Dynamics of spheroid self-assembly in liquid-overlay culture of DU 145 human prostate cancer cells

Abstract

The in vitro self‐assembly of multicellular spheroids generates highly organized structures in which the three‐dimensional structure and differentiated function frequently mimic that of in vivo tissues. This has led to their use in such diverse applications as tissue regeneration and drug therapy. Using Smoluchowski‐like rate equations, herein we present a model of the self‐aggregation of DU 145 human prostate carcinoma cells in liquid‐overlay culture to elucidate some of the physical parameters affecting homotypic aggregation in attachment‐dependent cells. Experimental results indicate that self‐aggregation in our system is divided into three distinct phases: a transient reorganization of initial cell clusters, an active aggregation characterized by constant rate coefficients, and a ripening phase of established spheroid growth. In contrast to the diffusion‐controlled aggregation previously observed for attachment‐independent cells, the model suggests that active aggregation in our system is reaction‐controlled. The rate equations accurately predict the aggregation kinetics of spheroids containing up to 30 cells and are dominated by spheroid adhesive potential with lesser con‐ tributions from the radius of influence. The adhesion probability increases with spheroid size so that spheroid–spheroid adhesions are a minimum of 2.5 times more likely than those of cell–cell, possibly due to the upregulation of extracellular matrix proteins and cell‐adhesion molecules. The radius of influence is at least 1.5 to 3 times greater than expected for spherical geometry as a result of ellipsoidal shape and possible chemotactic or Fröhlich interactions. Brownian‐type behavior was noted for spheroids larger than 30 μm in diameter, but smaller aggregates were more motile by as much as a factor of 10 for single cells. The model may improve spheroid fidelity for existing applications of spheroids and form the basis of a simple assay for quantitatively evaluating cellular metastatic potential as well as therapies that seek to alter this potential. © 2001 John Wiley & Sons, Inc. Biotechnol Bioeng 72: 579–591, 2001.

Dynamic analysis of hepatoma spheroid formation: roles of E-cadherin and β1-integrin

“…Enmon et al (2001) have established a kinetic model of spheroid selfassembly from DU-145 prostate cancer cells by using Smoluchowski-like rate equations to analyze the distributions of area projection from random cell aggregates formed in a liquid-overlay culture. Our study has employed a similar image-based dynamic analysis of spheroid assembly but emphasizes more the identification of molecular interactions contributing to spheroid selfassembly.…”

“…These methods in general might provide accurate measurements of the force of cell-cell interaction but are either destructive or unable to reveal the detail changes in compactness that occur during spheroid assembly. On the other hand, several studies have addressed the kinetics of spheroid aggregation through image analysis and mathematic modeling (Enmon et al 2001(Enmon et al , 2002Neelamegham et al 1997). However, few correlations between the proposed model and possible molecular mechanisms have been made.…”

Predicting Aggregation Kinetics of DU 145 Prostate Cancer Cells in Liquid-Overlay Culture

“…Images were captured with an Optronics DEI 750 digital camera attached to an Olympus IX 50 inverted light microscope (C 2 Corp., Orlando, FL) and analyzed using ImagePro Plus software (Media Cybernetics, Silver Springs, MD) as described by Enmon et al (2001). A total of 14,000-36,000 aggregates per time period were analyzed by this method.…”

“…Accumulation of aggregates of size i was modeled as population balance between their formation from smaller aggregates and depletion as they formed larger aggregates (Enmon et al 2001).…”

“…The kinetic rate constants form a matrix of diagonal terms, k i,i , that describe aggregation between aggregates of the same size i and off-diagonal terms, k i,j, that describe aggregation events between different sizes i and j. Model equations do not include terms for cell division and aggregate dissociation since these events were negligible in our static 12-h cultures (Enmon et al 2001). Differential equations were solved computationally by numerical integration using the Eu¨ler method (Chan Man Fong et al 2003) with a time step of 0.05 h. Kinetic rate constants were determined by a least-squares fitting to minimize the sum of the normalized, squared residual error between model results and experimental aggregate concentrations.…”