Influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise

Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing’s model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the “box-splitting” form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary “on average.

Power spectra methods for a stochastic description of diffusion on deterministically growing domains

A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state

Stochastic reaction & diffusion on growing domains: understanding the breakdown of robust pattern formation

Many biological patterns, from population densities to animal coat markings, can be thought of as heterogeneous spatiotemporal distributions of mobile agents. Many mathematical models have been proposed to account for the emergence of this complexity, but, in general, they have consisted of deterministic systems of differential equations, which do not take into account the stochastic nature of population interactions. One particular, pertinent criticism of these deterministic systems is that the exhibited patterns can often be highly sensitive to changes in initial conditions, domain geometry, parameter values, etc. Due to this sensitivity, we seek to understand the effects of stochasticity and growth on paradigm biological patterning models. In this paper, we extend spatial Fourier analysis and growing domain mapping techniques to encompass stochastic Turing systems. Through this we find that the stochastic systems are able to realize much richer dynamics than their deterministic counterparts, in that patterns are able to exist outside the standard Turing parameter range. Further, it is seen that the inherent stochasticity in the reactions appears to be more important than the noise generated by growth, when considering which wave modes are excited. Finally, although growth is able to generate robust pattern sequences in the deterministic case, we see that stochastic effects destroy this mechanism for conferring robustness. However, through Fourier analysis we are able to suggest a reason behind this lack of robustness and identify possible mechanisms by which to reclaim it

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases

Modelling biological invasions: individual to population scales at interfaces

Extracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility

Unveiling the prehistoric landscape at Stonehenge through multi-receiver EMI

YesArchaeological research at Stonehenge (UK) is increasingly aimed at understanding the dynamic of the wider archaeological landscape. Through the application of state-of-the-art geophysical techniques, unprecedented insight is being gathered into the buried archaeological features of the area. However, applied survey techniques have rarely targeted natural soil variation, and the detailed knowledge of the palaeotopography is consequently less complete. In addition, metallic topsoil debris, scattered over different parts of the Stonehenge landscape, often impacts the interpretation of geophysical datasets. The research presented here demonstrates how a single multi-receiver electromagnetic induction (EMI) survey, conducted over a 22 ha area within the Stonehenge landscape, offers detailed insight into natural and anthropogenic soil variation at Stonehenge. The soil variations that were detected through recording the electrical and magnetic soil variability, shed light on the genesis of the landscape, and allow for a better definition of potential palaeoenvironmental and archaeological sampling locations. Based on the multi-layered dataset, a procedure was developed to remove the influence of topsoil metal from the survey data, which enabled a more straightforward identification of the detected archaeology. The results provide a robust basis for further geoarchaeological research, while potential to differentiate between modern soil disturbances and the underlying sub-surface variations can help in solving conservation and management issues. Through expanding this approach over the wider area, we aim at a fuller understanding of the human–landscape interactions that have shaped the Stonehenge landscape

Practice transformations to optimize the delivery of HIV primary care in community healthcare settings in the United States: A program implementation study.

BackgroundThe United States HIV care workforce is shrinking, which could complicate service delivery to people living with HIV (PLWH). In this study, we examined the impact of practice transformations, defined as efficiencies in structures and delivery of care, on demonstration project sites within the Workforce Capacity Building Initiative, a Health Resources and Services Administration (HRSA) Ryan White HIV/AIDS Program Special Projects of National Significance (SPNS).Methods and findingsData were collected at 14 demonstration project sites in 7 states and the District of Columbia. Organizational assessments were completed at sites once before and 4 times after implementation. They captured 3 transformation approaches: maximizing the HIV care workforce (efforts to increase the number of existing healthcare workforce members involved in the care of PLWH), share-the-care (team-based care giving more responsibility to midlevel providers and staff), and enhancing client engagement in primary HIV care to reduce emergency and inpatient care (e.g., care coordination). We also obtained Ryan White HIV/AIDS Program Services Reports (RSRs) from sites for calendar years (CYs) 2014-2016, corresponding to before, during, and after transformation. The RSR include data on client retention in HIV care, prescription of antiretroviral therapy (ART), and viral suppression. We used generalized estimating equation (GEE) models to analyze changes among sites implementing each practice transformation approach. The demonstration projects had a mean of 18.5 prescribing providers (SD = 23.5). They reported data on more than 13,500 clients per year (mean = 969/site, SD = 1,351). Demographic characteristics remained similar over time. In 2014, a majority of clients were male (71% versus 28% female and 0.2% transgender), with a mean age of 47 (interquartile range [IQR] 37-54). Racial/ethnic characteristics (48% African American, 31% Hispanic/Latino, 14% white) and HIV risk varied (31% men who have sex with men; 31% heterosexual men and women; 7% injection drug use). A substantial minority was on Medicaid (41%). Across sites, there was significant uptake in practices consistent with maximizing the HIV care workforce (18% increase, p < 0.001), share-the-care (25% increase, p < 0.001), and facilitating patient engagement in HIV primary care (13% increase, p < 0.001). There were also significant improvements over time in retention in HIV care (adjusted odds ratio [aOR] = 1.03; 95% confidence interval [CI] 1.02-1.04; p < 0.001), ART prescription levels (aOR = 1.01; 95% CI 1.00-1.01; p < 0.001), and viral suppression (aOR = 1.03; 95% CI 1.02-1.04; p < 0.001). All outcomes improved at sites that implemented transformations to maximize the HIV care workforce or improve client engagement. At sites that implemented share-the-care practices, only retention in care and viral suppression outcomes improved. Study limitations included use of demonstration project sites funded by the Ryan White HIV/AIDS Program (RWHAP), which tend to have better HIV outcomes than other US clinics; varying practice transformation designs; lack of a true control condition; and a potential Hawthorne effect because site teams were aware of the evaluation.ConclusionsIn this study, we found that practice transformations are a potential strategy for addressing anticipated workforce challenges among those providing care to PLWH. They hold the promise of optimizing the use of personnel and ensuring the delivery of care to all in need while potentially enhancing HIV care continuum outcomes

Evaluating the impact of pyrethroid insecticide resistance on reproductive fitness in Sitobion avenae

Resistance to insecticides used to control pests is an issue of increasing concern for agriculture. The grain aphid, Sitobion avenae, is a pest of cereals and grasses worldwide, and one of growing concern due to the evolution of resistance to certain insecticides. Resistance confers benefits to insects by enabling them to survive exposure to insecticide compounds; however, the mutations conferring resistance may also penalise the insect in pesticide-free environments due to fitness costs associated with the new phenotype. Here we tested the hypothesis of a reproductive penalty linked to the knockdown resistance mutation (kdr) to pyrethroid insecticides. The mutation occurs predominantly in a single SA3 clone. To date, only heterozygous-resistant forms (kdr-SR) have been detected in populations in Ireland and the UK, and this suggests that a fitness penalty may preclude the formation of both male and female heterozygous-resistant sexual forms. By designing an experiment which included a resistant and a non-resistant clone, we were able to simulate reduced daylight and temperature conditions which, in nature, trigger sexual reproduction and therefore study the responses of each clone. This allowed us to detect the switch from asexual females to sexual females and males and report on the conditions associated with the production of sexual forms. The results showed that both aphid clones were able to produce sexual forms with no difference in the onset of sexual reproduction, although reproductive strategies differed between clones. The later onset of male forms in the SA3 clone may decrease the likelihood of mating interactions to create fully resistant (kdr-RR) genotypes and this may constitute a fitness penalty due to pyrethroid resistance