Fluctuations In Copy Number Research Articles

What makes the lac-pathway switch: identifying the fluctuations that trigger phenotype switching in gene regulatory systems.

Multistable gene regulatory systems sustain different levels of gene expression under identical external conditions. Such multistability is used to encode phenotypic states in processes including nutrient uptake and persistence in bacteria, fate selection in viral infection, cell-cycle control and development. Stochastic switching between different phenotypes can occur as the result of random fluctuations in molecular copy numbers of mRNA and proteins arising in transcription, translation, transport and binding. However, which component of a pathway triggers such a transition is generally not known. By linking single-cell experiments on the lactose-uptake pathway in E. coli to molecular simulations, we devise a general method to pinpoint the particular fluctuation driving phenotype switching and apply this method to the transition between the uninduced and induced states of the lac-genes. We find that the transition to the induced state is not caused only by the single event of lac-repressor unbinding, but depends crucially on the time period over which the repressor remains unbound from the lac-operon. We confirm this notion in strains with a high expression level of the lac-repressor (leading to shorter periods over which the lac-operon remains unbound), which show a reduced switching rate. Our techniques apply to multistable gene regulatory systems in general and allow to identify the molecular mechanisms behind stochastic transitions in gene regulatory circuits.

Stochastic simulation of prokaryotic two-component signalling indicates stochasticity-induced active-state locking and growth-rate dependent bistability.

Signal transduction by prokaryotes almost exclusively relies on two-component systems for sensing and responding to (extracellular) signals. Here, we use stochastic models of two-component systems to better understand the impact of stochasticity on the fidelity and robustness of signal transmission, the outcome of autoregulatory gene expression and the influence of cell growth and division. We report that two-component systems are remarkably robust against copy number fluctuations of the signalling proteins they are composed of, which enhances signal transmission fidelity. Furthermore, we find that due to stochasticity these systems can get locked in an active state for extended time periods when (initially high) signal levels drop to zero. This behaviour can contribute to a bet-hedging adaptation strategy, aiding survival in fluctuating environments. Additionally, autoregulatory gene expression can cause two-component systems to become bistable at realistic parameter values. As a result, two sub-populations of cells can co-exist-active and inactive cells, which contributes to fitness in unpredictable environments. Bistability proved robust with respect to cell growth and division, and is tunable by the growth rate. In conclusion, our results indicate how single cells can cope with the inevitable stochasticity occurring in the activity of their two-component systems. They are robust to disadvantageous fluctuations that scramble signal transduction and they exploit beneficial stochasticity that generates fitness-enhancing heterogeneity across an isogenic population of cells.

A single phosphatase can convert a robust step response into a graded, tunable or adaptive response

Many biological signalling pathways have evolved to produce responses to environmental signals that are robust to fluctuations in protein copy number and noise. Whilst beneficial for biology, this robustness can be problematic for synthetic biologists wishing to re-engineer and subsequently tune the response of a given system. Here we show that the well-characterized EnvZ/OmpR two-component signalling system from Escherichia coli possesses one such robust step response. However, the synthetic addition of just a single component into the system, an extra independently controllable phosphatase, can change this behaviour to become graded and tunable, and even show adaptation. Our approach introduces a new design principle which can be implemented simply in engineering and redesigning fast signal transduction pathways for synthetic biology.

Fluctuations in Tat copy number when it counts the most: a possible mechanism to battle the HIV latency

The HIV-1 virus can enter a dormant state and become inactive, which reduces accessibility by antiviral drugs. We approach this latency problem from an unconventional point of view, with the focus on understanding how intrinsic chemical noise (copy number fluctuations of the Tat protein) can be used to assist the activation process of the latent virus. Several phase diagrams have been constructed in order to visualize in which regions of the parameter space noise can drive the activation process. Essential to the study is the use of a hyperbolic coordinate system, which greatly facilitates quantification of how the various reaction rate combinations shape the noise behavior of the Tat protein feedback system. We have designed a mathematical manual of how to approach the problem of activation quantitatively, and introduce the notion of an “operating point” of the virus. For both noise-free and noise-based strategies we show how operating point off-sets induce changes in the number of Tat molecules. The major result of the analysis is that for every noise-free strategy there is a noise-based strategy that requires lower dosage, but achieves the same anti-latency effect. It appears that the noise-based activation is advantageous for every operating point.

Translation initiation of the replication initiator repB gene of promiscuous plasmid pMV158 is led by an extended non-SD sequence

RepB is the pMV158-encoded protein that initiates rolling-circle replication of this promiscuous plasmid. Availability of RepB is rate-limiting for the plasmid replication process, and therefore the repB gene encoding the protein is subjected to strict control. Two trans-acting plasmid elements, CopG and the antisense RNAII, are involved in controlling the synthesis of the initiator at the transcriptional and translational level, respectively. In addition to this dual control of repB expression that senses and corrects fluctuations in plasmid copy number, proper availability of RepB also relies on the adequate functionality of the transcription and translation initiation regulatory signals. Translation of repB has been postulated to depend on an atypical ribosome binding site that precedes its start codon, although such a hypothesis has never been proved. To define sequences involved in translation of repB, several mutations in the translation initiation region of the repB mRNA have been characterized by using an Escherichia coli in vitro expression system wherein the synthesis of RepB was detected and quantified. We showed that translation of repB is not coupled to that of copG and depends only on its own initiation signals. The atypical ribosome binding site, as it was defined, is not involved in translation initiation. However, the sequence just upstream of the repB start codon, encompassing the proximal box of the atypical ribosome binding site and the four bases immediately downstream of it, is indeed important for efficient translation of repB. The high degree of conservation of this sequence among the rep genes of plasmids of the same pMV158 family supports its relevancy as a translation initiation signal in mRNAs without a recognizable Shine-Dalgarno sequence.

Evaluating quantitative methods for measuring plasmid copy numbers in single cells

The life of plasmids is a constant battle against fluctuations: failing to correct copy number fluctuations can increase the plasmid loss rate by many orders of magnitude, as can a failure to more evenly divide the copies between daughters at cell division. Plasmids are therefore long-standing model systems for stochastic processes in cells, much thanks to the efforts of Kurt Nordström to whose memory this issue is dedicated. Here we analyze a range of experimental methods for measuring plasmid copy numbers in single cells, focusing on challenges, trade-offs, and necessary experimental controls. In particular we analyze published and unpublished strategies to infer copy numbers from expression of plasmid-encoded reporters, direct labeling of plasmids with fluorescent probes or DNA binding proteins fused to fluorescent reporters, PCR based methods applied to single cell lysates, and plasmid-specific replication arrest. We conclude that no method currently exists to measure plasmid copy numbers in single cells, and that most methods are overwhelmed by various types of experimental noise. We also discuss how accurate methods can be developed.

Robust Signal Processing in Living Cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations.

The landscape of inherited and de novo copy number variants in a plasmodium falciparum genetic cross

BackgroundCopy number is a major source of genome variation with important evolutionary implications. Consequently, it is essential to determine copy number variant (CNV) behavior, distributions and frequencies across genomes to understand their origins in both evolutionary and generational time frames. We use comparative genomic hybridization (CGH) microarray and the resolution provided by a segregating population of cloned progeny lines of the malaria parasite, Plasmodium falciparum, to identify and analyze the inheritance of 170 genome-wide CNVs.ResultsWe describe CNVs in progeny clones derived from both Mendelian (i.e. inherited) and non-Mendelian mechanisms. Forty-five CNVs were present in the parent lines and segregated in the progeny population. Furthermore, extensive variation that did not conform to strict Mendelian inheritance patterns was observed. 124 CNVs were called in one or more progeny but in neither parent: we observed CNVs in more than one progeny clone that were not identified in either parent, located more frequently in the telomeric-subtelomeric regions of chromosomes and singleton de novo CNVs distributed evenly throughout the genome. Linkage analysis of CNVs revealed dynamic copy number fluctuations and suggested mechanisms that could have generated them. Five of 12 previously identified expression quantitative trait loci (eQTL) hotspots coincide with CNVs, demonstrating the potential for broad influence of CNV on the transcriptional program and phenotypic variation.ConclusionsCNVs are a significant source of segregating and de novo genome variation involving hundreds of genes. Examination of progeny genome segments provides a framework to assess the extent and possible origins of CNVs. This segregating genetic system reveals the breadth, distribution and dynamics of CNVs in a surprisingly plastic parasite genome, providing a new perspective on the sources of diversity in parasite populations.

Gene Loss and Parallel Evolution Contribute to Species Difference in Flower Color

Although the importance of regulatory and functional sequence evolution in generating species differences has been studied to some extent, much less is known about the role of other types of genomic changes, such as fluctuation in gene copy number. Here, we apply analyses of gene function and expression of anthocyanin pigment pathway genes, as well as cosegregation analyses in backcross populations, to examine the genetic changes involved in the shift from blue to red flowers in Andean Iochroma (Solanaceae). We demonstrate that deletion of a gene coding for an anthocyanin pathway enzyme was necessary for the transition to red floral pigmentation. The downregulation of a second pathway gene was also necessary for the novel flower color, and this regulatory pattern parallels the genetic change in the two other red-flowered species in the sister family Convolvulaceae in which flower color change has been examined genetically. Finally, we document a shift in enzymatic function at a third locus, but the importance of this change in the transition to red flowers depends on the exact order with which the three changes occurred. This study shows that gene inactivation or loss can be involved in the origin of phenotypic differences between species, thereby restricting the possibility of reversion to the ancestral state. It also demonstrates that parallel evolution of red flowers in three different species occurs via a common developmental/regulatory change but by mutations in different genes.

Stochastic hybrid systems for studying biochemical processes

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

Refined method for the genomic integration of complex synthetic circuits

Genetic reconstruction of regulatory gene circuits is currently applied in systematic dynamics and structure-function studies of intact cellular networks in systems biology. We present a modified procedure for the integration of complex genetic circuits into the Escherichia coli genome, to provide an efficient synthetic approach for stochastic study and the artificial engineering of genetic networks. Linear artificial sequences of various lengths were easily integrated into the bacterial genome at one time. Comparison of the cellular concentrations of proteins encoded by genes carried on plasmids or the genome indicated that genome recombination could minimize the copy number noise in the genetic circuit, allowing precise design and interpretation of the cellular network. The refined recombination procedure allowed efficient construction of a single copy of a complex genetic circuit in cells, and the resultant reduced fluctuation in copy number led to accurate phenotypic behaviour of the genome-integrated synthetic switch corresponding to the design principle. The availability of long-fragment insertions makes the reconstruction of complex networks easy on the genome, and provides a powerful tool for precise engineering in synthetic and systems biology.

Long-term conservation vs high sequence divergence: the case of an extraordinarily old satellite DNA in bivalve mollusks

The ubiquity of satellite DNA (satDNA) sequences has raised much controversy over the abundance of divergent monomer variants and the long-time nucleotide sequence stability observed for many satDNA families. In this work, we describe the satDNA BIV160, characterized in nine species of the three main bivalve clades (Protobranchia, Pteriomorphia and Heteroconchia). BIV160 monomers are similar in repeat size and nucleotide sequence to satDNAs described earlier in oysters and in the clam Donax trunculus. The broad distribution of BIV160 satDNA indicates that similar variants existed in the ancestral bivalve species that lived about 540 million years ago; this makes BIV160 the most ancient satDNA described so far. In the species examined, monomer variants are distributed in quite a complex pattern. This pattern includes (i) species characterized by a specific group of variants, (ii) species that share distinct group(s) of variants and (iii) species with both specific and shared types. The evolutionary scenario suggested by these data reconciles sequence uniformity in homogenization-maintained satDNA arrays with the genomic richness of divergent monomer variants formed by diversification of the same ancestral satDNA sequence. Diversified repeats can continue to evolve in a non-concerted manner and behave as independent amplification-contraction units in the framework of a 'library of satDNA variants' representing a permanent source of monomers that can be amplified into novel homogeneous satDNA arrays. On the whole, diversification of satDNA monomers and copy number fluctuations provide a highly dynamic genomic environment able to form and displace satDNA sequence variants rapidly in evolution.

Intrinsic noise in post-transcriptional gene regulation by small non-coding RNA

Small non-coding RNA (sRNA) plays very important role in the post transcriptional regulation in various organisms. In complex regulatory networks, highly significant relative fluctuations in RNAs copy numbers can not be neglected due to very small copy number of individual RNA molecules. Here we consider two simple regulation schemes, where one is single target gene regulated by a sRNA and the other is two target mRNAs (mRNA R and mRNA T ) regulated by one sRNA. The Fano factor (a measure of the relative size of the internal fluctuations) formulae of RNA molecules in the post transcriptional regulation are theoretically derived by using of the Langevin theory. For single target gene regulated by a sRNA, it is shown that the intrinsic noise of both mRNA and sRNA approaches the bare Poissonian limit in the regimen of both target RNA silencing and surviving. However, the strong anti-correlation between the fluctuations of two components result in a large intrinsic fluctuations in the level of RNA molecules in the regimen of crossover. For two target mRNAs regulated by one sRNA, in the regimen of crossover, it is found that, with the increasing of transcription rate of target mRNA T , the maximal intrinsic fluctuation of RNA molecules is shifted from sRNA to target mRNA R , and then to target mRNA T . The intrinsic noise intensity of target mRNA R is determined by both the transcriptional rate of itself and that of sRNA, and independent of the transcriptional rate of the other target mRNA T .

Quantifying Origins of Cell-to-Cell Variations in Gene Expression

A general dynamic description of protein synthesis was employed to quantify different sources of gene expression noise in cellular systems. To test our approach, we use time-resolved expression data of individual human cells and, from this information, predict the stationary cell-to-cell variation in protein levels in a clonal population. For three of the four human genes investigated, the cellular variations in expression level are not due to fluctuations in promoter activity or transcript copy number, but are almost exclusively a consequence of long-term variations of gene regulatory factors or the global cellular state. Moreover, we show that a dynamic description is much more reliable to discriminate extrinsic and intrinsic sources of noise than it is on grounds of cell-cycle averaged descriptions. The excellent agreement between the theoretical predictions and the experimentally measured noise strengths shows that a quantitative description of gene expression noise is indeed possible on the basis of idealized stochastic processes.

Striking Similarities in the Genomic Distribution of Tandemly Arrayed Genes in Arabidopsis and Rice

In Arabidopsis, tandemly arrayed genes (TAGs) comprise >10% of the genes in the genome. These duplicated genes represent a rich template for genetic innovation, but little is known of the evolutionary forces governing their generation and maintenance. Here we compare the organization and evolution of TAGs between Arabidopsis and rice, two plant genomes that diverged ~150 million years ago. TAGs from the two genomes are similar in a number of respects, including the proportion of genes that are tandemly arrayed, the number of genes within an array, the number of tandem arrays, and the dearth of TAGs relative to single copy genes in centromeric regions. Analysis of recombination rates along rice chromosomes confirms a positive correlation between the occurrence of TAGs and recombination rate, as found in Arabidopsis. TAGs are also biased functionally relative to duplicated, nontandemly arrayed genes. In both genomes, TAGs are enriched for genes that encode membrane proteins and function in “abiotic and biotic stress” but underrepresented for genes involved in transcription and DNA or RNA binding functions. We speculate that these observations reflect an evolutionary trend in which successful tandem duplication involves genes either at the end of biochemical pathways or in flexible steps in a pathway, for which fluctuation in copy number is unlikely to affect downstream genes. Despite differences in the age distribution of tandem arrays, the striking similarities between rice and Arabidopsis indicate similar mechanisms of TAG generation and maintenance.

Noise-Induced Min Phenotypes in E. coli

The spatiotemporal oscillations of the Escherichia coli proteins MinD and MinE direct cell division to the region between the chromosomes. Several quantitative models of the Min system have been suggested before, but no one of them accounts for the behavior of all documented mutant phenotypes. We analyzed the stochastic reaction-diffusion kinetics of the Min proteins for several E. coli mutants and compared the results to the corresponding deterministic mean-field description. We found that wild-type (wt) and filamentous (ftsZ −) cells are well characterized by the mean-field model, but that a stochastic model is necessary to account for several of the characteristics of the spherical (rodA−) and phospathedylethanolamide-deficient (PE−) phenotypes. For spherical cells, the mean-field model is bistable, and the system can get trapped in a non-oscillatory state. However, when the intrinsic noise is considered, only the experimentally observed oscillatory behavior remains. The stochastic model also reproduces the change in oscillation directions observed in the spherical phenotype and the occasional gliding of the MinD region along the inner membrane. For the PE− mutant, the stochastic model explains the appearance of randomly localized and dense MinD clusters as a nucleation phenomenon, in which the stochastic kinetics at low copy number causes local discharges of the high MinDATP to MinDADP potential. We find that a simple five-reaction model of the Min system can explain all documented Min phenotypes, if stochastic kinetics and three-dimensional diffusion are accounted for. Our results emphasize that local copy number fluctuation may result in phenotypic differences although the total number of molecules of the relevant species is high.

Kid cleaves specific mRNAs at UUACU sites to rescue the copy number of plasmid R1

Stability and copy number of extra-chromosomal elements are tightly regulated in prokaryotes and eukaryotes. Toxin Kid and antitoxin Kis are the components of the parD stability system of prokaryotic plasmid R1 and they can also function in eukaryotes. In bacteria, Kid was thought to become active only in cells that lose plasmid R1 and to cleave exclusively host mRNAs at UA(A/C/U) trinucleotide sites to eliminate plasmid-free cells. Instead, we demonstrate here that Kid becomes active in plasmid-containing cells when plasmid copy number decreases, cleaving not only host- but also a specific plasmid-encoded mRNA at the longer and more specific target sequence UUACU. This specific cleavage by Kid inhibits bacterial growth and, at the same time, helps to restore the plasmid copy number. Kid targets a plasmid RNA that encodes a repressor of the synthesis of an R1 replication protein, resulting in increased plasmid DNA replication. This mechanism resembles that employed by some human herpesviruses to regulate viral amplification during infection.

Ty1 Copy Number Dynamics in Saccharomyces

To understand long terminal repeat (LTR)-retrotransposon copy number dynamics, Ty1 elements were reintroduced into a "Ty-less" Saccharomyces strain where elements had been lost by LTR-LTR recombination. Repopulated strains exhibited alterations in chromosome size that were associated with Ty1 insertions, but did not become genetically isolated. The rates of element gain and loss under genetic and environmental conditions known to affect Ty1 retrotransposition were determined using genetically tagged reference elements. The results show that Ty1 retrotransposition varies with copy number, temperature, and cell type. In contrast to retrotransposition, Ty1 loss by LTR-LTR recombination was more constant and not markedly influenced by copy number. Endogenous Ty1 cDNA was poorly utilized for recombination when compared with LTR-LTR recombination or ectopic gene conversion. Ty1 elements also appear to be more susceptible to copy number fluctuation in haploid cells. Ty1 gain/loss ratios obtained under different conditions suggest that copy number oscillates over time by altering the rate of retrotransposition, resulting in the diverse copy numbers observed in Saccharomyces.

Origin pairing ('handcuffing') as a mode of negative control of P1 plasmid copy number.

In one family of bacterial plasmids, multiple initiator binding sites, called iterons, are used for initiation of plasmid replication as well as for the control of plasmid copy number. Iterons can also pair in vitro via the bound initiators. This pairing, called handcuffing, has been suggested to cause steric hindrance to initiation and thereby control the copy number. To test this hypothesis, we have compared copy numbers of isogenic miniP1 plasmid monomer and dimer. The dimer copy number was only one-quarter that of the monomer, suggesting that the higher local concentration of origins in the dimer facilitated their pairing. Physical evidence consistent with iteron-mediated pairing of origins preferentially in the dimer was obtained in vivo. Thus, origin handcuffing can be a mechanism to control P1 plasmid replication.

Copy-Number Fluctuation by Unequal Crossing-Over in the Chicken Avidin Gene Family

The chicken avidin gene (AVD) forms a closely clustered gene family together with several avidin-related genes (AVRs). In this study, we used fluorescence in situ hybridization on extended DNA fibers (fiber-FISH) to show that the number of the AVD and AVR genes differs between individuals. Furthermore, the gene copy-number showed wide somatic variation in white blood cells of the individuals. The molecular mechanism underlying the fluctuation is most probably unequal crossing-over and/or unequal sister chromatid exchange, as judged by the Gaussian distribution of the gene counts. By definition, an increase in gene number on one locus should be accompanied by a decrease on the other locus in unequal sequence exchange. The results suggest that copy-number lability may be more common among gene families than previously thought. The chicken avidin gene family also provides an excellent model for studying the mechanisms of recombination and gene conversion.