Mean Flow Effects in Model Equations for Faraday Waves

We review model equations for parametric surface waves (Faraday waves) in the limit of small viscous dissipation. The equations account for two effects of viscosity, namely damping of the waves and slowly varying streaming and large scale flows (mean flow). Equations for the mean flow can be derived by a multiple scale analysis and are coupled to an order parameter equation describing the evolution of the surface waves. In addition, the equations incorporate a phenomenological damping term due to viscous dissipation. The nonlinear terms, which are undetermined by the derivation of the equation for the surface waves, are chosen so that the primary bifurcation is to a set of standing waves in the form of stripes. Results for the secondary instabilities of the primary waves are presented, including a weak amplification of both Eckhaus and Transverse Amplitude Modulation instabilities due to the mean flow, and a new longitudinal oscillatory instability which is absent without mean flow. Generation of mean flow due to dislocation defects in regular patterns is studied by numerical simulations

Epidemics with mutating infectivity on small-world networks

Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent’s infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation. © 2020, The Author(s)

Epidemics with mutating infectivity on small-world networks

Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent's infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation

Ryanodine Receptor Activation Induces Long-Term Plasticity of Spine Calcium Dynamics

A key feature of signalling in dendritic spines is the synapse-specific transduction of short electrical signals into biochemical responses. Ca2+ is a major upstream effector in this transduction cascade, serving both as a depolarising electrical charge carrier at the membrane and an intracellular second messenger. Upon action potential firing, the majority of spines are subject to global back-propagating action potential (bAP) Ca2+ transients. These transients translate neuronal suprathreshold activation into intracellular biochemical events. Using a combination of electrophysiology, two-photon Ca2+ imaging, and modelling, we demonstrate that bAPs are electrochemically coupled to Ca2+ release from intracellular stores via ryanodine receptors (RyRs). We describe a new function mediated by spine RyRs: the activity-dependent long-term enhancement of the bAP-Ca2+ transient. Spines regulate bAP Ca2+ influx independent of each other, as bAP-Ca2+ transient enhancement is compartmentalized and independent of the dendritic Ca2+ transient. Furthermore, this functional state change depends exclusively on bAPs travelling antidromically into dendrites and spines. Induction, but not expression, of bAP-Ca2+ transient enhancement is a spine-specific function of the RyR. We demonstrate that RyRs can form specific Ca2+ signalling nanodomains within single spines. Functionally, RyR mediated Ca2+ release in these nanodomains induces a new form of Ca2+ transient plasticity that constitutes a spine specific storage mechanism of neuronal suprathreshold activity patterns

Modulation of Elementary Calcium Release Mediates a Transition from Puffs to Waves in an IP3R Cluster Model

The oscillating concentration of intracellular calcium is one of the most important examples for collective dynamics in cell biology. Localized releases of calcium through clusters of inositol 1,4,5-trisphosphate receptor channels constitute elementary signals called calcium puffs. Coupling by diffusing calcium leads to global releases and waves, but the exact mechanism of inter- cluster coupling and triggering of waves is unknown. To elucidate the relation of puffs and waves, we here model a cluster of IP3R channels using a gating scheme with variable non-equilibrium IP3 binding. Hybrid stochastic and deterministic simulations show that puffs are not stereotyped events of constant duration but are sensitive to stimulation strength and residual calcium. For increasing IP3 concentration, the release events become modulated at a timescale of minutes, with repetitive wave-like releases interspersed with several puffs. This modulation is consistent with experimental observations we present, including refractoriness and increase of puff frequency during the inter-wave interval. Our results suggest that waves are established by a random but time-modulated appearance of sustained release events, which have a high potential to trigger and synchronize activity throughout the cell

A phenomenological model of weakly damped Faraday waves and the associated mean flow

A phenomenological model of parametric surface waves (Faraday waves) is introduced in the limit of small viscous dissipation that accounts for the coupling between surface motion and slowly varying streaming and large scale flows (mean flow). The primary bifurcation of the model is to a set of standing waves (stripes, given the functional form of the model nonlinearities chosen here). Our results for the secondary instabilities of the primary wave show that the mean flow leads to a weak destabilization of the base state against Eckhaus and Transverse Amplitude Modulation instabilities, and introduces a new longitudinal oscillatory instability which is absent without the coupling. We compare our results with recent one dimensional amplitude equations for this system systematically derived from the governing hydrodynamic equations.Comment: Complete paper with embedded figures (PostScript, 3 Mb) http://www.csit.fsu.edu/~vinals/mss/jmv1.p

Data-Driven Modelling of the Inositol Trisphosphate Receptor (IPR) and its Role in Calcium-Induced Calcium Release (CICR)

We review the current state of the art of data-driven modelling of the inositol trisphosphate receptor (IPR). After explaining that the IPR plays a crucial role as a central regulator in calcium dynamics, several sources of relevant experimental data are introduced. Single ion channels are best studied by recording single-channel currents under different ligand concentrations via the patch-clamp technique. The particular relevance of modal gating, the spontaneous switching between different levels of channel activity that occur even at constant ligand concentrations, is highlighted. In order to investigate the interactions of IPRs, calcium release from small clusters of channels, so-called calcium puffs, can be used. We then present the mathematical framework common to all models based on single-channel data, aggregated continuous-time Markov models, and give a short review of statistical approaches for parameterising these models with experimental data. The process of building a Markov model that integrates various sources of experimental data is illustrated using two recent examples, the model by Ullah et al. and the “Park–Drive” model by Siekmann et al. (Biophys. J. 2012), the only models that account for all sources of data currently available. Finally, it is demonstrated that the essential features of the Park–Drive model in different models of calcium dynamics are preserved after reducing it to a two-state model that only accounts for the switching between the inactive “park” and the active “drive” modes. This highlights the fact that modal gating is the most important mechanism of ligand regulation in the IPR. It also emphasises that data-driven models of ion channels do not necessarily have to lead to detailed models but can be constructed so that relevant data is selected to represent ion channels at the appropriate level of complexity for a given application

2q36.3 is associated with prognosis for oestrogen receptor-negative breast cancer patients treated with chemotherapy.

Large population-based registry studies have shown that breast cancer prognosis is inherited. Here we analyse single-nucleotide polymorphisms (SNPs) of genes implicated in human immunology and inflammation as candidates for prognostic markers of breast cancer survival involving 1,804 oestrogen receptor (ER)-negative patients treated with chemotherapy (279 events) from 14 European studies in a prior large-scale genotyping experiment, which is part of the Collaborative Oncological Gene-environment Study (COGS) initiative. We carry out replication using Asian COGS samples (n=522, 53 events) and the Prospective Study of Outcomes in Sporadic versus Hereditary breast cancer (POSH) study (n=315, 108 events). Rs4458204_A near CCL20 (2q36.3) is found to be associated with breast cancer-specific death at a genome-wide significant level (n=2,641, 440 events, combined allelic hazard ratio (HR)=1.81 (1.49-2.19); P for trend=1.90 × 10(-9)). Such survival-associated variants can represent ideal targets for tailored therapeutics, and may also enhance our current prognostic prediction capabilities

2q36.3 is associated with prognosis for oestrogen receptor-negative breast cancer patients treated with chemotherapy

Large population-based registry studies have shown that breast cancer prognosis is inherited. Here we analyse single-nucleotide polymorphisms (SNPs) of genes implicated in human immunology and inflammation as candidates for prognostic markers of breast cancer survival involving 1,804 oestrogen receptor (ER)-negative patients treated with chemotherapy (279 events) from 14 European studies in a prior large-scale genotyping experiment, which is part of the Collaborative Oncological Gene-environment Study (COGS) initiative. We carry out replication using Asian COGS samples (n=522, 53 events) and the Prospective Study of Outcomes in Sporadic versus Hereditary breast cancer (POSH) study (n=315, 108 events). Rs4458204-A near CCL20 (2q36.3) is found to be associated with breast cancer-specific death at a genome-wide significant level (n=2,641, 440 events, combined allelic hazard ratio (HR)=1.81 (1.49-2.19); P for trend=1.90 × 10 â ̂'9). Such survival-associated variants can represent ideal targets for tailored therapeutics, and may also enhance our current prognostic prediction capabilities

Genome-wide association study identifies 32 novel breast cancer susceptibility loci from overall and subtype-specific analyses.

Breast cancer susceptibility variants frequently show heterogeneity in associations by tumor subtype1-3. To identify novel loci, we performed a genome-wide association study including 133,384 breast cancer cases and 113,789 controls, plus 18,908 BRCA1 mutation carriers (9,414 with breast cancer) of European ancestry, using both standard and novel methodologies that account for underlying tumor heterogeneity by estrogen receptor, progesterone receptor and human epidermal growth factor receptor 2 status and tumor grade. We identified 32 novel susceptibility loci (P < 5.0 × 10-8), 15 of which showed evidence for associations with at least one tumor feature (false discovery rate < 0.05). Five loci showed associations (P < 0.05) in opposite directions between luminal and non-luminal subtypes. In silico analyses showed that these five loci contained cell-specific enhancers that differed between normal luminal and basal mammary cells. The genetic correlations between five intrinsic-like subtypes ranged from 0.35 to 0.80. The proportion of genome-wide chip heritability explained by all known susceptibility loci was 54.2% for luminal A-like disease and 37.6% for triple-negative disease. The odds ratios of polygenic risk scores, which included 330 variants, for the highest 1% of quantiles compared with middle quantiles were 5.63 and 3.02 for luminal A-like and triple-negative disease, respectively. These findings provide an improved understanding of genetic predisposition to breast cancer subtypes and will inform the development of subtype-specific polygenic risk scores