Crystallization dynamics on curved surfaces

García, Nicolás; Register, Richard A.; Vega, Daniel A.; Gómez, Leopoldo R.

doi:10.1103/physreve.88.012306

Cited by 26 publications

(40 citation statements)

References 44 publications

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“…Curved surfaces have recently been the object of theoretical [69] and experimental investigation [70], where the additional frustration introduced by the curvature inhibiting crystal formation can be partly reduced using different topological patterning and defects on the substrate surface. Density functional theory has also been used to reproduce qualitative aspects of heterogeneous crystallization in the vicinity of a variety of flat and curved substrates [71].…”

Section: Simulations Results On Heterogeneous Nucleation and Growth Omentioning

confidence: 99%

Solid phase properties and crystallization in simple model systems

Turci

Schilling

Yamani

et al. 2014

Eur. Phys. J. Spec. Top.

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Abstract. We review theoretical and simulational approaches to the description of equilibrium bulk crystal and interface properties as well as to the nonequilibrium processes of homogeneous and heterogeneous crystal nucleation for the simple model systems of hard spheres and Lennard-Jones particles. For the equilibrium properties of bulk and interfaces, density functional theories employing fundamental measure functionals prove to be a precise and versatile tool, as exemplified with a closer analysis of the hard sphere crystal-liquid interface. A detailed understanding of the dynamic process of nucleation in these model systems nevertheless still relies on simulational approaches. We review bulk nucleation and nucleation at structured walls and examine in closer detail the influence of walls with variable strength on nucleation in the Lennard-Jones fluid. We find that a planar crystalline substrate induces the growth of a crystalline film for a large range of lattice spacings and interaction potentials. Only a strongly incommensurate substrate and a very weakly attractive substrate potential lead to crystal growth with a non-zero contact angle.

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Section: Simulations Results On Heterogeneous Nucleation and Growth Omentioning

confidence: 99%

Solid phase properties and crystallization in simple model systems

Turci

Schilling

Yamani

et al. 2014

Eur. Phys. J. Spec. Top.

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“…We can use Gaussian curvature, the product of the maximum and minimum curvatures at a given point, to quantify the cellular topology 22 . Crystalline defects cluster at regions with high absolute values of Gaussian curvature such as the cell poles and division plane, while grain boundaries occur where Gaussian curvature approaches zero such as the cell body (Figure 1d) 20,21 .…”

Section: Main Textmentioning

confidence: 99%

Continuous, Topologically Guided Protein Crystallization Controls Bacterial Surface Layer Self-Assembly

Comerci

Herrmann

Yoon

et al. 2019

Preprint

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19Bacteria assemble the cell envelope using localized enzymes to account for growth and 20 division of a topologically complicated surface 1-3 . However, a regulatory pathway has not been 21 identified for assembly and maintenance of the surface layer (S-layer), a 2D crystalline protein 22 coat surrounding the curved 3D surface of a variety of bacteria 4,5 . By specifically labeling, 23 performed time-resolved, super-resolution fluorescence imaging and single-molecule tracking 47 (SMT) of S-layer assembly on living C. crescentus cells. In C. crescentus, the S-layer is made of 48 a single 98 kDa SLP, RsaA, which accounts for around 30% of the cell's total protein synthesis 7 . 49RsaA, like other SLPs, self-assembles into crystalline sheets upon the addition of divalent 50 calcium (Ca 2+ ) in vitro [8][9][10][11][12] . Given the many fitness-related functions ascribed to crystalline 51 bacterial S-layers, we hypothesized that SLP self-assembly may play a role in generating the S-52 layer coat in vivo 4,6 . 53RsaA covers the cellular surface of C. crescentus by forming a 22 nm-repeat hexameric 54 crystal lattice and is non-covalently anchored to an ~18 nm thick LPS outer membrane 13-17 55 (Figure 1a,b). The surface topology of stalked and predivisional C. crescentus includes a 56 cylindrical stalk measuring roughly 100 nm in diameter while the crescentoid cell body 57 approaches 800 nm in width 18,19 (Figure 1d). This large variety of curved topologies guarantees 58 that crystal distortion and defects within the S-layer lattice structure are present, defects which 59 enable complete coverage of the bacterial surface 4,13,20,21 . We can use Gaussian curvature, the 60 product of the maximum and minimum curvatures at a given point, to quantify the cellular 61 topology 22 . Crystalline defects cluster at regions with high absolute values of Gaussian curvature 62 such as the cell poles and division plane, while grain boundaries occur where Gaussian curvature 63 approaches zero such as the cell body (Figure 1d) 20,21 . 64Specifically labeling the S-layer in vivo has proven difficult due to the SLP's life cycle 65 and functions, which include secretion, refolding, anchoring, and crystallization 11,16,17,23,24 . 66

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“…Equation (18) can be accurately solved through a finite difference scheme, forward in time and centred in space and periodic boundary conditions 29,30 . In the case of systems with finite thickness, the simulations were performed by numerically solving equation (18) through finite elements, with periodic and null flux boundary conditions.…”

Section: Methodsmentioning

confidence: 99%

“…Although experiments and theoretical calculations have contributed to unveil equilibrium configurations and energetics of topological defects in curved space, dynamical processes like crystallization and melting still remain marginally explored [29][30][31][32] .…”

mentioning

confidence: 99%

Phase nucleation in curved space

et al. 2015

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Nucleation and growth is the dominant relaxation mechanism driving first-order phase transitions. In two-dimensional flat systems, nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study nucleation and growth of two-dimensional phases lying on curved surfaces and show that curvature modifies both critical sizes of nuclei and paths towards the equilibrium phase. In curved space, nucleation and growth becomes inherently inhomogeneous and critical nuclei form faster on regions of positive Gaussian curvature. Substrates of varying shape display complex energy landscapes with several geometry-induced local minima, where initially propagating nuclei become stabilized and trapped by the underlying curvature.

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Crystallization dynamics on curved surfaces

Cited by 26 publications

References 44 publications

Solid phase properties and crystallization in simple model systems

Solid phase properties and crystallization in simple model systems

Continuous, Topologically Guided Protein Crystallization Controls Bacterial Surface Layer Self-Assembly

Phase nucleation in curved space

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