Wrestling with pleiotropy: genomic and topological analysis of the yeast gene expression network

The vast majority (>95%) of single-gene mutations in yeast affect not only the expression of the mutant gene, but also the expression of many other genes. These data suggest the presence of a previously uncharacterized "gene expression network"--a set of interactions between genes which dictate gene expression in the native cell environment. Here, we quantitatively analyze the gene expression network revealed by microarray expression data from 273 different yeast gene deletion mutants.(1) We find that gene expression interactions form a robust, error-tolerant "scale-free" network, similar to metabolic pathways(2) and artificial networks such as power grids and the internet.(3-5) Because the connectivity between genes in the gene expression network is unevenly distributed, a scale-free organization helps make organisms resistant to the deleterious effects of mutation, and is thus highly adaptive. The existence of a gene expression network poses practical considerations for the study of gene function, since most mutant phenotypes are the result of changes in the expression of many genes. Using principles of scale-free network topology, we propose that fragmenting the gene expression network via "genome-engineering" may be a viable and practical approach to isolating gene function.     

A more efficient search strategy for aging genes based on connectivity

MOTIVATION: Many aging genes have been found from unbiased screens in model organisms. Genetic interventions promoting longevity are usually quantitative, while in many other biological fields (e.g. development) null mutations alone have been very informative. Therefore, in the case of aging the task is larger and the need for a more efficient genetic search strategy is especially strong. RESULTS: The topology of genetic and metabolic networks is organized according to a scale-free distribution, in which hubs with large numbers of links are present. We have developed a computational model of aging genes as the hubs of biological networks. The computational model shows that, after generalized damage, the function of a network with scale-free topology can be significantly restored by a limited intervention on the hubs. Analyses of data on aging genes and biological networks support the applicability of the model to biological aging. The model also might explain several of the properties of aging genes, including the high degree of conservation across different species. The model suggests that aging genes tend to have a higher number of connections and therefore supports a strategy, based on connectivity, for prioritizing what might otherwise be a random search for aging genes.     

Distributed robustness versus redundancy as causes of mutational robustness

A biological system is robust to mutations if it continues to function after genetic changes in its parts. Such robustness is pervasive on different levels of biological organization, from macromolecules to genetic networks and whole organisms. I here ask which of two possible causes of such robustness are more important on a genome-wide scale, for systems whose parts are genes, such as metabolic and genetic networks. The first of the two causes is redundancy of a system's parts: A gene may be dispensable if the genome contains redundant, back-up copies of the gene. The second cause, distributed robustness, is more poorly understood. It emerges from the distributed nature of many biological systems, where many (and different) parts contribute to system functions. I will here discuss evidence suggesting that distributed robustness is equally or more important for mutational robustness than gene redundancy. This evidence comes from the functional divergence of redundant genes, as well as from large-scale gene deletion studies. I also ask whether one can quantify the extent to which redundancy or distributed robustness contribute to mutational robustness.     

Robustness of the p53 network and biological hackers

The p53 protein interaction network is crucial in regulating the metazoan cell cycle and apoptosis. Here, the robustness of the p53 network is studied by analyzing its degeneration under two modes of attack. Linear Programming is used to calculate average path lengths among proteins and the network diameter as measures of functionality. The p53 network is found to be robust to random loss of nodes, but vulnerable to a targeted attack against its hubs, as a result of its architecture. The significance of the results is considered with respect to mutational knockouts of proteins and the directed attacks mounted by tumour inducing viruses.     

Epigenetics Decouples Mutational from Environmental Robustness. Did It Also Facilitate Multicellularity?

The evolution of ever increasing complex life forms has required innovations at the molecular level in order to overcome existing barriers. For example, evolving processes for cell differentiation, such as epigenetic mechanisms, facilitated the transition to multicellularity. At the same time, studies using gene regulatory network models, and corroborated in single-celled model organisms, have shown that mutational robustness and environmental robustness are correlated. Such correlation may constitute a barrier to the evolution of multicellularity since cell differentiation requires sensitivity to cues in the internal environment during development. To investigate how this barrier might be overcome, we used a gene regulatory network model which includes epigenetic control based on the mechanism of histone modification via Polycomb Group Proteins, which evolved in tandem with the transition to multicellularity. Incorporating the Polycomb mechanism allowed decoupling of mutational and environmental robustness, thus allowing the system to be simultaneously robust to mutations while increasing sensitivity to the environment. In turn, this decoupling facilitated cell differentiation which we tested by evaluating the capacity of the system for producing novel output states in response to altered initial conditions. In the absence of the Polycomb mechanism, the system was frequently incapable of adding new states, whereas with the Polycomb mechanism successful addition of new states was nearly certain. The Polycomb mechanism, which dynamically reshapes the network structure during development as a function of expression dynamics, decouples mutational and environmental robustness, thus providing a necessary step in the evolution of multicellularity.     

Inherent size constraints on prokaryote gene networks due to “accelerating” growth

Networks exhibiting “accelerating” growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from non-stationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value.     

Do scale-free regulatory networks allow more expression than random ones?

In this paper, we compile the network of software packages with regulatory interactions (dependences and conflicts) from Debian GNU/Linux operating system and use it as an analogy for a gene regulatory network. Using a trace-back algorithm we assemble networks from the pool of packages with both scale-free (real data) and exponential (null model) topologies. We record the maximum number of packages that can be functionally installed in the system (i.e., the active network size). We show that scale-free regulatory networks allow a larger active network size than random ones. This result might have implications for the number of expressed genes at steady state. Small genomes with scale-free regulatory topologies could allow much more expression than large genomes with exponential topologies. This may have implications for the dynamics, robustness and evolution of genomes.     

A scale-free structure prior for graphical models with applications in functional genomics

The problem of reconstructing large-scale, gene regulatory networks from gene expression data has garnered considerable attention in bioinformatics over the past decade with the graphical modeling paradigm having emerged as a popular framework for inference. Analysis in a full Bayesian setting is contingent upon the assignment of a so-called structure prior-a probability distribution on networks, encoding a priori biological knowledge either in the form of supplemental data or high-level topological features. A key topological consideration is that a wide range of cellular networks are approximately scale-free, meaning that the fraction, , of nodes in a network with degree is roughly described by a power-law with exponent between and . The standard practice, however, is to utilize a random structure prior, which favors networks with binomially distributed degree distributions. In this paper, we introduce a scale-free structure prior for graphical models based on the formula for the probability of a network under a simple scale-free network model. Unlike the random structure prior, its scale-free counterpart requires a node labeling as a parameter. In order to use this prior for large-scale network inference, we design a novel Metropolis-Hastings sampler for graphical models that includes a node labeling as a state space variable. In a simulation study, we demonstrate that the scale-free structure prior outperforms the random structure prior at recovering scale-free networks while at the same time retains the ability to recover random networks. We then estimate a gene association network from gene expression data taken from a breast cancer tumor study, showing that scale-free structure prior recovers hubs, including the previously unknown hub SLC39A6, which is a zinc transporter that has been implicated with the spread of breast cancer to the lymph nodes. Our analysis of the breast cancer expression data underscores the value of the scale-free structure prior as an instrument to aid in the identification of candidate hub genes with the potential to direct the hypotheses of molecular biologists, and thus drive future experiments.     

Sexual Dimorphism Increases Evolvability in a Genetic Regulatory Network

The majority of work on genetic regulatory networks has focused on environmental and mutational robustness, and much less attention has been paid to the conditions under which a network may produce an evolvable phenotype. Sexually dimorphic characters often show rapid rates of change over short evolutionary time scales and while this is thought to be due to the strength of sexual selection acting on the trait, a dimorphic character with an underlying pleiotropic architecture may also influence the evolution of the regulatory network that controls the character and affect evolvability. As evolvability indicates a capacity for phenotypic change and mutational robustness refers to a capacity for phenotypic stasis, increases in evolvability may show a negative relationship with mutational robustness. I tested this with a computational model of a genetic regulatory network and found that, contrary to expectation, sexually dimorphic characters exhibited both higher mutational robustness and higher evolvability. Decomposition of the results revealed that linkage disequilibrium within sex and linkage disequilibrium between sexes, two of the three primary components of additive genetic variance and evolvability in quantitative genetics models, contributed to the differences in evolvability between sexually dimorphic and monomorphic populations. These results indicate that producing two pleiotropically linked characters did not constrain either the production of a robust phenotype or adaptive potential. Instead, the genetic system evolved to maximize both quantities.     

酵母转录调控协作网络的分析

协作网通常被用于描述各种社会关系,相似的概念也可以应用到转录调控网络的研究中.针对被调控基因共享转录因子的相似性,可以建立一个被调控基因协作网,同样,根据转录因子调控基因的相似性可以建立一个相对较小的转录因子协作网.对被调控基因协作网的聚类研究发现,大部分的类都显著地富集一个或者多个GO功能注释.进一步的结果分析发现某些GO注释的基因更倾向于共享相似的调控机制.这表明,在协作网中,相对简单的调控机制相似性能捕捉生物功能相关的信息.并且,将在二部图分析中使用的概念--"异常点"引入到协作网的分析中,发现协作网的异常点和致死基因有相关性.综上所述,协作网的方法是分析转录调控网络的一个有用的补充.