Boolean factor graph model for biological systems: the yeast cell-cycle network

Background The desire to understand genomic functions and the behavior of complex gene regulatory networks has recently been a major research focus in systems biology. As a result, a plethora of computational and modeling tools have been proposed to identify and infer interactions among biological entities. Here, we consider the general question of the effect of perturbation on the global dynamical network behavior as well as error propagation in biological networks to incite research pertaining to intervention strategies. Results This paper introduces a computational framework that combines the formulation of Boolean networks and factor graphs to explore the global dynamical features of biological systems. A message-passing algorithm is proposed for this formalism to evolve network states as messages in the graph. In addition, the mathematical formulation allows us to describe the dynamics and behavior of error propagation in gene regulatory networks by conducting a density evolution (DE) analysis. The model is applied to assess the network state progression and the impact of gene deletion in the budding yeast cell cycle. Simulation results show that our model predictions match published experimental data. Also, our findings reveal that the sample yeast cell-cycle network is not only robust but also consistent with real high-throughput expression data. Finally, our DE analysis serves as a tool to find the optimal values of network parameters for resilience against perturbations, especially in the inference of genetic graphs. Conclusion Our computational framework provides a useful graphical model and analytical tools to study biological networks. It can be a powerful tool to predict the consequences of gene deletions before conducting wet bench experiments because it proves to be a quick route to predicting biologically relevant dynamic properties without tunable kinetic parameters.

A novel analysis of gene array data: yeast cell cycle

Many gene array studies of the yeast cell cycle have been performed (Cho RJ, Campbell MJ, Winzeler EA et al. A genome-wide transcriptional analysis of the mitotic cell cycle. Mol Cell 1998;2:65–73; Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944–7; Pramila T, Wu W, Miles S et al. The Forkhead transcription factor Hcm1 regulates chromosome segregation genes and fills the S-phase gap in the transcriptional circuitry of the cell cycle. Genes Dev 2006;20:2266–78; Spellman PT, Sherlock G, Zhang MQ et al. Comprehensive identification of cell cycle–regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. MBoC 1998;9:3273–97). Largely, these studies contain elements drawn from laboratory experiments. The present investigation determines cell division cycle (CDC) genes solely from the data (Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944–7). It is shown by simple reasoning that the dynamics of the approximately 6000 yeast genes are described by an approximately six-dimensional space. This leads a precisely determined cell-cycle period, along with the quality and timing of the identified CDC genes. Convincing evidence for the role of the identified genes is obtained. While these show good agreement with standard CDC gene representatives (Orlando DA, Lin CY, Bernard A et al. Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 2008;453:944–7; Spellman PT, Sherlock G, Zhang MQ et al. Comprehensive identification of cell cycle–regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. MBoC 1998;9:3273–97; de Lichtenberg U, Jensen LJ, Fausbøll A et al. Comparison of computational methods for the identification of cell cycle-regulated genes. Bioinformatics 2005;21:1164–71) several hundred newly revealed CDC genes appear, which merit attention. The present approach employs an adaptation of a method introduced to study turbulent flows (Schmid PJ. Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 2010;656:5–28), “dynamic mode decomposition” (DMD). From this, one can infer that singular value decomposition, analysis of the data entangles the underlying (gene) dynamics implicit in the data; and that DMD produces the disentangling transformation. It is the assertion of this study that a new tool now exists for the analysis of the gene array signals, and in particular for investigating the yeast cell cycle.

A Hybrid Stochastic Model of the Budding Yeast Cell Cycle

The growth and division of eukaryotic cells are regulated by complex, multi-scale networks. In this process, the mechanism controlling cell cycle progression has to be robust against inherent noise in the system. In this paper, a hybrid stochastic model is developed to study the effects of noise on the control mechanism of the budding yeast cell cycle. The modeling approach leverages, in a single multi-scale model, the advantages of two regimes: 1) the computational efficiency of a deterministic approach, and 2) the accuracy of stochastic simulations. Our results show that this hybrid stochastic model achieves high computational efficiency while generating simulation results that match very well with published experimental measurements.