What do gut bacterial colonies look like? My group has been exploring this question for years, and ever since our first forays peering inside larval zebrafish it has been evident that many bacterial species form dense, three-dimensional clusters (e.g. paper 1, blog post 1; paper 2, blog post 2). Especially after exploring the striking effects of antibiotics (paper, blog post), we began to think more seriously about understanding what sets the sizes, and especially the distribution of sizes, of gut bacterial aggregates. “We” is mainly former graduate student Brandon Schlomann, currently a postdoctoral fellow at UC Berkeley — the work described below is almost entirely his in both design and execution.
Why care about the size distribution of gut bacterial groups? Because a single snapshot of sizes might tell us about the processes that generated those sizes — for example, growth processes that respond to changes in diet or drugs — and it is likely to be easier to get a static snapshot than a dynamic movie. From the widths of tree rings, for example, we can infer the growth rates that occurred in the past without needing a movie of the developing tree. The shapes of snowflakes, the sizes of stars, and more are functions of their dynamics. In the case of the gut microbiome, we can peer into fairly transparent zebrafish larvae and watch the dynamics, but this can’t be done for a human. One might, however, get some sort of a snapshot, perhaps from a biopsy or a fecal sample. What might one infer with this data?
Do rules exist?
The first step in trying to understand the distribution of gut bacterial sizes is to ask whether a well-defined distribution exists! This isn’t at all obvious a priori. Perhaps in some guts bacteria are mostly discrete individuals; in some there are just a few giant clusters; in some its equally likely to have small, medium, or large clusters; and so on. It may be a mess! After all, these are guts, and though we’re physicist and nature often benevolently supplies us with well-behaved phenomena, this isn’t guaranteed. In addition, even if there is a clear form for one bacterial species’ distribution, it may be very different for other species.
We first, therefore, looked at the size distrubution for eight different gut bacterial species and strains, each colonizing zebrafish initially devoid of bacteria (“germ-free”), and therefore being the only species present. The data consisted of three-dimensional image data captured through light sheet fluorescence microscopy, and analyzed to identify clusters and individual bacteria (a challenging task). Surprisingly, all eight showed a similar, characteristic feature of the size distributions of their aggregates: the probability of finding an aggregate composed of n bacteria scales as a power of n, a bit shallower than 1/n2, and then becomes much shallower at large n. In other words, the probability of finding a cluster of 20 bacteria is about 4 times lower than of finding a cluster of 10 bacteria. A cluster twice as large again, with 40 bacteria, is another 4 times less common. This trend persists until one gets to very large clusters — how large depends on the species — when large clusters become more common than expected.
This raises the questions: Why a power law? Why this power law?
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Unrelated: if you haven’t already, check out my updated announcement for So Simple a Beginning — a pop-science book about biophysics! Last month, I pored over page proofs and wrote the index — the final steps (at least for me)! The book is scheduled to publish in the US on February 8, 2022. The publisher’s site is here; there are blurbs, and you can even pre-order!
Now back to bacterial dynamics
From observations, we believe that there are four key processes underlying bacterial colony dynamics: aggregation, fragmentation, growth, and expulsion. Brandon realized that growth and fragmentation are key to generating the power-law behavior, and moreover that the combination of growth and fragmentation maps exactly onto the classic “Yule-Simon model” that arises in all sorts of fields. In population dynamics, for example, the size distribution of groups with different mutations will depend on the mutation rate (like our fragmentation rate) and the growth rate (as groups grow). The distribution of word frequencies in a body of literature undergoes similar dynamics, as new words arise and occur more often the earlier they first appear. A Yule-Simon process gives a power-law distribution for aggregate sizes, with an exponent that depends (weakly) on the fragmentation rate and the physical mechanism of fragmentation. If fragmentation occurs at the cluster surface, at a low rate, the cluster size distribution should be a bit shallower than 1/n2, which is what we find.
Aggregation of clusters gives us the plateau at larger n, as large clusters preferentially glom together into even larger clusters. This is reminiscent of the gelation transition in a variety of soft materials (edible gelatin, for example), as individual units link together into clusters that can span the entire system — hence our description of the gut bacterial ensemble as a “living gel.” Expulsion and the finite size of our guts cut off the cluster size distribution. (We describe all this in more detail in the paper.)
There are two things that particularly excite me about our findings. First, it’s surprising that there is a fairly robust, comprehensible form to the size distribution of gut bacterial colonies. This living, churning environment, actively managed by a host with its own immune system, nutritional needs, and growth, could have been a hopeless mess in terms of physical structure. However, it is not! Second, this conclusion suggests routes to understanding the gut microbiota in systems that we can’t peer into, like the human gut. Measuring cluster sizes might reveal the dynamics that generated them, allowing inference of parameters like bacterial growth rates, disintegration rates induced by drugs, and so on. As we note in our paper: “Two decades ago, bacterial clusters spanning three orders of magnitude in volume were observed in gently dissociated fecal samples stained for mucus, but precise quantification of size statistics was not reported (van der Waaij et al., 1996).” Perhaps you, dear reader, would care to revisit this! (Yes, it’s rather gross; I’m not volunteering…)
Of course, our analysis is just on several single species of bacteria, each observed alone. Will all this persist in complex communities? What will that tell us? That, I hope, is something we’ll explore in future experiments.
Mountain (good), sunset (ok), water (bad). I watched this nice video and thought I’d try to get better at landscapes.
— Raghuveer Parthasarathy; October 14, 2021