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Wheat (Triticum spp.) grains contain large protein polymers constituted by two main classes of polypeptides: the highmolecular-weight glutenin subunits and the low-molecular-weight glutenin subunits (LMW-GS). These polymers are among the largest protein molecules known in nature and are the main determinants of the superior technological properties of wheat flours. However, little is known about the mechanisms controlling the assembly of the different subunits and the way they are arranged in the final polymer. Here, we have addressed these issues by analyzing the formation of interchain disulfide bonds between identical and different LMW-GS and by studying the assembly of mutants lacking individual intrachain disulfides. Our results indicate that individual cysteine residues that remain available for disulfide bond formation in the folded monomer can form interchain disulfide bonds with a variety of different cysteine residues present in a companion subunit. These results imply that the coordinated expression of many different LMW-GS in wheat endosperm cells can potentially lead to the formation of a large set of distinct polymeric structures, in which subunits can be arranged in different configurations. In addition, we show that not all intrachain disulfide bonds are necessary for the generation of an assembly-competent structure and that the retention of a LMW-GS in the early secretory pathway is not dependent on polymer formation.

We present a new approach or framework to model dynamic regulatory genetic activity. The framework is using a multi-scale analysis based upon generic assumptions on the relative time scales attached to the different transitions of molecular states defining the genetic system. At micro-level such systems are regulated by the interaction of two kinds of molecular players: macro-molecules like DNA or polymerases, and smaller molecules acting as transcription factors. The proposed genetic model then represents the larger less abundant molecules with a finite discrete state space, for example describing different conformations of these molecules. This is in contrast to the representations of the transcription factors which are-like in classical reaction kinetics-represented by their particle number only. We illustrate the method by considering the genetic activity associated to certain configurations of interacting genes that are fundamental to modelling (synthetic) genetic clocks. A largely unknown question is how different molecular details incorporated via this more realistic modelling approach lead to different macroscopic regulatory genetic models which dynamical behaviour might-in general-be different for different model choices. The theory will be applied to a real synthetic clock in a second accompanying article (Kirkilioniset al., Theory Biosci, 2011).

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Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a central bottleneck problem in many application areas, especially in cell biology where various such diagrams with different conventions describing molecular regulation are presently in use. In most situations these diagrams can only be interpreted by the use of both discrete and continuous variables during the modelling process, corresponding to both deterministic and stochastic hybrid dynamics. The conventions in genetics are well-known, and therefore we use this field for illustration purposes. In [25] and [26] the authors showed that with the help of a multi-scale analysis stochastic systems with both continuous variables and finite state spaces can be approximated by dynamical systems whose leading order time evolution is given by a combination of ordinary differential equations (ODEs) and Markov chains. The leading order term in these dynamical systems is called average dynamics and turns out to be an adequate concept to analyse a class of simplified hybrid systems. Once the dynamics is defined the mutual interaction of both ODEs and Markov chains can be analysed through the (reverse) introduction of the so called Interaction Graph, a concept originally invented for time-continuous dynamical systems, see [5]. Here we transfer this graph concept to the average dynamics, which itself is introduced as an heuristic tool to construct models of reaction or contact networks. The graphical concepts introduced form the basis for any subsequent study of the qualitative properties of hybrid models in terms of connectivity and (feedback) loop formation. arXiv:0803.0635v3 [q-bio.MN]

Abstract-Continuous glucose monitoring is increasingly used in the management of diabetes.Subcutaneous glucose profiles are characterized by a strong non-stationarity, which limits the application of correlation-spectral analysis. We derived an index of linear predictability by calculating the autocorrelation function of time series increments and applied detrended fluctuation analysis to assess the non-stationarity of the profiles. Time series from volunteers with both type 1 and type 2 diabetes and from control subjects were analysed. The results suggest that in control subjects, blood glucose variation is relatively uncorrelated, and this variation could be modelled as a random walk with no retention of 'memory' of previous values.In diabetes, variation is both greater and smoother, with retention of inter-dependence between neighboring values. Essential components for adequate longer term prediction were identified via a decomposition of time series into a slow trend and responses to external stimuli. Implications for diabetes management are discussed.

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