## Theoretical stem cell biology

Recent work on stem cells and induced pluripotency show that adult somatic cell retain the ability to be converted into other cell lineages. Such cellular plasticity holds great potential for regenerative therapies by converting cells to replace diseased cells.

To make informed decisions about how to reprogram cells, a good place to start is to look how cell fate decisions are controlled during normal development. By reverting the differentiation of a cell back to its multipotent progenitor state (dedifferentiation), cells can be shunted into another lineage.

Yet, the trajectory of a cell through various developmental stages during embryonic development presents only one of the many possible trajectories. It has been shown, for instance, that cells can be transdifferentiated directed, even across germ lines, without passing a state of multipotency.

Understanding the variety of possibilities has raised new interest in mathematical modeling of gene regulation, based on the seminal works of Delbrück (multistability), Jacob and Monod (transcriptional regulation), Waddington (epigenetic landscapes), and Kauffmann (cell types as attractors). Using dynamical systems theory, one can start to appreciate the fact that the high-dimensional state space of gene expression is subdivided into basin of attraction, and that reprogramming cells is to force the transition from one basin to another.

## Multicellular systems

Although many studies now take a dynamical systems approach to explain gene expression profiles, the multicellular context is rarely addressed, despite the fact that intercellular signaling is known to be a potent inducer of cell fates.

For instance, cell-cell adhesion molecules have been shown to regulate stem cell self-renewal and can control population ratios though modulation of symmetric/asymmetric cell divisions. Notch signaling is well-known receptor-ligand pathway that acts as a gatekeeper of cell fates and is ubiquitous in developmental systems, from neural tissues to the pancreas. It divides a population of progenitors into two lineages by Delta ligand-expressing cells suppressing adjacent cells from entering the same cell fate. Thereby, it generates spatial patterns within a developing tissue and determines its cell type ratios.

Because such cell-cell interactions directly affect cell fates, it is important to account for the multicellular context in understanding cell fate decisions. It advances our understanding of stem cell behavior during development and regeneration. Moreover, it may be exploited to reprogram cell fate by drug-induced inhibition of intercellular communication, rather than by commonly used genetic manipulation, providing safer and more effective reprogramming strategies.

These multicellular systems can be studied using the tools from dynamical systems theory (phase diagrams, stability analysis, bifurcation analysis), extended by a cell-based modeling approach in which cells are represented as discrete interacting entities.

I have developed a number of such models focusing on the cell fate decisions and spatial patterns in the pancreas, that are described below.

## Reprogramming the pancreas

The pancreas is an organ with a dual function. On the one hand, its exocrine acinar tissue produces digestive enzymes. On the other hand, the islets of Langerhans have an endocrine function, releasing hormones in the blood that regulate glucose levels. Dysfunctioning of $latex \beta$-cells in the islets of Langerhans causes diabetes. Replacing these nonfunctional cells with newly reprogrammed cells may restore normal glucose homeostasis in diabetic patients.

Interestingly, the exocrine and endocrine cell types, despite their diverse function, originate from a common pancreatic progenitor. Therefore, the abundant acinar cells are prime candidates for reprogramming into new $latex \beta$-cells. In fact, it has already been demonstrated that adult acinar cells can be reprogrammed into $latex \beta$-cells *in vivo* using key transcription factors (Zhou et al., 2008)*.*

To develop this type of reprogramming strategies by rational design, rather than trial-and-error, Joseph Xu Zhou formulated a mathematical model of the pancreatic transcriptional network (Zhou et al., 2011). Using this model, they were able to reproduce the key expression patterns during pancreatic development as well as various strategies for acinar-to-$latex \beta$ cell reprogramming.

However, this model did not account for intercellular signaling and was unable to account for the observed cell type ratios and the particular scattered spatial pattern of nascent endocrine and exocrine cells. To study these aspects in more detail, I developed a mathematical model, based on the work of Zhou and colleagues, that includes the multicellular context of cell fate decisions in the pancreas.

## Patterning in the developing pancreas

It is known that the cell fate decision of pancreatic progenitors cells into the exocrine or endocrine lineage is governed by the Delta-Notch pathway (Apelqvist et al., 1999). Therefore, according to mathematical models of Notch signaling, one would expect a salt-and-pepper or checkerboard-like spatial pattern (Collier et al., 1996) rather that the observed scattered patches of endocrine cells. This indicates that an additional mechanism must be in place that control this cell fate decision.

An important clue may come from experiments in which acinar cells from adult pancreatic tissues were isolated by enzymatic tissue dissociation. There, spontaneous dedifferentation to a progenitor-like state was observed as a result of isolating cells from their multicellular context (Baeyens et al., 2006). This suggests that acinar cells require their mutual contact to stabilize and retain their exocrine fate.

Combining these observations, I formulated a mathematical model that combines lateral inhibition with lateral stabilization. Through bifurcation analysis and simulation, I could demonstrate that crosstalk between these intercellular signaling mechanisms is sufficient to reproduce the observed scattered patterning as well as modulating cell type ratios between endocrine and exocrine cells.

## Transdifferentiation in the pancreas

Recent work on inducing pluripotency has convincingly shown that adult somatic cell can be reprogrammed into other cell lineages. Such cellular plasticity holds great potential for regenerative medicine by freshly converted cells replacing diseased cells, such as $latex \beta$-cells in diabetes.

Currently, reprogramming cells typically involves directly interfering at the genetic level (e.g. Zhou et al., 2008), but multipotency can also be induced by altering a cell’s microenvironment. Merely isolating cells from their normal tissue structure, for instance, has been reported to lead to de-differentiation of adult pancreatic acinar cells (Baeyens et al., 2006).

To understand this process from a systems perspective, I extended the previous mathematical model, again based on crosstalk between Notch-mediated lateral signaling and lateral stabilization, possibly mediated by cadherin signaling. Using bifurcation analysis and multicellular simulation, I analyzed the possibilities for dedifferentation and transdifferentiation.

Besides recapitulating developmental spatial patterning, I studied that effects of selectively inhibiting the two intercellular signaling pathways. I showed theoretically that the loss of lateral stabilization alone can shunt acinar cells to a islet fate, but through a slow and reversible process involving the dedifferentiation to a multipotent state. However, additional inhibition of Notch signaling accelerates the conversion process by transdifferentiation, direct conversion without an intermediate state of multipotency. These results provide a theoretical understanding of the experimental observations (Baeyens et al., 2009).

## Spatial patterning in mouse embryonic stem cells (mESCs)

Mouse embryonic stem cells (mESCs) have the potential to self-renew while retaining the capacity to differentiate into a multitude of different cell types and to contribute to embryonic development *in vivo* (pluripotency).

In this project, we focus on the analysis of regulatory mechanisms responsible for the maintenance of this unique pluripotent cell state. In particular, we aim towards a multi-level mathematical model describing the organization of mESCs from transcription factor (TF) networks up to the level of spatially extended cell populations.

Therefore, we integrate time-lapse microscopy data of fluorescent reporter cell lines. Using such a comprehensive approach we are able to analyze the functional relation between intra- and inter-cellular regulatory elements as well as the spatiotemporal patterning of mESC cultures. (Text adopted from Roeder lab at Medical faculty in Dresden.)