Over the years, we have worked on many different systems, including signal transduction (two-component signalling, MAPK, GPCRs), metabolic control, and molecular stochasticity. We always try to keep the mathematical models we develop as realistic as possible. In recent years, the projects have become more experimental. In fact, many of the researchers active in the group at the moment are spending most of their time in the lab. Still, we have strong experimental collaborations.

Our approach always involves mathematical modelling. Models are used to guide experimental design and obtain mechanistic understanding. The types models we make depend on the research question. We have experience with deterministic as well as stochastic models and genome-scale stoichiometric models.

Here follows an overview of the current projects and how we are integrating mathematical models and experiments:

**Biochemical and physical constraints on metabolic performance, regulation and evolution.**

The reactions in metabolic networks are catalysed by enzymes. Enzyme synthesis requires energy and resources (e.g. carbon, nitrogen, sulphate, …). Since nutrients are continuously being converted by metabolism, nutrients are never in excess. Thus, there exists always some pressure to synthesise enzymes that are required under the current condition and at the appropriate levels. What rules do cells follow in setting the protein levels? Can cells solve this problem in an optimal manner by using gene and signalling networks? These questions we address using theory and experiment. In the experiments, we compare alternative network designs and use titratable metabolic gene-expression systems to elucidate the costs and benefits of metabolic enzymes. Collaborators on these topics are: Douwe Molenaar and Bas Teusink; and the following PhD students: Meike Wortel, Evert Bosdries, Niclas Nordholt, and Iraes Rabbers.**Transcription stochasticity in yeast and mammalian cells.**The synthesis and degradation events of a specific molecule are never active in precise synchrony; thus, fluctuations in concentrations are inevitable and concentrations can only be in steady state when averaged over time. The size of these fluctuations are related to network structure and reaction kinetics. Fluctuations can scramble information processing by cells or help cells to successfully adapt to unpredictable changes in their environment. We have developed the software package StochPy to simulate stochastic systems. In addition, we have developed theory to understand propagation of “molecular noise” through networks and the origins of stochasticity in transcription regulation. Currently, we are using single-molecule RNA FISH to measure noise in living cells. From a theoretical point of view we aim to understand how the coupling of gene regulation, cell growth and fitness are affected by molecular stochasticity. Collaborators on these topics are: Pernette Verschure and Bas Teusink; and the following PhD students: Lisette Annink, Mannus Kempe, Anne Schwabe, and Timo Maarleveld.

**Optimal performance of metabolic networks.**Generally, we do not have good hypotheses about the objective of control circuitry in cells. Largely because this is very hard to figure out in the lab. For some systems – often small systems, the dynamic behaviour of the network suggests the objective, i.e. for chemotaxis the objective is to respond to a concentration change by cell swimming on short time scale then “forget” this response on a slower time scale and return to the basic sensing state to update the concentration measurement (“perfect adaptation”). For metabolism, and specifically for metabolic subsystems, it is often not known what the objective is. In such circumstances, optimisation can suggest interesting hypotheses that can be exactly phrased in terms of theory, worked out with models, and eventually tested in the lab. From this perspective we develop theory (optimisation of yields, maximisation growth rate at minimal nutrient concentrations, and specific flux values) and exploit experimental systems to test these hypotheses, i.e. chemostats, batch fermentors, and yield competition assays. In one project, we also ask the question to what extent stress responses of bacteria are actually optimal. Collaborators on these topics are: Douwe Molenaar, Bob Planque, Joost Hulshof and Bas Teusink; and the following PhD students: Meike Wortel, Evert Bosdriesz, Niclas Nordholt, and Iraes Rabbers.

**Signal integration by regulatory proteins and small signalling networks.**A basic characteristic of cells is that they respond to a great variety of extracellular signals. One of the question is how cells integrate signals, at the level of single regulatory proteins (e.g. G-protein coupled receptors or nuclear receptors) and at the level of networks. Currently, we focus on dimeric regulatory proteins that can bind several small molecules that engage in allosteric interactions on the protein. These binding events induce changes in protein conformation. Several of these conformations are selective for alternative downstream signalling events. We address these questions using mathematical models and in experiment using FRET constructs of G-proteins. Collaborators on these topics are: Joachim Goedhart, Dorus Gadella, Martine Smit, and Enikö Kallay; and the following PhD students: Susanne Roth, Domenico Bellomo (postdoc), Kobus van Unen, and many master students who visited us in 2013: Katy Wei (Delft), Jacomien Feilzer (VU), and Maarten Slagter (VU).

**Genome-scale models**Genome sequencing of organisms allows for the inference of their metabolic network topology and the stoichiometry of all metabolic reactions. This information allows for the development of genome-scale stoichiometric models that can be studied using methods from linear algebra and linear programming. One of our interests is to understand the solution spaces of such systems and to translate their mathematical description into simple biological terms. Another interest is to develop computational techniques to study microbial communities. Collaborators on these topics are: Michael Ferris, Leen Stougie, Bob Planque, Brett Olivier and Bas Teusink; and the following PhD students: Timo Maarleveld, Ruchir Kandelwal, Mark Hanemaaijer, and Meike Wortel.

**Biotechnological applications of our theories.**High biotechnological productivity has two requirements: high biomass (many cells) and high production rates per unit biomass. And eventually, a high yield of product from the supplied growth nutrients. Understanding how cells can be “fooled” in displaying this behaviour poses a fundamental problem, as cells usually do not achieve this by themselves and many of their control circuitry actively withstand any genetic changes made in that direction. This is exemplified for instance by the stringent response of bacteria. As a consequence, practical yields are often much lower than theoretically maximal yields, and attaining high production fluxes is quite a challenge. The theories we develop regarding yield and flux maximisations offer new ways to think about these “old” problems. In addition, we study how the control systems that regulate microbial growth rate function and can be “hijacked” in favour of biotechnological product formation. Collaborators on these topics are: Douwe Molenaar, Michael Ferris and Bas Teusink; and the following PhD students: Timo Maarleveld, Evert Bosdriesz, and Meike Wortel.