A time-space model for the growth of microalgae biofilms for biofuel production

A Mathematical Model of Diel Activity and Long Time Survival in Phototrophic Mixed-Species Subaerial Biofilms

Subaerial biofilms (SAB) are intricate microbial communities living on terrestrial surfaces, of interest in a variety of contexts including cultural heritage preservation, microbial ecology, biogeochemical cycling, and biotechnology. Here we propose a mathematical model aimed at better understanding the interplay between cyanobacteria and heterotrophic bacteria, common microbial SAB constituents, and their mutual dependence on local environmental conditions. SABs are modeled as thin mixed biofilm-liquid water layers sitting on stone. A system of ordinary differential equations regulates the dynamics of key SAB components: cyanobacteria, heterotrophs, polysaccharides and decayed biomass, as well as cellular levels of organic carbon, nitrogen and energy. These components are interconnected through a network of energetically dominant metabolic pathways, modeled with limitation terms reflecting the impact of biotic and abiotic factors. Daily cylces of temperature, humidity, and light intensity are considered as input model variables that regulate microbial activity by influencing water availability and metabolic kinetics. Relevant physico-chemical processes, including pH regulation, further contribute to a description of the SAB ecology. Numerical simulations explore the dynamics of SABs in a real-world context, revealing distinct daily activity periods shaped by water activity and light availability, as well as longer time scale survivability conditions. Results also suggest that heterotrophs could play a substantial role in decomposing non-volatile carbon compounds and regulating pH, thus influencing the overall composition and stability of the biofilm.

A mixture-like model for tumor-immune system interactions

We introduce a mathematical model based on mixture theory intended to describe the tumor-immune system interactions within the tumor microenvironment. The equations account for the geometry of the tumor expansion, and the displacement of the immune cells, driven by diffusion and chemotactic mechanisms. They also take into account the constraints in terms of nutrient and oxygen supply. The numerical investigations analyze the impact of the different modeling assumptions and parameters. Depending on the parameters, the model can reproduce elimination, equilibrium or escape phases and it identifies a critical role of oxygen/nutrient supply in shaping the tumor growth. In addition, antitumor immune cells are key factors in controlling tumor growth, maintaining an equilibrium while protumor cells favor escape and tumor expansion.

Experimental and theoretical investigations of rotating algae biofilm reactors (RABRs): Areal productivity, nutrient recovery, and energy efficiency

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). Experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory experimental findings. The predictive mathematical model development is coordinated with laboratory experiments of biofilm areal productivity associated with ammonia and inorganic phosphorus uptake by RABRs. The unified experimental and theoretical tool is used to investigate the effects of RABR rotating velocity, duty cycle (DC), and light intensity on algae biofilm growth, areal productivity, nutrient uptake efficiency, and energy efficiency in wastewater treatment. Our framework indicates that maintaining a reasonable light intensity range improves biomass areal productivity and nutrient uptake efficiency. Our framework also indicates that faster RABR rotation benefits biomass areal productivity. However, maximizing the nutrient uptake efficiency requires a reasonably low RABR rotating speed. Energy efficiency is strongly correlated with RABR rotating speed and DC.

Symbiotic relationship between filamentous algae (Halomicronema sp.) and extracellular polymeric substance-producing algae (Chlamydomonas sp.) through biomimetic simulation of natural algal mats

To lower the cost of biomass harvesting, the growth of natural biofilm is considered to be an optimal alternative to microalgae aggregation. This study investigated algal mats that naturally agglomerate into a lump and float on water surfaces. Halomicronema sp., a filamentous cyanobacterium with high cell aggregation and adhesion to substrates, and Chlamydomonas sp., which grows rapidly and produces high extracellular polymeric substances (EPS) in certain environments, are the main microalgae that make up selected mats through next-generation sequencing analysis. These two species play a major role in the formation of solid mats, and showed a symbiotic relationship as the medium and nutritional source, particularly owing to the large amount of EPS formed by the reaction between EPS and calcium ions through zeta potential and Fourier-transform infrared spectroscopy analysis. This led to the formation of an ecological biomimetic algal mat (BAM) that mimics the natural algal mat system, and this is a way to reduce costs in the biomass production process as there is no separate treatment process for harvesting.

Understanding photosynthetic biofilm productivity and structure through 2D simulation

We present a spatial model describing the growth of a photosynthetic microalgae biofilm. In this 2D-model we consider photosynthesis, cell carbon accumulation, extracellular matrix excretion, and mortality. The rate of each of these mechanisms is given by kinetic laws regulated by light, nitrate, oxygen and inorganic carbon. The model is based on mixture theory and the behaviour of each component is defined on one hand by mass conservation, which takes into account biological features of the system, and on the other hand by conservation of momentum, which expresses the physical properties of the components. The model simulates the biofilm structural dynamics following an initial colonization phase. It shows that a 75 μm thick active region drives the biofilm development. We then determine the optimal harvesting period and biofilm height which maximize productivity. Finally, different harvesting patterns are tested and their effect on biofilm structure are discussed. The optimal strategy differs whether the objective is to recover the total biofilm or just the algal biomass.

Microalgae have many industrial applications, ranging from aquaculture, pharmaceutics, food industry to green energy. Planktonic cultivation of microalgae is energy-consuming. Growing them under a biofilm form is a new trend with attracting promises. Biofilms are complex heterogeneous ecosystems composed of microorganisms embedded within a self-produced extracellular matrix and stuck to a surface. Most of the studies have focused on bacterial biofilms and knowledge about microalgae biofilms is still very limited. In this paper, we propose a mathematical model describing microalgae biofilm development. We simulate in 1D and 2D the impact of harvesting conditions on biofilm productivity. In agreement with available experimental observations, we find that there exist optimal frequencies and patterns that optimize the productivity. We also show that the optimal conditions differ whether for maximizing the productivity of microalgae or of the whole biofilm.

Study on Spirulina platensis growth employing non-linear analysis of biomass kinetic models

Spirulina platensis has been considered a promising source of food supplement to combat malnutrition worldwide. Numerous investigations have stated its immune activity, ability to absorb CO2 during the growth period, and antioxidant potential. Well-known theoretical biomass kinetic model sheds are capable of qualitative analysis of the fast microalgae growth. In this regard, we considered eight popular biomass models: Monod, Haldane, Andrews & Noack, Teissier, Hinshelwood, Yano & Koga, Webb and, Aiba model comprising analytical investigation within the numerical simulation. Besides, in this study, we establish a new mathematical biomass growth model by merging the well-known Hinshelwood and Yano & Koga models. We explored the most suitable Spirulina growth model to minimize the overstated and understated growth trends in the assorted eight biomass kinetic models. Our findings show microalgae biomass growth and substrate diminishes along with time, and these results were compared with available experimental data. Results present a high value of R2(0.9862), a low value of RSS (0.0813), AIC (-9.7277), and BIC (-8.2148) implied significantly fitted with the investigated data for the growth of Spirulina platensis compared with popular eight studied models.

Modeling and improving arrayed microalgal biofilm attached culture system

A microalgal biofilm-attached-system is an alternative cultivation method, that offers potential advantages of improved biomass productivity, efficient harvesting, and water saving. These biofilm systems have been widely tested and utilized for microalgal biomass production and wastewater treatment. This research a microalgal growth model for the biofilm attached culture system has been developed and experimentally validated, both, in single and arrayed biofilm systems. It has been shown that the model has the capability to accurately describe microalgae growth. Moreover, via the model simulation, it was observed that system structural parameters, light dilution rate, and light intensity significantly affected the culture performance. The limitations, and improvement aspects of the model, are also discussed in this study. To our knowledge, this is the first time that a mathematical model for an arrayed-biofilm-attached-system has been developed and validated. This model will certainly be helpful in the design, improvement, optimization, and evaluation of the biofilm-attached-systems.

Biogas and Methane Potential of Pre-Thermally Disintegrated Bio-Waste

One of the environmental solutions employed in order to achieve circular economy goals is methane fermentation—a technology that is beneficial both for the stabilization and reduction of organic waste and for alternative energy generation. The article presents the results of research aimed at determining the biogas and methane potential of bio-waste which has been pre-thermally disintegrated, and determining the influence of variable process parameters of disintegration on the kinetics of fermentation. A first-order kinetic model was used to describe the fermentation as well as two mathematical models: logistic and Gompertz. It has been found that process parameters such as time (0.5, 1 and 2 h) and temperature (between 55 to 175 °C) have a significant effect on the solubilization efficiency of the bio-waste. The methane fermentation of thermally disintegrated bio-waste showed that the highest biogas potential is characterized by samples treated, respectively, for 0.5 h at 155 °C and for 2 h at 175 °C. The best match for the experimental data of biogas production from disintegrated substrates was demonstrated for the Gompertz model.

The Architecture of Monospecific Microalgae Biofilms

Microalgae biofilms have been proposed as an alternative to suspended cultures in commercial and biotechnological fields. However, little is known about their architecture that may strongly impact biofilm behavior, bioprocess stability, and productivity. In order to unravel the architecture of microalgae biofilms, four species of commercial interest were cultivated in microplates and characterized using a combination of confocal laser scanning microscopy and FTIR spectroscopy. In all the species, the biofilm biovolume and thickness increased over time and reached a plateau after seven days; however, the final biomass reached was very different. The roughness decreased during maturation, reflecting cell division and voids filling. The extracellular polymeric substances content of the matrix remained constant in some species, and increased over time in some others. Vertical profiles showed that young biofilms presented a maximum cell density at 20 μm above the substratum co-localized with matrix components. In mature biofilms, the maximum density of cells moved at a greater distance from the substratum (30–40 μm), whereas the maximum coverage of matrix components remained in a deeper layer. Carbohydrates and lipids were the main macromolecules changing during biofilm maturation. Our results revealed that the architecture of microalgae biofilms is species-specific. However, time similarly affects the structural and biochemical parameters.

Microalgal biofilms: A further step over current microalgal cultivation techniques

The scientific community has turned its interest to microalgae lately, because of their countless applications such as wastewater treatment and pharmaceutical industry. Nevertheless, so far applied cultivation methods are still prohibitive. Ordinary cultivation techniques in which microalgae are suspended in liquid medium suffer from many bottlenecks, such as low biomass productivities, difficulty in biomass harvesting and recovery, high installation and operating cost, high water requirements etc. Although, microalgal biofilms are known to be a nuisance because of surfaces fouling, they have emerged as an innovative technology with which microalgae are developed attached to a solid surface. This technique seems to be advantageous as compared to conventional cultivation systems. Microalgal biofilm systems could resolve the problematic aspects of ordinary cultivation techniques such as low biomass productivities, water management and biomass recovery. A detailed description of this technique with respect to the parameters affecting them is reviewed in this work.

A mathematical model to investigate the key drivers of the biogeography of the colon microbiota

The gut microbiota, mainly located in the colon, is engaged in a complex dialogue with the large intestinal epithelium through which important regulatory processes for the health and well-being of the host take place. Imbalances of the microbial populations, called dysbiosis, are related to several pathological status, emphasizing the importance of understanding the gut bacterial ecology. Among the ecological drivers of the microbiota, the spatial structure of the colon is of special interest: spatio-temporal mechanisms can lead to the constitution of spatial interactions among the bacterial populations and of environmental niches that impact the overall colonization of the colon. In the present study, we introduce a mathematical model of the colon microbiota in its fluid environment, based on the explicit coupling of a population dynamics model of microbial populations involved in fibre degradation with a fluid dynamics model of the luminal content. This modeling framework is used to study the main drivers of the spatial structure of the microbiota, specially focusing on the dietary fibre inflow, the epithelial motility, the microbial active swimming and viscosity gradients in the digestive track. We found 1) that the viscosity gradients allow the creation of favorable niches in the vicinity of the mucus layer; 2) that very low microbial active swimming in the radial direction is enough to promote bacterial growth, which sheds a new light on microbial motility in the colon and 3) that dietary fibres are the main driver of the spatial structure of the microbiota in the distal bowel whereas epithelial motility is preponderant for the colonization of the proximal colon; in the transverse colon, fibre levels and chemotaxis have the strongest impact on the distribution of the microbial communities.