Evidence for soft bounds in Ubuntu package sizes and mammalian body masses.

The development of a complex system depends on the self-coordinated action of a large number of agents, often determining unexpected global behavior. The case of software evolution has great practical importance: knowledge of what is to be considered atypical can guide developers in recognizing and reacting to abnormal behavior. Although the initial framework of a theory of software exists, the current theoretical achievements do not fully capture existing quantitative data or predict future trends. Here we show that two elementary laws describe the evolution of package sizes in a Linux-based operating system: first, relative changes in size follow a random walk with non-Gaussian jumps; second, each size change is bounded by a limit that is dependent on the starting size, an intriguing behavior that we call "soft bound." Our approach is based on data analysis and on a simple theoretical model, which is able to reproduce empirical details without relying on any adjustable parameter and generates definite predictions. The same analysis allows us to formulate and support the hypothesis that a similar mechanism is shaping the distribution of mammalian body sizes, via size-dependent constraints during cladogenesis. Whereas generally accepted approaches struggle to reproduce the large-mass shoulder displayed by the distribution of extant mammalian species, this is a natural consequence of the softly bounded nature of the process. Additionally, the hypothesis that this model is valid has the relevant implication that, contrary to a common assumption, mammalian masses are still evolving, albeit very slowly.

Influence of homology and node age on the growth of protein-protein interaction networks.

Proteins participating in a protein-protein interaction network can be grouped into homology classes following their common ancestry. Proteins added to the network correspond to genes added to the classes, so the dynamics of the two objects are intrinsically linked. Here we first introduce a statistical model describing the joint growth of the network and the partitioning of nodes into classes, which is studied through a combined mean-field and simulation approach. We then employ this unified framework to address the specific issue of the age dependence of protein interactions through the definition of three different node wiring or divergence schemes. A comparison with empirical data indicates that an age-dependent divergence move is necessary in order to reproduce the basic topological observables together with the age correlation between interacting nodes visible in empirical data. We also discuss the possibility of nontrivial joint partition and topology observables.

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.

DnaA and the timing of chromosome replication in Escherichia coli as a function of growth rate.

BACKGROUND: In Escherichia coli, overlapping rounds of DNA replication allow the bacteria to double in faster times than the time required to copy the genome. The precise timing of initiation of DNA replication is determined by a regulatory circuit that depends on the binding of a critical number of ATP-bound DnaA proteins at the origin of replication, resulting in the melting of the DNA and the assembly of the replication complex. The synthesis of DnaA in the cell is controlled by a growth-rate dependent, negatively autoregulated gene found near the origin of replication. Both the regulatory and initiation activity of DnaA depend on its nucleotide bound state and its availability. RESULTS: In order to investigate the contributions of the different regulatory processes to the timing of initiation of DNA replication at varying growth rates, we formulate a minimal quantitative model of the initiator circuit that includes the key ingredients known to regulate the activity of the DnaA protein. This model describes the average-cell oscillations in DnaA-ATP/DNA during the cell cycle, for varying growth rates. We evaluate the conditions under which this ratio attains the same threshold value at the time of initiation, independently of the growth rate. CONCLUSIONS: We find that a quantitative description of replication initiation by DnaA must rely on the dependency of the basic parameters on growth rate, in order to account for the timing of initiation of DNA replication at different cell doubling times. We isolate two main possible scenarios for this, depending on the roles of DnaA autoregulation and DnaA ATP-hydrolysis regulatory process. One possibility is that the basal rate of regulatory inactivation by ATP hydrolysis must vary with growth rate. Alternatively, some parameters defining promoter activity need to be a function of the growth rate. In either case, the basal rate of gene expression needs to increase with the growth rate, in accordance with the known characteristics of the dnaA promoter. Furthermore, both inactivation and autorepression reduce the amplitude of the cell-cycle oscillations of DnaA-ATP/DNA.

Gene clusters reflecting macrodomain structure respond to nucleoid perturbations.

Focusing on the DNA-bridging nucleoid proteins Fis and H-NS, and integrating several independent experimental and bioinformatic data sources, we investigate the links between chromosomal spatial organization and global transcriptional regulation. By means of a novel multi-scale spatial aggregation analysis, we uncover the existence of contiguous clusters of nucleoid-perturbation sensitive genes along the genome, whose expression is affected by a combination of topological DNA state and nucleoid-shaping protein occupancy. The clusters correlate well with the macrodomain structure of the genome. The most significant of them lay symmetrically at the edges of the Ter macrodomain and involve all of the flagellar and chemotaxis machinery, in addition to key regulators of biofilm formation, suggesting that the regulation of the physical state of the chromosome by the nucleoid proteins plays an important role in coordinating the transcriptional response leading to the switch between a motile and a biofilm lifestyle.

Identity and divergence of protein domain architectures after the yeast whole-genome duplication event.

Gene duplication is a key mechanism in evolution for generating new functionality, and it is known to have produced a large proportion of genes. Duplication mechanisms include small-scale, or "local", events such as unequal crossing over and retroposition, together with global events, such as chromosomal or whole genome duplication (WGD). In particular, different studies confirmed that the yeast S. cerevisiae arose from a 100-150 million-year old whole-genome duplication. Detection and study of duplications are usually based on sequence alignment, synteny and phylogenetic techniques, but protein domains are also useful in assessing protein homology. We develop a simple and computationally efficient protein domain architecture comparison method based on the domain assignments available from public databases. We test the accuracy and the reliability of this method in detecting instances of gene duplication in the yeast S. cerevisiae. In particular, we analyze the evolution of WGD and non-WGD paralogs from the domain viewpoint, in comparison with a more standard functional analysis of the genes. A large number of domains is shared by genes that underwent local and global duplications, indicating the existence of a common set of "duplicable" domains. On the other hand, WGD and non-WGD paralogs tend to have different functions. We find evidence that this comes from functional migration within similar domain superfamilies, but also from the existence of small sets of WGD and non-WGD specific domain superfamilies with largely different functions. This observation gives a novel perspective on the finding that WGD paralogs tend to be functionally different from small-scale paralogs. WGD and non-WGD superfamilies carry distinct functions. Finally, the Gene Ontology similarity of paralogs tends to decrease with duplication age, while this tendency is weaker or not observable by the comparison of the domain architectures of paralogs. This suggests that the set of domains composing a protein tends to be maintained, while its function, cellular process or localization diversifies. Overall, the gathered evidence gives a different viewpoint on the biological specificity of the WGD and at the same time points out the validity of domain architecture comparison as a tool for detecting homology.

Ordered structure of the transcription network inherited from the yeast whole-genome duplication.

BACKGROUND: Gene duplication, a major evolutionary path to genomic innovation, can occur at the scale of an entire genome. One such "whole-genome duplication" (WGD) event among the Ascomycota fungi gave rise to genes with distinct biological properties compared to small-scale duplications. RESULTS: We studied the evolution of transcriptional interactions of whole-genome duplicates, to understand how they are wired into the yeast regulatory system. Our work combines network analysis and modeling of the large-scale structure of the interactions stemming from the WGD. CONCLUSIONS: The results uncover the WGD as a major source for the evolution of a complex interconnected block of transcriptional pathways. The inheritance of interactions among WGD duplicates follows elementary "duplication subgraphs", relating ancestral interactions with newly formed ones. Duplication subgraphs are correlated with their neighbours and give rise to higher order circuits with two elementary properties: newly formed transcriptional pathways remain connected (paths are not broken), and are preferentially cross-connected with ancestral ones. The result is a coherent and connected "WGD-network", where duplication subgraphs are arranged in an astonishingly ordered configuration.

Hydrodynamic synchronization of colloidal oscillators.

Two colloidal spheres are maintained in oscillation by switching the position of an optical trap when a sphere reaches a limit position, leading to oscillations that are bounded in amplitude but free in phase and period. The interaction between the oscillators is only through the hydrodynamic flow induced by their motion. We prove that in the absence of stochastic noise the antiphase dynamical state is stable, and we show how the period depends on coupling strength. Both features are observed experimentally. As the natural frequencies of the oscillators are made progressively different, the coordination is quickly lost. These results help one to understand the origin of hydrodynamic synchronization and how the dynamics can be tuned. Cilia and flagella are biological systems coupled hydrodynamically, exhibiting dramatic collective motions. We propose that weakly correlated phase fluctuations, with one of the oscillators typically processing the other, are characteristic of hydrodynamically coupled systems in the presence of thermal noise.

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.

Universal features in the genome-level evolution of protein domains.

BACKGROUND: Protein domains can be used to study proteome evolution at a coarse scale. In particular, they are found on genomes with notable statistical distributions. It is known that the distribution of domains with a given topology follows a power law. We focus on a further aspect: these distributions, and the number of distinct topologies, follow collective trends, or scaling laws, depending on the total number of domains only, and not on genome-specific features. RESULTS: We present a stochastic duplication/innovation model, in the class of the so-called 'Chinese restaurant processes', that explains this observation with two universal parameters, representing a minimal number of domains and the relative weight of innovation to duplication. Furthermore, we study a model variant where new topologies are related to occurrence in genomic data, accounting for fold specificity. CONCLUSIONS: Both models have general quantitative agreement with data from hundreds of genomes, which indicates that the domains of a genome are built with a combination of specificity and robust self-organizing phenomena. The latter are related to the basic evolutionary 'moves' of duplication and innovation, and give rise to the observed scaling laws, a priori of the specific evolutionary history of a genome. We interpret this as the concurrent effect of neutral and selective drives, which increase duplication and decrease innovation in larger and more complex genomes. The validity of our model would imply that the empirical observation of a small number of folds in nature may be a consequence of their evolution.

Statistical mechanics of the "Chinese restaurant process": lack of self-averaging, anomalous finite-size effects, and condensation.

The Pitman-Yor, or Chinese restaurant process, is a stochastic process that generates distributions following a power law with exponents lower than 2, as found in numerous physical, biological, technological, and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e., a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.