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

Identifying and analyzing power-law scaling in two-dimensional image datasets

Power-law distributions provide a general description of diverse natural phenomena in which events with a logarithmically increasing size occur with logarithmically decreasing probability. However, experimentally derived correlated two-dimensional information is often difficult to cleanly interpret as discrete events of defined size. Moreover, physical limitation of techniques such as those based on scanning probe microscopy, which can ideally be used to observe power-law behavior, reduce event number and thus render straightforward power-law fits even more challenging. Here we develop and compare different techniques to analyze event distributions from two-dimensional images. We show that tracking interface position allows the associated scaling parameters to be accurately extracted from both experimental and synthetic image-based datasets. We also show how these techniques can differentiate between power-law and non-power-law behavior by comparison of Hill, moments, and kernel estimators of this scaling parameter. We thus present computational tools to analyze power-law fits in two-dimensional datasets and identify the scaling parameters that best describe these distributions.

Dimensional crossover in Kardar-Parisi-Zhang growth

Two-dimensional (2D) Kardar-Parisi-Zhang (KPZ) growth is usually investigated on substrates of lateral sizes L_{x}=L_{y}, so that L_{x} and the correlation length (ξ) are the only relevant lengths determining the scaling behavior. However, in cylindrical geometry, as well as in flat rectangular substrates L_{x}≠L_{y} and, thus, the surfaces can become correlated in a single direction, when ξ∼L_{x}≪L_{y}. From extensive simulations of several KPZ models, we demonstrate that this yields a dimensional crossover in their dynamics, with the roughness scaling as W∼t^{β_{2D}} for t≪t_{c} and W∼t^{β_{1D}} for t≫t_{c}, where t_{c}∼L_{x}^{1/z_{2D}}. The height distributions (HDs) also cross over from the 2D flat (cylindrical) HD to the asymptotic Tracy-Widom Gaussian orthogonal ensemble (Gaussian unitary ensemble) distribution. Moreover, 2D to one-dimensional (1D) crossovers are found also in the asymptotic growth velocity and in the steady-state regime of flat systems, where a family of universal HDs exists, interpolating between the 2D and 1D ones as L_{y}/L_{x} increases. Importantly, the crossover scalings are fully determined and indicate a possible way to solve 2D KPZ models.

Unpredicted Scaling of the One-Dimensional Kardar-Parisi-Zhang Equation

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree. Yet recent numerical simulations in the tensionless (or inviscid) limit of the KPZ equation [C. Cartes et al., The Galerkin-truncated Burgers equation: Crossover from inviscid-thermalized to Kardar-Parisi-Zhang scaling, Phil. Trans. R. Soc. A 380, 20210090 (2022).PTRMAD1364-503X10.1098/rsta.2021.0090; E. Rodríguez-Fernández et al., Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation, Phys. Rev. E 106, 024802 (2022).PRESCM2470-004510.1103/PhysRevE.106.024802] unveiled a new scaling, with a critical dynamical exponent z=1 different from the KPZ one z=3/2. In this Letter, we show that this scaling is controlled by a fixed point which had been missed so far and which corresponds to an infinite nonlinear coupling. Using the functional renormalization group (FRG), we demonstrate the existence of this fixed point and show that it yields z=1. We calculate the correlation function and associated scaling function at this fixed point, providing both a numerical solution of the FRG equations within a reliable approximation, and an exact asymptotic form obtained in the limit of large wave numbers. Both scaling functions accurately match the one from the numerical simulations.

Effect of substrate heterogeneity and topology on epithelial tissue growth dynamics

Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure of the extracellular matrix and nutrient concentration. We used the CellSim3D model, a kinetic cell division simulator, to investigate the growth kinetics and interface roughness dynamics of epithelial tissue growth on heterogeneous substrates with varying topologies. The results show that the presence of quenched disorder has a clear effect on the colony morphology and the roughness scaling of the interface in the moving interface regime. In a medium with quenched disorder, the tissue interface has a smaller interface roughness exponent, α, and a larger growth exponent, β. The scaling exponents also depend on the topology of the substrate and cannot be categorized by well-known universality classes.

In silico testing of the universality of epithelial tissue growth

The universality of interfacial roughness in growing epithelial tissue has remained a controversial issue. Kardar-Parisi-Zhang (KPZ) and molecular beam epitaxy (MBE) universality classes have been reported among other behaviors including a total lack of universality. Here, we simulate tissues using the cellsim3d kinetic division model for deformable cells to investigate cell-colony scaling. With seemingly minor model changes, it can reproduce both KPZ- and MBE-like scaling in configurations that mimic the respective experiments. Tissue growth with strong cell-cell adhesion in a linear geometry is KPZ like, while weakly adhesive tissues in a radial geometry are MBE like. This result neutralizes the apparent scaling controversy.

Invasion front dynamics of interactive populations in environments with barriers

Invading populations normally comprise different subpopulations that interact while trying to overcome existing barriers against their way to occupy new areas. However, the majority of studies so far only consider single or multiple population invasion into areas where there is no resistance against the invasion. Here, we developed a model to study how cooperative/competitive populations invade in the presence of a physical barrier that should be degraded during the invasion. For one dimensional (1D) environment, we found that a Langevin equation as [Formula: see text] describing invasion front position. We then obtained how [Formula: see text] and [Formula: see text] depend on population interactions and environmental barrier intensity. In two dimensional (2D) environment, for the average interface position movements we found a Langevin equation as [Formula: see text]. Similar to the 1D case, we calculate how [Formula: see text] and [Formula: see text] respond to population interaction and environmental barrier intensity. Finally, the study of invasion front morphology through dynamic scaling analysis showed that growth exponent, [Formula: see text], depends on both population interaction and environmental barrier intensity. Saturated interface width, [Formula: see text], versus width of the 2D environment (L) also exhibits scaling behavior. Our findings show revealed that competition among subpopulations leads to more rough invasion fronts. Considering the wide range of shreds of evidence for clonal diversity in cancer cell populations, our findings suggest that interactions between such diverse populations can potentially participate in the irregularities of tumor border.

Roughness and dynamics of proliferating cell fronts as a probe of cell-cell interactions

Juxtacellular interactions play an essential but still not fully understood role in both normal tissue development and tumour invasion. Using proliferating cell fronts as a model system, we explore the effects of cell-cell interactions on the geometry and dynamics of these one-dimensional biological interfaces. We observe two distinct scaling regimes of the steady state roughness of in-vitro propagating Rat1 fibroblast cell fronts, suggesting different hierarchies of interactions at sub-cell lengthscales and at a lengthscale of 2-10 cells. Pharmacological modulation significantly affects the proliferation speed of the cell fronts, and those modulators that promote cell mobility or division also lead to the most rapid evolution of cell front roughness. By comparing our experimental observations to numerical simulations of elastic cell fronts with purely short-range interactions, we demonstrate that the interactions at few-cell lengthscales play a key role. Our methodology provides a simple framework to measure and characterise the biological effects of such interactions, and could be useful in tumour phenotyping.

Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer

We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent α=0.86 and the growth exponent β=0.73, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from (α=0.5,β=0.25) to (α=0.9,β=0.75), where the exponents α and β are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, α=0.74,β=0.68, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments with liquid-crystal turbulence, we determine the universal scaling functions that describe the height distribution and the spatial correlation of the interfaces growing outward from a ring. The scaling functions, controlled by a single dimensionless time parameter, show crossover from the statistical properties of the flat interfaces to those of the circular interfaces. Moreover, employing the KPZ variational formula to describe the case of the ring initial condition, we find that the formula, which we numerically evaluate, reproduces the numerical and experimental results precisely without adjustable parameters. This demonstrates that precise numerical evaluation of the variational formula is possible at all, and underlines the practical importance of the formula, which is able to predict the one-point distribution of KPZ interfaces for general initial conditions.

Effect of heterogeneity and spatial correlations on the structure of a tumor invasion front in cellular environments

Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the biological mechanisms of tumor growth have been gained. We develop a model to study how tumors' invasion front depends on the relevant properties of a cellular environment. To do so, we develop a model based on a nonlinear reaction-diffusion equation, the Fisher-Kolmogorov-Petrovsky-Piskunov equation, to model tumor growth. Our study aims to understand how heterogeneity in the cellular environment's stiffness, as well as spatial correlations in its morphology, the existence of both of which has been demonstrated by experiments, affects the properties of tumor invasion front. It is demonstrated that three important factors affect the properties of the front, namely the spatial distribution of the local diffusion coefficients, the spatial correlations between them, and the ratio of the cells' duplication rate and their average diffusion coefficient. Analyzing the scaling properties of tumor invasion front computed by solving the governing equation, we show that, contrary to several previous claims, the invasion front of tumors and cancerous cell colonies cannot be described by the well-known models of kinetic growth, such as the Kardar-Parisi-Zhang equation.

Eden model with nonlocal growth rules and kinetic roughening in biological systems

We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. The concentration of nutrients necessary for replication is assumed to be proportional to the voids connecting the replicating cells to the outer region, introducing therefore a nonlocal dependence on the replication rule. Our simulations point out that the Kadar-Parisi-Zhang (KPZ) universality class is a transient that can last for long periods in plentiful environments. For conditions of nutrient scarcity, we observe a crossover from regular KPZ to unstable growth, passing by a transient consistent with the quenched KPZ class at the pinning transition. Our analysis sheds light on results reporting on the universality class of kinetic roughening in akin experiments of biological growth.

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.

Automated contour analysis of multi-cellular spheroids spreading through high content imaging

The morphology of 2D cell colonies has been studied to understand tumor metastasis in the past decades. However, 2D cell cultures are lacking many features of 3D tissues, and their physiological behaviors are quite different from solid tumors in vivo. In this work, we studied the multi-cellular tumor spheroid (MCTS) spreading on the substrate, which keeps parts of 3D tissue characteristics and facilitates cell tracking through 2D imaging. By using a high content imaging system (HCS), we tracked multiple spheroids in one single 96-well plate for 36 h. An automated algorithm based on Otsu's method was developed to investigate the morphological details of spheroids through the quantification of radius length and its coefficients of variation. Spheroid spreading is altered by the PIP-platin, which was a novel platinum based drug previously reported by us with an inhibitory effect on cell migration. All parameters showed dose dependent decreases when PIP-platin concentration increased, indicating the inhibition of spheroid expansion by this compound. To investigate the surface roughness of spheroids affected by the drug, we applied the Fourier parameter β and the normalized standard deviation of the radius STD _r / [Formula: see text], which were found inversely proportional to the concentrations of PIP-platin. Particularly at the low drug concentrations, the indices of contour roughness appeared to be more sensitive than spheroid sizes, which could be the potential morphological markers for high content screening of drugs.

Kardar-Parisi-Zhang Interfaces with Inward Growth

We study the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an off-lattice Eden model, respectively. To realize the ring initial condition experimentally, we introduce a holography-based technique that allows us to design the initial condition arbitrarily. Then, we find that fluctuation properties of ingrowing circular interfaces are distinct from those for the curved or circular KPZ subclass and, instead, are characterized by the flat subclass. More precisely, we find an asymptotic approach to the Tracy-Widom distribution for the Gaussian orthogonal ensemble and the Airy_{1} spatial correlation, as long as time is much shorter than the characteristic time determined by the initial curvature. Near this characteristic time, deviation from the flat KPZ subclass is found, which can be explained in terms of the correlation length and the circumference. Our results indicate that the sign of the initial curvature has a crucial role in determining the universal distribution and correlation functions of the KPZ class.

Optimization of cell seeding in a 2D bio-scaffold system using computational models

The cell expansion process is a crucial part of generating cells on a large-scale level in a bioreactor system. Hence, it is important to set operating conditions (e.g. initial cell seeding distribution, culture medium flow rate) to an optimal level. Often, the initial cell seeding distribution factor is neglected and/or overlooked in the design of a bioreactor using conventional seeding distribution methods. This paper proposes a novel seeding distribution method that aims to maximize cell growth and minimize production time/cost. The proposed method utilizes two computational models; the first model represents cell growth patterns whereas the second model determines optimal initial cell seeding positions for adherent cell expansions. Cell growth simulation from the first model demonstrates that the model can be a representation of various cell types with known probabilities. The second model involves a combination of combinatorial optimization, Monte Carlo and concepts of the first model, and is used to design a multi-layer 2D bio-scaffold system that increases cell production efficiency in bioreactor applications. Simulation results have shown that the recommended input configurations obtained from the proposed optimization method are the most optimal configurations. The results have also illustrated the effectiveness of the proposed optimization method. The potential of the proposed seeding distribution method as a useful tool to optimize the cell expansion process in modern bioreactor system applications is highlighted.

Pinning-depinning transition in a stochastic growth model for the evolution of cell colony fronts in a disordered medium

We study a stochastic lattice model for cell colony growth, which takes into account proliferation, diffusion, and rotation of cells, in a culture medium with quenched disorder. The medium is composed of sites that inhibit any possible change in the internal state of the cells, representing the disorder, as well as by active medium sites that do not interfere with the cell dynamics. By means of Monte Carlo simulations we find that the velocity of the growing interface, which is taken as the order parameter of the model, strongly depends on the density of active medium sites (ρ_{A}). In fact, the model presents a (continuous) second-order pinning-depinning transition at a certain critical value of ρ_{A}^{crit}, such as, for ρ_{A}>ρ_{A}^{crit}, the interface moves freely across the disordered medium, but for ρ_{A}<ρ_{A}^{crit} the interface becomes irreversible pinned by the disorder. By determining the relevant critical exponents, our study reveals that within the depinned phase the interface can be rationalized in terms of the Kardar-Parisi-Zhang universality class, but when approaching the critical threshold, the nonlinear term of the Kardar-Parisi-Zhang equation tends to vanish and then the pinned interface belongs to the quenched Edwards-Wilkinson universality class.

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.

The universal growth rate behavior and regime transition in adherent cell colonies

In this work, we used five cell lineages, cultivated in vitro, to show they follow a common functional form to the growth rate: a sigmoidal curve, suggesting that competition and cooperation (usual mechanisms for systems with this behavior) might be present. Both theoretical and experimental investigations, on the causes of this behavior, are challenging for the research field; since the sigmoidal form to the growth rate seems to absorb important properties of such systems, e.g., cell deformation and statistical interactions. We shed some light on this subject by showing how cell spreading affects the radius behavior of the growing colonies. Doing numerical time derivatives of the experimental data, we obtained the growth rates. Using reduced variables for the time and rates, we obtained the collapse of all colonies growth rates onto one curve with sigmoidal shape. This suggests a universal-type behavior, with regime transition related to a morphological transition of adherent cell colonies.

Impact of graphene oxide on viability of Chinese hamster ovary and mouse hepatoma MH-22A cells

The evaluation of the cyto- and bio-compatibility is a critical step in the development of graphene oxide (GO) as a new promising material for in vivo biomedical applications. In this study, we report the impact of GO, with and without the addition of bovine serum albumin, on healthy (Chinese hamster ovary) and a cancer (mouse hepatoma MH-22A) cells viability and the estimation of the intracellular distribution of GO inside the cells in vitro. The viability tests were performed using a colony formation assay. The intracellular distribution of GO was estimated using Raman spectroscopy and imaging. The viability of both cell lines decreased with increasing concentration of graphene oxide (12.5-50.0 μg/ml): in the case of Chinese hamster ovary cells viability decreased from 44% to 11%, in the case of mouse hepatoma MH-22A cells--from 22% to 3%. These cell lines significantly differed in their response to GO and GO-BSA formulations. The results of viability tests correlate with results of atomic force microscopy and Raman spectroscopy and imaging findings. The GO influence on cell morphology changes, cell structure, cells colony growth dynamics and GO accumulation inside the cells was higher in the case of mouse hepatoma MH-22A cells.

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,β=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.

Basic ingredients for mathematical modeling of tumor growth in vitro: cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space.

Extremal paths, the stochastic heat equation, and the three-dimensional Kardar-Parisi-Zhang universality class

Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the 2+1 Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we return here to study, in depth, the three-dimensional (3D) radial KPZ problem, comparing common scaling phenomena exhibited by the pt-pt directed polymer in a random medium (DPRM), the stochastic heat equation (SHE) with multiplicative noise in three dimensions, and kinetic roughening phenomena associated with 3D Eden clusters. Examining variants of the 3D DPRM, as well as numerically integrating, via the Itô prescription, the constrained SHE for different values of the KPZ coupling, we provide strong evidence for universality within this 3D KPZ class, revealing shared values for the limit distribution skewness and kurtosis, along with universal first and second moments. Our numerical analysis of the 3D SHE, well flanked by the DPRM results, appears without precedent in the literature. We consider, too, the 2+1 KPZ equation in the deeply evolved kinetically roughened stationary state, extracting the essential limit distribution characterizing fluctuations therein, revealing a higher-dimensional relative of the 1+1 KPZ Baik-Rains distribution. Complementary, corroborative findings are provided via the Gaussian DPRM, as well as the restricted-solid-on-solid model of stochastic growth, stalwart members of the 2+1 KPZ class. Next, contact is made with a recent nonperturbative, field-theoretic renormalization group calculation for the key universal amplitude ratio in this context. Finally, in the crossover from transient to stationary-state statistics, we observe a higher dimensional manifestation of the skewness minimum discovered by Takeuchi [Phys. Rev. Lett. 110, 210604 (2013)] in 1+1 KPZ class liquid-crystal experiments.