Synchronisation of stochastic oscillators in biochemical systems

A formalism is developed which describes the extent to which stochastic oscillations in biochemical models are synchronised. It is based on the calculation of the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronisation of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronisation of the oscillations is explored, and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations

Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasi-cycles --- stochastic cycles sustained and amplified by the demographic noise --- previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity and chaos, are also investigated.Comment: 21 pages, 12 figure

Suppressing escape events in maps of the unit interval with demographic noise

We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between successive iterates of the process can result in probability leaking out of the unit interval, despite the fact that the noise is multiplicative and vanishes at the boundaries. By including higher-order terms in the mesoscopic expansion, we are able to capture the non-Gaussian nature of the noise distribution near the boundaries, but this does not preclude the possibility of a trajectory leaving the interval. We propose a number of prescriptions for treating these escape events, and we compare the results with those obtained for the metastable behavior of the microscopic model, where escape events are not possible. We find that, rather than truncating the noise distribution, censoring this distribution to prevent escape events leads to results which are more consistent with the microscopic model. The addition of higher moments to the noise distribution does not increase the accuracy of the final results, and it can be replaced by the simpler Gaussian noise.Comment: 14 pages, 13 figure

Turing instabilities from a limit cycle

The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a consequence, the system evolves towards a stationary, nonhomogeneous attractor. Stable patterns can be also obtained via oscillation quenching of an initially synchronous state of diffusively coupled oscillators. In the literature this is known as the oscillation death phenomenon. Here we show that oscillation death is nothing but a Turing instability for the first return map associated to the excitable system in its synchronous periodic state. In particular we obtain a set of closed conditions for identifying the domain in the parameters space that yields the instability. This is a natural generalisation of the original Turing relations, to the case where the homogeneous solution of the examined system is a periodic function of time. The obtained framework applies to systems embedded in continuum space, as well as those defined on a network-like support. The predictive ability of the theory is tested numerically, using different reaction schemes.Comment: 10 pages, 8 figure

Assessing the impact of imperfect adherence to artemether-lumefantrine on malaria treatment outcomes using within-host modelling.

Artemether-lumefantrine (AL) is the most widely-recommended treatment for uncomplicated Plasmodium falciparum malaria worldwide. Its safety and efficacy have been extensively demonstrated in clinical trials; however, its performance in routine health care settings, where adherence to drug treatment is unsupervised and therefore may be suboptimal, is less well characterised. Here we develop a within-host modelling framework for estimating the effects of sub-optimal adherence to AL treatment on clinical outcomes in malaria patients. Our model incorporates the data on the human immune response to the parasite, and AL's pharmacokinetic and pharmacodynamic properties. Utilising individual-level data of adherence to AL in 482 Tanzanian patients as input for our model predicted higher rates of treatment failure than were obtained when adherence was optimal (9% compared to 4%). Our model estimates that the impact of imperfect adherence was worst in children, highlighting the importance of advice to caregivers

Intrinsic noise and discrete-time processes

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the non-chaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.Comment: Modified version accepted for publication in Phys. Rev. E Rapid Communications. New figures adde

What causes the decrease in haematocrit during egg production?

1. Anaemia has been reported in wild animals, typically associated with traumatic events or ill health. However, female birds routinely become \u27anaemic\u27 during egg-laying; we sought to determine the causes of this reduction in haematocrit. 2. Haematocrit in female European Starlings (Sturnus vulgaris Linnaeus) decreased between pre-breeding and egg-laying in 3 out of 4 years (the decrease was marginally non-significant in the fourth year). This was independent of changes in ambient temperature altering the metabolic requirements for thermoregulation. 3. There was a positive relationship between haematocrit and plasma levels of the yolk precursor vitellogenin among egg-laying birds, supporting the hypothesis that the initial reduction in haematocrit is caused by increased blood volume associated with osmoregulatory adjustments to elevated levels of yolk precursors. 4. However, haematocrit did not always recover upon cessation of egg production, remaining low a.t clutch completion (2 of 4 years), incubation (1 of 2 years) and chick rearing (1 of 4 years), suggesting an additional cause of the prolonged reduction in haematocrit. 5. Given the magnitude and prolonged nature of the changes in haematocrit we report, and the interannual variation in haematocrit even during chick-rearing (47-54%), we suggest that \u27anaemia\u27 associated with egg production might have implications for aerobic performance during later stages of breeding

What causes the decrease in haematocrit during egg production?

1. Anaemia has been reported in wild animals, typically associated with traumatic events or ill health. However, female birds routinely become \u27anaemic\u27 during egg-laying; we sought to determine the causes of this reduction in haematocrit. 2. Haematocrit in female European Starlings (Sturnus vulgaris Linnaeus) decreased between pre-breeding and egg-laying in 3 out of 4 years (the decrease was marginally non-significant in the fourth year). This was independent of changes in ambient temperature altering the metabolic requirements for thermoregulation. 3. There was a positive relationship between haematocrit and plasma levels of the yolk precursor vitellogenin among egg-laying birds, supporting the hypothesis that the initial reduction in haematocrit is caused by increased blood volume associated with osmoregulatory adjustments to elevated levels of yolk precursors. 4. However, haematocrit did not always recover upon cessation of egg production, remaining low a.t clutch completion (2 of 4 years), incubation (1 of 2 years) and chick rearing (1 of 4 years), suggesting an additional cause of the prolonged reduction in haematocrit. 5. Given the magnitude and prolonged nature of the changes in haematocrit we report, and the interannual variation in haematocrit even during chick-rearing (47-54%), we suggest that \u27anaemia\u27 associated with egg production might have implications for aerobic performance during later stages of breeding

Causal claims about correlations reduced in press releases following academic study of health news

Background: Exaggerations in health news were previously found to strongly associate with similar exaggerations in press releases. Moreover such exaggerations did not appear to attract more news. Here we assess whether press release practice changed after these reported findings; simply drawing attention to the issue may be insufficient for practical change, given the challenges of media environments. Methods: We assessed whether rates of causal over-statement in press releases based on correlational data were lower following a seminal paper on the topic, compared to an equivalent baseline period in the preceding year. Results: We found that over-statements in press releases reduced from 28% (95% confidence interval = 16% to 45%) in 2014 to 13% (95% confidence interval = 6% to 25%) in 2015. A corresponding numerical reduction in exaggerations in news was not significant. The association between over-statements in news and press releases remained strong. Conclusions: Press release over-statements were less frequent following publication of Sumner et al. (2014), indicating that press release practice is malleable. However, this is correlational evidence and the reduction may be due to other factors