Now recruiting: Research Associate/Fellow in Antimicrobial Resistance Modelling

We are now recruiting the mathematical modelling post-doc for the EVAL-FARMS project. This post will work with me, Theo Kypraios in Maths, and the EVAL-FARMS team more generally, developing mathematical models for risk of emergence of AMR pathogens in agricultural waste, using all the exciting data that are being generated by the empirical researchers on the grant. Details of the advert, as well as links to it, are:

Research Associate/Fellow in Antimicrobial Resistance Modelling

Agricultural & Environmental Sciences

Location:  Sutton Bonington
Salary:  £26,052 to £38,183 per annum, depending on skills and experience (minimum £29301 with relevant PhD). Salary progression beyond this scale is subject to performance
Closing Date:  Wednesday 28 June 2017
Reference:  SCI158617

We are seeking an excellent researcher in modelling of antimicrobial resistance. The successful applicant will use mathematical and statistical models to make predictions on risk of emergence of antimicrobial resistant pathogens in a farm slurry system and slurry amended soil. The post is funded by NERC-led EVAL-FARMS project (Evaluating the Threat of Antimicrobial Resistance in Agricultural Manures and Slurries). Thus the role holder will work closely with an interdisciplinary team, including experimental researchers in microbiology and analytical chemistry, and social researchers in science and technology studies, in order to develop meaningful, data driven risk models that could inform policy and practise. The work will involve deterministic and stochastic models, Bayesian statistics, data analysis and presentation.

Applicants must have, or be very close to completing, a PhD in mathematical, computer or statistical models applied to a relevant area in the biological or environmental sciences. Research experience in applying such models in antimicrobial resistance, metagenomics, analytical chemistry and/or water quality would be desirable. Applicants must be able to demonstrate skills in Bayesian approaches, including relevant computational techniques such as MCMC, development and analysis of deterministic and stochastic models, programming in a relevant language (e.g. R, Python or Matlab) and a broader appreciation of science. Applicants must also be able to demonstrate research ambition through timely publication of research, coupled with commitment to the research project as part of their on-going career development. Excellent oral and written English language skills are essential.

The post is a joint appointment between the Schools of Biosciences and Mathematical Sciences. The post holder will normally work on the Sutton Bonington Campus, and will also have meetings on the University Park Campus with staff in the School of Mathematics and other collaborating schools.

Fixed term for 2 years from 1st September 2017

Applications can be made through the University of Nottingham web site. I am happy to receive informal enquiries.

New publication: The dynamic balance of import and export of zinc in Escherichia coli suggests a heterogeneous population response to stress

I am absolutely delighted to see the (online) publication today of our paper:

Takahashi H, Oshima T, Hobman JL, Doherty N, Clayton SR, Iqbal M, Hill PJ, Tobe T, Ogasawara N, Kanaya S and Stekel DJ 2015. The dynamic balance of import and export of zinc in Escherichia coli suggests a heterogeneous population response to stress. Journal of the Royal Society Interface DOI: .

The abstract is at the bottom of the post. First I want to say why I am so happy about this particular paper.

1. This is the first piece of work I have published in which I have made a successful funding application (I say “I” loosely, as Taku Oshima wrote the Japanese part of the bid along with Naotake Ogasawara, Shigehiko Kanaya and Toru Tobe, and Jon Hobman wrote much of the UK part of the bid; however, I was PI as this was a Systems Biology call); led the research (most of the hard work was done by Hiroki Takahashi and Taku Oshima); wrote the paper (different parts were written by different people – almost all authors made an important contribution); and have seen the paper published. A complete cycle of more than 5 years from grant application to publication.

2. This is the first paper on which I am corresponding author that contains new experimental results. More than that, I played an important role in devising many of the experiments (time courses and viable cell count assays) – not in terms of technical details (in which I have little expertise) but in terms of what experiments we need and why we need to do them.

3. This is the first time I have come a complete “Systems Biology” cycle: from experiments, to models, to predictions, to experimental confirmation, to a new model and then new predictions.

4. Some of the most important ideas in this paper came as a result of one of the most enjoyable weeks in my scientific career. Hiroki, Jon, Selina and I were all attending the Biometals Conference in Brussels in July 2012. While Hiroki and I attended a few sessions of the conference, most of the time we spent in our hotel lobby trying to get the model to fit the data. The first data we had were the LB data, which the model could fit without too much trouble. When Taku asked me what other data we needed, I said: “time series, with different concentrations of zinc”, and by the conference we had those data too. Only one problem: the model no longer fitted the data.

Hiroki and I spent that week trying to work out how to get the model to work. Each morning, we sat in the hotel lobby, and over endless cups of tea, we devised new versions of the model; each afternoon Hiroki would code them up, and then run them overnight on the supercomputer in Japan. And the next morning, the model would still not fit the data. By the last day we were tearing our hair out: nothing we could think of would work. We had one last (desperate) idea: ditch the 100uM zinc data. Boom! The model fitted the 12.5uM zinc data just fine! And this led to the heterogeneity hypothesis, the viable cell count assay, the stochastic model, and all the results that make this paper exciting. It is that kind of week that we go into careers in science for: the frustration and delight of grappling with and overcoming a difficult problem.

5. As alluded to in the previous points, it has been an absolute delight working with my coauthors on this paper, and I have many happy memories in the UK, Japan and Brussels.

6. Finally, on a more personal note: we received this funding on 17th March 2010. In between receiving the funding and having the paper published (5 years later) I have got married (July 2010), had a baby (July 2011), had another baby (November 2013) and am now more tired yet more happy than at any other point in my life 🙂

Now for the abstract!


Zinc is essential for life, but toxic in excess. Thus all cells must control their internal zinc concentration. We used a systems approach, alternating rounds of experiments and models, to further elucidate the zinc control systems in Escherichia coli. We measured the response to zinc of the main specific zinc import and export systems in the wild-type, and a series of deletion mutant strains. We interpreted these data with a detailed mathematical model and Bayesian model fitting routines. There are three key findings: first, that alternate, non-inducible importers and exporters are important. Second, that an internal zinc reservoir is essential for maintaining the internal zinc concentration. Third, our data fitting led us to propose that the cells mount a heterogeneous response to zinc: some respond effectively, while others die or stop growing. In a further round of experiments, we demonstrated lower viable cell counts in the mutant strain tested exposed to excess zinc, consistent with this hypothesis. A stochastic model simulation demonstrated considerable fluctuations in the cellular levels of the ZntA exporter protein, reinforcing this proposal. We hypothesize that maintaining population heterogeneity could be a bet-hedging response allowing a population of cells to survive in varied and fluctuating environments.

New Publication: Analysis of Occludin Trafficking, Demonstrating Continuous Endocytosis, Degradation, Recycling and Biosynthetic Secretory Trafficking

We are delighted that our work with Josh Rappoport‘s laboratory, supported by the Birmingham-Nottingham Strategic Collaboration Fund, has led to successful publication. Well done to all, especially Sarah Fletcher who carried out all the experimental work, Mudassar Iqbal who did the model data fitting, and Sara Jabbari who has helped out both Mudassar with the modelling and Sarah with sorting out journal requirements.

Fletcher, S.J., Iqbal, M., Jabbari, S., Stekel, D.J. and Rappoport, J.Z. 2014. Analysis of Occludin Trafficking, Demonstrating Continuous Endocytosis, Degradation, Recycling and Biosynthetic Secretory Trafficking. PLoS ONE DOI: 10.1371/journal.pone.0111176.


Tight junctions (TJs) link adjacent cells and are critical for maintenance of apical-basolateral polarity in epithelial monolayers. The TJ protein occludin functions in disparate processes, including wound healing and Hepatitis C Virus infection. Little is known about steady-state occludin trafficking into and out of the plasma membrane. Therefore, we determined the mechanisms responsible for occludin turnover in confluent Madin-Darby canine kidney (MDCK) epithelial monolayers. Using various biotin-based trafficking assays we observed continuous and rapid endocytosis of plasma membrane localised occludin (the majority internalised within 30 minutes). By 120 minutes a significant reduction in internalised occludin was observed. Inhibition of lysosomal function attenuated the reduction in occludin signal post-endocytosis and promoted co-localisation with the late endocytic system. Using a similar method we demonstrated that ~20% of internalised occludin was transported back to the cell surface. Consistent with these findings, significant co-localisation between internalised occludin and recycling endosomal compartments was observed. We then quantified the extent to which occludin synthesis and transport to the plasma membrane contributes to plasma membrane occludin homeostasis, identifying inhibition of protein synthesis led to decreased plasma membrane localised occludin. Significant co-localisation between occludin and the biosynthetic secretory pathway was demonstrated. Thus, under steady-state conditions occludin undergoes turnover via a continuous cycle of endocytosis, recycling and degradation, with degradation compensated for by biosynthetic exocytic trafficking. We developed a mathematical model to describe the endocytosis, recycling and degradation of occludin, utilising experimental data to provide quantitative estimates for the rates of these processes.

Modelling Biological Evolution 2013: Conference Highlights

Over the last couple of days I have been attending the Modelling Biological Evolution conference at the University of Leicester organized by Andrew Morozov.

For me, the most interesting theme to have emerged is work on evolutionary branching: conditions under which polymorphisms (or even speciation) might arise. These were all talked about in the context of mathematical models (ODE-type formulations based on generalized Lotka-Volterra systems). The best talk I attended was by Andrew White (Heriot Watt University). He described various system of parasite-host co-evolution, the most interesting of which demonstrated increases in diversity: a new host could emerge that was resistant to current parasites, following which a new parasite could emerge that would infect that host. He rather nicely linked that work to experimental work from Mike Brockhurst (University of York) on phage infections of bacteria showing similar patterns. The results could of course be interpreted at a speciation level, or, probably more fairly, at the level of molecular diversification (e.g. of MHC types in an immune system). What I really appreciated about this resut is that it spoke to the idea that increased diversity can result through a positive feedback mechanism: diversification leads to new niches and thus the potential for further diversification. I have thought for some time that this is the most important mechanism that drives diversification / speciation in natural systems and it was nice to see an example of the mechanism in action.

The other talk I particularly appreciated on the subject was by Claus Rueffler (University of Vienna). He spoke about a result on complexity and diversity in Doebeli and Ispolatov 2010 that also contains this feedback idea. This paper relies on a specific model to obtain its result on conditions for evolutionary branching. Rueffler demonstrated general conditions under which branching might take place that depend only upon the properties of the Hessian matrix associated with key parameters in model space. The important point is that the analysis is model-independent: it only considers the properties of the model forms needed to obtain the result.

Similar ideas were presented by Eva Kisdi (University of Helsinki). She focussed on models that include evolutionary trade-offs (e.g. between virulence and transmissibility): her point was that instead of choosing a function and analyzing its consequences, one could consider desired properties of a model (e.g. branching or limit cycles) and then use “critical function analysis” to derive conditions for possible trade-off functions that would admit the desired behaviour. Eva made the important point that many models make ad hoc choices of functions and thus lead to ad hoc results of little predictive value.

I think Eva’s point really touched on some of the weaknesses that emerged in many of the talks that I attended: there was a great deal of theory (some of which was very good), but very little interface with real biological data. I find this somewhat surprising: modelling in ecology and evolution has been around for very much longer that modelling in say molecular biology (where I currently work), and yet seems to be less mature. I think that the field would really benefit from far greater interaction between theoretical and experimental researchers. Ideally, models should be looking to generate empirically falsifiable hypotheses.

Perhaps the most entertaining talks were given by Nadav Shnerb and David Kessler (both Bar Ilan University). Nadav’s first talk was about power-law-like distributions observed in genus/species distributions. Core to his work is Stephen Hubbell’s neutral theory of biodiversity.
Nadav showed that distributions of number of species within genera could be explained by a neutral model for radiation and the genus and species level coupled with extinction. Nadav’s most important point was that if you wish to make an argument that a certain observed trait is adaptive, then you have to rule out the null hypothesis that it could arise neutrally through mutation/drift. I hope that is something we addressed with regards global regulators in gene regulatory networks in Jenkins and Stekel 2010. David spoke about biodiversity distributions also, showing that adaptive forces could explain biodiversity data (they are generally poor at this due to competitive exclusion that occurs in many models) if the fitness trait is allowed a continuous rather than discrete distribution.

Nadav’s second talk was about first names of babies. This was very interesting – especially as I have a young family (and a daughter with a very old-fashioned name). He looked at the error distribution (easily shown to be binomial-like noise proportional to square root of mean) that is superimposed on a deterministic increase and decrease in popularity of a name over a 60 year period. His thesis was that the error distribution due to external events would be proportional to mean (not root mean), and, as only 5 names in his data set (Norwegian names in ~ 20th Century) did not fit binomial noise, he ruled out external events (e.g. celebrity) as being a major driver. The problem I have with this is that he didn’t rule out external events in the deterministic part of the data (e.g. initiating a rise in popularity of a name that then follows the deterministic feedback law he proposed).

PhD opportunities at the University of Nottingham

The University of Nottingham and the Rothamsted Research Institute are now advertising for 42 fully funded four-year PhD places in their Doctoral Training Partnership. For applicants with a maths, physics or computing background interested in mathematical / computational biology, there are opportunities in all three themes to become involved in world-leading bioscience research. There are three projects on which I would be a second / third supervisor.

  1. Bayesian Inference for Dynamical Systems: From Parameter Estimation to Experimental Design with Theodore Kypraios (maths) as main supervisor. This project will be entirely mathematical / computational.
  2. The role of a novel zinc uptake system (C1265-7) in uropathogenic E. coli, with Jon Hobman as main supervisor. This project will be mostly experimental, but could involve a mathematical modelling component should the student be interested.
  3. Tunable zinc responsive bacterial promoters for controlled gene expression in E. coli, with Phil Hill as main supervisor. This project will be mostly experimental, but could involve a mathematical modelling component should the student be interested.

For more information, please visit the advert site on

Recent Advances in Statistical Inference for Mathematical Biology – report on MBI workshop

Today saw the end of the workshop at MBI on Recent Advances in Statistical Inference for Mathematical Biology. It has been a very enjoyable and thought-provoking workshop – definitely well worth the visit. My own talk received a good number of questions and plenty of interesting discussion. It was definitely at the more ‘applied’ end of the talks given; many of the talks described new methodologies and it is these that were particularly useful.

Perhaps the most interesting feature to emerge from this workshop is the work on identifiability or estimability of the parameters: it is the four talks most focussed on this topic that I will review very briefly below. The difference between these two terms is non-identifiability of parameters is a structural issue: no amount of additional data could help; non-estimability is a feature of the model and the data: the parameters cannot be estimated from the data at hand, but perhaps with different data they could be. This issue has certainly become an important concern in our own work: situations in which the Markov chain is unable to provide meaningful estimates for one or more parameters. On one level, this is useful, indeed it is one of the reasons why we are using these approaches: if we cannot estimate two parameters but could estimate (say) the ratio of two parameters then we want to know that, and the joint posterior distributions give that information. But in other cases it is holding us back: we have inference schemes that do not converge for one or more parameters, limiting our capacity to make scientific inductions, and we need good methods both to diagnoze a problem and to suggest sensible resolutions.

Two talks discussed approaches to simulations based on the geometric structure of the likelihood space. Mark Transtrum’s talk considered Riemannian geometric approaches to search optimization.  The solution space often describes a manifold in data coordinates that can have a small number of ‘long’ dimensions and many ‘narrow’ dimensions. The issue he was addressing a long canyons of ‘good’ solutions that are difficult for a classical MCMC or optimization scheme to follow. Interestingly, this leads to the classical Levenberg-Marquardt algorithm that allows optimal and rapid searching along the long dimensions – and Mark described an improvement to the algorithm. However, in discussions afterwards, he mentioned that following geodesics along the narrow dimensions to the manifold boundary can help identify combinations of parameters that cannot be estimated well from the data. Mark’s paper is Transtrum, M.K. et al. 2011. Phys. Rev. E. 83, 036701.

Similar work was described by Ben Calderhead. He described work trying to do inference on models with oscillatory dynamics, leading to difficult multi-model likelihood functions. The approach was also to use a Riemannian-manifold MCMC combined with running a chain with parallel temperatures that give different levels of weight of the (difficult) likelihood relative to the (smooth) prior. The aim again is to follow difficult ridges in the solution space, while also being able to escape and explore other regions. Ben’s methodological paper is Girolami, M. and Calderhead, B. 2011. J. Roy. Stat. Soc. 73: 123-214.

A very different approach was described by Subhash Lele. Here, the issue is diagnosing estimability and convergence of a chain using a simple observation: if you imagine ‘cloning’ the data, i.e. repeating the inference using two or more copies (N say) of your original data, then the more copies of the data you use, the more the process will converge to the maximum likelihood estimate. Fewer copies will weight the prior more. This means that if all is working well: (i) as N increases, the variance of the posterior should decrease; (ii) if you start with different priors, then as N increases, the posteriors should become more similar. If these do not happen, then you have a problem. The really nice thing about this approach is that it is very easy to explain and implement: methods based on Riemannian geometry are not for the faint-hearted and can only really be used by people with a strong mathematical background; data cloning methods are more accesible! Subhash’s papers on data cloning can be downloaded from his web site.

Finally, another approach to identifiability was described by Clemens Kreutz. He described ways of producing confidence intervals for parameters that involved following individual parameters and then re-optimizing for the other parameters. Although more computationally intensive, this looks useful for producing more reliable estimates both of parameter and model fit variability. Clemens’s work is available at

There were many more applied talks too, that I very much enjoyed, to a range of interesting applications and data. Barbel Finkenstadt gave a talk that included, in part, work carried out by Dafyd Jenkins, and I was filled with an up-welling of pride to see him doing so well! I also particularly appreciated Richard Boys’s honest attempt to build an inference scheme with a messy model and messy data and obtaining mixed results.

All-in-all, an enjoyable and interesting week, well worth the trip, and I look forward to following up on some interesting new methodologies.