Super-Rough Dynamics on Tumor Growth

Brú, Antonio; Pastor, M.; Fernaud, Isabel; Brú, Isabel; Melle, Sonia; Berenguer, Carolina

doi:10.1103/physrevlett.81.4008

Cited by 196 publications

(202 citation statements)

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“…The FKE has been used to model the spread of advantageous genes in animal populations (6), the growth of bacterial colonies (23)(24)(25), and the growth of complex cell organizations such as spreading of tumors (26), brain tumor growth (27), and wound healing (28), epidemics such as the spread of plague (29) and other pandemic diseases, social developments such as the spread of Neolithic farming practices (30), and the spread of Indo-European languages across Europe (31). Other important examples from biology include the frontal polymerization of actin (32) and microtubules (33).…”

Section: Implications Of Observationsmentioning

confidence: 99%

Propagating waves of self-assembly in organosilane monolayers

Douglas

Efimenko

Fischer

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

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Wavefronts associated with reaction-diffusion and self-assembly processes are ubiquitous in the natural world. For example, propagating fronts arise in crystallization and diverse other thermodynamic ordering processes, in polymerization fronts involved in cell movement and division, as well as in the competitive social interactions and population dynamics of animals at much larger scales. Although it is often claimed that self-sustaining or autocatalytic front propagation is well described by mean-field ''reaction-diffusion'' or ''phase field'' ordering models, it has recently become appreciated from simulations and theoretical arguments that fluctuation effects in lower spatial dimensions can lead to appreciable deviations from the classical mean-field theory (MFT) of this type of front propagation. The present work explores these fluctuation effects in a real physical system. In particular, we consider a high-resolution near-edge x-ray absorption fine structure spectroscopy (NEXAFS) study of the spontaneous frontal self-assembly of organosilane (OS) molecules into self-assembled monolayer (SAM) surface-energy gradients on oxidized silicon wafers. We find that these layers organize from the wafer edge as propagating wavefronts having well defined velocities. In accordance with two-dimensional simulations of this type of front propagation that take fluctuation effects into account, we find that the interfacial widths w(t) of these SAM self-assembly fronts exhibit a power-law broadening in time, w(t) Ϸ t ␤ , rather than the constant width predicted by MFT. Moreover, the observed exponent values accord rather well with previous simulation and theoretical estimates. These observations have significant implications for diverse types of ordering fronts that occur under confinement conditions in biological or materials-processing contexts.fluctuation-induced interfacial broadening ͉ frontal self-assembly ͉ mean-field Fisher-Kolmogorov equation ͉ reaction-diffusion fronts ͉ self-assembled monolayers I n the early 1990s, Chaudhury and Whitesides developed an extremely facile method of creating surface energy gradients using self-assembled monolayers (SAMs) (1). Rather than using a solution as a carrier for adsorption or a rubber stamp for direct deposition of SAM molecules, these researchers simply placed a volatile fluid of organosilane (OS) molecules at the edge of a silica-covered substrate and enclosed the entire system in a container to avoid convection effects (Fig. 1). The symmetry-breaking perturbation associated with placing the source of diffusing material to the side of the wafer imparts a direction to the self-assembly of the SAM layer and leads to the spontaneous formation of a concentration gradient of OS molecules on the substrate. This gradient may be fixed into position at any point in its development by simply removing the wafer from OS exposure (2). These kinetically ''frozen'' SAM patterns are then ready for further measurements in which surface energy gradients are required.Although this method of ...

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Section: Implications Of Observationsmentioning

confidence: 99%

Propagating waves of self-assembly in organosilane monolayers

Douglas

Efimenko

Fischer

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

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“…This is a matter of interest in processes involved in wound healing or malignant tumor growth [1,2]. One of these procedures is based upon the dynamic scaling analysis (DSA) of colony fronts [3][4][5][6][7][8][9][10][11][12]. In this approach, the two-dimensional (2D) cell colony front dynamics is characterized through a set of dynamic scaling exponents (α, β, z, the roughness, the growth, and the dynamic exponents, respectively) derived from DSA applied to the colony front profiles and by comparing them with those expected from different complex statistical models [13,14].…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media

et al. 2016

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To deal with complex systems, microscopic and global approaches become of particular interest. Our previous results from the dynamics of large cell colonies indicated that their 2D front roughness dynamics is compatible with the standard Kardar-Parisi-Zhang (KPZ) or the quenched KPZ equations either in plain or methylcellulose (MC)-containing gel culture media, respectively. In both cases, the influence of a non-uniform distribution of the colony constituents was significant. These results encouraged us to investigate the overall dynamics of those systems considering the morphology and size, the duplication rate, and the motility of single cells. For this purpose, colonies with different cell populations (N) exhibiting quasi-circular and quasi-linear growth fronts in plain and MC-containing culture media are investigated. For small N, the average radial front velocity and its change with time depend on MC concentration. MC in the medium interferes with cell mitosis, contributes to the local enlargement of cells, and increases the distribution of spatio-temporal cell density heterogeneities. Colony spreading in MC-containing media proceeds under two main quenching effects, I and II; the former mainly depending on the culture medium composition and structure and the latter caused by the distribution of enlarged local cell domains. For large N, colony spreading occurs at constant velocity. The characteristics of cell motility, assessed by measuring their trajectories and the corresponding velocity field, reflect the effect of enlarged, slowmoving cells and the structure of the medium. Local average cell size distribution and individual cell motility data from plain and MC-containing media are qualitatively consistent with the predictions of both the extended cellular Potts models and the observed transition of the front roughness dynamics from a standard KPZ to a quenched KPZ. In this case, quenching J Biol Phys (2016) 42:477-502 DOI 10.1007

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“…In the present work we extend the geometrical approach to tumor growth by developing and analyzing spherically symmetric equations describing both MBE and QEW dynamics. These equations model the behaviour found experimentally in the (1 + 1)−dimensional case [2,3,5], and allow us to predict what would happen in the more realistic and unexplored case of (2 + 1)−dimensional geometry. We also derive the equations using a more systematic technique, that allows us to conjecture what are the geometrical principles that drive tumor growth.…”

Section: Introductionmentioning

confidence: 70%

“…A different methodology was used by Brú et al [2,3], that employed some tools of fractal geometry, as scaling analysis, to characterize the rough interface of growing solid tumors.…”

Section: Introductionmentioning

confidence: 99%

Geometrical approach to tumor growth

Escudero

2006

Phys. Rev. E

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Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells/particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former article [C. Escudero, Phys.Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyse the unexplored three-dimensional case, for which new conclusions on tumor growth are derived.

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Super-Rough Dynamics on Tumor Growth

Cited by 196 publications

References 20 publications

Propagating waves of self-assembly in organosilane monolayers

Propagating waves of self-assembly in organosilane monolayers

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media

Geometrical approach to tumor growth

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