Dr. Tamas Czaran, Evolutionary Modeler

Recent research in PLoS ONE explored the evolutionary dynamics of cooperation in bacterial populations. It was found that cooperative behavior, along with metabolically costly systems to detect cooperative neighbors, evolves readily under conditions where the rate at which related bacteria are separated from each other is low. A summary of this research was published on Monday here. What follows is the transcript of a text-based interview with the principal author of this study, Dr. Tamas Czárán, who is affiliated with the Ecology and Theoretical Biology Research Group at the Hungarian Academy of Sciences and Eötvös University, Budapest in Hungary. His co-author, Dr. Rolf Hoekstra, is the Head of the Laboratory of Genetics at Wageningen University in the Netherlands.

1] I note from your publication history that you often try to better understand evolutionary paradoxes through mathematical modeling, particularly the emergence and persistence of metabolically costly phenotypes. Which of these paradoxical phenotypes most intrigue you?

Recently I am focused on the evolutionary maintenance of phenotypic traits related to cooperation under strong selective pressure in microorganisms. For me, one of the most exciting features of microbial cooperation and communication is that we can safely rule out any kind of “intentionality” from among the evolutionary mechanisms producing them – bacteria and yeasts do not have brains or nerves to mediate their behavior. Cooperation, communication and cheating – microbes obtain and evolve all these features through relatively simple genetical and biochemical mechanisms. This helps us understanding the driving forces of biological evolution in its purest form, without having to consider “cultural” aspects that could possibly complicate the issue. It just adds to the fun that sometimes we can easily translate the results into terms of animal or even human behavior.

2] What initially attracted you to the study of these systems through the lens of mathematical modeling?

I think that there is almost nothing in science that can be fully understood without modeling. Whether or not we are aware, when trying to solve a scientific problem we always think in terms of models, i.e., logical constructions deducing the consequences of a certain assembly of premises. This can be done in various ways, from using intuitively appealing metaphors and sometimes sloppy handwaving arguments to rigorous mathematical models and computer simulations. The latter are just the most reliable tools for arriving at the right conclusion from a given set of assumptions. Relatively simple evolutionary questions like the one we treated in this paper are usually approachable by mathematical or at least by computational methods, and provided that the methods are used appropriately, the results are unquestionable. What can always be questioned are the assumptions, of course…

3] Philosophically and/or aesthetically, what is more beautiful to you: the input, the output, or the mathematical model itself?

Each one, and each for a different reason. The input – the facts known about the biology of our microbes and relevant to our topic – are very interesting themselves, not just for their obvious social connotations, but also for the simple elegance of the biochemical machinery in which they are implemented. The methodology – devising and programming the simulation model – requires a very tight chain of logically structured steps, and those are usually a lot of fun to take too. But the output – the conclusions that could have never emerged without the model – is the ultimate source of professional and aesthetical satisfaction, especially if they are somewhat counter-intuitive, solve an unsettled problem, or go against the “conventional wisdom” of earlier theoretical work while staying in line with empirical observations.

4] In this paper, you used a cellular automaton in a spatial lattice approach to model cell behavior. Can you please explain what this technique is and what it means?

The name “cellular automaton” is somewhat misleading. It denotes a modeling framework fit for studying the collective behavior of any kind of locally interacting objects, whether they are living cells or something completely different. Solid state physicists are the real power users of this method, because they are mostly interested in the short-distance interactions of localized particles like atoms in a crystal. An example from the other end of the scale: sociologists use cellular automata to predict large-scale patterns of social interactions, considering whole settlements (villages or towns) as the interacting units.

The basic structure of a cellular automaton is ridiculously simple: take a square lattice of sites, and imagine a single object in each node of the lattice. These objects are called “cells”. In our model they happen to be cells – bacteria – indeed. Each cell is attributed one out of a few possible states. In our case the state of a cell was the genotype of the bacterium sitting in the given node (one of the possible 8 different genotypes). Now let the state of each cell change in every time unit, according to its own state and that of its immediate neighbors in the lattice. The instructions determining the next state of a cell are the “transition rules” of the cellular automaton. In our model the transition rules defined in what circumstances one bacterium may invade a neighbor’s node. That’s all – not very complicated, is it?

The power of the cellular automaton approach rests in the emergent collective properties of the whole lattice of cells it produces. Such emergent properties are the numbers of cells in the different genotypes after a certain number of time units elapsed, or the spatial distribution (pattern) of the genotypes, in our model. These are very difficult – in fact usually impossible – to predict from the transition rules themselves, and there is no mathematical (paper-and-pencil) method to determine the outcomes either. There are a few specific exceptions, but those are usually far too simple to be of interest for us. The sole tangible method to see the outcome of our model is computer simulation.

5] What advantage in modeling this scenario does the cellular automaton model offer over the cellular Potts model?

The cellular Potts model (CPM) is the generalized stochastic cellular automaton itself, in which the transition rules are not specified beyond universalities like the requirement for random updating. In that respect, our model is a CPM with a specific set of cell state definitions and transition rules.

6] In the paper you placed cooperative behavior in the context of metabolically costly common goods such as siderophore nutrient scavengers. In a complex ecology with a dynamic topology, such as the mammalian gut microbiota, could the same modeling principles be applied to bacteria-produced chemorepellants, such as indoles, or interspecies warfare bacteriocins?

Of course it could – in fact we (I mean, my co-author Rolf Hoekstra from Wageningen University, The Netherlands, and myself) already published a paper a few years back in PNAS on the spatial ecology of bacteriocin-producing bacteria, trying to explain the extraordinary diversity of bacterial strains in certain spatially constrained habitats like forest soils. There the idea was that bacteriocin production, as well as the production of resistance factors against the bacteriocin, are metabolically costly. Bacteriocin-producing Killer (K) strains pay the cost of both the toxin and the resistance factor, while resistants (R) pay only the latter. Sensitive (S) strains pay none of these costs, but are killed by the bacteriocin excreted by the (K) strain. This amounts to a circular pattern of competitive relations: K excludes S excludes R excludes K. This is like playing the Rock-Scissors-Paper game with all the neighbors in a lattice habitat. We show that this circular interaction pattern in the spatial setting is sufficient to maintain a huge diversity of different strains within the same habitat. I think the same principles can be transferred (mutatis mutandis) to the microbial ecology of the mammalian gut.

7] I found it particularly intriguing that the “Lame” phenotype of bacteria, which had a fully functional quorum sensing system but was unable to produce the common good, did not emerge in any significant fraction under any of the conditions tested. Is it possible that in a scenario with high spatial mixing and individual motility a “Lame” phenotype could indeed emerge to find a parasitize “Honest”, “Blunt”, and “Shy” individuals? Or would the concurrent presence of “Vain” phenotypes make “Lame” too metabolically risky?

I think there is a simple explanation for the (almost) complete lack of the “Lame” phenotype: the “Liar” is better in all respects and excludes it wherever they appear together. This is because the “Lame” pays the metabolic cost of both components (the signal molecules and the receptors with the signal transduction cascade) of the quorum sensing machinery, whereas the “Liar” pays just for signal production. This gives the “Liar” a metabolic advantage. The “Lame” operates the signal reception and transduction machinery, but gains nothing from it, because it does not have a working cooperation allele that the signal could switch on or off. In fact the price of signal detection is paid in vain by the “Lames”. If it comes to gain advantage from cheating, the “Liar” phenotype always does better. This could not be helped by any different spatial setting either. However, the intensity of spatial mixing does make a big difference regarding the overall outcome of the interaction: in a completely mixed habitat (like in a stirred batch culture) cooperation would never show up, therefore operating quorum sensing would be also a waste of energy. Thus the stirred habitat maintains only the “Ignorant” phenotype. Yet as we show through many simulations, at small to moderate mixing cooperation can be maintained, and quorum sensing is worth adopting either as a signaling system or as a “cheating device”.

8] With these results in hand, what do you hope to model next?

We are working on a new model that will hopefully shed some light on a mysterious phenomenon well known in fungi: the existence of many vegetative compatibility groups (VCG’s) within the same species. Fungi do crazy things sometimes that neither animals nor plants dare to do in general. Somatic fusion is one such thing: two different individuals (hyphae) may come together, fuse, and exchange cell nuclei. This is not a sexual process, since it involves neither meiosis nor any kind of chromosomal recombination: it is just the fusion of two vegetative bodies and exchange of nuclei. For some – largely unknown – reason this is worthwhile for many species of fungi to practice. Yet, they also restrict the occurrence of somatic fusion by developing different vegetative compatibility groups among which fusion is not possible, or if occurs then the fused hyphae die. Somatic fusion is allowed only between individuals belonging to the same VCG. Our main question is: why do fungi evolve VCG’s to constrain fusion, given the assumption that fusion is beneficial?

9] Lastly, just for fun, do you listen to music as you work? If so, what type or particular composer?

Yes, of course I do – while I wait for the simulations to complete, for example. Programming and writing the papers requires all my attention, then I need to be alone in silence. Otherwise I listen to Marillion, Pink Floyd, Jan Garbarek, Keith Jarrett, Mozart, Bach, among many others. My kids say I am a bit like an old dinosaur with my music, but I was happy to realize lately that they steal my CD-s sometimes .