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.     

Topology of gene expression networks as revealed by data mining and modeling

MOTIVATION: Interpretation of high-throughput gene expression profiling requires a knowledge of the design principles underlying the networks that sustain cellular machinery. Recently a novel approach based on the study of network topologies has been proposed. This methodology has proven to be useful for the analysis of a variety of biological systems, including metabolic networks, networks of protein-protein interactions, and gene networks that can be derived from gene expression data. In the present paper, we focus on several important issues related to the topology of gene expression networks that have not yet been fully studied. RESULTS: The networks derived from gene expression profiles for both time series experiments in yeast and perturbation experiments in cell lines are studied. We demonstrate that independent from the experimental organism (yeast versus cell lines) and the type of experiment (time courses versus perturbations) the extracted networks have similar topological characteristics suggesting together with the results of other common principles of the structural organization of biological networks. A novel computational model of network growth that reproduces the basic design principles of the observed networks is presented. Advantage of the model is that it provides a general mechanism to generate networks with different types of topology by a variation of a few parameters. We investigate the robustness of the network structure to random damages and to deliberate removal of the most important parts of the system and show a surprising tolerance of gene expression networks to both kinds of disturbance.     

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.     

Dynamic properties of network motifs contribute to biological network organization

Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property—stability or robustness to small perturbations—is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.     

Tracking of time-varying genomic regulatory networks with a LASSO-Kalman smoother

It is widely accepted that cellular requirements and environmental conditions dictate the architecture of genetic regulatory networks. Nonetheless, the status quo in regulatory network modeling and analysis assumes an invariant network topology over time. In this paper, we refocus on a dynamic perspective of genetic networks, one that can uncover substantial topological changes in network structure during biological processes such as developmental growth. We propose a novel outlook on the inference of time-varying genetic networks, from a limited number of noisy observations, by formulating the network estimation as a target tracking problem. We overcome the limited number of observations (small n large p problem) by performing tracking in a compressed domain. Assuming linear dynamics, we derive the LASSO-Kalman smoother, which recursively computes the minimum mean-square sparse estimate of the network connectivity at each time point. The LASSO operator, motivated by the sparsity of the genetic regulatory networks, allows simultaneous signal recovery and compression, thereby reducing the amount of required observations. The smoothing improves the estimation by incorporating all observations. We track the time-varying networks during the life cycle of the Drosophila melanogaster. The recovered networks show that few genes are permanent, whereas most are transient, acting only during specific developmental phases of the organism.     

Evolving Robust Gene Regulatory Networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.     

Comparative Evolutionary Analysis of Cell Cycle Proteins Networks in Fission and Budding Yeast

Fission yeast and budding yeast are the two distantly related species with common ancestors. Various studies have shown significant differences in metabolic networks and regulatory networks. Cell cycle regulatory proteins in both species have differences in structural as well as in functional organization. Orthologous proteins in cell cycle regulatory protein networks seem to play contemporary role in both species during the evolution but little is known about non-orthologous proteins. Here, we used system biology approach to compare topological parameters of orthologous and non-orthologous proteins to find their contributions during the evolution to make an efficient cell cycle regulation. Observed results have shown a significant role of non-orthologous proteins in fission yeast in maintaining the efficiency of cell cycle regulation with less number of proteins as compared to budding yeast.     

Robustness in phenotypic plasticity and heterogeneity patterns enabled by EMT networks

Epithelial-mesenchymal plasticity (EMP) is a key arm of cancer metastasis and is observed across many contexts. Cells undergoing EMP can reversibly switch between three classes of phenotypes: epithelial (E), mesenchymal (M), and hybrid E/M. While a large number of multistable regulatory networks have been identified to be driving EMP in various contexts, the exact mechanisms and design principles that enable robustness in driving EMP across contexts are not yet fully understood. Here, we investigated dynamic and structural robustness in EMP networks with regard to phenotypic heterogeneity and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous state space Boolean model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yielded similar phenotypic distributions. While the latter approach is useful for measurements of plasticity, the former model enabled us to extensively investigate robustness in phenotypic heterogeneity. Using perturbations to network topology and by varying network parameters, we show that multistable EMP networks are structurally and dynamically more robust compared with their randomized counterparts, thereby highlighting their topological hallmarks. These features of robustness are governed by a balance of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology-based approach to quantify robustness in the phenotypic heterogeneity and plasticity emergent from EMP networks.     

Cell Fate Reprogramming by Control of Intracellular Network Dynamics

Identifying control strategies for biological networks is paramount for practical applications that involve reprogramming a cell’s fate, such as disease therapeutics and stem cell reprogramming. Here we develop a novel network control framework that integrates the structural and functional information available for intracellular networks to predict control targets. Formulated in a logical dynamic scheme, our approach drives any initial state to the target state with 100% effectiveness and needs to be applied only transiently for the network to reach and stay in the desired state. We illustrate our method’s potential to find intervention targets for cancer treatment and cell differentiation by applying it to a leukemia signaling network and to the network controlling the differentiation of helper T cells. We find that the predicted control targets are effective in a broad dynamic framework. Moreover, several of the predicted interventions are supported by experiments.     

Agricultural intensification drives changes in hybrid network robustness by modifying network structure

Within ecological communities, species engage in myriad interaction types, yet empirical examples of hybrid species interaction networks composed of multiple types of interactions are still scarce. A key knowledge gap is understanding how the structure and stability of such hybrid networks are affected by anthropogenic disturbance. Using 15,169 interaction observations, we constructed 16 hybrid herbivore‐plant‐pollinator networks along an agricultural intensification gradient to explore changes in network structure and robustness to local extinctions. We found that agricultural intensification led to declines in modularity but increases in nestedness and connectance. Notably, network connectance, a structural feature typically thought to increase robustness, caused declines in hybrid network robustness, but the directionality of changes in robustness along the gradient depended on the order of local species extinctions. Our results not only demonstrate the impacts of anthropogenic disturbance on hybrid network structure, but they also provide unexpected insights into the structure‐stability relationship of hybrid networks.     

Dynamic-module redundancy confers robustness to the gene regulatory network involved in hair patterning of Arabidopsis epidermis

Redundancy among dynamic modules is emerging as a potentially generic trait in gene regulatory networks. Moreover, module redundancy could play an important role in network robustness to perturbations. We explored the effect of dynamic-module redundancy in the networks associated to hair patterning in Arabidopsis root and leaf epidermis. Recent studies have put forward several dynamic modules belonging to these networks. We defined these modules in a discrete dynamical framework that was previously reported. Then, we addressed whether these modules are sufficient or necessary for recovering epidermal cell types and patterning. After defining two quantitative estimates of the system's robustness, we also compared the robustness of each separate module with that of a network coupling all the leaf or root modules. We found that, considering certain assumptions, all the dynamic modules proposed so far are sufficient on their own for pattern formation, but reinforce each other during epidermal development. Furthermore, we found that networks of coupled modules are more robust to perturbations than single modules. These results suggest that dynamic-module redundancy might be an important trait in gene regulatory networks and point at central questions regarding network evolution, module coupling, pattern robustness and the evolution of development.     

Integration of New Genes into Cellular Networks,and Their Structural Maturation

It has been recently discovered that new genes can originate de novo from noncoding DNA, and several biological traits including expression or sequence composition form a continuum from noncoding sequences to conserved genes. In this article, using yeast genes I test whether the integration of new genes into cellular networks and their structural maturation shows such a continuum by analyzing their changes with gene age. I show that 1) The number of regulatory, protein–protein, and genetic interactions increases continuously with gene age, although with very different rates. New regulatory interactions emerge rapidly within a few million years, while the number of protein–protein and genetic interactions increases slowly, with a rate of 2–2.25 × 10⁻⁸/year and 4.8 × 10⁻⁸/year, respectively. 2) Gene essentiality evolves relatively quickly: the youngest essential genes appear in proto-genes ∼14 MY old. 3) In contrast to interactions, the secondary structure of proteins and their robustness to mutations indicate that new genes face a bottleneck in their evolution: proto-genes are characterized by high β-strand content, high aggregation propensity, and low robustness against mutations, while conserved genes are characterized by lower strand content and higher stability, most likely due to the higher probability of gene loss among young genes and accumulation of neutral mutations.