Sampling, storage and laboratory approaches for dissolved organic matter characterisation in freshwaters: Moving from nutrient fraction to molecular-scale characterisation.

Recent research has highlighted the importance of dissolved organic matter (DOM) for ecosystem function and because of this paradigm shift, it has become crucial to not only quantify its contribution to river nutrient loads but also to characterise its composition. There has been a significant research effort utilising optical methods, such as fluorescence and UV-Vis spectrophotometry, in order to start exploring DOM character. However, these methods still lack the granularity to understand the chemical composition at the molecular level, which is vital to properly understanding its functional role in freshwater ecosystems. As a direct result, there has been a shift towards including molecular-scale analyses to investigate the in-stream processing of the material. Alongside this, recent methodological advancements, particularly in mass spectrometry are opening new opportunities for probing one of the most complex environmental mixtures. However, in order to fully exploit these opportunities, it is key that the way that samples are collected, processed and stored is considered carefully such that sample integrity is maintained. There are additional challenges when collecting water samples for analysis at molecular scale, for example the ultra-low concentrations of individual compounds within DOM means that the samples are sensitive to contamination. This paper discusses current sample collection, processing and storage protocols for this C, N and P quantification and characterisation in freshwaters, and proposes a new standardised protocol suitable for both nutrient fraction quantification and molecular scale analyses, based on method development and testing undertaken in our UK Natural Environment Research Council large grant programme, characterising the nature, origins and ecological significance of Dissolved Organic Matter IN freshwater Ecosystems (DOMAINE).

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study.

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

Dissolved organic nutrient uptake by riverine phytoplankton varies along a gradient of nutrient enrichment.

The concentration of dissolved organic matter (DOM) in freshwaters is increasing in large areas of the world. In addition to carbon, DOM contains nitrogen and phosphorus and there is growing concern that these organic nutrients may be bioavailable and contribute to eutrophication. However, relatively few studies have assessed the potential for dissolved organic nitrogen (DON) or dissolved organic phosphorus (DOP) compounds to be bioavailable to natural river phytoplankton communities at different locations or times. Temporal and spatial variations in uptake, relative to environmental characteristics were examined at six riverine sites in two contrasting catchments in the UK. This study also examined how the uptake by riverine phytoplankton of four DON and four DOP compounds commonly found in rivers, varied with concentration. Total nitrogen (TN) and phosphorus (TP) concentrations, the proportion of inorganic nutrient species, and nutrient limitation varied temporally and spatially, as did the potential for DON and DOP uptake. All eight of the DOM compounds tested were bioavailable, but to different extents. Organic nutrient use depended on the concentration of the organic compound supplied, with simple compounds (urea and glucose-6-phosphate) supporting algal growth even at very low concentrations. DON use was negatively correlated with the TN and ammonia concentration and DOP use was negatively correlated with soluble reactive phosphorus (SRP) and dissolved organic carbon (DOC) concentration. The evidence indicates that DOM in rivers has been overlooked as a potential source of nutrients to phytoplankton and therefore as an agent of eutrophication.

Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process.

In this work, we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell-cell interactions. This is important as cell-cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work, therefore, describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell-cell adhesion or repulsion are known to play a significant role.

Variable species densities are induced by volume exclusion interactions upon domain growth.

In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long-term behavior of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behavior, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long-term behavior of multispecies populations and, in certain circumstances, establish spatially varying species densities.

Microbial use of low molecular weight DOM in filtered and unfiltered freshwater: Role of ultra-small microorganisms and implications for water quality monitoring.

Dissolved organic matter (DOM) plays a central role in regulating productivity and nutrient cycling in freshwaters. It is therefore vital that we can representatively sample and preserve DOM in freshwaters for subsequent analysis. Here we investigated the effect of filtration, temperature (5 and 25°C) and acidification (HCl) on the persistence of low molecular weight (MW) dissolved organic carbon (DOC), nitrogen (DON) and orthophosphate in oligotrophic and eutrophic freshwater environments. Our results showed the rapid loss of isotopically-labelled glucose and amino acids from both filtered (0.22 and 0.45µm) and unfiltered waters. We ascribe this substrate depletion in filtered samples to the activity of ultra-small (<0.45µm) microorganisms (bacteria and archaea) present in the water. As expected, the rate of C, N and P loss was much greater at higher temperatures and was repressed by the addition of HCl. Based on our results and an evaluation of the protocols used in recently published studies, we conclude that current techniques used to sample water for low MW DOM characterisation are frequently inadequate and lack proper validation. In contrast to the high degree of analytical precision and rigorous statistical analysis of most studies, we argue that insufficient consideration is still given to the presence of ultra-small microorganisms and potential changes that can occur in the low MW fraction of DOM prior to analysis.

Efficient parameter sensitivity computation for spatially extended reaction networks.

Reaction-diffusion models are widely used to study spatially extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for computing parametric sensitivities are required. In this work, we focus on the stochastic models of spatially extended chemical reaction systems that involve partitioning the computational domain into voxels. Parametric sensitivities are often calculated using Monte Carlo techniques that are typically computationally expensive; however, variance reduction techniques can decrease the number of Monte Carlo simulations required. By exploiting the characteristic dynamics of spatially extended reaction networks, we are able to adapt existing finite difference schemes to robustly estimate parametric sensitivities in a spatially extended network. We show that algorithmic performance depends on the dynamics of the given network and the choice of summary statistics. We then describe a hybrid technique that dynamically chooses the most appropriate simulation method for the network of interest. Our method is tested for functionality and accuracy in a range of different scenarios.

How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations.

Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviors, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are 'compartment-based': the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise.

Reconciling transport models across scales: The role of volume exclusion.

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far.

Inference of cell-cell interactions from population density characteristics and cell trajectories on static and growing domains.

A key feature of cell migration is how cell movement is affected by cell-cell interactions. Furthermore, many cell migratory processes such as neural crest stem cell migration [Thomas and Erickson, 2008; McLennan et al., 2012] occur on growing domains or in the presence of a chemoattractant. Therefore, it is important to study interactions between migrating cells in the context of domain growth and directed motility. Here we compare discrete and continuum models describing the spatial and temporal evolution of a cell population for different types of cell-cell interactions on static and growing domains. We suggest that cell-cell interactions can be inferred from population density characteristics in the presence of motility bias, and these population density characteristics for different cell-cell interactions are conserved on both static and growing domains. We also study the expected displacement of a tagged cell, and show that different types of cell-cell interactions can give rise to cell trajectories with different characteristics. These characteristics are conserved in the presence of domain growth, however, they are diminished in the presence of motility bias. Our results are relevant for researchers who study the existence and role of cell-cell interactions in biological systems, so far as we suggest that different types of cell-cell interactions could be identified from cell density and trajectory data.

An adaptive multi-level simulation algorithm for stochastic biological systems.

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, "Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics," SIAM Multiscale Model. Simul. 10(1), 146-179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the efficiency of our method using a number of examples.

Deriving appropriate boundary conditions, and accelerating position-jump simulations, of diffusion using non-local jumping.

In this paper we explore lattice-based position-jump models of diffusion, and the implications of introducing non-local jumping; particles can jump to a range of nearby boxes rather than only to their nearest neighbours. We begin by deriving conditions for equivalence with traditional local jumping models in the continuum limit. We then generalize a previously postulated implementation of the Robin boundary condition for a non-local process of arbitrary maximum jump length, and present a novel implementation of flux boundary conditions, again generalized for a non-local process of arbitrary maximum jump length. In both these cases we validate our results using stochastic simulation. We then proceed to consider two variations on the basic diffusion model: a hybrid local/non-local scheme suitable for models involving sharp concentration gradients, and the implementation of biased jumping. In all cases we show that non-local jumping can deliver substantial time savings for stochastic simulations.

Nitrogen speciation and phosphorus fractionation dynamics in a lowland Chalk catchment.

A detailed analysis of temporal and spatial trends in nitrogen (N) speciation and phosphorus (P) fractionation in the Wylye, a lowland Chalk sub-catchment of the Hampshire Avon, UK is presented, identifying the sources contributing to nutrient enrichment, and temporal variability in the fractionation of nutrients in transit from headwaters to lower reaches of the river. Samples were collected weekly from ten monitoring stations with daily sampling at three further sites over one year, and monthly inorganic N and total reactive P (TRP) concentrations at three of the ten weekly monitoring stations over a ten year period are also presented. The data indicate significant daily and seasonal variation in nutrient fractionation in the water column, resulting from plant uptake of dissolved organic and inorganic nutrient fractions in the summer months, increased delivery of both N and P from diffuse sources in the autumn to winter period and during high flow events, and lack of dilution of point source discharges to the Wylye from septic tank, small package Sewage Treatment Works (STW) and urban Waste Water Treatment Works (WwTW) during the summer low flow period. Weekly data show that contributing source areas vary along the river with headwater N and P strongly influenced by diffuse inorganic N and particulate P fluxes, and SRP and organic-rich point source contributions from STW and WwTW having a greater influence in the lower reaches. Long-term data show a decrease in TRP concentrations at all three monitoring stations, with the most pronounced decrease occurring downstream from Warminster WwTW, following the introduction of P stripping at the works in 2001. Inorganic N demonstrates no statistically significant change over the ten year period of record in the rural headwaters, but an increase in the lower reaches downstream from the WwTW which may be due to urban expansion in the lower catchment.

Absence of luminal riboflavin disturbs early postnatal development of the gastrointestinal tract.

An increase in the size and cellularity of duodenal crypts and a decreased incidence of bifurcating crypts is observed in response to very short-term feeding of a riboflavin-deficient diet to weanling rats. A study was conducted to determine whether the absence of riboflavin in the lumen of the small intestine impairs gastrointestinal development. Forty-eight female weanling Wistar rats were allocated to one of two treatment regimens, to receive either a riboflavin-deficient diet and a daily intraperitoneal injection of flavin mononucleotide (luminally deficient group) or a complete diet and a daily intraperitoneal injection of saline (control group). Animals were killed at 93, 141, or 165 hr from feeding. The flavin injection regimen maintained normal systemic riboflavin status in the luminally deficient group. In this group, however, crypt hypertrophy and reduced crypt bifurcation were evident by 141 hr of luminal riboflavin deprivation. The absence of riboflavin in the duodenal lumen impairs normal development, suggesting that a crypt sensing mechanism may be involved in the response to riboflavin deficiency.

Riboflavin deficiency: early effects on post-weaning development of the duodenum in rats.

The aim of this present study was to identify the earliest point at which riboflavin deficiency affects post-weaning bowel development in rats. After weaning, eighty Wistar rats were weight-matched as pairs, one animal being fed a normal synthetic diet and the other being fed the same diet but deficient in riboflavin. Body weight, feeding and rates of growth were monitored and eight pairs of animals were taken for analysis at 45, 69, 93, 117 and 141 h. Riboflavin status was monitored by determining the erythrocyte glutathione reductase activation coefficient (EGRAC), and hepatic flavins were measured by a fluorescence assay. Changes to the number and dimensions of villi and crypts in the duodenum were determined, as well as crypt division (bifurcation) and the DNA synthesis index of the crypt epithelium by bromodeoxyuridine (BrdU) labelling. Riboflavin deficiency was established in the experimental rats, as demonstrated by a significant increase in EGRAC after 45 h (P<0.001) and decreased liver flavins after 96 h (P<0.001). After 96 h a significant increase in the size and cellularity of the crypts (P<0.001 in both cases) was seen in these riboflavin-deficient animals, with a decreased incidence of bifurcating crypts and of BrdU-labelled cells. No changes to villus number or size were observed. The present study has demonstrated that developmental changes to the duodenal crypt arise shortly after circulating riboflavin measurements show evidence of deficiency. These changes primarily affect cell proliferation and crypt bifurcation, and precede long-term changes such as the reduction of villus number.

Pregnancy following intra-fallopian insemination of spermatozoa from a male with obstructive azoospermia.

A pregnancy obtained after intratubal insemination with epididymal spermatozoa recovered from a patient with obstructive azoospermia is reported. The successful outcome of the case emphasizes the beneficial nature of the intra-Fallopian environment.

Male-factor infertility and in vitro fertilization.

In vitro fertilization (IVF) was developed primarily as a treatment for female and idiopathic infertility. However, with the discovery that relatively few sperm are required to achieve fertilization in vitro, it was proposed that IVF could be used also as an effective treatment for male-factor infertility. This review deals with the work that has been carried out by various groups in this area of male-factor infertility. As the standards of classification and the presentation of results vary from group to group, this also shows that there is a need for some standardization of how patient selection and the presentation of results are carried out in the area of male-factor infertility.

Human pregnancy by in vitro fertilization (IVF) using sperm aspirated from the epididymis.

Spermatozoa were collected by microaspiration from the corpus epididymidis of a 42-year-old man with secondary obstructive azoospermia and used for in vitro fertilization. At insemination 61% of the spermatozoa were motile, with a motility index of 157. One of five eggs was fertilized and this was subsequently transferred to the patient's wife at the two-cell stage. Ultrasound examination and changing hormone levels confirmed an on-going pregnancy, which is currently at 30 weeks of gestation. This technique will provide a useful alternative for the management of some infertile men with obstructive azoospermia.

The effects of different photoperiods on circadian 5-HT rhythms in regional brain areas and their modulation by pinealectomy, melatonin and oestradiol.

Differential circadian rhythms in 5-HT levels were found in the hypothalamus and pineal (but not in the cortex, hippocampus or midbrain) in ferrets kept in either long (14 h light/10 h dark) or short (8 h light/16 h dark) photoperiods. 5-HT decreased during the first 6 h of illumination in all areas examined from animals kept in short photoperiods. In long photoperiods, 5-HT in the hypothalamus (particularly the anterior region) increased during the first 6 h after onset of light and levels in the pineal became arrhythmic. There were no differential effects of light on 5-HIAA/5-HT ratios. Removal of the pineal or the superior cervical ganglia abolished these differential rhythms, as did subcutaneous implants of oestradiol (releasing about 5 micrograms/day). Melatonin (1 mg/day) injected 8 h after the onset of light into animals kept in long photoperiods resulted in circadian 5-HT rhythms resembling those from animals exposed to short photoperiods, whereas melatonin given at 14 h after onset of light did not have this effect. It is suggested that 5-HT containing neural systems may play a role in the way the pineal transmits information about the duration of the photoperiod to the neural structures controlling the pituitary.