Level set method for free boundary of invasive cancer cell using different functions of matrix metalloproteinases

This paper proposes a meshless Galerkin level set method for structural shape and topology optimization of continua. To taking advantage of the implicit free boundary representation scheme, structural design boundary is represented through the introduction of a scalar level set function as its zero level set, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and also to construct the shape functions for mesh free function approximation. The meshless Galerkin global weak formulation is employed to implement the discretization of the state equations. This provides a pathway to simplify two numerical procedures involved in most conventional level set methods in propagating the discrete level set functions and in approximating the discrete equations, by unifying the two different stages at two sets of grids just in terms of one set of scattered nodes. The proposed level set method has the capability of describing the implicit moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function by finding the design variables of the size optimization in time. One benchmark example is used to demonstrate the effectiveness of the proposed method. The numerical results showcase that this method has the ability to simplify numerical procedures and to avoid numerical difficulties happened in most conventional level set methods. It is straightforward to apply the present method to more advanced shape and topology optimization problems.

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Invasive cancer cell lines exhibit biomechanical properties that are distinct from their noninvasive counterparts

Soft Matter ◽

10.1039/c1sm05532a ◽

2011 ◽

Vol 7 (24) ◽

pp. 11488 ◽

Cited By ~ 36

Author(s):

Oliver Jonas ◽

Claudia T. Mierke ◽

Josef A. Käs

Keyword(s):

Cell Lines ◽

Cancer Cell ◽

Biomechanical Properties ◽

Cancer Cell Lines ◽

Invasive Cancer ◽

Invasive Cancer Cell

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Measuring systematic changes in invasive cancer cell shape using Zernike moments

Integrative Biology ◽

10.1039/c6ib00100a ◽

2016 ◽

Vol 8 (11) ◽

pp. 1183-1193 ◽

Cited By ~ 24

Author(s):

Elaheh Alizadeh ◽

Samanthe Merrick Lyons ◽

Jordan Marie Castle ◽

Ashok Prasad

Keyword(s):

Cancer Cells ◽

Cancer Cell ◽

Cell Shape ◽

Zernike Moments ◽

Invasive Cancer ◽

Two Dimensional ◽

Dimensional Cell ◽

Invasive Cancer Cell

Cancer cells show similar changes in two dimensional cell shape analyzed using Zernike moments.

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Mammalian SIRT6 Represses Invasive Cancer Cell Phenotypes through ATP Citrate Lyase (ACLY)-Dependent Histone Acetylation

Genes ◽

10.3390/genes12091460 ◽

2021 ◽

Vol 12 (9) ◽

pp. 1460

Author(s):

Wei Zheng ◽

Luisa Tasselli ◽

Tie-mei Li ◽

Katrin F. Chua

Keyword(s):

Gene Expression ◽

Histone Acetylation ◽

Cancer Cells ◽

Cancer Cell ◽

Invasive Cancer ◽

Atp Citrate Lyase ◽

Acetyl Coa ◽

Citrate Lyase ◽

Cell Phenotypes ◽

Invasive Cancer Cell

The modulation of dynamic histone acetylation states is key for organizing chromatin structure and modulating gene expression and is regulated by histone acetyltransferase (HAT) and histone deacetylase (HDAC) enzymes. The mammalian SIRT6 protein, a member of the Class III HDAC Sirtuin family of NAD+-dependent enzymes, plays pivotal roles in aging, metabolism, and cancer biology. Through its site-specific histone deacetylation activity, SIRT6 promotes chromatin silencing and transcriptional regulation of aging-associated, metabolic, and tumor suppressive gene expression programs. ATP citrate lyase (ACLY) is a nucleo-cytoplasmic enzyme that produces acetyl coenzyme A (acetyl-CoA), which is the required acetyl donor for lysine acetylation by HATs. In addition to playing a central role in generating cytosolic acetyl-CoA for de novo lipogenesis, a growing body of work indicates that ACLY also functions in the nucleus where it contributes to the nutrient-sensitive regulation of nuclear acetyl-CoA availability for histone acetylation in cancer cells. In this study, we have identified a novel function of SIRT6 in controlling nuclear levels of ACLY and ACLY-dependent tumor suppressive gene regulation. The inactivation of SIRT6 in cancer cells leads to the accumulation of nuclear ACLY protein and increases nuclear acetyl-CoA pools, which in turn drive locus-specific histone acetylation and the expression of cancer cell adhesion and migration genes that promote tumor invasiveness. Our findings uncover a novel mechanism of SIRT6 in suppressing invasive cancer cell phenotypes and identify acetyl-CoA responsive cell migration and adhesion genes as downstream targets of SIRT6.

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SOME NUMERICAL ASPECTS OF THE LEVEL SET METHOD

Mathematical Modelling and Analysis ◽

10.3846/13926292.1998.9637097 ◽

1998 ◽

Vol 3 (1) ◽

pp. 140-151 ◽

Cited By ~ 1

Author(s):

Mathias Moog ◽

Rainer Keck ◽

Aivars Zemitis

Keyword(s):

Free Boundary ◽

Level Set Method ◽

Level Set ◽

Two Phase Flow ◽

New Method ◽

Phase Flow ◽

Two Phase ◽

Level Set Function ◽

Free Boundary Value Problems ◽

Linearized Problem

Many practical applications imply the solution of free boundary value problems. If the free boundary is complex and can change its topology, it will be hard to solve such problems numerically. In recent years a new method has been developed, which can handle boundaries with complex geometries. This new method is called the level set method. However, the level set method also has some drawbacks, which are mainly concerning conservation of mass or numerical instabilities of the boundaries. Our aim is to analyze some aspects of the level set method on the basis of two‐phase flow in a Hele‐Shaw cell. We investigate instabilities of two‐phase flow between two parallel plates. A solution of the linearized problem is obtained analytically in order to check whether the numerical schemes compute reasonable results. The developed numerical scheme is based on finite difference approximations and the level set method. The equations of two‐phase Hele‐Shaw flow are written in a modified formulation using the one‐dimensional Dirac delta‐function. Since the level set function is not smooth enough after re‐initialization, special attention during the computation of curvature is needed. We propose a method that can solve the problems for two‐phase Hele‐Shaw flow with changing topology. The numerical solution shows good agreement with the analytical solution of the linearized problem. We describe the method below and analyze the results.

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