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.

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.

Optical Force Enhancement Using an Imaginary Vector Potential for Photons.

The enhancement of optical forces has enabled a variety of technological applications that rely on the optical control of small objects and devices. Unfortunately, optical forces are still too small for the convenient actuation of integrated switches and waveguide couplers. Here we show how the optical gradient force can be enhanced by an order of magnitude by making use of gauge materials inside two evanescently coupled waveguides. To this end, the gauge materials inside the cores should emulate imaginary vector potentials for photons pointing perpendicularly to the waveguide plane. Depending on the relative orientation of the vector potentials in neighboring waveguides, i.e., pointing away from or towards each other, the conventional attractive force due to an even mode profile may be enhanced, suppressed, or may even become repulsive. This and other new features indicate that the implementation of complex-valued vector potentials with non-Hermitian waveguide cores may further enhance our control over mode profiles and the associated optical forces.