arXiv subjects

Bertrand Ottino-Loffler

Publications and source records attributed to Bertrand Ottino-Loffler.

5 recordsLinked to original sources

arXiv2024

On Possible Indicators of Negative Selection in Germinal Centers

A central feature of vertebrate immune response is affinity maturation, wherein antibody-producing B cells undergo evolutionary selection in microanatomical structures called germinal centers, which form in secondary lymphoid organs upon antigen exposure. While it has been shown that the median B cell affinity dependably increases over the course of maturation, the exact logic behind this evolution remains vague. Three potential selection methods include encouraging the reproduction of high affinity cells (``birth/positive selection''), encouraging cell death in low affinity cells (``death/negative selection''), and adjusting the mutation rate based on cell affinity (``mutational selection''). While all three forms of selection would lead to a net increase in affinity, different selection methods may lead to distinct statistical dynamics. We present a tractable model of selection, and analyze proposed signatures of negative selection. Given the simplicity of the model, such signatures should be stronger here than in real systems. However, we find a number of intuitively appealing metrics -- such as preferential ancestry ratios, terminal node counts, and mutation count skewness -- are all ill-suited for detecting selection method.

q-bio.PE↗

arXiv2017

Evolutionary dynamics of incubation periods

The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, the incubation period is highly variable. Some affected people take much longer than average to show symptoms, leading to a distribution of incubation periods that is right skewed and often approximately lognormal. Although this statistical pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease.

q-bio.PE↗

arXiv2016

Comparing the Locking Threshold for Rings and Chains of Oscillators

We present a case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a chain with the same initial conditions and the same random natural frequencies. The only difference is their boundary conditions: periodic for a ring, and open for a chain. For both topologies, stable phase-locked states exist if and only if the spread or "width" of the natural frequencies is smaller than a critical value called the locking threshold (which depends on the boundary conditions and the particular realization of the frequencies). The central question is whether a ring synchronizes more readily than a chain. We show that it usually does, but not always. Rigorous bounds are derived for the ratio between the locking thresholds of a ring and its matched chain, for a variant of the Kuramoto model that also includes a wider family of models.

math.DS↗

arXiv2016

Kuramoto model with uniformly spaced frequencies:Finite-N asymptotics of the locking threshold

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, $N$, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite $N$, the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite $N$ have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when $N \gg 1$. The leading correction to the infinite-$N$ result scales like either $N^{-3/2}$ or $N^{-1}$, depending on whether the frequencies are evenly spaced according to a midpoint rule or an endpoint rule. These scaling laws agree with numerical results obtained by Pazó [Phys. Rev. E 72, 046211 (2005)]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics.

math.DS↗

arXiv2016

Frequency Spirals

We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call "frequency spirals." These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reaction-diffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.

math.DS↗