Statistical Analysis of the Spatial Distribution of Operons in the Transcriptional Regulation Network of Escherichia coli

The Spatial Organization of Bacterial Transcriptional Regulatory Networks

The transcriptional regulatory network (TRN) is the central pivot of a prokaryotic organism to receive, process and respond to internal and external environmental information. However, little is known about its spatial organization so far. In recent years, chromatin interaction data of bacteria such as Escherichia coli and Bacillus subtilis have been published, making it possible to study the spatial organization of bacterial transcriptional regulatory networks. By combining TRNs and chromatin interaction data of E. coli and B. subtilis, we explored the spatial organization characteristics of bacterial TRNs in many aspects such as regulation directions (positive and negative), central nodes (hubs, bottlenecks), hierarchical levels (top, middle, bottom) and network motifs (feed-forward loops and single input modules) of the TRNs and found that the bacterial TRNs have a variety of stable spatial organization features under different physiological conditions that may be closely related with biological functions. Our findings provided new insights into the connection between transcriptional regulation and the spatial organization of chromosome in bacteria and might serve as a factual foundation for trying spatial-distance-based gene circuit design in synthetic biology.

The economy of chromosomal distances in bacterial gene regulation

In the transcriptional regulatory network (TRN) of a bacterium, the nodes are genes and a directed edge represents the action of a transcription factor (TF), encoded by the source gene, on the target gene. It is a condensed representation of a large number of biological observations and facts. Nonrandom features of the network are structural evidence of requirements for a reliable systemic function. For the bacterium Escherichia coli we here investigate the (Euclidean) distances covered by the edges in the TRN when its nodes are embedded in the real space of the circular chromosome. Our work is motivated by 'wiring economy' research in Computational Neuroscience and starts from two contradictory hypotheses: (1) TFs are predominantly employed for long-distance regulation, while local regulation is exerted by chromosomal structure, locally coordinated by the action of structural proteins. Hence long distances should often occur. (2) A large distance between the regulator gene and its target requires a higher expression level of the regulator gene due to longer reaching times and ensuing increased degradation (proteolysis) of the TF and hence will be evolutionarily reduced. Our analysis supports the latter hypothesis.

PhotoModPlus: A web server for photosynthetic protein prediction from genome neighborhood features

A new web server called PhotoModPlus is presented as a platform for predicting photosynthetic proteins via genome neighborhood networks (GNN) and genome neighborhood-based machine learning. GNN enables users to visualize the overview of the conserved neighboring genes from multiple photosynthetic prokaryotic genomes and provides functional guidance on the query input. In the platform, we also present a new machine learning model utilizing genome neighborhood features for predicting photosynthesis-specific functions based on 24 prokaryotic photosynthesis-related GO terms, namely PhotoModGO. The new model performed better than the sequence-based approaches with an F1 measure of 0.872, based on nested five-fold cross-validation. Finally, we demonstrated the applications of the webserver and the new model in the identification of novel photosynthetic proteins. The server is user-friendly, compatible with all devices, and available at bicep.kmutt.ac.th/photomod.

Photosynthetic protein classification using genome neighborhood-based machine learning feature

Identification of novel photosynthetic proteins is important for understanding and improving photosynthetic efficiency. Synergistically, genome neighborhood can provide additional useful information to identify photosynthetic proteins. We, therefore, expected that applying a computational approach, particularly machine learning (ML) with the genome neighborhood-based feature should facilitate the photosynthetic function assignment. Our results revealed a functional relationship between photosynthetic genes and their conserved neighboring genes observed by 'Phylo score', indicating their functions could be inferred from the genome neighborhood profile. Therefore, we created a new method for extracting patterns based on the genome neighborhood network (GNN) and applied them for the photosynthetic protein classification using ML algorithms. Random forest (RF) classifier using genome neighborhood-based features achieved the highest accuracy up to 87% in the classification of photosynthetic proteins and also showed better performance (Mathew's correlation coefficient = 0.718) than other available tools including the sequence similarity search (0.447) and ML-based method (0.361). Furthermore, we demonstrated the ability of our model to identify novel photosynthetic proteins compared to the other methods. Our classifier is available at http://bicep2.kmutt.ac.th/photomod_standalone, https://bit.ly/2S0I2Ox and DockerHub: https://hub.docker.com/r/asangphukieo/photomod.

Chromosomal origin of replication coordinates logically distinct types of bacterial genetic regulation

For a long time it has been hypothesized that bacterial gene regulation involves an intricate interplay of the transcriptional regulatory network (TRN) and the spatial organization of genes in the chromosome. Here we explore this hypothesis both on a structural and on a functional level. On the structural level, we study the TRN as a spatially embedded network. On the functional level, we analyze gene expression patterns from a network perspective (“digital control”), as well as from the perspective of the spatial organization of the chromosome (“analog control”). Our structural analysis reveals the outstanding relevance of the symmetry axis defined by the origin (Ori) and terminus (Ter) of replication for the network embedding and, thus, suggests the co-evolution of two regulatory infrastructures, namely the transcriptional regulatory network and the spatial arrangement of genes on the chromosome, to optimize the cross-talk between two fundamental biological processes: genomic expression and replication. This observation is confirmed by the functional analysis based on the differential gene expression patterns of more than 4000 pairs of microarray and RNA-Seq datasets for E. coli from the Colombos Database using complex network and machine learning methods. This large-scale analysis supports the notion that two logically distinct types of genetic control are cooperating to regulate gene expression in a complementary manner. Moreover, we find that the position of the gene relative to the Ori is a feature of very high predictive value for gene expression, indicating that the Ori–Ter symmetry axis coordinates the action of distinct genetic control mechanisms.

A Model for the Spatiotemporal Design of Gene Regulatory Circuits †

Mathematical modeling assists the design of synthetic regulatory networks by providing a detailed mechanistic understanding of biological systems. Models that can predict the performance of a design are fundamental for synthetic biology since they minimize iterations along the design-build-test lifecycle. Such predictability depends crucially on what assumptions (i.e., biological simplifications) the model considers. Here, we challenge a common assumption when it comes to the modeling of bacterial-based gene regulation: considering negligible the effects of intracellular physical space. It is commonly assumed that molecules, such as transcription factors (TF), are homogeneously distributed inside a cell, so there is no need to model their diffusion. We describe a mathematical model that accounts for molecular diffusion and show how simulations of network performance are decisively affected by the distance between its components. Specifically, the model focuses on the search by a TF for its target promoter. The combination of local searches, via one-dimensional sliding along the chromosome, and global searches, via three-dimensional diffusion through the cytoplasm, determine TF-promoter interplay. Previous experimental results with engineered bacteria in which the distance between TF source and target was minimized or enlarged were successfully reproduced by the spatially resolved model we introduce here. This suggests that the spatial specification of the circuit alone can be exploited as a design parameter in synthetic biology to select programmable output levels.

The E. coli transcriptional regulatory network and its spatial embedding

Usually complex networks are studied as graphs consisting of nodes whose spatial arrangement is of no significance. Several real biological networks are, however, embedded in space. In this paper we study the transcription regulatory network (TRN) of E. coli as a spatially embedded network. The embedding space of this network is the circular E. coli chromosome, i.e. it is practically one dimensional. However, the TRN itself is a high-dimensional network due to the existence of an adequate number of long-range connections. We find that nodes in short topological distance l = 1, 2 tend, on average, to be in shorter spatial distances r indicating an abundance of short-range connections as well. Community analysis of the TRN reveals the interesting fact that highly interconnected subnets consist of nodes that tend to be in spatial proximity on the circular chromosome. We also find indications that for certain transcriptional aspects of the E. coli it is advantageous to treat the circular genome as two line segments starting from the OriC and ending to Ter.

Deconvolution of Gene Expression Noise into Spatial Dynamics of Transcription Factor-Promoter Interplay

Gene expression noise is not only the mere consequence of stochasticity, but also a signal that reflects the upstream physical dynamics of the cognate molecular machinery. Soil bacteria facing recalcitrant pollutants exploit noise of catabolic promoters to deploy beneficial phenotypes such as metabolic bet-hedging and/or division of biochemical labor. Although the role of upstream promoter-regulator interplay in the origin of this noise is little understood, its specifications are probably ciphered in flow cytometry data patterns. We studied Pm promoter activity of the environmental bacterium Pseudomonas putida and its cognate regulator XylS by following expression of Pm-gfp fusions in single cells. Using mathematical modeling and computational simulations, we determined the kinetic properties of the system and used them as a baseline code to interpret promoter activity in terms of upstream regulator dynamics. Transcriptional noise was predicted to depend on the intracellular physical distance between regulator source (where XylS is produced) and the target promoter. Experiments with engineered bacteria in which this distance is minimized or enlarged confirmed the predicted effects of source/target proximity on noise patterns. This approach allowed deconvolution of cytometry data into mechanistic information on gene expression flow. It also provided a basis for selecting programmable noise levels in synthetic regulatory circuits.

Supra-operonic clusters of functionally related genes (SOCs) are a source of horizontal gene co-transfers

Adaptation of bacteria occurs predominantly via horizontal gene transfer (HGT). While it is widely recognized that horizontal acquisitions frequently encompass multiple genes, it is unclear what the size distribution of successfully transferred DNA segments looks like and what evolutionary forces shape this distribution. Here, we identified 1790 gene family pairs that were consistently co-gained on the same branches across a phylogeny of 53 E. coli strains. We estimated a lower limit of their genomic distances at the time they were transferred to their host genomes; this distribution shows a sharp upper bound at 30 kb. The same gene-pairs can have larger distances (up to 70 kb) in other genomes. These more distant pairs likely represent recent acquisitions via transduction that involve the co-transfer of excised prophage genes, as they are almost always associated with intervening phage-associated genes. The observed distribution of genomic distances of co-transferred genes is much broader than expected from a model based on the co-transfer of genes within operons; instead, this distribution is highly consistent with the size distribution of supra-operonic clusters (SOCs), groups of co-occurring and co-functioning genes that extend beyond operons. Thus, we propose that SOCs form a basic unit of horizontal gene transfer.

Coevolution of the Organization and Structure of Prokaryotic Genomes

The cytoplasm of prokaryotes contains many molecular machines interacting directly with the chromosome. These vital interactions depend on the chromosome structure, as a molecule, and on the genome organization, as a unit of genetic information. Strong selection for the organization of the genetic elements implicated in these interactions drives replicon ploidy, gene distribution, operon conservation, and the formation of replication-associated traits. The genomes of prokaryotes are also very plastic with high rates of horizontal gene transfer and gene loss. The evolutionary conflicts between plasticity and organization lead to the formation of regions with high genetic diversity whose impact on chromosome structure is poorly understood. Prokaryotic genomes are remarkable documents of natural history because they carry the imprint of all of these selective and mutational forces. Their study allows a better understanding of molecular mechanisms, their impact on microbial evolution, and how they can be tinkered in synthetic biology.

DNA-binding-protein inhomogeneity in E. coli modeled as biphasic facilitated diffusion

We have recently shown that nonspecifically bound lac repressors are spatially inhomogeneous in E. coli cells and depends upon the location of its encoding gene and the DNA compaction state [Kuhlman and Cox, Mol. Syst. Biol. 8, 610 (2012)]. Here we model this inhomogeneity as a consequence of diffusion within and exchange between two distinct intracellular phases: the condensed chromosomal DNA and an extrachromosomal compartment, the cytoplasm. We discuss the consequences of this model for the target search process.

Biological signal processing with a genetic toggle switch

Complex gene regulation requires responses that depend not only on the current levels of input signals but also on signals received in the past. In digital electronics, logic circuits with this property are referred to as sequential logic, in contrast to the simpler combinatorial logic without such internal memory. In molecular biology, memory is implemented in various forms such as biochemical modification of proteins or multistable gene circuits, but the design of the regulatory interface, which processes the input signals and the memory content, is often not well understood. Here, we explore design constraints for such regulatory interfaces using coarse-grained nonlinear models and stochastic simulations of detailed biochemical reaction networks. We test different designs for biological analogs of the most versatile memory element in digital electronics, the JK-latch. Our analysis shows that simple protein-protein interactions and protein-DNA binding are sufficient, in principle, to implement genetic circuits with the capabilities of a JK-latch. However, it also exposes fundamental limitations to its reliability, due to the fact that biological signal processing is asynchronous, in contrast to most digital electronics systems that feature a central clock to orchestrate the timing of all operations. We describe a seemingly natural way to improve the reliability by invoking the master-slave concept from digital electronics design. This concept could be useful to interpret the design of natural regulatory circuits, and for the design of synthetic biological systems.

Minimal effect of gene clustering on expression in Escherichia coli

Genes that interact or function together are often clustered in bacterial genomes, and it has been proposed that this clustering may affect gene expression. In this study, we directly compared gene expression in nonclustered arrangements and in three common clustered arrangements (codirectional, divergent, and operon) using synthetic circuits in Escherichia coli. We found that gene clustering had minimal effects on gene expression. Specifically, gene clustering did not alter constitutive expression levels or stochastic fluctuations in expression ("expression noise"). Remarkably, the expression of two genes that share the same chromosome position with the same promoter (operon) or with separate promoters (codirectional and divergent arrangements) was not significantly more correlated than genes at different chromosome positions (nonclustered arrangements). The only observed effect of clustering was increased transcription factor binding in codirectional and divergent gene arrangements due to DNA looping, but this is not a specific feature of clustering. In summary, we demonstrate that gene clustering is not a general modulator of gene expression, and therefore any effects of clustering are likely to occur only with specific genes or under certain conditions.

Physical descriptions of the bacterial nucleoid at large scales, and their biological implications

Recent experimental and theoretical approaches have attempted to quantify the physical organization (compaction and geometry) of the bacterial chromosome with its complement of proteins (the nucleoid). The genomic DNA exists in a complex and dynamic protein-rich state, which is highly organized at various length scales. This has implications for modulating (when not directly enabling) the core biological processes of replication, transcription and segregation. We overview the progress in this area, driven in the last few years by new scientific ideas and new interdisciplinary experimental techniques, ranging from high space- and time-resolution microscopy to high-throughput genomics employing sequencing to map different aspects of the nucleoid-related interactome. The aim of this review is to present the wide spectrum of experimental and theoretical findings coherently, from a physics viewpoint. In particular, we highlight the role that statistical and soft condensed matter physics play in describing this system of fundamental biological importance, specifically reviewing classic and more modern tools from the theory of polymers. We also discuss some attempts toward unifying interpretations of the current results, pointing to possible directions for future investigation.

Gene location and DNA density determine transcription factor distributions in Escherichia coli

The diffusion coefficient of the transcription factor LacI within living Escherichia coli has been measured directly by in vivo tracking to be D = 0.4 μm(2)/s. At this rate, simple models of diffusion lead to the expectation that LacI and other proteins will rapidly homogenize throughout the cell. Here, we test this expectation of spatial homogeneity by single-molecule visualization of LacI molecules non-specifically bound to DNA in fixed cells. Contrary to expectation, we find that the distribution depends on the spatial location of its encoding gene. We demonstrate that the spatial distribution of LacI is also determined by the local state of DNA compaction, and that E. coli can dynamically redistribute proteins by modifying the state of its nucleoid. Finally, we show that LacI inhomogeneity increases the strength with which targets located proximally to the LacI gene are regulated. We propose a model for intranucleoid diffusion that can reconcile these results with previous measurements of LacI diffusion, and we discuss the implications of these findings for gene regulation in bacteria and eukaryotes.

The operonic location of auto-transcriptional repressors is highly conserved in bacteria

Bacterial genes are commonly encoded in clusters, known as operons, which share transcriptional regulatory control and often encode functionally related proteins that take part in certain biological pathways. Operons that are coregulated are known to colocalize in the genome, suggesting that their spatial organization is under selection for efficient expression regulation. However, the internal order of genes within operons is believed to be poorly conserved, and hence expression requirements are claimed to be too weak to oppose gene rearrangements. In light of these opposing views, we set out to investigate whether the internal location of the regulatory genes within operons is under selection. Our analysis shows that transcription factors (TFs) are preferentially encoded as either first or last in their operons, in the two diverged model bacteria Escherichia coli and Bacillus subtilis. In a higher resolution, we find that TFs that repress transcription of the operon in which they are encoded (autorepressors), contribute most of this signal by specific preference of the first operon position. We show that this trend is strikingly conserved throughout highly diverged bacterial phyla. Moreover, these autorepressors regulate operons that carry out highly diverse biological functions. We propose a model according to which autorepressors are selected to be located first in their operons in order to optimize transcription regulation. Specifically, the first operon position helps autorepressors to minimize leaky transcription of the operon structural genes, thus minimizing energy waste. Our analysis provides statistically robust evidence for a paradigm of bacterial autorepressor preferential operonic location. Corroborated with our suggested model, an additional layer of operon expression control that is common throughout the bacterial domain is revealed.

Local gene regulation details a recognition code within the LacI transcriptional factor family

The specific binding of regulatory proteins to DNA sequences exhibits no clear patterns of association between amino acids (AAs) and nucleotides (NTs). This complexity of protein-DNA interactions raises the question of whether a simple set of wide-coverage recognition rules can ever be identified. Here, we analyzed this issue using the extensive LacI family of transcriptional factors (TFs). We searched for recognition patterns by introducing a new approach to phylogenetic footprinting, based on the pervasive presence of local regulation in prokaryotic transcriptional networks. We identified a set of specificity correlations –determined by two AAs of the TFs and two NTs in the binding sites– that is conserved throughout a dominant subgroup within the family regardless of the evolutionary distance, and that act as a relatively consistent recognition code. The proposed rules are confirmed with data of previous experimental studies and by events of convergent evolution in the phylogenetic tree. The presence of a code emphasizes the stable structural context of the LacI family, while defining a precise blueprint to reprogram TF specificity with many practical applications.

Transcriptional factors (TF) are proteins that bind specific short DNA sequences adjacent to the genes whose transcription they regulate. Although the nucleotide sequence recognized by a given regulator depends on the amino acids contacting the DNA, the mode in which amino acids and nucleotides interact is strongly influenced by the overall protein structure. This prevents the existence of a universal amino acid/nucleotide recognition code. However, recognition rules could be formulated for regulators sharing a similar structure, i.e., for a family or subfamily of TFs. In fact, such rules have already been described for several sets which, in each case, involved a limited number of related TFs. In this study, we ask to what extent a wide-coverage recognition code might actually be found. To answer this question, we use the extensive LacI family of transcriptional regulators. Our analysis suggests that a set of relatively consistent recognition rules does apply within a major subset of this family. These rules could ultimately act as a blueprint for the synthetic redesign of TFs with new specificities.

Periodic pattern detection in sparse boolean sequences

Background

The specific position of functionally related genes along the DNA has been shown to reflect the interplay between chromosome structure and genetic regulation. By investigating the statistical properties of the distances separating such genes, several studies have highlighted various periodic trends. In many cases, however, groups built up from co-functional or co-regulated genes are small and contain wrong information (data contamination) so that the statistics is poorly exploitable. In addition, gene positions are not expected to satisfy a perfectly ordered pattern along the DNA. Within this scope, we present an algorithm that aims to highlight periodic patterns in sparse boolean sequences, i.e. sequences of the type 010011011010... where the ratio of the number of 1's (denoting here the transcription start of a gene) to 0's is small.

Results

The algorithm is particularly robust with respect to strong signal distortions such as the addition of 1's at arbitrary positions (contaminated data), the deletion of existing 1's in the sequence (missing data) and the presence of disorder in the position of the 1's (noise). This robustness property stems from an appropriate exploitation of the remarkable alignment properties of periodic points in solenoidal coordinates.

Conclusions

The efficiency of the algorithm is demonstrated in situations where standard Fourier-based spectral methods are poorly adapted. We also show how the proposed framework allows to identify the 1's that participate in the periodic trends, i.e. how the framework allows to allocate a positional score to genes, in the same spirit of the sequence score. The software is available for public use at http://www.issb.genopole.fr/MEGA/Softwares/iSSB_SolenoidalApplication.zip.

Ranges of control in the transcriptional regulation of Escherichia coli

BACKGROUND

The positioning of genes in the genome is an important evolutionary degree of freedom for organizing gene regulation. Statistical properties of these distributions have been studied particularly in relation to the transcriptional regulatory network. The systematics of gene-gene distances then become important sources of information on the control, which different biological mechanisms exert on gene expression.

RESULTS

Here we study a set of categories, which has to our knowledge not been analyzed before. We distinguish between genes that do not participate in the transcriptional regulatory network (i.e. that are according to current knowledge not producing transcription factors and do not possess binding sites for transcription factors in their regulatory region), and genes that via transcription factors either are regulated by or regulate other genes. We find that the two types of genes ("isolated" and "regulatory" genes) show a clear statistical repulsion and have different ranges of correlations. In particular we find that isolated genes have a preference for shorter intergenic distances.

CONCLUSIONS

These findings support previous evidence from gene expression patterns for two distinct logical types of control, namely digital control (i.e. network-based control mediated by dedicated transcription factors) and analog control (i.e. control based on genome structure and mediated by neighborhood on the genome).

Information content based model for the topological properties of the gene regulatory network of Escherichia coli

Gene regulatory networks (GRN) are being studied with increasingly precise quantitative tools and can provide a testing ground for ideas regarding the emergence and evolution of complex biological networks. We analyze the global statistical properties of the transcriptional regulatory network of the prokaryote Escherichia coli, identifying each operon with a node of the network. We propose a null model for this network using the content-based approach applied earlier to the eukaryote Saccharomyces cerevisiae (Balcan et al., 2007). Random sequences that represent promoter regions and binding sequences are associated with the nodes. The length distributions of these sequences are extracted from the relevant databases. The network is constructed by testing for the occurrence of binding sequences within the promoter regions. The ensemble of emergent networks yields an exponentially decaying in-degree distribution and a putative power law dependence for the out-degree distribution with a flat tail, in agreement with the data. The clustering coefficient, degree-degree correlation, rich club coefficient and k-core visualization all agree qualitatively with the empirical network to an extent not yet achieved by any other computational model, to our knowledge. The significant statistical differences can point the way to further research into non-adaptive and adaptive processes in the evolution of the E. coli GRN.

Operons

Operons (clusters of co-regulated genes with related functions) are common features of bacterial genomes. More recently, functional gene clustering has been reported in eukaryotes, from yeasts to filamentous fungi, plants, and animals. Gene clusters can consist of paralogous genes that have most likely arisen by gene duplication. However, there are now many examples of eukaryotic gene clusters that contain functionally related but non-homologous genes and that represent functional gene organizations with operon-like features (physical clustering and co-regulation). These include gene clusters for use of different carbon and nitrogen sources in yeasts, for production of antibiotics, toxins, and virulence determinants in filamentous fungi, for production of defense compounds in plants, and for innate and adaptive immunity in animals (the major histocompatibility locus). The aim of this article is to review features of functional gene clusters in prokaryotes and eukaryotes and the significance of clustering for effective function.

How subdiffusion changes the kinetics of binding to a surface

Under molecular crowding conditions, biopolymers have been reported to subdiffuse, (r(2)(t)) approximately = t(alpha), with 0 <alpha < 1. Here we study the exchange dynamics of such a subdiffusing particle with a reactive boundary using a continuous time random walk approach. We derive the generalized boundary condition and consider the unbinding from the boundary. An ensuing weak ergodicity breaking has profound consequences for material exchange between the boundary and bulk. We discuss the effects in biological contexts such as gene regulation or membrane-bulk exchange processes. We also suggest various methods to experimentally probe the subdiffusive behavior.

Transcriptional regulation shapes the organization of genes on bacterial chromosomes

Transcription factors (TFs) are the key elements responsible for controlling the expression of genes in bacterial genomes and when visualized on a genomic scale form a dense network of transcriptional interactions among themselves and with other protein coding genes. Although the structure of transcriptional regulatory networks (TRNs) is well understood, it is not clear what constrains govern them. Here, we explore this question using the TRNs of model prokaryotes and provide a link between the transcriptional hierarchy of regulons and their genome organization. We show that, to drive the kinetics and concentration gradients, TFs belonging to big and small regulons, depending on the number of genes they regulate, organize themselves differently on the genome with respect to their targets. We then propose a conceptual model that can explain how the hierarchical structure of TRNs might be ultimately governed by the dynamic biophysical requirements for targeting DNA-binding sites by TFs. Our results suggest that the main parameters defining the position of a TF in the network hierarchy are the number and chromosomal distances of the genes they regulate and their protein concentration gradients. These observations give insights into how the hierarchical structure of transcriptional networks can be encoded on the chromosome to drive the kinetics and concentration gradients of TFs depending on the number of genes they regulate and could be a common theme valid for other prokaryotes, proposing the role of transcriptional regulation in shaping the organization of genes on a chromosome.

Recurring cluster and operon assembly for Phenylacetate degradation genes

Background

A large number of theories have been advanced to explain why genes involved in the same biochemical processes are often co-located in genomes. Most of these theories have been dismissed because empirical data do not match the expectations of the models. In this work we test the hypothesis that cluster formation is most likely due to a selective pressure to gradually co-localise protein products and that operon formation is not an inevitable conclusion of the process.

Results

We have selected an exemplar well-characterised biochemical pathway, the phenylacetate degradation pathway, and we show that its complex history is only compatible with a model where a selective advantage accrues from moving genes closer together. This selective pressure is likely to be reasonably weak and only twice in our dataset of 102 genomes do we see independent formation of a complete cluster containing all the catabolic genes in the pathway. Additionally, de novo clustering of genes clearly occurs repeatedly, even though recombination should result in the random dispersal of such genes in their respective genomes. Interspecies gene transfer has frequently replaced in situ copies of genes resulting in clusters that have similar content but very different evolutionary histories.

Conclusion

Our model for cluster formation in prokaryotes, therefore, consists of a two-stage selection process. The first stage is selection to move genes closer together, either because of macromolecular crowding, chromatin relaxation or transcriptional regulation pressure. This proximity opportunity sets up a separate selection for co-transcription.

The organization of the bacterial genome

Many bacterial cellular processes interact intimately with the chromosome. Such interplay is the major driving force of genome structure or organization. Interactions take place at different scales-local for gene expression, global for replication-and lead to the differentiation of the chromosome into organizational units such as operons, replichores, or macrodomains. These processes are intermingled in the cell and create complex higher-level organizational features that are adaptive because they favor the interplay between the processes. The surprising result of selection for genome organization is that gene repertoires change much more quickly than chromosomal structure. Comparative genomics and experimental genomic manipulations are untangling the different cellular and evolutionary mechanisms causing such resilience to change. Since organization results from cellular processes, a better understanding of chromosome organization will help unravel the underlying cellular processes and their diversity.

Functional models for large-scale gene regulation networks: realism and fiction

High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different conditions, times, environments. We now possess a certain amount of information about these two levels of description, stored in libraries, databases and ontologies. A current challenge is to bridge the gap between topology and function, i.e. developing quantitative models aimed at characterizing the expression patterns of large sets of genes. However, approaches that work well for small networks become impossible to master at large scales, mainly because parameters proliferate. In this review we discuss the state of the art of large-scale functional network models, addressing the issue of what can be considered as "realistic" and what the main limitations may be. We also show some directions for future work, trying to set the goals that future models should try to achieve. Finally, we will emphasize the possible benefits in the understanding of biological mechanisms underlying complex multifactorial diseases, and in the development of novel strategies for the description and the treatment of such pathologies.

Single DNA denaturation and bubble dynamics

While the Watson-Crick double-strand is the thermodynamically stable state of DNA in a wide range of temperature and salt conditions, even at physiological conditions local denaturation bubbles may open up spontaneously due to thermal activation. By raising the ambient temperature, titration, or by external forces in single molecule setups bubbles proliferate until full denaturation of the DNA occurs. Based on the Poland-Scheraga model we investigate both the equilibrium transition of DNA denaturation and the dynamics of the denaturation bubbles with respect to recent single DNA chain experiments for situations below, at, and above the denaturation transition. We also propose a new single molecule setup based on DNA constructs with two bubble zones to measure the bubble coalescence and extract the physical parameters relevant to DNA breathing. Finally we consider the interplay between denaturation bubbles and selectively single-stranded DNA binding proteins.

What determines the assembly of transcriptional network motifs in Escherichia coli?

Transcriptional networks are constituted by a collection of building blocks known as network motifs. Why do motifs appear? An adaptive model of motif emergence was recently questioned in favor of neutralist scenarios. Here, we provide a new picture of motif assembly in Escherichia coli which partially clarifies these contrasting explanations. This is based on characterizing the linkage between motifs and sensing or response specificity of their constituent transcriptional factors (TFs). We find that sensing specificity influences the distribution of autoregulation, while the tendency of a TF to establish feed-forward loops (FFLs) depends on response specificity, i.e., regulon size. Analysis of the latter pattern reveals that coregulation between large regulon-size TFs is common under a network neutral model, leading to the assembly of a great number of FFLs and bifans. In addition, neutral exclusive regulation also leads to a collection of single input modules -the fourth basic motif. On the whole, and even under the conservative neutralist scenario considered, a substantial group of regulatory structures revealed adaptive. These structures visibly function as fully-fledged working units.

Spatial effects on the speed and reliability of protein-DNA search

Strong experimental and theoretical evidence shows that transcription factors (TFs) and other specific DNA-binding proteins find their sites using a two-mode search: alternating between three-dimensional (3D) diffusion through the cell and one-dimensional (1D) sliding along the DNA. We show that, due to the 1D component of the search process, the search time of a TF can depend on the initial position of the TF. We formalize this effect by discriminating between two types of searches: global and local. Using analytical calculations and simulations, we estimate how close a TF and binding site need to be to make a local search likely. We then use our model to interpret the wide range of experimental measurements of this parameter. We also show that local and global searches differ significantly in average search time and the variability of search time. These results lead to a number of biological implications, including suggestions of how prokaryotes achieve rapid gene regulation and the relationship between the search mechanism and noise in gene expression. Lastly, we propose a number of experiments to verify the existence and quantify the extent of spatial effects on the TF search process in prokaryotes.

Chance and necessity in chromosomal gene distributions

By analyzing the spacing of genes on chromosomes, we find that transcriptional and RNA-processing regulatory sequences outside coding regions leave footprints on the distribution of intergenic distances. Using analogies between genes on chromosomes and one-dimensional gases, we constructed a statistical null model. We used this to estimate typical upstream and downstream regulatory sequence sizes in various species. Deviations from this model reveal bi-directional transcriptional regulatory regions in Saccharomyces cerevisiae and bi-directional terminators in Escherichia coli.

How gene order is influenced by the biophysics of transcription regulation

What are the forces that shape the structure of prokaryotic genomes: the order of genes, their proximity, and their orientation? Coregulation and coordinated horizontal gene transfer are believed to promote the proximity of functionally related genes and the formation of operons. However, forces that influence the structure of the genome beyond the level of a single operon remain unknown. Here, we show that the biophysical mechanism by which regulatory proteins search for their sites on DNA can impose constraints on genome structure. Using simulations, we demonstrate that rapid and reliable gene regulation requires that the transcription factor (TF) gene be close to the site on DNA the TF has to bind, thus promoting the colocalization of TF genes and their targets on the genome. We use parameters that have been measured in recent experiments to estimate the relevant length and times scales of this process and demonstrate that the search for a cognate site may be prohibitively slow if a TF has a low copy number and is not colocalized. We also analyze TFs and their sites in a number of bacterial genomes, confirm that they are colocalized significantly more often than expected, and show that this observation cannot be attributed to the pressure for coregulation or formation of selfish gene clusters, thus supporting the role of the biophysical constraint in shaping the structure of prokaryotic genomes. Our results demonstrate how spatial organization can influence timing and noise in gene expression.

Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with a finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with an identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar.

Locational distribution of gene functional classes in Arabidopsis thaliana

Background

We are interested in understanding the locational distribution of genes and their functions in genomes, as this distribution has both functional and evolutionary significance. Gene locational distribution is known to be affected by various evolutionary processes, with tandem duplication thought to be the main process producing clustering of homologous sequences. Recent research has found clustering of protein structural families in the human genome, even when genes identified as tandem duplicates have been removed from the data. However, this previous research was hindered as they were unable to analyse small sample sizes. This is a challenge for bioinformatics as more specific functional classes have fewer examples and conventional statistical analyses of these small data sets often produces unsatisfactory results.

Results

We have developed a novel bioinformatics method based on Monte Carlo methods and Greenwood's spacing statistic for the computational analysis of the distribution of individual functional classes of genes (from GO). We used this to make the first comprehensive statistical analysis of the relationship between gene functional class and location on a genome. Analysis of the distribution of all genes except tandem duplicates on the five chromosomes of A. thaliana reveals that the distribution on chromosomes I, II, IV and V is clustered at P = 0.001. Many functional classes are clustered, with the degree of clustering within an individual class generally consistent across all five chromosomes. A novel and surprising result was that the locational distribution of some functional classes were significantly more evenly spaced than would be expected by chance.

Conclusion

Analysis of the A. thaliana genome reveals evidence of unexplained order in the locational distribution of genes. The same general analysis method can be applied to any genome, and indeed any sequential data involving classes.

Hierarchy and feedback in the evolution of the Escherichia coli transcription network

The Escherichia coli transcription network has an essentially feedforward structure, with abundant feedback at the level of self-regulations. Here, we investigate how these properties emerged during evolution. An assessment of the role of gene duplication based on protein domain architecture shows that (i) transcriptional autoregulators have mostly arisen through duplication, whereas (ii) the expected feedback loops stemming from their initial cross-regulation are strongly selected against. This requires a divergent coevolution of the transcription factor DNA-binding sites and their respective DNA cis-regulatory regions. Moreover, we find that the network tends to grow by expansion of the existing hierarchical layers of computation, rather than by addition of new layers. We also argue that rewiring of regulatory links due to mutation/selection of novel transcription factor/DNA binding interactions appears not to significantly affect the network global hierarchy, and that horizontally transferred genes are mainly added at the bottom, as new target nodes. These findings highlight the important evolutionary roles of both duplication and selective deletion of cross-talks between autoregulators in the emergence of the hierarchical transcription network of E. coli.

Internal versus external effector and transcription factor gene pairs differ in their relative chromosomal position in Escherichia coli

Transcription factors (TFs) play an important role in the genetic regulation of transcription in response to internal and external cellular stimuli. However, little is known about their functional and dynamic aspects on a large scale, even in a well-studied bacterium like Escherichia coli. To understand the regulatory dynamics and to improve our knowledge about how TFs respond to endogenous and exogenous signals in this simple bacterium model, we previously proposed that TFs can be classified into three classes, depending on how they sense their allosteric or equivalent metabolite: external class, internal class, and hybrid sensing class. Classification of these groups was done without considering the relative chromosomal positions of the TFs and their corresponding effector genes. Here, we analyze the genome organization of the genetic components of these sensing systems, using the classification described earlier. We report the chromosomal proximity of transcription factors and their effector genes to sense periplasmic signals or transported metabolites (i.e. transcriptional sensing systems from the external class) in contrast to the components for sensing internally synthesized metabolites, which tend to be distant on the chromosome. We strengthen our finding that external sensing genetic machinery behaves like chromosomal modules of regulation to respond rapidly to variations in external conditions through co-expression of their genetic components, which is corroborated with microarray data for E. coli. Furthermore, we show several lines of evidence supporting the need for the coordinated activity of external sensing systems in contrast to that of internal sensing machinery, which can explain their close chromosomal organization. The observed functional correlation between the chromosomal organization and the genetic machinery for environmental sensing should contribute to our understanding of the logical functioning and evolution of the transcriptional regulatory networks in bacteria.

Diffusion of transcription factors can drastically enhance the noise in gene expression

We study by Green's Function Reaction Dynamics the effect of the diffusive motion of repressor molecules on the noise in mRNA and protein levels for a gene that is under the control of a repressor. We find that spatial fluctuations due to diffusion can drastically enhance the noise in gene expression. After dissociation from the operator, a repressor can rapidly rebind to the DNA. Our results show that the rebinding trajectories are so short that, on this timescale, the RNA polymerase (RNAP) cannot effectively compete with the repressor for binding to the promoter. As a result, a dissociated repressor molecule will on average rebind many times, before it eventually diffuses away. These rebindings thus lower the effective dissociation rate, and this increases the noise in gene expression. Another consequence of the timescale separation between repressor rebinding and RNAP association is that the effect of spatial fluctuations can be described by a well-stirred, zero-dimensional, model by renormalizing the reaction rates for repressor-DNA (un) binding. Our results thus support the use of well-stirred, zero-dimensional models for describing noise in gene expression. We also show that for a fixed repressor strength, the noise due to diffusion can be minimized by increasing the number of repressors or by decreasing the rate of the open complex formation. Lastly, our results emphasize that power spectra are a highly useful tool for studying the propagation of noise through the different stages of gene expression.

Physical nature of bacterial cytoplasm

We track the motion of individual fluorescently labeled mRNA molecules inside live E. coli cells. We find that the motion is subdiffusive, with an exponent that is robust to physiological changes, including the disruption of cytoskeletal elements. By modifying the parameters of the RNA molecule and the bacterial cell, we are able to examine the possible mechanisms that can lead to this unique type of motion, especially the effect of macromolecular crowding. We also examine the implications of anomalous diffusion on the kinetics of bacterial gene regulation, in particular, how transcription factors find their DNA targets.

Design of a network with state stability

Designing a network with given functions or reconstruct a network based on its dynamical behavior is an important problem in the study of complex systems. In this paper, we put forward certain principles in constructing a network with state stability. We show that a necessary and sufficient condition to design networks with a global fixed point is that active nodes inhibit inactive nodes, while the latter activate the former directly or indirectly. We also designed networks based on basic modules, where each basic module consists a sub-network, they communicate through the inhibition link from each activator in lower module to the inhibitor of upper module. We found that long activation links, i.e. indirect activation links are important to the formation of convergence trajectory. We believe that these principles may help us to understand the topology of biological networks.

Inference and analysis of the relative stability of bacterial chromosomes

The stability of genomes is highly variable, both in terms of gene content and gene order. Here I calibrate the loss of gene order conservation (GOC) through time by fitting a simple probabilistic model on pairwise comparisons involving 126 bacterial genomes. The model computes the probability of separation of pairs of contiguous genes per unit of time and fits the data better than previous ones while allowing a mechanistic interpretation for the loss of GOC with time. Although the information on operons is not used in the model, I observe, as expected, that most highly conserved pairs of genes are indeed within operons. However, even the other pairs are much more conserved than expected given the observed experimental rearrangement rates. After 500 Myr, about 50% of the originally contiguous orthologues remain so in the average genome. Hence, the large majority of rearrangements must be deleterious and random genome rearrangements are unlikely to provide for positively selected structural changes. I then use the deviations from the model to define an intrinsic measure of genome stability that allowed the comparison of distantly related genomes and the inference of ancestral states. This shows that clades differ in genome stability, with cyanobacteria being the least stable and gamma-proteobacteria the most stable. Without correction for phylogeny, free-living bacteria are the least stable group of genomes, followed by pathogens, and then endomutualists. However, after correction for phylogenetic inertia (or the removal of cyanobacteria from the analysis), there is no significant association between genome stability and lifestyle or genome size. Hence, although this method has allowed uncovering some of mechanisms leading to rearrangements, we still ignore the forces that differentially shape selection upon genome stability in different species.

Exploring the microbial biodegradation and biotransformation gene pool

Similar to the New World explorers of the 16th and 17th century, microbiologists today find themselves at the edge of unknown territory. It is estimated that only 0.1-1% of microorganisms can be cultivated using current techniques; the vastness of microbial lifestyles remains to be explored. Because the microbial metagenome is the largest reservoir of genes that determine enzymatic reactions, new techniques are being developed to identify the genes that underlie many valuable chemical biotransformations carried out by microbes, particularly in pathways for biodegradation of recalcitrant and xenobiotic molecules. Our knowledge of catabolic routes built on research during the past 40 years is a solid basis from which to venture on to the little-explored pathways that might exist in nature. However, it is clear that the vastness of information to be obtained requires astute experimental strategies for finding novel reactions.

The network of transcriptional interactions imposes linear constrains in the genome

Two prokaryotic organisms for which transcriptional regulatory interactions have been well elucidated by experimental means are Escherichia coli and Bacillus subtilis. Here we show, with the help of simulations and from known data, the importance of proximity of the transcription factor gene and the respective regulated gene in regulatory networks. We discuss the importance of the location of external sensing machinery close to the genes for transcription factors that regulate them in light of our finding.

Chemical Models of Genetic Toggle Switches†

We study by mean-field analysis and stochastic simulations chemical models for genetic toggle switches formed from pairs of genes that mutually repress each other. To determine the stability of the genetic switches, we make a connection with reactive flux theory and transition state theory. The switch stability is characterized by a well-defined lifetime tau. We find that tau grows exponentially with the mean number N of transcription factor molecules involved in the switching. In the regime accessible to direct numerical simulations, the growth law is well-characterized by tau approximately N(alpha) exp(bN), where alpha and b are parameters. The switch stability is decreased by phenomena that increase the noise in gene expression, such as the production of multiple copies of a protein from a single mRNA transcript (shot noise) and fluctuations in the number of proteins produced per transcript. However, robustness against biochemical noise can be drastically enhanced by arranging the transcription factor binding domains on the DNA such that competing transcription factors mutually exclude each other on the DNA. We also elucidate the origin of the enhanced stability of the exclusive switch with respect to that of the general switch; while the kinetic prefactor is roughly the same for both switches, the "barrier" for flipping the switch is significantly higher for the exclusive switch than that for the general switch.