The sliding motility of the bacilliform virions of Influenza A viruses.

Influenza A virus (IAV) infection relies on the action of the hemagglutinin (HA) and neuraminidase (NA) membrane proteins. The HA ligands anchor the IAV virion to the cell's surface by binding the sialic acid (SA) present on the host's receptors while NA is an enzyme capable of cleaving the SA from the extracellular environment. It is believed that the activity of NA ligands increases the motility of the virions favoring the propagation of the infection. In this work, we develop a numerical framework to study the dynamics of a virion moving across the cell surface for timescales much bigger than the typical ligand-receptor reaction times. We find that the rates controlling the ligand-receptor reactions and the maximal distance at which a pair of ligand-receptor molecules can interact greatly affect the motility of the virions. We also report on how different ways of organizing the two types of ligands on the virions' surface result in different types of motion that we rationalize using general principles. In particular, we show how the emerging motility of the virion is less sensitive to the rate controlling the enzymatic activity when NA ligands are clustered.

Model of neural induction in the ascidian embryo.

How cell specification can be controlled in a reproducible manner is a fundamental question in developmental biology. In ascidians, a group of invertebrate chordates, geometry plays a key role in achieving this control. Here, we use mathematical modeling to demonstrate that geometry dictates the neural-epidermal cell fate choice in the 32-cell stage ascidian embryo by a two-step process involving first the modulation of ERK signaling and second, the expression of the neural marker gene, Otx. The model describes signal transduction by the ERK pathway that is stimulated by FGF and attenuated by ephrin, and ERK-mediated control of Otx gene expression, which involves both an activator and a repressor of ETS-family transcription factors. Considering the measured area of cell surface contacts with FGF- or ephrin-expressing cells as inputs, the solutions of the model reproduce the experimental observations about ERK activation and Otx expression in the different cells under normal and perturbed conditions. Sensitivity analyses and computations of Hill coefficients allow us to quantify the robustness of the specification mechanism controlled by cell surface area and to identify the respective role played by each signaling input. Simulations also predict in which conditions the dual control of gene expression by an activator and a repressor that are both under the control of ERK can induce a robust ON/OFF control of neural fate induction.

Brownian motion in a growing population of ballistic particles.

We investigate the motility of a growing population of cells in a idealized setting: We consider a system of hard disks in which new particles are added according to prescribed growth kinetics, thereby dynamically changing the number density. As a result, the expected Brownian motion of the hard disks is modified. We compute the density-dependent friction of the hard disks and insert it in an effective Langevin equation to describe the system, assuming that the intercollision time is smaller than the timescale of the growth. We find that the effective Langevin description captures the changes in motility, in agreement with the simulation results. Our framework can be extended to other systems in which the transport coefficient varies with time.

Heavy-tailed abundance distributions from stochastic Lotka-Volterra models.

Microbial communities found in nature are composed of many rare species and few abundant ones, as reflected by their heavy-tailed abundance distributions. How a large number of species can coexist in those complex communities and why they are dominated by rare species is still not fully understood. We show how heavy-tailed distributions arise as an emergent property from large communities with many interacting species in population-level models. To do so, we rely on generalized Lotka-Volterra models for which we introduce a global maximal capacity. This maximal capacity accounts for the fact that communities are limited by available resources and space. In a parallel ad hoc approach, we obtain heavy-tailed abundance distributions from logistic models, without interactions, through specific distributions of the parameters. We expect both mechanisms, interactions between many species and specific parameter distributions, to be relevant to explain the observed heavy tails.

Cell geometry, signal dampening, and a bimodal transcriptional response underlie the spatial precision of an ERK-mediated embryonic induction.

Precise control of lineage segregation is critical for the development of multicellular organisms, but our quantitative understanding of how variable signaling inputs are integrated to activate lineage-specific gene programs remains limited. Here, we show how precisely two out of eight ectoderm cells adopt neural fates in response to ephrin and FGF signals during ascidian neural induction. In each ectoderm cell, FGF signals activate ERK to a level that mirrors its cell contact surface with FGF-expressing mesendoderm cells. This gradual interpretation of FGF inputs is followed by a bimodal transcriptional response of the immediate early gene, Otx, resulting in its activation specifically in the neural precursors. At low levels of ERK, Otx is repressed by an ETS family transcriptional repressor, ERF2. Ephrin signals are critical for dampening ERK activation levels across ectoderm cells so that only neural precursors exhibit above-threshold levels, evade ERF repression, and "switch on" Otx transcription.

Stochastic logistic models reproduce experimental time series of microbial communities.

We analyze properties of experimental microbial time series, from plankton and the human microbiome, and investigate whether stochastic generalized Lotka-Volterra models could reproduce those properties. We show that this is the case when the noise term is large and a linear function of the species abundance, while the strength of the self-interactions varies over multiple orders of magnitude. We stress the fact that all the observed stochastic properties can be obtained from a logistic model, that is, without interactions, even the niche character of the experimental time series. Linear noise is associated with growth rate stochasticity, which is related to changes in the environment. This suggests that fluctuations in the sparsely sampled experimental time series may be caused by extrinsic sources.

Non-monotonic auto-regulation in single gene circuits.

We theoretically study the effects of non-monotonic response curves in genetic auto-regulation by exploring the possible dynamical behaviors for such systems. Our motivation is twofold: we aim at conceiving the simplest genetic circuits for synthetic biology and at understanding the natural auto-regulation of the LrpB protein of the Sulfolobus solfataricus archaeon which exhibits non-monotonicity. We analyzed three toy models, based on mass-action kinetics, with increasing complexity and sought for oscillations and (fast) bistable switching. We performed large parameter scans and sensitivity analyses, and quantified the quality of the oscillators and switches by computing relative volumes in parameter space reproducing the sought dynamical behavior. All single gene systems need finely tuned parameters in order to oscillate, but bistable switches are more robust against parameter changes. We expected non-monotonic switches to be faster than monotonic ones, however solutions combining both auto-activation and repression in the physiological range to obtain fast switches are scarce. Our analysis shows that the Ss-LrpB system can not provide a bistable switch and that robust oscillations are unlikely. Gillespie simulations suggest that the function of the natural Ss-LrpB system is sensing via a spiking behavior, which is in line with the fact that this protein has a metabolic regulatory function and binds to a ligand.

Signatures of ecological processes in microbial community time series.

BACKGROUND: Growth rates, interactions between community members, stochasticity, and immigration are important drivers of microbial community dynamics. In sequencing data analysis, such as network construction and community model parameterization, we make implicit assumptions about the nature of these drivers and thereby restrict model outcome. Despite apparent risk of methodological bias, the validity of the assumptions is rarely tested, as comprehensive procedures are lacking. Here, we propose a classification scheme to determine the processes that gave rise to the observed time series and to enable better model selection. RESULTS: We implemented a three-step classification scheme in R that first determines whether dependence between successive time steps (temporal structure) is present in the time series and then assesses with a recently developed neutrality test whether interactions between species are required for the dynamics. If the first and second tests confirm the presence of temporal structure and interactions, then parameters for interaction models are estimated. To quantify the importance of temporal structure, we compute the noise-type profile of the community, which ranges from black in case of strong dependency to white in the absence of any dependency. We applied this scheme to simulated time series generated with the Dirichlet-multinomial (DM) distribution, Hubbell's neutral model, the generalized Lotka-Volterra model and its discrete variant (the Ricker model), and a self-organized instability model, as well as to human stool microbiota time series. The noise-type profiles for all but DM data clearly indicated distinctive structures. The neutrality test correctly classified all but DM and neutral time series as non-neutral. The procedure reliably identified time series for which interaction inference was suitable. Both tests were required, as we demonstrated that all structured time series, including those generated with the neutral model, achieved a moderate to high goodness of fit to the Ricker model. CONCLUSIONS: We present a fast and robust scheme to classify community structure and to assess the prevalence of interactions directly from microbial time series data. The procedure not only serves to determine ecological drivers of microbial dynamics, but also to guide selection of appropriate community models for prediction and follow-up analysis.

Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations.

We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.

Robust circadian oscillations in growing cyanobacteria require transcriptional feedback.

The remarkably stable circadian oscillations of single cyanobacteria enable a population of growing cells to maintain synchrony for weeks. The cyanobacterial pacemaker is a posttranslational regulation (PTR) circuit that generates circadian oscillations in the phosphorylation state of the clock protein KaiC. Layered on top of the PTR is transcriptional-translational feedback regulation (TTR), common to all circadian systems, consisting of a negative feedback loop in which KaiC regulates its own production. We found that the PTR circuit is sufficient to generate oscillations in growing cyanobacteria. However, in the absence of TTR, individual oscillators were less stable and synchrony was not maintained in a population of cells. Experimentally constrained mathematical modeling reproduced sustained oscillations in the PTR circuit alone and demonstrated the importance of TTR for oscillator synchrony.