Experimental analysis and modelling of in vitro HUVECs proliferation in the presence of various types of drugs

Objectives: This study focuses on experimental analysis and corresponding mathematical simulation of in vitro HUVECs (human umbilical vein endothelial cells) proliferation in the presence of various types of drugs. Materials and methods: HUVECs, once seeded in Petri dishes, were expanded to confluence. Temporal profiles of total count obtained by classic haemocytometry and cell size distribution measured using an electronic Coulter counter, are quantitatively simulated by a suitable model based on the population balance approach. Influence of drugs on cell proliferation is also properly simulated by accounting for suitable kinetic equations. Results and discussion: The models’ parameters have been determined by comparison with experimental data related to cell population expansion and cell size distribution in the absence of drugs. Inhibition constant for each type of drug has been estimated by comparing the experimental data with model results concerning temporal profiles of total cell count. The reliability of the model and its predictive capability have been tested by simulating cell size distribution for experiments performed in the presence of drugs. The proposed model will be useful in interpreting effects of selected drugs on expansion of readily available human cells.     

Experimental analysis and modelling of in vitro proliferation of mesenchymal stem cells

Objectives:  Stem cell therapies based on differentiation of adult or embryonic stem cells into specialized ones appear to be effective for treating several human diseases. This work addresses the mathematical simulation of proliferation kinetics of stem cells.
Materials and methods:  Sheep bone marrow mesenchymal stem cells (phenotype characterized by flow cytometry analysis) seeded at different initial concentrations in Petri dishes were expanded to confluence. Sigmoid temporal profiles of total counts obtained through classic haemocytometry were quantitatively interpreted by both a phenomenological logistic equation and a novel model based on a one-dimensional, single-staged population balance approach capable of taking into account contact inhibition at confluence. The models' parameters were determined by comparison with experimental data on population expansion starting from single seeding concentration. Reliability of the models was tested by predicting cell proliferation carried out starting from different seeding concentrations.
Results and discussion:  It was found that the proposed population balance modelling approach was successful in predicting the experimental data over the whole range of initial cell numbers investigated, while prediction capability of phenomenological logistic equation was more limited.     

Estimation of parameters in population models for Schizosaccharomyces pombe from chemostat data

The integro-differential growth model of Eakman, Fredriekson, and Tsuehiya has been employed to fit cell size distribution data for Schizosaccharomyces pombe grown in a chemostat under severe product inhibition by ethanol. The distributions were obtained with a Coulter aperture and an electronic system patterned after that of Harvey and Marr. Four parameters—mean cell division size, cell division size standard deviation, daughter cell size standard deviation, and a growth rate coefficient—were calculated for models where the cell growth rate was inversely proportional to size, constant, and proportional to size. A fourth model, one where sigmoidal growth behavior was simulated by two linear growth segments, was also investigated. Linear and sigmoidal models fit the distribution data best. While the mean cell division size remained relatively constant at all growth rates, standard deviation of division size distribution increased with increasing holding times. Standard deviation of the daughter size distribution remained small at all dilution rates. Unlike previous findings with other organisms, the average cell size of Schizosaccharomyces pobme increased at low growth rates.     

Using sample aerial surveys to estimate the abundance of the endangered Grevy’s zebra in northern Kenya

The effective management of endangered mammals requires reliable estimates of population size. This is challenging for species such as Grevy’s zebra (Equus grevyi) that are distributed over large areas at low densities. Less than 2500 Grevy’s zebra remain in the wild, scattered across 85,000 km² of savannah in northern Kenya and Ethiopia. An efficient, accurate and repeatable survey method is required to guide conservation planning for the species. Currently, total aerial counts are used to census endangered species within Kenya, but are costly in terms of resources. In this study, we evaluated the suitability of sample survey methods for Grevy’s zebra. We estimated population size using sample aerial counts for a known population of Grevy’s zebra in Lewa Wildlife Conservancy (LWC), providing the opportunity to test the accuracy of sample methods, while comparing resource costs with total count methods. We sampled one‐third of LWC using parallel 500‐ m strip transects at 1500‐ m intervals. The population estimate was comparable to the known population size and was less than half as expensive as the equivalent total count survey. Our results suggest sample aerial surveys provide an accurate and cost‐effective means of monitoring Grevy’s zebra and other endangered species in open habitats.     

A novel population balance model to investigate the kinetics of in vitro cell proliferation: part I. Model development

In biotechnology and biomedicine reliable models of cell proliferation kinetics need to capture the relevant phenomena taking place during the mitotic cycle. To this aim, a novel mathematical model helpful to investigate the intrinsic kinetics of in vitro culture of adherent cells up to confluence is proposed in this work. Specifically, the attention is focused on the simulation of proliferation (increase of cell number) and maturation (increase of cell size and DNA content) till contact inhibition eventually takes place inside a Petri dish. Accordingly, the proposed model is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases the cells of the entire population experienced during their own life. In particular, the proposed model has been developed as a 2D, multi-staged, and unstructured PB, by considering a different sub-population of cells for any single phase of the cell cycle. These sub-populations are discriminated through cellular volume and DNA content, that both increase during the mitotic cycle. The adopted mathematical expressions of the transition rates between two subsequent phases and the temporal increase of cell volume and DNA content are thoroughly analyzed and discussed with respect to those ones available in the literature. Specifically, the corresponding uncertainties and pitfalls are pointed out, by also taking into account the difficulties and the limitations involved in the quantitative measurements currently practicable for these biological systems. A novel mathematical expression for contact inhibition in line with the PB model developed is also formulated, along with a proper comparison between modeled and measurable DNA distributions. The strategy for a reliable, independent tuning of the adjustable parameters involved in the proposed model along with its numerical solution is outlined in Part II of this work, where it is also shown how it can be profitably used to gain a deeper insight into the phenomena involved during cell cultivation under microgravity conditions.     

A population balance model to modulate shear for the control of aggregation in Taxus suspension cultures

Cellular aggregation in plant suspension cultures directly affects the accumulation of high value products, such as paclitaxel from Taxus. Through application of mechanical shear by repeated, manual pipetting through a 10 ml pipet with a 1.6 mm aperture, the mean aggregate size of a Taxus culture can be reduced without affecting culture growth. When a constant level of mechanical shear was applied over eight generations, the sheared population was maintained at a mean aggregate diameter 194 μm lower than the unsheared control, but the mean aggregate size fluctuated by over 600 μm, indicating unpredictable culture variability. A population balance model was developed to interpret and predict disaggregation dynamics under mechanical shear. Adjustable parameters involved in the breakage frequency function of the population balance model were estimated by nonlinear optimization from experimentally measured size distributions. The optimized model predictions were in strong agreement with measured size distributions. The model was then used to determine the shear requirements to successfully reach a target aggregate size distribution. This model will be utilized in the future to maintain a culture with a constant size distribution with the goal of decreasing culture variability and increasing paclitaxel yields.     

Effects of re‐breeding rates on population size estimation of biennial breeders: results from a model based on albatrosses

Estimating total breeding populations (I) for species that exhibit biennial breeding is generally done from counts of individuals that breed in each year (N), but can be complicated by the fact that the proportion of individuals breeding varies from year to year. Partly, this reflects the proportion of individuals that re‐breed in successive years (re‐breeding rate, p), which is largely, although not exclusively, governed by reproductive failure. Here we show that variation in counts of breeding individuals not only reflects changes in total breeding population but can be sensitive to and powerfully driven by variation in p. A simulation of annual field counts of a bird exhibiting biennial breeding was constructed to explore the effect of re‐breeding attempts on estimations of the total breeding population. The model was used to simulate the consequences of adult mortality and different annual patterns of nesting failures on total breeding population estimates, and to explore the consequences of variation in p on N, when total breeding population remains constant. N is shown to be very sensitive to variations in p, so that even short‐term fluctuations in p can cause changes in N that oscillate for many years ahead. We compare our modelled results with real data for Grey‐headed Albatrosses Thalassarche chrysostoma and demonstrate that, when I is held constant in the model, actual counts may be simulated by variations in p only. Normally, I is unknown and is extrapolated from N on the assumption that N mirrors changes in the size of the total population. Consequently, applying average values of p can result in misleading estimates of total breeding population. We recommend that annual counts of breeding individuals are supplemented with annual estimates of p. Field protocols that aim to estimate annual breeding population size from counts of breeding individuals should be complemented by independent measures of rates of re‐breeding and nest failure.     

Community Structure of Tintinnid Ciliates of the Microzooplankton in the South West Pacific Ocean: Comparison of a High Primary Productivity with a Typical Oligotrophic Site

Transient ‘hot spots’ of phytoplankton productivity occur in the generally oligotrophic Southern Pacific Ocean and we hypothesized that the population structure of tintinnid ciliates, planktonic grazers, would differ from that of a typical oligotrophic sites. Samples were collected over a 1‐wk period at each of two sites between Fiji and Tahiti: one of elevated chlorophyll a concentrations and primary productivity with an abundance of N‐fixing cyanobacteria Trichodesmium, and a distant oligotrophic site. Tintinnid abundance differed between the sites by a factor of 2. A single species (Favella sp.), absent from the oligotrophic site, highly dominated the ‘hot spot’ site. However, total species richness was identical (71 spp.) as well as short‐term temporal variability (2–4 d). At both sites, species abundance distributions most closely fit a log‐series or log‐normal distribution and the abundance distributions of ecological types, forms of distinct lorica oral diameter, were the typical geometric. Morphological diversity was only slightly lower at the high productivity site. We found that communities of these plankton grazers in ‘hot spots’ of phytoplankton productivity in oligotrophic systems, although harboring different species, differ little from surrounding oligotrophic areas in community structure.     

Implication of persimmon fruit hemicellulose metabolism in the softening process. Importance of xyloglucan endotransglycosylase

Hemicellulosic polysaccharides from persimmon fruit ( Diospyros kaki L.) pericarp were extracted from depectinated cell walls with 0.5, 1 and 4 M KOH at different stages of development: (I) maximal growth corresponding to the first sigmoidal growth phase; (II) cessation of growth corresponding to the lag between the first and the second sigmoidal phases; (III) maximal growth corresponding to the second sigmoidal phase; and (IV) cessation of growth when the fruit had reached its maximum size and the change in colour (green to red) had taken place. During fruit development the amount of total hemicelluloses per unit dry mass cell wall decreased twofold. Xyloglucan was present in the three hemicellulosic fractions, and also decreased with fruit age, although its amount relative to other hemicelluloses increased. The amount of xyloglucan was especially high in the hemicelluloses extracted with 4 M KOH, representing more than 50% at stages III and IV. The average molecular mass of xyloglucan increased from stage I through stage II (0.5 M hemicellulosic fraction) or through stage III (I and 4 M hemicellulosic fractions) and decreased after that. The xyloglucan endotransglycosylase (XET: EC 2.4.1.-) activity was measured as the incorporation of [³H]XXXGol (reduced xyloglucan heptasaccharide labelled at position 1 of the glucitol moiety) into partially purified persimmon fruit xyloglucan. XET specific activity increased greatly between stages I and II. The importance of this enzyme during fruit ripening is discussed.     

Potential responses of the Lower Missouri River Shovelnose Sturgeon (Scaphirhynchus platorynchus) population to a commercial fishing ban

We developed an age‐structured population matrix model to perform population viability analysis for Lower Missouri River (LMR) shovelnose sturgeon (Scaphirhynchus platorynchus). We investigated potential effects of the commercial fishing moratorium put in place to help protect the similar‐appearing pallid sturgeon (S. albus). The model applies different components of total variance in life history parameters at different levels: sampling variance (parameter uncertainty) between model iterations; temporal variance (temporal environmental fluctuations) between time steps within iterations; and individual variance (individual differences) within each time‐step. The model predicted annual rates of population increase of 1.96% under historic fishing and 2.67% with removal of historic fishing. We identified combinations of fishing and harvest size restrictions that would permit a sustainable harvest of shovelnose sturgeon. Overall, the ban on commercial fishing of shovelnose sturgeon in the LMR due to similarity of appearance to pallid sturgeon should help the LMR shovelnose sturgeon population begin to rebound while decreasing any negative effects it may have had on pallid sturgeon populations.     

Spatio-temporal dynamics of corn rootworm, Diabrotica spp., adults and their spatial association with environment

Multiyear and multilocation studies were conducted to investigate the within‐ and the between‐year spatial dynamics of corn rootworms Diabrotica spp. (Coleoptera: Chrysomelidae), adults and their spatial associations with environmental factors in cornfields. Grid‐based spatial sampling was conducted by trapping adults emerging from the soil (i.e., ‘emergence‐trap counts’) and by counting the number of adults in the ear zone of corn plant (i.e., ‘ear‐zone count’). Spatial analysis with distance indices (SADIE) was used to determine spatial distribution patterns and to investigate spatial associations. Ear‐zone counts and emergence‐trap counts were spatially dynamic within a year and more frequently aggregated in the middle of growing seasons and random early and late in the season. However, during the peak population periods, spatial distribution of ear‐zone counts and emergence‐trap counts were significantly consistent between years, indicating predictability of future spatial distributions. Spatial distribution of emergence‐trap counts and ear‐zone counts were positively associated with soil moisture and presence of corn plants with silks, respectively. This study demonstrated that within‐year spatial distribution patterns were dynamic and that there was between‐year spatial consistency of corn rootworm adult distributions. Such information can be used to improve preventative management of corn rootworms.     

A population‐based temporal logic gate for timing and recording chemical events

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events.     

Optimizing surveys for marsh songbirds: does timing matter?

Analysis of data from point counts, a common method for monitoring bird population trends, has evolved to produce estimates of various population parameters (e.g., density, abundance, and occupancy) while simultaneously estimating detection probability. An important consideration when designing studies using point counts is to maximize detection probability while minimizing variation in detection probability both within and between counts. Our objectives were to estimate detection probabilities for three marsh songbirds, including Marsh Wrens (Cistothorus palustris), Swamp Sparrows (Melospiza georgiana), and Yellow‐headed Blackbirds (Xanthocephalus xanthocephalus), as a function of weather covariates and to evaluate temporal variability in detection probability of these three species. We conducted paired, unlimited radius, 10‐min point counts during consecutive morning and evening survey periods for our three focal species at 56 wetlands in Iowa from 20 April to 10 July 2010. Mean detection probabilities ranged from 0.272 (SE = 0.042) for Marsh Wrens to 0.365 (SE = 0.052) for Swamp Sparrows. Time of season was positively correlated with detection probability for Swamp Sparrows, but was negatively correlated with detection probability for Yellow‐headed Blackbirds, suggesting that detection probability increased during the breeding season for Swamp Sparrows and was highest early in the breeding season for Yellow‐headed Blackbirds. Understanding how detection probabilities of marsh songbirds vary throughout the breeding season allows targeted survey efforts that maximize detection probabilities for these species. Furthermore, consistent detection probabilities of marsh songbirds during morning and evening survey periods mean that investigators have more time to conduct surveys for these birds, allowing greater flexibility to increase spatial and temporal replication of surveys that could provide more precise estimates of desired population parameters.     

Effects of size‐ and sex‐selective harvesting: An integral projection model approach

Harvesting is often size‐selective, and in species with sexual size dimorphism, it may also be sex‐selective. A powerful approach to investigate potential consequences of size‐ and/or sex‐selective harvesting is to simulate it in a demographic population model. We developed a population‐based integral projection model for a size‐ and sex‐structured species, the commonly exploited pike (Esox lucius). The model allows reproductive success to be proportional to body size and potentially limited by both sexes. We ran all harvest simulations with both lower size limits and slot limits, and to quantify the effects of selective harvesting, we calculated sex ratios and the long‐term population growth rate (λ). In addition, we quantified to what degree purely size‐selective harvesting was sex‐selective, and determined when λ shifted from being female to male limited under size‐ and sex‐selective harvesting. We found that purely size‐selective harvest can be sex‐selective, and that it depends on the harvest limits and the size distributions of the sexes. For the size‐ and sex‐selective harvest simulations, λ increased with harvest intensity up to a threshold as females limited reproduction. Beyond this threshold, males became the limiting sex, and λ decreased as more males were harvested. The peak in λ, and the corresponding sex ratio in harvest, varied with both the selectivity and the intensity of the harvest simulation. Our model represents a useful extension of size‐structured population models as it includes both sexes, relaxes the assumption of female dominance, and accounts for size‐dependent fecundity. The consequences of selective harvesting presented here are especially relevant for size‐ and sex‐structured exploited species, such as commercial fisheries. Thus, our model provides a useful contribution toward the development of more sustainable harvesting regimes.     

Structure and diversity of intertidal benthic diatom assemblages in contrasting shores: a case study from the Tagus estuary1

The structure of intertidal benthic diatoms assemblages in the Tagus estuary was investigated during a 2‐year survey, carried out in six stations with different sediment texture. Nonparametric multivariate analyses were used to characterize spatial and temporal patterns of the assemblages and to link them to the measured environmental variables. In addition, diversity and other features related to community physiognomy, such as size‐class or life‐form distributions, were used to describe the diatom assemblages. A total of 183 diatom taxa were identified during cell counts and their biovolume was determined. Differences between stations (analysis of similarity (ANOSIM), R = 0.932) were more evident than temporal patterns (R = 0.308) and mud content alone was the environmental variable most correlated to the biotic data (BEST, ρ = 0.863). Mudflat stations were typically colonized by low diversity diatom assemblages (H′ ~ 1.9), mainly composed of medium‐sized motile epipelic species (250–1,000 μm³), that showed species‐specific seasonal blooms (e.g., Navicula gregaria Donkin). Sandy stations had more complex and diverse diatom assemblages (H′ ~ 3.2). They were mostly composed by a large set of minute epipsammic species (<250 μm³) that, generally, did not show temporal patterns. The structure of intertidal diatom assemblages was largely defined by the interplay between epipelon and epipsammon, and its diversity was explained within the framework of the Intermediate Disturbance Hypothesis. However, the spatial distribution of epipelic and epipsammic life‐forms showed that the definition of both functional groups should not be over‐simplified.     

Properties of cell death models calibrated and compared using Bayesian approaches

Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass‐action models of receptor‐mediated cell death. The width of the individual parameter distributions is largely determined by non‐identifiability but covariation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model‐based predictions whereas ignoring it (e.g., by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (～20‐fold) for competing ‘direct’ and ‘indirect’ apoptosis models having different numbers of parameters. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single‐cell data represent a generally useful and rigorous approach to discriminate between competing hypotheses in the face of parametric and topological uncertainty.     

Survival of root‐lesion nematodes (Pratylenchus thornei) after wheat growth in a vertisol is influenced by rate of progressive soil desiccation

The root‐lesion nematode (Pratylenchus thornei) is a major pathogen of wheat in the subtropical grain region of eastern Australia. Experiments were conducted to learn whether soil desiccation can account for the rapid fall in peak P. thornei population densities noted in the field after wheat matures. The decline in population densities of P. thornei after growth of wheat was measured on progressive desiccation of soil with roots by fast and slow drying methods. The vertisolic soil of initial moisture content 45% w/w (or matric potential of pF 3.3) was dried in 5% decrements to an air‐dried gravimetric moisture content of 15% (pF 5.6) taking 10.7 h for fast drying and 91.5 h for slow drying. After drying, live nematodes were extracted with Whitehead trays for 2 and 7 days and counted in four life stages (adults and juvenile stages J2, J3 and J4). Fast drying resulted in a sigmoidal decline in total P. thornei with only 5% of the population alive in soil at 15% moisture content, but slow drying had no significant effect on the population density. The percentage of nematodes extracted at 2 days compared with the total extracted over 7 days in undried soil (～89% of total) declined quadratically on desiccation to be 48% (fast drying) and 78% (slow drying) at 15% moisture content. With fast drying, the proportion of adults and J2 decreased whereas the proportion of J4 increased as the soil dried. With slow drying, the proportion of J2 and J3 stages decreased while the proportion of J4 increased. Thus the J4 or pre‐adult was the life stage most tolerant of soil desiccation. Time is required for P. thornei to go into a state of anhydrobiosis as a soil dries and this information can be used to model P. thornei survival in the field based on environmental parameters.     

Metacommunity‐scale biodiversity regulation and the self‐organised emergence of macroecological patterns

There exist a number of key macroecological patterns whose ubiquity suggests that the spatio‐temporal structure of ecological communities is governed by some universal mechanisms. The nature of these mechanisms, however, remains poorly understood. Here, we probe spatio‐temporal patterns in species richness and community composition using a simple metacommunity assembly model. Despite making no a priori assumptions regarding biotic spatial structure or the distribution of biomass across species, model metacommunities self‐organise to reproduce well‐documented patterns including characteristic species abundance distributions, range size distributions and species area relations. Also in agreement with observations, species richness in our model attains an equilibrium despite continuous species turnover. Crucially, it is in the neighbourhood of the equilibrium that we observe the emergence of these key macroecological patterns. Biodiversity equilibria in models occur due to the onset of ecological structural instability, a population‐dynamical mechanism. This strongly suggests a causal link between local community processes and macroecological phenomena.