Multistability of acinar and islet cell fates
Cell fates are characterized by stable patterns of gene expression. Whether a set of interacting genes is able to reach one or more stable states depends on their interaction topology as well as on the strengths of interaction. To investigate the cell fates that can appear in our model, we studied the existence of stable states and their dependence on parameter values for lateral signaling by performing a bifurcation analysis.
Due to lateral signaling, the fates of individual cells depend on the states of neighboring cells. Therefore, we analyzed a system of three cells representing a minimal tissue that is able to show all possible configurations present in larger systems (the mixed state does not occur for less than 3 cells). To study how the stability of cell fates changes while varying the strength of the lateral stabilization mechanism b, we recorded the summed expression level of exocrine factor Y. This reduces the high-dimensional state space to a single dimension and provides information on cell fates as well as their spatial pattern. The solid lines in the bifurcation diagram in Figure 2A show that Y expression has three stable states over a wide range of parameter values. For these values of b, the three cells can have either acinar fates (Y=3), islet cell fates (Y=0) or have mixed fates (Y=2), depending on initial conditions or history of gene expression.
This multistability of acinar and islet cell fates has several interesting consequences. The key observation is that a critical value b
c
exists, below which the stable steady state for the acinar fate disappears, while the islet cell fate remains stable. Thus, loss of the stabilizing effect of lateral signaling effectively moves the system towards a region in parameter space where the acinar cell fate no longer exists. Therefore, upon such a change in parameter values, acinar cells lose their exocrine markers and dedifferentiate spontaneously. In the presence of lateral inhibition (Figure 2A) cells adopt a multipotent progenitor-like fate. This state is stable against perturbations in Y, but unstable against perturbations in X, which implies that noise on X can change this state. If lateral stabilization is recovered at this multipotent stage, the system moves towards a steady state with mixed acinar and islet cell fates, recapitulating the cell fate decision and spatial pattern observed during pancreas development [39]. If, however, disruption of lateral stabilization continues, cells differentiate into the islet cell lineage. After completing the lineage conversion, the islet fate is stable in the sense that recovery of lateral stabilization does not reverse conversion.
Interestingly, the bifurcation analysis shows a different behavior in the absence of lateral inhibition (Figure 2B). In this case, multipotent progenitor-like steady state does not exist. This implies that acinar cells cannot dedifferentiate towards a progenitor-like state upon loss of lateral stabilization. Instead, cells undergo direct lineage conversion from the acinar to the islet lineage, rather than passing through a state of multipotency.
In conclusion, bifurcation analysis reveals (1) that lateral stabilization accommodates multistability of the acinar and islet cell states, (2) that transient loss of lateral stabilization can cause the conversion of acinar to islet cells and (3) that concomitant suppression of lateral inhibition leads to direct conversion, bypassing the multipotent progenitor-like state. Yet, bifurcation analysis does not provide insight into the spatiotemporal dynamics for which we next turn to numerical simulations.
Cell fate decision and patterning during pancreas development
Cells undergoing acinar-to-islet cell conversion transiently express various factors and activate signaling pathways normally only observed during development (Pdx1, Hnf6, Ngn3, Notch, Dll1) [21, 23]. This suggests that at least a part of the developmental regulatory network is reactivated [16] and that cell fate decisions during organogenesis and cell type conversion are governed by the same regulatory mechanisms. Under this assumption, the model proposed here for acinar-to-islet cell conversion is expected to reproduce the cell fate decision between the exocrine or endocrine lineage during embryonic development.
To test whether the proposed model holds for the conditions during embryonic development, we simulated the model using initial conditions that represent the gene expression in early pancreatic progenitor cells. In the mouse, the inductive factors Hnf6 and Hnf1 β, that act upstream of lineage-associated factors Ngn3 and Ptf1a, are first detected around E9 [38]. At this stage, Ngn3 and Ptf1a themselves are not yet expressed. Accordingly, the early embryonic state is accounted for in our model by the homogeneous expression of A (Table 1).
Figure 3B shows that during simulation, A activates the expression of both X and Y. For a transient period, these factors are co-expressed in all cells at low or intermediate levels of expression. The “promiscuous” co-expression is typical of multipotent progenitor cells and is also observed in pancreatic progenitors [40]. During this phase, mutual inhibition between cells maintains a low-level expression and thereby suppresses differentiation into either lineage, similar to the role of Notch signaling in pancreatic development known as “suppressive maintenance” [50]. After noise introduces variation in X expression between cells, these differences become amplified by lateral inhibition and result in a divergence of X expression. Factor X activates islet cell differentiation by activating Z and is only transiently expressed itself, as is known for Ngn3. Reversely, in the X− surrounding cells, Y is no longer inhibited and is upregulated. Through lateral stabilization, Y+ cells induce the expression of Y in neighboring progenitor cells (with low Y expression) which results in wave propagation, in a process traditionally known as homeogenetic induction [51]. Maturation into either lineage results in suppression of upstream factor A which leads to the downregulation of the pro-endocrine factor X, while Y is maintained by lateral stabilization. In line with experimental observations, both factors (Hnf6 and Ngn3) are not expressed after the cell fate decision and in the adult pancreas.
Interestingly, the spatial patterns generated by the model are also in line with reports of the scattered distribution of nascent islet cells in the early pancreatic epithelium [52]. The combination of lateral inhibition (creating an alternating pattern of acinar and islet cells) with lateral stabilization (creating homogeneous fields of acinar cells) results in the establishment of a scattered spatial distribution of endocrine cells in a mainly exocrine tissue (see Figure 3C) [39].
In short, under initial conditions representing early pancreas development, the key features of gene expression and patterning in the developing pancreas are reproduced by the model: (1) promiscuous expression of the lineage-associated factors Ngn3 and Ptf1a, (2) the transient expression of the pro-endocrine factor Ngn3 and (3) the scattered spatial patterning of committed islet cells.
Loss of lateral stabilization causes sequential conversion
To understand the dynamics of acinar-to-islet cell conversion upon loss of lateral stabilization, simulated cells were initialized with an acinar-like gene expression profile in which only the exocrine factor Y is expressed (see Table 1). The system was initialized with lateral stabilization strength b>b
c
to ensure the stability of the acinar-like state under these conditions. After a given period, lateral stabilization was lost, b=0, marking t=0.
As shown in Figure 3B’, the acinar state is stable as long as lateral stabilization strength b>b
c
, representing intact acinar tissue. However, immediately following the loss of lateral stabilization, cells lose the expression of exocrine marker Y. The lack of the maturation factor Y leads to the re-activation of the upstream factor A. Since A induces low levels of both X and Y, at this stage, the expression pattern is identical to the early embryonic situation. Thus, loss of lateral stabilization causes cells to return towards the multipotent progenitor-like cell state. If the absence of lateral stabilization continues, the subsequent dynamics differ from the embryonic cell fate decision discussed above. Specifically, nascent islet cells arise in an alternating spatial pattern as a result of lateral inhibition between X+ cells (Figure 3C). Yet, this pattern is not stable. After a cell has committed to the islet lineage by transactivating the endocrine marker Z, it looses expression of X. Therefore, cells adjacent to endocrine Z+ cells are no longer inhibited and will start to express X themselves. As a result, some of the neighboring cells also commit to the endocrine lineage, after which the process is repeated. This step-wise conversion of cells within the tissue results in a complex spatiotemporal patterning process (Figure 3C’). Under these idealized conditions, eventually all cells commit to the islet cell lineage. If, however, lateral stabilization is recovered before cells have redifferentiated, the cell type conversion is arrested which significantly decreases the efficiency of conversion (data not shown). Recovery does not revert newly committed islet cells back to acinar fate, since the islet cell state is stable, independent of lateral stabilization.
These results are in line with in vitro experiments showing spontaneous dedifferentiation upon enzymatic disassociation and disruption of cadherin-mediated cell-cell adhesion [13, 20–22]. Furthermore, these results suggest that acinar-to-islet cell conversion ensuing loss of lateral stabilization is a relatively slow process due to the fact that lateral inhibition prevents neighboring cells from completing transdifferentiation simultaneously.
Loss of lateral inhibition accelerates conversion
In the embryo, disruption of the Notch signaling pathway is known to cause precocious endocrine commitment [24]. Moreover, its inhibition in adult acinar cells can dramatically increase the efficiency of acinar-to-islet cell type conversion [23]. Since one of the roles of Notch signaling in the developing pancreas is lateral inhibition, we examined the dynamics of the model after a sudden loss of lateral inhibition. As before, we used the acinar-like initial conditions (Table 1), but now both lateral stabilization and lateral inhibition were lost, a=b=0, after a given period.
Immediately ensuing this manipulation, Y expression rapidly decreases, causing the reactivation of A expression, as described before. However, in this case, the dedifferentiated cells do not return to a multipotent state with “promiscuous” co-expression. Instead, all cells simultaneously upregulate the pro-endocrine factor X since they are not inhibited by their neighbors (see Figure 3B”). Finally, after the transactivation of Z by X, the factors A and X are suppressed again, leading to an adult islet fate in all cells. Compared to the loss of stabilization, the additional loss of lateral inhibition results in a much faster dynamical process of lineage conversion. In line with results obtained in vitro[23], our model shows that concomitant inhibition of lateral inhibition accelerates acinar-to-islet conversion. Here, this observation is explained by the fact that, under disruption of lateral inhibition, the unstable steady state representing the multipotent progenitor state does not exist, as predicted by bifurcation analysis (Figure 2B).
Note that disruption of lateral inhibition alone (a=0, b>b
c
) does not affect acinar cell stability, since the pro-endocrine factor X, which is involved in this feedback between cells, is not expressed in adult acinar cells. Therefore, without loss of lateral stabilization, cells maintain their acinar identity.
Cell density affects conversion efficiency
If the disruption of contact-mediated signaling influences the efficiency of acinar-to-islet cell conversion, loss of physical contacts between cells could replace molecular manipulation. To study the effect of cell-cell contacts, we performed simulations with varying densities of acinar cells. As expected, it was found that conversion efficiency increases with decreasing cell density (see Figure 4). For extreme cases, the reason behind this is evident. At high densities, most cells have many contacts with neighboring acinar cells and the stabilizing positive feedback prevents their dedifferentiation. Conversely, at low density, most cells are isolated and do not receive stabilizing (or inhibiting) cell-cell signals. Consequently, these cells can complete transdifferentiation. However, for more realistic intermediate cases in which cells are part of small aggregates, the situation becomes nontrivial. Here, the probability of cell conversion depends on both size and shape of the cellular aggregate. Although cells in larger clusters are generally more stable, this stability also depends on the spatial arrangement of cells in the aggregate (Figure 4C). Because the dedifferentiation of one cell weakens the stability of its neighboring cells, waves of dedifferentiation and conversion can propagate through the aggregate, depending on the average number of neighboring cells that reflects both density and configuration of a cell cluster.
These results show that, in the context of our model, the size and the structure of cellular aggregates affects the efficiency of lineage conversion. This implies that the degree of dissociation of acini by enzymatic digestion is predicted to have large impact on islet cell yield. More generally, the use of low cell densities or, alternatively, inhibition of reaggregation of cells, is predicted to increase the efficiency of acinar-to-islet cell conversion in vitro.