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

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

How delayed and non-adherent treatment contribute to onward transmission of malaria: a modelling study

Introduction Artemether-lumefantrine (AL) is the most widely-recommended treatment for uncomplicated Plasmodium falciparum malaria. Its efficacy has been extensively assessed in clinical trials. In routine healthcare settings, however, its effectiveness can be diminished by delayed access to treatment and poor adherence. As well as affecting clinical outcomes, these factors can lead to increased transmission, which is the focus of this study. Methods We extend a within-host model of Plasmodium falciparum to include gametocytes, the parasite forms responsible for onward transmission. The model includes a pharmacokineticpharmacodynamic model of AL, calibrated against both immature and mature gametocytes using individual-level patient data, to estimate the impact that delayed access and imperfect adherence to treatment can have on onward transmission of the parasite to mosquitoes. Results Using survey data from 7 African countries to determine the time taken to acquire antimalarials following fever increased our estimates of mean total infectivity of a malaria episode by up to 1.5- fold, compared to patients treated after 24 hours. Realistic adherence behaviour, based on data from a monitored cohort in Tanzania, increased the contribution to transmission by 2.2 to 2.4-fold, compared to a perfectly-adherent cohort. This was driven largely by increased rates of treatment failure leading to chronic infection, rather than prolonged gametocytaemia in patients who have slower, but still successful, clearance of parasites after imperfect adherence to treatment. Our model estimated that the mean infectivity of untreated infections was 29-51 times higher than that of treated infections (assuming perfect drug adherence), underlining the importance of improving treatment coverage. Conclusion Using mathematical modelling, we quantify how delayed treatment and non-adherent treatment can increase transmission compared to prompt effective treatment. We also highlight that transmission from the large proportion of infections which never receive treatment is substantially higher than those treated

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

Modelling upper respiratory viral load dynamics of SARS-CoV-2

Relationships between viral load, severity of illness, and transmissibility of virus, are fundamental to understanding pathogenesis and devising better therapeutic and prevention strategies for COVID-19. Here we present within-host modelling of viral load dynamics observed in the upper respiratory tract (URT), drawing upon 2172 serial measurements from 605 subjects, collected from 17 different studies. We developed a mechanistic model to describe viral load dynamics and host response, and contrast this with simpler mixed-effects regression analysis of peak viral load and its subsequent decline. We observed wide variation in URT viral load between individuals, over 5 orders of magnitude, at any given point in time since symptom onset. This variation was not explained by age, sex, or severity of illness, and these variables were not associated with the modelled early or late phases of immune-mediated control of viral load. We explored the application of the mechanistic model to identify measured immune responses associated with control of viral load. Neutralizing antibody correlated strongly with modelled immune-mediated control of viral load amongst subjects who produced neutralizing antibody. Our models can be used to identify host and viral factors which control URT viral load dynamics, informing future treatment and transmission blocking interventions

Modelling upper respiratory viral load dynamics of SARS-CoV-2.

Relationships between viral load, severity of illness, and transmissibility of virus are fundamental to understanding pathogenesis and devising better therapeutic and prevention strategies for COVID-19. Here we present within-host modelling of viral load dynamics observed in the upper respiratory tract (URT), drawing upon 2172 serial measurements from 605 subjects, collected from 17 different studies. We developed a mechanistic model to describe viral load dynamics and host response and contrast this with simpler mixed-effects regression analysis of peak viral load and its subsequent decline. We observed wide variation in URT viral load between individuals, over 5 orders of magnitude, at any given point in time since symptom onset. This variation was not explained by age, sex, or severity of illness, and these variables were not associated with the modelled early or late phases of immune-mediated control of viral load. We explored the application of the mechanistic model to identify measured immune responses associated with the control of the viral load. Neutralising antibodies correlated strongly with modelled immune-mediated control of viral load amongst subjects who produced neutralising antibodies. Our models can be used to identify host and viral factors which control URT viral load dynamics, informing future treatment and transmission blocking interventions