Morphology and dynamics of tumor cell colonies propagating in epidermal growth factor supplemented media.

The epidermal growth factor (EGF) plays a key role in physiological and pathological processes. This work reports on the influence of EGF concentration (c EGF) on the modulation of individual cell phenotype and cell colony kinetics with the aim of perturbing the colony front roughness fluctuations. For this purpose, HeLa cell colonies that remain confluent along the whole expansion process with initial quasi-radial geometry and different initial cell populations, as well as colonies with initial quasi-linear geometry and large cell population, are employed. Cell size and morphology as well as its adhesive characteristics depend on c EGF. Quasi-radial colonies (QRC) expansion kinetics in EGF-containing medium exhibits a complex behavior. Namely, at the first stages of growth, the average QRC radius evolution can be described by a t 1/2 diffusion term coupled with exponential growth kinetics up to a critical time, and afterwards a growth regime approaching constant velocity. The extension of each regime depends on c EGF and colony history. In the presence of EGF, the initial expansion of quasi-linear colonies (QLCs) also exhibits morphological changes at both the cell and the colony levels. In these cases, the cell density at the colony border region becomes smaller than in the absence of EGF and consequently, the extension of the effective rim where cell duplication and motility contribute to the colony expansion increases. QLC front displacement velocity increases with c EGF up to a maximum value in the 2-10 ng ml-1 range. Individual cell velocity is increased by EGF, and an enhancement in both the persistence and the ballistic characteristics of cell trajectories can be distinguished. For an intermediate c EGF, collective cell displacements contribute to the roughening of the colony contours. This global dynamics becomes compatible with the standard Kardar-Parisi-Zhang growth model, although a faster colony roughness saturation in EGF-containing medium than in the control medium is observed.

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

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, slow-moving 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 effects I and II cooperate and give rise to the quenched-KPZ equation. Seemingly, these results show a possible way of linking the cellular Potts models and the 2D colony front roughness dynamics.

Dynamic scaling analysis of two-dimensional cell colony fronts in a gel medium: a biological system approaching a quenched Kardar-Parisi-Zhang universality.

The interfacial two-dimensional spreading dynamics of quasilinear Vero cell colony fronts in methylcellulose (MC)-containing culture medium, under a constant average front displacement velocity regime, was investigated. Under comparable experimental conditions, the average colony front displacement velocity becomes lower than that reported for a standard culture medium. Initially, the presence of MC in the medium hinders both the colony spreading, due to a gradual change in the average size and shape of cells and their distribution in the colony, and the cell motility in the gelled medium. Furthermore, at longer culture times enlarged cells appear at random in the border region of the colony. These cells behave as obstacles (pinning sites) for the displacement of smaller cells towards the colony front. The dynamic scaling analysis of rough fronts yields the set of exponents α=0.63±0.04,ß=0.75±0.05, and z=0.84±0.05, which is close to that expected for a quenched Kardar-Parisi-Zhang model.

Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies.

The dynamics of in situ 2D HeLa cell quasi-linear and quasi-radial colony fronts in a standard culture medium is investigated. For quasi-radial colonies, as the cell population increased, a kinetic transition from an exponential to a constant front average velocity regime was observed. Special attention was paid to individual cell motility evolution under constant average colony front velocity looking for its impact on the dynamics of the 2D colony front roughness. From the directionalities and velocity components of cell trajectories in colonies with different cell populations, the influence of both local cell density and cell crowding effects on individual cell motility was determined. The average dynamic behaviour of individual cells in the colony and its dependence on both local spatio-temporal heterogeneities and growth geometry suggested that cell motion undergoes under a concerted cell migration mechanism, in which both a limiting random walk-like and a limiting ballistic-like contribution were involved. These results were interesting to infer how biased cell trajectories influenced both the 2D colony spreading dynamics and the front roughness characteristics by local biased contributions to individual cell motion. These data are consistent with previous experimental and theoretical cell colony spreading data and provide additional evidence of the validity of the Kardar-Parisi-Zhang equation, within a certain range of time and colony front size, for describing the dynamics of 2D colony front roughness.

Growth dynamics of cancer cell colonies and their comparison with noncancerous cells.

The two-dimensional (2D) growth dynamics of HeLa (cervix cancer) cell colonies was studied following both their growth front and the pattern morphology evolutions utilizing large population colonies exhibiting linearly and radially spreading fronts. In both cases, the colony profile fractal dimension was d(f)=1.20±0.05 and the growth fronts displaced at the constant velocity 0.90±0.05 µm min(-1). Colonies showed changes in both cell morphology and average size. As time increased, the formation of large cells at the colony front was observed. Accordingly, the heterogeneity of the colony increased and local driving forces that set in began to influence the dynamics of the colony front. The dynamic scaling analysis of rough colony fronts resulted in a roughness exponent α = 0.50±0.05, a growth exponent ß = 0.32±0.04, and a dynamic exponent z=1.5±0.2. The validity of this set of scaling exponents extended from a lower cutoff l(c)≈60 µm upward, and the exponents agreed with those predicted by the standard Kardar-Parisi-Zhang continuous equation. HeLa data were compared with those previously reported for Vero cell colonies. The value of d(f) and the Kardar-Parisi-Zhang-type 2D front growth dynamics were similar for colonies of both cell lines. This indicates that the cell colony growth dynamics is independent of the genetic background and the tumorigenic nature of the cells. However, one can distinguish some differences between both cell lines during the growth of colonies that may result from specific cooperative effects and the nature of each biosystem.

Dynamics and morphology characteristics of cell colonies with radially spreading growth fronts.

The dynamics of two-dimensional (2D) radially spreading growth fronts of Vero cell colonies was investigated utilizing two types of colonies, namely type I starting from clusters with a small number of cells, which initially exhibited arbitrary-shaped rough growth fronts and progressively approached quasicircular ones as the cell population increased; and type II colonies, starting from a relatively large circular three-dimensional (3D) cell cluster. For large cell population colonies, the fractal dimension of the fronts was D(F) = 1.20±0.05. For low cell populations, the mean colony radius increased exponentially with time, but for large ones the constant radial front velocity 0.20±0.02 µm min(-1) was reached. Colony spreading was accompanied by changes in both cell morphology and average size, and by the formation of very large cells, some of them multinuclear. Therefore the heterogeneity of colonies increased and local driving forces that set in began to influence the 2D growth front kinetics. The retardation effect related to the exponential to constant radial front velocity transition was assigned to a number of possible interferences including the cell duplication and 3D growth in the bulk of the colony. The dynamic scaling analysis of overhang-corrected rough colony fronts, after arc-radius coordinate system transformation, resulted in roughness exponent α = 0.50±0.05 and growth exponent ß = 0.32±0.04, for arc lengths greater than 100 µm. This set of scaling exponents agreed with that predicted by the Kardar, Parisi, and Zhang continuous equation. For arc lengths shorter than 2-3 cell diameters, the value α = 0.85±0.05 would be related to a cell front roughening caused by temporarily membrane deformations occasionally interfered by cell proliferation.

Morphology and dynamic scaling analysis of cell colonies with linear growth fronts.

The growth of linear cell colony fronts is investigated from the morphology of cell monolayer colonies, the cell size and shape distribution, the front displacement velocity, and the dynamic scaling analysis of front roughness fluctuations. At the early growth stages, colony patterns consist of rather ordered compact domains of small cells, whereas at advanced stages, an uneven distribution of cells sets in, and some large cells and cells exhibiting large filopodia are produced. Colony front profiles exhibit overhangs and behave as fractals with the dimension D(F)=1.25±0.05. The colony fronts shift at 0.22±0.02 µm min(-1) average constant linear velocity and their roughness (w) increases with time (t). Dynamic scaling analysis of experimental and overhang-corrected growth profile data shows that w versus system width l log-log plots collapse to a single curve when l exceeds a certain threshold value l(o), a width corresponding to the average diameter of few cells. Then, the influence of overhangs on the roughness dynamics becomes negligible, and a growth exponent ß=0.33±0.02 is derived. From the structure factor analysis of overhang-corrected profiles, a global roughness exponent α(s)=0.50±0.05 is obtained. For l>200 µm, this set of exponents fulfills the Family-Vicsek relationship. It is consistent with the predictions of the continuous Kardar-Parisi-Zhang model.

Morphology of platinum electrodeposits in the three-dimensional sublayer to full layer range produced under different potential modulations on highly oriented pyrolytic graphite.

The topography of platinum electrodes produced by electrodeposition (19 to 200 mC cm-2) on highly oriented pyrolytic graphite (HOPG) under different potential modulations was investigated by atomic force microscopy, scanning tunneling microscopy, and H-atom electrosorption voltammetry. To modulate electrodeposition, (i) triangular potential cycling at 0.1 V s-1, (ii) a linear cathodic potential at 0.1 V s-1 and anodic potential step cycling, and (iii) square wave potential cycling at 5000 Hz were utilized. AFM and STM imaging showed that at lower platinum loading the HOPG surface was partially covered by a 3D sublayer of platinum. Electrodes produced by procedure (i) were made of faceted platinum aggregates of about 200 nm and nanoclusters in the range of 5-20 nm; those that resulted from procedure (ii) consisted of anisotropic aggregates of nanoclusters arranged as quasi-parallel domains. These electrodes from (i) and (ii) behaved as fractal objects. The electrodes resulting from procedure (iii) exhibited a flat surface that behaved as a Euclidean object. For all WEs, as the platinum loading was increased the HOPG surface was fully covered by a thin 3D layer of platinum aggregates produced by electrodeposition and coalescence phenomena. Large platinum loading led to electrodes with fractal geometry. Statistical parameters (root-mean-square height, skewedness, kurtosis, anisotropy, Abbot curve, number of protrusions and valleys, and fractal dimension) were obtained from the analysis of AFM and STM imaging data. Platinum electrodeposition coupled to either H-adatom formation for procedures (i) and (ii) or phonon dispersion for (iii) was involved in the surface atom rearrangements related to electrofaceting. The H-adatom electrosorption voltammetry data were used to evaluate the real electrode surface area via the voltammetric charge and to advance a tentative explanation of the contribution of the different crystallographic facets to the global electrochemical process dominated by weak H-Pt adsorption interactions.

Influence of pinning effects on the electrochemical formation of silver patterns in agarose-containing sols and gels.

The formation of silver patterns via electrolysis from aqueous silver sulfate + x% w/v agarose sol and gel media, with and without supporting electrolyte, in a quasi-two-dimensional (2D) cylindrical cell at room temperature, is utilized as a reference system to investigate the complexity of pinning effects. From pattern morphology and electrochemical data, both delocalized and localized pinning in the bulk dominate the drift of the growth front, depending on the concentration of agarose in the heterogeneous media. Delocalized pinning results from mobile, small agarose aggregates at the growth front and from their accumulation by the front drift. For gels, localized pinning comes from their own percolated structure. A depinning/pinning transition is observed in going from sols to gels. The relative contribution of diffusion and advection in mass-transport-controlled silver electrodeposition depends on the plating bath composition. On the other hand, silver ion attachment to the cathode appears to be interfered with by some screening caused by weakly adsorbed, mobile agarose aggregates at the metal surface without slowing down the rate of the electron-transfer step at the cathode. Their relative contribution of a delocalized, localized pinning and screening effect to a great extent determines the morphology and transition in the growth mode of silver patterns in both media. The analysis of charge and current transients and the corresponding silver pattern morphologies for open and dense radial patterns is made. Results are qualitatively simulated with a novel, rather simple cellular automaton algorithm.

Stability analysis of branched silver electrodeposits: solid phase growth under a marginally stable regime.

The mass-transport controlled growth of silver deposits at the early stage of multiple bump formation, and when a silver single needle growth regime is attained, are investigated. Linear stability analysis as proposed by Barkey, Muller, and Tobias [J. Electrochem. Soc. 136, 2199 (1989)] is applied to kinetic mesoscale data. A reasonable correlation between the current density and the average amplitude of unstable perturbation is established.

The response of a bioelectrochemical cell with Saccharomyces cerevisiae metabolizing glucose under various fermentation conditions.

Working conditions of a biochemical fuel cell formed by an oxygen cathode and a platinum bioanode in a Saccharomyces cerevisiae suspension metabolizing glucose are described. The biocell response in terms of bioanode potential and current drainage under different fermentation conditions is reported. A kinetic equation relating the current, the number of microorganisms, and the substrate concentration is obtained. The bioanode potential corresponds to that of an oxygen concentration polarization cell.