Enumerating Designing Sequences in the HP Model

The hydrophobic/polar HP model on the square lattice has been widely used to investigate basics of protein folding. In the cases where all designing sequences (sequences with unique ground states) were enumerated without restrictions on the number of contacts, the upper limit on the chain length N has been 18-20 because of the rapid exponential growth of the numbers of conformations and sequences. We show how a few optimizations push this limit by about 5 units. Based on these calculations, we study the statistical distribution of hydrophobicity along designing sequences. We find that the average number of hydrophobic and polar clumps along the chains is larger for designing sequences than for random ones, which is in agreement with earlier findings for N up to 18 and with results for real enzymes. We also show that this deviation from randomness disappears if the calculations are restricted to maximally compact structures.Comment: 18 pages, 4 figure

Genetic networks with canalyzing Boolean rules are always stable

We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are dynamically stable. Furthermore, for architectures with few inputs per node, the dynamics of the networks is close to critical. In addition, the fraction of genes that are active decreases with the number of inputs per node. These results are based upon investigating ensembles of networks using analytical methods. Also, for different in-degree distributions, the numbers of fixed points and cycles are calculated, with results intuitively consistent with stability analysis; fewer inputs per node implies more cycles, and vice versa. There are hints that genetic networks acquire broader degree distributions with evolution, and hence our results indicate that for single cells, the dynamics should become more stable with evolution. However, such an effect is very likely compensated for by multicellular dynamics, because one expects less stability when interactions among cells are included. We verify this by simulations of a simple model for interactions among cells.Comment: Final version available through PNAS open access at http://www.pnas.org/cgi/content/abstract/0407783101v

Random Boolean Network Models and the Yeast Transcriptional Network

The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.Comment: 23 pages, 5 figure

Light and circadian regulation of clock components aids flexible responses to environmental signals

The circadian clock measures time across a 24h period, increasing fitness by phasing biological processes to the most appropriate time of day. The interlocking feedback loop mechanism of the clock is conserved across species; however, the number of loops varies. Mathematical and computational analyses have suggested that loop complexity affects the overall flexibility of the oscillator, including its responses to entrainment signals. We used a discriminating experimental assay, at the transition between different photoperiods, in order to test this proposal in a minimal circadian network (in Ostreococcus tauri) and a more complex network (in Arabidopsis thaliana). Transcriptional and translational reporters in O.tauri primarily tracked dawn or dusk, whereas in A.thaliana, a wider range of responses were observed, consistent with its more flexible clock. Model analysis supported the requirement for this diversity of responses among the components of the more complex network. However, these and earlier data showed that the O.tauri network retains surprising flexibility, despite its simple circuit. We found that models constructed from experimental data can show flexibility either from multiple loops and/or from multiple light inputs. Our results suggest that O.tauri has adopted the latter strategy, possibly as a consequence of genomic reduction

Complementary approaches to understanding the plant circadian clock

This is the final version of the article. Available from the Open Publishing Association via the DOI in this record.Proceedings - Third Workshop 'From Biology To Concurrency and back', Paphos, Cyprus, 27 March 2010Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock.The authors thank Gerben van Ooijen for TopCount data and Jane Hillston and Andrew Millar for their helpful comments. The Centre for Systems Biology at Edinburgh is a Centre for Integrative Systems Biology (CISB) funded by BBSRC and EPSRC, ref. BB/D019621/1. CT is supported by The International Human Frontier Science Program Organization

Light and circadian regulation of clock components aids flexible responses to environmental signals

PublishedJournal ArticleResearch Support, Non-U.S. Gov'tThe circadian clock measures time across a 24 h period, increasing fitness by phasing biological processes to the most appropriate time of day. The interlocking feedback loop mechanism of the clock is conserved across species; however, the number of loops varies. Mathematical and computational analyses have suggested that loop complexity affects the overall flexibility of the oscillator, including its responses to entrainment signals. We used a discriminating experimental assay, at the transition between different photoperiods, in order to test this proposal in a minimal circadian network (in Ostreococcus tauri) and a more complex network (in Arabidopsis thaliana). Transcriptional and translational reporters in O. tauri primarily tracked dawn or dusk, whereas in A. thaliana, a wider range of responses were observed, consistent with its more flexible clock. Model analysis supported the requirement for this diversity of responses among the components of the more complex network. However, these and earlier data showed that the O. tauri network retains surprising flexibility, despite its simple circuit. We found that models constructed from experimental data can show flexibility either from multiple loops and/or from multiple light inputs. Our results suggest that O. tauri has adopted the latter strategy, possibly as a consequence of genomic reduction.This research was supported by EU FP7 collaborative project TiMet (award 245143), BBSRC and EPSRC awards BB/F005237/1, BB/D019621/1 and BB/J009423 (to A.J.M. and others) and EPSRC award EP/I017445/1 (to O.E.A. and others). C.T.'s work was supported by the Human Frontiers Science Program and the Swedish Research Council (award 2010-5219)

SBSI:an extensible distributed software infrastructure for parameter estimation in systems biology

Complex computational experiments in Systems Biology, such as fitting model parameters to experimental data, can be challenging to perform. Not only do they frequently require a high level of computational power, but the software needed to run the experiment needs to be usable by scientists with varying levels of computational expertise, and modellers need to be able to obtain up-to-date experimental data resources easily. We have developed a software suite, the Systems Biology Software Infrastructure (SBSI), to facilitate the parameter-fitting process. SBSI is a modular software suite composed of three major components: SBSINumerics, a high-performance library containing parallelized algorithms for performing parameter fitting; SBSIDispatcher, a middleware application to track experiments and submit jobs to back-end servers; and SBSIVisual, an extensible client application used to configure optimization experiments and view results. Furthermore, we have created a plugin infrastructure to enable project-specific modules to be easily installed. Plugin developers can take advantage of the existing user-interface and application framework to customize SBSI for their own uses, facilitated by SBSI’s use of standard data formats

Gene Regulatory Networks: Dynamics and Stability

Life as we know it is based on cells that use proteins and RNA to carry out metabolism, self-replication, and other essential tasks. The genes that code for these molecules are encoded in DNA, and through the processes of transcription and translation the cell expresses its genes. Some proteins are transcription factors that regulate the transcription rate of genes, so genes interact and form a gene regulatory network. In a random Boolean network the genes are modeled as being either on or off, and the regulatory interactions are drawn from some ensemble that may be based on biological observations. Here, the average behavior of observables of dynamics (e.g., attractor count) and stability (e.g., robustness to perturbations) is studied, both in the original Kauffman model and in models based on data from yeast. Signal transduction, the propagation of information about the external and internal environment of the cell, often affects transcription factors, thereby altering gene expression levels. Signaling pathway profiling is proposed as a way to reduce the complexity of microarray data and find biologically relevant signals. The core regulatory system of embryonic stem cells is a concrete example of a network where attractor basins and stability are important for biological function, and we explore its dynamics in a continuous model. Finally, the what effect transcriptional regulation has on fitness is studied in the context of metabolism in a very simple system, and the benefit of regulation is made clear