280 research outputs found
The Two Regime method for optimizing stochastic reaction-diffusion simulations
The computer simulation of stochastic reaction-diffusion processes in biology is often done using either compartment-based (spatially discretized) simulations or molecular-based (Brownian dynamics) approaches. Compartment-based approaches can yield quick and accurate mesoscopic results but lack the level of detail that is characteristic of the more computationally intensive molecular-based models. Often microscopic detail is only required in a small region but currently the best way to achieve this detail is to use a resource intensive model over the whole domain. We introduce the Two Regime Method (TRM) in which a molecular-based algorithm is used in part of the computational domain and a compartment-based approach is used elsewhere in the computational domain. We apply the TRM to two test problems including a model from developmental biology. We thereby show that the TRM is accurate and subsequently may be used to inspect both mesoscopic and microscopic detail of reaction diffusion simulations according to the demands of the modeller
Multiscale stochastic reaction-diffusion modelling: application to actin dynamics in filopodia
Two multiscale (hybrid) stochastic reaction-diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction-diffusion models. The first hybrid model is based on the models previously\ud
developed in the literature. The second hybrid model is based on the application of recently developed two-regime method (TRM) to a fully molecular-based model which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, “The two-regime method for optimizing stochastic reaction-diffusion simulations,” J. R. Soc., Interface9, 859–868 (Year: 2012)]10.1098/rsif.2011.0574 in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration and high cooperativity
Multiscale reaction-diffusiion algorithms: PDE-assisted Brownian dynamics
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented
Crystalline Order on a Sphere and the Generalized Thomson Problem
We attack generalized Thomson problems with a continuum formalism which
exploits a universal long range interaction between defects depending on the
Young modulus of the underlying lattice. Our predictions for the ground state
energy agree with simulations of long range power law interactions of the form
1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain
boundaries is studied in the context of tilted crystalline order and the
generality of our approach is illustrated with new results for square tilings
on the sphere.Comment: 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference
typo fixe
An investigation of microtubule organization and functions in living Drosophila embryos by injection of a fluorescently labeled antibody against tyrosinated alpha-tubulin.
A scoping review of mathematical models of Plasmodium vivax
Plasmodium vivax is one of the most geographically widespread malaria
parasites in the world due to its ability to remain dormant in the human liver
as hypnozoites and subsequently reactivate after the initial infection (i.e.
relapse infections). More than 80% of P. vivax infections are due to hypnozoite
reactivation. Mathematical modelling approaches have been widely applied to
understand P. vivax dynamics and predict the impact of intervention outcomes.
In this article, we provide a scoping review of mathematical models that
capture P. vivax transmission dynamics published between January 1988 and May
2023 to provide a comprehensive summary of the mathematical models and
techniques used to model P. vivax dynamics. We aim to assist researchers
working on P. vivax transmission and other aspects of P. vivax malaria by
highlighting best practices in currently published models and highlighting
where future model development is required. We provide an overview of the
different strategies used to incorporate the parasite's biology, use of
multiple scales (within-host and population-level), superinfection, immunity,
and treatment interventions. In most of the published literature, the rationale
for different modelling approaches was driven by the research question at hand.
Some models focus on the parasites' complicated biology, while others
incorporate simplified assumptions to avoid model complexity. Overall, the
existing literature on mathematical models for P. vivax encompasses various
aspects of the parasite's dynamics. We recommend that future research should
focus on refining how key aspects of P. vivax dynamics are modelled, including
the accumulation of hypnozoite variation, the interaction between P. falciparum
and P. vivax, acquisition of immunity, and recovery under superinfection
A model for malaria treatment evaluation in the presence of multiple species
Plasmodium (P.) falciparum and P. vivax are the two most common causes of
malaria. While the majority of deaths and severe morbidity are due to P.
falciparum, P. vivax poses a greater challenge to eliminating malaria outside
of Africa due to its ability to form latent liver stage parasites
(hypnozoites), which can cause relapsing episodes within an individual patient.
In areas where P. falciparum and P. vivax are co-endemic, individuals can carry
parasites of both species simultaneously. These mixed infections complicate
dynamics in several ways; treatment of mixed infections will simultaneously
affect both species, P. falciparum can mask the detection of P. vivax, and it
has been hypothesised that clearing P. falciparum may trigger a relapse of
dormant P. vivax. When mixed infections are treated for only blood-stage
parasites, patients are at risk of relapse infections due to P. vivax
hypnozoites.
We present a stochastic mathematical model that captures interactions between
P. falciparum and P. vivax, and incorporates both standard schizontocidal
treatment (which targets blood-stage parasites) and radical treatment (which
additionally targets liver-stage parasites). We apply this model to assess the
implications of different treatment coverage of radical cure for mixed and P.
vivax infections and a so-called "unified radical cure" treatment strategy for
P. falciparum, P. vivax and mixed infections. We find that a unified radical
cure strategy, with G6PD screening, leads to a substantially lower incidence of
malaria cases and deaths overall. We perform a one-way sensitivity analysis to
highlight important model parameters
Spatio-temporal Models of Lymphangiogenesis in Wound Healing
Several studies suggest that one possible cause of impaired wound healing is
failed or insufficient lymphangiogenesis, that is the formation of new
lymphatic capillaries. Although many mathematical models have been developed to
describe the formation of blood capillaries (angiogenesis), very few have been
proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a
markedly different process from angiogenesis, occurring at different times and
in response to different chemical stimuli. Two main hypotheses have been
proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the
edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic
endothelial cells first pool in the wound region following the lymph flow and
then, once sufficiently populated, start to form a network. Here we present two
PDE models describing lymphangiogenesis according to these two different
hypotheses. Further, we include the effect of advection due to interstitial
flow and lymph flow coming from open capillaries. The variables represent
different cell densities and growth factor concentrations, and where possible
the parameters are estimated from biological data. The models are then solved
numerically and the results are compared with the available biological
literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total
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