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!

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.

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 findaphd.com

New Publication: Adaptation for Protein Synthesis Efficiency in a Naturally Occurring Self-Regulating Operon

Dorota’s second paper has just been published in PLoS ONE as:

Herman, D., Thomas, C.M. and Stekel, D.J. 2012. Adaptation for Protein Synthesis Efficiency in a Naturally Occurring Self-Regulating Operon. PLoS ONE 7(11): e49678.

We are particularly pleased with this work, and had some very nice comments from the reviewers. The quotes (from two different reviewers) here are reproduced with permission from PLoS ONE:

“the kinds of questions the authors address appear to be the most rewarding uses of computational/mathematical uses in biology”

“I found this paper important because it investigates a system with biological plausible parameters, thus, revealing whether the results of previous purely theoretical studies are biologically plausible.”

We are hoping for that sort of reception more generally in the community!

The abstract of the paper is:

The korAB operon in RK2 plasmids is a beautiful natural example of a negatively and cooperatively self-regulating operon. It has been particularly well characterized both experimentally and with mathematical models. We have carried out a detailed investigation of the role of the regulatory mechanism using a biologically grounded mechanistic multi-scale stochastic model that includes plasmid gene regulation and replication in the context of host growth and cell division. We use the model to compare four hypotheses for the action of the regulatory mechanism: increased robustness to extrinsic factors, decreased protein fluctuations, faster response-time of the operon and reduced host burden through improved efficiency of protein production. We find that the strongest impact of all elements of the regulatory architecture is on improving the efficiency of protein synthesis by reduction in the number of mRNA molecules needed to be produced, leading to a greater than ten-fold reduction in host energy required to express these plasmid proteins. A smaller but still significant role is seen for speeding response times, but this is not materially improved by the cooperativity. The self-regulating mechanisms have the least impact on protein fluctuations and robustness. While reduction of host burden is evident in a plasmid context, negative self-regulation is a widely seen motif for chromosomal genes. We propose that an important evolutionary driver for negatively self-regulated genes is to improve the efficiency of protein synthesis.

Research grant award from the BBSRC

On Friday we heard good news from the BBSRC that our research grant application for the analysis of Biolog data has been successful. This is a joint bid with Katherine Smart, Jon Hobman, Helen West and Theodore Kypraios. The relevant quote from the BBSRC is:

Dear Dr Stekel,

I am please to inform you that application BB/J01558X/1 – ‘High throughput analysis of cell growth data from phenotype arrays’ submitted to the BBSRC 2011 Responsive Mode Grant Round 3 (RM3) has been successful.  We are currently in the process of preparing the grants for announcement. 

There will be a postdoctoral position associated with this grant which will be advertised in due course according to usual University of Nottingham procedures.

Lay Summary for the Research Grant

Fifty people died as a result of the recent E. coli outbreak in Germany. Four thousand people were infected. With a growing global human population, how do we ensure that we all have access to safe food? Fossil fuels will run out, and the recent Fukushima disaster highlighted the risks of nuclear energy. How do we provide sustainable sources of fuel to meet our energy and transport needs in the context of a population that is not just growing, but also developing?

These are major challenges, and a key strategy for overcoming them is the study of microbes. In the case of E. coli the disease is caused by harmful bacteria, and we need to understand how harmful bacteria survive in farms, soil, food production, storage and preparation facilities, as well as in animal and human hosts. In the case of fuels, microbes provide an opportunity for a new generation of biofuels. Biofuels are carbon neutral technologies, but conventional biofuels need similar materials or land that could otherwise be used for food. We are now seeking to develop biofuels from plant matter that cannot be used for food and is currently wasted. To do this, we need to find new strains of yeast that can convert this plant matter into fuel.

In recent years, new technologies have been developed that enable us to read the full genome sequence of a microbe in just a day. This is indeed remarkable, but the genome sequence is a set of instructions in a language that we can only begin to understand. What really matters is how a microbe behaves in different environments: on what foods does it thrive, on what foods does it starve? What potential toxins can it survive and what toxins kill it? These questions are essential for understanding how we can combat harmful food-borne bacteria, or develop new bioenergy producing agents. And if we can link these answers to the genome sequence, we have a powerful way of decoding the language of the genes.

This proposal is focussed on a technology, called Biolog Phenotype Microarrays, that precisely measure how well microbes thrive in thousands of conditions, including different food sources and potential toxins. The arrays generate time courses that plot each condition at a regular point in time, with several hundred measurements of cell activity during the course of an experiment. Each time course encodes a wealth of information: how long does it take before the microbes start to become active? How quickly do they grow? Are they able to use more than one food source, and if so, is one better than the other? How much do they grow? Remarkably, there are no analysis methods available that allow users of Biolog arrays to obtain this information from the Biolog output: instead, users typically use a single datum, such as the end-point, or total growth, and discard most of the valuable information.

The aim of this proposal is to bridge this gap. To do so, we intend to build mathematical models that describe cell activity in Biolog arrays; these need to reflect the details of the technology, as well as the complexity of the conditions in which the cells are grown. We propose to develop automated ways of working out which model best fits any given set of data, and identify the key parameters describing microbial behaviour. Automation is essential, because a single experiment can generate 2000 microbial time courses. The methods have to be accessible to the wider scientific community, not just mathematicians, so we need to develop user-friendly interfaces to the methods we develop, and provide training for Biolog users in these methods.

Finally, in our established research programmes, we have generated vast quantities of Biolog data on survival of harmful E. coli strains, microbial soil contamination and the development of new yeast strains for producing biofuel from non-food plant material. We will directly address the food safety and bioenergy challenges by applying our methods to these data.

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.

Title:

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

Abstract:

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.

 

Poster at ICSB 2011

This week Dorota has been presenting a poster at the 12th International Conference on Systems Biology in Heidelberg/Mannheim.

Cooperative regulation speeds up initiation of plasmid RK2 conjugative transfer

Dorota Herman1, Christopher M Thomas2 and Dov J Stekel3

1Center for Systems Biology, School of Biosciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

2School of Biosciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

3Integrative Systems Biology, School of Biosciences, University of Nottingham, LE12 5RD, UK

 

Plasmid RK2 belongs to the group of broad host range plasmids and encodes for multi-antibiotic resistance. They can transfer themselves horizontally by conjugative transfer. A switch between expression of proteins involved either in replication or conjugation is regulated by two global regulators, KorA and KorB, which are encoded in the central control operon. This operon is autoregulated negatively and cooperatively by dimers of KorA and KorB. We seek to explore a hypothesis that could explain the evolution of cooperative autoregulation of the central control operon: a speed-up of conjugative transfer after plasmid transjection to a new host.

We have built a multi-scale model of the RK2 central control operon and its regulation of the switch between expression of proteins involved either in replication (TrfA) or conjugative transfer (Trb proteins). The model also includes plasmid replication, host cell growth and cell division. The comparison analyses were conducted between models with cooperative and non-cooperative KorA and KorB regulation of the central control operon and the switch. The analyses concerned the dynamics of protein expression of both the regulators and the conjugative transfer proteins after plasmid transjection to a new host.  For the regulatory proteins KorA and KorB, the cooperative model shows a slightly faster rise time than the model without cooperativity. However, considering the time of first expression of the conjugative transfer proteins, the cooperative model is considerably faster than the model without cooperative regulation.

In conclusion, the cooperative regulation between KorA and KorB on the central control operon could have evolved as a mechanism to speed up the preparation for conjugative plasmid transfer. We also show that a small speed-up of regulatory protein expression can result in a faster speed-up of the expression of the regulated proteins.