Evolution as an Information Dynamic System

The project (EPSRC grant EP/H031936/1) was envisaged at the Maths of Life Sandpit organised by the EPSRC in the summer of 2009. This is where the future co-investigators of the project first met. The pictures below show Alastair, Chris and Roman during one of the first discussions and John at one of numerous presentations at the sandpit.

The main motivation of the collaboration was to achieve better understanding of evolutionary dynamics by exploring new theoretical ideas of information theory and information geometry, and combining them with computational and biological experiments. Here is the summary and the objectives of the project as they were stated in the proposal. The project received £423,142 from EPSRC and an additional support from the Wellcome Trust and continued between 2010--2013.


In our first meetings we are trying to understand each other, which is not easy given our different backgrounds. We are also joined by a PhD student Elizabeth Aston, who immediately finds a lot of relevant literature we all have to read. Our focus is on mutation and its role in evolutionary dynamics and adaptation. Information theory predicts that if there is some information communicated by the environment about biological fitness of the organisms, then this information could be used to increase fitness of the organisms in future generations (i.e. their offspring), for example by controlling the mutation rate (opt.letters, jogo). To test theoretical predictions, Alastair with the help of Liz develops a two-layer evolutionary optimiser (Meta-GA), which allows us to `evolve' optimal mutation rates in various artificial and biological landscapes (e.g. on Transcription Factor binding scores). The speed of this Meta-GA optimiser was improved greatly by moving the code to Nvidia's CUDA many-core (GPGPU).

Above is one of our first meetings at Keele (Feb 2010). Alastair in the background is instructing his Meta-GA to run another series of tests.


The work is still mainly theoretical and computational. We analysed geometry and combinatorics of discrete sequence spaces (specifically Hamming spaces), and re-evaluated Fisher's geometric model of adaptation. I spent the whole Christmas break of 2010-11 trying to crack combinatorics of Hamming spaces. This allowed us to derive optimal mutation rates for DNA sequences as functions of Hamming distance from the optimum. The optimal mutation rate control functions were obtained for different conditions (e.g. different time horizons, cumulative and information-geometric criteria, see dis11). These mutation rate `curves' (as Alastair called them) were then evaluated against those obtained computationally by our Meta-GA. We presented our first results at the European Conference on Artificial Life in Paris (ecal1, ecal2) and IEEE Information Theory Workshop in Paraty, Brazil (itw11).


We were joined by Rok Krasovec, who began experimental work with Chris at Manchester. We obtained Escherichia coli from Richard Lensky's lab and began growing cultures under various conditions. The main idea is to manipulate biological fitness of the microbes (e.g. using an antibiotic, such as rifampicin) and measure their mutation rates.

By the end of summer 2012 we had our first results showing that mutation rates in E. coli increased by almost a factor at low fitness. Although it was encouraging to see that mutation and fitness changed together, as theory predicted, it was not clear what was causing it (i.e. environment or the organisms?). Perhaps, the most surprising and interesting was the fact that the best (if not the only) explaining factor was final population density of the cultures. Although there is a relation with fitness (i.e. low fitness corresponds to low replication rates, and hence lower population densities), the result hinted at the possibility that population density could be that information from the environment microbes needed to regulate their mutation. Rok and Chris came up with an idea to `disable' quorum sensing of the microbes and see what happens. On theoretical front the work continued in the direction of analysis of non-monotonic landscapes. A paper draft is now beyond 50 pages.

Above is the moment at our meeting in Manchester in October 2012, when Chris (right) explained how quorum sensing of our E. coli could be `switched off' by knocking out their lux-S gene. John (left) contributed greatly to statistical analysis of data from numerous experiments.


We have our first results from experiments with lux-S mutants of E.coli. There are many details, but roughly speaking, without correctly functioning quorum sensing, we see no relation between population density (or fitness) and mutation rate. Our results suggest that microbes use cell-cell interaction to regulate and optimise their mutation rates. We also want to find out which signal of the quorum sensing microbes are using. Results suggest that the most obvious candidate, autoinducer 2 (AI-2), is not the culprit. Another candidate is autoinducer 3 (AI-3), but its molecule is still unknown to science in 2013. We receive assistance from Bharat Rash, Manikandan Kadirvel and Sarah Forbes at Manchester.

Above: Rok and Chris explaining various effects of the lux-S gene on quorum sensing (Manchester, May 2013).

While additional experiments are ongoing, the task is now to publish our results. We submit the paper to a major journal in summer 2013 (now published in Nature Communications 10.1038/ncomms4742). Elizabeth is also about to finish her PhD. Her work on critical mutation rate is published in PLOS ONE (10.1371/journal.pone.0083438). The attempts to optimise mutation rates in simple genetic algorithms also lead to interesting ideas in information geometry (qbic11, gsi13). I present the work at Geometric Science of Information in Paris and Quantum Probability 34 in Moscow. I dedicated the talks to my late father, who passed away in November 2012. The project has finished in June 2013, but the feeling is that the work has only just began. We are working on the next projects.


Nature Communications has published our paper: Mutation-rate-plasticity in rifampicin resistance depends on Escherichia coli cell-cell interactions.