Growth-rate-dependent dynamics of a bacterial genetic oscillator

Gene networks exhibiting oscillatory dynamics are widespread in biology. The minimal regulatory designs giving rise to oscillations have been implemented synthetically and studied by mathematical modeling. However, most of the available analyses generally neglect the coupling of regulatory circuits with the cellular "chassis" in which the circuits are embedded. For example, the intracellular macromolecular composition of fast-growing bacteria changes with growth rate. As a consequence, important parameters of gene expression, such as ribosome concentration or cell volume, are growth-rate dependent, ultimately coupling the dynamics of genetic circuits with cell physiology. This work addresses the effects of growth rate on the dynamics of a paradigmatic example of genetic oscillator, the repressilator. Making use of empirical growth-rate dependences of parameters in bacteria, we show that the repressilator dynamics can switch between oscillations and convergence to a fixed point depending on the cellular state of growth, and thus on the nutrients it is fed. The physical support of the circuit (type of plasmid or gene positions on the chromosome) also plays an important role in determining the oscillation stability and the growth-rate dependence of period and amplitude. This analysis has potential application in the field of synthetic biology, and suggests that the coupling between endogenous genetic oscillators and cell physiology can have substantial consequences for their functionality.Comment: 14 pages, 9 figures (revised version, accepted for publication

Modelling the evolution of transcription factor binding preferences in complex eukaryotes

Transcription factors (TFs) exert their regulatory action by binding to DNA with specific sequence preferences. However, different TFs can partially share their binding sequences due to their common evolutionary origin. This `redundancy' of binding defines a way of organizing TFs in `motif families' by grouping TFs with similar binding preferences. Since these ultimately define the TF target genes, the motif family organization entails information about the structure of transcriptional regulation as it has been shaped by evolution. Focusing on the human TF repertoire, we show that a one-parameter evolutionary model of the Birth-Death-Innovation type can explain the TF empirical ripartition in motif families, and allows to highlight the relevant evolutionary forces at the origin of this organization. Moreover, the model allows to pinpoint few deviations from the neutral scenario it assumes: three over-expanded families (including HOX and FOX genes), a set of `singleton' TFs for which duplication seems to be selected against, and a higher-than-average rate of diversification of the binding preferences of TFs with a Zinc Finger DNA binding domain. Finally, a comparison of the TF motif family organization in different eukaryotic species suggests an increase of redundancy of binding with organism complexity.Comment: 14 pages, 5 figures. Minor changes. Final version, accepted for publicatio

Stochastic timing in gene expression for simple regulatory strategies

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such "timing fluctuations", and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fuctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while selfactivation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.Comment: 10 pages, 5 figure

Gene autoregulation via intronic microRNAs and its functions

Background: MicroRNAs, post-transcriptional repressors of gene expression, play a pivotal role in gene regulatory networks. They are involved in core cellular processes and their dysregulation is associated to a broad range of human diseases. This paper focus on a minimal microRNA-mediated regulatory circuit, in which a protein-coding gene (host gene) is targeted by a microRNA located inside one of its introns. Results: Autoregulation via intronic microRNAs is widespread in the human regulatory network, as confirmed by our bioinformatic analysis, and can perform several regulatory tasks despite its simple topology. Our analysis, based on analytical calculations and simulations, indicates that this circuitry alters the dynamics of the host gene expression, can induce complex responses implementing adaptation and Weber's law, and efficiently filters fluctuations propagating from the upstream network to the host gene. A fine-tuning of the circuit parameters can optimize each of these functions. Interestingly, they are all related to gene expression homeostasis, in agreement with the increasing evidence suggesting a role of microRNA regulation in conferring robustness to biological processes. In addition to model analysis, we present a list of bioinformatically predicted candidate circuits in human for future experimental tests. Conclusions: The results presented here suggest a potentially relevant functional role for negative self-regulation via intronic microRNAs, in particular as a homeostatic control mechanism of gene expression. Moreover, the map of circuit functions in terms of experimentally measurable parameters, resulting from our analysis, can be a useful guideline for possible applications in synthetic biology.Comment: 29 pages and 7 figures in the main text, 18 pages of Supporting Informatio

Statistics of shared components in complex component systems

Many complex systems are modular. Such systems can be represented as "component systems", i.e., sets of elementary components, such as LEGO bricks in LEGO sets. The bricks found in a LEGO set reflect a target architecture, which can be built following a set-specific list of instructions. In other component systems, instead, the underlying functional design and constraints are not obvious a priori, and their detection is often a challenge of both scientific and practical importance, requiring a clear understanding of component statistics. Importantly, some quantitative invariants appear to be common to many component systems, most notably a common broad distribution of component abundances, which often resembles the well-known Zipf's law. Such "laws" affect in a general and non-trivial way the component statistics, potentially hindering the identification of system-specific functional constraints or generative processes. Here, we specifically focus on the statistics of shared components, i.e., the distribution of the number of components shared by different system-realizations, such as the common bricks found in different LEGO sets. To account for the effects of component heterogeneity, we consider a simple null model, which builds system-realizations by random draws from a universe of possible components. Under general assumptions on abundance heterogeneity, we provide analytical estimates of component occurrence, which quantify exhaustively the statistics of shared components. Surprisingly, this simple null model can positively explain important features of empirical component-occurrence distributions obtained from data on bacterial genomes, LEGO sets, and book chapters. Specific architectural features and functional constraints can be detected from occurrence patterns as deviations from these null predictions, as we show for the illustrative case of the "core" genome in bacteria.Comment: 18 pages, 7 main figures, 7 supplementary figure

Zipf and Heaps laws from dependency structures in component systems

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here, we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless, and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sub-linear and saturating) that we characterize quantitatively

Heaps' law, statistics of shared components and temporal patterns from a sample-space-reducing process

Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component frequencies. Stochastic processes based on a sample-space-reducing (SSR) mechanism, in which the number of accessible states reduces as the system evolves, have been recently proposed as a simple explanation for the ubiquitous emergence of this law. However, many complex component systems are characterized by other statistical patterns beyond Zipf's law, such as a sublinear growth of the component vocabulary with the system size, known as Heap's law, and a specific statistics of shared components. This work shows, with analytical calculations and simulations, that these statistical properties can emerge jointly from a SSR mechanism, thus making it an appropriate parameter-poor representation for component systems. Several alternative (and equally simple) models, for example based on the preferential attachment mechanism, can also reproduce Heaps' and Zipf's laws, suggesting that additional statistical properties should be taken into account to select the most-likely generative process for a specific system. Along this line, we will show that the temporal component distribution predicted by the SSR model is markedly different from the one emerging from the popular rich-gets-richer mechanism. A comparison with empirical data from natural language indicates that the SSR process can be chosen as a better candidate model for text generation based on this statistical property. Finally, a limitation of the SSR model in reproducing the empirical "burstiness" of word appearances in texts will be pointed out, thus indicating a possible direction for extensions of the basic SSR process.Comment: 14 pages, 4 figure