Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

A Model of Lung Tumor Angiogenesis in a Biomimetic Poly(ethylene glycol)-based Hydrogel System

Tumor angiogenesis is critical to tumor growth and metastasis, yet much is unknown about the role vascular cells play in the tumor microenvironment. A major outstanding challenge associated with studying tumor angiogenesis is that existing preclinical models are limited in their recapitulation of in vivo cellular organization in 3D. This disparity highlights the need for better approaches to study the dynamic interplay of relevant cells and signaling molecules as they are organized in the tumor microenvironment. In this thesis, we combined 3D culture of lung adenocarcinoma cells with adjacent 3D microvascular cell culture in 2-layer cell-adhesive, proteolytically-degradable poly(ethylene glycol) (PEG)-based hydrogels to study tumor angiogenesis and the impacts of neovascularization on tumor cell behavior.

In initial studies, 344SQ cells, a highly metastatic, murine lung adenocarcinoma cell line, were characterized alone in 3D in PEG hydrogels. 344SQ cells formed spheroids in 3D culture and secreted proangiogenic growth factors into the conditioned media that significantly increased with exposure to transforming growth factor beta 1 (TGF-β1), a potent tumor progression-promoting factor. Vascular cells alone in hydrogels formed tubule networks with localized activated TGF-β1. To study cancer cell-vascular cell interactions, the engineered 2-layer tumor angiogenesis model with 344SQ and vascular cell layers was employed. Large, invasive 344SQ clusters developed at the interface between the layers, and were not evident further from the interface or in control hydrogels without vascular cells. A modified model with spatially restricted 344SQ and vascular cell layers confirmed that observed 344SQ cluster morphological changes required close proximity to vascular cells. Additionally, TGF-β1 inhibition blocked endothelial cell-driven 344SQ migration.

Two other lung adenocarcinoma cell lines were also explored in the tumor angiogenesis model: primary tumor-derived metastasis-incompetent, murine 393P cells and primary tumor-derived metastasis-capable human A549 cells. These lung cancer cells also formed spheroids in 3D culture and secreted proangiogenic growth factors into the conditioned media. Epithelial morphogenesis varied for the primary tumor-derived cell lines compared to 344SQ cells, with far less epithelial organization present in A549 spheroids. Additionally, 344SQ cells secreted the highest concentration of two of the three angiogenic growth factors assessed. This finding correlated to 344SQ exhibiting the most pronounced morphological response in the tumor angiogenesis model compared to the 393P and A549 cell lines.

Overall, this dissertation demonstrates the development of a novel 3D tumor angiogenesis model that was used to study vascular cell-cancer cell interactions in lung adenocarcinoma cell lines with varying metastatic capacities. Findings in this thesis have helped to elucidate the role of vascular cells in tumor progression and have identified differences in cancer cell behavior in vitro that correlate to metastatic capacity, thus highlighting the usefulness of this model platform for future discovery of novel tumor angiogenesis and tumor progression-promoting targets.