A Robust Structural PGN Model for Control of Cell-Cycle Progression Stabilized by Negative Feedbacks

The cell division cycle comprises a sequence of phenomena controlled by a stable and robust genetic network. We applied a probabilistic genetic network (PGN) to construct a hypothetical model with a dynamical behavior displaying the degree of robustness typical of the biological cell cycle. The structure of our PGN model was inspired in well-established biological facts such as the existence of integrator subsystems, negative and positive feedback loops, and redundant signaling pathways. Our model represents genes interactions as stochastic processes and presents strong robustness in the presence of moderate noise and parameters fluctuations. A recently published deterministic yeast cell-cycle model does not perform as well as our PGN model, even upon moderate noise conditions. In addition, self stimulatory mechanisms can give our PGN model the possibility of having a pacemaker activity similar to the observed in the oscillatory embryonic cell cycle.     

Identifying responsive modules by mathematical programming: an application to budding yeast cell cycle

High-throughput biological data offer an unprecedented opportunity to fully characterize biological processes. However, how to extract meaningful biological information from these datasets is a significant challenge. Recently, pathway-based analysis has gained much progress in identifying biomarkers for some phenotypes. Nevertheless, these so-called pathway-based methods are mainly individual-gene-based or molecule-complex-based analyses. In this paper, we developed a novel module-based method to reveal causal or dependent relations between network modules and biological phenotypes by integrating both gene expression data and protein-protein interaction network. Specifically, we first formulated the identification problem of the responsive modules underlying biological phenotypes as a mathematical programming model by exploiting phenotype difference, which can also be viewed as a multi-classification problem. Then, we applied it to study cell-cycle process of budding yeast from microarray data based on our biological experiments, and identified important phenotype- and transition-based responsive modules for different stages of cell-cycle process. The resulting responsive modules provide new insight into the regulation mechanisms of cell-cycle process from a network viewpoint. Moreover, the identification of transition modules provides a new way to study dynamical processes at a functional module level. In particular, we found that the dysfunction of a well-known module and two new modules may directly result in cell cycle arresting at S phase. In addition to our biological experiments, the identified responsive modules were also validated by two independent datasets on budding yeast cell cycle.     

Superstability of the yeast cell-cycle dynamics: ensuring causality in the presence of biochemical stochasticity

Gene regulatory dynamics are governed by molecular processes and therefore exhibits an inherent stochasticity. However, for the survival of an organism it is a strict necessity that this intrinsic noise does not prevent robust functioning of the system. It is still an open question how dynamical stability is achieved in biological systems despite the omnipresent fluctuations. In this paper we investigate the cell cycle of the budding yeast Saccharomyces cerevisiae as an example of a well-studied organism. We study a genetic network model of 11 genes that coordinate the cell-cycle dynamics using a modeling framework which generalizes the concept of discrete threshold dynamics. By allowing for fluctuations in the process times, we introduce noise into the model, accounting for the effects of biochemical stochasticity. We study the dynamical attractor of the cell cycle and find a remarkable robustness against fluctuations of this kind. We identify mechanisms that ensure reliability in spite of fluctuations: 'Catcher states' and persistence of activity levels contribute significantly to the stability of the yeast cell cycle despite the inherent stochasticity.     

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.     

Identification of a Topological Characteristic Responsible for the Biological Robustness of Regulatory Networks

Attribution of biological robustness to the specific structural properties of a regulatory network is an important yet unsolved problem in systems biology. It is widely believed that the topological characteristics of a biological control network largely determine its dynamic behavior, yet the actual mechanism is still poorly understood. Here, we define a novel structural feature of biological networks, termed ‘regulation entropy’, to quantitatively assess the influence of network topology on the robustness of the systems. Using the cell-cycle control networks of the budding yeast (Saccharomyces cerevisiae) and the fission yeast (Schizosaccharomyces pombe) as examples, we first demonstrate the correlation of this quantity with the dynamic stability of biological control networks, and then we establish a significant association between this quantity and the structural stability of the networks. And we further substantiate the generality of this approach with a broad spectrum of biological and random networks. We conclude that the regulation entropy is an effective order parameter in evaluating the robustness of biological control networks. Our work suggests a novel connection between the topological feature and the dynamic property of biological regulatory networks.     

The transition from differential equations to Boolean networks: a case study in simplifying a regulatory network model

Methods for modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without much closer correspondence to each other. With the example system of the fission yeast cell cycle control network, we here discuss these two approaches with respect to each other. We find that a Boolean network model can be formulated as a specific coarse-grained limit of the more detailed differential equations model for this system. This demonstrates the mathematical foundation on which Boolean networks can be applied to biological regulatory networks in a controlled way.     

Dissecting the fission yeast regulatory network reveals phase-specific control elements of its cell cycle

Background  

Fission yeast Schizosaccharomyces pombe and budding yeast Saccharomyces cerevisiae are among the original model organisms in the study of the cell-division cycle. Unlike budding yeast, no large-scale regulatory network has been constructed for fission yeast. It has only been partially characterized. As a result, important regulatory cascades in budding yeast have no known or complete counterpart in fission yeast.     

A mathematical model for cell size control in fission yeast

Experimental investigations of cell size control in fission yeast Schizosaccharomyces pombe have illustrated that the cell cycle features ‘sizer’ and ‘timer’ phases which are distinguished by a growth rate changing point. Based on current biological knowledge of fission yeast size control, we propose here a model of ordinary differential equations (ODEs) for a possible explanation of the facts and control mechanism which is coupled with the cell cycle. Simulation results of the ODE model are demonstrated to agree with experimental data for the wild type and the cdc2-33 mutant. We show that the coupling of cell growth to cell division by translational control may account for observed properties of size control in fission yeast. As the translational control in the expression of cycle proteins Cdc13 and Cdc25 constructs positive feedback loops, the dynamical activities of the key components undergoes a rapid rising after a preliminary stage of slow increase. The coupling of this dynamical behavior to the elongation of the cell naturally gives rise to a rate change point and to ‘sizer’ and ‘timer’ phases, which characterize the cell cycle of fission yeast.     

Neutral space analysis for a Boolean network model of the fission yeast cell cycle network

Background

Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle.

Results

Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G₁ fixed point was found for deterministic updating schemes.

Conclusions

In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.     

How do prokaryotic cells cycle?

This issue of Current Biology features five reviews covering various key aspects of the eukaryotic cell cycle. The topics include initiation of chromosome replication, assembly of the mitotic spindle, cytokinesis, the regulation of cell-cycle progression, and cell-cycle modeling, focusing mainly on budding yeast, fission yeast and animal cell model systems. The reviews underscore common themes as well as key differences in the way these processes are carried out and regulated among the different model organisms. Consequently, an important question is how cell-cycle mechanisms and controls have evolved, particularly in the broader perspective of the three domains of life.     

A novel copper-regulated promoter system for expression of heterologous proteins in Schizosaccharomyces pombe

The increasing use of the fission yeast Schizosaccharomyces pombe as a model organism for elucidating the mechanisms of critical biological processes such as cell-cycle control, DNA replication, and stress-mediated signal transduction has fostered the development and utilization of expression systems for gene function analysis. Using the promoter of the ctr4(+) copper transporter gene from S. pombe, we created a series of vectors, named pctr4(+)-X, which regulate the expression of heterologous genes as a function of copper availability. In this system, the addition of copper ions at levels that are non-toxic to yeast cells represses gene expression, while copper deprivation strongly induces gene expression. Conveniently, changes of growth medium or carbon sources are not required to shut down or induce gene expression. The Cu-starvation-mediated inducible expression system is rapid, producing heterologous proteins within 3 h, with sustained expression of proteins that persists for several hours. The pctr4(+)-X expression vectors harbor unique restriction sites constructed in-frame to DNA sequences encoding for epitope tags, which facilitate the detection or purification of the heterologous proteins using commercially available antibodies and affinity columns. Furthermore, the pctr4(+)-X copper-regulatable protein expression vectors have been constructed with three different selectable markers, offering more versatility for studying gene function in fission yeast.     

Additive functions in boolean models of gene regulatory network modules

Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome's evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate.     

The Saccharomyces cerevisiae gene SDS22 encodes a potential regulator of the mitotic function of yeast type 1 protein phosphatase.

In higher eukaryotes, the activity and specificity of the type 1 protein serine-threonine phosphatase (PP1) catalytic subunit is thought to be controlled by its association with a number of regulatory or targeting subunits. Here we describe the characterization of a gene encoding one such potential polypeptide in the yeast Saccharomyces cerevisiae. The gene which we have isolated (termed SDS22) encodes a product with a high degree of sequence identity to the fission yeast sds22 protein, a known regulator of the mitotic function of PP1 in Schizosaccharomyces pombe. Using two different criteria, we have demonstrated that Sds22p and the catalytic subunit of PP1 (Glc7p) interact in yeast cells. We have also generated a temperature-sensitive allele of GLC7 (glc7-12) which causes a block to the completion of mitosis at the restrictive temperature. Additional copies of SDS22 lead to allele-specific suppression of the glc7-12 mutant, strongly suggesting that the interaction between the two proteins is of functional significance. Sds22p is therefore likely to be the second example of a PP1 regulatory subunit identified in S. cerevisiae.     

Bottleneck genes and community structure in the cell cycle network of S. pombe

The identification of cell cycle–related genes is still a difficult task, even for organisms with relatively few genes such as the fission yeast. Several gene expression studies have been published on S. pombe showing similarities but also discrepancies in their results. We introduce a network in which the weight of each link is a function of the phase difference between the expression peaks of two genes. The analysis of the stability of the clustering through the computation of an entropy parameter reveals a structure made of four clusters, the first one corresponding to a robustly connected M–G1 component, the second to genes in the S phase, and the third and fourth to two G2 components. They are separated by bottleneck structures that appear to correspond to cell cycle checkpoints. We identify a number of genes that are located on these bottlenecks. They represent a novel group of cell cycle regulatory genes. They all show interesting functions, and they are supposed to be involved in the regulation of the transition from one phase to the next. We therefore present a comparison of the available studies on the fission yeast cell cycle and a general statistical bioinformatics methodology to find bottlenecks and gene community structures based on recent developments in network theory.     

Trade-off between responsiveness and noise suppression in biomolecular system responses to environmental cues

When living systems detect changes in their external environment their response must be measured to balance the need to react appropriately with the need to remain stable, ignoring insignificant signals. Because this is a fundamental challenge of all biological systems that execute programs in response to stimuli, we developed a generalized time-frequency analysis (TFA) framework to systematically explore the dynamical properties of biomolecular networks. Using TFA, we focused on two well-characterized yeast gene regulatory networks responsive to carbon-source shifts and a mammalian innate immune regulatory network responsive to lipopolysaccharides (LPS). The networks are comprised of two different basic architectures. Dual positive and negative feedback loops make up the yeast galactose network; whereas overlapping positive and negative feed-forward loops are common to the yeast fatty-acid response network and the LPS-induced network of macrophages. TFA revealed remarkably distinct network behaviors in terms of trade-offs in responsiveness and noise suppression that are appropriately tuned to each biological response. The wild type galactose network was found to be highly responsive while the oleate network has greater noise suppression ability. The LPS network appeared more balanced, exhibiting less bias toward noise suppression or responsiveness. Exploration of the network parameter space exposed dramatic differences in system behaviors for each network. These studies highlight fundamental structural and dynamical principles that underlie each network, reveal constrained parameters of positive and negative feedback and feed-forward strengths that tune the networks appropriately for their respective biological roles, and demonstrate the general utility of the TFA approach for systems and synthetic biology.