Probable effects of algal bloom on the growth ofPhragmites australis (Cav.) Trin. ex Steud.

The effects of blue-green algal blooms on an emergent reed plant,Phragmites australis (Cav.) Trin. ex Steud., were investigated in a eutrophic lake in central Japan. The plants showed conspicuous withering of bottom leaves in spring of 1982, after an early occurrence of the bloom. In June, the plants in the area of algal infestation had about half the shoot length and dry weight of normalP. australis without the algal infestation. Reductions in water transparency, dissolved oxygen in bottom water and redox potentials of surface soil corresponded to the presence of algal bloom and plant damage.     

Fermentation process diagnosis using a mathematical model

Summary Intriguing physiology of a solvent-producing strain ofClostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active tansport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.     

Simulation of field data by a basic three-dimensional model of interactive root growth

Published field data for lupins grown in a deep sandy soil in the wheatbelt of south-western Australia were used to test the predictive ability of a model of three-dimensional root growth. The model has the capacity to simulate the growth of individual root sections in response to the supply and demand for water and nitrate. N mineralisation was not modelled explicitly, but was accounted for through the use of a seasonally variable mineralisation input derived from the field data. Simulated nitrogen and water contents and root length densities in the soil profile agreed well with observed profiles, although all were slightly under-predicted. A sensitivity analysis revealed that model predictions were most sensitive to the drained upper limit values (v/v) and the mineralisation rates (gN m^–3 s^–1) incorporated as external inputs to the model, along with the unit rate of N₂ fixation (mol nodule^–1 s^–1) and unit root growth rates (m mol^–1 s^–1) which are physiological parameters previously calibrated for lupins. The amount of nitrate leached was predicted well. Spatial plots of nitrate leaching were a close inverse of the root length density plots, with the highest nitrate leaching below the inter-plant zones, and the least nitrate leaching directly below each plant. These results suggest that the root distribution of a legume species such as lupin can have an effect on the leaching of nitrate to depth. It may thus be possible to reduce the total amount of nitrate leached under lupin crops by investigating factors such as the spatial deployment of roots, planting densities and intercropping.     

A mathematical framework for estimating pathogen transmission fitness and inoculum size using data from a competitive mixtures animal model

We present a method to measure the relative transmissibility (transmission fitness) of one strain of a pathogen compared to another. The model is applied to data from competitive mixtures experiments in which animals are co-infected with a mixture of two strains. We observe the mixture in each animal over time and over multiple generations of transmission. We use data from influenza experiments in ferrets to demonstrate the approach. Assessment of the relative transmissibility between two strains of influenza is important in at least three contexts: 1) Within the human population antigenically novel strains of influenza arise and compete for susceptible hosts. 2) During a pandemic event, a novel sub-type of influenza competes with the existing seasonal strain(s). The unfolding epidemiological dynamics are dependent upon both the population's susceptibility profile and the inherent transmissibility of the novel strain compared to the existing strain(s). 3) Neuraminidase inhibitors (NAIs), while providing significant potential to reduce transmission of influenza, exert selective pressure on the virus and so promote the emergence of drug-resistant strains. Any adverse outcome due to selection and subsequent spread of an NAI-resistant strain is exquisitely dependent upon the transmission fitness of that strain. Measurement of the transmission fitness of two competing strains of influenza is thus of critical importance in determining the likely time-course and epidemiology of an influenza outbreak, or the potential impact of an intervention measure such as NAI distribution. The mathematical framework introduced here also provides an estimate for the size of the transmitted inoculum. We demonstrate the framework's behaviour using data from ferret transmission studies, and through simulation suggest how to optimise experimental design for assessment of transmissibility. The method introduced here for assessment of mixed transmission events has applicability beyond influenza, to other viral and bacterial pathogens.     

A mathematical study of a two-regional population growth model

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.     

Methane flux in Peltandra virginica (Araceae) wetlands: comparison of field data with a mathematical model

We present a mathematical model of the diffusive flux of methane through Peltandra virginica. Data on the diurnal changes in both the petiolar [CH₄] gradient and the values of the radial bulk exchange coefficient, E_r, are entirely consistent with this model and the assertion that changes in stomatal conductance regulate the rate of methane efflux in P. virginica. The differences between the values of E_r calculated for daytime and nighttime conditions are -40% for the submerged condition and -54% for the emergent condition. The axial diffusivity of CH₄ through the petiole of P. virginica is estimated in vitro to be 0.771 cm² min^-1. Using our model, we estimate the equilibrium rate of methane efflux under daytime (97 ng CH₄ min ¹ petiole^-1) and nighttime (65 ng CH₄ min^-1 petiole^-1) emergent conditions. Numerical solutions of the model equations in the time domain offer a way of providing a dynamic model of the gas exchange responses of P. virginica to changing environmental conditions.     

Subconductance states of Cx30 gap junction channels: data from transfected HeLa cells versus data from a mathematical model

Human HeLa cells expressing mouse connexin30 were used to study the electrical properties of gap junction channel substates. Experiments were performed on cell pairs using a dual voltage-clamp method. Single-channel currents revealed discrete levels attributable to a main state, a residual state, and five substates interposed, suggesting the operation of six subgates provided by the six connexins of a gap junction hemichannel. Substate conductances, gamma(j,substate), were unevenly distributed between the main-state and the residual-state conductance (gamma(j,main state) = 141 pS, gamma(j,residual state) = 21 pS). Activation of the first subgate reduced the channel conductance by approximately 30%, and activation of subsequent subgates resulted in conductance decrements of 10-15% each. Current transitions between the states were fast (<2 ms). Substate events were usually demarcated by transitions from and back to the main state; transitions among substates were rare. Hence, subgates are recruited simultaneously rather than sequentially. The incidence of substate events was larger at larger gradients of V(j). Frequency and duration of substate events increased with increasing number of synchronously activated subgates. Our mathematical model, which describes the operation of gap junction channels, was expanded to include channel substates. Based on the established V(j)-sensitivity of gamma(j,main state) and gamma(j,residual state), the simulation yielded unique functions gamma(j,substate) = f(V(j)) for each substate. Hence, the spacing of subconductance levels between the channel main state and residual state were uneven and characteristic for each V(j).     

Analysis of a mathematical model for the growth of tumors

 In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary condition for the existence of a unique stationary solution with radius r=R ₀ (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that (i) lim inf _t→∞ s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that (ii) If c is sufficiently small then s(t)→R ₀ exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further, (iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then lim sup _t→∞ s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞. Received: 25 February 1998 / Revised version: 30 April 1998     

A mathematical model of tumour-induced capillary growth

The corneal limbal vessels of an animal host respond to the presence of a source of Tumour Angiogenesis Factor (TAF) implanted in the cornea by the formation of new capillaries which grow towards the source. This neovasculature can be easily seen and studied and this paper describes a mathematical model of some of the important features of the growth. The model includes the diffusion of TAF, the formation of sprouts from pre-existing vessels and models the movement of these sprouts to form new capillaries as a chemotactic response to the presence of TAF. Numerical results are produced for various values of the parameters which characterize the model and it is suggested that the model might form the framework for further theoretical work on related phenomena such as wound healing or to develop strategies for the investigation of anti-angiogenesis.     

A mathematical model for the determination of steady-state cardiolipin remodeling mechanisms using lipidomic data

Technical advances in lipidomic analysis have generated tremendous amounts of quantitative lipid molecular species data, whose value has not been fully explored. We describe a novel computational method to infer mechanisms of de novo lipid synthesis and remodeling from lipidomic data. We focus on the mitochondrial-specific lipid cardiolipin (CL), a polyglycerol phospholipid with four acyl chains. The lengths and degree of unsaturation of these acyl chains vary across CL molecules, and regulation of these differences is important for mitochondrial energy metabolism. We developed a novel mathematical approach to determine mechanisms controlling the steady-state distribution of acyl chain combinations in CL . We analyzed mitochondrial lipids from 18 types of steady-state samples, each with at least 3 replicates, from mouse brain, heart, lung, liver, tumor cells, and tumors grown in vitro. Using a mathematical model for the CL remodeling mechanisms and a maximum likelihood approach to infer parameters, we found that for most samples the four chain positions have an independent and identical distribution, indicating they are remodeled by the same processes. Furthermore, for most brain samples and liver, the distribution of acyl chains is well-fit by a simple linear combination of the pools of acyl chains in phosphatidylcholine (PC), phosphatidylethanolamine (PE), and phosphatidylglycerol (PG). This suggests that headgroup chemistry is the key determinant of acyl donation into CL, with chain length/saturation less important. This canonical remodeling behavior appears damaged in some tumor samples, which display a consistent excess of CL molecules having particular masses. For heart and lung, the "proportional incorporation" assumption is not adequate to explain the CL distribution, suggesting additional acyl CoA-dependent remodeling that is chain-type specific. Our findings indicate that CL remodeling processes can be described by a small set of quantitative relationships, and that bioinformatic approaches can help determine these processes from high-throughput lipidomic data.     

Describing force-induced bone growth and adaptation by a mathematical model

This work proposes a mathematical model that qualitative describes the process of mechanically force-induced bone growth and adaptation. The mathematical model includes osteocytes as the key interfacing layer connecting tissue, cellular and molecular signaling levels. Specifically, in the presence of an increase in the mechanical stimuli, osteocytes respond by mechano-transduction releasing the local factors nitric oxide (NO) and prostaglandin E(2) (PGE(2)). These local factors act as the signaling recruitment signals for bone cells progenitors and influence the coupling activity among osteoblasts and osteoclasts during the process of bone remodeling. The model is in agreement with qualitative observations found in the literature concerning the process of bone adaptation and the cellular interactions during a local bone remodeling cycle induced by mechanical stimulation.     

Evaluation of a fatigue model using data from published napping studies

The authors have previously published the development and empirical validation of a work-related fatigue model. However, published work has not involved data from napping studies. The aim of this paper is to determine how closely the model predicts changes in subjective and objective measures from data published from napping studies. The regression results between the model outputs and logical reasoning, multiple sleep latency test scores, self-rated alertness, profile of mood state fatigue, visual vigilance and reaction time were all strong to very strong (R2 = 0.4-0.9). Only digit symbol substitution revealed moderate (R2 = 0.1-0.2) regression values. The outputs of the model reflect changes due to naps of varying duration and timing measured at varying periods following a nap. Together with the outputs from previous investigations, these results further support the potential use of the fatigue model in operational settings. This appears to be true in settings that utilise napping as well as those that do not.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.     

Kinetic study of a heterogeneous tumor cell population using a mathematical model

A mathematical model of a heterogenous tumor as a system of interrelating cell populations is described, including a pool of quiescent cells, cell-to-cell variability in maturation rates, and cell migration from growth area to necrotic one. Computer simulation results are given, model labeled mitoses and labeled index curves for the Lewis carcinoma are compared with experimental data.     

Description of electromyograms using a mathematical model of single joint movement

A mathematical model for motor control over one-joint fast and slow movements is proposed based on the equilibrium point (EP) hypothesis. Equations describing a reaction of the muscle with its servo to an EP shift are presented. EMG level is estimated as a function of kinematic and control variables. Voluntary movements are performed by a ramp EP shift for the muscles subserving a given joint. EMG patterns obtained by a computer simulation are in good agreement with the experimental data.