Complex behaviour is associated with animals having nervous systems but decision making and learning also occur in non-neural organisms [1], including singly-nucleated cells [2, 3, 4, 5] and multi-nucleate synctia [6, 7, 8]. Ciliates are single-cell eukaryotes, widely dispersed in aquatic habitats [9], with an extensive behavioural repertoire [10, 11, 12, 13]. In 1906, Herbert Spencer Jennings [14, 15] described in the sessile ciliate Stentor roeseli a hierarchy of responses to repeated stimulation, which are among the most complex behaviours reported for a singlynucleated cell [16, 17]. These results attracted widespread interest [18, 19] and exert continuing fascination [7, 20, 21, 22] but were discredited during the behaviourist orthodoxy by claims of non-reproducibility [23]. These claims were based on experiments with the motile ciliate Stentor coeruleus. We acquired and maintained the correct organism in laboratory culture and used micromanipulation and video microscopy to confirm Jennings' observations. Despite significant individual variation, not addressed by Jennings, S. roeseli exhibits avoidance behaviours in a characteristic hierarchy of bending, ciliary alteration, contractions and detachment, which is distinct from habituation or conditioning. Remarkably, the choice of contraction versus detachment is consistent with a fair coin toss. Such behavioural complexity may have had an evolutionary advantage in protist ecosystems and the ciliate cortex may have provided mechanisms for implement-⇤

Background: Robustness of the Escherichia coli isocitrate dehydrogenase (IDH) regulatory system has been experimentally demonstrated. Results: A biochemically and structurally realistic mathematical model of the IDH system was developed. Conclusion: The model identifies features of the system, including homodimerization of IDH and bifunctionality of its regulatory enzyme, that lead to robustness. Significance: Mathematical modeling can connect enzymology and systems biology.

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Experimental and theoretical studies have suggested that bifunctional enzymes catalyzing opposing modification and demodification reactions can confer steady-state concentration robustness to their substrates. However, the types of robustness and the biochemical basis for them have remained elusive. Here we report a systematic study of the most general biochemical reaction network for a bifunctional enzyme acting on a substrate with one modification site, along with eleven sub-networks with more specialized biochemical assumptions. We exploit ideas from computational algebraic geometry, introduced in previous work, to find a polynomial expression (an invariant) between the steady state concentrations of the modified and unmodified substrate for each network. We use these invariants to identify five classes of robust behavior: robust upper bounds on concentration, robust two-sided bounds on concentration ratio, hybrid robustness, absolute concentration robustness (ACR), and robust concentration ratio. This analysis demonstrates that robustness can take a variety of forms and that the type of robustness is sensitive to many biochemical details, with small changes in biochemistry leading to very different steady-state behaviors. In particular, we find that the widely-studied ACR requires highly specialized assumptions in addition to bifunctionality. An unexpected result is that the robust bounds derived from invariants are strictly tighter than those derived by ad hoc manipulation of the underlying differential equations, confirming the value of invariants as a tool to gain insight into biochemical reaction networks. Furthermore, invariants yield multiple experimentally testable predictions and illuminate new strategies for inferring enzymatic mechanisms from steady-state measurements.

Planarians are an important model organism for regeneration and stem cell research. A complete understanding of stem cell and regeneration dynamics in these animals requires time-lapse imaging in vivo, which has been difficult to achieve due to a lack of tissue-specific markers and the strong negative phototaxis of planarians. We have developed the Planarian Immobilization Chip (PIC) for rapid, stable immobilization of planarians for in vivo imaging without injury or biochemical alteration. The chip is easy and inexpensive to fabricate, and worms can be mounted for and removed after imaging within minutes. We show that the PIC enables significantly higher-stability immobilization than can be achieved with standard techniques, allowing for imaging of planarians at sub-cellular resolution in vivo using brightfield and fluorescence microscopy. We validate the performance of the PIC by performing time-lapse imaging of planarian wound closure and sequential imaging over days of head regeneration. We further show that the device can be used to immobilize Hydra, another photophobic regenerative model organism. The simple fabrication, low cost, ease of use, and enhanced specimen stability of the PIC should enable its broad application to in vivo studies of stem cell and regeneration dynamics in planarians and Hydra.

BackgroundThe yeast Saccharomyces cerevisiae relies on the high-osmolarity glycerol (HOG) signaling pathway to respond to increases in external osmolarity. The HOG pathway is rapidly activated under conditions of elevated osmolarity and regulates transcriptional and metabolic changes within the cell. Under normal growth conditions, however, a three-component phospho-relay consisting of the histidine kinase Sln1, the transfer protein Ypd1, and the response regulator Ssk1 represses HOG pathway activity by phosphorylation of Ssk1. This inhibition of the HOG pathway is essential for cellular fitness in normal osmolarity. Nevertheless, the extent to and mechanisms by which inhibition is robust to fluctuations in the concentrations of the phospho-relay components has received little attention.ResultsWe established that the Sln1-Ypd1-Ssk1 phospho-relay is robust—it is able to maintain inhibition of the HOG pathway even after significant changes in the levels of its three components. We then developed a biochemically realistic mathematical model of the phospho-relay, which suggested that robustness is due to buffering by a large excess pool of Ypd1. We confirmed experimentally that depletion of the Ypd1 pool results in inappropriate activation of the HOG pathway.ConclusionsWe identified buffering by an intermediate component in excess as a novel mechanism through which a phospho-relay can achieve robustness. This buffering requires multiple components and is therefore unavailable to two-component systems, suggesting one important advantage of multi-component relays.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0158-y) contains supplementary material, which is available to authorized users.

Edited by Ruma Banerjee Monoallelic point mutations in the gene encoding the cytosolic, NADP ؉-dependent enzyme isocitrate dehydrogenase 1 (IDH1) cause increased production of the oncometabolite 2-hydroxyglutarate (2-HG) in multiple cancers. Most IDH1 mutant tumors retain one wildtype (WT) IDH1 allele. Several studies have proposed that retention of this WT allele is protumorigenic by facilitating substrate channeling through a WT-mutant IDH1 heterodimer, with the WT subunit generating a local supply of ␣-ketoglutarate and NADPH that is then consumed by the mutant subunit to produce 2-HG. Here, we confirmed that coexpression of WT and mutant IDH1 subunits leads to formation of WT-mutant hetero-oligomers and increases 2-HG production. An analysis of a recently reported crystal structure of the WT-R132H IDH1 heterodimer and of in vitro kinetic parameters for 2-HG production, however, indicated that substrate channeling between the subunits is biophysically implausible. We also found that putative carbon-substrate flux between WT and mutant IDH1 subunits is inconsistent with the results of isotope tracing experiments in cancer cells harboring an endogenous monoallelic IDH1 mutation. Finally, using a mathematical model of WT-mutant IDH1 heterodimers, we estimated that the NADPH:NADP ؉ ratio is higher in the cytosol than in the mitochondria, suggesting that NADPH is unlikely to be limiting for 2-HG production in the cytosol. These findings argue against supply of either substrate being limiting for 2-HG production by a cytosolic IDH1 mutant and suggest that the retention of a WT allele in IDH1 mutant tumors is not due to a requirement for carbon or cofactor flux between WT and mutant IDH1.

Excitation-contraction coupling in smooth muscle is mediated by the Ca - and calmodulin-dependent regulation of myosin light chain kinase. The precise mechanism of this regulation remains controversial, and several mathematical models have been proposed for the interaction of the three species. These models have previously been analyzed at steady state primarily by numerical simulation of differential equations, for which parameter values must be estimated from data. Here, we use the linear framework for timescale separation to demonstrate that models of this general kind can be solved analytically for an equilibrium steady state, without having to determine parameter values. This analysis leads to parameter-independent methods for discriminating between the models, for which we propose experiments that could be performed with existing methods.