Kinetic control of liposome size by direct lipid transfer

Spontaneous lipid vesiculation and related size distribution are traditionally studied in the framework of equilibrium thermodynamics and continuum mechanics, overlooking the kinetic aspects of the process. In the scenario of liposomes consisting of different lipid molecules dispersed in the same medium - a non-equilibrium situation -, the system evolves driven by lipid monomer transfer among the different liposomes. This process encompasses time-dependent changes in liposome size and size distribution, thus predicting size and composition at a given time would entail the control of the size of liposomes by kinetic means, an asset in the framework of diagnostics and synthetic biology. We introduce a direct transfer model, based on the fact that monomers are highly reactive species and apply it to saturated phospholipid molecules differing in hydrophobic chain length. Considering a well-defined gamma-type liposome size distribution, we demonstrate a clear liposome size-composition correlation and are able to predict liposome size and size distribution at any time in the transfer process. The size-composition correlation opens up new prospects for the control of the self-assembling properties of lipids and thereby the control of the liposome size.

PREDIG: Web application to model and predict the enzymatic saccharification of plant cell wall

Enzymatic digestion of lignocellulosic plant biomass is a key step in bio-refinery approaches for the production of biofuels and other valuable chemicals. However, the recalcitrance of this material in conjunction with its variability and heterogeneity strongly hampers the economic viability and profitability of biofuel production. To complement both academic and industrial experimental research in the field, we designed an advanced web application that encapsulates our in-house developed complex biophysical model of enzymatic plant cell wall degradation. PREDIG (https://predig.cs.hhu.de/) is a user-friendly, free, and fully open-source web application that allows the user to perform in silico experiments. Specifically, it uses a Gillespie algorithm to run stochastic simulations of the enzymatic saccharification of a lignocellulose microfibril, at the mesoscale, in three dimensions. Such simulations can for instance be used to test the action of distinct enzyme cocktails on the substrate. Additionally, PREDIG can fit the model parameters to uploaded experimental time-course data, thereby returning values that are intrinsically difficult to measure experimentally. This gives the user the possibility to learn which factors quantitatively explain the recalcitrance to saccharification of their specific biomass material.

Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data

We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs)-and the closures that lead to them- from high-fidelity, individual-based stochastic simulations of Escherichia coli bacterial motility. The fine scale, chemomechanical, hybrid (continuum-Monte Carlo) simulation model embodies the underlying biophysics, and its parameters are informed from experimental observations of individual cells. Using a parsimonious set of collective observables, we learn effective, coarse-grained "Keller-Segel class" chemotactic PDEs using machine learning regressors: (a) (shallow) feedforward neural networks and (b) Gaussian Processes. The learned laws can be black-box (when no prior knowledge about the PDE law structure is assumed) or gray-box when parts of the equation (e.g. the pure diffusion part) is known and "hardwired" in the regression process. More importantly, we discuss data-driven corrections (both additive and functional), to analytically known, approximate closures.

Locally adaptive aggregation of organisms under death risk in rock-paper-scissors models

We run stochastic simulations of the spatial version of the rock-paper-scissors game, considering that individuals use sensory abilities to scan the environment to detect the presence of enemies. If the local dangerousness level is above a tolerable threshold, individuals aggregate instead of moving randomly on the lattice. We study the impact of the locally adaptive aggregation on the organisms' spatial organisation by measuring the characteristic length scale of the spatial domains occupied by organisms of a single species. Our results reveal that aggregation is beneficial if triggered when the local density of opponents does not exceed 30%; otherwise, the behavioural strategy may harm individuals by increasing the average death risk. We show that if organisms can perceive further distances, they can accurately scan and interpret the signals from the neighbourhood, maximising the effects of the locally adaptive aggregation on the death risk. Finally, we show that the locally adaptive aggregation behaviour promotes biodiversity independently of the organism's mobility. The coexistence probability rises if organisms join conspecifics, even in the presence of a small number of enemies. We verify that our conclusions hold for more complex systems by simulating the generalised rock-paper-scissors models with five and seven species. Our discoveries may be helpful to ecologists in understanding systems where organisms' self-defence behaviour adapts to local environmental cues.

Spatial organisation plasticity reduces disease infection risk in rock-paper-scissors models

We study a three-species cyclic game system where organisms face a contagious disease whose virulence may change by a pathogen mutation. As a responsive defence strategy, organisms' mobility is restricted to reduce disease dissemination in the system. The impact of the collective self-preservation strategy on the disease infection risk is investigated by performing stochastic simulations of the spatial version of the rock-paper-scissors game. Our outcomes show that the mobility control strategy induces plasticity in the spatial patterns with groups of organisms of the same species inhabiting spatial domains whose characteristic length scales depend on the level of dispersal restrictions. The spatial organisation plasticity allows the ecosystems to adapt to minimise the individuals' disease contamination risk if an eventual pathogen alters the disease virulence. We discover that if a pathogen mutation makes the disease more transmissible or less lethal, the organisms benefit more if the mobility is not strongly restricted, thus forming large spatial domains. Conversely, the benefits of protecting against a pathogen causing a less contagious or deadlier disease are maximised if the average size of groups of individuals of the same species is significantly limited, reducing the dimensions of groups of organisms significantly. Our findings may help biologists understand the effects of dispersal control as a conservation strategy in ecosystems affected by epidemic outbreaks.

Mathematical Modeling to Guide Experimental Design: T Cell Clustering as a Case Study

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.

LigninGraphs: lignin structure determination with multiscale graph modeling

Lignin is an aromatic biopolymer found in ubiquitous sources of woody biomass. Designing and optimizing lignin valorization processes requires a fundamental understanding of lignin structures. Experimental characterization techniques, such as 2D-heteronuclear single quantum coherence (HSQC) nuclear magnetic resonance (NMR) spectra, could elucidate the global properties of the polymer molecules. Computer models could extend the resolution of experiments by representing structures at the molecular and atomistic scales. We introduce a graph-based multiscale modeling framework for lignin structure generation and visualization. The framework employs accelerated rejection-free polymerization and hierarchical Metropolis Monte Carlo optimization algorithms. We obtain structure libraries for various lignin feedstocks based on literature and new experimental NMR data for poplar wood, pinewood, and herbaceous lignin. The framework could guide researchers towards feasible lignin structures, efficient space exploration, and future kinetics modeling. Its software implementation in Python, LigninGraphs, is open-source and available on GitHub.

Rules of Engagement: A Guide to Developing Agent-Based Models

Agent-based models (ABM), also called individual-based models, first appeared several decades ago with the promise of nearly real-time simulations of active, autonomous individuals such as animals or objects. The goal of ABMs is to represent a population of individuals (agents) interacting with one another and their environment. Because of their flexible framework, ABMs have been widely applied to study systems in engineering, economics, ecology, and biology. This chapter is intended to guide the users in the development of an agent-based model by discussing conceptual issues, implementation, and pitfalls of ABMs from first principles. As a case study, we consider an ABM of the multi-scale dynamics of cellular interactions in a microbial community. We develop a lattice-free agent-based model of individual cells whose actions of growth, movement, and division are influenced by both their individual processes (cell cycle) and their contact with other cells (adhesion and contact inhibition).

Transcription factors and chaperone proteins play a role in launching a faster response to heat stress and aggregation

Proteins, under conditions of cellular stress, typically tend to unfold and form lethal aggregates leading to neurological diseases like Parkinson's and Alzheimer's. A clear understanding of the conditions that favor dis-aggregation and restore the cell to its healthy state after they have been stressed is therefore important in dealing with these diseases. The heat shock response (HSR) mechanism is a signaling network that deals with these undue protein aggregates and aids in the maintenance of homeostasis within a cell. This framework, on its own, is a mathematically well studied mechanism. However, not much is known about how the various intermediate mis-folded protein states of the aggregation process interact with some of the key components of the HSR pathway such as the Heat Shock Protein (HSP), the Heat Shock Transcription Factor (HSF) and the HSP-HSF complex. In this article, using kinetic parameters from the literature, we propose and analyze two mathematical models for HSR that also include explicit reactions for the formation of protein aggregates. Deterministic analysis and stochastic simulations of these models show that the folded proteins and the misfolded aggregates exhibit bistability in a certain region of the parameter space. Further, the models also highlight the role of HSF and the HSF-HSP complex in reducing the time lag of response to stress and in re-folding all the mis-folded proteins back to their native state. These models, therefore, call attention to the significance of studying related pathways such as the HSR and the protein aggregation and re-folding process in conjunction with each other.

Switching environments, synchronous sex, and the evolution of mating types

While facultative sex is common in sexually reproducing species, for reasons of tractability most mathematical models assume that such sex is asynchronous in the population. In this paper, we develop a model of switching environments to instead capture the effect of an entire population transitioning synchronously between sexual and asexual modes of reproduction. We use this model to investigate the evolution of the number of self-incompatible mating types in finite populations, which empirically can range from two to thousands. When environmental switching is fast, we recover the results of earlier studies that implicitly assumed populations were engaged in asynchronous sexual reproduction. However when the environment switches slowly, we see deviations from previous asynchronous theory, including a lower number of mating types at equilibrium and bimodality in the stationary distribution of mating types. We provide analytic approximations for both the fast and slow switching regimes, as well as a numerical scheme based on the Kolmogorov equations for the system to quickly evaluate the model dynamics at intermediate parameters. Our approach exploits properties of integer partitions in number theory. We also demonstrate how additional biological processes such as selective sweeps can be accounted for in this switching environment framework, showing that beneficial mutations can further erode mating type diversity in synchronous facultatively sexual populations.

Seed dispersal as a search strategy: dynamic and fragmented landscapes select for multi-scale movement strategies in plants

BACKGROUND

Plant dispersal is a critical factor driving ecological responses to global changes. Knowledge on the mechanisms of dispersal is rapidly advancing, but selective pressures responsible for the evolution of dispersal strategies remain elusive. Recent advances in animal movement ecology identified general strategies that may optimize efficiency in animal searches for food or habitat. Here we explore the potential for evolution of similar general movement strategies for plants.

METHODS

We propose that seed dispersal in plants can be viewed as a strategic search for suitable habitat, where the probability of finding such locations has been optimized through evolution of appropriate dispersal kernels. Using model simulations, we demonstrate how dispersal strategies can optimize key dispersal trade-offs between finding habitat, avoiding kin competition, and colonizing new patches. These trade-offs depend strongly on the landscape, resulting in a tight link between optimal dispersal strategy and spatiotemporal habitat distribution.

RESULTS

Our findings reveal that multi-scale seed dispersal strategies that combine a broad range of dispersal scales, including Lévy-like dispersal, are optimal across a wide range of dynamic and patchy landscapes. At the extremes, static and patchy landscapes select for dispersal strategies dominated by short distances, while uniform and highly unpredictable landscapes both select for dispersal strategies dominated by long distances.

CONCLUSIONS

By viewing plant seed dispersal as a strategic search for suitable habitat, we provide a reference framework for the analysis of plant dispersal data. Consideration of the entire dispersal kernel, including distances across the full range of scales, is key. This reference framework helps identify plant species' dispersal strategies, the evolutionary forces determining these strategies and their ecological consequences, such as a potential mismatch between plant dispersal strategy and altered spatiotemporal habitat dynamics due to land use change. Our perspective opens up directions for future studies, including exploration of composite search behaviour and 'informed searches' in plant species with directed dispersal.

The levels of artificial insemination and missing sire information make genomic selection not always beneficial in meat sheep

Numerous meat sheep breeding programs in developed and developing countries are characterized by incomplete sire information and a predominant use of natural matings. These two parameters potentially affect the benefit of genomic selection (GS), especially for the selection of a late-in-life trait. Using stochastic simulations, the genetic gains obtained using genomic and conventional strategies for a maternal trait were evaluated in meat sheep population. Natural mating and artificial insemination (AI)-based designs, inspired by the current diversity of designs used for French meat sheep breeds, were modeled and three genomic strategies were tested and compared with a conventional selection strategy: parentage assignment, GS based on a male or a male and female reference population. Genomic selection based on a male reference population did not always outperform conventional selection. Its benefit depended on the design, the level of missing information on dam sires, and the level of AI. Genomic selection based on a male and female reference population always outperformed the conventional selection strategy, even if only 25 % of the females in the nucleus were genotyped.

Using Models to (Re-)Design Synthetic Circuits

Mathematical models play an important role in the design of synthetic gene circuits, by guiding the choice of biological components and their assembly into novel gene networks. Here, we present a guide for biologists to build and utilize models of gene networks (synthetic or natural) to analyze dynamical properties of these networks while considering the low numbers of molecules inside cells that results in stochastic gene expression. We start by describing how to write down a model and discussing the level of details to include. We then briefly demonstrate how to simulate a network's dynamics using deterministic differential equations that assume high numbers of molecules. To consider the role of stochastic gene expression in single cells, we provide a detailed tutorial on running stochastic Gillespie simulations of a network, including instructions on coding the Gillespie algorithm with example code. Finally, we illustrate how using a combination of quantitative experimental characterization of a synthetic circuit and mathematical modeling can guide the iterative redesign of a synthetic circuit to achieve the desired properties. This is shown using a classic synthetic oscillator, the repressilator, which we recently redesigned into the most precise and robust synthetic oscillator to date. We thus provide a toolkit for synthetic biologists to build more precise and robust synthetic circuits, which should lead to a deeper understanding of the dynamics of gene regulatory networks.

Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination

Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

The impact of community-wide, mass drug administration on aggregation of soil-transmitted helminth infection in human host populations

Background

Soil-transmitted helminths (STH) are intestinal parasites estimated to infect over 1.5 billion people. Current treatment programmes are aimed at morbidity control through school-based deworming programmes (targeting school-aged children, SAC) and treating women of reproductive age (WRA), as these two groups are believed to record the highest morbidity. More recently, however, the potential for interrupting transmission by treating entire communities has been receiving greater emphasis and the feasibility of such programmes are now under investigation in randomised clinical trials through the Bill & Melinda Gates Foundation funded DeWorm3 studies. Helminth parasites are known to be highly aggregated within human populations, with a small minority of individuals harbouring most worms. Empirical evidence from the TUMIKIA project in Kenya suggests that aggregation may increase significantly after anthelminthic treatment.

Methods

A stochastic, age-structured, individual-based simulation model of parasite transmission is employed to better understand the factors that might induce this pattern. A simple probabilistic model based on compounded negative binomial distributions caused by age-dependencies in both treatment coverage and exposure to infection is also employed to further this understanding.

Results

Both approaches confirm helminth aggregation is likely to increase post-mass drug administration as measured by a decrease in the value of the negative binomial aggregation parameter, k. Simple analytical models of distribution compounding describe the observed patterns well.

Conclusions

The helminth aggregation that was observed in the field was replicated with our stochastic individual-based model. Further work is required to generalise the probabilistic model to take account of the respective sensitivities of different diagnostics on the presence or absence of infection.

Rac activation is key to cell motility and directionality: An experimental and modelling investigation

Cell migration is a tightly-regulated process that involves protein gradients formed by the Rho family of GTPases, including Rho and Rac. The front (rear) of cells is generally characterized by higher active Rac (Rho) and lower active Rho (Rac) concentrations. Protein clusters, called adhesions, that anchor cells to their external environment have been shown to be dynamic and small (stable and large) at the cell front (rear), forming the force-transmission points necessary for persistent movement. Differences in adhesion sizes and dynamics have been linked to gradients in Rac and Rho activity. Here, we study the effects of Rac activation and gradients in Rac and Rho concentrations and activities on cellular polarity and adhesion size using mathematical and experimental approaches. The former is accomplished by expanding an existing reaction-diffusion model to a 2D domain utilizing stochastic dynamics. The model revealed that a hysteresis between the induced/uninduced states (corresponding to higher/lower Rac concentrations, respectively) along with Rac and Rho activation gradients, generated by chemical cues, were vital for forming polarity. Experimentally, the induced state was generated by increasing the cellular βPIX (a Rac-GEF) level and/or decreasing ROCK (a Rac-GAP effector protein) activity with Y-27632 (a ROCK-inhibitor). In agreement with the simulations, our results showed that cells with elevated RacGTP migrated faster, indicating more robust cellular polarization. However, the directionality of cells was not changed significantly, suggesting that external and/or internal physical or chemical cues were needed. Complementing the faster migration observed, adhesions were smaller, generating the phenotype expected with the induced state.

Stochastic simulations data for figure 1 and the phase diagram construction for defining monotonic and non-monotonic regimes of the velocity as a function of k off

We have compared our theoretical expressions of the normalized reaction velocities with that of simulation data points generated when the substrate fluctuations are present and absent, for the reaction schemes represented in Figure 1 Singh and Chaudhury, 2019 in the general monotonic as well as the conditional non-monotonic limit. We have also constructed the phase diagrams for the schemes given in Figure 1 Singh and Chaudhury, 2019 separating different regimes of the monotonic and the non-monotonic behaviors observed in the reaction rate.

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.

Genetic toggle switch controlled by bacterial growth rate

Background

In favorable conditions bacterial doubling time is less than 20 min, shorter than DNA replication time. In E. coli a single round of genome replication lasts about 40 min and it must be accomplished about 20 min before cell division. To achieve such fast growth rates bacteria perform multiple replication rounds simultaneously. As a result, when the division time is as short as 20 min E. coli has about 8 copies of origin of replication (ori) and the average copy number of the genes situated close to ori can be 4 times larger than those near the terminus of replication (ter). It implies that shortening of cell cycle may influence dynamics of regulatory pathways involving genes placed at distant loci.

Results

We analyze this effect in a model of a genetic toggle switch, i.e. a system of two mutually repressing genes, one localized in the vicinity of ori and the other localized in the vicinity of ter. Using a stochastic model that accounts for cell growth and divisions we demonstrate that shortening of the cell cycle can induce switching of the toggle to the state in which expression of the gene placed near ter is suppressed. The toggle bistability causes that the ratio of expression of the competing genes changes more than two orders of magnitude for a two-fold change of the doubling time. The increasing stability of the two toggle states enhances system sensitivity but also its reaction time.

Conclusions

By fusing the competing genes with fluorescent tags this mechanism could be tested and employed to create an indicator of the doubling time. By manipulating copy numbers of the competing genes and locus of the gene situated near ter, one can obtain equal average expression of both genes for any doubling time T between 20 and 120 min. Such a toggle would accurately report departures of the doubling time from T.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0483-4) contains supplementary material, which is available to authorized users.

Modelling the effects of booster dose vaccination schedules and recommendations for public health immunization programs: the case of Haemophilus influenzae serotype b

Background

Haemophilus influenzae serotype b (Hib) has yet to be eliminated despite the implementation of routine infant immunization programs. There is no consensus regarding the number of primary vaccine doses and an optimal schedule for the booster dose. We sought to evaluate the effect of a booster dose after receiving the primary series on the long-term disease incidence.

Methods

A stochastic model of Hib transmission dynamics was constructed to compare the long-term impact of a booster vaccination and different booster schedules after receiving the primary series on the incidence of carriage and symptomatic disease. We parameterized the model with available estimates for the efficacy of Hib conjugate vaccine and durations of both vaccine-induced and naturally acquired immunity.

Results

We found that administering a booster dose substantially reduced the population burden of Hib disease compared to the scenario of only receiving the primary series. Comparing the schedules, the incidence of carriage for a 2-year delay (on average) in booster vaccination was comparable or lower than that observed for the scenario of booster dose within 1 year after primary series. The temporal reduction of symptomatic disease was similar in the two booster schedules, suggesting no superiority of one schedule over the other in terms of reducing the incidence of symptomatic disease.

Conclusions

The findings underscore the importance of a booster vaccination for continued decline of Hib incidence. When the primary series provides a high level of protection temporarily, delaying the booster dose (still within the average duration of protection conferred by the primary series) may be beneficial to maintain longer-term protection levels and decelerate the decline of herd immunity in the population.

Electronic supplementary material

The online version of this article (10.1186/s12889-017-4714-9) contains supplementary material, which is available to authorized users.

Improving dynamic phytoplankton reserve-utilization models with an indirect proxy for internal nitrogen

Ecologists have often used indirect proxies to represent variables that are difficult or impossible to measure directly. In phytoplankton, the internal concentration of the most limiting nutrient in a cell determines its growth rate. However, directly measuring the concentration of nutrients within cells is inaccurate, expensive, destructive, and time-consuming, substantially impairing our ability to model growth rates in nutrient-limited phytoplankton populations. The red chlorophyll autofluorescence (hereafter "red fluorescence") signal emitted by a cell is highly correlated with nitrogen quota in nitrogen-limited phytoplankton species. The aim of this study was to evaluate the reliability of including flow cytometric red fluorescence as a proxy for internal nitrogen status to model phytoplankton growth rates. To this end, we used the classic Quota model and designed three approaches to calibrate its model parameters to data: where empirical observations on cell internal nitrogen quota were used to fit the model ("Nitrogen-Quota approach"), where quota dynamics were inferred only from changes in medium nutrient depletion and population density ("Virtual-Quota approach"), or where red fluorescence emission of a cell was used as an indirect proxy for its internal nitrogen quota ("Fluorescence-Quota approach"). Two separate analyses were carried out. In the first analysis, stochastic model simulations were parameterized from published empirical relationships and used to generate dynamics of phytoplankton communities reared under nitrogen-limited conditions. Quota models were fitted to the dynamics of each simulated species with the three different approaches and the performance of each model was compared. In the second analysis, we fit Quota models to laboratory time-series and we calculate the ability of each calibration approach to describe the observed trajectories of internal nitrogen quota in the culture. Results from both analyses concluded that the Fluorescence-Quota approach including per-cell red fluorescence as a proxy of internal nitrogen substantially improved the ability of Quota models to describe phytoplankton dynamics, while still accounting for the biologically important process of cell nitrogen storage. More broadly, many population models in ecology implicitly recognize the importance of accounting for storage mechanisms to describe the dynamics of individual organisms. Hence, the approach documented here with phytoplankton dynamics may also be useful for evaluating the potential of indirect proxies in other ecological systems.

Modelling the impact of vaccination on curtailing Haemophilus influenzae serotype 'a'

Haemophilus influenzae serotype a (Hia) is a human-restricted bacterial pathogen transmitted via direct contacts with an infectious individual. Currently, there is no vaccine available for prevention of Hia, and the disease is treated with antibiotics upon diagnosis. With ongoing efforts for the development of an anti-Hia protein-polysaccharide conjugated vaccine, we sought to investigate the effect of vaccination on curtailing Hia infection. We present the first stochastic model of Hia transmission and control dynamics, and parameterize it using available estimates in the literature. Since both naturally acquired and vaccine-induced immunity wane with time, model simulations show three important results. First, vaccination of only newborns cannot eliminate the pathogen from the population, even when a booster program is implemented with a high coverage. Second, achieving and maintaining a sufficiently high level of herd immunity for pathogen elimination requires vaccination of susceptible individuals in addition to a high vaccination coverage of newborns. Third, for a low vaccination rate of susceptible individuals, a high coverage of booster dose may be needed to raise the level of herd immunity for Hia eradication. Our findings highlight the importance of vaccination and timely boosting of the individual׳s immunity within the expected duration of vaccine-induced protection against Hia. When an anti-Hia vaccine becomes available, enhanced surveillance of Hia incidence and herd immunity could help determine vaccination rates and timelines for booster doses necessary to eliminate Hia from affected populations.

A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion

Cell-cell adhesion plays a key role in the collective migration of cells and in determining correlations in the relative cell positions and velocities. Recently, it was demonstrated that off-lattice individual cell based models (IBMs) can accurately capture the correlations observed experimentally in a migrating cell population. However, IBMs are often computationally expensive and difficult to analyse mathematically. Traditional continuum-based models, in contrast, are amenable to mathematical analysis and are computationally less demanding, but typically correspond to a mean-field approximation of cell migration and so ignore cell-cell correlations. In this work, we address this problem by using an off-lattice IBM to derive a continuum approximation which does take into account correlations. We furthermore show that a mean-field approximation of the off-lattice IBM leads to a single partial integro-differential equation of the same form as proposed by Sherratt and co-workers to model cell adhesion. The latter is found to be only effective at approximating the ensemble averaged cell number density when mechanical interactions between cells are weak. In contrast, the predictions of our novel continuum model for the time-evolution of the ensemble cell number density distribution and of the density-density correlation function are in close agreement with those obtained from the IBM for a wide range of mechanical interaction strengths. In particular, we observe 'front-like' propagation of cells in simulations using both our IBM and our continuum model, but not in the continuum model simulations obtained using the mean-field approximation.