Pluripotent embryonic stem cells (ESCs) can differentiate into all somatic cell types, making them a useful platform for studying a variety of cellular phenomena. Furthermore, ESCs can be induced to form aggregates which recapitulate the dynamics of development and morphogenesis. However, many different factors such as gradients of soluble morphogens, direct cell-to-cell signaling, and cell-matrix interactions have all been implicated in directing ESC differentiation. Though the effects of individual factors have been investigated independently, assaying combinatorial effects has proven inherently difficult due to the spatial and temporal dynamics associated with such cues. Dynamic computational models of ESC differentiation can provide powerful insight into how different cues function in combination, both spatially and temporally. By combining particle based diffusion models, cellular agent based approaches, and physical models of morphogenesis, a multiscale rules based modeling framework was created to investigate complex regulatory cues which govern complex morphogenic behavior in 3D ESC aggregates. The objective of this study was to examine how spatial patterns of differentiation by ESCs arise as a function of the microenvironment. The central hypothesis was that heterogeneity associated with soluble morphogens and cell-cell signaling leads to complex spatial patterns in ESC aggregates.

To test this hypothesis, a computational modeling framework capable of modeling diffusive soluble gradients and cell-cell interactions in multicellular aggregates was developed. Agent based modeling (ABM) captured complex spatio-temporal patterns associated with ESC aggregate differentiation, while a mass spring description accurately captured dynamic cellular behaviors such as movement and division. This served to approximate the physical properties of both the cells and the aggregate, while providing a means to keep track of local cell-cell interactions in a network structure. Soluble interactions via paracrine/autocrine signaling mechanisms were tested within a robust lattice-based diffusion solver by modulating parameters associated with soluble and local cell-cell interactions.

One major issue with agent based modeling of cellular aggregates is quantifying the spatial pattern of differentiation in a manner that is amenable to experimental validation. To address this shortcoming, a novel spatial pattern recognition system was developed which utilized network theory to extract meaningful spatial metrics from networks in which cells are represented as nodes, and the connections between cells are edges. Images were converted to networks using a combination of image analysis algorithms and custom code to create digital networks. By describing the experimental images and computational results in a common space, quantitative comparisons between spatial images and computational models were performed. This technique uncovered a putative paracrine mechanism which could explain size-dependent differences in differentiation of ESC aggregates.

To further probe the molecular mechanism which could lead to pattern formation in early differentiation of ESC aggregates, a multiscale stochastic ordinary differential equation (ODE) system was constructed. This model included mechanisms for soluble LIF signaling and FGF4 signaling, which are produced by ESCs during the differentiation process. The stochastic ODE based model created in this study captured a wide range of spatial patterns, and showed that FGF4 signaling and inherent stochasticity associated with expression of the pluripotency associated transcription factor Nanog play a key role in modulating spatial pattern associated with differentiation. This model provides key insight into why cellular aggregates cultured in different conditions may display different spatial differentiation signatures.

This study further demonstrated the modulatory of network based spatial pattern classification and tested a variety of input image types (2D images, 3D confocal stacks, and 2D histological sections) and a wide range of model systems (mesenchymal and neural differentiation in ESC aggregates and gastrulation in cichlid fish). In the context of cichlid fish, this technique was able to segregate fish into different stages of gastrulation based on spatio-temporal differences in protein and RNA expression. Network derived metrics significantly improved classification of mesenchymal phenotypes, and enabled comparisons across different experiments to describe patterns associated with mesenchymal phenotypes in histological samples. Furthermore, this approach predicted novel feedback mechanisms which can help explain the switch from motor neuron production to oligodendrocyte production (the glial switch) in neural differentiation.

This work represents the first attempt to understand emergent dynamic differentiation patterning that result from integration of multiple cues governing ESC aggregate morphogenesis in 3D via computational modeling strategies. Furthermore, this network approach represents a significant and novel advance in the field of pattern recognition and quantitative biology as the first pattern classification platform which utilizes single cell spatial information and modularly compares across multiple systems of interest.