Fungal Growth Model Research Articles

SIMPLIFIED PREDICTION METHOD FOR FUNGAL GROWTH RISK IN INDOOR ENVIRONMENT COUPLED WITH HEAT AND MOISTURE TRANSFER IN BUILDING MATERIALS

In the present study, a mathematical model that reproduces fungal proliferation and morphological colony formation was developed on the basis of a reaction diffusion modeling approach. In this modeling, fungus was separated into two states, active and inactive, and it was assumed that active fungus moves by diffusion and reaction while generating and producing inactive fungus. The effects of temperature and humidity on fungal growth were explicitly incorporated in the reaction term of nutrient consumption/generation of active fungus in this governing equation. The damping function, which reproduces the effects of temperature and humidity on fungal growth, was developed and explicitly based on the fungal index proposed by K. Abe. The fungal index expresses the growth response of three representative fungi as a function of atmospheric temperature and relative humidity. In order to estimate the sensitivity of the proposed numerical fungal growth model, fungal growth on the surface of building materials was analyzed for four types of building materials, and the prediction results were compared with the results of WUFI-Bio and the fungal index proposed by Abe. In the three prediction models, fungal index expressed high sensitivity for atmospheric temperature and humidity and the prediction results of the reaction diffusion model and WUFI-Bio model were reasonably consistent with each other.

MEASUREMENT OF HYPHAL GROWTH RATE UNDER VARIOUS HUMIDITY CONDITIONS AND DEVELOPMENT OF FUNGAL GROWTH MODEL

The overarching objective of this study is to develop the numerical model based on logistic equations that predict fungal proliferation and colony forming by taking into account the influence of moisture, temperature and surface characteristics of building materials for various fungi. Toward this end, this paper provides the results of fundamental experiment which measure the responses of fungal mycelium length and colony size on culture media under various environmental conditions. The characteristic of this experiment is to make the suspension that strictly controls the density of the spores, and to execute both the mycelium growth experiment on glass plate and the colony formation experiment on culture media with the same slurry of fungal spores. We focus on humidity effect on fungal growth and mycelium lengths were directly measured by using the digital image data with the microscope that had been taken a picture every 24 hours. Obvious humidity dependence of fungal growth was confirmed in this experiment. In this research, we propose the fungous growth model based on a logistic expression and reports on the result of doing the fitting of the model coefficient by using the experiment data. The results of fungal growth model by logistic expression were in reasonable agreement with the experimental data.

A fungal growth model fitted to carbon‐limited dynamics of Rhizoctonia solani

Here, a quasi-steady-state approximation was used to simplify a mathematical model for fungal growth in carbon-limiting systems, and this was fitted to growth dynamics of the soil-borne plant pathogen and saprotroph Rhizoctonia solani. The model identified a criterion for invasion into carbon-limited environments with two characteristics driving fungal growth, namely the carbon decomposition rate and a measure of carbon use efficiency. The dynamics of fungal spread through a population of sites with either low (0.0074 mg) or high (0.016 mg) carbon content were well described by the simplified model with faster colonization for the carbon-rich environment. Rhizoctonia solani responded to a lower carbon availability by increasing the carbon use efficiency and the carbon decomposition rate following colonization. The results are discussed in relation to fungal invasion thresholds in terms of carbon nutrition.

Biomass recycling: a key to efficient foraging by fungal colonies

Using an existing fungal growth model that captures the physiological processes of vegetative growth and development of a fungal colony, and in particular incorporates, for the first time, a recycling of biomass mechanism, we explore the effects of recycling in various environmental contexts. Here we test whether resource density thresholds exist, below which finite colony expansion occurs, in three dimensions based on the number of randomly removed resource sites. We then test the effect of recycling on resource density thresholds. Modelled soil structure, derived from experiments, is combined with the fungal growth model. The effect of recycling on foraging efficiency is investigated for resource distributed homogeneously and heterogeneously throughout the modelled soil structure. The simulated results show that resource density thresholds do exist in three dimensions and that the recycling mechanism decreases the threshold value. Our results indicate that recycling promotes persistence and a recycling mechanism is crucial for those fungi that reside in a resource patchy and limited environment.

A two-phase kinetic model for fungal growth in solid-state cultivation

A new two-phase kinetic model including exponential and logistic models was applied to simulate the growth rate of fungi at various temperatures. The model parameters, expressed as a function of temperature, were determined from the oxygen consumption rate of Aspergillus niger during cultivation on wheat bran. The model can describe the whole growth curve including the lag phase and the cessation of growth in the latter stages of the cultivation with an adequate approximation. Furthermore, the model describes the growth rate of Aspergillus oryzae on wheat properly. Comparisons between the current, logistic and previous two-phase kinetic models indicate that the new model can predict growth rate of fungi more accurately.

Scale and scalability

Scale and scalability

Potentiation of antifungal activity of amphotericin B by essential oil fromCinnamomum cassia

The antifungal activity of the essential oil from Cinnamomum cassia, alone or combined with amphotericin B, a drug widely used for most indications despite side-effects was investigated. The composition of the oil was analysed by GC/MS and characterized by its very high content of cinnamaldehyde (92.2%). The minimal inhibitory concentration (MIC 80%), used to evaluate the antifungal activity against Candida albicans, was determined by a macrobroth dilution method followed by a modelling of fungal growth. The essential oil of Cinnamomum cassia exhibited strong antifungal effect (MIC 80% = 0.169 microL/mL and K(aff) = 18,544 microL/mL). A decrease of the MIC 80% of amphotericin B was obtained when the culture medium contained essential oil concentrations ranging from 0.08 to 0.1 microL/mL. The strongest decrease (70%) was obtained when the medium contained 0.1 microL/mL of essential oil. This potentiation of amphotericin B obtained in vitro may show promise for the development of less toxic and more effective therapies especially for the treatment of HIV infection.

Modelling the growth of Trichoderma virens with limited sampling of digital images.

Using limited digital image sampling, a model of fungal growth in soil that considers both hyphal production and lysis was constructed for two strains of Trichoderma virens over a range of four temperatures. A growth model was developed by fitting the radial cross sectional data with a modified form of the Ratkowsky equation to determine maximum growth rate and a modified Arrhenius equation to determine maximal rate of decrease in area covered by mycelia. The parameters obtained from a combined equation were then verified by using the data obtained from the whole colony to determine the appropriateness of the model. Using a limited data set and a combination of the Ratkowsky and Arrhenius equations, the mycelial coverage of the T. virens colony was determined, relating microscopic hyphal growth to macroscopic colony growth. This model was sufficiently robust to predict growth across four temperatures for a genetically modified and wild-type strain of T. virens. By using simple assumptions for the increase and eventual decline in fungal growth on a resource-limited medium, this model constructs an initial framework onto which additional parameters such as nutrient consumption could be incorporated for prediction of fungal growth.

A mathematical approach to studying fungal mycelia

The study of filamentous fungi can be difficult through experimental means alone due to the complexity of their natural growth habitat (e.g. soils) and the microscopic scale of growth (e.g. tip vesicle translocation and hyphal tip extension). Mathematical modelling provides a complimentary, powerful and efficient method of investigation. In this article, earlier mathematical models are briefly reviewed, before an overview of the construction and resultant predictions of a new model for fungal growth and function is given. Model predictions are compared to experimentally obtained data, giving new insight into the complex interaction between the developing mycelium and its environment.

Quasi-steady state approximation to a fungal growth model

In a previous paper, we proposed a fungal growth model (Lamour et al., 2001 IMA J. Math. Appl. Med. Biol., 17, 329–346), describing the colonization and decomposition of substrate, subsequent uptake of nutrients, and incorporation into fungal biomass, and performed an overall‐steady‐state analysis. In this paper we assume that where nutrient dynamics are much faster than the dynamics of fungal biomass and substrate, the system will reach a quasi‐steady‐state relatively quickly. We show how the quasi‐steady‐state approximation is a simplification of the full fungal growth model. We then derive an explicit fungal invasion criterion, which was not possible for the full model, and characterize parameter domains for invasion and extinction. Importantly, the fungal invasion criterion takes two forms: one for systems where carbon is limiting, another for systems where nitrogen is limiting. We focus attention on what happens in the short term immediately following the introduction of a fungus to a fungal‐free system by analysing the stability of the trivial steady state, and then check numerically whether the fungus is able to persist. The derived invasion criterion was found to be valid also for the full model. Knowledge of the factors that determine invasion is essential to an understanding of fungal dynamics. The simplified model allows the invasion criterion to be tested with experimental data.

Quasi-steady state approximation to a fungal growth model

In a previous paper, we proposed a fungal growth model (Lamour et al., 2001 IMA J. Math. Appl. Med. Biol., 17, 329-346), describing the colonization and decomposition of substrate, subsequent uptake of nutrients, and incorporation into fungal biomass, and performed an overall-steady-state analysis. In this paper we assume that where nutrient dynamics are much faster than the dynamics of fungal biomass and substrate, the system will reach a quasi-steady-state relatively quickly. We show how the quasi-steady-state approximation is a simplification of the full fungal growth model. We then derive an explicit fungal invasion criterion, which was not possible for the full model, and characterize parameter domains for invasion and extinction. Importantly, the fungal invasion criterion takes two forms: one for systems where carbon is limiting, another for systems where nitrogen is limiting. We focus attention on what happens in the short term immediately following the introduction of a fungus to a fungal-free system by analysing the stability of the trivial steady state, and then check numerically whether the fungus is able to persist. The derived invasion criterion was found to be valid also for the full model. Knowledge of the factors that determine invasion is essential to an understanding of fungal dynamics. The simplified model allows the invasion criterion to be tested with experimental data.

A positive numerical scheme for a mixed-type partial differential equation model for fungal growth

We describe a numerical scheme for the solution of a mixed-type PDE system which arises in the modelling of fungal growth. Given the application, conservation of mass and preservation of positivity are of paramount importance. The scheme employs a method of lines approach in which the system is split into hyperbolic and parabolic parts. Positivity and conservation of mass are ensured by the use of generalised flux functions and, in particular, flux limiters. The spatial discretisation results in stiff and non-stiff components which are solved using implicit and explicit methods respectively. Properties of the scheme are investigated via comparison with experimental data and performance is compared with another method of solution.

Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Growth of soil-borne fungi is poorly described and understood, largely because non-destructive observations on hyphae in soil are difficult to make. Mathematical modelling can help in the understanding of fungal growth. Except for a model by Paustian & Schnürer (1987a), fungal growth models do not consider carbon and nitrogen contents of the supplied substrate, although these nutrients have considerable effects on hyphal extension in soil. We introduce a fungal growth model in relation to soil organic matter decomposition dealing with the detailed dynamics of carbon and nitrogen. Substrate with a certain carbon: nitrogen ratio is supplied at a constant rate, broken down and then taken up by fungal mycelium. The nutrients are first stored internally in metabolic pools and then incorporated into structural fungal biomass. Standard mathematical procedures were used to obtain overall-steady states of the variables (implicitly from a cubic equation) and the conditions for existence. Numerical computations for a wide range of parameter combinations show that at most one solution for the steady state is biologically meaningful, specified by the conditions for existence. These conditions specify a constraint, namely that the ‘energy’ (in terms of carbon) invested in breakdown of substrate should be less than the ‘energy’ resulting from breakdown of substrate, leading to a positive carbon balance. The biological interpretation of the conditions for existence is that for growth the ‘energy’ necessary for production of structural fungal biomass and for maintenance should be less than the mentioned positive carbon balance in the situation where all substrate is colonized. In summary, the analysis of this complicated fungal growth model gave results with a clear biological interpretation.

Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Growth of soil-borne fungi is poorly described and understood, largely because non-destructive observations on hyphae in soil are difficult to make. Mathematical modelling can help in the understanding of fungal growth. Except for a model by Paustian & Sch urer (1987a), fungal growth models do not consider carbon and nitrogen contents of the supplied substrate, although these nutrients have considerable effects on hyphal extension in soil. We introduce a fungal growth model in relation to soil organic matter decomposition dealing with the detailed dynamics of carbon and nitrogen. Substrate with a certain carbon : nitrogen ratio is supplied at a constant rate, broken down and then taken up by fungal mycelium. The nutrients are first stored internally in metabolic pools and then incorporated into structural fungal biomass. Standard mathematical procedures were used to obtain overall-steady states of the variables (implicitly from a cubic equation) and the conditions for existence. Numerical computations for a wide range of parameter combinations show that at most one solution for the steady state is biologically meaningful, specified by the conditions for existence. These conditions specify a constraint, namely that the 'energy' (in terms of carbon) invested in breakdown of substrate should be less than the 'energy' resulting from breakdown of substrate, leading to a positive carbon balance. The biological interpretation of the conditions for existence is that for growth the 'energy' necessary for production of structural fungal biomass and for maintenance should be less than the mentioned positive carbon balance in the situation where all substrate is colonized. In summary, the analysis of this complicated fungal growth model gave results with a clear biological interpretation.

A logistic model of subsurface fungal growth with application to bioremediation

The goal of this research was to determine the potential of the fungal sterol ergosterol as an indicator of fungal biomass and to determine the growth response of the transformed strain of T. virens (GvT6) to added substrate and changes in temperature. Experiments in liquid culture and agar plates containing a rich medium of glucose, yeast extract, and casein (GYEC), or a soil extract medium supplemented with maltose (SE) showed that the ergosterol content of GvT6 was greatest when grown on GYEC agar plates (14.02 mg/g dry biomass). For both media, plate cultures produced higher specific ergosterol values than liquid cultures. Changes in specific ergosterol values over time were generally not significant. A value of 5.41 mg ergosterol / g dry biomass, determined for SE plate cultures, was used to convert ergosterol values to biomass values in growth experiments in soil bioreactors. Data from experiments in soil bioreactors treated with different levels of substrate (0.5–8 mg maltose / g dry soil) at three different temperatures (22, 27, 32°C) showed subsurface growth of GvT6 can be described by the logistic equation. Culture conditions of 32°C and 8 mg/g substrate produced the highest levels of biomass, but growth at 32°C and 4 mg/g substrate was somewhat faster than at the higher substrate level.

Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Growth of soil-borne fungi is poorly described and understood, largely because non-destructive observations on hyphae in soil are difficult to make. Mathematical modelling can help in the understanding of fungal growth. Except for a model by Paustian & Schnürer (1987a), fungal growth models do not consider carbon and nitrogen contents of the supplied substrate, although these nutrients have considerable effects on hyphal extension in soil. We introduce a fungal growth model in relation to soil organic matter decomposition dealing with the detailed dynamics of carbon and nitrogen. Substrate with a certain carbon : nitrogen ratio is supplied at a constant rate, broken down and then taken up by fungal mycelium. The nutrients are first stored internally in metabolic pools and then incorporated into structural fungal biomass. Standard mathematical procedures were used to obtain overall-steady states of the variables (implicitly from a cubic equation) and the conditions for existence. Numerical computations for a wide range of parameter combinations show that at most one solution for the steady state is biologically meaningful, specified by the conditions for existence. These conditions specify a constraint, namely that the 'energy' (in terms of carbon) invested in breakdown of substrate should be less than the 'energy' resulting from breakdown of substrate, leading to a positive carbon balance. The biological interpretation of the conditions for existence is that for growth the 'energy' necessary for production of structural fungal biomass and for maintenance should be less than the mentioned positive carbon balance in the situation where all substrate is colonized. In summary, the analysis of this complicated fungal growth model gave results with a clear biological interpretation.

Aggregation and collapse in a mechanical model of fungal tip growth.

Interconnected hyphal tubes form the mycelia of a fungal colony. The growth of the colony results from the elongation and branching of these single hyphae. The material being incorporated into the extending hyphal wall is supplied by vesicles which are formed further back in the hyphal tip. Such wall-destined vesicles appear conspicuously concentrated in the interior of the hypha, just before the hyphal apex, in the form of an apical body or Spitzenkörper. The cytoskeleton of the hyphal tube has been implicated in the organisation of the Spitzenkörper and the transport of vesicles, but as yet there is no postulated mechanism for this. We propose a mechanism by which forces generated by the cytoskeleton are responsible for biasing the movement of vesicles. A mathematical model is derived where the cytoskeleton is described as a viscoelastic fluid. Viscoelastic forces are coupled to the conservation equation governing the vesicle dynamics, by weighting the diffusion of vesicles via the strain tensor. The model displays collapse and aggregation patterns in one and two dimensions. These are interpreted in terms of the formation of the Spitzenkörper and the initiation of apical branching.

Advances in the predictive modelling of fungal growth in food

Mathematical modelling of fungal growth, and the ability to predict whether a particular fungus will grow in a food, and if so at what rate, has not received a similar degree of interest as modelling of bacterial growth. One of the main problems is the difficulty of acquiring sufficient, reproducible data that are suitable for modelling. In this review, we aim to introduce the principles of modelling of fungal growth and summarize some of the recent literature that describes the application of modelling and predictive techniques to yeasts and moulds. Particular attention has been paid to the use of automated methods for assessing growth.

MODELING THE EFFECTS OF PROPIONIC ACID BACTERIA IN SILAGE

A simulation model of the growth and fermentation of propionic acid bacteria (PAB) in silage was developed from literature data with pure cultures or mixed cultures with lactic acid bacteria (LAB). Effects of temperature, pH, water activity, and lactate, acetate, and propionate concentrations on growth rate and end product formation were included. The PAB were assumed to grow in succession to the LAB in silage and to ferment only lactate. A three-stage simulation was performed: LAB fermentation using a previous silage-fermentation model, PAB fermentation using the present model, and aerobic deterioration using a previous fungal-growth model. Inoculation with PAB was predicted to increase the aerobic stability of alfalfa silages of 20, 35, or 45% dry matter (DM), but to effect only minor improvements in 35% DM corn silage. Inoculation of PAB in combination with LAB at ensiling had a synergistic effect on aerobic stability. Comparison with two silage studies from the literature suggests uncertainty in the pH sensitivity of PAB in silage which may reduce the effect of LAB and PAB inoculation. In general, inoculation of PAB was predicted to have the smallest potential benefit for silages most prone to aerobic deterioration.

An L‐systems approach to the modelling of fungal growth

AbstractA parametric L‐system is developed to model the growth and structure of the fungus Aspergillus nidulans. The model uses biological understanding of the flow of nutrients through the fungus to control the simulation of growth, with L‐systems productions being dependent on the levels of nutrients, stored as parameters, in various parts of the model. This produces a structural model that is consistent with previous observations of the natural fungus. Visual interpretation of the L‐systems string uses a turtle graphics method. When stochastic rules are implemented to model specific features of Aspergillus nidulans, the simulation is convincing both visually and structurally. Other potential applications for the method are suggested.