The people behind the papers – Philip Greulich

Can you give us your scientific biography and the questions your group is trying to answer?

I studied physics in Germany, first in Heidelberg and then in Cologne, and then did a PhD in theoretical physics at Saarland University, completing it in 2010. Studying theoretical physics gave me a good foundation in maths, yet already during my Master's and PhD projects I was fascinated by biological questions, when I had studied models of active intracellular transport. I then widened my portfolio in mathematical modelling of biological systems when I moved to Edinburgh for a postdoc position, studying bacterial population dynamics and antibiotic mode of action. Eventually, my focus shifted to stem cells and their proliferative/differentiation dynamics when doing a postdoc in Cambridge (from 2013) with Ben Simons – himself a theoretical physicist turned quantitative biologist.

I started my group in Southampton in 2016 when I became lecturer and PI, and our research questions are mainly around stem cell fate dynamics, both in developing and adult tissues. On the one hand, we look at specific tissues like mammary gland or brain during development and regeneration, working with experimentalists to develop and verify particular hypotheses about stem cell dynamics. We do this by translating biological hypotheses into mathematical models and then testing them on the experimental data; that lets us exclude or accept hypotheses, thereby learning about the fate choices of stem cells. But, on the other hand, we also do pure theoretical work to find generic principles, as in the paper published here, because we think that such principles can eventually guide and simplify experimental approaches.

What is network theory and why might it be helpful to address issues around the stem cell concept?

Network theory generally considers the connections (called ‘links’) between things (called ‘nodes’). These connections may be interactions between components of a complex system, or the links may represent the transitions between states, which then are the nodes of the network. In this paper, we identified nodes as the detailed molecular states of a cell while the directed links mark the possible transitions between cell states when they change over time, for example when differentiating. This also allows to define cell state ‘trajectories’ – a concept commonly used in development – as sequences of links (a path) in that network.

There has always been some ambiguity regarding what actually defines a cell type and stem cells in particular. Cell types are commonly defined as cells that are very similar by morphology or in their molecular composition. However, we noticed that it is not always feasible to assess this in an unambiguous way (e.g. by ‘clustering’ of single-cell RNA-sequencing data), and, at least in the developmental context, this can sometimes lead to unreasonable interpretations. For example, during the cell cycle, a cell's molecular content and morphology changes dramatically, and taking molecular similarity as a criterion would mean that different stages of the cell cycle would need to be classified as different cell types, which is not reasonable. It is more suitable to consider cyclic cell state transitions as part of one cell type and to ensure that cells of the same type have the same lineage potential. And here network theory comes into play: it turns out that there is a common way to represent directed networks, namely by a decomposition of the network into so-called ‘strongly connected components’. Our key insight was that this decomposition achieves exactly what is needed in the developmental context: states grouped as strongly connected components are those connected via cyclic trajectories, which also means that they have the same lineage potential (that is, outgoing trajectories); it is just a natural choice to group states as such and define them as a cell type. Furthermore, such a grouping naturally leads to a hierarchical ‘tree-like’ structure as one usually considers lineage hierarchies.

Can you give us the key results of the paper in a paragraph?

We considered tissues in homeostasis – that is, normal adult tissue where cell divisions and differentiation are tightly balanced, so that cell numbers remain constant over time. The necessity of such a balance constrains the possible cell population dynamics substantially, and we were wondering whether this also limits the ways in which cell lineage hierarchies are structured. We found, by a rigorous mathematical reasoning, that for homeostasis to prevail there must be a ‘self-renewing’ cell type at the top of a homeostatic lineage hierarchy, and only there. ‘Self-renewal’ is one of the characteristic properties of adult stem cells, namely the ability to keep dividing while maintaining their numbers, i.e. they remain homeostatic on their own. The second characteristic property of adult stem cells is ‘maximal lineage potential’, i.e. they are at the top of the hierarchy and can differentiate into any cell of that lineage. Now, our finding shows that in homeostasis, these two seemingly independent properties actually imply each other and are thus equivalent. If one wishes to identify adult stem cells, one usually needs to check for both these characteristics separately, but our finding tells experimentalists that they only need to measure one of these characteristics, and they get the other one for free. In particular, any self-renewing cell in homeostasis can safely be called an adult stem cell. This purely theoretical finding, therefore, also has direct practical use.

How well do your results fit with experimental evidence?

That self-renewing cells are at the top of the adult lineage hierarchy is indeed what is commonly observed. There are examples for which ‘dormant’ stem cells reside above other self-renewing cell types in that hierarchy; however, the name ‘dormant’ already indicates it: they are not actively dividing and differentiating under normal, homeostatic conditions, and are therefore not part of the homeostatic lineage, which our theory considers. Instead, they only become active in stressed conditions, for example when the tissue is injured.

Another system in which two stem cells are seemingly in a hierarchical relationship to each other is long-term and short-term stem cells in the blood lineage. However, we are convinced that, as suggested by our theory, either one of these cell types is not genuinely self-renewing, or not participating in homeostasis, or both can interconvert. In the latter case, they would, according to our definition, actually constitute a single cell type, since they could be connected by a cyclic trajectory. Of course, then this would be a matter of definition, but we believe that our definition of a cell type is very useful, because it simplifies our understanding of cell lineages.

Your work focuses on renewing tissues in which homeostasis is key. What about developing tissues: do they have similar principles of lineage architecture?

It would be fascinating to find similar principles also in developing tissues. Certainly, those lineages would be less restricted than in homeostasis, because the constraints which homeostasis impose do not apply to developing tissues. Nonetheless, the principles we found for homeostasis actually also indirectly tell us something about development. First of all, although in development there are of course cell types above adult stem cells in the lineage hierarchy, they must be transient and gradually disappear when approaching an adult, homeostatic state. Furthermore, from our analysis it becomes clear that developing stem cells, for example embryonic stem cells, are fundamentally different to adult stem cells. Although the defining characteristic of adult stem cells is self-renewal potential, developmental stem cells are, in contrast, not self-renewing: they have a broad lineage potential, to differentiate into a variety of cell types, but they must disappear at some point in time; we do not want to have embryonic stem cells in adult bodies. Embryonic stem cells are thus not self-renewing in vivo; only when put in a dish and exposed to the appropriate stimulus by a medium, do they become self-renewing and can be cultured.

When doing the work, did you have any particular result or eureka moment that has stuck with you?

There were several such moments, but the biggest ‘eureka moment’ was certainly when we saw that by defining cell types through cyclic cell state trajectories (that is, strongly connected components of the cell state network), everything seemed to fall in place. It then became immediately clear that we always have a clear lineage hierarchy and this was only a step from showing that self-renewing cell types must be at the top of that hierarchy.

And what about the flipside: any moments of frustration or despair?

We found an inconsistency in a mathematical proof very late in the project, which was very frustrating. This proof was addressing only a side-result of the work, so it wouldn't have been catastrophic if not remedied, but finding something that late before publication is indeed annoying. However, this turned out to be positive, after all. This inconsistency actually told us something very deep about homeostasis and, by adjusting our results, we saw that the concept of homeostasis should possibly be seen in a broader light. In particular, we found a condition for feedback regulation of homeostasis, but instead of ensuring homeostasis in a strict sense, meaning that the (expected) cell numbers are in a strict steady state and do not change at all over time, after a revision we found that actually oscillations of the cell numbers are also a possibility. In fact, such an oscillating state may actually also be a viable adult state, as tissues that vary periodically over time exist, for example the uterus during the menstrual cycle, or hair follicles in epidermis. In a strict sense, this would not be considered homeostatic, but one might wish to widen the concept of homeostasis to include such ‘dynamic’ homeostatic states whereby the tissue cell composition oscillates periodically.

What do you think about the general standing of mathematical and theoretical approaches like yours in developmental biology?

In recent times, mathematical approaches have become more and more accepted by the biological community, in particular in developmental biology, and are now becoming widely employed. This has, of course, something to do with the fact that we have more quantitative experimental data available, for example from -omics assays. Therefore, very data-oriented mathematical approaches, such as statistical analysis and modelling, have become prevalent in developmental biology. Nonetheless, I have the feeling that mathematical approaches are mainly seen as useful tools for advanced data analysis and interpretation – which of course they are, and the bulk of my research work is taking this approach. But theoretical/mathematical approaches can do much more than that; they can provide us with a deep understanding of how things are connected and unveil generic principles behind the nitty-gritty details and differences between individual biological systems, beyond just looking at a particular biological system and data.

Think, for example, of Waddington's epigenetic landscape: the idea to represent developmental processes as dynamics in a landscape, a common approach in physics, is based on a plain theoretical and conceptional work, without explicitly ‘fitting’ a particular set of data. And it represents a generic developmental principle, not bound to a particular tissue or organism. Yet Waddington's concept has transformed our thinking about development and cell fate decisions and, it is only in recent years, now that the corresponding data are available, that we have discovered how much ahead of his time Waddington was with this principle. In our work, we were guided by this way of thinking, to reveal generic principles rather than ‘fitting’ particular data, and I hope that our work contributes to this tradition and can help to revive the interest in broader theoretical approaches.

Where will this story go next, and what other current projects are you excited by?

In the current paper, we look mainly at lineage hierarchy, i.e. the network links between cell types. Our plans are now to look at the cell state transitions within the same cell type. The question is: can we get hints at whether a cell type is self-renewing or transient by analysing the topology of its cell state network? Furthermore, we are having a closer look at how homeostasis is controlled and the implications of this. We already gave a criterion for feedback regulation of (dynamical) homeostasis in the current paper, and we wish to have a closer look at this. In particular, we are interested in what happens to cells that are under homeostatic feedback control, when cells are added or removed, or mutations occur that change the feedback response.

Finally let's move outside the lab – what do you like to do in your spare time in Southampton?

I love spending time with my family and friends, in particular outside in nature, going for a walk or having picnics and barbecues. During the lockdown, much of that wasn't possible, but I hope now we can get back to meet friends and hopefully travel soon.