A new measure of the robustness of biochemical networks

MOTIVATION: The robustness of a biochemical network is defined as the tolerance of variations in kinetic parameters with respect to the maintenance of steady state. Robustness also plays an important role in the fail-safe mechanism in the evolutionary process of biochemical networks. The purposes of this paper are to use the synergism and saturation system (S-system) representation to describe a biochemical network and to develop a robustness measure of a biochemical network subject to variations in kinetic parameters. Since most biochemical networks in nature operate close to the steady state, we consider only the robustness measurement of a biochemical network at the steady state. RESULTS: We show that the upper bound of the tolerated parameter variations is related to the system matrix of a biochemical network at the steady state. Using this upper bound, we can calculate the tolerance (robustness) of a biochemical network without testing many parametric perturbations. We find that a biochemical network with a large tolerance can also better attenuate the effects of variations in rate parameters and environments. Compensatory parameter variations and network redundancy are found to be important mechanisms for the robustness of biochemical networks. Finally, four biochemical networks, such as a cascaded biochemical network, the glycolytic-glycogenolytic pathway in a perfused rat liver, the tricarboxylic acid cycle in Dictyostelium discoideum and the cAMP oscillation network in bacterial chemotaxis, are used to illustrate the usefulness of the proposed robustness measure.     

Neural G0: a quiescent‐like state found in neuroepithelial‐derived cells and glioma

Single‐cell RNA sequencing has emerged as a powerful tool for resolving cellular states associated with normal and maligned developmental processes. Here, we used scRNA‐seq to examine the cell cycle states of expanding human neural stem cells (hNSCs). From these data, we constructed a cell cycle classifier that identifies traditional cell cycle phases and a putative quiescent‐like state in neuroepithelial‐derived cell types during mammalian neurogenesis and in gliomas. The Neural G0 markers are enriched with quiescent NSC genes and other neurodevelopmental markers found in non‐dividing neural progenitors. Putative glioblastoma stem‐like cells were significantly enriched in the Neural G0 cell population. Neural G0 cell populations and gene expression are significantly associated with less aggressive tumors and extended patient survival for gliomas. Genetic screens to identify modulators of Neural G0 revealed that knockout of genes associated with the Hippo/Yap and p53 pathways diminished Neural G0 in vitro, resulting in faster G1 transit, down‐regulation of quiescence‐associated markers, and loss of Neural G0 gene expression. Thus, Neural G0 represents a dynamic quiescent‐like state found in neuroepithelial‐derived cells and gliomas.     

Analysis of gene network robustness based on saturated fixed point attractors

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.     

The Escherichia coli FtsH protein is a prokaryotic member of a protein family of putative ATPases involved in membrane functions, cell cycle control, and gene expression.

The ftsH gene is essential for cell viability in Escherichia coli. We cloned and sequenced the wild-type ftsH gene and the temperature-sensitive ftsH1(Ts) gene. It was suggested that FtsH protein was an integral membrane protein of 70.7 kDa (644 amino acid residues) with a putative ATP-binding domain. The ftsH1(Ts) gene was found to have two base substitutions within the coding sequence corresponding to the amino acid substitutions Glu-463 by Lys and Pro-587 by Ala. Homology search revealed that an approximately 200-amino-acid domain, including the putative ATP-binding sequence, is highly homologous (35 to 48% identical) to the domain found in members of a novel, eukaryotic family of putative ATPases, e.g., Sec18p, Pas1p, CDC48p, and TBP-1, which function in protein transport pathways, peroxisome assembly, cell division cycle, and gene expression, respectively. Possible implications of these observations are discussed.     

A Markov-blanket-based model for gene regulatory network inference

An efficient two-step Markov blanket method for modeling and inferring complex regulatory networks from large-scale microarray data sets is presented. The inferred gene regulatory network (GRN) is based on the time series gene expression data capturing the underlying gene interactions. For constructing a highly accurate GRN, the proposed method performs: 1) discovery of a gene's Markov Blanket (MB), 2) formulation of a flexible measure to determine the network's quality, 3) efficient searching with the aid of a guided genetic algorithm, and 4) pruning to obtain a minimal set of correct interactions. Investigations are carried out using both synthetic as well as yeast cell cycle gene expression data sets. The realistic synthetic data sets validate the robustness of the method by varying topology, sample size, time delay, noise, vertex in-degree, and the presence of hidden nodes. It is shown that the proposed approach has excellent inferential capabilities and high accuracy even in the presence of noise. The gene network inferred from yeast cell cycle data is investigated for its biological relevance using well-known interactions, sequence analysis, motif patterns, and GO data. Further, novel interactions are predicted for the unknown genes of the network and their influence on other genes is also discussed.     

Entamoeba histolytica: cloning and expression of the poly(A) polymerase EhPAP

In eukaryotes, polyadenylation of pre-mRNA 3' end is essential for mRNA export, stability, and translation. Here we identified and cloned a gene codifying for a putative nuclear poly(A) polymerase (EhPAP) in Entamoeba histolytica. Protein sequence alignments with eukaryotic PAPs showed that EhPAP has the RNA-binding region and the PAP central domain with the catalytic nucleotidyl transferase domain described for other nuclear PAPs. Recombinant EhPAP expressed in bacteria was used to generate specific antibodies, which recognized two EhPAP isoforms of 60 and 63kDa in nuclear and cytoplasmic extracts by Western blot assays. RT-PCR assays showed that EhPap mRNA expression varies in multidrug-resistant trophozoites growing in different emetine concentrations. Moreover, EhPap mRNA expression is about 10- and 7-fold increased in G1 and S phase, respectively, through cell cycle progression. These results suggest the existence of a link between EhPAP expression and MDR and cell cycle regulation, respectively.     

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.     

Ensemble Modeling for Robustness Analysis in engineering non-native metabolic pathways

Metabolic pathways in cells must be sufficiently robust to tolerate fluctuations in expression levels and changes in environmental conditions. Perturbations in expression levels may lead to system failure due to the disappearance of a stable steady state. Increasing evidence has suggested that biological networks have evolved such that they are intrinsically robust in their network structure. In this article, we presented Ensemble Modeling for Robustness Analysis (EMRA), which combines a continuation method with the Ensemble Modeling approach, for investigating the robustness issue of non-native pathways. EMRA investigates a large ensemble of reference models with different parameters, and determines the effects of parameter drifting until a bifurcation point, beyond which a stable steady state disappears and system failure occurs. A pathway is considered to have high bifurcational robustness if the probability of system failure is low in the ensemble. To demonstrate the utility of EMRA, we investigate the bifurcational robustness of two synthetic central metabolic pathways that achieve carbon conservation: non-oxidative glycolysis and reverse glyoxylate cycle. With EMRA, we determined the probability of system failure of each design and demonstrated that alternative designs of these pathways indeed display varying degrees of bifurcational robustness. Furthermore, we demonstrated that target selection for flux improvement should consider the trade-offs between robustness and performance.     

Wild-type p53 restores cell cycle control and inhibits gene amplification in cells with mutant p53 alleles.

Loss of cell cycle control and acquisition of chromosomal rearrangements such as gene amplification often occur during tumor progression, suggesting that they may be correlated. We show here that the wild-type p53 allele is lost when fibroblasts from patients with the Li-Fraumeni syndrome (LFS) are passaged in vitro. Normal and LFS cells containing wild-type p53 arrested in G1 when challenged with the uridine biosynthesis inhibitor PALA and did not undergo PALA-selected gene amplification. The converse occurred in cells lacking wild-type p53 expression. Expression of wild-type p53 in transformants of immortal and tumor cells containing mutant p53 alleles restored G1 control and reduced the frequency of gene amplification to undetectable levels. These studies reveal that p53 contributes to a metabolically regulated G1 check-point, and they provide a model for understanding how abnormal cell cycle progression leads to the genetic rearrangements involved in tumor progression.     

RASSF1A对黑色素瘤A375细胞基因网络的影响

RASSF1A(Ras association domain family 1 isoform A)是定位于染色体3p21.3区域的抑瘤基因,编码一个由340个氨基酸残基构成的微管相关蛋白.该基因在包括恶性黑色素瘤在内的多种肿瘤中因启动子高甲基化而表达沉默.本研究建立了RASSF1A稳定表达的恶性黑色素瘤A375细胞系,通过全基因组表达谱基因芯片分析RASSF1A过表达对A375细胞基因表达谱的影响,发现RASSF1A引起184个基因表达上调,26个基因表达下调.通过Realtime RT-PCR对部分差异表达基因进行验证,结果表明与芯片筛选结果一致.RASSF1A影响的差异表达基因功能上归属于细胞生长与增殖、细胞周期、细胞凋亡、细胞间黏附、信号传导等生物过程.采用STRING软件构建了RASSF1A影响的差异表达基因调控网络,结果表明RASSF1A调控的差异表达基因构成一个高连接度的基因网络.其中,炎症细胞因子、转录因子位于网络中央.RASSF1A通过影响炎症细胞因子与转录因子之间的表达,影响A375细胞基因网络,调节黑色素瘤恶性生物学行为.     

Synchronization of Caulobacter Crescentus for Investigation of the Bacterial Cell Cycle

The cell cycle is important for growth, genome replication, and development in all cells. In bacteria, studies of the cell cycle have focused largely on unsynchronized cells making it difficult to order the temporal events required for cell cycle progression, genome replication, and division. Caulobacter crescentus provides an excellent model system for the bacterial cell cycle whereby cells can be rapidly synchronized in a G0 state by density centrifugation. Cell cycle synchronization experiments have been used to establish the molecular events governing chromosome replication and segregation, to map a genetic regulatory network controlling cell cycle progression, and to identify the establishment of polar signaling complexes required for asymmetric cell division. Here we provide a detailed protocol for the rapid synchronization of Caulobacter NA1000 cells. Synchronization can be performed in a large-scale format for gene expression profiling and western blot assays, as well as a small-scale format for microscopy or FACS assays. The rapid synchronizability and high cell yields of Caulobacter make this organism a powerful model system for studies of the bacterial cell cycle.     

Quantifying robustness and dissipation cost of yeast cell cycle network: the funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio (RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.