We wrote a paper for a special issue celebrating the 50th anniversary of Metabolic Control Analysis

Which metabolic enzymes should a cell change in concentration to give rise to a large change in steady-state metabolic flux? Which enzymes should an experimentalist inhibit to reduce the flux the most?
Why are some kinase-phosphatase couples in cellular signal transduction ultra-sensitive to changes in signals, while others are not? What is the function of negative feedback in metabolic pathways? How can you design metabolic pathways that are insensitive to particular environmental changes and highly sensitive to others?

Answering such questions requires consideration of enzymes active in networks, as their activity and network influence depend on their reactant concentrations, which are co-determined by all enzymes in the network. Answering such questions therefore needs a systems perspective. One that is quantitative also; as all enzymes influence the network’s functions but to different degrees. The concept of a single rate-limiting step is therefore generally overly simplistic.

Now about 50 years ago, two papers were published, one by Burns & Kacser and another by Heinrich & Rapoport, which dealt with a sensitivity analysis of metabolic pathways to change in enzyme activities and concentrations. They also managed to derive theorems relating sensitivity coefficients. Those coefficients come in two forms: elasticity coefficients and control coefficients, and their products are called response coefficients. We invite you to check out those papers, they have not aged. The entire framework is called Metabolic Control Analysis (MCA).

Bas (Teusink) and myself grew up as young scientists in the scientific community of MCA due to our PhD supervisor, Prof Dr Hans Westerhoff, who was one of the pioneers and advocates of MCA. MCA was therefore part of our training and thinking, and we have published papers about this theory.

What always attracted me (Frank) as how Christine Reder‘s formulation of MCA makes the relation between reaction stoichiometry and enzyme kinetics so clear, and in completely general terms. By using concepts from linear algebra and enzyme kinetics, the control of enzymes on steady-state properties of enzyme networks could be written down in completely general terms. This gave me confidence that a general theory about cellular metabolism and growth can be derived, applicable across all domains of life. Aiming for this has been a research theme throughout my career.

One aspect of Reder’s theory is that the null space of the stoichiometric matrix is used to derive the summation theorems of MCA. But the null space is not unique, which always bothered me when I was a PhD student. This was changed when David Fell, Stefan Schuster and Thomas Dandekar generalised the definition of metabolic pathways in a unique manner, using a concept that is related to the null space of the stoichiometric matrix. They showed that any steady-state flux solution of a stoichiometric matrix is convex combination of a set of unique flux vectors, called elementary flux modes (EFMs). This solved the problem of the entire set of summation theorems (although I do not know whether any one ever published this). EFMs are (beautiful) mathematical objects with extremely appealing mathematical properties for biotechnology and evolutionary biology.

We worked for quite some time on EFMs in the context of the optimisation of stoichiometric models and of dynamic models (containing stoichiometry and enzyme kinetics). It turns that EFMs are the solution of optimisations of enzyme networks, given enzyme kinetics, where one aims to maximise a steady-state flux by optimising enzyme concentrations that sum to a fixed total. They are also the elementary solutions of flux balance analysis computations, considering only reaction stoichiometry and not enzyme kinetics.

If evolution maximises the growth rate of cells then what would be the flux control coefficients of all the optimally expressed enzymes? MCA suggests that you cannot answer this question, because you do not know the enzyme kinetics, and therefore you do not know the elasticity coefficients. But it turns out that you can! This was realised by Klipp & Heinrich, and even earlier by Burn & Kacser in a more simplified setting (in Burn’s thesis). The context of Klipp & Heinrich is regrettably also too simplified to consider the entire metabolic network of a cell that is growing at its maximal rate by having expressed all its enzymes optimally.

The solution to this problem we offer in our paper to the special issue of Biosystems celebrating the 50th anniversary of MCA. You can find the paper here. It is quite a read, we know, but it contains all the main ideas from start to end. We hope that it inspires you to become familiar with MCA, enzyme kinetics, and stoichiometric modelling concepts.

State of the union of the lab at the Hortus Botanicus

A custom of our lab is to start the academic year with a state-of-the-union day at the Hortus Botanicus of Amsterdam.

During this day, the PIs give an research overview of the last year, an outlook on the coming year, current duties, and their long-term research vision in the presence of the research (support) staff and all the researchers working on funded projects (PhDs and postdocs).

Bas gave an overview of the Holomicrobiome “groeifonds” project proposal that he is involved in, as an organising member. This is a 240 million euro project that aims to link Dutch microbiome research and company demands: to together drive innovations that will improve the quality of our soils, water, crops and human health by improved methods and technologies. The outlook is that this should give an input to the Dutch economy in an environmentally friendly and sustainable manner. The proposal needs to be reshaped in the coming months, resubmitted, and reevaluated by an independent committee on behalf of the Dutch government for approval (or rejection). Exciting times!

Matti chaired a session on the reconsideration of the logo of our lab, which now has effectively turned this into competition between groups of colleagues. Let’s see what they come up with!

A perspective on physiological trade offs and finite resources for protein-expression

Together with Ralf Steuer (Humboldt-University of Berlin, Germany) we recently wrote a review for Bioessays, see https://doi.org/10.1002/bies.202300015. It addresses how we currently view the consequences of finite biosynthetic resources (for protein expression) for cellular tasks such as stress tolerance, growth and adaptation to new conditions.

We focus on Escherichia coli and Saccharomyces cerevisiae. We acknowledge that the advanced understanding we have of their physiology may not be extrapolatable to microorganisms with a qualitatively different evolutionary history. We argue that these two microorganisms optimise the expression levels of needed metabolic enzymes, given that some fraction of biosynthetic resources is allocated to proteins needed to adapt to new conditions. That latter fraction of non-growth associated protein decreases with cellular growth rate (nutrient quality) and therefore makes fast growing E. coli and S. cerevisiae cells less stress tolerant and adaptive to new nutrients. This is an example of a trade off between growth and adaptation due to finite biosynthetic resources.

If you are interested in such ideas, how they emerge from computational models, and what their precise experimental evidence is then the review we wrote might be of interest to you.

A new paper published on optimal H ATP synthase expression in E coli

We recently published a new paper, https://febs.onlinelibrary.wiley.com/doi/10.1111/febs.16401. Below you find a short reflection on this paper.

Microbial behaviour has been shaped by evolution. Our understanding is that the best adapted genetic variants are outcompeting the others — which explains their frequency increase and their selection. These fit variants generate novel genetic variants, which perform even better, equally good or worse. So perhaps we can rationalise the behaviour of microbes from the viewpoint of fitness maximisation by natural selection? More specifically, maybe we can understand phenotypic adaptations, e.g. protein expression, of particular microorganisms as fitness-maximising adaptations? 

At least two problems are associated with this view. The first problem is that fitness of a genotype is related to the performance over a long period. Fitness may therefore not be measurable at one particular moment in time. Instead, we should take the evolutionary history into account — recreate it somehow in the lab—, but these conditions we do not know. So assessing the fitness of a microbe is perhaps not so straightforward and fundamentally impossible? A second problem is that the winning genotype may not be close to an optimal fitness, it was after all merely better than its competitors and not necessarily optimal. How then can we make sense of microbes in the light of fitness?

In a recent paper, we took a very simple, perhaps-ignorant approach. At the outset we realised that: i. long-term fitness over a particular period equals the time-averaged growth rate over that period and ii. growth rate depends on metabolic protein concentrations that are limited by biosynthetic constraints. One corollary of this is that expression of unneeded proteins should reduce the immediate growth rate and another is that an optimal, immediate-growth-rate maximising protein expression level exists for needed proteins. Both have been experimentally verified. 

However, this optimal expression level maximises the immediate growth rate, which is not necessarily a strategy for long-term fitness (average growth rate) maximisation — which is what truly matters in evolution. 

This was our simple idea: We assumed that Escherichia coli does not have a recollection of its precise environmental history and generally lives in unpredictable environments. Given this, it made sense to us that E. coli may strive for long-term fitness maximisation (average growth rate maximisation) by maximising its immediate growth rate by optimal expression of metabolic proteins. An implicit hypothesis was that biochemical regulation can optimise metabolic systems, for which we had obtained theoretical evidence already. Finally, we were aware of literature showing immediate-growth-rate-maximising expression of particular other proteins. What was not known is whether cells can do this robustly, so across a great many conditions — representing an unpredictable environment. 

To test this, we took a protein that is ubiquitously expressed and expensive for the cell to make: its membrane embedded FoF1 ATP-synthase, which makes ATP at the expense of the proton motive force, which is maintained by oxidative phosphorylation. This process is the only ATP synthesising step when ATP is not made via substrate-level phosphorylation in glycolysis. So during growth on gluconeogenic carbon sources. Since the growth rate on those carbon sources greatly varies, the ATP demand per unit time will too, and therefore the needed level of ATP-synthase may vary accordingly. We tested 28 different conditions and we found that in all cases the expression level of this vital protein lies within a few percent of the optimal level that maximises the immediate growth rate. So, an E. coli cell has a growth-rate-maximising expression level of its ATP synthase.

This work is intriguing and puzzling at the same time. In biology, we rarely know the objective of molecular control systems. That objective may be ultimately related to the performance of the organism, but how it relates to that is often not understood. Here we found such an objective: expression regulation of ATP-synthase has growth-rate maximisation as its objective. How it achieves this is not understood, but the regulation of other systems points to possible mechanisms. What’s puzzling is how our results can be reconciled with seemingly conflicting data indicating that other metabolic proteins may be over-expressed, such as enzymes in lower glycolysis and the overcapacity of the ribosome? Is this occurring because cells can then faster transit to new conditions? Why is this not the case for ATP-synthase, which is likely also needed during transitions? Or are those cases not really cases of overexpression, but is having a low v/Vmax ratio actually the optimal behaviour required for immediate growth rate maximisation? On all of these questions, the field does not yet have satisfactory answers. 

Before this study, one could have argue that the fitness-maximisation question cannot really by answered because we do not know the evolutionary history, but this study (and others) suggests that perhaps many regulatory aspects of bacteria boil down to immediate fitness maximisation, because they live in such unpredictable environments. Perhaps their best bet on a high long-term fitness is to bet on immediate fast growth.

We reviewed more than a decade of research on the search for principles of microbial physiology

When Bas Teusink and Douwe Molenaar came to the VU University, about a decade ago, they had just published a thought-provoking paper on how microbial physiology can result from optimal allocation of biosynthetic resources, such as ribosomes, RNA polymerases, amino acids, energy, etc., in order to maximise growth rate (https://doi.org/10.1038/msb.2009.82). Roughly at the same time, a paper from Terry Hwa’s lab was published providing experimental evidence for the potential of thinking in terms of allocation of limited biosynthetic resources — regardless of any optimality assumption (https://science.sciencemag.org/content/330/6007/1099). Some of those ideas can be traced back to the ideas of Kjeldgaard, Schaechter and Maaløe several decades ago (e.g. O. Maaløe, An analysis of bacterial growth, Developmental Biology Supplement, 3, 33-58, 1969). Many of developments of the last decade have now been reviewed by us in FEMS Microbiology Reviews (https://doi.org/10.1093/femsre/fuaa034).

What has become clear in the last decade is that the assumption of maximal (per capita of specific) growth rate is a very powerful one to understand the behaviour of (model) microorganisms, such as Escherichia coli and Saccharomyces cerevisiae. Why they express certain metabolic pathways, to which degree they tune expression of proteins, what the fitness effects are of unneeded protein expression, and what limits growth can all be predicted in the current theoretical framework, which matches experimental data remarkably well.

This review also indicates the great potential of theory in microbiology and the likely universality of the underlying causes of many metabolic behaviours.

We hope that you enjoy reading the review, we certainly had a lot of fun writing it, and performing some of the research mentioned in it.

What makes steady-state population growth possible? – a new paper by us in Current Biology

Growing cells in constant conditions at a fixed exponential growth rate in a shake flask — balanced growth — is arguably the most basic experiment in microbiology. We are so used to it that we sometimes forget to realise that this is not at all so obvious.

Not only the average growth rate remains fixed, but also the average cell size at birth and division. Either this emerges for free, and no active homeostatic mechanisms are required, or balanced growth requires evolved regulatory mechanisms. Analysis of experimental data, using a deceptively, simple theory, by Susan et al. [1], indicates that active homeostatic mechanisms are at work during steady-state growth and that without those balanced growth would be possible.

That cell-size homeostasis mechanisms exist and are required for balanced growth was already known — mostly from work by Suckjoon Jun’s lab. But what about growth-rate homeostasis? Do active mechanisms exist that maintain a constant average (and variance) of single-cell growth rate? Here we show that that is indeed the case for Bacillus subtilis.

We also found that its cell cycle is composed out of two phases. A first one, during which cells with variations in birth size correct size differences — they behave as “sizers” — and a second one during which cells behave as “timers” — they grow for a nearly fixed duration.

Our most surprising, and novel, finding was that cells experience a great disturbance of growth rate at division, with smaller cells outgrowing larger ones, while at division that growth rate variation has largely disappeared and growth rate became independent of cell size at birth.

So, also a growth-rate homeostasis mechanism is at work in Bacillus subtilis— like it is for cell size. How it works, we are currently figuring out.

You can find our paper here: https://www.cell.com/current-biology/fulltext/S0960-9822(20)30544-3.


  1. Susman, L., Kohram, M., Vashistha, H., Nechleba, J.T., Salman, H., andBrenner, N. (2018). Individuality and slow dynamics in bacterial growth ho-meostasis. Proc. Natl. Acad. Sci. USA 115, E5679–E5687.

Daan de Groot made it 5th at the 2018 EC Duathlon — Talking about resource allocation!

For those of you who do not know Daan. He is a PhD student in our lab, working on a mathematical theory about optimal metabolism for microbial growth-rate maximisation and its experimental testing. One of the principles underlying his theory is optimal allocation of limited resources for the synthesis of metabolic enzymes. What turns out is that Daan is also an expert in allocating his own limited resources.

Daan is a talented road cyclist. A decade ago he competed with riders who are currently riding the tours of Italy, France and Spain. (I regularly wish I had those skills, but let us not go there.) During multiple day cycling events, which can even last several weeks, it is all about staying fit and focussed, while your body is slowing draining resources, which you cannot readily supplement with food. We call this fatigue. Cyclists learn how to the optimise their balance of performance and fatigue, which is one closely associated with optimal resource allocation. Recently, Daan has added a new resource-allocation trick on his sleeve.

He started duathlon, a run then bike then run event. Duathlon is a growing sport in the Netherlands and highly popular in the USA. It is closely related to triathlon, an Olympic sport. During a run-bike-run it is all about allocation of energy resources. Daan found an optimal way of solving this problem during last weekend’s European Championship (EC), in Vejle (Denmark), by focussing on what he does best.

Daan cycles better than he runs. His strategy during the EC was to save resources during the first run, go as fast as possible on his bike, and then run until he can no longer stand. And what a wise choice this was! After the first run he was amongst the slowest, he was the fastest cyclist and was 5th when crossing the finish line. We congratulate Daan with this major achievement!

For more information about the Vejle EC Duathlon 2018 see this link.

Here you see Daan riding earlier this year when he won the Duathlon in Geluwe (Belgium).