Fractal boundaries underpin the 2D melting of biomimetic rafts

Bolmatov, Dima; Zav'yalov, Dmitry; Carrillo, Jan-Michael; Katsaras, John

doi:10.1016/j.bbamem.2020.183249

Title: Fractal boundaries underpin the 2D melting of biomimetic rafts

Abstract

Melting studies of two-dimensional (2D) hard disks and polygons using computational algorithms have yielded some interesting insights regarding soft matter systems. However, the 2D melting of polygons with fractal boundaries has yet to be thoroughly explored, even though such boundaries are important in the self-assembly of biological materials. Here in this paper, we report on 2D melting Monte Carlo (MC) simulations of non-convex polygons with fractal boundaries, model systems mimicking lipid rafts with fractal boundaries surrounded by voids. We describe 2D melting scenarios whereby, a continuous phase transition can be altered to a first order transition through the number of Koch curve iterations imposed on a hexagon. Melting transitions of non-convex polygons (i.e., from solid-to-hexatic and hexatic-to-liquid phases) exhibit sharp local density shifts, in contrast to prototypical hard disks and convex n-gons. Furthermore, we calculate mean square displacements (MSDs) and show that the fractal boundary of the n-th iteration plays a key role in the 2D melting of biomimetic rafts. Importantly, modifying the biomimetic raft boundary from a convex to a fractal geometry leads to hexatic phase narrowing because the self-assembly of polygons is facilitated. Finally, we discuss the implications of 2D melting regarding the self-assembly of lipid domains withmore » proteins (i.e., lipid rafts).« less

Authors:: Bolmatov, Dima; Zav'yalov, Dmitry; Carrillo, Jan-Michael; Katsaras, John

Publication Date:: Sat Aug 01 00:00:00 EDT 2020

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

OSTI Identifier:: 1811563

Alternate Identifier(s):: OSTI ID: 1684660; OSTI ID: 1691821

Grant/Contract Number:: DEAC05-00OR22725; AC05-00OR22725; ACI-1548562

Resource Type:: Published Article

Journal Name:: Biochimica et Biophysica Acta. Biomembranes

Additional Journal Information:: Journal Name: Biochimica et Biophysica Acta. Biomembranes Journal Volume: 1862 Journal Issue: 8; Journal ID: ISSN 0005-2736

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 59 BASIC BIOLOGICAL SCIENCES

Citation Formats


                    Bolmatov, Dima, Zav'yalov, Dmitry, Carrillo, Jan-Michael, and Katsaras, John. Fractal boundaries underpin the 2D melting of biomimetic rafts.  Netherlands: N. p., 2020. 
Web.  doi:10.1016/j.bbamem.2020.183249.

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                    Bolmatov, Dima, Zav'yalov, Dmitry, Carrillo, Jan-Michael, & Katsaras, John. Fractal boundaries underpin the 2D melting of biomimetic rafts.  Netherlands.  https://doi.org/10.1016/j.bbamem.2020.183249

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                    Bolmatov, Dima, Zav'yalov, Dmitry, Carrillo, Jan-Michael, and Katsaras, John. Sat .  
"Fractal boundaries underpin the 2D melting of biomimetic rafts".  Netherlands.  https://doi.org/10.1016/j.bbamem.2020.183249.

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@article{osti_1811563,

  title        = {Fractal boundaries underpin the 2D melting of biomimetic rafts},

  author       = {Bolmatov, Dima and Zav'yalov, Dmitry and Carrillo, Jan-Michael and Katsaras, John},

  abstractNote = {Melting studies of two-dimensional (2D) hard disks and polygons using computational algorithms have yielded some interesting insights regarding soft matter systems. However, the 2D melting of polygons with fractal boundaries has yet to be thoroughly explored, even though such boundaries are important in the self-assembly of biological materials. Here in this paper, we report on 2D melting Monte Carlo (MC) simulations of non-convex polygons with fractal boundaries, model systems mimicking lipid rafts with fractal boundaries surrounded by voids. We describe 2D melting scenarios whereby, a continuous phase transition can be altered to a first order transition through the number of Koch curve iterations imposed on a hexagon. Melting transitions of non-convex polygons (i.e., from solid-to-hexatic and hexatic-to-liquid phases) exhibit sharp local density shifts, in contrast to prototypical hard disks and convex n-gons. Furthermore, we calculate mean square displacements (MSDs) and show that the fractal boundary of the n-th iteration plays a key role in the 2D melting of biomimetic rafts. Importantly, modifying the biomimetic raft boundary from a convex to a fractal geometry leads to hexatic phase narrowing because the self-assembly of polygons is facilitated. Finally, we discuss the implications of 2D melting regarding the self-assembly of lipid domains with proteins (i.e., lipid rafts).},

  doi          = {10.1016/j.bbamem.2020.183249},

  journal      = {Biochimica et Biophysica Acta. Biomembranes},

  number       = 8,

  volume       = 1862,

  place        = {Netherlands},

  year         = {Sat Aug 01 00:00:00 EDT 2020},

  month        = {Sat Aug 01 00:00:00 EDT 2020}

}

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Title: Fractal boundaries underpin the 2D melting of biomimetic rafts

Abstract

Citation Formats

X‐ray structural studies of freely suspended ordered hydrated DMPC multimembrane films journal, April 1990

Mechanical Properties of Nanoscopic Lipid Domains journal, October 2015

Disappearance of the Hexatic Phase in a Binary Mixture of Hard Disks journal, September 2017

Crossover from picosecond collective to single particle dynamics defines the mechanism of lateral lipid diffusion journal, November 2018

Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon journal, November 1981

Phase Separation and Fractal Domain Formation in Phospholipid/Diacetylene-Supported Lipid Bilayers journal, October 2007

Fractal structures in nonlinear dynamics journal, March 2009

Pre-transition effects mediate forces of assembly between transmembrane proteins journal, February 2016

Bilayer Thickness Mismatch Controls Domain Size in Model Membranes journal, February 2013

Effect of a potential softness on the solid-liquid transition in a two-dimensional core-softened potential system journal, November 2014

Domains on a Sphere: Neutron Scattering, Models, and Mathematical Formalism journal, August 2019

On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: A review journal, November 2013

Lateral organization of binary-lipid membranes—Evidence for fractal-like behaviour in the gel-fluid coexistence region journal, March 1997

Elasto-plasticity in wrinkled polymerized lipid membranes journal, January 2014

Emergent Optical Phononic Modes upon Nanoscale Mesogenic Phase Transitions journal, May 2017

Theory of Two-Dimensional Melting journal, July 1978

Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition journal, October 2011

Revealing the mechanism of passive transport in lipid bilayers via phonon-mediated nanometre-scale density fluctuations journal, May 2016

The Shape/Morphology Balance: A Study of Stealth Liposomes via Fractal Analysis and Drug Encapsulation journal, June 2013

Onset of Percolation and Fractal Classification Scheme for Multilamellar Lipid Vesicles journal, March 1999

Hexatic Phase in the Two-Dimensional Gaussian-Core Model journal, June 2011

Diffusion in disordered media journal, January 1987

Deciphering Melatonin-Stabilized Phase Separation in Phospholipid Bilayers journal, August 2019

Density Affects the Nature of the Hexatic-Liquid Transition in Two-Dimensional Melting of Soft-Core Systems journal, August 2016

Reversible and irreversible aggregation of magnetic liposomes journal, January 2017

Melting and the vector Coulomb gas in two dimensions journal, February 1979

Size and mobility of lipid domains tuned by geometrical constraints journal, July 2017

The Molecular Structure of the Liquid-Ordered Phase of Lipid Bilayers journal, January 2014

The in vivo structure of biological membranes and evidence for lipid domains journal, May 2017

Molecular dynamics simulation of nanomaterials using an artificial neural net journal, November 2004

Lipid Rafts As a Membrane-Organizing Principle journal, December 2009

Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature journal, November 2011

Ordering in Lipid Monolayers Studied by Synchrotron X-Ray Diffraction and Fluorescence Microscopy journal, May 1987

Lipid rafts and signal transduction journal, October 2000

Enzymes fraternize with fractals journal, July 2019

Fractal avalanche ruptures in biological membranes journal, October 2010

Growth of lipid vesicle structures: From surface fractals to mass fractals journal, July 2008

Ordering, metastability and phase transitions in two-dimensional systems journal, April 1973

Strong scaling of general-purpose molecular dynamics simulations on GPUs journal, July 2015

Biomaterials in non-integer dimensions journal, June 2019

Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome’s Facet journal, March 2016

Functional rafts in cell membranes journal, June 1997

Water-Floating Giant Nanosheets from Helical Peptide Pentamers journal, September 2016

Models for randomly distributed nanoscopic domains on spherical vesicles journal, June 2018

The self-organization of lipids and proteins of myelin at the membrane interface. Molecular factors underlying the microheterogeneity of domain segregation journal, July 2008

Fractal properties of macrophage membrane studied by AFM journal, December 2012

Stimulus-responsive self-assembly of protein-based fractals by computational design journal, June 2019

α-Synuclein Oligomers Stabilize Pre-Existing Defects in Supported Bilayers and Propagate Membrane Damage in a Fractal-Like Pattern journal, November 2016

Phase Behavior of Model Lipid Bilayers † journal, April 2005

X‐ray structural studies of freely suspended ordered hydrated DMPC multimembrane films
journal, April 1990

Mechanical Properties of Nanoscopic Lipid Domains
journal, October 2015

Disappearance of the Hexatic Phase in a Binary Mixture of Hard Disks
journal, September 2017

Crossover from picosecond collective to single particle dynamics defines the mechanism of lateral lipid diffusion
journal, November 2018

Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon
journal, November 1981

Phase Separation and Fractal Domain Formation in Phospholipid/Diacetylene-Supported Lipid Bilayers
journal, October 2007

Fractal structures in nonlinear dynamics
journal, March 2009

Pre-transition effects mediate forces of assembly between transmembrane proteins
journal, February 2016

Bilayer Thickness Mismatch Controls Domain Size in Model Membranes
journal, February 2013

Effect of a potential softness on the solid-liquid transition in a two-dimensional core-softened potential system
journal, November 2014

Domains on a Sphere: Neutron Scattering, Models, and Mathematical Formalism
journal, August 2019

On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: A review
journal, November 2013

Lateral organization of binary-lipid membranes—Evidence for fractal-like behaviour in the gel-fluid coexistence region
journal, March 1997

Elasto-plasticity in wrinkled polymerized lipid membranes
journal, January 2014

Emergent Optical Phononic Modes upon Nanoscale Mesogenic Phase Transitions
journal, May 2017

Theory of Two-Dimensional Melting
journal, July 1978

Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition
journal, October 2011

Revealing the mechanism of passive transport in lipid bilayers via phonon-mediated nanometre-scale density fluctuations
journal, May 2016

The Shape/Morphology Balance: A Study of Stealth Liposomes via Fractal Analysis and Drug Encapsulation
journal, June 2013

Onset of Percolation and Fractal Classification Scheme for Multilamellar Lipid Vesicles
journal, March 1999

Hexatic Phase in the Two-Dimensional Gaussian-Core Model
journal, June 2011

Diffusion in disordered media
journal, January 1987

Deciphering Melatonin-Stabilized Phase Separation in Phospholipid Bilayers
journal, August 2019

Density Affects the Nature of the Hexatic-Liquid Transition in Two-Dimensional Melting of Soft-Core Systems
journal, August 2016

Reversible and irreversible aggregation of magnetic liposomes
journal, January 2017

Melting and the vector Coulomb gas in two dimensions
journal, February 1979

Size and mobility of lipid domains tuned by geometrical constraints
journal, July 2017

The Molecular Structure of the Liquid-Ordered Phase of Lipid Bilayers
journal, January 2014

The in vivo structure of biological membranes and evidence for lipid domains
journal, May 2017

Molecular dynamics simulation of nanomaterials using an artificial neural net
journal, November 2004

Lipid Rafts As a Membrane-Organizing Principle
journal, December 2009

Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature
journal, November 2011

Ordering in Lipid Monolayers Studied by Synchrotron X-Ray Diffraction and Fluorescence Microscopy
journal, May 1987

Lipid rafts and signal transduction
journal, October 2000

Enzymes fraternize with fractals
journal, July 2019

Fractal avalanche ruptures in biological membranes
journal, October 2010

Growth of lipid vesicle structures: From surface fractals to mass fractals
journal, July 2008

Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973

Strong scaling of general-purpose molecular dynamics simulations on GPUs
journal, July 2015

Biomaterials in non-integer dimensions
journal, June 2019

Theoretical Study of the Initial Stages of Self-Assembly of a Carboxysome’s Facet
journal, March 2016

Functional rafts in cell membranes
journal, June 1997

Water-Floating Giant Nanosheets from Helical Peptide Pentamers
journal, September 2016

Models for randomly distributed nanoscopic domains on spherical vesicles
journal, June 2018

The self-organization of lipids and proteins of myelin at the membrane interface. Molecular factors underlying the microheterogeneity of domain segregation
journal, July 2008

Fractal properties of macrophage membrane studied by AFM
journal, December 2012

Stimulus-responsive self-assembly of protein-based fractals by computational design
journal, June 2019

α-Synuclein Oligomers Stabilize Pre-Existing Defects in Supported Bilayers and Propagate Membrane Damage in a Fractal-Like Pattern
journal, November 2016

Phase Behavior of Model Lipid Bilayers ^†
journal, April 2005