Cell geometry and leaflet bilayer asymmetry regulate domain formation in plasma membranes

Md Zulfikar Ali, Kerwyn Casey Huang, Ned S. Wingreen, and Ranjan Mukhopadhyay

Phys. Rev. E 99, 012401 – Published 2 January 2019

Abstract

We model how pattern formation in a multicomponent lipid bilayer pinned to an elastic substrate is governed by the interplay between lipid phase separation and the tendency of domains of high intrinsic curvature lipids to deform the membrane away from a stiff substrate such as the cell wall. The emergent patterns, which include compact and striped lipid microdomains, are anticorrelated across the two leaflets and depend on leaflet asymmetry, the ability of lipids to flip between leaflets, and the global geometry. We characterize analytically the dependence of stripe width on lipid parameters, and consider the implications of interleaflet patterning for curvature-dependent lipid localization.

Received 23 June 2017
Revised 19 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.012401

Physics Subject Headings (PhySH)

Cellular bilayers Membrane structure Membranes Phase separation driven self-assembly

Physics of Living SystemsPolymers & Soft Matter

Authors & Affiliations

Md Zulfikar Ali¹, Kerwyn Casey Huang^2,3,4, Ned S. Wingreen⁵, and Ranjan Mukhopadhyay^1,*

¹Department of Physics, Clark University, Worcester, Massachusetts 01610, USA
²Department of Bioengineering, Stanford University, Stanford, California 94305, USA
³Department of Microbiology and Immunology, Stanford University School of Medicine, Stanford, California 94305, USA
⁴Chan Zuckerberg Biohub, San Francisco, California 943158, USA
⁵Department of Molecular Biology, Princeton University, Princeton, New Jersey 08540, USA

^*ranjan@clarku.edu

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Vol. 99, Iss. 1 — January 2019

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Images

Figure 1
Lipids in a two-component membrane can form domains or stripes depending on the intrinsic curvature of the lipids. Shown are typical membrane configurations from simulations of a flat cell surface in the absence of lipid flipping between the leaflets. Blue (dark gray, in print) and red (intermediate gray, in print) represent lipid A locations solely in the inner and outer leaflet, respectively; light gray (green) represents locations occupied by lipid B (lipid A) in both leaflets. (a–c) For equal lipid A fractions $ϕ_{in} = ϕ_{out} = 0.075$ in the two leaflets, increasing $γ$ leads to a transition from a single domain to stripes with width inversely proportional to $γ$ . (d) For asymmetric composition $ϕ_{in} = 0.2$ and $ϕ_{out} = 0.05$ , a combination of stripes and microdomains occurs.
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Figure 2
Transition from microdomains to stripe formation as leaflet asymmetry is reduced. The total amounts of lipid A and B are held fixed, while partitioning between the leaflets is varied. (a–c) Increasing lipid A fraction in the inner leaflet, for fixed intrinsic curvature $γ$ . For subfigure (a), $ϕ_{in} = 0.25$ and $ϕ_{out} = 0.75$ , for (b) $ϕ_{in} = 0.4$ and $ϕ_{out} = 0.6$ , and for (c) $ϕ_{in} = ϕ_{out} = 0.5$ . As in the previous figure, blue (dark gray, in print) and red (intermediate gray, in print) represent lipid A located solely in the inner and outer leaflet, respectively, while light gray (green) represents regions occupied by lipid B (lipid A) in both leaflets. (d) Stripe width as a function of $γ$ , estimated from the Fourier transform of the configuration of lipid A molecules (circles) and estimated from our analytical calculation (solid curve). Inset: Fourier transform from a simulation with parameters of (c). The stripe width is inversely proportional to the radius of the ring in Fourier space. (e) Variation of scaled stripe width from simulation (circles) and calculated analytically (curve) for line tension $τ = 1.68 k_{B} T {nm}^{- 1}$ .
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Figure 3
Substrate curvature $γ_{0}$ inhibits stripe formation when lipids are free to flip between leaflets. (a) The lipid A fraction in the inner leaflet increases with increasing substrate curvature $γ_{0}$ . (b–d) Typical equilibrated membrane configurations for various values of $γ_{0}$ .
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Figure 4
Polar localization of domains of lipids with large intrinsic curvature requires low outer leaflet fraction. (a–c) Rectangles on the left and right represent bacterial cell poles with cell-wall curvature $γ_{0} = 0.04 {nm}^{- 1}$ . $ϕ_{in} = 0.075$ is fixed in all simulations. Shown are typical equilibrated membrane configurations for various values of $γ$ and $ϕ_{out}$ .
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Figure 5
(a) Schematic showing stripes of conical lipid in the inner (blue) and outer (red) leaflet of a bilayer. (b) Energy of the bilayer calculated using Eq. (B6) versus stripe width ( $w_{s}$ ) for estimated line tension $τ = 1.68 k_{B} T {nm}^{- 1}$ and different intrinsic curvatures $γ$ .
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Figure 6
Effect of pinning potential $λ$ on stripe width. (a–d) Membrane configurations for $γ = 0.4 {nm}^{- 1}$ (left) and $0.8 {nm}^{- 1}$ (right) for $λ = 0.001 k_{B} T {nm}^{- 4}$ (top) and $0.1 k_{B} T {nm}^{- 4}$ (bottom). (e) Variation of stripe width calculated analytically (solid and dashed curves) for line tension $τ = 1.68 k_{B} T {nm}^{- 1}$ and obtained by simulation (filled and open circles).
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