Mathematical modeling of the glucagon challenge test.

A model for the homeostasis of glucose through the regulating hormones glucagon and insulin is described. It contains a subsystem that models the internalization of the glucagon receptor. Internalization is a mechanism in cell signaling, through which G-protein coupled receptors are taken from the surface of the cell to the endosome. The model is used to interpret data from a glucagon challenge test in which subjects have been under treatment with a novel glucagon receptor anti-sense drug which is aimed at reducing the number of receptors in the liver. It is shown how the receptor internalization results in tolerance of the blood glucose concentration to glucagon-induced hyperglycemia. We quantify the reduction of the number of receptors using the model and the data before and after treatment.

Variational approach to coarse-graining of generalized gradient flows.

In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (a) a natural interaction between the duality structure and the coarse-graining, (b) application to systems with non-dissipative effects, and (c) application to coarse-graining of approximate solutions which solve the equation only to some error. As examples, we use this technique to solve three limit problems, the overdamped limit of the Vlasov-Fokker-Planck equation and the small-noise limit of randomly perturbed Hamiltonian systems with one and with many degrees of freedom.

A chaotic self-oscillating sunlight-driven polymer actuator.

Nature provides much inspiration for the design of materials capable of motion upon exposure to external stimuli, and many examples of such active systems have been created in the laboratory. However, to achieve continuous motion driven by an unchanging, constant stimulus has proven extremely challenging. Here we describe a liquid crystalline polymer film doped with a visible light responsive fluorinated azobenzene capable of continuous chaotic oscillatory motion when exposed to ambient sunlight in air. The presence of simultaneous illumination by blue and green light is necessary for the oscillating behaviour to occur, suggesting that the dynamics of continuous forward and backward switching are causing the observed effect. Our work constitutes an important step towards the realization of autonomous, persistently self-propelling machines and self-cleaning surfaces powered by sunlight.

Automated design of programmable enzyme-driven DNA circuits.

Molecular programming allows for the bottom-up engineering of biochemical reaction networks in a controlled in vitro setting. These engineered biochemical reaction networks yield important insight in the design principles of biological systems and can potentially enrich molecular diagnostic systems. The DNA polymerase-nickase-exonuclease (PEN) toolbox has recently been used to program oscillatory and bistable biochemical networks using a minimal number of components. Previous work has reported the automatic construction of in silico descriptions of biochemical networks derived from the PEN toolbox, paving the way for generating networks of arbitrary size and complexity in vitro. Here, we report an automated approach that further bridges the gap between an in silico description and in vitro realization. A biochemical network of arbitrary complexity can be globally screened for parameter values that display the desired function and combining this approach with robustness analysis further increases the chance of successful in vitro implementation. Moreover, we present an automated design procedure for generating optimal DNA sequences, exhibiting key characteristics deduced from the in silico analysis. Our in silico method has been tested on a previously reported network, the Oligator, and has also been applied to the design of a reaction network capable of displaying adaptation in one of its components. Finally, we experimentally characterize unproductive sequestration of the exonuclease to phosphorothioate protected ssDNA strands. The strong nonlinearities in the degradation of active components caused by this unintended cross-coupling are shown computationally to have a positive effect on adaptation quality.

Stripe patterns and a projection-valued formulation of the eikonal equation.

We describe recent work on striped patterns in a system of block copolymers. A by-product of the characterization of such patterns is a new formulation of the eikonal equation. In this formulation, the unknown is a field of projection matrices of the form P=e⊗e, where e is a unit vector field. We describe how this formulation is better adapted to the description of striped patterns than the classical eikonal equation, and illustrate this with examples.

Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law.

A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical metabolic control analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient, cannot be applied to spatially separated protein networks. The present paper unravels the principles that govern the control over the fluxes and intermediate concentrations in spatially heterogeneous reaction networks. Our main results are two types of control summation theorems. The first type is a non-trivial generalization of the classical theorems to systems with spatially and temporally varying concentrations. In this generalization, the process of diffusion, which enters as the result of spatial concentration gradients, plays a role similar to other processes such as chemical reactions and membrane transport. The second summation theorem is completely novel. It states that the control by the membrane transport, the diffusion control coefficient multiplied by two, and a newly introduced control coefficient associated with changes in the spatial size of a system (e.g., cell), all add up to one and zero for the control over flux and concentration. Using a simple example of a kinase/phosphatase system in a spherical cell, we speculate that unless active mechanisms of intracellular transport are involved, the threshold cell size is limited by the diffusion control, when it is beginning to exceed the spatial control coefficient significantly.

Why the phosphotransferase system of Escherichia coli escapes diffusion limitation.

We calculated the implications of diffusion for the phosphoenolpyruvate:glucose phosphotransferase system (glucose-PTS) of Escherichia coli in silicon cells of various magnitudes. For a cell of bacterial size, diffusion limitation of glucose influx was negligible. Nevertheless, a significant concentration gradient for one of the enzyme species, nonphosphorylated IIA(Glc), was found. This should have consequences because the phosphorylation state of IIA(Glc) is an important intracellular signal. For mammalian cell sizes we found significant diffusion limitation, as well as strong concentration gradients in many PTS components, and strong effects on glucose and energy signaling. We calculated that the PTS may sense both extracellular glucose and the intracellular free-energy state. We discuss i), that the effects of diffusion on cell function should prevent this highly effective bacterial system from functioning in eukaryotic cells, ii), that in the larger eukaryotic cell any similar chain of mobile group-transfer proteins can neither sustain the same volumetric flux as in bacteria nor transmit a signal far into the cell, and iii), that systems such as these may exhibit spatial differentiation in their sensitivity to different signals.

Flux control of the bacterial phosphoenolpyruvate:glucose phosphotransferase system and the effect of diffusion.

We analyzed the role of diffusion and cell size on the flux control properties of the glucose-PTS of Escherichia coli, in silicon cells under various metabolic conditions. To our surprise, the influence of the concentration of phosphoryl-donor PEP on the distribution of control was small. We found for cells of bacterial size that PTS-flux control was mainly located in processes taking place in the membrane and that diffusion hardly controlled the flux (< 2.8 %). Enlargement of the cells shifted the control from membrane to cytoplasm and from process rates to diffusion rates, the latter now having a total control of about 38 %. In the presence of glucose, nearly all diffusion flux control resided in the component that links the cytoplasmic processes to those in the membrane.

The adaptiveness of defence strategies against cuckoo parasitism.

Host bird species of the Eurasian Cuckoo, Cuculus canorus, often display egg-discrimination behaviour but chick-rejection behaviour has never been reported. In this paper, we analyse a host-cuckoo association in which both population dynamics and evolutionary dynamics are explored in a discrete-time model. We introduce four host types, each with their own defence behaviour, displaying either egg or chick rejection, neither or both, We also introduce fitness functions for each of these host types. Although we can characterize the long term behaviour in many cases by a simple heuristic argument which is in accordance with common views in ecology, there are a number of other phenomena that are not explained within this framework: we describe stable oscillatory behaviour and coexistence of two defensive host types. We analyse the scenarios in which chick rejection may establish itself and give a first explanation as to why this defence trait has never been recorded in nature. We find that chick rejectors generally are at an intrinsic disadvantage with respect to a host type that rejects eggs. Hosts benefit more from rejecting cuckoo eggs than cuckoo chicks, and our model suggests that this is chiefly responsible for the absence of chick rejection. Moreover, even though it seems that chick rejection must be useful as an extra defence, it is shown that hosts with both defence strategies are less likely to establish themselves in competition with egg-rejectors than hosts which reject chicks only. These results provide insight in the extent to which adaptations may be perfected by natural selection.