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

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

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

Perfect Edge-Transmitting Recombination of Permutations

Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation order. Recombination of edges without errors is thought to be an NP-hard problem, typically approximated by heuristics that either introduce new edges or are only able to produce a small variety of offspring. Here, we derive an algorithm for crossover of permutations that achieves perfect transmission of edges and produces a uniform sampling of all possible offspring, in quadratic average computation time. The algorithm and its derivation reveal a link between cycle crossover (CX) and edge assembly crossover (EAX), offering a new perspective on these well-established algorithms. We also describe a modification of the algorithm that generates the mathematically optimal offspring for the asymmetric travelling salesman problem

PHOREST: a web-based tool for comparative analyses of expressed sequence tag data

Comparative analysis of expressed sequence tags is becoming an important tool in molecular ecology for comparing gene expression in organisms grown in certain environments. Additionally, expressed sequence tag database information can be used for the construction of DNA microarrays and for the detection of single nucleotide polymorphisms. For such applications, we present PHOREST, a web-based tool for managing, analysing and comparing various collections of expressed sequence tags. It is written in PHP (PHP: Hypertext Preprocessor) and runs on UNIX, Microsoft Windows and Macintosh (Mac OS X) platforms

Is Transcriptional Regulation of Metabolic Pathways an Optimal Strategy for Fitness?

Background. Transcriptional regulation of the genes in metabolic pathways is a highly successful strategy, which is virtually universal in microorganisms. The lac operon of E. coli is but one example of how enzyme and transporter production can be made conditional on the presence of a nutrient to catabolize. Methodology. With a minimalist model of metabolism, cell growth and transcriptional regulation in a microorganism, we explore how the interaction between environmental conditions and gene regulation set the growth rate of cells in the phase of exponential growth. This in silico model, which is based on biochemical rate equations, does not describe a specific organism, but the magnitudes of its parameters are chosen to match realistic values. Optimizing the parameters of the regulatory system allows us to quantify the fitness benefit of regulation. When a second nutrient and its metabolic pathway are introduced, the system must further decide whether and how to activate both pathways. Conclusions. Even the crudest transcriptional network is shown to substantially increase the fitness of the organism, and this effect persists even when the range of nutrient levels is kept very narrow. We show that maximal growth is achieved when pathway activation is a more or less steeply graded function of the nutrient concentration. Furthermore, we predict that bistability of the system is a rare phenomenon in this context, but outline a situation where it may be selected for

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

Transcriptional Dynamics of the Embryonic Stem Cell Switch

Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4–SOX2–NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4–SOX2–NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched on/off by input environmental signals. The switch stabilizes the expression levels of the three genes, and through their regulatory roles on the downstream target genes, leads to a binary decision: when OCT4, SOX2, and NANOG are expressed and the switch is on, the self-renewal genes are on and the differentiation genes are off. The opposite holds when the switch is off. The model is extremely robust to parameter changes. In addition to providing a self-consistent picture of the transcriptional circuit, the model generates several predictions. Increasing the binding strength of NANOG to OCT4 and SOX2, or increasing its basal transcriptional rate, leads to an irreversible bistable switch: the switch remains on even when the activating signal is removed. Hence, the stem cell can be manipulated to be self-renewing without the requirement of input signals. We also suggest tests that could discriminate between a variety of feedforward regulation architectures of the target genes by OCT4, SOX2, and NANOG

BioArray Software Environment (BASE): a platform for comprehensive management and analysis of microarray data

The microarray technique requires the organization and analysis of vast amounts of data. These data include information about the samples hybridized, the hybridization images and their extracted data matrices, and information about the physical array, the features and reporter molecules. We present a web-based customizable bioinformatics solution called BioArray Software Environment (BASE) for the management and analysis of all areas of microarray experimentation. All software necessary to run a local server is freely available