[Show abstract][Hide abstract] ABSTRACT: The mean size of exponentially dividing E. coli cells cultured at a fixed
temperature but different nutrient conditions is known to depend on the mean
growth rate only. The quantitative relation between these two variables is
typically explained in terms of cell cycle control. Here, we measure the
fluctuations around the quantitative laws relating cell size, doubling time and
individual growth rate. Our primary result is a predominance of cell
individuality: single cells do not follow the dependence observed for the means
between size and either growth rate or inverse doubling time. Additionally, the
population and the individual-cell growth rate differ in their dependencies on
division time, so that individuals with the same interdivision time but coming
from colonies in different growth conditions grow at different rates. An
interesting crossover in this cell individuality separates fast- and
slow-growth conditions, possibly relating these findings to genome replication
control. Secondly, extending previous findings focused on a single growth
condition, we also establish that the spread in both size and doubling times is
a linear function of the population means of these variables. By contrast, the
fluctuations in single-cell growth rates do not show the same universality.
Estimates of the division rate as a function of the measurable parameters imply
a link between the universal and individual trends followed by single cells and
a cell division control process which is sensitive to cell size as well as to
additional variables, but which encodes a single intrinsic length-scale.
[Show abstract][Hide abstract] ABSTRACT: Constraints can affect dramatically the behavior of diffusion processes.
Recently, we analyzed a natural and a technological system and reported that
they perform diffusion-like discrete steps displaying a peculiar constraint,
whereby the increments of the diffusing variable are subject to
configuration-dependent bounds. This work explores theoretically some of the
revealing landmarks of such phenomenology, termed "soft bound". At long times,
the system reaches a steady state irreversibly (i.e., violating detailed
balance), characterized by a skewed "shoulder" in the density distribution, and
by a net local probability flux, which has entropic origin. The largest point
in the support of the distribution follows a saturating dynamics, expressed by
the Gompertz law, in line with empirical observations. Finally, we propose a
generic allometric scaling for the origin of soft bounds. These findings shed
light on the impact on a system of such "scaling" constraint and on its
possible generating mechanisms.
Physical review. E, Statistical, nonlinear, and soft matter physics. 09/2014; 90(3-1).
[Show abstract][Hide abstract] ABSTRACT: We monitored the dynamics of cell dimensions and reporter GFP expression in individual E. coli cells growing in a microfluidic chemostat using time-lapse fluorescence microscopy. This combination of techniques allows us to study the dynamical responses of single bacterial cells to nutritional shift-down or shift-up for longer times and with more precision over the chemical environment than similar experiments performed on conventional agar pads. We observed two E. coli strains containing different promoter-reporter gene constructs and measured how both their cell dimensions and the GFP expression change after nutritional upshift and downshift. As expected, both strains have similar adaptation dynamics for cell size rearrangement. However, the strain with a ribosomal RNA promoter dependent reporter has a faster GFP production rate than the strain with a constitutive promoter reporter. As a result, the mean GFP concentration in the former strain changes rapidly with the nutritional shift, while that in the latter strain remains relatively stable. These findings characterize the present microfluidic chemostat as a versatile platform for measuring single-cell bacterial dynamics and physiological transitions.
[Show abstract][Hide abstract] ABSTRACT: Recent experimental results suggest that the E. coli chromosome feels a
self-attracting interaction of osmotic origin, and is condensed in foci by
bridging interactions. Motivated by these findings, we explore a generic
modeling framework combining solely these two ingredients, in order to
characterize their joint effects. Specifically, we study a simple polymer
physics computational model with weak ubiquitous short-ranged self attraction
and stronger sparse bridging interactions. Combining theoretical arguments and
simulations, we study the general phenomenology of polymer collapse induced by
these dual contributions, in the case of regularly-spaced bridging. Our results
distinguish a regime of classical Flory-like coil-globule collapse dictated by
the interplay of excluded volume and attractive energy and a switch-like
collapse where bridging interaction compete with entropy loss terms from the
looped arms of a star-like rosette. Additionally, we show that bridging can
induce stable compartmentalized domains. In these configurations, different
"cores" of bridging proteins are kept separated by star-like polymer loops in
an entropically favorable multi-domain configuration, with a mechanism that
parallels micellar polysoaps. Such compartmentalized domains are stable, and do
not need any intra-specific interactions driving their segregation. Domains can
be stable also in presence of uniform attraction, as long as the uniform
collapse is above its theta point.
[Show abstract][Hide abstract] ABSTRACT: The physical nature of the bacterial chromosome has important implications for its function. Using high-resolution dynamic tracking, we observe the existence of rare but ubiquitous 'rapid movements' of chromosomal loci exhibiting near-ballistic dynamics. This suggests that these movements are either driven by an active machinery or part of stress-relaxation mechanisms. Comparison with a null physical model for subdiffusive chromosomal dynamics shows that rapid movements are excursions from a basal subdiffusive dynamics, likely due to driven and/or stress-relaxation motion. Additionally, rapid movements are in some cases coupled with known transitions of chromosomal segregation. They do not co-occur strictly with replication, their frequency varies with growth condition and chromosomal coordinate, and they show a preference for longitudinal motion. These findings support an emerging picture of the bacterial chromosome as off-equilibrium active matter and help developing a correct physical model of its in vivo dynamic structure.
[Show abstract][Hide abstract] ABSTRACT: Prokaryotes vary their protein repertoire mainly through horizontal transfer and gene loss. To elucidate the links between these processes and the cross-species gene-family statistics, we perform a large-scale data analysis of the cross-species variability of gene-family abundance (the number of members of the family found on a given genome). We find that abundance fluctuations are related to the rate of horizontal transfers. This is rationalized by a minimal theoretical model, which predicts this link. The families that are not captured by the model show abundance profiles that are markedly peaked around a mean value, possibly because of specific abundance selection. Based on these results, we define an abundance variability index that captures a family's evolutionary behavior (and thus some of its relevant functional properties) purely based on its cross-species abundance fluctuations. Analysis and model, combined, show a quantitative link between cross-species family abundance statistics and horizontal transfer dynamics, which can be used to analyze genome 'flux'. Groups of families with different values of the abundance variability index correspond to genome sub-parts having different plasticity in terms of the level of horizontal exchange allowed by natural selection.
Nucleic Acids Research 05/2014; · 8.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The coordination of cell growth and division is a long-standing problem in biology. Focusing on Escherichia coli in steady growth, we quantify cell division control using a stochastic model, by inferring the division rate as a function of the observable parameters from large empirical datasets of dividing cells. We find that (i) cells have mechanisms to control their size, (ii) size control is effected by changes in the doubling time, rather than in the single-cell elongation rate, (iii) the division rate increases steeply with cell size for small cells, and saturates for larger cells. Importantly, (iv) the current size is not the only variable controlling cell division, but the time spent in the cell cycle appears to play a role, and (v) common tests of cell size control may fail when such concerted control is in place. Our analysis illustrates the mechanisms of cell division control in E. coli. The phenomenological framework presented is sufficiently general to be widely applicable and opens the way for rigorous tests of molecular cell-cycle models.
Proceedings of the National Academy of Sciences 02/2014; · 9.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Recent biophysical approaches have provided key insights into the enthalpic and entropic forces that compact the nucleoid in the cell. Our biophysical approach combines two complementary, non-invasive and label-free techniques: a precisely timed steerable optical trap and a high throughput microcapillary Coulter counter. We demonstrate the ability of the latter technique to probe the physical properties and size of many purified nucleoids, at the individual nucleoid level. The DNA-binding protein H-NS is central to the organization of the bacterial genome. Our results show that nucleoids purified from the Δhns strain in the stationary phase expand approximately five fold more than the form observed in WT bacteria. This compaction is consistent with the role played by H-NS in regulating the nucleoid structure and the significant organizational changes that occur as the cell adapts to the stationary phase. We also study the permeability to the flow of ions and find that in the experiment nucleoids behave as solid colloids.
[Show abstract][Hide abstract] ABSTRACT: 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.
Proceedings of the National Academy of Sciences 12/2013; · 9.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In bacteria, chromosomal architecture shows strong spatial and temporal organization, and regulates key cellular functions, such as transcription. Tracking the motion of chromosomal loci at short timescales provides information related to both the physical state of the nucleo-protein complex and its local environment, independent of large-scale motions related to genome segregation. Here we investigate the short-time (0.1-10 s) dynamics of fluorescently labelled chromosomal loci in Escherichia coli at different growth rates. At these timescales, we observe for the first time a dependence of the loci's apparent diffusion on both their subcellular localization and chromosomal coordinate, and we provide evidence that the properties of the chromosome are similar in the tested growth conditions. Our results indicate that either non-equilibrium fluctuations due to enzyme activity or the organization of the genome as a polymer-protein complex vary as a function of the distance from the origin of replication.
[Show abstract][Hide abstract] ABSTRACT: We examine the phenomenon of hydrodynamic-induced cooperativity for pairs of flagellated micro-organism swimmers, of which spermatozoa cells are an example. We consider semiflexible swimmers, where inextensible filaments are driven by an internal intrinsic force and torque-free mechanism (intrinsic swimmers). The velocity gain for swimming cooperatively, which depends on both the geometry and the driving, develops as a result of the near-field coupling of bending and hydrodynamic stresses. We identify the regimes where hydrodynamic cooperativity is advantageous and quantify the change in efficiency. When the filaments' axes are parallel, hydrodynamic interaction induces a directional instability that causes semiflexible swimmers that profit from swimming together to move apart from each other. Biologically, this implies that flagella need to select different synchronized collective states and to compensate for directional instabilities (e.g., by binding) in order to profit from swimming together. By analyzing the cooperative motion of pairs of externally actuated filaments, we assess the impact that stress distribution along the filaments has on their collective displacements.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 03/2013; 87(3).
[Show abstract][Hide abstract] ABSTRACT: The H-NS chromosome-organizing protein in E. coli can stabilize genomic DNA loops, and form oligomeric structures connected to repression of gene expression. Motivated by the link between chromosome organization, protein binding and gene expression, we analyzed publicly available genomic data sets of various origins, from genome-wide protein binding profiles to evolutionary information, exploring the connections between chromosomal organization, gene-silencing, pseudo-gene localization and horizontal gene transfer. We report the existence of transcriptionally silent contiguous areas corresponding to large regions of H-NS protein binding along the genome, their position indicates a possible relationship with the known large-scale features of chromosome organization.
[Show abstract][Hide abstract] ABSTRACT: Open-source software is a complex system; its development depends on the
self-coordinated action of a large number of agents. This study follows the
size of the building blocks, called "packages", of the Ubuntu Linux operating
system over its entire history. The analysis reveals a multiplicative diffusion
process, constrained by size-dependent bounds, driving the dynamics of the
package-size distribution. A formalization of this into a quantitative model is
able to match the data without relying on any adjustable parameters, and
generates definite predictions. Finally, we formulate the hypothesis that a
similar non-stationary mechanism could be shaping the distribution of mammal
[Show abstract][Hide abstract] ABSTRACT: We generated a genome-wide replication profile in the genome of Lachancea kluyveri and assessed the relationship between replication and base composition. This species diverged from Saccharomyces cerevisiae before the ancestral whole genome duplication. The genome comprises 8 chromosomes among which a chromosomal arm of 1 Mb has a G+C-content much higher than the rest of the genome. We identified 252 active replication origins in L. kluyveri and found considerable divergence in origin location with S. cerevisiae and with L. waltii. Although some global features of S. cerevisiae replication are conserved: centromeres replicate early while telomeres replicate late, we found that replication origins both in L. kluyveri and L. waltii do not behave as evolutionary fragile sites. In L. kluyveri, replication timing along chromosomes alternates between regions of early and late activating origins, except for the 1 Mb GC-rich chromosomal arm. This chromosomal arm contains an origin consensus motif different from other chromosomes and is replicated early during S-phase. We showed that precocious replication results from the specific absence of late firing origins in this chromosomal arm. In addition, we found a correlation between GC-content and distance from replication origins as well as a lack of replication-associated compositional skew between leading and lagging strands specifically in this GC-rich chromosomal arm. These findings suggest that the unusual base composition in the genome of L. kluyveri could be linked to replication.
Genome Biology and Evolution 01/2013; · 4.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We designed a microfluidic chemostat consisting of 600 sub-micron trapping/growth channels connected to two feeding channels. The microchemostat traps E. coli cells and forces them to grow in lines for over 50 generations. Excess cells, including the mother cells captured at the start of the process, are removed from both ends of the growth channels by the media flow. With the aid of time-lapse microscopy, we have monitored dynamic properties such as growth rate and GFP expression at the single-cell level for many generations while maintaining a population of bacteria of similar age. We also use the microchemostat to show how the population responds to dynamic changes in the environment. Since more than 100 individual bacterial cells are aligned and immobilized in a single field of view, the microchemostat is an ideal platform for high-throughput intracellular measurements. We demonstrate this capability by tracking with sub-diffraction resolution the movements of fluorescently tagged loci in more than one thousand cells on a single device. The device yields results comparable to conventional agar microscopy experiments with substantial increases in throughput and ease of analysis.
[Show abstract][Hide abstract] ABSTRACT: 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 dependencies 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.
Physical Review E 01/2013; 87(1-1):012726. · 2.31 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Often, laboratory evolution experiments for large populations of microorganisms which cannot recombine show two distinct phases: an initial rapid increase in fitness followed by a slower regime. In order to explore the population structure and the evolutionary tree in the later stages of adaptation, we evolved a very large population of about 3×10(10) Acinetobacter baylyi bacteria for approximately 2800 generations from a single clone, while maintaining it in a chemostat at high dilution rate. Nitrate in limiting amount and as the sole nitrogen source was used as a selection pressure. Analysis via resequencing of genomes extracted from populations give proofs that diversity can establish in chemostat at long term in a very simple medium. To find out which biological parameters were targeted by adaptation, we measured the maximum growth rate, the nitrate uptake and the resistance to starvation. Overall, we find that maximum growth rate could be a reasonably good proxy for fitness. The late slow adaptation is compatible with selection coeffcients spanning a typical range of 10(-3) - 10(-2) per generation as estimated by resequencing, pointing to a possible subpopulations structuring.
Genome Biology and Evolution 12/2012; · 4.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Nucleoid shaping transcription factors (NSTFs) are DNA binding proteins that alter the shape of the bacterial nucleoid at both global and local levels. The activity of NSTFs depends on their environment, most notably the growth rate of the cell. Understanding how these proteins affect the shape of the bacterial nucleoid, in particular their role on the transcription network, is a challenging problem. One possible approach to study the binding is microrheology, where we track the mobility of fluorescently tagged chromosomal loci to obtain information about the local environment surrounding a DNA-bound NSTF.
We have taken a two-pronged approach towards these experiments. In the classical method, we grow colonies of E. coli cells from single parents on agar. While this approach is simple, the throughput is limited. More importantly, the nutrients become depleted as the population grows, leading to changes in the growth rate with time. To circumvent the limitations of the classic method, we designed a microfluidic chemostat that traps the E. coli cells, forcing them to grow in lines for many generations while maintaining a constant chemical environment. By carefully controlling the channel geometry, we can immobilize the E. coli cells without impacting their growth. We can thus monitor the growth rate at the single cell level and track the movements of fluorescently tagged loci in more than one thousand cells at a time using time-lapse microscopy.
Using both methods, we have obtained high resolution data for the mobility of 14 loci across the chromosome under four different growth conditions, two on our microchemostat and two on agar. At short-time scales (0.1-10s) we have observed a dependence of loci mobility on chromosomal position. Ter proximate loci have a decreased mobility with respect to Ori proximate loci, and the pattern of loci mobility is roughly symmetric with distance along the replichore arm. By examining loci dynamics as a function of sub-cellular position, we observed a tendency of Ter proximate loci to be located at the cell poles and at mid-cell and a corresponding decrease in the mobility of loci at these sub-cellular positions.
On the other hand, mean-square displacements (MSD) of all loci scale as γ×(Δt)α, where the mean exponent α (despite its wide distribution) seems to be close to 0.4. The exponent is independent of the growth rate, cell cycle time, positions of loci, or the type of experiment (microdevice versus agar). We formulate the hypothesis that this universal dynamical property could be related to a viscoelasticity caused by the genome through a dense fractal organization, and not as a consequence of the action of extrinsic cytoskeletal elements as previously speculated.
[Show abstract][Hide abstract] ABSTRACT: The adaptive evolution of large asexual populations is generally
characterized by competition between clones carrying different beneficial
mutations. This interference phenomenon slows down the adaptation speed and
makes the theoretical description of the dynamics more complex with respect to
the successional occurrence and fixation of beneficial mutations typical of
small populations. A simplified modeling framework considering multiple
beneficial mutations with equal and constant fitness advantage captures some of
the essential features of the actual complex dynamics, and some key predictions
from this model are verified in laboratory evolution experiments. However, in
these experiments the relative advantage of a beneficial mutation is generally
dependent on the genetic background. In particular, the general pattern is
that, as mutations in different loci accumulate, the relative advantage of new
mutations decreases, trend often referred to as "diminishing return" epistasis.
In this paper, we propose a phenomenological model that generalizes the
fixed-advantage framework to include in a simple way this feature. To evaluate
the quantitative consequences of diminishing returns on the evolutionary
dynamics, we approach the model analytically as well as with direct
simulations. Finally, we show how the model parameters can be matched with data
from evolutionary experiments in order to infer the mean effect of epistasis
and derive order-of-magnitude estimates of the rate of beneficial mutations.
Applying this procedure to two experimental data sets gives values of the
beneficial mutation rate within the range of previous measurements.