Probability distributed time delays: integrating spatial effects into temporal models

Background In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive. Results We present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation. Conclusions Our proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere.

“Scary” heterosexualities in a rural Australian mining town

This paper draws upon Hubbard's (1999, p. 57) term ‘scary heterosexualities,’ that is non-normative heterosexuality, in the context of the rural drawing on data from fieldwork in the remote Western Australian mining town of Kalgoorlie. Our focus is ‘the skimpie’ – a female barmaid who serves in her underwear and who, in both historical and contemporary times, is strongly associated with rural mining communities. Interviews with skimpies and local residents as well as participant observation reveal how potential fears and anxieties about skimpies are managed. We identify the discursive and spatial processes by which skimpie work is contained in Kalgoorlie so that the potential scariness ‘the skimpie’ represents to the rural is muted and buttressed in terms of a more conventional and less threatening rural heterosexuality.

Cognitive processes and strategies employed by children to learn spatial representations

Children often have difficulties in learning spatial representations. This study investigated the effect of four different instructional formats on learning outcomes and strategies used when dealing with spatial tasks such as assembly procedures. It was hypothesised that instructional material that imposed least extraneous cognitive load would facilitate enhanced learning. Forty secondary students were presented with four types of instruction; orthographic drawing, isometric drawing, physical model and, isometric and physical model together. The findings provide evidence to suggest that working from physical models caused least extraneous cognitive load compared to the isometric and orthographic groups. The model group took less time, had more correctly completed models, required fewer extra looks, spent less time studying the instruction and made fewer errors. Problem decomposition, forward working and attending to information in the foreground of the graphical representation strategies were analysed.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Seasonal and spatial variations in rare earth elements to identify inter-aquifer linkages and recharge processes in an Australian catchment

With the aim of elucidating the seasonal behaviour of rare earth elements (REEs), surface and groundwaters were collected under dry and wet conditions in different hydrological units of the Teviot Brook catchment (Southeast Queensland, Australia). Sampled waters showed a large degree of variability in both REE abundance and normalised patterns. Overall REE abundance ranged over nearly three orders of magnitude, and was consistently lower in the sedimentary bedrock aquifer (18ppt<∑REE<477ppt) than in the other hydrological systems studied. Abundance was greater in springs draining rhyolitic rocks (∑REE=300 and 2054ppt) than in springs draining basalt ranges (∑REE=25 and 83ppt), yet was highly variable in the shallow alluvial groundwater (16ppt<∑REE<5294ppt) and, to a lesser extent, in streamwater (85ppt<∑REE<2198ppt). Generally, waters that interacted with different rock types had different REE patterns. In order to obtain an unbiased characterisation of REE patterns, the ratios between light and middle REEs (R(M/L)) and the ratios between middle and heavy REEs (R(H/M)) were calculated for each sample. The sedimentary bedrock aquifer waters had highly evolved patterns depleted in light REEs and enriched in middle and heavy REEs (0.17spatial variations. Samples collected from the alluvium exhibited an increasing influence of the sedimentary bedrock from upgradient to downgradient; typically they showed flat patterns in the upstream section of the alluvium (median R(M/L)=0.21 and median R(H/M)=-0.06) gradually evolving towards patterns depleted in light REEs and enriched in middle and heavy REEs downgradient (median R(M/L)=0.48 and median R(H/M)=0.38). To document the seasonal variations in REE patterns, the difference in ratios between dry and wet sampling campaigns was determined for each repeated sampling location. Contributions from the sedimentary bedrock water to the alluvium during the wet season were identified at two locations (increase from R(H/M)=0.03 and 0.35 to R(H/M)=0.62 and 0.89). The effect of recharge through fractured igneous rocks was also observed in two boreholes intercepting the sedimentary bedrock, where the freshly recharged waters likely contributed to the deeper groundwater flow during the wet season (decrease from R(M/L)=0.81 and 0.56 to R(M/L)=0.46 and 0.17). Results from this study suggest that REEs may be usefully applied as indicators of recharge processes and inter-aquifer mixing. They also underline the importance of conducting seasonal sampling campaigns to capture possible short-term variations in REE patterns and abundance, which is essential to enable a better understanding of hydrological and hydrochemical processes in complex geological settings

Special Issue on Spatial Moment Techniques for Modelling Biological Processes

Over the last two decades, there has been an increasing awareness of, and interest in, the use of spatial moment techniques to provide insight into a range of biological and ecological processes. Models that incorporate spatial moments can be viewed as extensions of mean-field models. These mean-field models often consist of systems of classical ordinary differential equations and partial differential equations, whose derivation, at some point, hinges on the simplifying assumption that individuals in the underlying stochastic process encounter each other at a rate that is proportional to the average abundance of individuals. This assumption has several implications, the most striking of which is that mean-field models essentially neglect any impact of the spatial structure of individuals in the system. Moment dynamics models extend traditional mean-field descriptions by accounting for the dynamics of pairs, triples and higher n-tuples of individuals. This means that moment dynamics models can, to some extent, account for how the spatial structure affects the dynamics of the system in question.

Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Spatial information infrastructure : what can it possibly mean?

Investment begins with imagining that doing something new in the present will lead to a better future. Investment can vary from incidental improvements as safe and beneficial side-effects of current activity through to a more dedicated and riskier disinvestment in current methods of operation and reinvestment in new processes and products. The role of government has an underlying continuity determined by its constitution that authorises a parliament to legislate for peace, order and good government. ‘Good government’ is usually interpreted as improving the living standards of its citizens. The requirements for social order and social cohesion suggest that improvements should be shared fairly by all citizens through all of their lives. Arguably, the need to maintain an individual’s metabolism has a social counterpart in the ‘collective metabolism’ of a sustainable and productive society.

Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Persistent ocean monitoring with underwater gliders : towards accurate reconstruction of dynamic ocean processes

Ocean processes are dynamic and complex events that occur on multiple different spatial and temporal scales. To obtain a synoptic view of such events, ocean scientists focus on the collection of long-term time series data sets. Generally, these time series measurements are continually provided in real or near-real time by fixed sensors, e.g., buoys and moorings. In recent years, an increase in the utilization of mobile sensor platforms, e.g., Autonomous Underwater Vehicles, has been seen to enable dynamic acquisition of time series data sets. However, these mobile assets are not utilized to their full capabilities, generally only performing repeated transects or user-defined patrolling loops. Here, we provide an extension to repeated patrolling of a designated area. Our algorithms provide the ability to adapt a standard mission to increase information gain in areas of greater scientific interest. By implementing a velocity control optimization along the predefined path, we are able to increase or decrease spatiotemporal sampling resolution to satisfy the sampling requirements necessary to properly resolve an oceanic phenomenon. We present a path planning algorithm that defines a sampling path, which is optimized for repeatability. This is followed by the derivation of a velocity controller that defines how the vehicle traverses the given path. The application of these tools is motivated by an ongoing research effort to understand the oceanic region off the coast of Los Angeles, California. The computed paths are implemented with the computed velocities onto autonomous vehicles for data collection during sea trials. Results from this data collection are presented and compared for analysis of the proposed technique.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

A software tool for simulating spatial separation and kinetics in biological membranes

Self-segregation and compartimentalisation are observed experimentally to occur spontaneously on live membranes as well as reconstructed model membranes. It is believed that many of these processes are caused or supported by anomalous diffusive behaviours of biomolecules on membranes due to the complex and heterogeneous nature of these environments. These phenomena are on the one hand of great interest in biology, since they may be an important way for biological systems to selectively localize receptors, regulate signaling or modulate kinetics; and on the other, they provide an inspiration for engineering designs that mimick natural systems. We present an interactive software package we are developing for the purpose of simulating such processes numerically using a fundamental Monte Carlo approach. This program includes the ability to simulate kinetics and mass transport in the presence of either mobile or immobile obstacles and other relevant structures such as liquid-ordered lipid microdomains. We also present preliminary simulation results regarding the selective spatial localization and chemical kinetics modulating power of immobile obstacles on the membrane, obtained using the program.

Will the application of spatial multi criteria evaluation technique enhance the quality of decision-making to resolve boundary conflicts in the Philippines?

Systematic studies that evaluate the quality of decision-making processes are relatively rare. Using the literature on decision quality, this research develops a framework to assess the quality of decision-making processes for resolving boundary conflicts in the Philippines. The evaluation framework breaks down the decision-making process into three components (the decision procedure, the decision method, and the decision unit) and is applied to two ex-post (one resolved and one unresolved) and one ex-ante cases. The evaluation results from the resolved and the unresolved cases show that the choice of decision method plays a minor role in resolving boundary conflicts whereas the choice of decision procedure is more influential. In the end, a decision unit can choose a simple method to resolve the conflict. The ex-ante case presents a follow-up intended to resolve the unresolved case for a changing decision-making process in which the associated decision unit plans to apply the spatial multi criteria evaluation (SMCE) tool as a decision method. The evaluation results from the ex-ante case confirm that the SMCE has the potential to enhance the decision quality because: a) it provides high quality as a decision method in this changing process, and b) the weaknesses associated with the decision unit and the decision procedure of the unresolved case were found to be eliminated in this process.