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: 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).

Job opportunity: two-month postdoctoral position in mathematical modelling / inference

Research Associate/ Fellow

Closing Date
Friday, 8th February 2013
Job Type
Research & Teaching
School of Biosciences – Division of Agricultural & Environmental Science, Multidisciplinary Centre for Integrative Biology
£24766 to £29541 per annum depending on skills and experience, minimum £27,854 per annum with relevant PhD.

This full-time post is available on a fixed term contract for a period of two months.

Applications are invited to join a highly motivated multi-disciplinary team of research scientists working the Universities of Nottingham and Birmingham. The successful candidate will join a jointly funded project to carry out modeling of occludin trafficking during epithelial polarization and wound healing. The post could be located either in the School of Biosciences at the University of Nottingham’s Sutton Bonington Campus, or at the School of Biosciences at the University of Birmingham.

The work will include (i) developing a mathematical models (using ODEs) to describe the turnover of occludin protein in the cell as well as the kinetic trafficking of occludin between cellular compartments; (ii) to estimate model parameter values from experimentally derived data using Monte Carlo Markov Chain approaches; and (iii) to iteratively improve the model, with cycles of model and data comparison, in order to provide greater certainty about the important mechanisms involved that can explain the experimental data. Other duties will include contributing to publication of this research in peer-reviewed journals, contributing to writing of research grant applications, and generally collaborating between disciplines and institutions.

The successful candidate must have a PhD or equivalent in mathematical modelling or statistics or a related area. Research experience within a mathematical biology or systems biology research area would be desirable but not essential. Candidates must to be able to demonstrate excellent mathematical ability, especially in the areas of ordinary differential equations and statistical analysis of data; experience of application of these skills to biological research would be desirable. Candidates must also be able to evidence excellent computing skills in a suitable environment (e.g. R or Matlab). Excellent English language oral and written communication skills are also essential. This post will require the person appointed to be able to work independently and as part of a multi-disciplinary team, to be motivated, flexible and willing to learn.

Full details, including how to apply, can be found on the University of Nottingham’s vacancy system.

Informal enquiries may be addressed to Dr Dov Stekel, email: or Dr Josh Rappoport, email:

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.

Speaking at Workshop: Recent Advances in Statistical Inference for Mathematical Biology

Today I will be presenting at at the Mathematical Biosciences Institute at Ohio State University which this week is hosting the workshop Recent Advances in Statistical Inference for Mathematical Biology. I will be giving a talk about Hiroki’s work (abstract here and below), while Dorota will be presenting a poster about her work.

I am very excited about this workshop as it is the first to my knowledge to bring together mathematical modelling with statistical inference. In my view, this marriage is crucial to the future development of mathematical biology as a field.


Inferring the gap between mechanism and phenotype in dynamical models of gene regulation


Dynamical (differential equation) models in molecular biology are often cast in terms of biological mechanisms such as transcription, translation and protein-protein and protein-DNA interactions. However, most molecular biological measurements are at the phenotypic level, such as levels of gene or protein expression in wild type and chemically or genetically perturbed systems. Mechanistic parameters are often difficult or impossible to measure. We have been combining dynamical models with statistical inference as a means to integrate phenotypic data with mechanistic hypotheses. In doing so we are able to identify key parameters that determine system behaviour, and parameters with insufficient evidence to estimate, and thus make informed predictions for further experimental work. We are also able to use inferred parameters to build stochastic and multi-scale models to investigate behaviour at single-cell level. We apply these ideas to two systems in microbiology: global gene regulation in the antibiotic-resistance bearing RK2 plasmids, and zinc uptake and efflux regulation in Escherichia coli.