Ultrasensitivity in phosphorylation-dephosphorylation cycles with little substrate

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with [Formula: see text] phosphosites, we find an upper bound of the Hill number of [Formula: see text], and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells

Tracing the Sources of Cellular Variation

As the adage says, variety is the spice of life, and despite our best attempts, cells, even those with the same genome, never seem to behave the same. By combining mathematical and experimental analyses, Colman-Lerner and colleagues propose, in a recent issue of Nature, a method to delicately unravel the sources of this variation (Colman-Lerner et al., 2005). Applying their technique to the pheromone response in budding yeast, they show that much of the observed variation originates from cell cycle effects and is dependent on levels of pathway input

Accurate prediction of gene feedback circuit behavior from component properties

A basic assumption underlying synthetic biology is that analysis of genetic circuit elements, such as regulatory proteins and promoters, can be used to understand and predict the behavior of circuits containing those elements. To test this assumption, we used time‐lapse fluorescence microscopy to quantitatively analyze two autoregulatory negative feedback circuits. By measuring the gene regulation functions of the corresponding repressor–promoter interactions, we accurately predicted the expression level of the autoregulatory feedback loops, in molecular units. This demonstration that quantitative characterization of regulatory elements can predict the behavior of genetic circuits supports a fundamental requirement of synthetic biology

BioJazz : In silico evolution of cellular networks with unbounded complexity using rule-based modeling

Systems biologists aim to decipher the structure and dynamics of signaling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. Here we introduce BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for the evolution of cellular networks with unbounded complexity by combining rule-based modeling with an encoding of networks that is akin to a genome. We show that BioJazz can be used to implement biologically realistic selective pressures and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. BioJazz is provided as an open-source tool to facilitate its further development and use. Source code and user manuals are available at: http://oss-lab.github.io/biojazz and http://osslab.lifesci.warwick.ac.uk/BioJazz.aspx

Multiple nutrient transporters enable cells to mitigate a rate-affinity tradeoff

Eukaryotic genomes often encode multiple transporters for the same nutrient. For example, budding yeast has 17 hexose transporters (HXTs), all of which potentially transport glucose. Using mathematical modelling, we show that transporters that use either facilitated diffusion or symport can have a rate-affinity tradeoff, where an increase in the maximal rate of transport decreases the transporter's apparent affinity. These changes affect the import flux non-monotonically, and for a given concentration of extracellular nutrient there is one transporter, characterised by its affinity, that has a higher import flux than any other. Through encoding multiple transporters, cells can therefore mitigate the tradeoff by expressing those transporters with higher affinities in lower concentrations of nutrients. We verify our predictions using fluorescent tagging of seven HXT genes in budding yeast and follow their expression over time in batch culture. Using the known affinities of the corresponding transporters, we show that their regulation in glucose is broadly consistent with a rate-affinity tradeoff: as glucose falls, the levels of the different transporters peak in an order that mostly follows their affinity for glucose. More generally, evolution is constrained by tradeoffs. Our findings indicate that one such tradeoff often occurs in the cellular transport of nutrients

Facile: a command-line network compiler for systems biology

<p>Abstract</p> <p>Background</p> <p>A goal of systems biology is the quantitative modelling of biochemical networks. Yet for many biochemical systems, parameter values and even the existence of interactions between some chemical species are unknown. It is therefore important to be able to easily investigate the effects of adding or removing reactions and to easily perform a bifurcation analysis, which shows the qualitative dynamics of a model for a range of parameter values.</p> <p>Results</p> <p>We present Facile, a Perl command-line tool for analysing the dynamics of a systems biology model. Facile implements the law of mass action to automatically compile a biochemical network (written as, for example, <monospace>E + S <-> C</monospace>) into scripts for analytical analysis (Mathematica and Maple), for simulation (XPP and Matlab), and for bifurcation analysis (AUTO). Facile automatically identifies mass conservations and generates the reduced form of a model with the minimum number of independent variables. This form is essential for bifurcation analysis, and Facile produces a C version of the reduced model for AUTO.</p> <p>Conclusion</p> <p>Facile is a simple, yet powerful, tool that greatly accelerates analysis of the dynamics of a biochemical network. By acting at the command-line and because of its intuitive, text-based input, Facile is quick to learn and can be incorporated into larger programs or into automated tasks.</p

Predicting metabolic adaptation from networks of mutational paths

The structure and dynamics of microbial communities reflect trade-offs in the ability to use different resources. Here, Josephides and Swain incorporate metabolic trade-offs into an eco-evolutionary model to predict networks of mutational paths and the evolutionary outcomes for microbial communities