by controlled release of vesicles passing through strong confinement.
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Affiliation(s)
- Ashley Gannon
- Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA.
| | - Bryan Quaife
- Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA.
| | - Y-N Young
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA.
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2
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Bureau L, Coupier G, Salez T. Lift at low Reynolds number. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:111. [PMID: 37957450 DOI: 10.1140/epje/s10189-023-00369-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 10/19/2023] [Indexed: 11/15/2023]
Abstract
Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.
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Affiliation(s)
- Lionel Bureau
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000, Grenoble, France.
| | | | - Thomas Salez
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France.
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Tang X, Li S, Lowengrub JS, Wise SM. Phase field modeling and computation of vesicle growth or shrinkage. J Math Biol 2023; 86:97. [PMID: 37219647 PMCID: PMC10596721 DOI: 10.1007/s00285-023-01928-2] [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: 10/03/2022] [Revised: 02/01/2023] [Accepted: 04/07/2023] [Indexed: 05/24/2023]
Abstract
We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of the phase field parameter that describes the shape of the vesicle and a Cahn-Hilliard-type equation describing the evolution of the ionic fluid. We establish conditions for vesicle growth or shrinkage via a common tangent construction using free energy curves. During the membrane deformation, the model ensures total mass conservation of the ionic fluid, and we weakly enforce a surface area constraint of the vesicle. We develop a stable numerical scheme and an efficient nonlinear multigrid solver to evolve the phase and concentration fields, and we use this to evolve the fields to near equilibrium for 2D vesicles. Convergence tests confirm an [Formula: see text] accuracy for our scheme and near-optimal convergence for our multigrid solver. Numerical results reveal that the diffuse interface model captures the main features of cell shape dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.
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Affiliation(s)
- Xiaoxia Tang
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA
| | - Shuwang Li
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA
| | - John S Lowengrub
- Department of Mathematics, The University of California, Irvine, CA, 92697, USA
| | - Steven M Wise
- Department of Mathematics, The University of Tennessee, Knoxville, TN, 37996, USA.
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Xiao W, Liu K, Lowengrub J, Li S, Zhao M. Three-dimensional numerical study on wrinkling of vesicles in elongation flow based on the immersed boundary method. Phys Rev E 2023; 107:035103. [PMID: 37072945 DOI: 10.1103/physreve.107.035103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 02/15/2023] [Indexed: 04/20/2023]
Abstract
We study the wrinkling dynamics of three-dimensional vesicles in a time-dependent elongation flow by utilizing an immersed boundary method. For a quasispherical vesicle, our numerical results well match the predictions of perturbation analysis, where similar exponential relationships between wrinkles' characteristic wavelength and the flow strength are observed. Using the same parameters as in the experiments by Kantsler et al. [V. Kantsler et al., Phys. Rev. Lett. 99, 178102 (2007)0031-900710.1103/PhysRevLett.99.178102], our simulations of an elongated vesicle are in good agreement with their results. In addition, we get rich three-dimensional morphological details, which are favorable to comprehend the two-dimensional snapshots. This morphological information helps identify wrinkle patterns. We analyze the morphological evolution of wrinkles using spherical harmonics. We find discrepancies in elongated vesicle dynamics between simulations and perturbation analysis, highlighting the importance of the nonlinear effects. Finally, we investigate the unevenly distributed local surface tension, which largely determines the position of wrinkles excited on the vesicle membrane.
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Affiliation(s)
- Wang Xiao
- School of Mathematics and Statistics, Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Kai Liu
- College of Education for the Future, Beijing Normal University, Zhuhai 519087, China
| | - John Lowengrub
- Department of Mathematics, University of California Irvine, Irvine, California 92697, USA
| | - Shuwang Li
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Meng Zhao
- School of Mathematics and Statistics, Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
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Tran PD, Blanpied TA, Atzberger PJ. Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods. Phys Rev E 2022; 106:044402. [PMID: 36397472 DOI: 10.1103/physreve.106.044402] [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: 10/04/2021] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.
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Affiliation(s)
- Patrick D Tran
- Physics, College of Creative Studies, University of California, Santa Barbara, Santa Barbara, California 93106-3080, USA
| | - Thomas A Blanpied
- Department of Physiology, University of Maryland, Baltimore, Maryland 21201, USA
| | - Paul J Atzberger
- Department of Mathematics and Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106-3080, USA
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Brandão R, Carvalho GD, Miranda JA. Mode-coupling approach to near-cuspidal patterns in planar fluid flows. Phys Rev E 2021; 103:063102. [PMID: 34271760 DOI: 10.1103/physreve.103.063102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2021] [Accepted: 05/24/2021] [Indexed: 11/07/2022]
Abstract
We investigate the evolution of the interface separating two Newtonian fluids of different viscosities in two-dimensional Stokes flow driven by suction or injection. A second-order, mode-coupling theory is used to explore key morphological aspects of the emerging interfacial patterns in the stage of the flow that bridges the purely linear and fully nonlinear regimes. In the linear regime, our analysis reveals that an injection-driven expanding interface is stable, while a contracting motion driven by suction is unstable. Moreover, we find that the linear growth rate associated with this suction-driven instability is independent of the viscosity contrast between the fluids. However, second-order results tell a different story, and show that the viscosity contrast is crucial in determining the morphology of the interface. Our theoretical description is applicable to the entire range of viscosity contrasts, and provides insights on the formation of near-cusp pattern-forming structures. Reproduction of fully nonlinear, n-fold symmetric near-cuspidal shapes previously obtained through conformal mapping techniques substantiates the validity of our mode-coupling approach.
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Affiliation(s)
- Rodolfo Brandão
- Department of Mathematics, Imperial College London, London SW7 2AZ United Kingdom
| | - Gabriel D Carvalho
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
| | - José A Miranda
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil
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Priti Sinha K, Das S, Karyappa RB, Thaokar RM. Electrohydrodynamics of Vesicles and Capsules. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:4863-4886. [PMID: 32275824 DOI: 10.1021/acs.langmuir.9b03971] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Giant unilamellar vesicles (GUVs) made up of phospholipid bilayer membranes (liposomes) and elastic capsules with a cross-linked, polymerized membrane, have emerged as biomimetic alternatives to investigating biological cells such as leukocytes and erythrocytes. This feature article looks at the similarities and differences in the electrohydrodynamics (EHD) of vesicles and capsules under electric fields that determines their electromechanical response. The physics of EHD is illustrated through several examples such as the electrodeformation of single and compound, spherical and cylindrical, and charged and uncharged vesicles in uniform and nonuniform electric fields, and the relevance and challenges are discussed. Both small and large deformation results are discussed. The use of EHD in understanding complex interfacial kinetics in capsules and the synthesis of nonspherical capsules using electric fields are also presented. Finally, the review looks at the large electrodeformation of water-in-water capsules and the relevance of constitutive laws in their response.
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Affiliation(s)
- Kumari Priti Sinha
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Sudip Das
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Rahul Bapusaheb Karyappa
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Rochish M Thaokar
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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Klotz AR, Soh BW, Doyle PS. Equilibrium structure and deformation response of 2D kinetoplast sheets. Proc Natl Acad Sci U S A 2020; 117:121-127. [PMID: 31811027 PMCID: PMC6955370 DOI: 10.1073/pnas.1911088116] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The considerable interest in two-dimensional (2D) materials and complex molecular topologies calls for a robust experimental system for single-molecule studies. In this work, we study the equilibrium properties and deformation response of a complex DNA structure called a kinetoplast, a 2D network of thousands of linked rings akin to molecular chainmail. Examined in good solvent conditions, kinetoplasts appear as a wrinkled hemispherical sheet. The conformation of each kinetoplast is dictated by its network topology, giving it a unique shape, which undergoes small-amplitude thermal fluctuations at subsecond timescales, with a wide separation between fluctuation and diffusion timescales. They deform elastically when weakly confined and swell to their equilibrium dimensions when the confinement is released. We hope that, in the same way that linear DNA became a canonical model system on the first investigations of its polymer-like behavior, kinetoplasts can serve that role for 2D and catenated polymer systems.
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Affiliation(s)
- Alexander R Klotz
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02142
- Department of Physics and Astronomy, California State University, Long Beach, CA 90840
| | - Beatrice W Soh
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02142
| | - Patrick S Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02142;
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Gera P, Salac D. Three-dimensional multicomponent vesicles: dynamics and influence of material properties. SOFT MATTER 2018; 14:7690-7705. [PMID: 30177985 DOI: 10.1039/c8sm01087k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this work, the nonlinear hydrodynamics of a three-dimensional multicomponent vesicle in shear flow are explored. Using a volume- and area-conserving projection method coupled to a gradient-augmented level set and surface phase field method, the dynamics are systematically studied as a function of the membrane bending rigidity difference between the components, the speed of diffusion compared to the underlying shear flow, and the strength of the phase domain energy compared to the bending energy. Using a pre-segregated vesicle, three dynamics are observed: stationary phase, phase-treading, and a new dynamic called vertical banding. These regimes are very sensitive to the strength of the domain line energy, as the vertical banding regime is not observed when the line energy is larger than the bending energy. The findings demonstrate that a complete understanding of multicomponent vesicle dynamics requires that the full three-dimensional system be modeled, and show the complexity obtained when considering heterogeneous material properties.
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Affiliation(s)
- Prerna Gera
- Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260-4400, USA.
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