How temperature variation affects white-rot fungi mycelial growth dynamics: a nonlinear mixed models approach
Introduction
Currently, climate change due to global warming is causing changes in the population dynamics of various species and affecting the balance of diverse ecosystems. Basidiomycetes are important decomposers in nature involved in nutrient cycling; most of the basidiomycete biodegrade lignin, which is the most recalcitrant wood component remained in the forest litter. After removing lignin from wood, the same shows whitish appearance, thus being named white rot fungi. Many interactions between fungi species and other decomposers of the microbial community are influenced by temperature, therefore playing an important role on their colonization and biodegradation capacity (Magan, 2008).
White-rot fungi have been primarily studied due to their ability to produce and secrete several types of ligninolytic enzymes (Cañas and Camarero, 2010; Baldrian, 2006; Ostrofsky et al., 1997). Exploring their potential, many commercial enzymes have been used for several industrial processes (Schafer et al., 2007). Due to that, microbiological manipulation requires knowledge of physiological factors that could affect growth, temperature being considered one of the most important (Schubert et al., 2010). Although mycelial growth of fungi is a superficially simple and common subject, there are few studies that explore the mathematical modeling of this phenomenon.
With a series of repeated measurements of growth achieved in each of several individuals, nonlinear mixed-effects models are widely used for data analysis, characterizing the measures at both the individual unit level and the population level (Harring and Blozis, 2014; Xu et al., 2014; Regadas Filho et al., 2014; Li and Jiang, 2013; Arce et al., 2010; Wang and Zuidhof, 2004). When measurements are taken in the same experimental unit, one must consider the dependence structure between residuals in the chosen model. The adoption of a structure of independent and homogeneous errors can lead to problems when testing fixed effects.
The aim of fitting nonlinear mixed-effects models may not only be able to quantify growth, but also to make comparisons between treatment groups. A possible approach is to fit the curves and compare the resulting parameters to assess differences between them (Regadas Filho et al., 2014; Strathe et al., 2010; Peek et al., 2002; Song and Kuznetsova, 2001). The parameters should have a meaningful interpretation and include the asymptotic growth limit, maximum growth rate and a lag time after that growth accelerates, which is relevant to microbiological studies (Zwietering et al., 1990; Mendes et al., 2011).
The objectives of this study were i) to determine which of the chosen non linear regression models would better fit fungi growth in the factorial experiment; ii) to verify the effect of temperature in parameters of the non linear models previously selected. Finally, after fitting the models, it was possible to determine which range of temperature provided faster mycelial growth and earlier lag time.
Section snippets
Fungi species and preparation
Data were obtained from a completely randomized factorial experiment with two species of basidiomycetes fungi. The fungi species Stereum ostrea and Trametes villosa were deposited in the Culture Collection of Algae, Cyanobacteria and Fungi of Botanic Institute e CCIBt, São Paulo-SP, Brazil, with respective numbers CCIBt 38201 and CCIBt 38210. They cultivated at 21, 23, 25, 27 and 29 °C, in order to verify the influence of theoretical maximum growth, maximum growth rate and lag time in the
Nonlinear regressions models – a fixed effects approach
The results from the first-step analysis, i.e. the adjustments of the models (2) to (5), are displayed in Table 1 and the adjustments by growth phases, in Table 2. The iterative process of fit showed % of convergence. The logistic adjustment was worse than the other functions, regardless of the chosen criteria (Table 1, Table 2). Gompertz, Weibull and von Bertalanffy had similar fits, although the last two functions were better. The von Bertalanffy fitted well (showing the smallest value of the
Discussion
Based on the factorial-treatments structure, aspects such as competition between nonlinear regression models, the introduction of random variables to the fixed parameters, use of dummy variables to consider the factorial structure of treatments, as well as modeling the error covariance structure to account for heteroscedasticity and autocorrelation in errors were considered. From the choice of the Gompertz and the von Bertalanffy models, there were observed statistical differences between the
Conclusion
The contributions of the current study can be applied in several assays that involve fungi. By fitting Gompertz and the von Bertalanffy mixed models, a precise optimum of temperature has been found.
Conflicts of interest
The authors declare there is not conflict of interest. The research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Acknowledgments
This work was supported by the Brazilian Foundation FAPESP (N. 2013/15747–4). The authors want to express our sincere appreciation to Prof. Marli Teixeira de Almeida Minhoni and Prof. Edson Luiz Furtado for providing the infrastructure and scientific support, and to Carolina Vaz Passos for her grammar review and corrections. The first author thanks to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil for providing the scholarship.
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Current address: Brazilian Biorenewables National Laboratory (LNBR), Brazilian Center for Research in Energy and Materials (CNPEM), Campinas, SP, Brazil.