Mathematical modeling of colony formation in algal blooms: phenotypic plasticity in cyanobacteria

In this paper, we analyzed a mathematical model of algal-grazer dynamics, including the effect of colony formation, which is an example of phenotypic plasticity. The model consists of three variables, which correspond to the biomasses of unicellular algae, colonial algae, and herbivorous zooplankton. Among these organisms, colonial algae are the main components of algal blooms. This aquatic system has two stable attractors, which can be identified as a zooplankton-dominated (ZD) state and an algal-dominated (AD) state, respectively. Assuming that the handling time of zooplankton on colonial algae increases with the colonial algae biomass, we discovered that bistability can occur within the model system. The applicability of alternative stable states in algae-grazer dynamics as a framework for explaining the algal blooms in real lake ecosystems, thus, seems to depend on whether the assumption mentioned above is met in natural circumstances.

A Kinetic-Based Model of Radiation-Induced Intercellular Signalling

It is now widely accepted that intercellular communication can cause significant variations in cellular responses to genotoxic stress. The radiation-induced bystander effect is a prime example of this effect, where cells shielded from radiation exposure see a significant reduction in survival when cultured with irradiated cells. However, there is a lack of robust, quantitative models of this effect which are widely applicable. In this work, we present a novel mathematical model of radiation-induced intercellular signalling which incorporates signal production and response kinetics together with the effects of direct irradiation, and test it against published data sets, including modulated field exposures. This model suggests that these so-called "bystander" effects play a significant role in determining cellular survival, even in directly irradiated populations, meaning that the inclusion of intercellular communication may be essential to produce robust models of radio-biological outcomes in clinically relevant in vivo situations.

Mathematical modelling of quantum yield enhancements of methyl orange photooxidation in aqueous TiO2 suspensions under controlled periodic UV LED illumination

Quantum yields of the photocatalytic degradation of methyl orange under controlled periodic illumination (CPI) have been modelled using existing models. A modified Langmuir-Hinshelwood (L-H) rate equation was used to predict the degradation reaction rates of methyl orange at various duty cycles and a simple photocatalytic model was applied in modelling quantum yield enhancement of the photocatalytic process due to the CPI effect. A good agreement between the modelled and experimental data was observed for quantum yield modelling. The modified L-H model, however, did not accurately predict the photocatalytic decomposition of the dye under periodic illumination.

Bdellovibrio predation in the presence of decoys:Three-way bacterial interactions revealed by mathematical and experimental analyses

Bdellovibrio bacteriovorus is a small, gram-negative, motile bacterium that preys upon other gram-negative bacteria, including several known human pathogens. Its predation efficiency is usually studied in pure cultures containing solely B. bacteriovorus and a suitable prey. However, in natural environments, as well as in any possible biomedical uses as an antimicrobial, Bdellovibrio is predatory in the presence of diverse decoys, including live nonsusceptible bacteria, eukaryotic cells, and cell debris. Here we gathered and mathematically modeled data from three-member cultures containing predator, prey, and nonsusceptible bacterial decoys. Specifically, we studied the rate of predation of planktonic late-log-phase Escherichia coli S17-1 prey by B. bacteriovorus HD100, both in the presence and in the absence of Bacillus subtilis nonsporulating strain 671, which acted as a live bacterial decoy. Interestingly, we found that although addition of the live Bacillus decoy did decrease the rate of Bdellovibrio predation in liquid cultures, this addition also resulted in a partially compensatory enhancement of the availability of prey for predation. This effect resulted in a higher final yield of Bdellovibrio than would be predicted for a simple inert decoy. Our mathematical model accounts for both negative and positive effects of predator-prey-decoy interactions in the closed batch environment. In addition, it informs considerations for predator dosing in any future therapeutic applications and sheds some light on considerations for modeling the massively complex interactions of real mixed bacterial populations in nature.

Mathematical Modeling to Assess the Drivers of the Recent Emergence of Typhoid Fever in Blantyre, Malawi

BACKGROUND: Multiyear epidemics of Salmonella enterica serovar Typhi have been reported from countries across eastern and southern Africa in recent years. In Blantyre, Malawi, a dramatic increase in typhoid fever cases has recently occurred, and may be linked to the emergence of the H58 haplotype. Strains belonging to the H58 haplotype often exhibit multidrug resistance and may have a fitness advantage relative to other Salmonella Typhi strains.

METHODS: To explore hypotheses for the increased number of typhoid fever cases in Blantyre, we fit a mathematical model to culture-confirmed cases of Salmonella enterica infections at Queen Elizabeth Central Hospital, Blantyre. We explored 4 hypotheses: (1) an increase in the basic reproductive number (R0) in response to increasing population density; (2) a decrease in the incidence of cross-immunizing infection with Salmonella Enteritidis; (3) an increase in the duration of infectiousness due to failure to respond to first-line antibiotics; and (4) an increase in the transmission rate following the emergence of the H58 haplotype.

RESULTS: Increasing population density or decreasing cross-immunity could not fully explain the observed pattern of typhoid emergence in Blantyre, whereas models allowing for an increase in the duration of infectiousness and/or the transmission rate of typhoid following the emergence of the H58 haplotype provided a good fit to the data.

CONCLUSIONS: Our results suggest that an increase in the transmissibility of typhoid due to the emergence of drug resistance associated with the H58 haplotype may help to explain recent outbreaks of typhoid in Malawi and similar settings in Africa.

Identification and bisection of temporal durations and tone frequencies: Common models for temporal and non-temporal stimuli.

Two experiments examined identification and bisection of tones varying in temporal duration (Experiment 1) or frequency (Experiment 2). Absolute identification of both durations and frequencies was influenced by prior stimuli and by stimulus distribution. Stimulus distribution influenced bisection for both stimulus types consistently, with more positively skewed distributions producing lower bisection points. The effect of distribution was greater when the ratio of the largest to smallest stimulus magnitude was greater. A simple mathematical model, temporal range frequency theory, was applied. It is concluded that (a) similar principles describe identification of temporal durations and other stimulus dimensions and (b) temporal bisection point shifts can be understood in terms of psychophysical principles independently developed in nontemporal domains, such as A. Parducci's (1965) range frequency theory.

Economic modelling of antenatal screening and ultrasound scanning programmes for identification of fetal abnormalities

Objective Within the framework of a health technology assessment and using an economic model, to determine the most clinically and cost effective policy of scanning and screening for fetal abnormalities in early pregnancy. Design A discrete event simulation model of 50,000 singleton pregnancies. Setting Maternity services in Scotland. Population Women during the first 24 weeks of their pregnancy. Methods The mathematical model was populated with data on uptake of screening, prevalence, detection and false positive rates for eight fetal abnormalities and with costs for ultrasound scanning and serum screening. Inclusion of abnormalities was based on the relative prevalence and clinical importance of conditions and the availability of data. Six strategies for the identification of abnormalities prenatally including combinations of first and second trimester ultrasound scanning and first and second trimester screening for chromosomal abnormalities were compared. Main outcome measures The number of abnormalities detected and missed, the number of iatrogenic losses resulting from invasive tests, the total cost of strategies and the cost per abnormality detected were compared between strategies. Results First trimester screening for chromosomal abnormalities costs more than second trimester screening but results in fewer iatrogenic losses. Strategies which include a second trimester ultrasound scan result in more abnormalities being detected and have lower costs per anomaly detected. Conclusions The preferred strategy includes both first and second trimester ultrasound scans and a first trimester screening test for chromosomal abnormalities. It has been recommended that this policy is offered to all women in Scotland.

Artificial gravity reveals that economy of action determines the stability of sensorimotor coordination.

Background
When we move along in time with a piece of music, we synchronise the downward phase of our gesture with the beat. While it is easy to demonstrate this tendency, there is considerable debate as to its neural origins. It may have a structural basis, whereby the gravitational field acts as an orientation reference that biases the formulation of motor commands. Alternatively, it may be functional, and related to the economy with which motion assisted by gravity can be generated by the motor system.
Methodology/Principal Findings
We used a robotic system to generate a mathematical model of the gravitational forces acting upon the hand, and then to reverse the effect of gravity, and invert the weight of the limb. In these circumstances, patterns of coordination in which the upward phase of rhythmic hand movements coincided with the beat of a metronome were more stable than those in which downward movements were made on the beat. When a normal gravitational force was present, movements made down-on-the-beat were more stable than those made up-on-the-beat.
Conclusions/Significance
The ubiquitous tendency to make a downward movement on a musical beat arises not from the perception of gravity, but as a result of the economy of action that derives from its exploitation.

Coupled heat and moisture transfer in multi-layer building materials

A dynamic mathematical model for simulating the coupled heat and moisture migration through multilayer porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The discretization of the governing equations was done by the finite difference approach. A new experimental set-up was also developed in this study. The evolution of transient temperature and moisture distributions inside specimens were measured. The method for determining the temperature gradient coefficient was also presented. The moisture diffusion coefficient, temperature gradient coefficient, sorption–desorption isotherms were experimentally evaluated for some building materials (sandstone and lime-cement mortar). The model was validated by comparing with the experimental data with good agreement. Another advantage of the method lies in the fact that the required transport properties for predicting the non-isothermal moisture flow only contain the vapor diffusion coefficient and temperature gradient coefficient. They are relatively simple, and can be easily determined.